Low Complexity High Resolution Maximum Likelihood Channel Estimation in Spread Spectrum Navigation Systems

Traditionally, the low complexity maximum likelihood (ML) estimation of several closely-spaced superimposed signal replicas in a communications or navigation receiver is performed using expectation maximization (EM) or space alternating generalized expectation maximization (SAGE) methods. However, the componentwise decomposition of a multidimensional log-likelihood function according to the EM or SAGE algorithm fails for realistic time-variant channels. Thus, we consider the minimization of a multidimensional log likelihood function for the closely-spaced channel delays. To get this log-likelihood function, we use a decomposition of the highly time-variant channel path phasors based on Slepian´s subspaces. The obtained log likelihood function enables a coherent averaging over several hundred codewords even for high-mobility receivers. Therefore, we avoid the squaring loss (SL) that appears for the conventional incoherent averaging and incoherent log-likelihood functions. Our simulations show that the minimization of coherent log-likelihood functions based on Slepian´s functions yields a root mean square error (RMSE) of the line of sight (LOS) delay estimation that approximates the Cramer-Rao bound (CRB) rather closely.