Coordinated Uplink Precoding for Spatially Consistent mmWave Channel Covariance Measurements

We are interested in deducing whether two users in a cellular system are at nearby physical locations from measuring similarity of their covariance matrices at a base station. This becomes challenging in multiple-input-multiple-output mmWave channels, as the semi-optical nature of mmWave radio propagation gives rise to non-Kronecker correlation. Hence, the estimated BS covariance matrix depends on the UE pilot beamformer, and moreover, on the direction of movement in the radio environment. A coordinated UE pilot transmission approach is needed to make measured covariances spatially consistent. We formulate the UE pilot beamformer selection problem as an optimization problem aiming to preserve the spatial consistency of a set of UEs moving in the same large-scale radio environment. We use the collinearity matrix distance to measure the similarity of the BS covariance matrices of UEs in the radio environment. Covariance matrix and instantaneous channel state based UE pilot beamformers with different ranks are considered. Simulations are used to evaluate the spatial consistency provided by coordinated uplink precoding methods. Depending on the expected signal-to-noise ratio, there is an optimal rank for the UE pilot transmission, which maximizes the similarity between covariances estimated from transmissions of different UEs in the same large-scale fading environment.