Spread spectrum sequence estimation and bit synchronization using an EM-type algorithm

The maximum likelihood (ML) estimation method for simultaneous amplitude, time delay, and data demodulation in direct sequence spread spectrum communication is proposed. The likelihood function is analytically intractable, so we consider a recursive estimation algorithm. The expectation-maximization (EM) algorithm has found increasing use in similar problems, however, for this case it is analytically intractable. 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 allows for simple sequential updates of the parameters. The resulting algorithm maximizes the penalized likelihood function, where the penalty is chosen to ensure good synchronization performance. Simulation results show that the algorithm has fast convergence, and essentially achieves optimal performance