Exact and approximate maximum-likelihood parameter estimation for quasi-synchronous CDMA signals

In order to construct the optimal decorrelator for a quasi-synchronous (QS) code-division multiple-access receiver, it is necessary to estimate the user delays. However, in a QS system, it is shown that delay estimation is equivalent to estimating a parameter vector which is related linearly to the received signal. An exact maximum-likelihood (ML) solution using alternating maximization is first developed for joint estimation of the user delay vectors and amplitudes. Suboptimal recursive least squares (RLS) and least mean square algorithms are then presented which approximate the true ML solution. It is shown that the optimal decorrelator and demodulated symbols are also generated by the RLS algorithm. Simulation and analytical results are presented for the bit-error rate performance of the adaptive receiver, and the average squared error of the estimated delay vectors is compared with the Cramer-Rao bound.