Channel modeling for spread spectrum via evolutionary transform

Given the importance of direct sequence spread spectrum (DSSS) communications, the modeling of its transmission channel is of great interest. Due to multipath and Doppler effects in the transmission channel, the transmitted signal is spread in both time and frequency. Transmission channels that spread the message in time and frequency are modeled as random, time-varying systems. It is shown that the estimation of the parameters of such models is possible by means of the spreading function which is related to the time-varying frequency response of the system and the associated evolutionary kernel of the DSSS signal. Applying the time-frequency or frequency-frequency discrete evolutionary transforms, we show how to compute the spreading function from the received DSSS signal. The procedure is efficiently implemented with the discrete evolutionary transform. Once the number of paths, delays, Doppler frequencies and gains characterizing the channel are found, we use this information to obtain an estimate of the pseudo-noise and a decision parameter to determine the bit sent. Our procedure is illustrated with simulations of the process, and the corresponding bit-error rate.