John G. Proakis, McGraw Hill. Communication Systems / 4th Edition. -- Simon
Haykin, John Wiley & Sons, Inc. Digital Communications – Fundamentals and ...
Wireless Information Transmission System Lab.
Introduction to Digital Communications System
Institute of Communications Engineering
National Sun Yat-sen University
Recommended Books Digital Communications / Fourth Edition (textbook) -- John G. Proakis, McGraw Hill Communication Systems / 4th Edition -- Simon Haykin, John Wiley & Sons, Inc. Digital Communications – Fundamentals and Applications / 2nd Edition -- Bernard Sklar, Prentice Hall Principles of Communications / Fifth Edition -- Rodger E. Ziemer and William H. Tranter, John Wiley & Sons, Inc. Modern Digital and Analog Communication Systems -- B.P. Lathi, Holt, Rinehart and Winston, Inc. 2
Example of Communications System Local Loop Switch Transmission Equipment Central Office
Local Loop Switch Transmission Equipment Central Office
Local Loop Switch Transmission Equipment Central Office
Mobile Switching Center
T1/E1 Facilities regenerator
Base Station
A/D Conversion (Digitization) T1/E1 Facilities regenerator
SONET SDH
M U X
T1/E1 Facilities
A/D Conversion (Digitization) T1/E1 Facilities regenerator
Mobile Switching Center
A/D Conversion (Digitization)
Public Switched Telephone Network (PSTN) 3
Base Station
Basic Digital Communication Nomenclature Textual Message: information comprised of a sequence of characters. Binary Digit (Bit): the fundamental information unit for all digital systems. Symbol (mi where i=1,2,…M): for transmission of the bit stream; groups of k bits are combined to form new symbol from a finite set of M such symbols; M=2k. Digital Waveform: voltage or current waveform representing a digital symbol. Data Rate: Symbol transmission is associated with a symbol duration T. Data rate R=k/T [bps]. Baud Rate: number of symbols transmitted per second [baud]. 4
Nomenclature Examples
5
Messages, Characters, and Symbols
6
Typical Digital Communications System From Other Sources Information Bits
Source Bits
Source Encoding
Format
Encryption
Channel Bits Channel Encoding
Multiplexing
Interleaving
Modulation
Frequency Spreading
Multiple Access
TX RF PA
si (t ) Digital Input
C H A N N E L
mi
Bit Stream
Synchronization
Digital Waveform
Digital Output
mˆ i
Format
sˆi (t ) Source Decoding
Information Sink
Decryption
Source Bits
Channel Decoding
Demultiplexing
Deinterleaving
Channel Bits
Optional Essential
To Other Destinations
7
Demodulation
Frequency Despreading
Multiple Access
RX RF IF
Wireless Information Transmission System Lab.
Format
Institute of Communications Engineering
National Sun Yat-sen University
Typical Digital Communications System From Other Sources Information Bits
Source Bits
Source Encoding
Format
Encryption
Channel Bits Channel Encoding
Multiplexing
Interleaving
Modulation
Frequency Spreading
Multiple Access
si (t )
Digital Input
C H A N N E L
mi
Bit Stream
Synchronization
Digital Waveform
Digital Output
mˆ i
Format
TX RF PA
sˆi (t ) Source Decoding
Information Sink
Decryption
Source Bits
Channel Decoding
Demultiplexing
Deinterleaving
Channel Bits
Optional Essential
To Other Destinations
9
Demodulation
Frequency Despreading
Multiple Access
RX RF IF
Formatting and Baseband Transmission
10
Sampling Theorem
11
Sampling Theorem Sampling Theorem: A bandlimited signal having no spectral components above fm hertz can be determined uniquely by values sampled at uniform intervals of Ts seconds, where 1 TS ≤ or sampling rate f S ≥ 2 f m 2 fm In sample-and-hold operation, a switch and storage mechanism form a sequence of samples of the continuous input waveform. The output of the sampling process is called pulse amplitude modulation (PAM). 12
Sampling Theorem
1 X S ( f ) = X ( f ) ∗ Xδ ( f ) = TS 13
∞
∑ X ( f − nf
n = −∞
S
)
Spectra for Various Sampling Rates
14
Natural Sampling
15
Pulse Code Modulation (PCM) PCM is the name given to the class of baseband signals obtained from the quantized PAM signals by encoding each quantized sample into a digital word. The source information is sampled and quantized to one of L levels; then each quantized sample is digitally encoded into an ℓ-bit (ℓ=log2L) codeword.
16
Example of Constructing PCM Sequence
17
Uniform and Non-uniform Quantization
18
Statistical Distribution of Single-Talker Speech Amplitudes 50% of the time, speech voltage is less than ¼ RMS. Only 15% of the time, voltage exceeds RMS. Typical voice signal dynamic range is 40 dB.
19
Problems with Linear Quantization Fact: Unacceptable S/N for small signals. Solution: Increasing quantization levels – price is too high. Applying nonlinear quantization – achieved by first distorting the original signal with a logarithmic compression characteristic and then using a uniform quantizer.
At the receiver, an inverse compression characteristic, called expansion, is applied so that the overall transmission is not distorted. The processing pair is referred to as companding. 20
Implementation of Non-linear Quantizer
21
Companding Characteristics In North America: μ-law compression: loge [1 + μ ( x / xmax )] ⋅ sgn x y = ymax loge (1 + μ ) where ⎧+ 1 for x ≥ 0 sgn x = ⎨ ⎩−1 for x < 0
In Europe: A-law compression: ⎧ A( x / x max ) ⋅ sgn x ⎪ y max 1 + log e A ⎪ y=⎨ ⎪ y 1 + log e [ A( x / x max )] ⋅ sgn x ⎪⎩ max 1 + log e A 22
0
W
Raised Cosine Filter Characteristics
74
Raised Cosine Filter Characteristics
75
Equalization In practical systems, the frequency response of the channel is not known to allow for a receiver design that will compensate for the ISI. The filter for handling ISI at the receiver contains various parameters that are adjusted with the channel characteristics. The process of correcting the channel-induced distortion is called equalization.
76
Equalization
77
Introduction to RAKE Receiver Multiple versions of the transmitted signal are seen at the receiver through the propagation channels. Very low correlation between successive chips is in CDMA spreading codes. If these multi-path components are delayed in time by more than a chip duration, they appear like uncorrelated noise at a CDMA receiver. Combine Coherently
Equalization is NOT necessary 78
Introduction to RAKE Receiver To utilize the advantages of diversity techniques, channel parameters are necessary to be estimated. Arrival time of each path, Amplitude, and Phase.
Maximal Ratio Combiner (MRC): The combiner that achieves the best performance is one in which each output is multiplied by the corresponding complexvalued (conjugate) channel gain. The effect of this multiplication is to compensate for the phase shift in the channel and to weight the signal by a factor that is proportional to the signal strength. 79
Maximum Ratio Combining (MRC) MRC: Gi=Aie-jqi G1
G2
Coherent Combining
GL
Channel Estimation Best Performance Receiver
80
Maximum Ratio Combining (MRC) L
Received Envelope:rL = ∑ Gl ⋅ rl l =1
L
Total Noise Power: σ = ∑ Gl σ n2,l 2 n
2
l =1 L
r = SNR: SNRL = 2 2 ⋅σ n 2 L
∑G ⋅r l =1 L
l
2
l
2 ⋅ ∑ Gl ⋅ σ n2,l 2
l =1
L
Since
∑G ⋅r l =1
l
l
2
⎛ rl = ∑ Glσ n ,l ⎜ ⎜σ l =1 ⎝ n ,l L
81
⎞ ⎟⎟ ⎠
2
Maximum Ratio Combining (MRC) 2
L
L
L
Chebychev's Inequality : ∑ Gl ⋅ rl ≤ ∑ Glσ n ,l ⋅ ∑ l =1
L
SNRL ≤
Gσ ∑ 1 l =1
2
l
L
2 n ,l
L
⋅∑ l =1
2
l =1
l =1
rl
2
σ n ,l
2
rl
σ n ,l
2
L rl 1 = ∑ 2 = ∑ SNRl 2 l =1 σ n ,l l =1 L
2 G σ ∑ l n ,l 2
l =1
With equality hold : Glσ n ,l = k
rl*
σ n ,l
⇒ Output SNR = Sum of SNRs from all branches @ Gl ∝ rl* 82
Advantages of RAKE Receiver Consider a receiver with only one finger: Once the output of a single correlator is corrupted by fading, large bit error is expected.
Consider a RAKE receiver If the output of a single correlator is corrupted by fading, the others may NOT be. Diversity is provided by combining the outputs Overcome fading Improve CDMA reception
83
