Finite impulse response filter implementation using LMS algorithm

Abstract

The principle objective this project is to determine the coefficients of the FIR filters that met desired specifications. The determinations of coefficients involve channel equalization, system identification and SNR vs. BER plot using LMS algorithm. This project is to investigate the performance of an FIR filter equalizer for data transmission over a channel that causes intersymbol interference. FIR filter removes unwanted parts of the signal, such as random noise, or extracts the useful parts of the signal, such as the components lying within a certain frequency range. In signal processing, there are many instances in which an input signal to a system contains extra unnecessary content or additional noise which can degrade the quality of the desired portion. In such cases we may remove or filter out the useless samples using FIR filters. Here by using LMS algorithm in channel equalization we determined coefficients in Matlab programming. In project by inducing white Gaussian signal or random signal (noise) with data signal we equalize for data transmission over a channel. They can easily be designed to be "linear phase" (and usually are). Put simply, linearphase filters delay the input signal, but don’t distort its phase. They are simple to implement. On most DSP microprocessors, the FIR calculation can be done by looping a single instruction. They are suited to multi-rate applications. By multi-rate, we mean either "decimation" (reducing the sampling rate), "interpolation" (increasing the sampling rate), or both. Whether decimating or interpolating, the use of FIR filters allows some of the calculations to be omitted, thus providing an important computational efficiency. In contrast, if IIR filters are used, each output must be individually calculated, even if it that output will discard (so the feedback will be incorporated into the filter). They have desirable numeric properties. In practice, all DSP filters must be implemented using "finite-precision" arithmetic, that is, a limited number of bits. The use of finiteprecision arithmetic in IIR filters can cause significant problems due to the use of feedback, but FIR filters have no feedback, so they can usually be implemented using fewer bits, and the designer has fewer practical problems to solve related to non-ideal arithmetic. In the implementation of FIR in system identification estimated channel parameters are almost same as channel parameter. So FIR filter provides effective way to remove unwanted signals, channel equalization and system identification.