Subspace Tracking and Least Squares Approaches to Channel Estimation in Millimeter Wave Multiuser MIMO

The problem of multiple-input multiple-output (MIMO) channel estimation at millimeter-wave frequencies, both in single-user setting and in multi-user setting, is tackled in this paper. Using a subspace approach, we develop a protocol enabling the estimation of the right (respectively, left) singular vectors at the transmitter (respectively, receiver) side; then, we adapt the projection approximation subspace tracking with deflation and the orthogonal Oja algorithms to our framework and obtain two-channel estimation algorithms. We also present an alternative algorithm based on the least squares approach. The hybrid analog/digital nature of the beamformer is also explicitly taken into account at the algorithm design stage. In order to limit the system complexity, a fixed analog beamformer is used at both sides of the communication links. The obtained numerical results, showing the accuracy in the estimation of the channel matrix dominant singular vectors, the system achievable spectral efficiency, and the system bit error rate, prove that the proposed algorithms are effective and that they compare favorably, in terms of the performance-complexity tradeoff, with respect to several competing alternatives.