Optimum Resource Allocation in OFDM Systems ...

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Optimum Resource Allocation in OFDM Systems using FRBS and Particle Swarm Optimization 1,2

Atta-ur-Rahman

1

Barani Institute of Information Technology, Rawalpindi, Pakistan 2 Institute of Signals, Systems and Soft-computing (ISSS), Islamabad, Pakistan [email protected] Abstract—Optimum allocation of resources is demand of every modern communication system. In this way the transmission parameters like code rate, modulation size and power are optimally chosen to enhance the overall system throughput while satisfying certain constraints at the same time. A similar constrained optimization problem is focused for OFDM environment and solved by proposed Fuzzy Rule Based System (FRBS) and Particle Swarm Optimization (PSO). In this proposal FRBS is used for adapting code rate and modulation size while PSO is used for adaptive power. Significance of the proposed scheme is shown through the simulations. Keywords-component; PSO; OFDM; FRBS; BER; Adaptive Modulation and Coding; Modulation Code Pair

I.

INTRODUCTION

Usage of evolutionary, soft-computing and hybrid intelligent techniques for solution of various optimization problems in various fields of engineering is an emerging area of research nowadays. These algorithms are suboptimum yet attractive compared to their optimum counterparts in terms of complexity and implementation. Orthogonal Frequency Division Multiplexing (OFDM) is one of the prominent candidates for many 3rd Generation (3G) and 4th Generation (4G) Communication Systems. In this technique a single very high data rate stream is divided into several low data rate streams using Inverse Fast Fourier Transform (IFFT). Then these streams are modulated over different orthogonal subcarriers. This is to divide one large frequency selective channel into a number of frequency nonselective sub-channels. Moreover, addition of appropriate cyclic prefix (CP) and interleaver makes the system almost inter-symbol-interference (ISI) free. In OFDM every subchannel experiences a different channel condition so the use of same modulation and code rate may not be suitable for all subcarriers. Similarly, flat power would not be beneficial since sub-channels may need different power. This situation demands adaptive resource allocations for an optimum utilization. A Multiuser subcarrier and bit allocation along with adaptive cell selection for transmission was proposed by [1] where 1.6dB gain was achieved compared to fixed subcarrier allocation. A low complexity algorithm for proportional resource allocation in OFDMA system was proposed in [2], where linear method and root finding algorithm were used to allocate power and data rates to users. In [3] a gradient based solution was proposed for single user downlink scheduling and resource allocation for downlink OFDM wireless systems and a 96.6% utility was

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achieved. In [4] an Adaptive data transmission in downlink MIMO-OFDM system with pre-equalization was investigated using Water-filling algorithm and adaptive LQ decomposing. A Genetic Algorithm (GA) based adaptive resource allocation scheme was proposed by Reddy [5], to increase the user data rate where water-filling principle was used as a fitness function. Moreover, it was shown that chromosome length helps to achieve optimum power requirement. A subchannel allocation based on bidding model and auction algorithm proposed by [6], where throughput was sustained but user data rates were compromised. Moreover, auction algorithm use to allocate subchannel to the appropriate most user who require that subchannel. A novel efficient resource allocation algorithm for multiuser OFDM system using a joint allocation method and root finding algorithm to achieve good performance even with low SNR was proposed by [7]. Another interesting paper with adaptive resource allocation based on modified GA and particle swarm optimization (PSO) for multiuser OFDM system was proposed by [8]. GA has been modified by using a fractional generation gap. It converges faster than the original one and it was found that PSO performs better than GA. An approach akin to the previous one, ant colony optimization (ACO) evolutionary technique for subcarrier allocation in OFDMA-based wireless system was proposed by [9]. Technique was capable of finding one optimal solution in a short period of time. Adaptive subcarrier and power allocation with fairness for multi-user space-time block-coded OFDM system was investigated in contrast to Greedy algorithm as well as water-filling principle [10]. An optimization problem for power constraints and use GA to maximize the sum capacity of OFDM system with the total power constraint was investigated in [11]. Also it was shown that GA is better than conventional methods. A scheme for resource allocation in downlink MIMOOFDMA with proportional fairness where dominant Eigen channels obtained from MIMO state matrix are used to formulate the scheme with low complexity in [12], scheme provides much better capacity gain than static allocation method. A PSO based Adaptive multicarrier cooperative communication technique which utilizes the subcarrier in deep fade using a relay node in order to improve the bandwidth efficiency [13] where centralized and distributed versions of PSO were investigated.

A low complexity subcarrier and power allocation technique based upon GA to maximize the sum of user data rates in MIMO-OFDMA system was proposed in [14]. Another GA based efficient real-time subcarrier and bit allocation for multiuser OFDM transmission technique was proposed in which overall transmit power was minimized under user constraint [15]. A subcarrier-chunk based technique in which resource allocation problem for the downlink of Orthogonal Frequency Division Multiple Access (OFDMA) wireless systems was proposed in [16]. The scheme dramatically reduces the complexity and fairness among users’ data rates is very satisfactory despite the loss with respect to the unconstrained case where the only target is the maximization of the sum data rate. Atta-ur-Rahman et. al. in [17] proposed a Fuzzy Rule Based System (FRBS) for adaptive coding and modulation in OFDM systems where convolutional codes were used as forward error correction (FEC) codes. In [18], same authors proposed FRBS for Product codes as FEC. In both of these papers, power was kept constant while code rate and modulation was adaptive. In [19], same authors used GA and Water-filling principle in conjunction with FRBS for adaptive coding, modulation and power in OFDM systems, where GA was used to adapt the power. In this paper we proposed a Fuzzy Rule Base System (FRBS) and PSO to adapt the code rate, modulation symbol and power according to the varying channel conditions. The remainder of this paper is organized as follows. In section 2, system model is introduced. Performance of coded modulation is presented in section 3. Section 4 formulates a constrained optimization problem. In section 5 a brief introduction to FRBS is given. Section 6 contains introduction to PSO; Section 7 contains the performance comparison of the scheme, while section 8 concludes the paper. II.

SYSTEM MODEL

The system model considered is OFDM equivalent baseband model with N number of subcarriers. It is assumed that complete channel state information (CSI) is known at receiver. The frequency domain representation of system is given by; rk = h k . p k .x k + z k ; k = 1, 2,......, N (1) where rk , hk , p k , x k and z k denote received signal, channel coefficient, transmit amplitude, transmit symbol and the Gaussian noise of subcarrier k = 1, 2,......, N , respectively. The overall transmit power of the system is

Ptotal = ∑ k =1 p k N

where α k is Rayleigh distributed random variable of kth subcarrier, and the phase θ k is uniformly distributed over

[ 0, 2π ] . The proposed adaptation model is given in Fig-1.

OFDM PHY Transmitter

OFDM Channel

PHY layer Receiver

Quality of Service (QoS) Demand/ Subcarrier

Sub-channel Estimates

Feedback Channel

New Modulation Code rate Power

Link Adaptation using Fuzzy Rule Based System (FRBS) and PSO

Figure 1. Brief diagram of proposed System

III.

CODED MODULATION

In this section performance of standard modulation and codes being used in IEEE 802.11n/g/b are analyzed in terms of bit error rate (BER) and SNR. For experimentation the sequence of operations is carried out in same way as given in fig-2. Following is the detail of each component.

A. Coding Scheme The codes used in adaptive coding and modulation are non-recursive convolutional codes with code rates taken from the set C with constraint length 7. Set C is given below; C = {1/ 4,1/ 3,1/ 2, 2 / 3,3 / 4} (3) B. Modulation Scheme In this paper we have utilized Quadrature Amplitude Modulation (M-QAM) for adaptive coding and modulation, with rectangular constellation. The modulation symbols are taken from the following set. Set M is given by; M = {2,4,8,16,32,64,128} (4) C. Channel Additive White Gaussian Noise (AWGN) channel is assumed for simulations. This channel is proven to be a good representative of channel condition at OFDM subcarrier. Bit loading

FEC Encoder

QAM Modulator

and the noise distribution is complex

Gaussian with zero mean and unit variance. It is assumed that signal transmitted on the kth subcarrier is propagated over Rayleigh flat fade channel and each subcarrier faces a different amount of fading independent of each other. This can be given mathematically as; (2) hk = α k e j θ k ; k = 1, 2,......, N

AWGN Channel Bit Receiving

FEC Decoder

QAM Demodulator

Figure 2. Brief diagram of simulations

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The total number of MCPs can be given by; (5) P = CxM = {(c i , m j ); ∀c i ∈ C , ∀m j ∈ M } Then graph for each MCP is obtained and some of these graphs are depicted in the fig-3 and fig-4 according to the sequence of operations shown in fig-2.

where rk = (log 2 (M ))k R k is the bit rate of kth subcarrier which is product of code rate and bits/symbol. PT is the total transmit power and BERQoS k is target BER that depends upon a specific quality of service (QoS) request or application requirement over ith subcarrier, while N is total number of subcarriers in OFDM system. V.

FUZZY RULE BASE SYSTEM

In this section FRBS is designed for optimum selection MCP per subcarrier based upon received SNR and QoS. The steps involved in creation of FRBS are described below.

Figure 3. BER comparison of different QAM using rate 1/4 code

A. Data Acquisition From the results obtained in section-III, those codemodulation pairs that fulfill different BER demands depending upon different quality of services i.e. BERT = 10−5 ,10 −4 ,10 −3 ,10 −2 etc are obtained. This is obtained by drawing straight horizontal lines on the graphs shown in figures 2-5, on certain BER values. Then the points of intersection of these lines and the curves (representing a code and a modulation) are noted and according SNR value is noted. This information can be expressed as “for a given SNR and specific QoS which modulation code pair can be used”. B. Rule Formulation Rules for every pair are obtained by the appropriate fuzzy set used. That is by putting complete pair in input/output set and a rule generated for each pair.

Figure 4. BER comparison of different QAM using rate 1/2 code

IV. RATE OPTIMIZATION In order to maximize the data rate for the overall OFDM system, following constrained optimization problem is considered.

max RTotal =

1 N

N

∑r

k

k =1

s.t, BER k ≤ BER QoS k and N

PTotal = ∑ p k < PT k =1

176

(6)

C. Elimination of Conflicting Rule The rules having same IF part but different THEN parts are known as conflicting rules. This appears when more than one modulation code pair (MCP) are available for given specification. For instance, there is a rule whose THEN part contains three different MCP namely, [8, 1/2], [16, 2/3] and [16, 3/4]. Now [16, 3/4] is best among the rest since its throughput is 4x3/4=3 while others have 3x1/2=1.5 and 4x2/3=2.67 respectively. Similarly, sometime there could be two different pairs with same throughput like [2, 1/2] and [4, 1/4] both have same throughput that is 1x1/2=0.5, then [2, 1/2] is chosen since it exhibits less modulation/demodulation and coding/decoding cost. D. Completion of Lookup Table Since in lookup table scheme we may not have complete number of IO pairs, then those parts are filled by heuristic or expert knowledge. For example, a modulation code pair is suggested by rule for a certain SNR and QoS. Then that rule can also be used for slightly above SNR and poor QoS. For instance, [128,3/4] is suggested for 25dB SNR and BER 10−3 , then this pair can be used for 26-30dB SNR and 10−2

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BER cases as well. Since if a modulation code pair performs for lower SNR, then it can easily sustain in higher SNR situations. Similarly, if a MCP performs for a good QoS then it can sustain for poor QoS demands.

Fig-5 shows the impact on throughput for different values of SNR and QoS demand after incorporating the constraint. In this diagram a higher numbered MCPair reflects a high throughput.

E. Fuzzy Rule Base Creation Using the Lookup table in above phase, Fuzzy Rule Base is created using Fuzzy Logic Toolbox in MATLAB. Further details are given in next section. Table look-up scheme for design of this fuzzy rule base system is used. The input-output pairs for design of FRBS are of the form; (x 1s , x 2s ; y s ); s = 1, 2,3.......S (7) where x 1s represents received SNR, x 2s represents required BER (QoS) and y s represents the output MCP suggested by FRBS, so the rule format can be given as below; {IF ( x 1 is L1 and x 2 is Q7) THEN y is P2} Following is the brief description of different components of fuzzy rule based system used. Design of the FRBS is carried out in MATLAB 7.0 standard Fuzzy System Toolbox. •

Fuzzy Sets Sufficient numbers of fuzzy sets are used to cover the input output spaces. There are two input variables namely received SNR and minus log bit error rate (MLBER) that represents a QoS. The reason taking MLBER is because BER of a required QoS is given by 10−2 ,10−3 ,10−4 etc while the range of fuzzy variable should be equally spaced and quantifiable. So following operation is done first; MLBER = − log(BER )

BER = 10−q

(8) −q

MLBER = − log(10 ) = q There is one output variable for modulation code pair MCP. •

Fuzzifier Standard triangular fuzzifier is used with AND as MIN and OR as MAX. •

Rule Base Rule base contains rules against all the IO pairs. As there are thirty-one sets (L0 to L30) for first input variable named SNR and about sixteen sets (Q1 to Q16) for input variable MLBER. Hence there are 496 rules in rule base. •

Inference Engine Standard Mamdani Inference Engine (MIE) is used that will infer which input pair will be mapped on to which output point. •

De-Fuzzifier Standard Center Average Defuzzifier (CAD) is used for defuzzification.

Figure 5. Rule surface

VI.

ADAPTIVE LOADING TECHNIQUES

A. Water-filling Principle Water-filling principle has been used for multicarrier loading problems. It is stated as; “Maximize the bit rate RTotal for the entire multichannel transmission system; through an optimal sharing of the total transmit power PT between the N sub-channels, subject to the constraint that PT is maintained constant.” In contrast to our system this phenomenon can be written mathematically as, σ k2 pi + = K ;1 ≤ k ≤ N (9) 2 H (f k ) Where p k is transmit power, σ k2 is noise variance (power)

H (f k ) magnitude response at subchannel k respectively. The choice of constant K depends upon application and it is under designer control. That is, the sum of the transmit power and noise variance (power) scaled by inverse of square of channel (subchannel) magnitude response must be maintained constant for each subchannel. This can also be written as; 1 pi + = K ;1 ≤ k ≤ N (10) (CINR ) k Where 2 H (f k ) (CINR ) k = (11) σ k2 We have used the value of K from [19]. 1 N 1 K = Pavg + ∑ (12) N k =1 (CINR ) k where Pavg is the average transmit power per subcarrier. The throughput of this loading algorithm will be calculated by eq. (13), while the power vector P will be found by water-filling algorithm using eq. (10). and

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B. Particle Swarm Optimization PSO is a population based stochastic optimization technique developed by [20]. It is inspired by social behavior of bird flocking or fish schooling which involves individual learning as well as collective learning. There are some commonalities between PSO and GA. Both update the population and search for optimum with random techniques. However PSO does not have genetic operators like crossover and mutation. Compared to GA, PSO is computationally light. With few parameters to adjust and easy to implement it has much faster convergence. We have utilized soft PSO for finding the optimum power vector for all subcarriers depending upon the channel conditions and their QoS demand. The fitness block for local and global particles is given in fig6. Mathematically as; 1 N R = ∑ rk N k =1 1 N = ∑ (log 2 (M )) k R k (13) N k =1 1 N = ∑ FRBS ( p kPSO , α k ,QoS k ) N k =1 Quality of Service Vector Q

α N2

Fig-7 to Fig-10 show the comparison of PSO with Fuzzy Rule Base System (PSO-FRBS) assisted Adaptive Coding, Modulation and Power (ACMP) scheme; Water-Filling with Fuzzy Rule Base System (WF-FRBS) assisted ACMP; and simple FRBS assisted Adaptive Coding and Modulation (ACM). In this figure Quality of Service (QoS) demand per subcarrier was assumed to be 10−2 ,10−3 ,10−4 and 10−5 respectively.

Figure 7. Comparison of proposed schemes with QoS=10e-2 per subcarrier

(MCP) 2

1 N

N

∑r

i

i =1

(MCP) N

Figure 6. Fitness Block

Figure 8. Comparison of proposed schemes with QoS=10e-3 per subcarrier

According to fig-6, for a given set of channel coefficients and QoS vector, PSO will be used to find the vector that maximize the throughput. After a number of iterations the final vector is obtained as the fittest. VII. RESULTS In this section proposed scheme is compared with other schemes. Table-1 contains the simulation parameters. Table-1 Simulation Parameters Sr. 1 2

Parameter Number of Subcarriers N Fitness Function for PSO

3 4

PSO particle length and iterations Channel considered for simulation

5

Channel Coefficients range

178

10e-2,10e-3,10e-4 and 10e-5 PSO-FRBS Code rate, Modulation and power

Throughput

Transmit Power Vector (P)

α22

Quality of Service (QoS) Adaptive Criterion Parameters being adapted

(MCP) 1 Fuzzy Rule Base System (FRBS)

α

2 1

6 7 8

Value 1024 Fuzzy Rule Base System Equation (10) 1024x50 IEEE 802.11n indoor channel (WIFI) [0.1-0.4]

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while adaptive power is achieved by PSO algorithm and Water-filling principle. So by using the above schemes, system would be able to adapt code rate, modulation symbol as well as transmit power in order to achieve a certain bit error rate (QoS) and to enhance the overall data rate of the OFDM system. Simulation results show that PSO-FRBS outperforms compare to other schemes. In future other evolutionary algorithms, multiuser systems and different OFDM channel models may also be investigated. REFERENCES [1]

[2] Figure 9. Comparison of proposed schemes with QoS=10e-4 per subcarrier [3]

[4]

[5]

[6] [7]

[8] Figure 10. Comparison of proposed schemes with QoS=10e-5 per subcarrier

In fig-7 the proposed scheme was compared with WF principle based adaptive power and fixed power case as well, and the target BER=10e-2. In fig-8, 9, 10 same is carried out for target BER=10e-3, 10e-4 and 10e-5 respectively. From the above figures it can easily be deduced that PSO-FRBS assisted Adaptive coding, modulation and power scheme performs better than WF-FRBS assisted ACMP while WFFRBS assisted ACMP scheme performs better than that of FRBS assisted ACM with fixed transmit power. It is also apparent from the figures above that adaptive power adds about 1bit/s/Hz in the throughput compared the fixed power for all target bit error rates. The above simulations are carried out in MATLAB 7.0.

[9]

[10]

[11]

[12]

[13]

VIII. CONCLUSIONS In this paper adaptive resource allocation schemes are proposed and investigated for OFDM systems. First scheme is Particle Swarm Optimization and Fuzzy Rule Based System assisted Adaptive Coding, Modulation and Power scheme. Second scheme is Water-Filling and Fuzzy Rule Base System assisted Adaptive Coding, Modulation and Power scheme. In these techniques adaptive coding and modulation is obtained by the Fuzzy Rule Base System

[14]

[15]

[16]

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Guarantee “,Dept. of Electr. & Comput. Eng., Univ. of Patras, Rio, Greece 2011,pp: 377 – 379. [17] Atta-ur-Rahman, Qureshi I.M., Malik A.N.,“A Fuzzy Rule Base Assisted Adaptive Coding and Modulation Scheme for OFDM Systems”, J. Basic Appl. Sci. Res. Vol. 2(5), pp. 4843-4853, 2012. [18] Atta-ur-Rahman, Qureshi I.M. and Muzaffar M.Z. “Adaptive Coding and Modulation for OFDM Systems using Product Codes and Fuzzy Rule Base System”. International Journal of Computer Applications (IJCA), Vol. 35(4), pp.41-48, December 2011.

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[19] Atta-ur-Rahman, Qureshi I.M., Malik A.N.,“Adaptive Resource Allocation in OFDM Systems using GA and Fuzzy Rule Base System”, World Applied Sciences Journal, Vol. 18(6), pp. 836-844, 2012. [20] Eberhart, R. C. and Kennedy, J., “A new optimizer using particle swarm theory” , Proceedings of the sixth international symposium on micro machine and human science, pp. 39-43. IEEE service center, Piscataway, NJ, Nagoya, Japan, 1995.

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