Ilan Sharfer and Alfred O. Hero III. A Maximum Likelihood Digital Receiver Using Coordinate Ascent and the Discrete Wavelet Transform

ABSTRACT
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 multi-resolution 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 multi-resolution 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 to theoretical lower bounds
establishes that the algorithm achieves nearly optimal error performance.

Key Words: Wireless communications, sequence estimation, bit synchronization, carrier phase
recovery, impulsive noise mitigation.

Submitted to IEEE Trans. on Signal Processing (1996)