eve Expansion of the WSSUS Channel Output and Its Application to Efficient Simulation

This paper derives a Karhunen-Lo` eve (K-L) expan- sion of the time-varying output of a multipath Rayleigh fading wide-sense-stationary uncorrelated-scattering (WSSUS) channel. It is shown that under the same mean-squared error condition, the number of terms required by the truncated K-L expansion is less than that of the series expansion obtained by using the discrete-path approximation of the channel so that simulation using the K-L expansion is more efficient. This computational advantage becomes more significant as higher simulation accu- racy is required. The derived K-L expansion is applied to develop an efficient simulation technique for digital transmission over a multipath Rayleigh fading WSSUS channel using an optimum receiver. We show that the proposed technique requires shorter computation time than two other known simulation techniques.