LMS AND SMI ALGORITHMS FOR SPATIAL ADAPTIVE INTERFERENCE REJECTION 3 Contents.pdfVIP

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LMS AND SMI ALGORITHMS FOR SPATIAL ADAPTIVE INTERFERENCE REJECTION 3 Contents.pdf

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LMS AND SMI ALGORITHMS FOR SPATIAL ADAPTIVE INTERFERENCE REJECTION 3 Contents

March 16, 2001 LMS AND SMI ALGORITHMS FOR SPATIAL ADAPTIVE INTERFERENCE REJECTION VIJAYA CHANDRAN RAMASAMI 1 2 VIJAYA CHANDRAN RAMASAMI Abstract. Adaptive Antenna Arrays promise an enormous bandwidth increase for Wireless Com- munications using Spatial domain processing which is considered to be the last frontier than can provide substantial capacity increase. The aim of this project is to set up and simulate an adap- tive spatial filtering problem, using antenna arrays, where an estimate of the desired signal is constructed from a received signal consisting of additional interfering signals and background noise. The filtering is done in an iterative fashion using the LMS and the SMI algorithms. LMS AND SMI ALGORITHMS FOR SPATIAL ADAPTIVE INTERFERENCE REJECTION 3 Contents List of Figures 4 1. The Spatial Filtering Problem 5 1.1. Statement 5 1.2. Problem Setup 5 1.3. The Adaptive Processor 6 1.4. Assumptions 6 2. The Wiener MMSE Solution 7 3. Case - I : The LMS Algorithm 8 3.1. The Method of Steepest Descent 8 3.2. The LMS Simplification 9 3.3. The Algorithm 9 3.4. Stability 9 3.5. Convergence 9 4. Case II : Sampled Matrix Invariance 10 4.1. Motivation 10 4.2. Formulation 10 4.3. Adaptation in the SMI algorithm 10 4.4. Stability 11 4.5. Convergence 11 5. Results - LMS Algorithm 12 5.1. Demonstration 12 5.2. Effect of μ 14 5.3. Dynamic Channel Variations 16 5.4. Convergence of the Weight Vector 17 5.5. Effect of Changing the SIR 18 6. Results - SMI Algorithm 19 6.1. Effect of varying the Block Size 21 6.2. Dynamic Variations in the Channel 22 7. Appendix - I : MATLAB Code 23 7.1. LMS Algorithm 23 7.2. Sample Matrix Inversion 24 7.3. Generate Signal 25 7.4. SteeringVector 26 7.5. CalcCovarianceMatrix 26 7.6. CrossCorrelationVector 27 References 28 4 VIJAYA CHANDRAN RAMASAMI List of Figures 1 An Uniform Linear Array (ULA) 5 2 The Adaptive Processor 6 3 Example MSE Surface for N = 2 8 4 Array Factor Plot (Rectangular) for the Example Configuration 12 5 Array Factor Plot