# Introduction n satellite communication systems, the receiver receives extremely weak signals from the satellite. To enhance reception and radiation patterns dynamically in response to the signal environment, such technologies depend on adaptive array signal processing. An adaptive antenna is an array of antenna elements followed by a sophisticated signal processor that can adjust or adapt its own radiation pattern in order to focus the reception of the antenna array in a certain direction and rejects the signal from other direction. The necessity to remove the effect of the undesired signal to the desired one motivates advances in communication receiver antenna and hence synthesizing methods [1][2][3][4]. An adaptive antenna array combines the outputs of antenna elements. The directional gain of the antenna is controlled by adjusting phase or amplitude or both at each individual element. The weighted signals are summed and the output is fed to a controller. These weights are computed adaptively to adapt to the changes in the signal environment. Different adaptive beamforming algorithms are employed to minimize the error between the desired signal and the array output that adjusts the weights to satisfy an optimization criterion [5][6][7][8][9][10][11]. The capability of adaptive antenna array lies in forming higher gain in the user directions and lower gain in the interferer directions. There are different adaptive beamforming algorithms studied in literature which are used in the adaptive antenna array [12][13][14][15][16][17][18][19][20][21][22][23][24]. Beamformers based upon statistically optimum blind and non-blind adaptive beamforming are analyzed and compared on the basis of beamforming capability and rate of convergence. It is observed that the convergence rate of Least Mean Square (LMS) is slowest where as Constant CGM is the fastest among all. SMI is found to have more computational complexity. Recursive Least Square (RLS) is found to have higher side lobe level (SLL) and null depths as compared to CGM [16]. It was observed that the conventional Adaptive Beamforming (ABF) technique like Minimum Variance Distortionless Response (MVDR) improves the signal-to-interferenceplus-noise ratio (SINR) but unable to reduce the SLL [17]. Hence to improve the SINR with reduced SLL, many optimization techniques have been used in ABF application. Adaptive Mutated Boolean Particle Swarm Optimization (AMBPSO) technique takes the uncorrelated desired and interferer signal directions and succeed in providing good SINR value with lower SLL as compared to conventional MVDR [18]. Adaptive Dispersion Invasive Weed Optimization (ADIWO) shows improvement in steering ability regarding the main lobe and the nulls, faster as compared to PSO and achieves better SLL than the PSO and MVDR [19]. Hybrid Particle Swarm Optimization with Gravitational Search Algorithm (Hybrid PSOGSA) shows its ability for optimization in beam-forming for a larger number of user signals and speedy computation using parallel GSA as compared to sequential stand alone algorithms but cannot maximise the gain along the user direction [20][21]. Mementic algorithm shows optimal radiation pattern design to maximise the signal to interference ratio (SIR) by perturbing the phase-position [22]. But, for the case of adaptive antennas, the position of the antenna elements cannot be changed so it should be kept fixed. As the required phase controls are available at no extra cost. Hence only phase weights are considered for optimal radiation pattern which shows good null depth along the undesired direction but the array factor (AF) gain along the main lobe is not satisfactory [23][24] . In all of the above adaptive beamforming techniques proposed so far try to minimize the error between the desired and actual signal and maximize the signal to interference ratio (SIR). But in severe interference environment when the actual signal is weak, the effect of SNR on the radiation pattern needs to be considered. The present study analyses different adaptive techniques such as non-blind LMS, blind CMA and evolutionary PSO. The performance of beamforming algorithms are studied through MATLAB simulation by varying SNR parameter for different desired and interference direction. Different weights are obtained using this beamforming algorithm to optimize the radiation pattern. The parameters for comparison are the main beam and null placement for different angles of user and interferer. The mean SLL and directivity are also studied. The rest of the paper is arranged as follows: Section II describes the mathematical model of signal, Section III formulates the adaptive beamforming problem, Section IV, V and VI describes adaptive beamforming using PSO, LMS and CMA, Section VII compares the results and Section V concludes the whole study. # II. # Signal Model Consider a Uniform Linear Array (ULA) with N elements as shown in Figure 1. Let S(k) is the S X1 signal vector from the S th source with DOA equal to ? S. [ ] ) ( ... ... ) ( ) ( ) ( 2 1 k S k S k S k S s = (1) We define the input signals as X 1 (k), X 2 (k),.........X N (k). As they reach the antenna elements, the N X 1 signal vector X(k) can be written as ? = = s s s s SV k S k X 1 ) ( * ) ( ) ( ? (2) Where SV (?) is the steering vector or array response vector of N X 1 which controls the direction of antenna beam. T N j j j SV ))] sin( ) 1 ( exp( .... .... )) sin( 2 exp( )) sin( exp( 1 [ ) ( ? ? ? ? ? ? ? ? ? ? = (3) Now if the signal 1,2??S consist of U number of desired user arriving from ? 1 ,? 2 ,? 3 ,??? U , I number of interferences arriving from ? 1 ,? 2 ,? 3 ,??? I with variance ? i 2 and noise with variance ? n 2 , then the input signal consist of user signal S u , interferer signal S i and noise N. The received signal can be written as ) ( ) ( * ) ( ) ( * ) ( ) ( 1 1 k N SV k S SV k S k X I i i i U s u u + + = ? ? = = ? ? (4) # Global )) sin( ) 1 ( exp( ..... )) sin( exp( 1 ) ( u u u N j j SV ? ? ? ? ? ? ? ? = is the steering vector of the desired signal along the user and [ ] )) sin( ) 1 ( exp( ..... )) sin( exp( 1 ) ( i i i N j j SV ? ? ? ? ? ? ? ? = is the steering vector along the interferer direction. # III. # Adaptive Beamforming Problem Formulations An ULA will receive the incoming signals which will be multiplied by the weights of antenna elements which are then summed to get the output in the form of received signal. The received signal will be graphical represented in the form of the radiation properties as a function of space coordinates known as radiation pattern. The radiation pattern of the linear array for far field is represented in terms of array factor (AF) by [15], n N n w k X AF * ) ( 1 ? = = (5) where N= number of elements, In adaptive antenna beamforming, the radiation pattern of ULA is controlled through various adaptive algorithms. Adaptive algorithm dynamically optimizes the radiation pattern according to the changing electromagnetic environment. The output or received signal is given to the adaptive algorithm where it checks the output radiation pattern with the desired radiation pattern. If the received actual radiation pattern does not meet the user demands, then adaptive algorithm will try to adjust the weights of the antenna array such that the actual and desired radiation pattern remains same. The antenna array pattern is optimized to have maximum possible gain in the direction of the desired signal and nulls in the direction of the interferers. Figure 2 shows the block diagram of an adaptive antenna array. Particle Swarm Optimization (PSO) was developed by Eberhart and Shi [25]. It is used as adaptive algorithm to search the optimized adaptive antenna radiation pattern. This is done using the algorithm summarized in the Table 1 [26]. In every iteration, PSO algorithm will try to increase the AF gain of the desired user and decrease the AF gain of the interfering user as compared of the previous iteration. The converged value of weights produces an optimized adaptive antenna radiation pattern. The amplitudes excitations are kept constant whereas the phase excitations are selected as the optimization parameters. Hence the AF can be written as Step-1: Initialize population, number of iterations, tuning parameters ) ( Step-2: Step-3: Evaluate the fitness function for each particle b n (i). Compute FF (i, k) as per the equation (7). Step-4: Compute pbest(i, k) = FF(i, k) and gbest(i) = max (pbest (i, k)) with its location pbest (k) and gbest. Step-5: Update velocity v (i+1, k) and position b n (i+1, k) using ) ( )) , ( ) ( ( 2 ) ( )) , ( ) ( ( 1 ) , ( ) , 1 ( i u k i b ib g i u k i b ik b p k i v w k i v n n n n ? + ? + * = + ? ? ) , 1 ( ) , ( ) , 1 ( k i v k i b k i b n n + + = + Step-6: Update fitness function FF(i+1, k). Step-7: If FF(i+1, k) > FF(i, k), then pbest(i+1, k)=FF(i+1, k). Step-8: Update gbest (i+1, k) = max (pbest(i+1,k)). Step-9: If ii max , then stop, otherwise go to step (3) to update output, error and weight. VI. # Adaptive Beamforming Using Constant Modulus Algorithm The constant modulus algorithm (CMA) was first proposed by Godward. It is used for blind equalization of signals that have a constant modulus where reference signals are not available. The algorithm contains three major steps in each recursion: the computation of the output signal with the current set of weights, the generation of the error, and the adjustment of the weights with the new error information. The following Table 3 summarize the above three steps [16]. Step-( 1): Initialize number of iteration i max and the value of µ. Step-( 2): Initialize weight W CMA , error E CMA and output y CMA as 0. Step-( 3 ): Compute Output, y CMA (i, k)= W CMA (i, k) H x(k). Step-(4): Compute Error, E CMA (i, k) = y CMA (i, k)/ |y CMA (i, k)|-y CMA (i, k). Step- (5) : Compute Weight, W CMA (i+1, k) =W CMA (i, k)+µx(k)E CMA *(i, k) Step-( 6): If i>i max , then stop, otherwise go to step (3) to update output, error and weight. VII. # Numerical Simulation Results A 16 element ULA with ?/2 interelement spacing is taken. PSO, LMS and CMA were applied on a 16-element ULA. Three algorithms were compared on the basis of the SNR. In order to compare the performance, the simulations are done using MATLAB. All the algorithms were executed for 200 iterations and the termination criterion is set for the number of iterations. For PSO, the population size is assumed as 100 and tuning parameter 1 ? and 2 ? are set to 2.0. Phase excitation b n is chosen as the design variable in the PSO with lower and upper limit taken in the range of [-2?, 2?] with initial values of position and velocities are taken as random. For LMS and CMA, µ is taken as 0.001 and the initial weight and error are set to 0. Based upon the aims to maximize the AF gain of the desired user and minimize the AF gain of the interfering user. PSO will try to maximize the value of the AF gain along User1 while minimize the AF gain along interferer1 and interferer2. LMS will recursively computes and updates the weight vector between the output signal and the desired signal. CMA will update the information based upon the new error information. To validate the study, two different scenarios are studied with different position of interferer. In scenario#1, the ULA receives a desired signal arriving from angle 1 towards 1 i ? and 2 i ? . The AF gain along the main lobe is 0 dB whereas the AF gain towards the null is -20 dB to -50 dB as shown in Table 4. The maximum SLL is -15dB to -17dB with directivity of 7 dB as shown in Figure 3 and Figure 4. LMS algorithm also produces main lobe gain of 0 dB along the 1 s ? direction and null gain of -33 dB to -66dB for SNR=30dB to SNR=-10dB as shown in Table 4. As SNR reduces more than -10 dB, LMS fail to point the main beam and null along the user and the interferer direction in both the scenarios. CMA algorithm works well for SNR=30 dB to SNR=10dB. As SNR starts deteriorating CMA does not produce main beam along the user and fails to point lower gain along the interferer as shown in Table 4. In both the scenarios, LMS and CMA gives reduced SLL. The comparative Table 5 for both the scenario shows that PSO is better as compared to LMS and CMA for every value of SNR. LMS and CMA fail to adapt for lower value of SNR. However LMS and CMA shows better SLL as compared to PSO. Table 6 gives the optimized excitation weights for PSO, LMS and CMA for SNR=30dB. (W PSO )#1 (W PSO )#2 (W LMS )#1 (W LMS )#2 (W CMA )#1 (W CMA )#21 1.00 + 0.00i 1.00 + 0.00i 1.00 + 0.00i 1.00 + 0.00i 1.00 + 0.00i 1.00 + 0.00i 2 0.84 -0.54i -0.28 + 0.95i 0.99 + 0.00i 0.99 + 0.00i 1.00 -0.02i 0.99 + 0.00i 3 0.59 + 0.80i 0.88 -0.46i 0.99 + 0.00i 0.98 + 0.00i 0.98 -0.00i 0.98 + 0.01i 4 0.99 + 0.02i -0.09 + 0.995i 0.99 + 0.00i 0.99 + 0.00i 0.97 + 0.00i 0.99 + 0.01i 5 0.53 -0.84 0.66 + 0.750i 0.99 + 0.00i 0.99 + 0.01i 0.99 + 0.02i 0.99 + 0.01i 6 -0.04 -0.99i -0.72 + 0.688i 0.99 + 0.00i 0.98 + 0.00i 0.99 -0.00i 0.99 + 0.01i 7 0.66 -0.74i 0.63 + 0.770i 1.00 + 0.00i 0.99 + 0.00i 0.97 -0.00i 0.99 -0.00i 8 0.54 + 0.83i -0.99 + 0.032i 1.00 + 0.00i 0.99 + 0.00i 0.98 -0.00i 0.98 + 0.01i 9 -0.29 -0.95i 0.29 -0.954i 0.99 + 0.00i 0.98 + 0.00i 0.98 + 0.00i 0.98 + 0.01i 10 -0.92 -0.37i -0.40 + 0.912i 0.99+ 0.00i 0.99 + 0.00i 0.98 -0.01i 1.00 + 0.00i 11 -0.14 + 0.98i 0.82 -0.571i 0.99 + 0.00i 0.99 + 0.00i 0.99 -0.01i 1.00 + 0.00i 12 -0.79 + 0.60i 0.03 -0.999i 0.99 + 0.00i 0.99 + 0.00i 0.98 + 0.00i 0.99 + 0.00i 13 0.17 + 0.98i -0.34 + 0.939i 0.99 -0.00i 0.99 -0.00i 0.99 + 0.01i 0.99-0.00i 14 -0.62 -0.78i 0.44 -0.896i 0.99 + 0.00i 0.99 + 0.00i 0.99 -0.00i 0.98 + 0.00i 15 0.82 -0.56i -0.44 + 0.896i -0.99 + 0.00i 0.99 + 0.00i 0.97 -0.01i 0.99 + 0.00i 16 0.21 -0.97i 0.90 -0.431i 1.00 + 0.00i 0.98 + 0.00i 0.97 + 0.00i 0.99 + 0.00i # Conclusions In this paper, ABF based on PSO, LMS and CMA method have been simulated for 16 elements ULA. A performance analysis and validation is done by changing the values of SNR for two different positions of interferers. The main lobe gain and null depth are calculated to validity this approach. It is shown that the PSO-based beamformer provides accurate 0dB main beam gain and null depth of -20dB to -50dB with better SLL for each case of SNR. However, CMA fail to provide main beam and null placement for SNR< 0dB and LMS for SNR< -20dB. Therefore, the PSO method seems to be simple and appropriate in ABF applications based on the fitness function. ABF using PSO shows mean side lobe level (SLL) of -15 dB to -17 dB with a directivity of 7dB for each case of SNR. LMS and CMA show better SLL than PSO. It can be further studied with complex fitness functions in order to improve the value of SLL. 1![Figure 1: Uniform Linear Array Let S narrowband signals are received at ULA with different direction of arrivals (DOAs) ? 1 , ? 2 ,?..,? S.Let S(k) is the S X1 signal vector from the S th source with DOA equal to ? S.](image-2.png "Figure 1 :") ![at element n, n a = amplitude weight at element n, n b =phase shift weight at element n.](image-3.png "") 1 3 4scenario#2 (*MB-Main Beam, * NP-Null Position)SNRScenarioPSOLMSCMA(dB)G_S1G_I1G_I2G_S1G_I1G_I2G_S1G_I1G_I230#10-30-230-33-380-32-37#20-32-420-48-400-40-4720#10-25-530-32-500-37-43#20-22-210-43-360-37-3410#10-34-450-48-360-30-28#20-44-300-35-360-39-260#10-32-370-34-40*MB and *NP are not exact#20-38-450-39-44*NP are not exact-10#10-34-350-37-39*MB and *NP are not exact#20-51-480-66-38*MB and *NP are not exact-20#10-41-42*MB and *NP are not exact*MB and *NP are not exact#20-50-34*MB and *NP are not exact*MB and *NP are not exact-30#10-35-35*MB and *NP are not exact*MB and *NP are not exact#20-36-28*MB and *NP are not exact*MB and *NP are not exact 5SNRPSOScenario#1 LMSCMAPSOScenario#2 LMSCMA30*C*C*C*C*C*C20*C*C*C*C*C*C10*C*C*C*C*C*C0*C*C*NC*C*C*NC-10*C*C*NC*C*C*NC-20*CNC*NC*C*NC*NC-30*CNC*NC*C*NC*NC 6 Effect of Signal to Noise Ratio on Adaptive Beamforming Techniques © 2017 Global Journals Inc. (US) © 2017 Global Journals Inc. (US) * C ABalanis Antenna Theory: Analysis and Design. 3 rd Edition New York John Willy & Sons Inc 2005 * Smart antenna design for wireless communication using adaptive beam-forming approach SDas TENCON 2008 -2008 IEEE Region 10 * Conference 5 1 19-21 Nov. 2008 * Adaptive antenna arrays for satellite personal communication systems LianKeng Jin Virginia polytechnic institute and state university Blacksburg January 27, 1997 Master of science thesis * Multifunctional phased array antenna design for satellite tracking ACanabal RPJedicka AGPino Elsveier Journal 57 December 2005 * Optimizing adaptive linear array antenna pattern under intensive interference environment using Genetic Algorithm WJiancheng QHui CJianming fourth International Conference on Intelligent Computation Technology and Automation 2011 * Linear Antenna Array Synthesis to Reduce the Interference in the Side Lobe using Continuous Genetic Algorithm SBanerjee VVDwivedi IEEE Fifth International Conference on Advances in Computing and Communications 2015 * Adaptive Beamforming Algorithm for Interference Suppression in GNSS Receivers ShaheraHossain MohammadTariqulIslam SeiichiSerikawa Adaptive Beamforming Algorithms for Smart Antenna Systems" International Conference on Control Coex Korea8Seoul LianZhao Hongwei FengBaowang Juan 2008. Oct. 14-17. 2008. Oct 2011 3 Automation and Systems * Adaptive antenna systems BWidrow Proc. IEEE IEEE 12 Dec., 1967 55 * Adaptive Arrays, tech. rep SPApplebaum Reprinted in IEEE Transactions on Antennas and Propagation 1965. 1976 Syracuse University Research Corporation * Robust Adaptive Beamforming for Steering Vector Uncertainties Based on Equivalent DOAs Method YJGu ZGShi KSChen YLi Progress In Electromagnetics Research 2008 * Adaptive antenna array for Satellite Communication Systems SangeetaKamboj Dr. RatnaDahiya Proceedings of the International Multi Conference of Engineers and Computer Scientists the International Multi Conference of Engineers and Computer ScientistsHong Kong 2008. 2008, 19-21 March 2008 * An LMS Adaptive Antenna Array SBanerjee VVDwivedi International Journal of Advanced Research in Engineering and Technology 4 6 Sep-Oct. 2013 * Review of adaptive linear antenna array pattern optimization SBanerjee VVDwivedi International Journal of Electronics and Communication Engineering (IJECE) 2 1 2013 * Linear array synthesis using Schelkunoff polynomial method and particle swarm optimization SBanerjee VVDwivedi IEEE International Conference on Advances in Computer Engineering and Applications ICACEA 2015 * Performance Analysis of Adaptive Beamforming Algorithms for Smart Antennas PrernaSaxena AGKothari International Conference on Future Information Engineering, IERI Procedia 10 2014 * Robust MVDR beamformer for nulling level control via multiparametric quadratic programming FLiu JWang CYSun RDu Progress In Electromagnetics Research C 20 2011 * A Novel Adaptive Beamforming Technique Applied on Linear Antenna Arrays using Adaptive Mutated Boolean PSO ZDZaharis TVYioultsis Progress In Electromagnetics Research 117 2011 * Improved Antenna Array Adaptive Beam-Forming with Low Side Lobe Level using A Novel Adaptive Invasive Weed Optimization Method ZDZaharis CSkeberis TDXenos Progress In Electromagnetics Research 124 2012 * Performance Enhancement for Adaptive Beam-Forming Application Based Hybrid PSOGSA Algorithm AMagdy OMEl-Ghandour HF AHamed 10.4236/%20jemaa.2015.74014 Journal of Electromagnetic Analysis and Applications 7 2015 * Adaptive Beam-forming Optimization Based Hybrid PSOGSA Algorithm for Smart Antennas Systems AhmedMagdy MOsama El-Ghandour FAHesham Hamed Progress In Electromagnetics Research Symposium Proceedings Prague, Czech Republic July 6-9, 2015 * Memetic Algorithms for Optimizing Adaptive Linear Array Patterns By Phase-Position Perturbations HsingChao Wen-JyeHsu Shyr Circuits Systems Signal Processing 24 4 2005 * Adaptive radiation pattern optimization for antenna arrays by phase perturbations using particle swarm optimization VirgilioZuniga AhmetTErdogan TughrulArslan IEEE NASA/ESA Conference on Adaptive Hardware and Systems (AHS) June 2010 * Interference Suppression in Multiple Beams Adaptive Linear Array using Genetic Algorithm ARao NV S NSarma Antenna Test and Measurement Society 2011 * Particle swarm optimization: developments, applications and resources, evolutionary computation RCEberhart YLu Proceedings of the 2001 Congress on Evolutionary Computation the 2001 Congress on Evolutionary Computation 2001 1 * R KArora Optimization: Algorithms and Applications, 1 st Edition New York CRC Press 2015