Joint maximum-likelihood parameter estimation for burst DS spread-spectrum transmission

We first derive the joint optimal maximum-likelihood (ML) estimator of the carrier phase, both Doppler shift and Doppler rate, and the spreading code delay for a short burst direct sequence/spread spectrum (DS/SS) transmission in the absence of the data modulation. The typical burst duration is three data bit periods (60 ms). The performance of the joint estimator is analytically derived separately for high and low carrier-to-noise ratio (CNR) values. A suboptimal ML estimator based on the method of averaged periodogram is proposed for the data modulation present case, allowing the joint estimation of the data bit values. Then the above parameters are assumed correctly estimated and a segmentation approach is adopted, deriving the optimal joint ML estimator for the bit synchronization epoch and data. Simulations show the joint estimators perform reliable down to a CNR of approximately 30 dB·Hz