Non-Coherent Estimator-Correlators for Unresolved Multipath Ricean Channels

Abstract—This paper considers detection techniques for unresolved Ricean/Rayleigh fading multipath channels. It is wellknown that the optimal receiver has an estimator-correlator form, with a Minimum Mean-Square Error (MMSE) estimate. With known multipath delays and unknown specular phases, the Ricean non-coherent multipath channel is a case where the received noiseless signal process is non-Gaussian, and the MMSE estimator is non-linear in the observation. This work presents novel, explicit expressions for such a MMSE estimator. It is shown that the MMSE estimate has the same multipath format as the noiseless received signal, with the unknown parameters replaced by corresponding estimates. The MMSE estimator scales down contributions from specular multipath components with poor phase estimates, reducing their effect on the detection process. The estimator includes a multipath decorrelation operation which is essential to avoid error floors over unresolved multipath channels. Based on matched filter bounds, it is shown that little degradation gains are obtained by employing suboptimal linear estimator-correlators, provided that they include the decorrelation operation.