Frame-theoretic Precoding and Beamforming Design for Robust mmWave Channel Estimation

We propose a new method for the design of TX-precoders and RX-beamformers to improve the robustness of millimeter wave (mmWave) channel estimation, focusing on a frame-theoretic approach and a sparse formulation of the mmWave channel estimation problem. Concretely, the high-level design criteria of the transmit precoders and receive beamformers are modeled through a single frame, while their practical realization is achieved by distributed frames, related to the latter by the Kronecker product. We prove that the desirable frame properties are invariant to the derived Kronecker decomposition allowing for the same strategy to be applicable both in the design of a joint measurement matrix - leading to optimal but theoretical-only performance - as well as in the design of practical TX/RX precoding/beamforming matrices. Simulations outline both the improvement achieved by the proposed scheme against the state-of-the-art, as well as its trend towards optimality for systems with large number of antennas and/or subjected to high noise variances.