Using Firefly Algorithm for Total ICI Cancellation of OFDM Communication System Deepak P. M., C.K.Ali Department of Electronics and Communication Engineering National Institute of Technology Calicut Kerala India Email:
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Abstract—Orthogonal frequency division multiplexing is an efficient transmission strategy to combat frequency selective fading and is part of many of the emerging wireless standards. Orthogonality of subcarriers is an important attribute in the performance of OFDM system. Carrier frequency offset effects orthogonality of subcarriers and the resulting interference causes severe performance degradation in OFDM. Thus, frequency synchronization is a challenging problem especially in mobile scenario. Estimation based cancellation and self cancellation schemes are the common techniques employed in combating the effect of CFO. Both these strategies achieves performance improvement at the cost of reduced data rate and the performance achieved after compensation is far from ideal scenario. In this paper OFDM system is analyzed in the presence of CFO and using the results of analysis, a blind interference cancellation technique is proposed which transforms the ICI cancellation problem into a conventional optimization problem. Firefly algorithm which is a class of high performance metaheuristic algorithm, is used to find a solution for the optimization problem. The proposed scheme is simulated using matlab and tested under various channel conditions. The simulation result shows that proposed scheme ensures interference free performance without compromising on data rate. Also, the conventional firefly algorithm is modified based on the characteristics of the optimization problem for reduced computational load and early convergence. Index Terms—OFDM, Inter carrier Interference, Carrier frequency offset, Firefly algorithm
I. I NTRODUCTION Orthogonal frequency division multiplexing (OFDM) received considerable acceptance as a transmission strategy because of its high spectral efficiency and resistance to impairments introduced by frequency selectivity of the channel. Local oscillator mismatches and doppler spread causes loss of orthogonality of subcarriers resulting in interference and performance degradation [1]. Various authors analyzed the effect of CFO in OFDM and proposed various schemes to compensate its effect. The common techniques employed for CFO compensation are self cancellation and estimation based techniques. Self-cancellation scheme make use of the slowly varying nature of ICI coefficient and reduces its effect by transmitting data on multiple subcarriers and performing joint detection at receiver [2] [3] [4] [5]. Estimation based techniques estimate the value of CFO using pilot transmission and estimated value is used for ICI compensation [6]. A firefly algorithm based technique to jointly estimate CFO and channel is proposed in [7]. An
excellent review of frequency synchronization problem and various compensation techniques involved can be found in [8]. All these techniques achieves performance improvement at the cost of reduced data rate due to redundant data transmission. Also, performance improvement achieved is limited. An alternate bandwidth efficient way of ICI cancellation is using blind cancellation schemes, which make use of the typical feature of received signal to estimate CFO and cancel its effect at receiver. A blind CFO compensator which uses the redundancy associated with cyclic prefix to estimate CFO can be found in [9]. In [10] a CFO compensator for constant modulus signaling OFDM system is proposed, which formulate the cost function based on the assumption that channel response will vary slowly over adjacent subcarriers. A more generalized version of [10], which cancels ICI by smoothing power spectrum of received signal is given in [11]. Both the schemes assume constant channel frequency response on adjacent subcarriers and performance deteriorate as channel selectivity become pronounced. Total ICI cancellation scheme in [12] uniformly quantizes the range of CFO into M discrete values and orthogonality of interference matrix is used to cancel its effect at receiver. Thus, M estimates are made on transmitted data. Optimum decision among these estimates is obtained by minimum euclidean distance criterion between actual received symbol and received symbols recreated by these estimates. Total ICI cancellation scheme can be viewed as a conventional optimization problem with euclidean distance between actual and recreated received symbols as the function to be optimized with respect to the quantized CFO values. Even though [12] is able to cancel ICI completely for lower order modulation schemes, uniformly quantizing the range without considering the nature of function to be optimized results in unnecessary calculation load as modulation order increases. Also, it doesn’t bring improvement in system performance. Thus, in this paper the ICI cancellation problem in OFDM is modeled as conventional optimization problem and firefly algorithm [13] [14] is applied to obtain optimum solution. Based on the typical nature of the objective function total ICI cancellation is used with reduced number of quantization levels to get strong initial set of fireflies and the parameter values of conventional FFA are chosen appropriately for early convergence and improved accuracy. The proposed scheme
978-1-4799-1823-2/15/$31.00 ©2015 IEEE
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where W denote AWGN in frequency domain, denote the diagonal matrix containing the dft of circulant sequence of H and S is the circulant interference matrix and is given by [15]
64 QAM 16 QAM QPSK
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Frequency domain equalization(Weq ) is carried out based on zero forcing or MMSE criterion to compensate for the channel to get an estimate of transmitted symbol as
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is simulated using matlab and is compared with total ICI cancellation scheme for QAM modulations. Simulation results validate the effectiveness of proposed scheme over its counterparts. Rest of the paper is organized as follows. Section II gives a glance of the impairment introduced by CFO on OFDM system. A brief description of the ICI cancellation scheme in [12] and the typical nature of the objective function to be minimized is given in section III. Conventional firefly algorithm is described in section IV followed by proposed modifications and ICI cancellation scheme in section V. Validation of proposed scheme through simulations is done in section VI followed by Conclusion and references. II. OFDM S YSTEM MODEL Consider an OFDM system with N subcarriers, let x=(x0 , x1 , ......, xN 1 )T denote the data symbols to be transmitted. N point IFFT operation is used to modulate data symbols onto subcarriers to get y = FNH x where FN is N × N DFT matrix whose elements are given by [F ]p,q = ej2pq/N
f or p, q = 0, 1, .......N 1
(1)
Cyclic prefix of length (Ncp ) is added to y and is transmitted through a L tap (L < Ncp ) multipath channel having impulse response h=[h0 , h1 , .........hL1 ]T . Assume that channel introduces a normalized CFO (offset f normalized with subcarrier bandwidth f0 ) on the transmitted signal then received signal after cyclic prefix removal can be written in the form r = Hy + w
(2)
where H is N × N circulant matrix describing the channel, w is additive white gaussian noise with zero mean and variance 2 and is the diagonal CFO matrix given by w = diag(ej2m/N )
f or m = 0, 1, .......N 1
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where diag(x) represents diagonal matrix with x as diagonal entries. The received signal after DFT processing can be written as R = FN r = SX + W
(4)
ˆ = Weq R = Weq SX + W X
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ˆ The decision about transmitted data is to be made using X and equation (6) represent the system model for fading channel case. Expression has uncompensated interference matrix S and will introduce errors in decoding. III. T OTAL ICI C ANCELLATION SCHEME BASED ON UNIFORM Q UANTIZATION Orthogonality of interference matrix S is utilized in canceling its effect at the receiver as ˜ = S H R = X + S H W R
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But the problem is interference matrix which depends on value of is unknown to the receiver. In order to find an estimate of , the range of is quantized into M equally spaced values so that the quantized values are given by k =k for k=0,1.....M1 where = (max - min )/M. Using each of these k values an estimate of CFO matrix can be calculated as k = diag(ej2k m/N ) f or m = 0, 1, .......N 1
(8)
Now each k is used in (5) to calculate corresponding interference matrix Sk and is substituted in (7) followed by equalization and decision making to get an estimate of data ˜ k as symbol X ˜ k = dec(Weq SkH R) f or k = 0, 1, 2, ......, M 1 X
(9)
where dec(x) denote decision about observation x. Now we have M estimates of transmitted data out of which one minimizing the function f (k ) in (10) is taken as the optimum solution. ˜ k R2 f (k ) = Sk X (10) Based on the above discussion, the ICI cancellation problem reduces to conventional single variable optimization problem with f (k ) being the objective function to be minimized with respect to k . Fig.1 shows the plot of objective function vs k for various modulations schemes at constant snr value of 12dB and actual CFO =0.15. From figure it is clear that global minima of the function occur at the actual CFO value and the spread of this minima decreases as modulation order increases. Thus, for higher modulation order, uniformly increasing the number of quantization levels as in [12] will not increase the accuracy of estimate. Also it results in unnecessary calculations. Thus firefly algorithm based optimization approach is proposed in this paper, which will converge to optimum value with high accuracy and in minimum number of iterations.
IV. F IREFLY A LGORITHM Nature inspired metaheuristic algorithms received considerable attention these days for the optimization of complex functions and firefly algorithm(FFA) is a strong candidate among them which works based on the flashing behavior of fireflies. It has been applied successfully for optimization problems in various fields and different modifications has been proposed for the same based on the characteristics of the optimization problem [16] [17] [18]. Basic rules used to construct the basic firefly algorithm are: all fireflies are unisex, which means any firefly can be attracted to any other brighter one. The second rule is brightness of a firefly is determined from the encoded objective function. The last rule is that attractiveness is directly proportional to brightness and it decreases with distance, and a firefly will move towards the brighter one, and if there is no brighter one, it will move randomly. FFA works on a population of fireflies for a number of generations. In each generation, algorithm calculate the value of the objective function with the population of fireflies. The intensity of the firefly is directly proportional to the value of the objective function with that firefly and it decreases with distance as 2 (11) I(r) = I0 er where I0 and I(r) represent the intensity of the firefly at source and distance r from the source respectively. is defined as the absorption coefficient of the media and is usually taken in the range 0.1 to 10 for practical applications. In each generation, fireflies keep moving randomly biased towards the optimum solution and the movement between fireflies is controlled by the attractiveness parameter, proportional to intensity seen by other firefly. The attractiveness between ith and j th firefly can be written as 2 (12) = 0 erij where 0 represents the source attractiveness and rij represents the d dimensional cartesian distance between fireflies i and j given as d (13) r = x x | = (x x )2 ij
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The movement of ith firefly towards brighter j th one is governed by the equation (14), in which xi and xi denote values of ith firefly in present and very next generation respectively. Second term denotes the attractive pull towards the brighter firefly j and third term corresponds to randomness in movement with as the randomization parameter. In the basic FFA algorithm 0 =1, [0, 1] and i is a vector of random numbers drawn from gaussian or uniform distribution. 2
xi = xi + 0 erij (xj xi ) + i
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The appropriate selection of parameters will determine the strength of the attractiveness and randomness in the movement of firefly and is dependent on the nature of objective function.
V. P ROPOSED SCHEME A. Modified Firefly Algorithm In this section the conventional FFA described in section IV is slightly modified based on the characteristics of the function to be optimized. As inferred from Fig.1, the global minima of the objective function differ widely from the local minima and thus initial population of fireflies is chosen uniformly within the range rather than random selection. Also, the initial population size is chosen such that a good estimate of the location of the global minima can be obtained and a good set of fireflies can be generated for further generations. After first generation let p denote the optimum solution, then the range for further iterations is modified as range = [p 1/M, p + 1/M ]
(15)
where M denote the size of initial population. This step assumes that the optimum solution lies in the initial population size (M) neighborhood of p so that newly generated set of fireflies (pop) refine our search and unwanted calculations are eliminated. Thus, the value of M must be wisely chosen depending on the spread of global minima. For example in Fig.1 global minima corresponding to 64-QAM has less spread than 16-QAM and hence the value of M for 64-QAM system must be chosen on the higher side compared to 16-QAM case in order to increase the reliability of the above assumption. Instead of defining constant source attractiveness for all the fireflies, it is varied depending on the relative intensity of the firefly or relative magnitude of objective function [18]. ie. ith firefly will move towards a brighter firefly j with source attractiveness defined as 0j = f (j )/f (i )
(16)
As FFA proceeds through generations the accuracy of the estimate keep on increasing. Thus, the randomization parameter in equation (14) is tuned as per equation (17) so that the randomness in selection of fireflies keep decreasing with generation [17]. t = 1 t f or 0 < < 1
(17)
where p in general denote values of randomization parameter for pth generation and denoting the cooling factor, which determines the rate of decrease of the randomization parameter. B. Total ICI cancellation with Modified FFA The initial population size is appropriately chosen as described in previous section and the range of CFO is quantized to obtain initial population of fireflies. The value of objective function is evaluated at these firefly locations and the best one is chosen. Now the range of FFA is modified as in equation(15) and modified FFA is applied in the newly defined range to obtain the optimum value of k . The value of ˜ k corresponding to optimum value of k is chosen as the X demodulated symbol.
Number of Subcarriers (N) Channel Modulation scheme Equalization Cyclic prefix length CFO range population size (pop) 1 i No. of iterations
256 AWGN and Rayleigh QAM MMSE 20 -0.5 to 0.5 5 0.1 0.95 rand-1/2 1 > 103
C. Complexity analysis A brief discussion on the computational complexity of the proposed scheme is done in this section. The number of objective function evaluations required to reach final estimate of can be taken as the measure of computational load. The total number of objective function evaluations for total ici cancellation scheme is equal to the number of quantization levels M whereas for proposed scheme it is M + pop × maxgen. Just like total ICI cancellation scheme with uniform quantization, here also computational complexity increases with values of population size and maximum generation. Even though large values for pop and maxgen increases accuracy of CFO estimate, it is obvious from above discussion that complexity of the system grows linearly with these parameters. Hence, appropriate selection FFA parameters results in ICI free performance with moderate computational load.
compared to total ICI cancellation scheme. Figure also shows MSE in estimating using conventional FFA and is clear from figure that lack of modifications especially initialization step causes performance degradation in case of conventional FFA, thus validating the effectiveness of the proposed modifications. The variation of mean square estimation error with SNR for 64 QAM OFDM system is compared in Fig.3. Value of M is chosen as 30 for total ICI cancellation scheme whereas M=15, pop=5 and maxgen=3 for modified FFA to make total number of objective function evaluations same. Even though performance of both the schemes coincide for smaller SNR values, modified FFA outperforms total ICI cancellation scheme as SNR increases. Figure also shows the performance of proposed scheme with M=10 pop=5 and maxgen=4 as FFA parameters. As mentioned in previous section inappropriate selection of initial population size resulted in performance degradation of the proposed scheme. 2
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OFDM system with proposed FFA based ICI cancellation scheme is simulated using MATLAB and performance is compared with the total ICI cancellation scheme in [12]. The channel model used for simulations is the vehicular A outdoor channel which has six Rayleigh fading taps at delays of 0, 310, 710, 1090, 1730 and 2510 ns, with relative powers of 0 dB, -1 dB, -9 dB, -10 dB, -15 dB and -20 dB, respectively. As mentioned in previous section, choice of initial population size(M) depends on the spread of the global minima and is taken value M=15 for 64-QAM OFDM whereas M=10 for 16QAM. Other parameters of simulation are tabulated in Table I. The simplest way to see the effectiveness of proposed scheme is to apply modified FFA based ICI cancellation scheme to estimate the value of CFO from received OFDM signal. The plot of mean square estimation error with computational complexity for 64 QAM OFDM system in random CFO case is shown in Fig.2. In figure initial quantization level and population size are kept constant at 15 and 5 respectively and maxgen is varied. It can be inferred from figure that accuracy of the estimate increases with increase in computational load initially and it stabilizes thereafter. Also, for a particular estimation error computational load is minimum for modified FFA scheme, thus ensuring early convergence to actual CFO value
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BER performance of OFDM in AWGN channel with proposed ICI compensation schemes is shown in Fig.4. In figure dotted line corresponds to 16 QAM and solid ones to 64 QAM. The value of are taken uniformly in the interval [-0.5, 0.5] and performance is compared with total ICI cancellation scheme with quantization levels M=30. From figure it is clear that even with M=30 total ICI cancellation scheme is not able to estimate accurately and error in estimation become significant as modulation order become higher, causing deviation of BER plot from ideal one. At the same time modified FFA
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uniform quantization based total ICI cancellation scheme in various scenarios. From simulation results it is seen that uniform quantization scheme involves unnecessary calculations as we move to higher modulation order and the accuracy of the estimate is not enought to cancel ICI completely. At the same time proposed FFA based blind estimation scheme is able to estimate CFO with high accuracy and is able to cancel ICI completely for the same computational load as that of total ICI cancellation scheme.
Proposed scheme with pop=5 maxgen=3 Total ICI cancellation M=30 64 QAM without cfo Proposed scheme pop=5 maxgen=4 Total ICI cancellation M=30 16 QAM without cfo
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Proposed scheme random CFO Total ICI cancellation M=20 random CFO Total ICI cancellation M=10 random CFO Proposed scheme constant CFO Total ICI cancellation M=20 constant CFO Without CFO 5
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scheme with same computational load estimates with more accuracy and is able to cancel ICI more effectively. The effectiveness of the proposed scheme in fading channel for 64 QAM OFDM is shown in Fig.5. In the simulations we assume presence of channel information at the receiver, which is a common assumption made in all the ICI cancellation schemes. BER vs SNR plot with random between transmitter and receiver is plotted in solid lines whereas with constant (=0.125) is shown in dotted lines. Authors in [12] show that M=10 is sufficient value for their scheme in OFDM with QPSK modulation. From Fig.5 it is clear that with M=10 performance is far from ideal as we move to higher order modulation. At the same time, modified FFA scheme is able to compensate ICI completely and achieves ICI free performance, also the performance is superior compared to total ICI cancellation scheme with same computational complexity. VII. C ONCLUSION Frequency synchronization and ICI cancellation in OFDM is an important issue in communication system especially in highly mobile scenario. In this paper OFDM system is analyzed in the presence of CFO and conventional ICI cancellation problem is modeled as an optimization problem. Firefly algorithm, which is powerful class of metaheuristics algorithm is used to find solution for the optimization problem. Also the conventional FFA is modified based on the characteristics typical optimization problem for reduced computational load and easy convergence. The proposed scheme is compared with
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