In this paper, a maximum likelihood (ML) method is presented for joint estimation of amplitude, phase, time delay, and data symbols in a single-user direct-sequence spread-spectrum communication system. Since maximization of the likelihood function is analytically intractable, a novel coordinate ascent algorithm is used to obtain sequential updates of the data symbols and all unknown nuisance parameters. The novelty of the algorithm is due to the use of a multiresolution expansion of the received signal and the use of polynomial rooting in the complex plane in place of a line search over the signal delay parameter. The multiresolution structure of the algorithm is exploited to reduce sensitivity to impulsive noise via wavelet thresholding. Computer simulations of the single-user system show that the algorithm has fast convergence, and comparison with theoretical lower bounds establishes that the algorithm achieves nearly optimal error performance.
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