Low-Rank Spatial Channel Estimation for Millimeter Wave Cellular Systems

The tremendous bandwidth available in the millimeter wave frequencies above 10 GHz have made these bands an attractive candidate for next-generation cellular systems. However, reliable communication at these frequencies depends critically on beamforming with very high-dimensional antenna arrays. Estimating the channel sufficiently accurately to perform beamforming can be challenging due to both low coherence time and a large number of antennas. Also, the measurements used for channel estimation may need to be made with analog beamforming, where the receiver can "look" in only one direction at a time. This paper presents a novel method for estimation of the receive-side spatial covariance matrix of a channel from a sequence of power measurements made in different angular directions. It is shown that maximum likelihood estimation of the covariance matrix reduces to a non-negative matrix completion problem. We show that the non-negative nature of the covariance matrix reduces the number of measurements required when the matrix is low-rank. The fast iterative methods are presented to solve the problem. Simulations are presented for both single-path and multi-path channels using models derived from real measurements in New York City at 28 GHz.