Joint maximum-likelihood data and bit synchronization epoch estimation for burst direct sequence spread-spectrum transmission

We derive the optimal joint maximum-likelihood (ML) estimator of the bit synchronization epoch and data bit values for a short burst direct-sequence spread-spectrum (DSSS) transmission, for both the white and colored noise environments. The DSSS signal is assumed already downconverted and despread. We show that the additional computational burden incurred by using the estimator derived for the colored noise case is not justified. We then develop a fast acquisition suboptimal algorithm and analyze its performance. The suboptimal algorithm reduces the computational cost by more than one order of magnitude on the average, at no accuracy expense for carrier-to-noise ratios which insure the reliable estimation of the carrier phase, carrier Doppler and spreading code epoch.