Effect of variation in filter length on adaptive equalization in frequency selective channels

Adaptive equalizer is an integral component of modern communication systems that combats the effects of channel fading especially in multipath environment. In long term evolution (LTE) the number of multipath are standardized as seven and nine for extended pedestrian and extended vehicular-A channel respectively. The number of filter taps is an important design parameter that determines the performance and the rate of convergence of the adaptive filter. This paper analyzes the effect of the mentioned parameter on the overall performance of the system and quantifies the loss for a given range of signal to noise ratio (SNR). The performance is measured in terms of bit error rate (BER) and mean square error (MSE) both for least mean square (LMS) and recursive least square (RLS) techniques. The channel under consideration is frequency selective and time invariant in nature with an exponentially decaying power delay profile (PDP). Through simulations it is demonstrated that using RLS for channel equalization in a digital communication system it has an overall of 4 dB SNR gain as compared to LMS. Further more the convergence is almost same in case of LMS by increasing filter taps but at the cost of abrupt change in BER while in RLS the convergence time becomes slow by increasing filter length but with a small change in BER based performance.