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A Handbook on Cellular Mobile Communication Laboratory A MATLAB-Based Approach RONY K. SAHA

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Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

A Handbook on Cellular Mobile Communication Laboratory A MATLAB-Based Approach

Rony K. Saha PhD (ongoing) Electrical Engineering

1

Author’s Declaration Because of numerous requests from academicians, researchers, students, and many a like from different parts of the world, the author is happy and would like to share this manual for serving personal use only purposes. This manual is not a commercial release, and the author holds solely the copyright of this manual. The author does not give any guarantees on the materials used in this manual are accurate and is not liable for any consequences from using this manual. The readers must take any necessary prerequise measures to use this manual and be liable solely for using the contents in this manual.

Preface User demands for rich multimedia services at high data rates are ever increasing. Telecommunication vendors and operators have been consistently putting significant efforts to fulfill the user needs. To address the high demand of cellular mobile communication (CMC) services, hands-on experienced workforce is a prerequisite that are primarily supposed to be provided by the universities. Because most universities lack heavily from sufficient funding, resources, and facilities, it is difficult to setup physical laboratory of CMC to provide students with hands-on experiences. This huge investment for physical setup can be saved by developing a virtual environment using MATLAB software tools. With a software based CMC laboratory, students can model many features of CMC, analyze and evaluate the performance in both link and system level. In this handbook, we present a MATLAB based cellular mobile communication (CMC) laboratory course that comprises a total of ten experiments, covering the fundamental design parameters, considerations, and estimations of CMC both in the radio interface and core network levels. In the radio interface side, estimation of path loss, fading, power delay profile, and received bit error probability, while in the core network side, estimation of link budget of earth-satellite-earth communication, inland microwave communication, and radio resource allocation and scheduling are included. In addition, a fundamental to the MATLAB is also introduced at the very beginning for allowing students to understand of how to code in MATLAB. We consider a stepwise approach to develop each experiment as follows. Step01: introduction into which relevant background, problem statement, objective, and significance of the experiment is described. Step02: system or link model that incorporates three parts: conceptual model, analytical model, and simulation model. The Conceptual model incorporates the system or link architecture and configuration. The analytical model incorporates necessary mathematical expressions that transform the conceptual model into a methodical demonstration. The simulation model incorporates typical simulation parameters, assumptions, and scenarios which are used to simulate the system or link behavior based on the analytical model for performance evaluation. In addition, simulation experimental procedure of each experiment such as simulation algorithm is included. Step03: performance analysis and evaluation where the simulation result at system or link level is analyzed and performance is evaluated with regard to realistic results. Step04: predefined experimental question-answer into which a number of predefined questions are included, and students are asked to answer these questions using MATLAB simulator to investigate the degree of change in performance with the variation of system or link parameters. Step05: references section cites all the materials that are used for developing the experiment and recommended for further study. Step06: appendices include mainly help documents, e.g. relevant MATLAB functions and simulation m- files including MATLAB codes for performance measures of an experiment.

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

Organization of the Handbook CMCL 00: Introduction to MATLAB: This experiment is designed to give students an overview on how to define and use operators, functions, variables, etc. in MATLAB emphasizing considerably on common mathematical functions, complex numbers, elementary matrices, vector and matrix calculations, numerical operations and transformations of matrices, operator precedence, general and logical functions, data manipulation commands, and graphics. CMCL 01: Mobile Wireless Propagation Models and Path Loss Estimation: In this experiment, we primarily carry out the impact of carrier frequency and distance on path loss. In addition, a sensitivity analysis is carried out that provides critical parameters such as base station (BS) antenna height, mobile station (MS) antenna height is incorporated for the system design and planning purpose. CMCL02: Estimation of Received Bit Energy for Data Rates in Wireless Communications: In this experiment, students can understand how the received signal strength varies with the physical parameters of the environment. This estimation provides students with information regarding fundamental trade-offs between received power and channel bandwidth requirements. CMCL 03: Multipath Fading in Cellular Mobile Communications: In this experiment, students simulate the small-scale multipath fading effect on the transmitted signal. The fading effect is investigated under both frequency-flat and frequency-selective channel conditions in order to understand the effect of multipath propagation over the single path. The effect of change in Doppler spread, symbol duration, and the Rician K-factor on the channel response is also analyzed. CMCL 04: Cellular Mobile System Design: This experiment gives the students an overview on cellular mobile system design. With changing system scenario, students are able to understand how the system design parameters and requirements change for optimal performance. Given such an explicit system scenario, students are able to estimate system design requirements and parameters such as frequency reuse factor, minimum co-channel cell reuse ratio, spectral efficiency, system capacity, number of cells required for the coverage area, channel allocations with or without sectorization, new transmit power after cell splitting, etc. CMCL 05: Channel Classification in Cellular Radio System: This experiment provides students with how to classify channels by evaluating power-delay profile and Doppler spectrum in cellular mobile communication. Based on the relative magnitude of maximum possible transmission bandwidth over channel bandwidth and maximum possible transmitted symbol duration over transmitted symbol duration, the channel can be classified. CMCL 06: Inland Digital Microwave Link Design: In this experiment, students study the basic concepts of high frequency wave propagation, optical and radio horizon, ducting phenomenon, Fresnel zones, earth bulge, and factor k: a ratio of effective earth radius to the true earth radius and its effect on the link range. At the end of the experiment, students will be able to design and simulate a microwave link applying these concepts. CMCL 07: Estimation of Bit Error Probability for Various Modulation Schemes in Wireless Communications: In this experiment, students will be primarily concerned with finding an appropriate modulation scheme at the transmitting side using bit error probability measurement. Modulation schemes such as M-PAM, M-PSK, M-QAM and M-point orthogonal signal sets are considered. CMCL 08: Radio Resource Allocations and Scheduling in 4G Cellular Mobile Communications: In this experiment, students evaluate the performance of the generic schedulers such as Round Robin 3

(RR), Max-SNR, and Proportional Fair (PF) in terms of average cell spectral efficiency and Jain’s fairness index in a macrocell of LTE-Advanced systems. CMCL 09: Satellite Link Design: In this experiment, students study the fundamental issues and constraints in designing earth-satellite-earth communication link.

Acknowledgements The author would like to acknowledge the numerous contributions that help develop this handbook. Foremost, the author would like to acknowledge the wonderful lecture notes on cellular mobile systems and telecommunication networks of Professor Kazi Mohiuddin, former faculty of telecommunications field of study, Asian Institute of Technology, Thailand that have laid the foundation of the conceptual and analytical modeling of cellular mobile communications used extensively and explicitly with or without modifications in texts, illustrations, expressions, etc. in preparing this handbook. The author also acknowledge the lecture notes on digital communications of Dr. Poompat Saengudomlert, former faculty of telecommunications and ICT fields of study, Asian Institute of Technology, Thailand that contributed mostly in the handbook for theatrical and analytical modeling of a number of experiments. Many outstanding text books such as wireless communications by Thedore S. Rappaport, and 4G LTE/LTE-Advanced for mobile broadband by Erik Dahlman, et al. contributed significantly in modeling a large number of experiments. The theories, figures, tables, mathematical expressions, any other form of information used in the handbook may be found in the mentioned references of the handbook and the references there-in with little or no modifications. The author fully acknowledges these contributions without which it may not be possible to develop the handbook. The handbook is developed with a view to helping students gain some practical insights in virtual environments using a standard tool such as MATLAB. The handbook is developed as companion, not a text book, to a theory course on cellular mobile communications. The MATLAB software developed by The MathWorks, Inc. was used for the simulation purpose and considered because of its availability on computing platforms in numerous universities and in a low-cost student version. For further insights to and up-to-date information about MATLAB may be found at http://www.mathworks.com. All MATLAB m-files appended at the end of each experiment have been verified execute accurately and developed by the author. The m-files are included as mere examples, not absolute solutions to problems. Any performance evaluation in an experiment can be carried out with a different logic in MATLAB on the reader’s own way.

The author

Rony K. Saha PhD-ongoing (EE), MEng (ICT), BSc Engg (EEE) 19 JULY 2016

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

CMCL 00: Introduction to MATLAB Introduction Initially, MATLAB was simply a MATrix LABoratory. It is an interactive software package that is developed to perform numerical calculations on vectors and matrices. Now-a-day, it is one of the most powerful tools for Scientist and Engineers because of its easy to handle feature of many of the computations involved in Mathematics [1]. Into MATLAB, usually, you see a prompt », called the MATLAB prompt that receives a user input command and processes it to provide the output on the following line. An important advantage of MATLAB is that it provides a help menu when you need help to figure out a command by writing help which means to enter whatever command you would need to know about. This experiment is designed to give an overview on how to define operators, functions, variables, etc. in MATLAB. Since this laboratory is MATLAB simulator based, it is essential to get familiarized with the use of this tool. Since MATLAB simulator is vast is applications, we will limit our focus on using those instructions that will be more frequent to apply to simulate objectives of this laboratory experiments only. However, for further information, the readers are advised to consult with the references mentioned herein this experiment. We use large portion of the information documented herein based on Ref [1] and can help you much for further information. Variables Variables are defined to store numerical values. A valid name for a MATLAB variable is a character string containing letters (upper or lower case), digits, and underscores where the first character must be a letter. For example, you can store the value 5 in the variable x by entering >> x = 5; Note that nothing will be printed out because semicolons follow each command. If you want everything printed out then type >>x = 5 The output will be then >> x=5 x= 5 MATLAB contains some predefined variables. Many of these are contained in the table below.

break case catch classdef

continue else elseif end

Table 0.1: Some predefined variables in MATLAB. for otherwise spmd function parfor switch global persistent try if return while 5

Common Mathematical Functions MATLAB contains a large number of mathematical functions. For example >> sin(3) returns as output in radians >> sin(3) ans = 0.1411 Note that the factorial function, i.e., n! = 1.2. 3… n is calculated by >> factorial(n) For example >> factorial(5) ans = 120

Some Common Real Mathematical Functions abs(x) exp(x) cos(x) sin(x)

The absolute value of x. ex cos x. sin x

factorial(n) fix(x)

floor(x) log(x) log10(x) rem(x, y) round(x) sign(x)

n! for n a non-negative integer.

If x  0 this is the largest integer which is  x. If x < 0 this is the smallest integer which is  x. This is the largest integer which is  x. The natural log of x, i.e., logex. The common log of x, i.e., log10x. The remainder of x/y. This is the same as mod(x, y) if x, y > 0 The integer which is closest to x. If x > 0 this returns +1, if x < 0 this returns -1, and

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

if x = 0 this returns 0 sqrt(x) tan(x)

x. tan x.

Complex Numbers There are standard commands for obtaining the real part, the imaginary part, and the complex conjugate of a complex number or variable. For example >> x = 3 - 4i >> real(x) >> imag(x) >> conj(x) returns ans = 3

ans = -4

ans = 3.0000 + 4.0000i Some Common Complex Mathematical Functions abs(z) angle(z) conj(z) imag(z) real(z)

The absolute value of z = x + iy. The angle of z. This is calculated by atan2(y, x). z*= x - iy. The imaginary part of z, i.e., y. The real part of z, i.e., x.

Help The on-line help facility in MATLAB is quite extensive. If you type >> help you will get a list of all the topics that you can peruse further by typing help followed by the name of the topic. If you want help on a specific command, simply type help followed by the name of the command, i.e., >> help For example, type 7

>> help sin Returns with SIN Sine of argument in radians. SIN(X) is the sine of the elements of X. See also asin, sind.

Reference page in Help browser doc sin

Arrays: Vector and Matrix Calculations Generating Matrices To generate the matrix below 1 2 3  4 5 6   7 8 9

type >> A = [1, 2, 3; 4, 5, 6; 7, 8, 9] returns with A= 1 4 7

2 5 8

3 6 9

or type >> A = [1  2  3; 4  5  6; 7  8  9] (where “  " denotes one or more spaces) In MATLAB the transpose of a matrix A, denoted as A , is calculated by A . (i.e., a period followed by a single quote mark). T

For example The vector

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

1  2    3 x     1 2 3 4 5 6 T 4  5   6 can be entered as x  1 2 3 4 5 6 . Returns with x= 1 2 3 4 5 6 The element xi of the vector x is x(i) in MATLAB. For example to create the column vector x=(1,2,3, …,10), enter  >> x  1 : 10 returns with x= 1 2 3 4 5 6 7 8 9 10 Also the length of x can be found using length (x) returns the number of elements in vector x. For example >> length(x) ans = 10 9

Elementary Matrices MATLAB also has a number of commands that can generate matrices. For example, >> b = zeros(5) or >> b = zeros(5, 5) generates a 5X5 zero matrix. type the following. >> b=zeros(3) returns with b= 0 0 0

0 0 0

0 0 0

Also, >> b = zeros(3, 5) generates a 3X5 zero matrix. Type the following. >> b = zeros(3, 5) returns with b= 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Similarly, you can generate a matrix with all ones by ones(n) or ones(m, n) For example >> b = ones(3, 5) returns with b= 1 1 1

1 1 1

1 1 1

1 1 1

1 1 1

You can also generate the identity matrix, i.e., the matrix with ones on the main diagonal and zeroes off of it, by using the command eye with the same arguments as above. For example

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

>> b=eye(3) returns with b= 1 0 0

0 1 0

0 0 1

Another useful matrix is a random matrix, that is, a matrix whose elements are all random numbers. This is generated by the rand command, which takes the same arguments as above. Specifically, the elements are uniformly distributed random numbers in the interval (0; 1). For example >> rand returns with ans = 0.8147 The command randn generates a random matrix where the elements are normally distributed (i.e., Gaussian distributed) random numbers with mean 0 and standard deviation 1. For example >> randn ans = -0.4326 MATLAB also makes it convenient to assemble matrices in “pieces", that is, to put matrices together to make a larger matrix. That is, the original matrices are submatrices of the final matrix. For specificity, let us continue with b where b is a diagonal matrix as given before. Suppose you want a 5X3 matrix whose first three rows are the rows of b and whose last two rows are all ones. This can be generated by >> [ b ; ones(2, 3) ] For example >> [ b ; ones(2, 3) ] returns with ans = 1

0

0 11

0 0 1 1

1 0 1 1

0 1 1 1

The semicolon indicates that a row has been completed and so the next rows consist of all ones. The fact that b is a matrix in its own right is immaterial. All that is necessary is that the number of columns of b be the same as the number of columns of ones(2, 3).) This matrix could also be generated by >> [ b ; ones(1, 3) ; ones(1, 3) ] or by >> [ b ; [1 1 1] ; [1 1 1] ] or even by >> [ b ; [1 1 1 ; 1 1 1] ] Try these.

Similarly, to generate a 3X4 matrix whose first three columns are the columns of b and whose last column is (2, 4, 8)T type

 >> x  b ; 2 4 8  For example >> x=[b; [2 4 8]]' returns with x= 1 0 0

0 1 0

0 0 1

2 4 8

(The semicolon following the b indicates that the next column is to follow. The fact that the next entry is a column vector is immaterial. All that is necessary is that the number of rows of b be the same as the number of rows in the new last column.) Also type the followings size(b) : The size of a matrix. size(A) returns a two-vector of the number of rows and columns, or [m,n] = size(A) returns m and n as separate arguments. For example >> size(x)

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

returns with ans = 3

4

numel(x) : The total number of elements in a vector or matrix. For example >> numel(x) returns with ans = 12

The Colon Operator For real numbers a and b the MATLAB command >> [a:b] or >> a:b generates the row vector (a; a + 1; a + 2, . . ., a + k) where the integer k satisfies a + k  b and a + (k + 1) > b. If c is also a real number the MATLAB command >> [a:c:b] or >> a:c:b generates a row vector where the difference between successive elements is c. Thus, we can generate numbers in any arithmetic progression using the colon operator. For example, typing >> [5:-1:0] returns with ans = 5

4

3

2

1

0

Relational Operators < Less than Greater than 13

>= Greater than or equal to = = Equal to ~= Not equal to Logical Operators & AND | OR ~ NOT Simple Arithmetical Operations Matrix Addition If A, B  C mn then the MATLAB operation >> A + B means A  B  ai j   bi j   ai j  bi j  . That is, the i, j th element of A + B is ai j  bi j . For Example A= 1 0 0

0 1 0

0 0 1

>> B=ones(3) B= 1 1 1

1 1 1

1 1 1

>> A+B returns with ans = 2 1 1

1 2 1

1 1 2

Matrix Subtraction If A, B  C mn then the MATLAB operation >> A - B means A  B  ai j   bi j   ai j  bi j  .

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

For Example >> A-B returns with ans = 0 -1 -1 -1 0 -1 -1 -1 0 Matrix Multiplication by a scalar If A C mn then for any scalar c the MATLAB operation >> c*A means cA= cai j   c ai j  For Example >> c=6; >> c*A returns with ans = 6 0 0

0 6 0

0 0 6

Matrix Multiplication If A C ml and B  C l n then the MATLAB operation >> A*B means AB = ai j  bi j 

For Example A= 1 0 0

0 1 0

0 0 1

>> B B= 15

1 1 1

1 1 1

1 1 1

>> A*B returns with ans = 1 1 1

1 1 1

1 1 1

Matrix Exponentiation If A C nn and p is a positive integer, then the MATLAB operation >> A p  means A p  A . A . . . A (p times) For Example >> p = 2 >> A = 6 0 0

0 6 0

0 0 6

>> A^p returns with ans = 36 0 0 0 36 0 0 0 36

Matrix Inversion The inverse of a matrix A is inv(A) For Example >> inv(A)

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

returns with ans = 0.1667 0 0 0 0.1667 0 0 0 0.1667

Elementwise Multiplication If A, B  C mn then the MATLAB operation >> A.* B means a i j bi j  . That is, That is, the i, j th element of A .* B is a i j bi j . For Example A= 6 0 0

0 6 0

0 0 6

1 1 1

1 1 1

>> B B= 1 1 1

>> A.*B returns with ans = 6 0 0

0 6 0

0 0 6

Elementwise Division If A, B  C mn then the MATLAB operation >> A . / B means a i j / bi j  . For Example 17

>> A./B returns with ans = 6 0 0

0 6 0

0 0 6

>> B./A returns with ans = 0.1667 Inf Inf Inf 0.1667 Inf Inf Inf 0.1667

Elementwise Exponentiation If A C nn then the MATLAB operation >> A.  p means aipj  For Example p= 2 >> A.^p returns with ans = 36 0 0 0 36 0 0 0 36 Also if A, B  C mn then the MATLAB operation >> A. B means aibj  ij

For Example A=

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

6 0 0

0 6 0

0 0 6

1 1 1

1 1 1

>> B B= 1 1 1

>> A.^B returns with ans = 6 0 0

0 6 0

0 0 6

>> B.^A returns with ans = 1 1 1

1 1 1

1 1 1

Operator Precedence It is important to list the precedence for MATLAB operators. That is, if an expression uses two or more MATLAB operators, in which order does MATLAB do the calculations? The following table shows the precedence of all MATLAB operators, that is, the order in which it evaluates an expression. The precedence is from highest to lowest. Operators with the same precedence are evaluated from left to right in an expression [1]. The unary plus and minus are the plus and minus signs in x = +1 and x = -1. The plus and minus signs for addition and subtraction are, for example, x = 5 + 1 and x = 10 - 13. Thus, 1:n+1 is 1:(n+1) because \ +" has higher precedence than \ :". For Example >> n=3 n= 3 19

>> 1:n+1 returns with ans = 1

2

3

4

Also, A*C\b = (A*C)\b because \ *" and \ \" have the same precedence and so the operations are evaluated from left to right. For Example C= 1 1 1

1 1 1

1 1 1

0 6 0

0 0 6

>> A A= 6 0 0 >> b=2 b= 2 >> A*C/b returns with ans = 3 3 3

3 3 3

3 3 3

since >> A*C returns with ans = 6

6

6

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

6 6

6 6

6 6

Table 0.2 Precedence of all MATLAB operators.

1 2 3 4 5 6 7 8 9 10 11

Operator precedence [highest to lowest] Operators with the same comma are separated with line (,) .’ .^ ‘ ^ + [unary plus] [unary minus] ~ .* ./ .\ * / \ + [addition] -[subtraction] : < >= == ~= & &&

Logical Functions if…else…end if conditionally execute statements. The general form of the IF statement is if expression statements elseif expression statements else statements end The statements are executed if the real part of the expression has all non-zero elements. The else and elseif parts are optional. Zero or more elseif parts can be used as well as nested if's. The expression is usually of the form expr rop expr where rop is ==, , =, or ~=. For example Type as the following. >> x=5; >> y=2; >> if x>y % start of the loop z=0; else % check alternate condition z=1; end % end of the loop >> z

21

returns with z= 0 For … end Repeat statements a specific number of times. The general form of a FOR statement is: for variable = expr, statement, ..., statement END The columns of the expression are stored one at a time in the variable and then the following statements, up to the END, are executed. The expression is often of the form X:Y, in which case its columns are simply scalars. Some examples (assume N has already been assigned a value). For example >> for ii=1:2:10 zz=ii+1 end

% start: step: end

executes 5 times until ii=10. And returns with zz = 2

zz = 4

zz = 6

zz = 8

zz = 10

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

While … end while Repeat statements an indefinite number of times. The general form of a WHILE statement is: WHILE expression statements END The statements are executed while the real part of the expression has all non-zero elements. The expression is usually the result of expr rop expr where rop is ==, , =, or ~=. The BREAK statement can be used to terminate the loop prematurely.

For example >> ii=1; zz=1; while ii < 10 zz=ii+2 ii=ii+3; end returns with zz = 3

zz = 6

zz = 9

Some General Functions clear load save size clc edit

Data Manipulation Commands MATLAB has a number of “simple" commands which are used quite frequently. 23

To calculate the maximum value of the vector x, type >> m = max(x) For Example >> x=[2 6 1 5] x= 2

6

1

5

>> max(x) returns with ans = 6 If you also want to know the element of the vector which contains this maximum value, type >> [m, i] = max(x) For Example x= 2

6

1

5

>> [m i]=max(x) returns with m=

% maximum value

6

i=

% element number 2

If the elements of the vector are all real, the result of this command is the element which has the maximum value. However, if any of the elements of x are complex (i.e., non-real), this command has no mathematical meaning. MATLAB defines this command to determine the element of the vector which has the maximum absolute value of the elements of x. Some Useful Data Manipulation Commands max(x) The maximum element of a real vector. [m, i] = max(x) also returns the element which contains the maximum value in i.

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

max(A) A row vector containing the maximum element in each column of a matrix. [m, i] = max(A) also returns the element in each column which contains the maximum value in i. max(A,B) Returns an array which is the same size as A and B (they must be the size or one can be a scalar) and which contains the larger value in each element of A or B. prod(x) prod(A) The product of the elements of a vector, or a row vector containing the product of the elements in each column in a matrix. sort(x) sort(A) Sorts the elements in increasing order of a real vector, or in each column of a real matrix. std(x) std(A) The standard deviation of the elements of a vector, or a row vector containing the standard deviation of the elements in each column in a matrix. sum(x) sum(A) The sum of the elements of a vector, or a row vector containing the sums of the elements in each column in a matrix.

Graphics 2D Graphs Plot plot(y) plots the columns of Y versus their index. For example x= linspace(0,2*pi,30); y=sin(x); plot(y), title('y vs x'); returns with the following graph.

25

subplot Create axes in tiled positions. H = subplot(m,n,p) breaks the Figure window into an m-by-n matrix of small axes, selects the p-th axes for the current plot, and returns the axis handle. The axes are counted along the top row of the Figure window, then the secondrow, etc. For example x= linspace(0,2*pi,30); y=sin(x); z=cos(x); subplot(2,1,1) plot(y), title('plot y vs x'); subplot(2,1,2) plot(z), title('plot x vs x'); plots y on the top half of the window and z on the bottom half and returns with

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

Some other useful 2-D commands >>semilogx Plotting with a logarithmically scaled x-axis >>semilogy Plotting with a logarithmically scaled y-axis >>loglog plotting both axes logarithmically >>area(x,y) the area under the plot for x and y is filled with color xlabel() Puts a label on the x-axis. ylabel() Puts a label on the y-axis. title() Puts a title on the top of the plot. stairs(x,y) Plots a stairstep graph, i.e., plots a step function. hist(x) Plots a histogram of the data in a vector using 10 bins. hist(x, ) changes the number of bins. hist(x, c) lets you choose the midpoint of each bin. 3D Graphs plot3 plot3() is a three-dimensional analogue of PLOT(). plot3(x,y,z), where x, y and z are three vectors of the same length, plots a line in 3-space through the points whose coordinates are the elements of x, y and z. For example 27

>> t = 0:pi/50:10*pi; plot3(sin(t),cos(t),t); returns with a helix as follows.

Some other useful 3-D commands >> mesh(x,y,z,c) plots the colored parametric mesh defined by four matrix arguments. The view point is specified by VIEW. The axis labels are determined by the range of X, Y and Z, or by the current setting of AXIS. The color scaling is determined by the range of C, or by the current setting of CAXIS. The scaled color values are used as indices into the current COLORMAP >> surf(x,y,z,c) plots the colored parametric surface defined by four matrix arguments. The view point is specified by VIEW. The axis labels are determined by the range of X, Y and Z, or by the current setting of AXIS. The color scaling is determined by the range of C, or by the current setting of CAXIS. The scaled color values are used as indices into the current COLORMAP. The shading model is set by SHADING.

References [1] Ed Overman, “A MATLAB Tutorial”, Department of Mathematics, The Ohio State University, June, 2011. [2] Luisa Corrado, “Some Matlab Guidelines”, S230: Topics in Advanced Macroeconomics Faculty of Economics, University of Cambridge, September 2006. Web. http://www.econ.cam.ac.uk/faculty/corrado/index.htm. [3] MATLAB Beginner’s Guide. Source: MATLAB_GUIDE_www.bumatek.boun.edu.tr.

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

CMCL 01: Mobile Wireless Propagation Models and Path Loss Estimation 1.1 Introduction Radio-frequency propagation is fuzzy in nature in multipath environments because of irregular terrain, RF barriers, and scattering phenomena. The performance of mobile communication systems is limited by the radio channel, and the transmission path between transmitter and receiver varies randomly from simple line of sight (LOS) to one obstructed severely by building and foliage [3]. Most cellular radio system operates in urban environment there is no direct wave at the receiver. Rather, an integrated wave resulting from diffraction, reflection, and scattering from various obstacles (buildings, moving objects, etc.). Propagation models traditionally focus on the prediction of signal strength at the receiver, and distance (d) between transmitter and receiver plays the most critical role on the received signal strength. Figure 1.1 illustrates a typical point-to-point mobile wireless communication system. A very common thing that could come in mind is what would be the distance d that can provide good received signal quality, and the relevant factors that influence largely to increase d the longest possible so as to increase cell coverage and consequently cost from investment. The simplistic answer is to increase transmit power. However, increasing transmit power causes additional interference such as intra-cell interference, inter-cell interference. In this experiment, we focus on changes in the system parameters (other than transmit power) that result in increasing separation distance d, i.e. cell coverage. Figure 1.2 illustrates these parameters in the system. We will primarily carry out the impact of carrier frequency f (MHz) and distance d (km) on path loss. In addition, sensitivity analysis that provides critical parameters in the system with most impact on d is incorporated for the system design and planning purpose. We consider the very optimistic Free-space model, the very pessimistic ITU-R model, and the more realistic Hata model. All models are conceptually and analytically described, followed by respective simulation performance evaluation. We finish this experiment with a comparison of these path loss model simulation results in graph using the computational tool MATLAB. Gain (Gt)

Gain (Gr)

Antenna

Antenna RF signal propagation

Transmitter

Wireless communication medium

Transmit power (Pt)

Cable loss (Lc)

Path loss (LT)

Receiver

Cable loss (Lc)

Receive power (Pr)

Figure 1.1: A typical mobile wireless communication system.

29

Distance between base station and mobile station (d)

Base station antenna

Angle of incident wave (Ø)

Mobile station direction of travel

Mobile station antenna

Building

Street width (w)

Building

Building

Building

Building separation (b)

Street level Base station antenna height (ht )

Building height (hB )

Mobile station antenna height (hm )

Figure 1.2: Typical path loss variables (of physical medium) in mobile wireless communication system. 1.2 System Model 1.2.1 Generic model A generic Radio Frequency (RF) transmission system is already shown in Figure 1.1. The transmit power is given by Equation 1.1.

Pt  Pr  Gt  LT

(1.1)

where, the symbols represent as follows. Pt is the transmit power (consider from the base station (BS)), Pr is the receive power (at the mobile station (MS)), Gt is the total antenna gain experiences by the signal, and LT is the total loss experiences by the signal. Hence, rearranging Equation 1.1, path loss between BS and MS is given by

LT  Pt  Pr  Gt (1.2) 1.2.2 Free-space model Free-space model is the simplest path loss model that takes only frequency (f) and distance (d) into account. In free-space (no obstacles and atmospheric effects) propagation, the path loss is given by Pr  Pt Gt Gr (

 4 d

)2

(1.3)

where, Pr represents receive power, Pt represents transmit power, Gt and Gr represent gain of transmitter and receiver respectively, and d is the distance between transmitter and receiver. Equation 1.3 can be rewritten as follows for path loss.

LT  FS  32.45  20Log10 (d km )  20Log10 ( f MHz ) (1.4)

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

Hence, putting the value of LT-FS in Equation 1.1 and solving for d will provide with the maximum distance between transmitter and receiver as follows.

d km = antiLog10 [(LT

FS

- 32.45 - 20Log10 (f MHz ))/20]

1.2.3 CCIR (ITU-R) model This model [1] takes terrain profile and its induced path loss into account in addition to the free space path loss and is given by

Lccir  69.55  26.16Log10 ( f MHz )  13.82Log(hb )  a(hm )  [44.9  6.55Log10 (hb )]Log10 (dkm )  B (1.5) where, a(hm )  [1.1Log10 ( f MHz )  0.7]hm  [1.56Log10 ( f MHz )  0.8] B = (% area covered by building) So, the maximum distance in ITU-R model is given by d ccir  antiLog10[ Pt  GT  Pr  69.55  26.16Log10 ( f MHz )  13.82 Log (hb )  a(hm )  B]

[44.9  6.55Log10 (hb )]

(1.6)

1.2.4 Hata Model The Hata model is the empirical formulization of the graphical path loss information provided by Okumora [3]. It is based on ITU-R model and extensive measurements of urban as well as suburban radio propagation losses. This model provides a standard formula for path loss in urban environment and correction equations for other environments (suburban and rural as well) and is given by

LT  Hata (urban )  69.55  26.16 log10 f c  13.82 log10 hte  a(hre )  (44.9  6.55log10 hte ) log10 d

(1.7)

where, LT-Hata : Hata path loss in dB, fc : carrier frequency in MHz (150-1500), hte (effective base station height), 30-200m, hre : mobile antenna height in m (1-10), d : distance between transmitter and receiver in km, and a(hre) : correction factor for effective mobile antenna height (function of the service area or city). For small to medium sized city, a(hre )  (1.1log10 f c  0.7)hre  (1.56 log10 f c  0.8)dB And for a large city, a(hre )  {8.29(log10 1.54hre ) 2  1.1}dB( f c  300MHz ) a(hre )  [3.2{log10 (11.75hre )}2  4.97]dB( f c  300MHz )

For suburban area, the path loss is give by f LT  Hata  LT  Hata (urban )  2[log10 ( c )]2  5.4 dB 28

(1.8)

For open areas (rural), the formula is modified as LT  Hata  LT  Hata (urban )  4.78(log10 f c ) 2  18.33log 10 f c  40.98 dB

(1.9) 31

Hence, the maximum distance in Hata model is given by d Hata  antiLog10[ Pt  GT  Pr  69.55  26.16 log10 f c  13.82 log10 hte  a(hre )]

(44.9  6.55 log10 hte )

For higher carrier frequencies [2] of 1500 – 2000 MHz, the following modification of Hata model for urban area has been proposed.

LT  Hata (urban )  46.3  33.9 log10 f ( MHz)  13.82 log10 hte  a(hre )  (44.9  6.55 log10 hte ) log10 d  C (1.10) Additional correction factor, C = 0 dB for medium-sized cities and = 3 dB for metropolitan centers. These modified equations have been successfully used for cellular mobile network design at 1800 MHz band. However, it should be noted that (modified) Hata model is only valid for macrocell (d > 1 km) design. Note that in the aforementioned models, hb and hte, hm and hre, as well as f (MHz) and fc are used interchangeably. 1.3 Simulation Experimental Procedure 1.3.1 Set values to simulation variables for path loss models as follows. Free-space model Carrier frequency, f (MHz) = 900 and 1800, Transmit power Pt = 39 dBm, Cable loss Lc= 4 dB (total), Antenna gain Gt =28 dBi (total). CCIR model hb=35 m, hm=1 m, B=25% area is covered by buildings, Carrier frequency, f (MHz) = 900 and 1800, Transmit power Pt = 39 dBm, Cable loss Lc= 4 dB (total), Antenna gain Gt =28 dBi (total). Hata model hb=35 m, hm=1 m, Carrier frequency, f (MHz) = 900 and 1800, Transmit power Pt = 39 dBm, Cable loss Lc= 4 dB (total), Antenna gain Gt =28 dBi (total), for f (MHz) = 1800; C = 0 dB for medium-sized cities, = 3 dB for metropolitan area. 1.3.2 Simulation Algorithm 1. Path loss versus distance (cell coverage)

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

Step 1 define variables; Step 2 set values for dmax , f(MHz), Pt , Lc , Gt , hb, hm, a(hm), B; Step 3 define path loss expressions for Free-space, CCIR, and Hata model (with various cases: urban, suburban, and rural); Step 4 repeat step 2 up to d=dmax ; Step 5 plot distance versus path losses for all models and cases or display any result. 2. Develop other algorithms in similar on your own for the report question-answer part. 1.4 Performance Evaluation Plot experimental graphs and evaluate performance with relevant and appropriate methods. The following is an example line graph for path loss versus distance performance evaluation. Using

Figure 1.3: Path loss versus distance estimation. f(MHz)=900; hm (m)=1, hb (m)=8, and d (km)=1 to 10. MATLAB simulator, evaluate other performances relevant to this experiment (see report question-answer part). 1.5 Experiment report question-answer Question 01 Plot the path losses as a function of distance for all considered models. Draw a conclusion on which model you should consider, based on the results, using comparative analysis method. Question 02 Plot the received signal power Pr as a function of distance (similar to Question 01). Assume transmit power Pt = 39 dBm, total antenna gain Gt = 28 dBi (14 dBi for each antenna: Tx and Rx), total cable loss Lc = 4 dB (2 dB at each side; Tx and Rx). Hint: use Equation 1.1. 33

Question 03 How much dB (link budget or received signal strength) should there be increased so as to increase the distance by double, covered by a cell. Carry out estimations for all considered models. Assume all parameters remain unchanged. Question 04 Find the variables that influence most the maximum distance allowed by Hata model. This gives you the maximum distance sensitivity analysis, and consequently the considerations during planning phase of the system. Hints: vary transmit power, transmit antenna height, carrier frequency, antenna gain, and receive power in percentage (+/-1 to +/-8), and find the corresponding percentage change in distance. Use graph for representing the result. Question 05 Write a summary on what you have learned, observed, things went wrong (if in your experiment, you have not had the predicted result), and how you can overcome the similar problem in future. 1.6 References [1] W. Debus, “RF Path Loss & Transmission Distance Calculations”, Technical Memorandum, Axonn LLC, August 4, 2006. [2] K. M. Ahmed, “Cellular Mobile Systems” Lecture notes: AT77.07, Asian Institute of Technology, Thailand, January 2010. [3] R. K. Saha, “A Report On Path Loss Models Used In Mobile Communications and a Comparative Analysis of these Models for Urban Case using Suitable Parameters” Report on AT77.07: Cellular Mobile Systems, Asian Institute of Technology, Thailand, January 2010. 1.8 Appendix: M-file: path loss versus distance estimation %+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++ % Wireless Communications Laboratory %+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ++ % CMCL 01: Wireless propagation models and path loss estimation %----------------------------------------------------------------------------------------------------------------------------- ------------------% Part I: Define Variables fMHz=900; Pt=39; dis_inc=1; dis_max=10;

% define RF carrier frequency in MHz % define BS transmitting power in dBm % define incremental distance for the graph % define maximum distance (cell-edge distance) % define path loss variable for different models LT_FS=randint(1,dis_max,[0 0]); % free-space LT_ccir=randint(1,dis_max,[0 0]); % CCIR or ITU-R LT_Hata_ur_smci=randint(1,dis_max,[0 0]); % Hata urban: small/medum city LT_Hata_sur_smci=randint(1,dis_max,[0 0]); % Hata suburban LT_Hata_op_smci=randint(1,dis_max,[0 0]); % Hata open or rural LT_Hata_ur_lci=randint(1,dis_max,[0 0]); % Hata urban; large city %======================================================================================= == % Part II: Path loss versus distance estimation for d_km=1:dis_inc:dis_max %======================================================================================= = % Model 1: Free-space path loss model

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

LT_FS(d_km)=32.45+(20*log10(d_km))+(20*log10(fMHz)); % path loss %======================================================================================= = % Model 2: CCIR (ITU-R) path loss model hb=8; % define BS height in m hm=1; % define MS height in m a_hm=((1.1*log10(fMHz)-0.7)*hm)-(1.56*log10(fMHz)-0.8); B=log10(0.25); % 25% area covered by buildings LT_ccir(d_km)=69.55+(26.16*log10(fMHz))-(13.82*log10(hb))-a_hm+((44.9-(6.55*log10(hb)))*log10(d_km))-B; % path loss %======================================================================================= = % Model 3: Hata path loss model hte=hb; hre=hm;

% define BS height in m % define MS height in m

% correction factor for small and medium sized city a_hre_smci=(1.1*log10(fMHz)-0.7)*hre-(1.56*log10(fMHz)-0.8); % Hata path loss for urban area: small and medium sized city LT_Hata_ur_smci(d_km)=69.55+26.16*log10(fMHz)-13.82*log10(hte)-a_hre_smci+(44.9-6.55*log10(hte))*log10(d_km); % Hata path loss for suburban area LT_Hata_sur_smci(d_km)=LT_Hata_ur_smci(d_km)-2*(log10(fMHz/28))^2-5.4; % Hata path loss for open (rural) area LT_Hata_op_smci(d_km)=LT_Hata_ur_smci(d_km)-4.78*(log10(fMHz))^2+18.33*log10(fMHz)-40.98; % correction factor for large city, carrier frequency>300 MHz a_hre_lci=3.2*((log10(11.75*hre))^2)-4.97; % Hata path loss for urban area: large city LT_Hata_ur_lci(d_km)=69.55+26.16*log10(fMHz)-13.82*log10(hte)-a_hre_lci+(44.9-6.55*log10(hte))*log10(d_km); %====================================================================================== end %====================================================================================== % Define Output variables disp('Path loss versus distance for wireless propagation models'); s=1:dis_inc:dis_max; plot(s,LT_FS,s,LT_ccir,s,LT_Hata_ur_smci,s,LT_Hata_sur_smci,s,LT_Hata_op_smci,s,LT_Hata_ur_lci),grid legend('Free-space','ITU-R','Hata urban: small and medium city','Hata suburban','Hata open (rural)','Hata urban: large city'); %======================================================================================

35

CMCL 02 Estimation of received bit energy for data rates in wireless communications 2.1 Introduction Estimating the required received per bit energy is inevitably a crucial need for designing reliable wireless communication systems. The estimation provides with information regarding fundamental trade-off between received power and channel bandwidth requirements. The other way around, it defines regions that are constrained either by received power or available channel bandwidth. According to Shannon’s theory of channel capacity, channel capacity is constrained fundamentally by available channel bandwidth (BW) and signal-to-noise ( S N ), assuming the channel is noise-limited only, as such can be expressed by Equation 2.1.



C  BW log 2 1  S

N



(2.1)

where, the symbols represent as follows. C is channel capacity in bits/s, BW is channel bandwidth in Hz, S is received signal power in watt, N is receiver noise power in watt. Hence the basic constrains because of why the radio channel capacity is limited are available channel BW and signal-to-noise ( S N ). 2.2 System Model Denote per bit energy by Eb (watt-s), data rate by R (bits/s) and noise power spectral density by N0 (Watt/Hz), received signal power S can be expressed as S = Eb. R and received noise power N can be expressed as S = N0. BW. Note that the receiver noise is assumed constant over the channel BW. From Equation 2.1, it can be found that, in principle, data rate R is upper limited by channel capacity, i.e. mathematically can be expressed as follows. R  C (2.2)

Denote bandwidth utilization of a radio channel link by  , which can be mathematically expressed as follows. In words, bandwidth utilization of a radio link is the data rates over the available BW for the link.   R BW

(2.3)

Hence, using Equations 2.1 and 2.2 and putting the values of S and N as aforementioned, channel bandwidth utilization can be explored, which is upper limited by the following. 

  log 2 1   

Eb   N 0 

(2.4)

This gives the lower limit, i.e. the minimum received per bit energy Eb (normalized to N0) in terms of  as follows.

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

 E  2  1 Eb  min  b   N0   N0 

(2.5)

2.3 Simulation algorithm Step 1 Set value for  and use equation 2.5 for the corresponding values Step 2 Repeat step 1 as long as  reaches its maximum defined value. Step 3 Plot (use semi-log graph)

Eb in dB. N0

Eb [dB] versus  [bits/s per Hz]. N0

Step 4 Define power-limited region and bandwidth-limited region on the plot. 2.4 Performance Evaluation If we plot

Eb as a function of  ; the following Figure can be found1. N0

Figure 2.1: Minimum received signal normalized (to N0) per bit energy utilization  .

Eb as a function of bandwidth N0

Figure 2.1 gives a number of points that can be expressed as follows.  As long as   1 , i.e. data rate R is lower or equal to channel bandwidth BW , irrespective of data rate increase over the channel BW, channel BW does not impact significantly the required

Eb to achieve N0

higher data rates since the plot shows approximately flat over this region (    1 ). The other way around, this implies that within this region only signal power can help increase the achievable increase in data rate. Since any increase in data rate in this region requires a proportionate increase in received 1

Students are supposed to plot Figure 2.1 on their own as part of the experiment using MATLAB).

37



signal power, assuming noise power is constant over the channel BW, with no or insignificant impact of channel BW, this region is called power-limited region. However, for   1 , any increase in data rate requires much larger increase in received signal power if channel BW remain unchanged. This large increase in received power can be compensated by a proportionate increase in channel BW with data rate. That is why this region is called bandwidthlimited region.

The above discussion can simply be understood by the fact that for R  BW, there is no limitation from channel BW irrespective of the degree of increase in R. this means the only way is to increase data rate (see Equation 2.1) is to increase received signal power (moreover, log2 (1+x)  x as long as x is small enough, otherwise log2(1+x)  log2(x)). For R>BW, received signal power varies logarithmically (log2(x)). Hence much signal power is needed for a small change in data rates. However, a proportionate change in channel BW is enough to provide the required increase in data rates and hence reduction in received signal power required for the increase in data rates. 2.5 Experiment report question-answer Question 01 Plot received signal normalized (to N0) per bit energy

Eb as a function of bandwidth utilization  . Define N0

power-limited and bandwidth-limited regions on the plot. Is the plot consistence with Figure 2.1? If it is not such as so mention the reasons. Question 02 What does power-limited and bandwidth-limited region mean? Consider a noise-only-limited mobile wireless communication channel. Assume receiver noise is flat over the channel bandwidth B. As being system designer; you are given with the following scenarios for an arbitrary data rate R.   

Scenario 1: R=0.3B, Scenario 2: R=B, Scenario 3: R=3B.

Identify which region in the plot (obtained from Question 1) you would rather consider to operate the system and mention your considerations for designing the system for all these scenarios. Question 03 Explain the role of minimum

Eb on wireless communication channel design considerations. N0

Question 04 Write a summary on what you have learned, observed, things went wrong (if in your experiment, you have not had the predicted result), and how you can overcome the similar problem in future. 2.6 References [1] E. Dahlman, S. Parkvall & J. Sköld, “4G LTE/LTE-advanced for Mobile Broadband”, Academic Press, UK, 2011.

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

2.8 Appendix: M-file: path loss versus distance estimation %================================================================================== % Wireless Communications Laboratory %================================================================================== % CMCL 02: Estimation of received bit energy for data rates in wireless Communications %================================================================================== % Define variables rr=100; Eb_No_min=randint(1,rr,[0 0]); Eb_No_min_dB=randint(1,rr,[0 0]); gamma=randint(1,rr,[0 0]); gamma(1)=0.1;

% minimum Eb/N0 in dB % bandwidth utilization

%================================================================================= for i=1:1:rr %find values of Eb/N0 corresponds to bandwidth utilization Eb_No_min(i)=((2^gamma(i))-1)/gamma(i); Eb_No_min_dB(i)=10*log10(Eb_No_min(i)); gamma(i+1)=gamma(i)+0.1; end %================================================================================ % Output variables i=0.1:0.1:10; semilogx(i,Eb_No_min_dB); % plot the graph in semilog format %================================================================================

39

CMCL 03: Multipath Fading in Cellular Mobile Communications 3.1 Basic Propagation Mechanisms and Concept of Fading Reflection is a phenomenon (Figure 3.1) that occurs when an EM wave impinges upon an obstruction with dimensions very large compared to the radio wave wavelength such as earth surface, building, or wall. Diffraction occurs from the signal obstruction obstructed by a surface (earth, buildings, or walls) with sharp irregularities (edges), which may interfere constructively or destructively at the receiver.  According to Huygens principle, all points on a wave front can be considered as point sources for the production of secondary wavelets, and these wavelets combine to produce a new wave front in the direction of propagation (Figure 3.2).  Diffraction is caused by the secondary wavelets into the shadowed region and the strength of the diffracted waves is the sum of all secondary wavelets in the shadowed region. Scattering occurs when the dimension of the obstacles is small compared to the wavelength and the number of obstacles per unit volume is quite large.

ve d wa e t c Refe

Receiver

Transmitter

Direct wave

Earth Ground Distance (d)

Figure 3.1: Two ray ground reflection model. But in reality, because of having such obstructions in the way of signal propagation as reflection, diffraction, and scattering of radio waves occurred, which causes multipath propagation (varies with the type and area of obstruction). These signals have longer path than direct signal, and the magnitude as well as the phase difference varies with the path length of the signals. The received signals from various radio paths are summed at the MS antenna. This summing can be either constructive or destructive. In the destructive case, the sum signal has power that is clearly smaller than the average level of the received signal, and the received signal is said to be in a fade. The effect can cause fluctuations in the received signal’s amplitude, phase, and angle of arrival. The overall phenomenon of radio propagation is called multipath fading. The urban environment is the most common and unpredictable propagation environment in cellular communication systems, which is characterized by dense urban, urban, and suburban environments with

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

Q Huygens secondary sources

P

ge e ed Knif

Source

Receiver in shadowed region

h

d2

d1

Figure 3.2: Knife-edge diffraction. the density of civil structure variation. The signal received at the receiver is a result of direct rays, reflected rays, and shadowing as shown in Figure 3.3. Figure 3.3 shows a typical urban environment showing direct path and multipath propagation.

Figure 3.3: Multipath fading. Figure 3.4 represents an overview of fading channel manifestations. It starts with two types of fading effects that characterize mobile communications: large-scale and small-scale fading. In this experiment, we limit our focus on small scale fading.

41

Fading Channel manifestations

Large scale fading

Mean signal attenuation vs distance

Variations about the mean

Time delay domain description

Frequency selective fading

Frequency selective fading

Small scale fading

Time spreading of the signal

Frequency domain description

Time variance of the channel

Time domain description

Flat fading

Flat fading

Fast fading

Fast fading

Doppler shift domain description

Slow fading

Slow fading

Figure 3.4: Different types of fading. 3.2 Small-scale fading Small-scale fading refers to the dramatic changes in signal amplitude and phase that can be experienced as a result of small changes (as small as a half-wavelength) in the spatial separation between a receiver and transmitter. Small-scale fading manifests itself in two mechanisms, namely, time-spreading of the signal (or signal dispersion) and time-variant behavior of the channel. For mobile radio applications, the channel is time-variant because of motion between the transmitter and receiver that results in propagation path changes. The rate of change of these propagation conditions accounts for the fading rapidity (rate of change of the fading impairments). Small-scale fading is also called Rayleigh fading because if the multiple reflective paths are large in number, and there is no line-of-sight signal component, the envelope of the received signal is statistically described by a Rayleigh distribution as follows.

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

p(r ) 

r



2

e

r

2

2 2

,

for r  0 (3.1)

p(r )  0,

for r < 0 where r is the envelope amplitude of the received signal, and σ2 is the predetection mean power of the multipath signal. However, when there is a dominant non fading signal component present such as a line-of-sight propagation path, the small-scale fading envelope is described by a Rician pdf.

3.4 Simulation algorithm 3.4.1 Rayleigh fading model Step 1 Call Rayleigh fading function rayleighchan(ts,fd) for frequency flat fading channel response and define symbol duration ts and maximum Doppler spread fd; Step 2 define signal function to generate transmitted signal; Step 3 pass signal through the channel using filter (signal, channel response); Step 4 now call Rayleigh fading function rayleighchan(ts,fd,tau,pdb) for frequency selective fading channel response and define symbol duration ts, maximum Doppler spread fd, a vector of path delays, tau, each specified in seconds, and a vector of average path gains, pdb , each specified in dB. Step 5 again defines signal function to generate transmitted signal; Step 6 again pass signal through the channel using filter (signal, channel response); Step 7 plot Rayleigh faded signal power versus sample number for all cases or display any result. 3.4.2. Rician fading model In similar way, Step 1 Call Rician fading function ricianchan(ts,fd,k) for frequency flat fading (single-path) channel response and define symbol duration ts , maximum Doppler spread fd, and rician K- factor; Step 2 define signal function to generate transmitted signal; Step 3 pass the signal through the channel using filter (signal, channel response); Step 4 now call Rician fading function ricianchan(ts,fd,k,tau,pdb) for frequency selective fading channel response and define symbol duration ts, maximum Doppler spread fd, a vector of path delays, tau each specified in seconds, a vector of average path gains, pdb each specified in dB and and rician K-factor. Step 5 again defines signal function to generate transmitted signal; Step 6 again passes the signal through the channel using filter (signal, channel response); Step 7 plot Rician faded signal power versus sample number for all cases or display any result. 3.4.3 Develop other algorithms in similar on your own for the report question-answer part. 43

3.5 Fading Channels Simulation After you have created a channel object as described in Specify Fading Channels, you can use the filter function to pass a signal through the channel. The arguments to filter are the channel object and the signal. At the end of the filtering operation, the channel object retains its state so that you can find out the final path gains or the total number of samples that the channel has processed since it was created or reset. An example Rayleigh fading as well as Rician fading channel responses is shown in the following figure. The simulation code is attached at the final page/s for your instruction. Please take note that this code is one of several ways to simulate the similar responses.

Figure 3.7: Raileigh and Rician Fading channel response. 3.6 Experiment report question-answer Question 01 What is the basic difference between frequency-flat and frequency-selective fading. In simulation how you develop frequency selective channel properties. Question 02 In Rayleigh fading, now change the value of Doppler spread, fd and symbol duration, Ts. Show the respective channel response to these changes, and draw a conclusion on the effect of change in one to another. Question 03 In Rician fading, change the value of K-factor from 1 to 10000. Show the respective channel response to these changes, and draw a conclusion on the effect of change in K-factor on the channel response. Question 04

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

Multipath propagation is helpful in some situations such as receivers with multiple outputs. Do you agree or disagree. Explain your opinion with reasonable justifications. Question 05 Mention some ways to overcome multipath fading effects on cellular mobile communications.

3.7 References [1] R. K. Saha & A B M Siddique Hossain, “Student Handout: Cellular Mobile Communications Technologies, Standards, and Systems”, edi 01, v 02, May 2011. [2] Jeruchim, M. C., Balaban, P., and Shanmugan, K. S., “Simulation of Communication Systems, Second Edition”, New York, Kluwer Academic/Plenum, 2000 [3] MathWorks. Source: http://www.mathworks.com/help/toolbox/comm/ug/ a1069449399.html #a1071598663b1.

3.9 Appendix: M-file: Multipath Fading in Cellular Mobile Communications Rayleigh Fading Channel % Rayleigh Fading Model %------------------------------------------------------% Frequency Flat Rayleigh fading %-------------------------------------------------Ray_c_ff = rayleighchan(1/10000,100); sig = 1i*ones(2000,1); % Generate signal Ray_y_ff = filter(Ray_c_ff,sig); % Pass signal through channel %------------------------------------------------------% frequency Selective Rayleigh fading %-------------------------------------------------Ray_c_fs = rayleighchan(1/10000,100,[0 0.5/50000;],[0 -10]); sig = 1i*ones(2000,1); % Generate signal Ray_y_fs = filter(Ray_c_fs,sig); % Pass signal through channel %----------------------------------------------------% Display all properties of the Rayleigh Fadedchannel disp(Ray_c_ff) disp(Ray_c_fs) %----------------------------------------------------% Plot power of faded signal, versus sample number. subplot 221 plot(20*log10(abs(Ray_y_ff))),grid title('Rayleigh frequency flat') xlabel('Sample number') ylabel('Faded signal power')

subplot 222 plot(20*log10(abs(Ray_y_fs))),grid title('Rayleigh frequency selective') xlabel('Sample number') ylabel('Faded signal power')

45

%--------------------------------------------------------Rician Fading Channel %-------------------------------------------------------% Rician fading Model %-------------------------------------------------------%------------------------------------------------------% Frequency Flat rician fading %-------------------------------------------------Ric_c_ff = ricianchan(1/10000,100,3); sig = 1i*ones(2000,1); % Generate signal Ric_y_ff = filter(Ric_c_ff,sig); % Pass signal through channel %------------------------------------------------------% frequency Selective Rayleigh fading %-------------------------------------------------% c_fs = ricianchan(1/10000,100,3,[0 0.5/50000;],[0 -10],3); Ric_c_fs = ricianchan(1/10000,100,3,[0 0.5/50000;],[0 -10]); sig = 1i*ones(2000,1); % Generate signal Ric_y_fs = filter(Ric_c_fs,sig); % Pass signal through channel %----------------------------------------------------------------------------------% Output1 %---------------------------------------------------------------------------------% Display all properties of the Rayleigh Faded channel disp(Ric_c_ff) disp(Ric_c_fs) %----------------------------------------------------------------------------------% Output2 %---------------------------------------------------------------------------% Plot power of faded signal, versus sample number %-----------------------------------------------------------------------------subplot 223 plot(20*log10(abs(Ric_y_ff))),grid title('Rician frequency flat') xlabel('Sample number') ylabel('Faded signal power') subplot 224 plot(20*log10(abs(Ric_y_fs))),grid title('Rician frequency selective') xlabel('Sample number') ylabel('Faded signal power') %---------------------------------------------------

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

CMCL 04: Cellular Mobile System Design 4.1 Introduction The system design objective of early mobile radio systems was to achieve a large coverage area by using a single, high powered transmitter with an antenna mounted on a tall tower. However, with this approach, it was impossible to reuse the same frequencies throughout the system because of frequency reuse results in interference. A good example is the Bell mobile system in New York City (in the 1970s) that could only support a maximum of twelve simultaneous calls over a thousand square miles. In addition, government regulatory agencies could not make spectrum allocations in proportion to the increasing demand for mobile services. Considering these constraints, it became essential to restructure the radio telephone system to achieve high capacity with limited radio spectrum that covers very large areas as well. And the cellular concept was applied in restructuring the early radio telephone system. 4.2 Cellular System Design Concept and Theory The cellular concept is a system level idea where  A single, high power transmitter (large cell) is replaced with many low power transmitters (small cells) and each small cell provides coverage to only a small portion of the service area.  Each base station is allocated a portion of the total number of channels available to the entire system.  And nearby base stations is assigned different groups of channels so that all the available channels are assigned to a relatively small number of neighboring base stations, and the interference between base stations (and the mobile users under their control) is minimized.  Base stations and their channel groups are systematically spaced throughout a market so that the available channels are distributed throughout the geographic region and may be reused as many times as necessary so long as the interference between co-channel stations is kept below acceptable levels.  With the demand for service increases, i.e. as more channels are needed within a particular market), the number of base stations may be increased along with a corresponding decrease in transmitter power to avoid added interference.  Thereby, it provides additional radio capacity with no additional increase in radio spectrum – the fundamental principle, which is the foundation for all modem wireless communication systems. Hence, the cellular concept enables a fixed number of channels to serve an arbitrarily large number of subscribers by reusing the channels throughout the coverage region. Furthermore, the cellular concept allows every piece of subscriber equipment within a country or continent to be manufactured with the same set of channels, so that any mobile may be used anywhere within the region. 4.3 Cellular Frequency Reuse Concept  

In cellular system, each cellular base station is allocated a group of radio channels to be used within a small geographic area called a cell. Base stations in adjacent cells are assigned channel groups which contain completely different channels than neighboring cells. The base station antennas are designed to achieve the desired coverage within the particular cell.

47

 

By limiting the coverage area to within the boundaries of a cell, the same group of channels may be used to cover different cells that are separated from one another by distances large enough to keep interference levels within tolerable limits. The design process of selecting and allocating channel groups for all of the cellular base stations within a system is called frequency reuse or frequency planning. Figure 4.1 illustrates the concept of cellular frequency reuse, where cells labeled with the same letter use the same group of channels.

Note that the hexagonal cell shape shown in Figure 4.1 is conceptual and is a simplistic model of the radio coverage for each base station. However, it has been universally adopted since the hexagon permits easy and manageable analysis of a cellular system. The actual radio coverage of a cell is known as the footprint and is determined from field measurements or propagation prediction models. Although the real footprint is amorphous in nature, a regular cell shape is needed for systematic system design and adaptation for future growth. While it might seem natural to choose a circle to represent the coverage area of a base station, adjacent circles cannot be overlaid upon a map without leaving gaps or creating overlapping regions. Thus, when considering geometric shapes which cover an entire region without overlap and with equal area, there are three sensible choices: a square; an equilateral triangle; and a hexagon. However, for a given distance between the center of a polygon and its farthest perimeter points, the hexagon has the largest area of the three. Thus, by using the hexagon geometric, the fewest number of cells can cover a geographic region, and the hexagon closely approximates a circular radiation pattern which would occur for an omni-directional base station antenna and free space propagation. Note of course that the actual cellular footprint is determined by the contour in which a given transmitter serves the mobiles successfully. G F

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Figure 4.1: Illustration of the cellular frequency reuse concept. Cells with the same letter use the same set of frequencies. A cell cluster is outlined in bold and replicated over the coverage area. In this example, the cluster size N is equal to seven, and the frequency reuse factor is 1/7. When using hexagons to model coverage areas, base station transmitters are depicted as either being in the center of the cell, center-excited cells or on three of the six cell vertices, edge-excited cells. Normally,

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

omnidirectional antennas are used in center-excited cells, and sectored directional antennas are used in corner-excited cells. Practical considerations usually do not allow base stations to be placed exactly as they appear in the hexagonal layout. Most system designs permit a base station to be positioned up to one-fourth the cell radius away from the ideal location. Consider a cellular system with the followings.  S duplex channels available for use  Each cell is allocated a group of k channels (k < S) and  S channels are divided among N cells (into unique and disjoint channel groups, which each have the same number of channels). The total number of available radio channels can be expressed as S = k.N (4.1) The N cells which collectively use the complete set of available frequencies is called a cluster. If a cluster is replicated M times within the system, the total number of duplex channels, C can be used as a measure of capacity and is given by C = M.k.N = M.S (4.2) Note from equation (4.2) that the capacity of a cellular system is directly proportional to the number of times a cluster is replicated in a fixed service area. The factor N is called the cluster size and is typically equal to 4, 7, or 12. The value of N plays an important role in system design and performance. If the cluster size N is reduced while the cell size is kept constant, more clusters are required to cover a given area. And hence, more capacity (a larger value of C) is achieved. In addition, the value for N is a function of how much interference a mobile or base station can tolerate while maintaining a sufficient quality of communications. Note that a large cluster size indicates that the ratio between the cell radius (R) and the distance between co-channel cells (D) is large. Conversely, a small cluster size indicates that co-channel cells are located much closer together. From a design viewpoint, the smallest possible value of N is desirable in order to maximize capacity over a given coverage area, i.e. to maximize C. The frequency reuse factor of a cellular system is given by 1/N since each cell within a cluster is only assigned 1/N of the total available channels in the system. To design network without gaps between adjacent cells, the geometry of hexagons is such that the number of cells per cluster N can only have values which satisfy equation (4.3). N=i2+ij+j2 (4.3) where i and j are non-negative integers, and i  j are called shift parameters. Note that in order to find the nearest co-channel neighbors of a particular cell, the followings steps should consider. Step 1 move i cells along any chain of hexagons, then Step 2 turn 60 degrees counter-clockwise, and finally Step 3 move j cells; the jth cell is the co-channel cell. 49

or Step 1 move j cells along any chain of hexagons, then Step 2 turn 60 degrees clockwise, and finally Step 3 move i cells; the ith cell is the co-channel cell. This is illustrated in Figure 4.2 for i = 2 and j = 1, hence N = 7; an example illustration. G F

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Figure 4.2: Method of locating co-channel cells in a cellular system (for i = 2 and j = 1, hence N= 7). 4.3.1 Channel Assignment Strategies A variety of channel assignment strategies have been developed to achieve the objectives: increasing capacity and minimizing interference for efficient utilization of the radio spectrum. Channel assignment strategies can be classified as either fixed or dynamic. Channel assignment strategy impacts the performance of the system, particularly during handing off a mobile phone from one cell to another. In a fixed channel assignment strategy,  Each cell is allocated a predetermined set of voice channels.  Any call attempt within the cell can only be served by the unused channels in that particular cell.  If all the channels in that cell are occupied, the call is blocked and the subscriber does not receive service. Note that several variations of the fixed assignment strategy exist such as borrowing strategy where a cell is allowed to borrow channels from a neighboring cell if all of its own channels are already occupied. The

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

mobile switching center (MSC) supervises such borrowing procedures and ensures that the borrowing of a channel does not disrupt or interfere with any of the calls in progress in the donor cell. In a dynamic channel assignment strategy,  Voice channels are not allocated to different cells permanently. Instead, each time a call request is made, the serving base station requests a channel from the MSC.  The switch then allocates a channel to the requested cell following an algorithm that takes into account the likelihood of future blocking within the cell, the frequency of use of the candidate channel, the reuse distance of the channel, and other cost functions.  Accordingly, the MSC only allocates a given frequency if that frequency is not presently in use in the cell or any other cell which falls within the minimum restricted distance of frequency reuse to avoid co-channel interference. Dynamic channel assignment reduces the likelihood of blocking which increases the trunking capacity of the system since all the available channels in a market are accessible to all of the cells. However, dynamic channel assignment strategies require the MSC to collect real-time data on channel occupancy, traffic distribution, and radio signal strength indications (RSSI) of all channels on a continuous basis. This increases the storage and computational load on the system. The following table shows the assignment of traffic channels for the first half (Block A) of the 666 channel AMPS system (where 42 channels are reserved as control channels) for the frequency reuse factor K = 7 and 3 sectors per cell. It can be easily seen that in any group the minimum frequency separation between channels is 21. Table 4.1: Assignment of traffic channels. Group number 1A 2A 3A 4A 5A 6A 7A 1B 2B 3B 4B 5B 6B 7B 1C 2C 3C 4C 5C 6C 7C

Channel Assignment 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63

64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105

106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147

148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168

169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189

190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210

211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231

232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252

253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273

274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294

295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 -

The following Figure 4.3 shows a channel assignment corresponding to the table, when each 2π/3 sector antenna is located in the corner of hexagonal cell.

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Figure 4.3: A channel assignment corresponding to the table 4.1. 4.3.2 Interference in Cellular Systems Interference is the major limiting factor in the performance of cellular radio systems. Sources of interference include another mobile in the same cell, a call in progress in a neighboring cell, other base stations operating in the same frequency band, or any non-cellular system which inadvertently leaks energy into the cellular frequency band.  Interference on voice channels causes cross talk, where the subscriber hears interference in the background due to an undesired transmission. On control channels, interference leads to missed and blocked calls due to errors in the digital signaling.  Interference is more severe in urban areas, due to the greater high frequency (HF) noise floor and the large number of base stations and mobiles.  Interference has been recognized as a major bottleneck in increasing capacity and is often responsible for dropped calls.  The two major types of system-generated cellular interference are co-channel interference and adjacent channel interference.  They are difficult to control in practice due to random propagation effects and more so is the interference due to out-of-band users, which arises without warning due to front end overload of subscriber equipment or intermittent inter-modulation products. In practice, the transmitters from competing cellular carriers are often a significant source of out-of-band interference, since competitors often locate their base stations in close proximity to one another in order to provide comparable coverage to customers. 4.3.3 Co-channel Interference Frequency reuse implies that in a given coverage area, there are several cells that use the same set of frequencies. These cells are called co-channel cells (Figure 4.4), and the interference between signals from these cells is called co-channel interference. Note that unlike thermal noise which can be overcome by increasing the signal-to-noise ratio (SNR), cochannel interference cannot be combated by simply increasing the carrier power of a transmitter. This is because an increase in carrier transmit power increases the interference to neighboring co-channel cells. To reduce co-channel interference, co-channel cells must be physically separated by a minimum distance to provide sufficient isolation due to propagation.

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

A A D+R D+R

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First tier of co-channel cells of the cell A

Figure 4.4: Illustration of the first tier of co-channel cells for a cluster size of N=7. When the mobile is at the cell boundary (point A), it experiences worst case co-channel interference on the forward channel. The marked distances between the mobile and different co-channel cells are based on approximations made for easy analysis. 4.3.4 Adjacent Channel Interference Interference resulting from signals which are adjacent in frequency to the desired signal is called adjacent channel interference. Adjacent channel interference results from imperfect receiver filters which allow nearby frequencies to leak into the passband. The problem can be particularly serious if an adjacent channel user is transmitting in very close range to a subscriber's receiver, while the receiver attempts to receive a base station on the desired channel. This is referred to as the near-far effect, where a nearby transmitter (which may or may not be of the same type as that used by the cellular system) captures the receiver of the subscriber. Alternatively, the near-far effect occurs when a mobile close to a base station transmits on a channel close to one being used by a weak mobile. The base station may have difficulty in discriminating the desired mobile user from the bleedover caused by the close adjacent channel mobile.     

Adjacent channel interference can be minimized through careful filtering and channel assignments. Since each cell is given only a fraction of the available channels, a cell need not be assigned channels which are all adjacent in frequency. By keeping the frequency separation between each channel in a given cell as large as possible, the adjacent channel interference may be reduced considerably. Thus instead of assigning channels which form a contiguous band of frequencies within a particular cell, channels are allocated such that the frequency separation between channels in a given cell is maximized. By sequentially assigning successive channels in the frequency band to different cells, many channel allocation schemes are able to separate adjacent channels in a cell by as many as N channel bandwidths, where N is the cluster size. Some channel allocation schemes also prevent a secondary source of adjacent channel interference by avoiding the use of adjacent channels in neighboring cell sites.

4.3.5 Improving Capacity in Cellular Systems 53

Techniques such as cell splitting, sectoring, and coverage zone approaches are used in practice to expand the capacity of cellular systems. Cell splitting allows an orderly growth of the cellular system. Sectoring uses directional antennas to further control the interference and frequency reuse of channels. The zone microcell concept distributes the coverage of a cell and extends the cell boundary to hard-to-reach places. While cell splitting increases the number of base stations in order to increase capacity, sectoring and zone microcells rely on base station antenna placements to improve capacity by reducing co-channel interference. Cell splitting and zone microcell techniques do not suffer the trunking inefficiencies experienced by sectored cells, and enable the base station to oversee all handoff chores related to the microcells and thus reducing the computational load at the MSC. In this lab we consider investigating Cell splitting and sectorization. 4.3.6 Cell Splitting Cell splitting is the process of subdividing a congested cell into smaller cells, each with its own base station and a corresponding reduction in antenna height and transmitter power. Cell splitting increases the capacity of a cellular system since it increases the number of times that channels are reused. By defining new cells which have a smaller radius than the original cells and by installing these smaller cells between the existing cells, capacity increases due to the additional number of channels per unit area. An example of cell splitting is shown in Figure 4.5. In Figure 4.5, the base stations are placed at corners of the cells, and the area served by base station A is assumed to be saturated with traffic (i.e., the blocking of base station A exceeds acceptable rates). New base stations are therefore needed in the region to increase the number of channels in the area and to reduce the area served by the single base station. Note in the figure that the original base station A has been surrounded by six new microcell base stations. In the example shown in Figure 4.5, the smaller cells were added in such a way as to preserve the frequency reuse plan of the system. For example, the new cell base station labeled G was placed half way between two larger stations utilizing the same channel set G. This is also the case for the other new cells in the figure. As can be seen from Figure 4.5, cell splitting merely scales the geometry of the cluster. In this case, the radius of each new microcell is half that of the original cell. For the new cells to be smaller in size, the transmit power of these cells must be reduced. The transmit power of the new cells with radius half that of the original cells can be found by examining the received power at the new and old cell boundaries and setting them equal to each other. This is necessary to ensure that the frequency reuse plan for the new microcells behaves exactly as for the original cells. For Figure 4.5, Pr at old cell boundary  Pt1 R n (4.4) Pr (at new cell boundary ) ∝Pt 2 ( R / 2 )

n

(4.5)

where Pt1 and Pt2 are the transmit powers of the larger and smaller cell base stations, respectively, and n is the path loss exponent. If we take n = 4 and set the received powers equal to each other, then Pt 2 

Pt1 (4.6) 16

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

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Figure 4.5: Illustration of cell splitting. In other words, the transmit power must be reduced by 12 dB (- 4*10log10 (1/2) dB) in order to fill in the original coverage area with microcells, while maintaining the S/I requirement. In practice, not all cells are split at the same time. It is often difficult for service providers to find real estate that is perfectly situated for cell splitting. Therefore, different cell sizes will exist simultaneously. In such situations, special care needs to be taken to keep the distance between co-channel cells at the required minimum, and hence channel assignments become more complicated. When there are two cell sizes in the same region as shown in figure 4.5, one cannot simply use the original transmit power for all new cells or the new transmit power for all the original cells. If the larger transmit power is used for all cells, some channels used by the smaller cells would not be sufficiently separated from co-channel cells. On the other hand, if the smaller transmit power is used for all the cells, there would be parts of the larger cells left unserved. For this reason, channels in the old cell must be broken down into two channel groups, one that corresponds to the smaller cell reuse requirements and the other that corresponds to the larger cell reuse requirements. The larger cell is usually dedicated to high speed traffic so that handoffs occur less frequently. At the beginning of the cell splitting process, there will be fewer channels in the small power groups. However, as demand grows, more channels will be required, and thus the smaller groups will require more channels. This splitting process continues until all the channels in an area are used in the lower power group, at which point cell splitting is complete within the region, and the entire system is rescaled to have a smaller radius per cell. Antenna down tilting (oriented), which deliberately focuses radiated energy from the base station towards the ground rather than towards the horizon (sphere), is often used to limit the radio coverage of newly formed microcells. 4.3.7 Sectoring Cell splitting achieves capacity improvement by essentially rescaling the system. By decreasing the cell radius R and keeping the co-channel reuse ratio D/R unchanged, cell splitting increases the number of' channels per unit area. 55

However, another way to increase capacity is to keep the cell radius unchanged and seek methods to decrease the D/R ratio. In this approach, capacity improvement is achieved by reducing the number of cells in a cluster and thus increasing the frequency reuse. However, in order to do this, it is necessary to reduce the relative interference without decreasing the transmit power. The co-channel interference in a cellular system may be decreased by replacing a single omni-directional antenna at the base station by several directional antennas, each radiating within a specified sector. By using directional antennas, a given cell will receive interference and transmit with only a fraction of the available co-channel cells. The technique for decreasing co-channel interference and thus increasing system capacity by using directional antennas is called sectoring. The factor by which the co-channel interference is reduced depends on the amount of sectoring used. A cell is normally partitioned into three 1200 sectors or six 600 sectors as shown in Figure 4.6 (a) and (b). When sectoring is employed, the channels used in a particular cell are broken down into sectored groups and are used only within a particular sector, as illustrated in figure 4.6 (a) and (b). Assuming 7-cell reuse, for the case of 120° sectors, the number of interferers in the first tier is reduced from 6 to 2. This is because only 2 of the 6 co-channel cells receive interference with a particular sectored channel group. Referring to Figure 4.7, consider the interference experienced by a mobile located in the right-most sector in the center cell labeled “5”. There are 3 co-channel cell sectors labeled "5" to the right of the center cell, and 3 to the left of the center cell. Out of these 6 co-channel cells, only 2 cells have sectors with antenna patterns which radiate into the center cell, and hence a mobile in the center cell will experience interference on the forward link from only these two sectors. The resulting S/I for this case can be found to be 24.2 dB, which is a significant improvement over the omni-directional case in, where the worst case S/I was 17 dB. In practical systems, further Improvement in S/I is achieved by downtilting the sector antennas such that the radiation pattern in the vertical (elevation) plane has a notch at the nearest co-channel cell distance. Thus, sectoring reduces interference, which amounts to an increase in capacity by a factor of 12/7 or 1.714. In practice, the reduction in interference offered by sectoring enable planners to reduce the cluster size N and provides an additional degree of freedom in assigning channels. The penalty for improved S/I and the resulting capacity improvement is an increased number of antennas at each base station, and a decrease in trunking efficiency due to channel sectoring at the base station. Since sectoring reduces the coverage area of a particular group of channels, the number of handoffs increases, as well. Fortunately, many modern base stations support sectorization and allow mobiles to be handed off from sector to sector within the same cell without intervention from the MSC, so the handoff problem is often not a major concern. It is the loss of traffic due to decreased trunking efficiency that causes some operators to shy away from the sectoring approach, particularly in dense urban areas where the directional antenna patterns are somewhat ineffective in controlling radio propagation. Because sectoring uses more than one antenna per base station, the available channels in the cell must be subdivided and dedicated to a specific antenna. This breaks up the available trunked channel pool into several smaller pools, and decreases trunking efficiency.

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

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Figure 4.7: Illustration of how 1200 sectoring reduces interference from co-channel cells. Out of the 6 co-channel cells in the first tier, only 2 of them interfere with the center cell. If omni-directional antennas were used at each base station, all 6 co-channel cells would interfere with the center cell.

4.4 System Modeling 4.4.1 Frequency Reuse Factor   

The frequency reuse is one of the most important design challenges in cellular networks. The base stations (BSs) of the cellular network should be located as near to each other as possible to maximize the number of simultaneous users, but should not be so close that the co-channel interference results in unacceptable speech quality. The reuse distance, i.e. distance between co-channel cells D is an important parameter that determines the reuse pattern within the cellular network.

Specifically, we assume that      

all co-channel base stations have same transmitter power, the path loss is proportional to d-4, noise level is negligible when compared to interference level there are 6 equidistant interferers at the channel, and the interference from interferers, that are further away, can be neglected, cell radius is R, and the distance between co-channel cells is D. 57

We can approximately analyze the co-channel interference on basis of the figure 4.4. Hence, the signal to co-channel interference ratio is given as, considering each co-channel cell is at the equidistance from the center cell. C C = 6 I ∑I i i =1

R = 6D

4 4

so that C (4.7) I The ratio of co-channel cell site distance to the cell radius R is given by D  R4 6

D  R

3K

(4.8)

For K=7 and i=2 and j=1, the desired carrier-to-interference ratio at the cell site is given by

C C C  6  IT 6I ∑I i i 1

1 R -n  6 D - R -n 1 DR    6 R 

n

We can then express frequency reuse factor K as, 1 1  C  n  K   6  1 I T  3  

2

(4.9)

Note that “for low value of CIR, K is reduced. Hence, larger number of channels per cell and a large traffic capacity”. For n=4, and CIR=18 dB, K  10 , Neglecting 1, for a higher CIR and n = 4,

2 C    3  I T  Hence if CIR increases that results in decrease in co-channel interference and so results higher value of K. K

If Nf is the number of channels per cell, then

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

Nf 

Ba KBc Ba

 Bc

2 C  3  I T

  

4.4.2 Cell Splitting Typically the area of a cell is split into 4 new cells, which means that the radius of each new cell is one half of the radius of the original cell. Assume 40 dB/decade pathloss so that the power can be reduced by 12 dB. Thus, after n splitting, the new traffic capacity within the original area will be Tn  4n T0 (4.10) and the new power of the transmitters will be Pn dB  P0  12n (4.11) The spectral efficiency of cellular systems (FDMA and TDMA) can be expressed in terms of number of channels per cell as follows. B ( tot ) Bc Nf  Kc Btot Bc  2C    3  I  min where Btot is the total bandwidth of the system Bc is the (equivalent) bandwidth of a single channel (C/I)min is the minimum acceptable signal-to-interference ration K is the reuse factor Hence it is shown that we can increase the spectral efficiency by either decreasing the channel bandwidth Bc or decreasing the C/I requirement. 4.4.3 Bit Transfer Capacity We can calculate the bit transfer capacity: number of bits transmitted within one second in bandwidth of one Hertz in a single cell of the network. Rt (4.12) c Bc K 4.4.4 System Capacity For an allocation of N frequency channels for a coverage area A, the capacity of the system can be assessed in terms of number of simultaneous calls, which can be calculated as A N (4.13) c   ABS  K  59

where ABS is the area of a single base station. For hexagonal cells, this area can be calculated from the cell radius as 3 ABS  3R 2 2  2.6 R 2 The number of cells is A (4.14) N BS  ABS The number of simultaneous calls in the system is

n  N BS

N K

(4.15)

4.4.5 Adjacent Channel Interference and Traffic Channel Assignment Note that what follows is all about describing fixed channel assignment, where each cell is permanently allocated a preselected set of frequency channels. Adjacent channel interference occurs when signal energy spills over from one channel into another channel that is adjacent to it in the frequency spectrum. The most important adjacent channel interference is caused by the immediately preceding and following channels. In principle it is possible to control adjacent channel interference completely through filtering at the transmitter and the receiver. However, tight filtering makes mobile units more expensive and introduces ISI in the received signal. Assume a relatively simple receiving filter with 6 dB/oct low-pass equivalent attenuation characteristics, we can calculate for a 30 kHz channel the attenuation from the edge of the band at f1 = 15 kHz to frequency offset f2 as f  6 AdB  log 2  (4.16) log2   f1  For f2 = 120 kHz and (f2/f1) = 8, i.e. 4 channels away, we get the attenuation of 18 dB. Thus, if we require C/I ratio of 18 dB as for cochannel interference, the three adjacent channels to any channel in use cannot be used for traffic. Adjacent channel interference can be reduced by maintaining maximum frequency separation between channels in any given cell. For maximum frequency separation between channels, the frequencies k, k+K, k+2K ... should be assigned to the kth cell, when the frequency reuse factor K is used. The following table shows the procedure of the frequency allocation used for the AMPS system for the frequency reuse factor K = 7.The letters A, B and C refer to 3 sectors of directional antennas that are used in each BS. Table 4.3: Procedure of the frequency allocation used for the AMPS system for the frequency reuse factor K = 7. Group Channel assignment number A B C A B C A B 1 8 15 22 29 36 43 50 … 1 2 9 16 23 30 37 44 51 … 2

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

3 4 5 6 7

3 4 5 6 7    

10 11 12 13 14

17 18 19 20 21

24 25 26 27 28

31 32 33 34 35

38 39 40 41 42

45 46 47 48 49

52 53 54 55 56

… … … … …

Since the adjacent group numbers contain adjacent frequency channels, they should not be assigned to neighboring sectors in cells. It should be noted that for small reuse factors (e.g. K = 4), it is impossible (especially, without sectoring) to avoid using immediately adjacent frequency channels in some of the neighboring six cells. Already, for K = 7, it is very difficult without sectoring to find a channel assignment in which the use of immediately adjacent frequency channels could be avoided. However, for K = 9, we can find a channel assignment (see following Figure) in which immediately adjacent frequency channels are never used in neighboring cells.

3 9

2

4

8 5

2

1 7

6

4 1

7

2

3 8

9 6

3

9

7

5 4

2 1

8 A cluster

Figure 4.9: Channel assignment for K=9. An example of adjacent Channel frequency separation for two channels which are used in a 12-cell cluster is shown below. Here K=12, Ch. 1, 13, 25, 30 kHz is channel bandwidth center to center is 360 kHz Edge to edge is 330 kHz. Desired channel Channel 01

System adjacent channel Channel 13 360 kHz

30 kHz

30 kHz

Figure 4.10: Frequency separation between desired and system-adjacent channel. 61

4.4.6 Near-End-to-Far-End Ratio When the mobile units are moving within a cell, we often encounter a situation, where two MSs are transmitting simultaneously to the BS at different channels. And one of the MSs is much nearer to the BS than the other. Assuming that the mobile transmits the same power, the signal received at the cell site is proportional to the geographical distance between the cell site and the MS. When the separation from two MS operating on adjacent channels is widely different, a situation can arise when the power received at the cell site from a nearby MS is far higher than that of from another MS farther away. Base station (BS)

d1 d2

Cell area Mobile stations (MSs)

Figure 4.11: Near-far effects. These unbalanced received powers are due to different path losses and known as near-end (NE) to farend (FE) ratio interference (NE / FE) = (path loss due to path d1) / (path loss due to path d2), where nearby distance d1 is from interfering MS and farther distance d2 is from the desired MS. If n=4, then NE  d1    FE  d 2 

4

(4.17)

This large imbalance in the received levels makes the problem of adjacent channel interference even more severe, and as a consequence it also increases the required frequency separation between channels. For example, in a case the distances of MSs from the BS are 0.5 and 10 km and assuming 40 dB/dec pathloss, the ratio of received powers at the BS is 52 dB. This ratio of received powers due to different locations of two transmitters is called near-end-to-far-end ratio. If we still require C/I ratio of 18 dB, the required attenuation of the lowpass-equivalent receiving filter for the lower-level channel is 52 + 18 = 70 dB. Even if we assume a slightly better receiving filter with 12 dB/oct attenuation characteristics, the required frequency ratio f2/f1 is 58.

4.5 Simulation Procedure Develop a MATLAB file to answer the followings. Given that as input C/I = 18 dB. System BW = 25 MHz Channel BW = 30 kHz

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

Path loss exponent= 4 Area to be covered = x km2 Receiver filter wit 6 dB/oct LPE attenuation characteristics Call arrival rate is 1 per second and Poisson distributed Holding time 0.5 second Inter arrival time is negative exponentially distributed and M/M/n system Cell Layout and Co-Channel Interference        

Find the minimum co-channel cell reuse ratio D/R. Find the co-channel cell reuse ratio K Find Layout the cells to cover the given area x Find the area of a cell Find the number of cells required to cover the area Find the maximum number of channels per cell Find the maximum number of channels in the system BW (channel efficiency) Find the number of simultaneous calls (max) in the system within the coverage (spectral efficiency)

Cell Splitting If each cell is splitted into 4 new but smaller cells,  Find the new capacity (number of users simultaneously served)  Find the new power requirement for each cellsite Bit Transfer Capacity 

Calculate the bit transfer capacity: number of bits transmitted within one second in bandwidth of one Hertz in a single cell of the network.

Adjacent Channel Interference 

Find the minimum adjacent channel frequency separation to avoid interferences from adjacent as well as co-channel interference

Channel Assignment 

Level (fixed channel allocation) all cells to allocate channels to cells such that maximum separation between channels is possible with sectorization (3-sectored and 6-sectored) and without sectorization. Use the following strategy. A cell k should be assigned with a channel given by the following expression. k+i*K; where i (sector number)== 1,…,S where S 3 for 3-sectored and =6 for 6-sectored cells

4.6 Simulation Results 01 minimum co-channel cell reuse ratio = 4.4110 02 frequency reuse factor = 63

7 03 Area of a hexagonal cell in m2= 2600000 04 number of cells required to cover the given area = 9.0000 05 system capacity in maximum number of users = 125 06 new system capacity after cell splitting in maximum number of users = 500 07 new system transmit power requirement after cell splitting in dB = 34 08 Bit transfer capacity in bps/Hz/cell = 5.1231e-004 09 receiver filter attenuation characteristics in dB/octave = 6 10 Fixed channel assignment strategy (no sectorization) = Columns 1 through 11 1 2 3 4 5 6 7

8 15 22 29 36 43 50 57 64 71 9 16 23 30 37 44 51 58 65 72 10 17 24 31 38 45 52 59 66 73 11 18 25 32 39 46 53 60 67 74 12 19 26 33 40 47 54 61 68 75 13 20 27 34 41 48 55 62 69 76 14 21 28 35 42 49 56 63 70 77

Columns 12 through 18 78 79 80 81 82 83 84

85 86 87 88 89 90 91

92 93 94 95 96 97 98

99 100 101 102 103 104 105

106 107 108 109 110 111 112

113 114 115 116 117 118 119

120 121 122 123 124 125 0

10 Fixed channel assignment strategy (for 3-sector cell) = 1 22 43 64 85 106 2 23 44 65 86 107 3 24 45 66 87 108 4 25 46 67 88 109 5 26 47 68 89 110 6 27 48 69 90 111

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

7

28

49

70

91 112

10 Fixed channel assignment strategy (for 6-sector cell) = 1 43 85 2 44 86 3 45 87 4 46 88 5 47 89 6 48 90 7 49 91

4.7 References [1] K. M. Ahmed, “Cellular Mobile Systems” Lecture notes: AT77.07, Asian Institute of Technology, Thailand, January 2010. [2] R. K. Saha & A B M Siddique Hossain, “Student Handout: Cellular Mobile Communications Technologies, Standards, and Systems”, edi 01, v 02, May 2011. 4.9 Appendix: M-File for Cellular Mobile System Design % Denote variables %-------------------------------------------------------------------------c_i=18; % Carrier-to-interference ratio at the receiver (dB) c_i_abs=10^1.8; % in absolute value sys_bw=25*10^6; % System bandwidth in Hz ch_bw=200*10^3; % Channel bandwidth in Hz p_loss_exp=4; % Pathloss exponent equals to 4 area_covered=(2.6*9)*10^6; % Area to be covered is 23.4 km2 cell_radius=1*10^3; % Cell radious is 1 km (consider hexagonal cell) call_rate=1; % call arrival rate is 1 per second hold_time=0.5; % call holding time is 0.5 seconds rec_filter_ch=6; % receiver filter characteristics 6 dB per octave pt_old=46; % transmit power 46 dBm split=1; % number of splitting the original cell bit_rate=1000; % bit rate 1 kbps system level

%-------------------------------------------------------------------------% part 01 cell layout and c0-channel interference %-------------------------------------------------------------------------% 01 minimum co-channel cell reuse ratio D_R=(6*c_i_abs)^(1/p_loss_exp); % consider only first-tier interferer

% 02 frequency reuse factor K=1/3*(D_R+1)^2; % 03 Area of a hexagonal cell area_cell=2.6*cell_radius^2;

% 04 number of cells required to cover the given area cell_no=area_covered/area_cell;

65

% 05 number of channels per cell channel_no_cell=sys_bw/(ch_bw*K);

% 05 maximum number of channels in the system (no of users) % or system capacity channel_no_sys=sys_bw/ch_bw; % system capacity sys_capa_old=channel_no_sys;

%-------------------------------------------------------------------------% Part 02 Cell splitting % consider each cell is splitted into 4 new cells %-------------------------------------------------------------------------% 06 new system capacity after cell splitting sys_capa_new=4^split*sys_capa_old;

% 07 new system transmit power requirement after cell splitting pt_new=pt_old-12*split;

%-------------------------------------------------------------------------% Part 03 Bit transfer capacity per cell %-------------------------------------------------------------------------% 08 Bit transfer capacity per Hz per cell bit_trans_capa_cell=bit_rate/(ch_bw*K); % bps/hz/cell

%-------------------------------------------------------------------------% Part 04 receiver filter attenuatuation characteristics for no adjacent channel % interference %-------------------------------------------------------------------------f1=15; f2=120; f2_f1=f2/f1;

% difference between channels (frequencies) apart

% 09 receiver filter attenuation characteristics filter_atten_cha=c_i*(log10(2)/log10(f2_f1));

% in dB/octave

%-------------------------------------------------------------------------% Part 05 Channel assignment strategy in cells %-------------------------------------------------------------------------%10 Fixed channel assignment strategy %channel_no_sys=125; K=7; i=1; % for no sectorrization % i=3; % for 3-sector % i=6; % for 6-sector

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

cha_cell=round(channel_no_sys/(K*i)); cha_cell_ind_sec01=zeros(K,cha_cell); chanl=1:1:channel_no_sys; chanl_no=zeros(K,channel_no_sys); %-----------------------------------------------for k1=1:1:K for j=k1:i*K:channel_no_sys chanl_no(k1,j)=j; end end

for i2=1:K s=0; for j2=1:channel_no_sys xx=chanl_no(i2,j2); if xx>0 s=s+1; cha_cell_ind_sec01(i2,s)=xx; end end end %-----------------------------------------------% note that for sectorization, for example 3-sector, the output gives only % for one sector. For other sectors, readers are advised to try on their % own. set i=1 for no sectorization. %---------------------------------------------------------% output %----------------------------------------------------------

disp('01 minimum co-channel cell reuse ratio = ') disp(D_R)

disp('02 frequency reuse factor = ') disp(K)

disp('03 Area of a hexagonal cell in m2= ') disp(area_cell)

disp('04 number of cells required to cover the given area = ') disp(cell_no)

disp('05 system capacity in maximum number of users = ') disp(sys_capa_old)

67

disp('06 new system capacity after cell splitting in maximum number of users = ') disp(sys_capa_new)

disp('07 new system transmit power requirement after cell splitting in dB = ') disp(pt_new)

disp('08 Bit transfer capacity in bps/Hz/cell = ') disp(bit_trans_capa_cell)

disp('09 receiver filter attenuation characteristics in dB/octave = ') disp(filter_atten_cha)

disp('10 Fixed channel assignment strategy = ') disp(cha_cell_ind_sec01) %------------------------------------------------------------

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

CMCL 05: Power Delay Profile and Channel Classification in Cellular Mobile Communications 5.1 Introduction A mobile radio channel generally exhibits both Delay and Doppler shift spreading. Delay spreading corresponds to time dispersion in time domain and to frequency-selective fading in frequency domain. Doppler spreading corresponds to frequency dispersion in frequency domain and to time-selective fading in time domain. These effects are shown by any mobile radio channel, but their importance varies according to the symbol duration and the bandwidth of the transmitted signal. 5.2 Fading Channel Characteristics 5.2.1 Power-Delay Profile Random and complicated radio-propagation channels can be characterized using the impulse-response approach. For each point in the three-dimensional environment, the channel is a linear filter with impulse response h(t). The impulse response provides a wideband characterization of the propagating channel, and contains all of the information necessary to simulate or analyze any type of radio transmission through that channel. If the input signal is a unit impulse  (t ) , the output will be the channel impulse response, which can be written as N

h t    An exp jn   t   n 

(5.1)

n 1

where An,  n and  n are the attenuation, delay in time of arrival, and phase, corresponding to path n respectively. Multipath propagation causes severe dispersion of the transmitted signal and the expected degree of dispersion is determined through the measurement of the power-delay profile of the channel. The power-delay profile provides an indication of the dispersion or distribution of transmitted power over various paths in a multipath model for propagation. The power-delay profile of the channel is calculated by taking the spatial average of ht  2 over a local area. By making several local-area measurements of ht  2 for different locations, it is possible to build an ensemble of power delay profiles, each one representing a possible small-scale multipath channel state. The parameters which characterize the delay spread can be classified as  First-Arrival delay,  Mean access delay,  RMS delay spread, and  Excess delay spread. First-Arrival Delay (  A ) This is a time delay corresponding to the arrival of the first transmitted signal at the receiver. It is usually measured at the receiver. This delay is set by the minimum possible propagation path delay from the transmitter to the receiver. It serves as a reference, and all delay measurements are made relative to it. Any measured delay longer than this reference delay is called an excess delay. 69

Mean Excess Delay (  e or  ) This is the first moment of the power-delay profile with respect to the first delay. It is expressed as

∑P (τ )τ τ = ∑P (τ ) k

k

k

(5.2)

k

k

RMS Delay (  RMS or  ) This is the square root of the second central moment of a power-delay profile. It is the standard deviation about the mean excess delay, and is expressed as στ =

2

(5.3)

∑P(τ ) τ = ∑P(τ )

2 k

k

where τ 2

τ 2 - (τ )

k

k

k

The RMS delay is a good measure of the multipath spread. It gives an indication of the nature of the intersymbol interference (ISI). It is also used to give an estimate of the maximum data rate for transmission. Maximum Excess Delay (  m ) This is measured with respect to a specific power level, which is characterized as the threshold of the signal. When the signal level is lower than the threshold, it is processed as noise. For example, the maximum excess delay spread can be specified as the excess delay (  m ) for which P (  ) falls below -30 dB with respect to its peak value. Thus, maximum excess delay  m is τ m = τ X - τ0

(5.4)

where  0 is the first arriving signal and  X is the maximum delay at which a multipath component is within X dB of the strongest arriving multipath signal (which does not necessarily arrive at  0 ). 5.2.2 Time Dispersion and Frequency-Selective Fading Time dispersion and frequency-selective fading are both manifestations of multipath propagation with delay spread. Presence of one implies the presence of the other. Time dispersion stretches a signal in time so that the duration of the received signal is greater than that of the transmitted signal. Frequency selective fading filters the transmitted signal, attenuating certain frequencies more than the others. Two frequency components closely spaced receive approximately the same attenuation. However, if they are far apart, they often receive vastly different attenuations. In digital systems it results as inter symbol interference. The minimum transmission bandwidth at which time dispersion is observable is inversely proportional to the maximum excess delay of the channel τm, where the excess delay is the actual delay minus the delay of the first arrival path. The constant of proportionality is normally taken as ¼, although it is system dependent. So, delay spread has 2 observable effects: distortion and dispersion. 5.2.3 Coherence Bandwidth

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

Coherence Bandwidth (Bc) is the measure of maximum possible transmission bandwidth at which distortion becomes appreciable. Bc indicates the frequency separation at which the attenuation of amplitudes of two frequency components become decorreleted such that the envelope correlation coefficient ρ (Δf, Δt) reaches a pre designated value. This value can vary from 0.9 to 0.37. Note that a value of 0.5 can safely be taken for mobile communications. We can define

 f , t  

a

2 1

a1 a 2  a1 a 2  a1

2

 a

2 2

 a1

2



(5.5)

where ‹ › denotes the ensemble average. a1 and a2 represent the amplitudes of signals at frequencies f1 and f2 respectively and at time t1 and t2 respectively. Note that f1 - f2= Δf and t1-t2 = Δt. Coherence bandwidth can be characterized as  Range of frequencies over which the channel can be considered flat, meaning that the channel passes all spectral components with approximately equal gain and linear phase.  Frequency components in this bandwidth have a strong correlation in amplitude. For envelopes of two signals to vary uncorrelatedly their frequencies should be separated by more than the coherence bandwidth of the channel Bc. The coherence bandwidth can be approximately calculated from the envelope correlation coefficient between two signals separated by Δf Hz and Δt seconds. When we consider correlation as function of frequency separation only and set Δt to zero, the coherence bandwidth Bc is defined as the bandwidth Δf, where the envelope correlation coefficient between two signals has fallen to one half of its maximum value. 1 ρ(Bc ,0 ) = = 0.5 ( 1 + 2 ΠBc )2 δ 2 The solution to this is 1 1 Bc = ≈ (5.6) 2 Πδ 6 δ A typical delay spread value of 3 μs in urban environment corresponds to coherence bandwidth of about 50 kHz. The typical coherence bandwidths in different kinds of manmade environments are: Bc = 50 kHz for δ = 3 μs in urban areas

Bc = 300 kHz for δ = 0.5 μs in suburban areas Bc = 800 kHz for δ = 0.2 μs in open areas

5.2.4 Frequency-flat and Frequency-selective fading If the bandwidth of the modulated signal is less than the coherence bandwidth of the channel, all the frequency components of the signal encounter (approximately) same fading and the fading is called frequency-flat fading. On the other hand, if the bandwidth of the modulated signal is much greater than the coherence bandwidth of the channel, different frequency components of the signal encounter different fading characteristics and the fading is called frequency-selective fading. Frequency-selective channels are also called time dispersive channels, because the long delay spread corresponds to lengthening of the duration of the

71

transmitted symbols. In this case the channel has clear filtering effect on the transmitted pulse. And besides the amplitude, also the shape of the pulse is changed2. In digital mobile communications, the propagation phenomena are highly dependent on the ratio of the symbol duration to the delay spread of the time variant radio channel. If the transmission bit rate is so high that each data symbol significantly spreads into adjacent symbols, severe inter symbol interference (ISI) occurs. If we want the interference between adjacent symbols to be low, we have exactly the same equation for maximum transmission symbol rate as for coherence bandwidth, i.e.

1 2 Πδ

Rt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> %Case 01: Single carrier per transponder disp('...................................................................') disp('Case 01: single carrier per transponder') disp('...................................................................') %>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

% ...................................................................... % Earth-Satellite Uplink Design %....................................................................... %01: Carrier EIRP EIRP_carrier_tx_dBW=power_tx_dB+gain_tx_dB; % in dBW %02: uplink free space loss up_loss=(4*pi*carrier_freq_uplink*dis_earth_sat)/(3*10^8); uplink_FS_loss_abs=(up_loss)^2; uplink_FS_loss_dB=10*log10(uplink_FS_loss_abs); % in dB %03: uplink carrier-to-noise ratio loss_uplink=track_loss_uplink_dB+uplink_FS_loss_dB; k_B_uplink=k_boltz_dBW+noise_BW_uplink_dB; C_N_uplink_dB=EIRP_carrier_tx_dBW-loss_uplink+gain_to_noise_sat_dB-k_B_uplink; C_N_uplink_abs=10^(C_N_uplink_dB/10); % in absolute value

disp(['01:carrier EIRP in dBW = ',num2str(EIRP_carrier_tx_dBW)])

129

disp(['02:uplink free space loss in dB = ',num2str(uplink_FS_loss_dB)]) disp(['03:uplink carrier-to-noise ratio = ',num2str(C_N_uplink_abs)]) disp(['04:uplink carrier-to-noise ratio in dB = ',num2str(C_N_uplink_dB)]) % ...................................................................... % Satellite-Earth Downlink Design %....................................................................... %04: satellite EIRP (or power) EIRPS_sat_tx_dBW=44; % in dBW %05: downlink free space loss down_loss=(4*pi*carrier_freq_downlink*dis_earth_sat)/(3*10^8); downlink_FS_loss_abs=(down_loss)^2; downlink_FS_loss_dB=10*log10(downlink_FS_loss_abs); % in dB %06: downlink carrier-to-noise ratio loss_downlink=track_loss_downlink_dB+downlink_FS_loss_dB; k_B_downlink=k_boltz_dBW+noise_BW_downlink_dB; C_N_downlink_dB=EIRPS_sat_tx_dBW-loss_downlink+gain_to_noise_earth_dB-k_B_downlink; C_N_downlink_abs=10^(C_N_downlink_dB/10); % in absolute value

disp(['04:satellite EIRP in dBW = ',num2str(EIRPS_sat_tx_dBW)]); disp(['05:downlink free space loss in dB =', num2str(downlink_FS_loss_dB)]) disp(['06:downlink carrier-to-noise ratio = ',num2str(C_N_downlink_abs)]) disp(['07:downlink carrier-to-noise ratio in dB = ',num2str(C_N_downlink_dB)]) %.................................................................... % Earth-Satellite-Earth Total link Design %...................................................................... % 07:Total satellite link (earth-satellite-earth) carrier-to-noise ratio C_N_link_abs=(1/((1/C_N_uplink_abs)+(1/C_N_downlink_abs))); C_N_link_dB=10*log10(C_N_link_abs); % in dB

disp(['08:total satellite link (earth-satellite-earth) carrier-to-noise ratio = ',num2str(C_N_link_abs)]) disp(['09:total satellite link (earth-satellite-earth) carrier-to-noise ratio in dB = ',num2str(C_N_link_dB)]) %........................................................................ % Analysis of the satellite link %........................................................................ disp('10:satellite characteristics: ') if C_N_uplink_abs>C_N_downlink_abs disp('satellite is downlink limited') else disp('satellite is uplink limited') end %..........................................................................

disp('...................................................................') disp('...................................................................')

%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> %Case 02: Multi-carrier per transponder disp('Case 02: multiple carriers per transponder')

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

disp('...................................................................') %>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> %satellite TWTA operating characteristics TWTA_BO_input=10; % in dB TWTA_BO_output=5; % in dB % 100 carriers per transponder number_carrier=100; % ...................................................................... % Earth-Satellite Uplink Design %....................................................................... %08: per Carrier EIRP EIRP_carrier_tx_dBW_multiple=power_tx_dB+gain_tx_dB-10*log10(number_carrier); % in dBW %09: per Carrier EIRP(saturated) EIRP_carrier_tx_dBW_saturated_multiple=EIRP_carrier_tx_dBW_multiple+TWTA_BO_input; % in dBW

%10: uplink free space loss up_loss=(4*pi*carrier_freq_uplink*dis_earth_sat)/(3*10^8); uplink_FS_loss_abs=(up_loss)^2; uplink_FS_loss_dB=10*log10(uplink_FS_loss_abs); % in dB %11: uplink carrier-to-noise ratio loss_uplink=track_loss_uplink_dB+uplink_FS_loss_dB; k_B_uplink=k_boltz_dBW+noise_BW_uplink_dB; C_N_uplink_dB_multiple=EIRP_carrier_tx_dBW_multiple-loss_uplink+gain_to_noise_sat_dB-k_B_uplink; C_N_uplink_abs_multiple=10^(C_N_uplink_dB_multiple/10); % in absolute value

disp(['11:carrier EIRP in dBW = ',num2str(EIRP_carrier_tx_dBW_multiple)]) disp(['12:uplink free space loss in dB = ',num2str(uplink_FS_loss_dB)]) disp(['13:uplink carrier-to-noise ratio = ',num2str(C_N_uplink_abs_multiple)]) disp(['14:uplink carrier-to-noise ratio in dB = ',num2str(C_N_uplink_dB_multiple)]) % ...................................................................... % Satellite-Earth Downlink Design %....................................................................... %12: satellite EIRP (or power) is 44 dB W EIRPS_sat_tx_dBW_multiple=44-10*log10(number_carrier); % in dBW %Satellite saturation EIRPs (saturated) EIRPS_sat_tx_dBW_saturated_multiple=EIRPS_sat_tx_dBW_multiple+TWTA_BO_output; % in dBW %13: downlink free space loss down_loss=(4*pi*carrier_freq_downlink*dis_earth_sat)/(3*10^8); downlink_FS_loss_abs=(down_loss)^2; downlink_FS_loss_dB=10*log10(downlink_FS_loss_abs); % in dB %14: downlink carrier-to-noise ratio loss_downlink=track_loss_downlink_dB+downlink_FS_loss_dB; k_B_downlink=k_boltz_dBW+noise_BW_downlink_dB; C_N_downlink_dB_multiple=EIRPS_sat_tx_dBW_multiple-loss_downlink+gain_to_noise_earth_dB-k_B_downlink; C_N_downlink_abs_multiple=10^(C_N_downlink_dB_multiple/10); % in absolute value

disp(['15:satellite EIRP in dBW = ',num2str(EIRPS_sat_tx_dBW_multiple)]) disp(['16:downlink free space loss in dB = ',num2str(downlink_FS_loss_dB)]) disp(['17:downlink carrier-to-noise ratio = ',num2str(C_N_downlink_abs_multiple)]) disp(['18:downlink carrier-to-noise ratio in dB = ',num2str(C_N_downlink_dB_multiple)])

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%.................................................................... % Earth-Satellite-Earth Total link Design %...................................................................... % 15: Total satellite link (earth-satellite-earth) carrier-to-noise ratio C_N_link_abs_multiple=(1/((1/C_N_uplink_abs_multiple)+(1/C_N_downlink_abs_multiple))); C_N_link_dB_multiple=10*log10(C_N_link_abs_multiple); % in dB

disp(['19:total satellite link (earth-satellite-earth) carrier-to-noise ratio = ',num2str(C_N_link_abs_multiple)]) disp(['20:total satellite link (earth-satellite-earth) carrier-to-noise ratio in dB = ',num2str(C_N_link_dB_multiple)]) %........................................................................ % 16: Analysis of the satellite link %........................................................................ disp('21:satellite characteristics: ') if C_N_uplink_abs_multiple>C_N_downlink_abs_multiple disp('Satellite is downlink limited') else disp('Satellite is uplink limited') end %.......................................................................... %..................................end of program..........................

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

Appendix A Help Documents A1.1 MATLAB Functions Following MATLAB functions would be helpful for the simulation of experiments. randint (1, x, [p q]): Generate one dimensional matrix of uniformly distributed random integers between p and q with a maximum of x number. for i=1:0.5:10 end from

: this command continues a loop for a maximum of 10 with an increment of 0.5 starting 1.

plot(x,y): plots vector y versus vector x. disp(‘x’): display x on the command window. legend(x1,x2,...): puts a legend on the current plot using the specified strings as labels (x1, x2). legend works on line graphs, bar graphs, pie graphs, etc. semilogx(x) is the same as the command plot(x), but a logarithmic (with base 10) scale is used for the xaxis. rayleighchan(ts,fd): constructs a frequency-flat, single path, Rayleigh fading channel object where ts is the sample time of the input signal in seconds and fd is the maximum Doppler shift in hertz. y = filter(chan,x): model the effect of the channel on a signal x. rayleighchan(ts,fd,tau,pdb): constructs a frequency-selective, multiple path, fading channel object that models each discrete path as an independent Rayleigh fading process where tau is a vector of path delays in seconds, and pdb is a vector of average path gains in dB. Note that a smaller fd, typically a few hertz to a fraction of a hertz, leads to slower variations, and a larger fd, typically a couple of hundred hertz, to faster variations. ricianchan(ts,fd,k): constructs a frequency-flat, single path, Rician fading-channel object where ts is the sample time of the input signal in seconds, and fd is the maximum Doppler shift in hertz, and k is the Rician K-factor in linear scale. ricianchan(ts,fd,k,tau,pdb): constructs a frequency-selective, multiple paths, fading-channel object where tau is a vector of path delays in seconds, and pdb is a vector of average path gains in dB. If k is a scalar, then the first discrete path is a Rician fading process, i.e. it contains a line-of-sight component with a Kfactor of k, while the remaining discrete paths are independent Rayleigh fading processes with no lineof-sight component. However, if k is a vector of the same size as tau, then each discrete path is a Rician fading process with a K-factor given by the corresponding element of the vector k. ricianchan(ts,fd,k,tau,pdb,fdLOS): specifies fdlos as the Doppler shift(s) of the line-of-sight component(s) of the discrete path(s) in hertz. Note that fdlos must be the same size as k. If k and fdlos are scalars, the lineof-sight component of the first discrete path has a Doppler shift of fdlos, while the remaining discrete paths are independent Rayleigh fading processes. If fdlos is a vector of the same size as k, the line-of-sight 133

component of each discrete path has a Doppler shift given by the corresponding element of the vector fdlos. Note also that by default, fdlos is 0. sqrt(x): gives the square root of the elements of x. log10(x): gives the base 10 logarithm of the elements of x erf(x): is the error function for each element of x. note that x must be real. x=1:1:y: gives a one dimensional array with an increment by 1 (if -1; decrement by 1 and also y and 1 are replaced one another in position) up to y. Note that y must be real and integer. A1.2 Things May Get Confused array(x): define any value of an one dimensional matrix array [x] with a variable x defines the position of the element in the matrix. array[x]: defines an one dimensional matrix. A1.3 Things May Get Remembered Any line in MATLAB must end with a semicolon (;) If you do not know any command or the functionality of a command, simply write help space that command in the command window. Example, help disp A1.4 Notes MATLAB has a number of built-in M-files, which will guide you during your simulation once called upon them in the command window. It is a good way to write the program in separate M-file and save that file as .m since writing directly on the command window may get you lost the written program, if you either forget to save or clear the command window.

Rony K. Saha, A Handbook on Cellular Mobile Communication Laboratory-A MATLAB based Approach

Author’s Biography Rony Kumer Saha is currently a doctoral student in Electrical Engineering, who received the Master of Engineering in Information and Communications Technologies (ICT) from Asian Institute of Technology (AIT), Thailand. Mr. Saha is the recipient of AIT Scholarship and AIT Fellowship in graduate level and the Merit Based Scholarship in undergraduate level. Mr. Saha has been in the research and academia for about ten years. He offered several graduate and undergraduate level courses in telecommunications engineering, including digital signal processing, cellular mobile communications, digital communications, GSM and cellular Systems, and 3G and beyond mobile communications. Mr. Saha worked as LTE Research Intern at Nokia Siemens Networks (NSN), Bangkok, Thailand. Mr. Saha has several research publications in reputed journal and conference proceedings. His researches involve resource allocations and scheduling, small cell network densification, and 5G mobile systems.

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