Channel Estimation via Orthogonal Matching Pursuit for Hybrid MIMO Systems in Millimeter Wave Communications

We propose an efficient open-loop channel estimator for a millimeter-wave (mm-wave) hybrid multiple-input multiple-output (MIMO) system consisting of radio-frequency (RF) beamformers with large antenna arrays followed by a baseband MIMO processor. A sparse signal recovery problem exploiting the sparse nature of mm-wave channels is formulated for channel estimation based on the parametric channel model with quantized angles of departures/arrivals (AoDs/AoAs), called the angle grids. The problem is solved by the orthogonal matching pursuit (OMP) algorithm employing a redundant dictionary consisting of array response vectors with finely quantized angle grids. We suggest the use of non-uniformly quantized angle grids and show that such grids reduce the coherence of the redundant dictionary. The lower and upper bounds of the sum-of-squared errors of the proposed OMP-based estimator are derived analytically: the lower bound is derived by considering the oracle estimator that assumes the knowledge of AoDs/AoAs, and the upper bound is derived based on the results of the OMP performance guarantees. The design of training vectors (or sensing matrix) is particularly important in hybrid MIMO systems, because the RF beamformer prevents the use of independent and identically distributed random training vectors, which are popular in compressed sensing. We design training vectors so that the total coherence of the equivalent sensing matrix is minimized for a given RF beamforming matrix, which is assumed to be unitary. It is observed that the estimation accuracy can be improved significantly by randomly permuting the columns of the RF beamforming matrix. The simulation results demonstrate the advantage of the proposed OMP with a redundant dictionary over the existing methods such as the least squares method and the OMP based on the virtual channel model.