Estimation of MC-DS-CDMA Fading Channels Based on Kalman Filtering with High Order Autoregressive Models

Abstract

This paper deals with the estimation of rapidly time- varying Rayleigh fading channels in synchronous multi-carrier direct-sequence code division multiple access (MC-DS-CDMA) systems. When the fading channel is approximated by an autoregressive (AR) process, it can be estimated by means of Kalman filtering for instance. Nevertheless, this requires the a priori estimation of the AR parameters. One standard solution consists in first fitting the AR process autocorrelation function to the Jakes one and then solving the resulting Yule-Walker equations (YWE). However, due to the band-limited nature of the Jakes Doppler spectrum, severely ill-conditioned YWE are unavoidable for all but very small AR model orders. Therefore, previous studies focused only on 1st and 2nd order AR models. To overcome the ill-conditioning problem, a very small positive bias can be added to the main diagonal of the autocorrelation matrix in the YWE. Even if the resulting process is not band-limited and corresponds to an AR process+noise model, the approximation can be of interest. Indeed, according to our simulation results, high-order AR models+noise yield significant results in terms of spectrum approximation and bit error rate (BER). However, to reduce the computational cost, a 5th order AR model can be considered.