A maximum likelihood CDMA receiver using the EM algorithm and the discrete wavelet transform

A maximum likelihood (ML) method for joint estimation of amplitude, phase, time delay, and data demodulation in a single-user direct sequence spread spectrum communication system is developed. The likelihood function is analytically intractable, so a recursive estimation algorithm is considered. The expectation maximization (EM) algorithm has been used in similar problems, however, in this case it is not computationally efficient. A variant of the EM algorithm, called space alternating generalized EM (SAGE), has been derived. We apply the SAGE algorithm to the sequence estimation problem in a way which results in simple sequential updates of all the estimated parameters. An important feature of the proposed algorithm is the use of a discrete wavelet decomposition of the received signal as a sufficient statistic. The consequence is that all the information is still available to the receiver, while the complicated estimation problem is considerably simplified. Computer simulations of a single user system were performed. It is shown that the algorithm has a fast convergence, and essentially achieves optimal performance