Message passing-based sparse channel estimation under partially coherent Wiener phase errors

Compressive sensing (CS) is key to reduce the overhead in estimating sparse high dimensional channels at millimeter wave or terahertz frequencies. The channel measurements in CS are usually perturbed by random phase errors, commonly modeled as a Wiener process, at the oscillators. CS algorithms that ignore such phase errors fail to accurately estimate the channel. In practice, the phase errors are similar within a batch of measurements acquired in a short burst and the errors vary significantly across different batches, resulting in partially coherent measurements. We develop a message passing-based channel estimation algorithm that exploits the sparse structure of the channel together with the Wiener statistics of the phase errors. To this end, we absorb the phase errors into the sparse channel, and introduce three hidden variables to model its support, magnitude, and phase. We derive the message flows between these variables while incorporating Wiener phase noise statistics. Finally, we use alternating optimization to decouple the sparse channel and the phase errors from the vector estimated with our message-passing technique. Using simulations, we show that the proposed algorithm achieves better channel reconstruction than comparable benchmarks.