Finite data record performance analysis of rapid synchronization and combined demodulation algorithms

We investigate the coarse synchronization performance of matched-filter-type (MF) and minimum-variance-distortion less-response-type (MF) near self-synchronized receivers for asynchronous direct-sequence code-division-multiple-access communications under finite data record adaptation. Analytic expressions are derived that approximate closely the probability of coarse synchronization error and provide low-cost highly-accurate alternatives to the computationally demanding performance evaluation through simulations. The expressions are explicit functions of the data record size N and the filter order p and reveal the effect of short-data-record sample-matrix-inversion (SMI) implementations on the coarse synchronization performance