In wireless communications, the channel is typically modeled as a random, linear, time-varying system that spreads the transmitted signal in both time and frequency due to multipath propagation and Doppler effects. Estimated channel parameters allow system designers to develop coherent receivers that increase the system performance. In this paper, we show how time-frequency analysis can be used to model and estimate the time-varying channel of a multi-carrier spread spectrum (MCSS) system using a complex quadratic sequence as the spreading code. We will show that for this spreading code, the effects of time delays and Doppler frequency shifts, caused by the mobility of environment objects, can be combined and represented effectively as time shifts. The discrete evolutionary transform (DET), as a time-frequency analysis method, enables us to estimate the effective time shifts via a spreading function and to use them to equalize the channel. Using the effective time shifts, the time-varying channel can be represented simply as linear-time invariant system by embedding the Doppler shifts that characterize the time-varying channel into effective time shifts. The channel parameters are used to estimate the data bit sent. To illustrate the performance of the proposed method we perform several simulations with different levels of channel noise, jammer interference, and Doppler frequency shifts. (c) 2005 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.