<p> JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN ELECTRONICS AND COMMUNICATION ENGINEERING TO ANALYZE THE EFFECT OF VARIANCE AND IMPLEMENTATION OF ADAPTIVE EQUALIZATION FOR BROADCAST CHANNEL </p><p>1 MR. KRUNAL H CHAUDHARI, 2 PROF.N .B. GOHIL, </p><p>1M.E.[Electronics and Communication] Student, Department Of Electronics and Communication Engineering, Shantilal Shah College Of Engineering, Bhavnagar, Gujarat 2 Asst. Professor, Department Of Electronics and Communication Engineering, Shantilal Shah College Of Engineering, Bhavnagar, Gujarat</p><p>[email protected], [email protected]</p><p>ABSTRACT : This Paper addresses the effect of variance in Broadcast Channel Equalization problem. Here we developed a Broadcast channel equalization method for Single-Input Single-Output (SISO Here) communication systems using Adaptive algorithms like LMS (Least Mean Square) and RLS (Recursive Least Square) Algorithms. Aim of this paper is a comparative analysis of these two algorithms (LMS and RLS). We also developed here simulink model and taking a result of Broadcast channel Equalization using these two algorithms. After simulink result we conclude that RLS algorithm converges much faster than the LMS algorithm.</p><p>Keywords— Broadcast channel, Channel estimation, Equalization, LMS, RLS</p><p>1. INTRODUCTION the error or residual is itself defined as the difference Identification and equalization of nonlinear systems between some desired response and the actual filter are problems of practical interest in many problems output. where the systems cannot be accurately modeled as A signal is a varying phenomenon that can be linear. Last but not least, the problem of system measured. It is often a physical quantity that varies identification in a noisy environment. A system that with time, though it could vary with another works well in noise-free conditions, usually shows parameter, such as space. Signals may include error considerable degradation in performance when due to limitations of the measuring device, or due to background noise is present. It is clear that a strong the environment. A signal can be thought of as a demand for reliable system identification methods (continuous or discrete) sequence of (continuous or exist that efficiently separate the noise from signal. discrete) values. That is, a continuous signal may For this problem, one of the earliest and most have values at any arbitrary index value. A discrete successful applications of adaptive filters is adaptive signal, however, has restrictions on the index, channel Estimation and equalization in digital typically that it must be an integer. communication systems. The classical systems for noise suppression rely on the usage of adaptive linear filtering and the application of digital filters with finite impulse response. The strong points of this approach are the simple analysis of the linear systems in the process of adaptation and the guaranteed stability of FIR structures. It is worth mentioning the existence of relatively simple and well investigated adaptive algorithms for such kind of systems as least mean squares (LMS) and recursive least squares (RLS) algorithms. Here the approach to the development of linear Fig 1. System’s block diagram adaptive filtering algorithm is based on the method of least squares. According to this method, we minimize From Figure1, The signal u(n) is transmitted via a a cost function or an index of performance that is broadcast channel and corrupted by an additive noise defined as the sum of weighted error squares, where estimated by using any kind of Channel equalization</p><p>ISSN: 0975 – 6779| NOV 11 TO OCT 12 | VOLUME – 02, ISSUE - 01 Page 216 JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN ELECTRONICS AND COMMUNICATION ENGINEERING method. The main aim of most channel estimation measurements of the pertinent correlation functions, algorithms is to minimize the mean squared error nor does it require matrix inversion. Indeed, it i.e. the (MMSE) i.e., between the received signal and its simplicity of the LMS algorithm that has made it the estimate, while utilizing as little computational standard against which other linear adaptive filtering resources as possible in the estimation process. In the algorithms are benchmarked. Figure1 we have unknown broadcast channel that has to be estimated with an adaptive filter whose weight are updated based on some criterion so that (2) coefficients of adaptive filter should be as close as possible to the unknown channel. Where, 2. BROADCAST CHANNEL w(n) = distortion of channel The term broadcast implies the existence of a single In equation (2), The sequence of tap weight denoted channel on which only one node (processor) can by h1, h2,…,hM-1. Represent the spatial mapping of transmit at one time, while all the others receive the weighting or impulse response of the channel. message simultaneously. In a broadcast channel in Determining the capacity region for a general which one transmitter serves to receivers, the broadcast channel is one of the most important open capacity region highly depends on the amount of problems for broadcast channel. Broadcast strategy is channel state information (CSI) at the transmitter. an extension of the single input single output (SISO) From a practical perspective, obtaining CSI at the broadcast approach. Perfect channel state information receivers is basically an estimation problem which in (CSI) is assumed known at the receiver end only. general cannot be error free. Therefore it would be This strategy facilitates to adapt the reliably decoded worth-while to understand the effect of channel rate to the actual channel state without having any estimation error on the capacity region and feedback link to the transmitter. scheduling schemes in Broadcast Channel. The LMS algorithm is simple and yet capable of Assuming that the transmitter knows the SNR of all achieving satisfactory performance under the right the receivers, opportunistic strategy maximizes the conditions. Its major limitations are relatively slow throughput (sum-rate) of the system. It is usually rate of convergence and sensitivity to variations in assumed that CSI is accurate; however, evaluating the condition number of the correlation matrix of the the SNR is basically an estimation problem in the tap inputs. the LMS algorithm is highly popular and receiver which cannot be done without error. widely used in a variety of applications Obtaining CSI at the receivers is basically an . estimation problem which in general cannot be error free. Therefore, it would be worthwhile to understand the effect of channel estimation error on the capacity region and scheduling schemes in Broadcast Channel.</p><p>Fig. 3 Filter Tap for LMS At 0.001 variance</p><p>Fig. 2 Broadcast Channel Model (N2 < N1). The Channel output is given by,</p><p>(1) Fig. 4 Filter Tap for LMS At 0.1 variance Where, are samples of the received symbols, are the transmitted complex symbols. is the Gaussian noise variable ( ) and h(t) is the fading coefficient (Channel Response). 3. Simulation results A significant feature of the LMS algorithm is its simplicity. Moreover, it does not require</p><p>ISSN: 0975 – 6779| NOV 11 TO OCT 12 | VOLUME – 02, ISSUE - 01 Page 217 JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN ELECTRONICS AND COMMUNICATION ENGINEERING</p><p>The RLS algorithms are known to pursue fast convergence even when the Eigen value spread of the input signal correlation matrix is large. These algorithms have excellent performance when working in time-varying environments. All these advantages come with the cost of an increased computational complexity and some stability problems, which are not as critical in LMS-based algorithms. An important feature of RLS filter is that its rate of convergence is typically an order of magnitude faster</p><p>Fig. 5 Filter Tap for LMS At 1.0 than that of the simple LMS filter, due to the fact that variance the RLS filter whitens the input data by using the inverse correlation matrix of the data assumed to be of zero mean. The improvement in performance is achieved at the expanse of an increase in computational complexity of the RLS filter. RLS filter is an algorithm which recursively finds the filter co-efficient that minimize the weighted liner least squares cost function.</p><p>Fig. 7 Filter Tap for RLS At 0.001 Fig. 6 Squared errors for LMS variance</p><p>Fig. 8 Filter Tap for RLS At 0.1 variance</p><p>Table I</p><p>Table I, Shows the different types of values of input parameter which is used and shows particular outputs of the weights (co-efficient). From Table I we Fig. 9 Filter Tap for RLS At 1.0 variance conclude that when the variance of the channel is 0.001, get maximum value of the tap-weights of the channel means that Tap- weight of the channel is maximum when the variance of the channel is minimum. During whole process of equalization filter length of the LMS filter is constant.</p><p>ISSN: 0975 – 6779| NOV 11 TO OCT 12 | VOLUME – 02, ISSUE - 01 Page 218 JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN ELECTRONICS AND COMMUNICATION ENGINEERING</p><p>[2] Jiaozuo, “Design of Adaptive Equalizer Based on Variable Step LMS Algorithm.” ISBN 978-952- 5726-10-7, Proceedings of the Third International Symposium on Computer Science and Computational Technology(ISCSCT ’10) P. R. China, 14-15,August 2010, pp. 256-258 [3] Guanghan Xu , Hui Lui,Lang Tong and and Thomas Kailath “Least square approach to a blind channel equalization”. IEEE Transaction on signal processing, vol.43, no.12, December 1995 [4] Michele Morelli, Luca Sanguinetti and Umberto Mengali, “Channel Estimation for Adaptive Frequency-Domain Equalization”, IEEE Transactions on Wireless Communications, vol. 4, no. 5, 2005, pp no. 2508-2518. </p><p>Fig. 10 Squared errors for RLS</p><p>Table II</p><p>Table II, shows the different values of input parameter which is used for simulation result. From the values in Table. II and also according to graphically results of the variance we prove that the RLS algorithm converges much faster than the LMS algorithm.</p><p>4. CONCLUSION The work presented here is a process of channel estimation and equalization with the use of different types of algorithms. This Paper point of view, used adaption algorithm for the channel estimation and equalization using LMS and RLS Algorithm and analyze the effect of variance. In this paper interpretation of the whole process of channel estimation using different types of adaption algorithm, According to simulink results we conclude that RLS filter provided better performance than the LMS channel estimation and equalization.</p><p>5. REFERENCES [1] S. Haykin “Adaptive filter” 3th edition.</p><p>ISSN: 0975 – 6779| NOV 11 TO OCT 12 | VOLUME – 02, ISSUE - 01 Page 219</p>