A recursive parallel algorithm for acquisition of direct sequence spread spectrum signals with doppler
Paul G. Flikkema, L. Davisson · 1992
We consider the acquisition of direct sequence spread-spectrum signals with frequency and PN chip clock (spreading sequence) epoch uncertainty due to Doppler. Our objective is to address the problem in the context of low-powered radio networks where the Doppler effect induces both large initial uncertainty and considerable dynamics during the acquisition. This is applicable, for example, to networks with earth-based nodes communicating via a network of low-earth orbiting satellites. The proposed acquisition algorithm is recursive in the sense that Doppler estimation using a dynamic programming algorithm is performed jointly with detection of the PN epoch by active correlation. It is also parallel since at any time instant all possible PN epochs and carrier frequency offsets (within the limits of quantization) are tested simultaneously. Because of the Doppler dynamics, we employ coherent/incoherent detection, where the usual optimal detection is employed over short intervals and those results are combined incoherently. Because the Doppler affects both the carrier frequency and the chip clock rate, we must search for the PN epoch and actual carrier frequency over a 2-D uncertainty region. We quantize this region in both dimensions, so the estimated process evolves in time over a lattice. Our approach exploits the fact that the Doppler dynamics of the signal can be modeled as a Markov process. The process proceeds through the lattice, creating a trellis-like path. For this reason, we refer to it as the trellis algorithm. The performance analysis of the technique is based on second-order properties of the spreading sequences and channel noise. We obtain analytical results for the coherent/incoherent correlation statistics using two simplifying approximations, and provide validation of the approximations using an alternate direct derivation. Due to the recursive nature of the algorithm, a Monte Carlo simulation using the analytical results is used to determine numerical performance figures.