Beamforming Algorithm for Adaptive or Smart Antenna

Beamforming algorithmic program for Adaptive or Smart overture*Satgur Singh, **Er. Mandeep kaurAbstractThe Demand of unsettled Communication systems is increasing day by day. New concepts and modes be necessary which required the need for new Technologies to satisfy the demand of this world of network. Smart Antenna system is one of those, which reduces the co-channel interference and maximize the exploiter capacity of conference system, By shaping and locating the charge of the antenna on the mobile or the target thus decreasing interference to other users. The Main purpose of smart antenna system is the selection of smart algorithmic ruleic ruleic rules for adaptive array. By exploitation beam forming algorithms the encumbrance down of antenna arrays can be adjusted to form certain amount of adaptive beam to track corresponding users automatically and to diminish interference arising from other users by introducing nulls in their directions. Thus interferences can be suppressed and the desired signals can be extracted. Many algorithms are introduced due to advancement in technology. Every algorithms has different convergence characteristics and complexity of algorithm, according to our need we use particular algorithm in discourse system.Keywords Smart Antenna, LMS (Least mean square), RLS (Recursive least square), NLMS (Normalized Least Mean Square), Sample Matrix Inversion (SMI), Constant Modulus Algorithm (CMA), VSSNLMS (Variable step sizing NLMS).I. INTRODUCTIONConventional base station antennas in exist communication systems are either Omni directional or sectorised. There is waste of resources since the majority of transmitted signal place radiates in directions other than the desired user directions and signal power radiated through and through the Cell area will be interference by any other user than the desired one. Signal power radiated throughout the cell area will increase interference and reduce SNR. Although sector antenna de creases the interference by dividing entire cell into sector, But some(a)(a) levels of interface still exist.To overcome the above paradox of the communication system the Smart antenna introduced. Smart Antenna system combines an antenna array with a digital signal-processing capability to transmit and receive in an adaptive manner. Such a configuration technically enhances the capacity of a wireless link through a combination of diversity gain, array gain and interference reduction. Increased capacity translates to higher info rates for a given number of users or more users for a given data rate per user.In other manner, the system which can automatically change the directionality of its radiation patterns in rejoinder to its signal environment. By this manner, increase the performance characteristics (such as capacity) of a wireless system. All elements of theFig 1 Block Diagram of Smart Antenna systemadaptive antenna array have to be combined in order to adapt to the current channel and user. A Smart antenna is consequently a phased or adaptive array that adjusts to the environment that is, for the adaptive array, the beam pattern changes as the desired user and the interference move and for the phased array the beam is steered or different beams is selected as the desired user moves. This weight adaptation is the smart part of the smart antenna system. It is possible to investigate a entire range of beam forming algorithms without the need to modify the system hardware for every algorithm. For this, now we are focusing on improving the performance of the beam forming algorithms rather than on designing new hardware, which is very expensive and age consumption. There are many algorithms for beamforming concept ,Every algorithm has its own merits and demerits ,according to our need we use that algorithm which satisfies our need,which are given below-II) BEAMFORMING TECHNIQUES-A) Least Mean Square AlgorithmThis algorithm was first developed by Widrow and Hoff in 1960. Shahera HOSSAIN et al.(2008) proposed that LMS is a gradient establish technique where in a quadratic performance surface is assumed. The performance surface that is cost function can be established by determination the Mean Square Error (MSE). The cost function is a quadratic function of the weight sender w. The minimum of the performance surface is reached when the MSE tends to its minimum survey this is made possible by finding out the gradient of MSE with respect to weight vectors equating it to zero. The Weights of adaptive antenna are adjusted in the disconfirming direction of the gradient to minimize the error. In LMS, the weights are updated using,w(k+1) = w(k)+ e*(k)x(k)whereas e(k) =d(k) wH (k)x(k)=Step size that determines the stronghold of convergence of LMS algorithm.The weights here will be computed using LMS algorithm based on Minimum Squared Error (MSE).y(n)=wH (n)x(n)e(n) =d(n) y(n)w (k+1) = w(k)+ e*(k)x(k)step size is a positive real-v alued constant which controls the size of the incremental subject field applied to the weight vector as we proceed from one iteration cycle to the next.The performance of the algorithm depends on the step size parameter, which controls the convergence speed. The LMS algorithm is initiated with an arbitrary value W(0) for the weight vector at n= 1, 6, 23, 25.For the weight vector is seen to converge and stay stable for0maxWhereas max is the maximum eigen value of the hyaloplasm R.The Response of the LMS algorithm is determined by three principal factors step-size parameter, number of weights, and Eigen value of the correlation matrix of the input data vector. The LMS Algorithm has many drawbacks which are solved by other algorithm.B) Sample Matrix Inversion (SMI) AlgorithmT.B. LAVATE et al.(2010) 5proposed that LMS algorithm is slow in convergence not suitable for mobile communication this drawback of LMS is eliminated by sample matrix inversion (SMI) mode. The sample matrix i s a clip average estimate of the array co-relation matrix using K time samples. If the random process is ergodic in the co-relation the time average estimate will equal the actual co-relation matrix .If we use a K-length block of data we define the matrix Xk(k) as the kth block of x vectors ranging over K data snapshots, the time average estimate of array co-relation matrix is,R=XK(k) XKH (k)/KAnd the time average estimate of the co-relation vector is,r= d*(k) XK(k)/KThe SMI weights for kth block of length K asWSMI = R-1rWSMI = XK(k) XKH H (k)-1 d*(k) XK(k)From equation (4) it is seen that the weights of the antenna array will be updated for each incoming block of data.C) NLMS (Normalized Least Mean Square) AlgoritmShahera HOSSAIN et al.(2008)4 proposed ,the Normalized least-mean-square (NLMS) algorithm, which is also known as the projection algorithm, is a utilizable method for adapting the coefficients of a finite-impulse response (FIR) filter for a number of signal processin g and control applications. It can persist over a wide range of step-sizes. Theoretically, LMS method is the most basic method for calculating the weight vectors. However, in practice, an improved LMS method, the Normalized-LMS (NLMS) is apply to attain stable calculation and faster convergence. The NLMS algorithm can be formulated as a natural modification of the LMS algorithm based on stochastic gradient algorithmGradient noise amplification problem occurs in the standard form of LMS algorithm. This is be attempt the product vector xne*nin Equation (11) at iteration, n applied to the weight vector wnis directly proportional to the input vector xn. This can be solved by normalized the product vector at iterationn 1 with the square Euclidean norm of the input vector xnat iteration n. The final weight vector can be updated by,W(n+1)= w(n)+ /x(n)2.x(n) e*(n)Where the NLMS algorithm reduces the step size to make the full-size changes in the update weight vectors.This prevents the u pdate weight vectors from move and makes the algorithm more stable and faster converging than when a fixed step size is used. Equation ( ) represents the normalized version of LMS (NLMS), because step size is divided by the norm of the input signal to avoid gradient noise amplification due to x(n) Sometimes x(k) which is the Input signal becomes very small which may cause W(K + 1) to be unbounded. However, to avoid this situation which is a constant value is added to the denominator which made the NLMS algorithm be described asW(n+1)= w(n)+ / + x(n)2.x(n) e*(n)we can conclude that NLMS has a better performance than LMS algorithm.D) Constant Modulus AlgorithmSusmita Das 8proposed that the configuration of CMA adaptive beamforming is the same as that of the Sample Matrix Inversion system except that it requires no reference signal. It is a gradient-based algorithm that works on the theory that the existence of interference causes changes in the amplitude of the transmitted signal, which otherwise has a constant gasbag (modulus). The minimum shift key (MSK) signal, for example,is a signal that has the property of a constant modulus .The weight is updated by the equationW(n+1)=W(n)+ x(n)e(n)*where is the step-size parameter(n) is the input vector,ande(n)=y(n)(R2-Y(n)2 where R2=E.X(n)4/X(n)2 .D) RLS ALGORITHMIn Recursive least square (RLS) algorithm, the weights are updated by the following equation.W(n)=W(n 1)+K(n)* (n) n=1,2,Where, K(n) is referred to as the gain vector and (n) is a priori estimation error which is given by the equation (n)=d(n)-w(n-1)x(n)The RLS algorithm does not require any matrix inversion calculations as the inverse correlation matrix is computed directly. It requires reference signal and correlation matrix information.E) VSSNLMS(Variable step size NLMS) AlgorithmAli Hakam et al.(2014) proposed that the main aim of the developed Variable Step Size (VSS) NLMS algorithm is to replace the fixed step size that is used in NLMS by a variab le quantity one. This is to avoid a trade-off issue between convergence rate and pixilated-state MSE. In this algorithm a large step size is used in the initial stages to speed the rate of convergence and a smaller step size is used near to the steady state of the Mean Square Error (MSE) to obtain an optimum value. To achieve this, is multiplied by P(k) which is randomly chosen from the uniform distribution 0 1and each time of the N iteration times. Then to control the variable step value, it is multiplied by a curve function that isas follows(k) = (6/N)2(K-(N/6)2+0.001 1kN/6.001 N/6Where N is the input signal number.By Multiplying equation (9) by the random numbers P(k) and the normalized step sizeparameter , the variable step size develops to(K) = P(K) (K) Substituting the variable step size (10) to the conventional fixed step size NLMS algorithm (8), the proposed algorithm is shown asW(k+1)=W(K)+(K)e(K)x(k)/+ x(K)TABLE proportional ANALYSIS OF DIFFERENT ALGORITHMSLMSEasily impl emented method for on-line estimation of time-varying system parameters.The performance of the algorithm depends on the step size parameter, which controls the convergence speed and the variation of the learning curve.The LMS algorithm do not involve any matrix operations.LMS algorithm is least demanding in computational complexity.Simplicity and ease of computationIt does not require off-line gradientestimations or repetition of data.The rate of convergence is slow for a small value of but this gives a effective estimationof the gradient vector since a large amount of data istaken into account. The algorithm requires knowledgeof the transmitted signal sending periodically some known pilot sequences that is known to the receiverRLSIt requires reference signal and correlation matrixInformationThe RLSalgorithm also converges much more quickly than the LMSalgorithmRLS algorithm does not require any matrix inversioncomputations as the inverse correlation matrix is computeddirectlythec omputationalcomplexityhasbeen increased.CMAworks on the theory that the existence ofinterference causes changes in the amplitude of thetransmitted signal, which otherwise has a constant envelope(modulus)usefulness of CMA when channel conditions are rapidly changing. disfavour of the CMA is slow convergencetime. The slow converges limits the usefulness of thealgorithm inthe dynamicenvironmentNLMSknown as the projectionalgorithm, is a useful method for adapting thecoefficients of a finite-impulse response (FIR) filter fora number of signal processing and control applications.It can persist over a wide range of step-sizes.Normalized LMS(NLMS) is used to achieve stable calculation and faster convergence.prevents the update weight vectors from divergingand makes the algorithm more stable and fasterconverging than when a fixed step size is used.NLMS algorithmrequires a minimum of one additional multiply, divide,and addition over the LMS algorithm to implement forshift input data.IV) APPL ICATIONSUse of adaptive antenna in existing systems will reduce power consumption and interference while enhancing spectral density in wireless system which is the need of wireless communication systems.V) CONCLUSIONSmart Antenna systems are antennas with intelligence and the radiation pattern can be varied without any mechanically changed. The principle reason for the increase interest in smart antenna systems is the capacity increase and low power consumption. Smart antennas will increase the SIR by simultaneously increasing the useful received signal level and lowering the interference level.VI) REFERENCES1 Ali Hakam, Raed Shubair, Shihab Jimaa, and Ehab Salahat,Robust Interference Suppression Using a New LMS Based Adaptive Beamforming Algorithm in seventeenth IEEE Mediterranean ElectrotechnicalConference,Beirut,Lebanon,13-16 April 2014.2 H. Takekawa,T. Shimamura and S. Jimaa, An efficient and effective variable step size NLMS algorithm, in 42nd Asilomar Conference on Signals, S ystems and Computers, October, 2008.3 Leandro Vieira dos Santos, Jacqueline Silva Pereira,Least Mean Square Algorithm Analysis for a High Capacity Mobile Long Term Evolution Network IEEE 2013.4 Shahera HOSSAIN, Mohammad Tariqul ISLAM and Seiichi SERIKAWA, Adaptive Beamforming Algorithms for Smart Antenna Systems,International Conference on Control, automation and Systems 2008,Oct. 14-17, 2008 in COEX, Seoul, Korea.5 T.B. Lavate, V.K. Kokate, G.S. 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