Principles of a Linear Adaptive Equalizer with LMS Algorithm Implementation

This document examines the block diagram principles of a linear adaptive equalizer, with reference to the application schematic illustrated on page 275 of "Introduction to Modern Digital Signal Processing". The implementation utilizes the Least Mean Squares (LMS) algorithm, which iteratively adjusts filter coefficients using the gradient descent method. Key steps include: 1. Initializing FIR filter weights to zeros 2. Processing 500-sample training sequences through the adaptive filter 3. Calculating instantaneous error as e(n) = desired_output(n) - filter_output(n) 4. Updating coefficients via w(n+1) = w(n) + μ·e(n)·x(n) where μ denotes the step size We visualize convergence by plotting the squared error curve across iterations for a single experiment and extract the final optimized filter coefficients. To validate statistical performance, 20 independent trials are executed with different noise realizations. Comparative analysis examines three step-size values (e.g., μ=0.01, 0.05, 0.1) to demonstrate trade-offs between convergence speed and steady-state error. MATLAB code structures would typically involve: - `lms_filter = dsp.LMSFilter('Length',11,'StepSize',mu)` - `[y,err,weights] = lms_filter(x,d)` - Mean-squared error computation via `mse = mean(err.^2)`