19CM798 ROBUST SYNTHESIS OF BEAMFORMING WEIGHTS IN LINEAR ANTENNA ARRAY A PROJECT REPORT Submitted by ATHIRA P S (CB.EN.P2CST20004) Under the guidance of Dr. Natarajamani S and Ms.Prabha G In partial fulfillment for the award of the degree of MASTER OF TECHNOLOGY IN COMMUNICATION SYSTEMS ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING AMRITA SCHOOL OF ENGINEERING AMRITA VISHWA VIDYAPEETHAM AMRITANAGAR, COIMBATORE - 641 112 JANUARY 2022 AMRITA VISHWA VIDYAPEETHAM AMRITA SCHOOL OF ENGINEERING COIMBATORE - 641 112 BONAFIDE CERTIFICATE This is to certify that the project report entitled ROBUST SYNTHESIS OF BEAMFORMING WEIGHTS IN LINEAR ANTENNA ARRAY submitted by ATHI RA P S (CB.EN.P2CST20004) in partial fulfillment of the requirements for the award of the Degree of Master of Technology in COMMUNICATION SYSTEMS is a Bonafide record of the work carried out under my guidance and supervision at Amrita School of Engineering, Coimbatore . Project Advisor: Dr. Natarajamani S , Ms.Prabha G Designation: Asst.Prof, ECE Program Coordinator: Dr.Ramanadhan Designation: Asst.Prof, ECE Dr. M. Jayakumar Chairperson Department of Electronics and Communication Engineering The project was evaluated by us on: Internal Examiner External Examiner ACKNOWLEDGEMENT I take this opportunity to humbly express my sincere gratitude and thanks to all those concerned with my M.Tech Dissertation. I express my sincere gratitude to Dr.Natarajamani, Ms.Prabha for providing valuable guidance and appropriate suggestion during the course of the dissertation because of which I was able to complete the first phase of the dissertation process satisfactorily. I am obliged to Dr.Ramanadhan Program Coordinator, whose valuable inputs and guidance helpedto improve the quality of the dissertation work. Also, I am thankful to the project review panel consisting of Dr.Jayakumar.M (Chairperson, ECE),Dr.Ramanadhan (Asst.Prof ,ECE) and Dr.GandhiRaj (Asst.Professor,ECE) for their ample inputs during each review process and pointing out the areas to improve specifically, and thus guiding to improve the quality of dissertation. ABSTRACT To meet future wireless communications networks increasing demand Smart Antenna technology will have a widespread application. The ability of smart antennas to respond to interference in the real-time environment is the major factor for the use of smart antennas. The ability to place nulls in an undesired direction and major lobes in the desired direction is known as Adaptive beamforming. Due to their ability to isolate noise signals from desired signals smart antennas have major applications in wireless communications. Smart Antenna technology increases directivity towards the desired directions, also noise resistive and better capacity for a wireless communication system. Adaptive Beamforming algorithms are used by Smart Antennas to steer the main lobe towards the desired direction, in turn, placing nulls in an undesired direction. The steering of the beam pattern is done by calculating the weights required based on the angle of the desired direction. This is done by adaptive algorithms that are programmed in the DSP. This project presents an extensive study of the basics of Smart Antenna systems and the functioning of Smart Antennas. Simulation of the Smart antenna algorithms for 5G frequency is carried out through MATLAB software based on real-time antenna parameters like the distance between antenna elements, several Antenna elements, etc. Comparison based on the simulation of different algorithms will be carried and the conclusion is drawn for an algorithm that has better performance for a given environmental condition. i TABLE OF CONTENTS CONTENTS PAGE NO. 1. INTRODUCTION .......................................................................................................................7 1.1 Problem definition …………………………………………………………………………………..7 1.2 Scope of the work …………………………………………………………………………………... 7 1.3 Overview of Antenna and Arrays .......................................................................................................8 1.3.1 Need of Array Antenna …………………………………………………………………….8 1.3.2 Block Diagram of Antenna Array and its working ..................................................................8 1.4 Smart Antenna System ........................................................................................................................9 1.4.1 Definition………………………………………………...…………………………………9 1.4.2 Analogy for Smart Antenna ………………………………………………………………..9 1.4.3 Smart Antenna………………………………………………………………………………10 1.4.4 Need for Smart Antenna…………………………………………………………………….10 1.4.5 Architecture of Smart Antenna System……………………………………………………10 1.5 Beamforming in Smart Antenna System………………………………………………………….11 1.5.1 Types of Beamforming……………………………………………………………………12 1.6 Features of Smart antenna Technology…………………………………………………………...14 1.7 Benefits of Smart antenna Technology …………………………………………………………..14 1.8 Summary ……………………………………………………………………………………………14 2. LITERATURE SURVEY……………………………………………………………………16 3. PROPOSALS AND CONTRIBUTIONS……………………………………………………18 4. METHODOLOGY……………………………………………………………………………19 ii 4.1 Least Mean Square(LMS)……………………………………………………………………........19 4.2 Sample Matrix Inversion(SMI)........................................................................................................22 4.3 Recursive Least Square(RLS)...........................................................................................................22 4.4 Normalized Least Mean Square.......................................................................................................23 5. RESULTS AND DISCUSSIONS..................................................................................................25 5.1 Flow chart of an implementation of algorithms..............................................................................25 5.2 Comparative performance analysis of LMS, NLMS, SMI, RLS, LMS/SMI, and Combined NLMS algorithms in the adaptive array.............................................................................................26 5.2.1 comparison of null depth,and maximum SLL for varying number of antenna elements............26 5.3 Results of implementation of LMS algorithm...............................................................................29 5.3.1 Effect of varying number of elements........................................................................................29 5.3.2 efEfect of varying inter elements spacing..................................................................................30 5.4 Summary...........................................................................................................................................31 5.5 Results and implementation of LMS-RLS algorithm...................................................................31 5.6 Comparison of null depth, and maximum SLL for LMS, LMS-RLS.........................................33 REFERENCES.......................................................................................................................................34 PUBLICATION STATUS..................................................................................................................... 36 iii LIST OF ABBREVIATIONS ABBREVIATIONS EXPANSIONS PAGE NO LMS Least Mean Square 14 SMI Sample Matrix Inversion 14 RLS Recursive Least Square 14 NLMS Normalized Least Mean Square 14 SLL Sidelobe level 14 SA Smart Antenna 4 RF Radio Frequency 5 DSP Digital Signal Processing 12 MSE Mean Square Error 19 iv LIST OF FIGURES FIGURE NO TITLE PAGE NO 1 Block diagram of the antenna array 8 2 Block diagram of the adaptive antenna array 11 3 Beamforming pattern for the desired signal 12 and interfering signals 4 Switched beamforming pattern 13 5 Adaptive beamforming pattern 14 6 LMS algorithm adaptive beamforming 22 network 7 RLS algorithm adaptive beamforming 25 network 8 Flow chart of algorithm implementation 27 9 Array elements N = 8 28 10 Array elements N = 16 29 11 Array elements N = 21 29 12 4 element linear array 31 13 8 element linear array 31 14 16 element linear array 31 15 21 element linear array 31 16 d = 0.3 lambda 32 17 d = 0.5 lambda 32 18 d = 2 lambda 33 19 Polar plot of LMS-RLS for d =0.5 34 20 Rectangular 34 v LIST OF TABLES TITLE Array performance of different TABLE NO 1 PAGE NO 30 algorithms with varying antenna elements Performance of combined adaptive 2 35 beamforming algorithms with LMS vi 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 CHAPTER 1 INTRODUCTION 1.1 Problem Definition As the growing demand for wireless communication is constantly increasing, the need for better coverage, improved capacity, and higher transmission quality rises. Thus, more efficient use of the radio spectrum is required. One of the promising technologies is the use of a smart antenna system. A smart antenna system is capable of efficiently utilizing the radio spectrum and is a promise for an effective solution to the present wireless system problems while achieving reliable and robust high-speed, high-data-rate transmission. Traditional antennas emit a distributed beam whereas in smart antennas the beam of the antenna is highly directional and pointed only towards the desired user and the interferences are rejected. Adaptive beamforming is one of the main and most famous aspects of the development of smart antenna technologies[1]. A smart antenna system consists of multiple numbers of elements. Using a beamforming algorithm smart antenna is able to form the main beam towards the desired user and null in the direction of interfering signals. This beam moves with the user, this improves the power utilization of the antenna. The main focus of this project is a brief account of the Smart Antenna (SA) system in the context of adaptive beamforming. The goal is put null in the direction of the interferer and maximum in the desired direction. 1.2 Scope of the work A smart antenna is an array of radiating antenna elements combined with digital signal processing to transmit and receive in the adaptive manner. Adaptively in the sense, it automatically adjusts the directionality of its radiation pattern in response to the signal environment. Smart antennas can increase signal range, reduce signal fading, suppress interfering signals, and increase the capacity of wireless systems. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 7 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 1.3 Overview of Antennas Arrays 1.3.1 Need of Array antenna. Conventional single element antennas have various drawbacks compared to array antennas. Single element antennas have no noise cancellation property. The following points represent the need for array antennas over a conventional antenna system.[2] i. Signal strength increases. ii. The high directivity is obtained iii. Minor lobes are reduced iv. High signal to noise ratio achieved. v. High gain is obtained. vi. Power wastage is reduced. vii. Better performance is obtained 1.3.2 Block diagram of Antenna Array and its working An antenna with more no of elements is called an Antenna array. The Antenna array consists of individual radiators and elements.. The radiation pattern produced by them would be the vector sum of individual ones. It can radiate individually but when it is an array, it sums up the radiation of all the elements to form a radiation beam, which has high gain, high directivity, and better performance with minimum losses.[4]. The below images indicate the Antenna array M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 8 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 Figure 1: Block diagram of the Antenna Array. The applications of array antennas are used in satellite communication, wireless communication, radar communication. 1.4 Smart Antenna Systems. 1.4.1 Definition. A smart antenna is a system with multiple antenna elements in an array with an ability to change their beam pattern in response to interferer signals in the receiver and increase radiation towards desired signals. 1.4.2 Analogy for Smart Antennas. Adaptive smart antenna systems can be easily understood with a simple analogy. Consider when we stand in a room with our eyes closed and conversing with a person. Consider the person is moving into the room while speaking. We can receive the audio through our ears and be able to detect the location of the person even with our eyes closed. As the person moves from side to side, audio reaches to our both ears at different times. Our brain can process the audio and be able to determine the side where the person is present. The working of Adaptive Antenna M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 9 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 systems is also similar but with an antenna having multiple antenna elements arranged in an array pattern.[5] 1.4.3 Smart Antenna. The name smart antenna doesn’t mean that the antenna is smart. The antennas are usually attached to the base station, but when the antenna is combined with a Digital Signal processor with intelligent algorithms of beamforming to receive and transmit signals in the environment make the antenna smart.[1] This configuration increases the system capable of the wireless communication system. Various parameters such as array gain, interference mitigation are considerably increasing with smart antenna systems. Smart antenna systems can be more efficient when replaced with conventional systems which have the effects of multipath fading and co-channel interference. 1.4.4 Need for Smart Antenna. The main aim of a smart antenna system is to improve the signal quality of a receiving signal by increasing beam pattern transmission towards the direction of the desired signal by taking advantage of adaptive algorithms. Smart antenna makes a system more efficient and increases the capacity of a conventional antenna system. Smart antennas are widely employed in modern wireless systems to combat the increasing applications and increased capacity to which the conventional antennas have to serve.[2] 1.4.5 Architecture of Smart Antenna System. In smart antenna system, the radiation pattern of the antenna is controlled via certain algorithms using digital signal processors. The inputs to the antenna arrays are assumed as the desired signal, interfering signals. Using some adaptive algorithms, the array weights are controlled and subsequently the output error is minimized. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 10 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 There are N antennas placed at the input side of the block diagram. All the antenna elements together can be called as Antenna Arrays. The adaptive algorithm is used to minimize the error e(n) between desired signal d(n) and array output y(n). The antennas combine with the weights and form the output. The error e(n) gets the difference of the desired output d(n) and actual output y(n).The error e(n) goes to the Adaptive Algorithm and updates the weights. This process goes on until it gets the desired direction. Figure 2: Block diagram of an Adaptive Antenna Array The radiation pattern produced by them would be the vector sum of individual ones. The distance between the elements and the length of the elements relative to the wavelength is important during antenna design. It can radiate individually but when it is an array, it sums up the radiation of all the elements to form a radiation beam, which has better gain, good directivity, and increased performance with lower losses.[1] 1.5 Beamforming in Smart Antenna. Beamforming is a type of technique used to send strong signals and focus the signal on a targeted device. The process of cutting an interfering signal and constructing a pattern is called Beamforming.[3] M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 11 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 Figure 3: Beamforming pattern for desired and interfering signals 1.5.1 Types of Beamforming. Beamforming is categorized into two types based on the method the antenna array uses to steer the beam dynamically. 1. Switched Beamforming. The switched beam system functions by having a set of predefined beam patterns of array antennas combined and switching the beam in response to the signal environment. These antennas will have high directivity, which helps to achieve some gain. In this, there will be numerous amounts of fixed beams amongst which one beam will turn on or will be steered towards the wanted signal. This can be done only with adjustment in the phase. The below figure indicates the Switched beam Figure 4: Switched beamforming pattern. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 12 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 Switched beam antenna systems form different fixed beams with heightened sensitivity in particular directions. These antenna systems identify signal strength, choose from one of several predetermined, fixed beams, and switch from one beam to another as the mobile moves throughout the sector.[5] The main drawback of this beam is that the inter-cell interferences among the beams are needed to be handled. 2. Adaptive Beamforming In this type , there will be a change in the beam pattern according to the movement wanted by the user and the movement of the interference. These are the antenna arrays that dynamically change the antenna pattern to control the interference, multipath, and noise.[6].The significance of using the Adaptive antenna is that the generated antenna beams can adaptively track the signal direction. In this there is no inter-cell issue is found due to the continuous tracking of users. In this, the capacity to a greater extent than switched beam. They can have extensive signal processing through DSP. The main drawback of these antennas is that the cost of installation is very high. The below figure shows the Adaptive array Figure 5: Adaptive beamforming pattern Using a variety of new signal-processing algorithms, the adaptive system takes advantage of its capacity to effectively locate and track various types of signals to effectively minimize interference and maximize intended signal reception. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 13 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 1.6 Features of Smart Antenna Technology. 1. Signal Gain 2. Interference Rejection 3. Spatial Diversity 4. Power Efficiency 5. Better range/ Coverage 6. Increased Capacity 7. Multipath Rejection). 1.7 Benefits of Smart Antenna Technology 1. Reduction in co-channel interference. 2. Range improvement. 3. Increase in capacity. 4. Reduction in transmitted power 1.8 Summary Work carried out investigates the performance of LMS (Least Mean Square), RLS (Recursive Least Square), SMI(Sample Matrix Inversion), NLMS(Normalised Least Mean Square), Combined NLMS, LMS/SMI ,LMS-RLS beamforming algorithms to steer the antenna beam in the particular desired direction. Algorithms are simulated for a linear antenna array with different sizes, and results are discussed in terms of their Max SLL, and Null depths . The simulation is carried out using MATLAB. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 14 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 Chapter 1 explains the Adaptive arrays used in smart antennas and the problem overview. There are various types of smart antennas present. But we used only the appropriate one i.e Adaptive antenna array. The adaptive Antenna Array and its operation have been explained with the help of a block diagram. Adaptive Beamforming algorithms are used by Smart Antennas to steer the main lobe towards the desired direction, in turn, placing nulls in an undesired direction. The steering of the beam pattern is done by calculating the weights required based on the angle of the desired direction. This is done by adaptive algorithms that are programmed in the DSP. Chapter 2 explains what the literature survey has been carried through. Chapter 3 explains the proposals and contributions of work. Chapter 4 expalins different types of beamforming algorithms for smart antennas Chapter 5 explains the implementation and the results of Adaptive beamforming Algorithms for smart antennas. It explains and shows the factors that are taken for the implementation of the results of the adaptive algorithms. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 15 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 CHAPTER 2 LITERATURE SURVEY. [1] Presents the survey-styled introduction to the concept to the concept of adaptive beamforming techniques. [2] gives the overall introduction to the various adaptive antenna beamforming algorithms(LMS,RLS,NLMS,SMI)and some combined algorithms(combined NLMS, LMS/SMI). Found that the RLS, SMI gives better performance, LMS, NLMS, Combined NLMS introduce the lowest SLL, RLS, SMI, LMS/SMI show deep nulls and have the highest SLL.In [3] LMS, RLS, SMI algorithms are analyzed by varying numbers of elements in the uniform linear antenna array.It is observed that as the number of elements increases the improvement in terms of narrow beam width and deepest null at interfere becomes superior. [4] discusses two types of adaptive beamforming algorithms. The beamforming performance is studied by varying the element spacing and the number of antenna array elements for each algorithm. These algorithms are compared for their rate of convergence, beamforming, and null steering performance (beamwidth, null depths, and maximum sidelobe level). From the results obtained in the paper it is evident that d = 0.5 λ is used as optimal distance between antenna.This paper,[5] , examined the performance analysis of LMS adaptive beamforming algorithm for smart antenna system in the form of normalized array factor and mean square error. The authors have presented performance of the antenna system for different spacing between array elements, number of array elements, different geometry. The following are the conclusions made in this paper οΌ when increase spacing between elements beamwidth becomes narrower, but for higher values sidelobe level M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 16 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 οΌ When increase number of elements ,beamwidth becomes narrower and also sidelobe levels are decreases οΌ Beamwidth of planar array is narrower than other geometry and side lobe level decreases than other geometry οΌ Planar array gives a good array factor compared to others A full digital beamforming array with nonreciprocal TX/Rx beam patterns is proposed in [6]. The paper discusses how Nonreciprocal arrays can achieve a wider coverage in the uplink and provide high gain beams for the downlink. Introduced a novel idea to incorporate the actual nonisotropic radiation pattern produced by the array elements and the mutual coupling into two popular deterministic BF methods in,[7]. Two popular beamforming methods minimum variance distortionless response (MVDR) method and the null steering beamforming (NSB) method are modified according to this new idea in order to be applied on a realistic microstrip linear antenna array. In,[8], the linear arrays are evaluated on the basis of the number of elements and the distance between the elements for beamforming. The analysis is done to find the relationship of the gain and the beam width with the number of the elements and the spacing between the elements. In,[9], compared the two algorithm by varying different parameters like number of elements, spacing between array elements and step-size.In,[10],the authors investigates the performance of sample matrix inversion with least mean square (SMI-LMS), sample matrix inversion with recursive least square (SMI-RLS) and least mean square with recursive least square (LMS-RLS) algorithm. Side lobe level, null depth and error plot of adaptive beam formation for different signal-to-noise (SNR) with different element spacing are simulated and compared. It is found that performance of LMS-RLS algorithm is better than SMI-LMS and SMI-RLS algorithm. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 17 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 CHAPTER 3 PROPOSALS AND CONTRIBUTION The project proposal is to design and implementation of antenna arrays , beamforming algorithms for antenna arrays and evaluate the performance analysis of both. Work carried out investigates the performance of LMS (Least Mean Square), RLS (Recursive Least Square), SMI(Sample Matrix Inversion), NLMS(Normalised Least Mean Square), Combined NLMS, LMS/SMI , beamforming algorithms to steer the antenna beam in the particular desired direction. Algorithms are simulated for a linear antenna array with different sizes, and results are discussed in terms of their Max SLL, and Null depths . The simulation is carried out using MATLAB. Comparing based on side lobe radiation and main lobe radiation of all adaptive algorithms, found that some combined algorithms provide better results. Beams of a smart antenna are generated by combined approaches using LMS-RLS. These combined algorithms are applied for beamforming for various values of step size (for LMS), forgetting factor (for RLS) best results are reported. In LMS-RLS, first weights are updated using LMS and then again updated using RLS. The contribution of this project includes the implementation of adaptive beamforming algorithms, namely LMS, NLMS, SMI, and RLS, LMS/SMI, LMS-RLS, Combined NLMS. Furthermore, a comparative performance analysis is carried out and evaluated in terms of null depth, maximum sidelobe level for the number of antenna elements, and spacing. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 18 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 CHAPTER 4 METHODOLOGY Beamforming algorithms can be classified into two classes, namely non-blind & blind algorithms. In the case of nonblind adaptive algorithms, a reference signal is used in the process of adjusting the array weights function. On the other hand, no reference signal is used in blind adaptive algorithms. However, when compared with their non-blind counterparts, these algorithms tend to be more computation-intensive, and often provide lower accuracy and slower convergence rate. In the non-blind algorithms, the adaptive weights of the array beamformer are usually adapted according to a specified criterion, such as minimization of mean square error (MMSE). An error signal, produced by comparing the output signal with a reference signal, is used to iteratively adjust the weights of the beamformer to their optimal values, Wopt, to obtain the minimum MSE. The trained algorithms could be classified according to their adaptive criterion: leastmean squares method (LMS), sample matrix inversion (SMI) , recursive least-squares method (RLS),normalized least mean square method(NLMS). 4.1 Least Mean Square Algorithm (LMS). The LMS algorithm is an adaptive algorithm that uses a gradient-based approach of steepest descent. Minimum Square Error (MSE) criteria are employed by LMS Algorithm to the derivation of the weight vector. In the training period, the reference signal is transmitted and received at the other end which is used to calculate the error signal. Error is minimized by the gradient-based method of steepest descent. LMS algorithm makes continuous correction of weight vector by a small amount in an iterative manner based on the gradient vector, called a step size, which outputs the minimum square error. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 19 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 LMS algorithm is simple compared to others since it does not require any complex calculations. The LMS algorithm continuously calculates the error between the desired signal and the actual signal until the error becomes minimum. When the error becomes minimum the weights adaption reaches their optimal stage. Array antenna receives the incoming signal x(n) and multiplied with the weight factors W, which alters the phase and amplitude of the incoming signal. These altered weighted signals are summed up and give the output signal y(n). Then the error is minimized by an adaptive algorithm by calculating the difference between the output signal y(n) and the desired signal d(n), by updating the weight vector.[1-5] Figure 6 : LMS algorithm adaptive beamforming network The algorithm is used to minimize the error e(n) between desired signal d(n) and array output y(n), as e(n) = d(n) – y(n) (1) The output of adaptive beamformer, at a time ‘n’, is given by a linear combination of the data at the N antenna elements, can be expressed as y(n) = wH x(n) M.Tech.CST (2) Department of ECE Amrita Vishwa Vidyapeetham 20 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 w = [w1,w2,….wN]H Where, H denotes Hermitian (complex conjugate) transpose. The weight vector w is a complex vectors. Signal received by multiple antenna elements is x(n) = [x1(n),x2(n),…….xN(n)] LMS algorithm updates the weight vectors according to the equation w(n+1) = w(n) + µ x(n) e*(n) (3) Where μ is the step size varies from 0 to 1 which is relatively small. The LMS calculation speed depends on the step size and it ranging between 0< µ< 1 πππx ππππ₯ represents the maximum eigenvalue of the correlation matrix R which is the limit for a step size value. The speed of the algorithm depends on the value of the step size. If the value of step size is small then the speed of the algorithm is slow and if the value of step size is the large speed of the algorithm is fast. The LMS algorithms adopt a gradient-based approach, where it also tries to decrease the mean square error[MSE]. Based on the MSE the algorithm changes the values of the weights to counter the MSE. If the MSE is more the values of weights are decreased and if MSE is negative the weights will be more positive so that the error becomes optimal. If the step size is smaller the convergence rate of the algorithm will be high and if the step size is larger the convergence rate is faster making the system unstable at MSE value. Hence a proper step size needs to be chosen. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 21 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 4.2 Sample Matrix Inversion (SMI). In the SMI algorithm, the weight calculation is different from the LMS algorithm which makes SMI faster than LMS. SMI algorithm uses its estimated value in place of the correlation matrix to calculate its weight, wherein the LMS algorithm uses many iterations which ultimately converge the error to the minimum and update its weights which is a slower computational speed than the SMI. Weights are calculated by equation π€πππΌ = π π₯π₯(π) −1 ∗ π(π) (4) Where π π₯π₯ (π) = r(n) = ∑ ∑ . x(n) ∗ x π»(π) (5) (6) π₯(π) ∗ π(π) In the rapidly changing environmental conditions, this is the most suitable for beamforming since the rate of convergence is faster than the LMS algorithm.[1-5] 4.3 Recursive Least Squares (RLS) Even though the SMI algorithm is faster in convergence than the LMS algorithm its complexity can cause potential singularities that can cause problems in calculations of weights which is a drawback.[1-5] The equation for the correlation matrix and the vector is given by equation π xx(k) = πΌπ xx(k − 1) + π₯Μ (k) xH(k) (7) πΜ π₯π₯(k) = πΌπΜ π₯π₯(k − 1) + π* (k)πΜ (k) (8) where πΌ is the forgetting factor; that is a positive constant value ranging from 0 < πΌ < 1. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 22 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 The weights of the RLS algorithm is updated as given by π€(k) = π€(k − 1) + π(k)(π* (k) − π₯ π»(k)π€(k − 1)) (9) Where the gain vector π(π) is defined as given by equation π(π) = πΌ −1π π₯π₯(k−1)π₯(k) (10) 1+πΌ−1π₯Μ π» π π₯π₯(k−1)π₯(k) Figure 7: RLS adaptive beamforming network 4.4 NLMS The LMS algorithm is the most basic method for calculating weights and the algorithm requires large number of iterations before satisfactory convergence. Also,the stability and convergence time of the LMS algorithm are dependent upon the step-size parameter. To overcome this dependency, the NLMS algorithm is introduced. The NLMS algorithm is used to achieve good stability and faster convergence.[1-5].The weight update equation for the NLMS algorithm is given as w(n+1) = w(n) + μ NLMS .x(n). e*(n) (11) ||x(n)||2 + α M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 23 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 The equation represents the final weight update for the NLMS algorithm where the step-size is divided by the normalized value of the input signal x(n). In Equation, to avoid the denominator being zero for no signal condition, a small positive constant ‘α’ is added to the denominator.[910]. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 24 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 CHAPTER 5 RESULTS AND DISCUSSIONS Simulation of adaptive algorithms is carried out using MATLAB software. The array factor of the array antenna is plotted against the angle of arrival of the signal. The Y-axis represents the array factor of an array antenna and X-axis represents the angles of signals. Various simulation input parameters are listed below: 1. The number of Antenna elements. 2. Distance between antenna elements. 3. The angle of the desired signal. 4. The angle of the interfering signal 5.1 Flow chart of Implementation of Algorithm start Initialize element spacing ,element number,angle of desired signal ,interference signal Initialize weights to zero Calculate weights using algorithms Updates new weights End Figure 8: Flow chart for Algorithm Implementation M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 25 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 5.2 Comparative performance analysis of LMS, NLMS, SMI, RLS, LMS/SMI, and Combined NLMS algorithms in the adaptive array. The performance studies of the above-mentioned algorithms are done by using MATLAB, in varying parameters, for example, null depth, maximum SLL, rate of convergences. . Here, initially smart antenna system is designed by taking a uniform linear array (ULA) with interelemental spacing (d) equal to half wavelength distance. 5.2.1Comparison of null depth, and maximum SLL for varying number of antenna elements For the variation of array elements of the LMS, NLMS, SMI, LMS/SMI, Combined NLMS and RLS algorithms, have considered fixed element spacing at 0.5 of wavelengths (π). Figures 9, 10, and 11 illustrate the array patterns of the desired signal and null steering toward interferers with the variation of antenna elements for 8,16, and 21, respectively Figure 9 : Array element N = 8 M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 26 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 Figure 10 : Array elements N = 16 Figure 11 : Array elements N = 21 Table 1 presents a summary of the results for varying antenna elements. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 27 19CM798 Dissertation Algorithms LMS RLS SMI NLMS LMS/SMI Combined NLMS ATHIRA P S and CB.EN.P2CST20004 Antenna elements Maximum sidelobe level(dB ) JANUARY and 2022 Maximum null depth(dB) 8 6.2 -7.03 16 12.48 -14.14 21 6.05 -6.79 8 7.84 -9.85 16 15.68 -20.00 21 7.77 -9.85 8 7.84 16 15.68 21 7.77 8 7.84 -7.89 16 15.68 -15.78 21 7.77 -7.75 8 7.61 -8.79 16 15.25 -17.58 21 7.62 -8.79 8 7.4 -9.63 16 14.92 -19.26 21 7.44 -9.63 TABLE 1: Array performance of different algorithms with varying antenna elements The plots indicate that if the number of antenna elements increases keeping element spacing at 0.5π, the antenna beamwidth becomes narrower. The maximum SLL slightly varies and the maximum null depths remain almost the same. It can be observed that the RLS, NLMS, and LMS with SMI weights initialization show deep nulls, on the other hand, RLS, SMI, NLMS have the highest SLL. Whereas LMS, and combined NLMS introduce the lowest SLL, where both NLMS and combined NLMS have deeper null than LMS. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 28 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 5.3 Results of Implementation of LMS Algorithm 5.3.1 Effect of Varying Number of Elements For this simulation, the inter-element spacing is set to be π /2, where π is the wavelength. Figure 12,13,14,15 illustrates the polar radiation pattern for 4, 8, 16, and 21 elements linear arrays. Figure 12 : 4 element linear array Figure 13 : 8 element linear array Figure 14 : 16 element linear array Figure 15 : 21element linear array M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 29 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 Simulations results obtained have proved that an increase in the number of elements in a linear array would result in higher directivity, as well as a sharper and narrower beamwidth, but this brings about more side-lobes. It has been shown that the interference rejection capability of the array improves as the number of antenna elements increases. 5.3.2 Effect of Varying Inter-elements Spacing Figure 16,17,18 illustrates the polar radiation pattern for an 8-elements linear array for an interelement spacing (d) of 0.3 wavelengths, half wavelength, double wavelength . The angle of the desired signal is 90° and the angle of the interference signal is take as 0° . Figure 16 : d = 0.3 lambda Figure 17: M.Tech.CST d = 0.5 lambda Department of ECE Amrita Vishwa Vidyapeetham 30 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 Figure 18 : d = 2 lambda It is observed that an increase in inter-element spacing in a linear array will result in higher directivity and smaller beamwidth, it is found that the number of undesirable side lobes also increases with increasing inter-element spacing. 5.4 Summary Comparing based on side lobe radiation and main lobe radiation LMS algorithm has shown the lowest SLL, RLS showed deep nulls. As the distance between the antenna elements increases more than 0.5 π, the radiation pattern shows multiple major lobes that are not required. At an optimal value of 0.5 π of element spacing, the algorithms have maximum radiation in the desired direction. 5.5 Results of Implementation of LMS-RLS Algorithm beams of smart antenna are generated by combined approaches using LMS-RLS. These combined algorithms are applied for beamforming for various values of step size (for LMS), forgetting factor (for RLS) best results are reported. In LMS-RLS, first weights are updated using LMS and then again updated using RLS. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 31 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 Figure 19,20 illustrates the polar and linear radiation pattern for an 8-elements linear array for an inter-element spacing (d) of half wavelength. The angle of the desired signal is 90° and the angle of the interference signal is taken as 0°. Figure 19 : Polar plot of LMS-RLS for d=0.5 Figure 20 : Rectangular plot of LMS-RLS M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 32 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 5.6 Comparison of null depth, and maximum SLL for LMS, LMS-RLS The parameters, like, maximum side lobe level (SLLmax), null depth, direction of user(90 0) and direction of interferer(00 )of LMS and LMS-RLS algorithms in adaptive beamforming are tabulated in Table 2. Algorithms Antenna elements Antenna spacing Maximum Maximum null sidelobe level depth (dB) (dB) LMS 8 0.5λ 6.2 -7.03 LMS-RLS 8 0.5λ -31 -114.68 Table 2: Performances of combined adaptive beamforming algorithms with LMS It is found that the lowest side lobe levels can be achieved by LMS-RLS algorithms for spacing of 0.5λ. Also LMS-RLS algorithm produces deepest null as compared to LMS. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 33 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 REFERENCES [1] Prathviraj Khande et al (2021). An overview of Algorithms for Adaptive Beam Forming (ABF) for Smart Antenna System (SAS). South Asian Res J Eng Tech, 3(1): 23-30 [2] M. Abualhayja'a and M. Hussein, "Comparative Study of Adaptive Beamforming Algorithms for Smart antenna Applications," 2020 International Conference on Communications, Signal Processing, and their Applications (ICCSPA), 2021, pp. 1-5. [3] D. N. Patel, B. J. Makwana and P. B. Parmar, "Comparative analysis of adaptive beamforming algorithm LMS, SMI and RLS for ULA smart antenna," 2016 International Conference on Communication and Signal Processing (ICCSP), 2016, pp. 1029-1033. [4] Ayodele S. Oluwole and Viranjay M. Srivastava, " Analysis and Synthetic Model of Adaptive Beamforming for Smart Antenna Systems in Wireless Communication," Journal of Communications, vol. 13, no. 8, pp. 436-442, 2018 [5] Ashwini D Pandhare and Khyati Zalawadia. Performance Analysis of LMS Adaptive Beamforming Algorithm for Smart Antenna System. International Journal of Computer Applications 179(28):34-37, March 2018. [6] C. Guo et al., "Design and Implementation of a Full-Digital Beamforming Array With Nonreciprocal Tx/Rx Beam Patterns," in IEEE Antennas and Wireless Propagation Letters, vol. 19, no. 11, pp. 1978-1982, Nov. 2020 [7] Z. D. Zaharis, I. P. Gravas, P. I. Lazaridis, T. V. Yioultsis, C. S. Antonopoulos and T. D. Xenos, "An Effective Modification of Conventional Beamforming Methods Suitable for Realistic Linear Antenna Arrays," in IEEE Transactions on Antennas and Propagation, vol. 68, no. 7, pp. 5269-5279, July 2020,. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 34 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 [8] “Evaluation of Beam Forming Capability of Linear Antenna Array for Smart Antenna System “ , Sarmistha Satrusallya and Mihir Narayan Mohanty , Research Article , Department of Electronics and Communication Engineering, Institute of Technical Education and Research, Siksha O’ Anusandhan (Deemed to be University), Bhubaneswar, Odisha, India. [9] A. Udawat, P. C. Sharma and S. Katiyal, "Performance analysis and comparison of adaptive beam forming algorithms for Smart Antenna Systems," International Conference on Next Generation Networks, 2019, pp. 1-5,. [10] Senapati, Anupama, and Jibendu Sekhar Roy. "Performances of some combined algorithms for adaptive beamforming in smart antenna using linear array." Asian Journal of AppliedSciences 4.3(2016). M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 35 19CM798 Dissertation ATHIRA P S and CB.EN.P2CST20004 JANUARY and 2022 PUBLICATION STATUS The literature that is to be submitted to a conference is to be written. The before hand works for the same is in process and the writing of the literature will be started soon. Need to explore a bit deeper to get some new results by manipulation of the considered parameters and to finalize theconference in which the paper is to be published and the work for the same is in process. M.Tech.CST Department of ECE Amrita Vishwa Vidyapeetham 36