In this paper, we tackle channel estimation in millimeter-wave hybrid multiple-input multiple-output systems by considering off-grid effects. In particular, we assume that spatial parameters can take any value in the angular domain, and need not fall on predefined discretized angles. Instead of increasing the number of discretized points to combat off-grid effects, we use implicit Dirichlet kernel structure in the Fourier domain, which conventional compressed sensing methods do not use. We propose greedy low-complexity algorithms based on orthogonal matching pursuit (OMP); our core idea is to traverse the Dirichlet kernel peak using estimates of the discrete Fourier transform. We demonstrate the efficacy of our proposed algorithms compared to standard OMP reconstruction. Numerical results show that our proposed algorithms obtain smaller reconstruction errors when off-grid effects are accounted for.
The virtual channel model describes the channel with respect to (w.r.t.) fixed basis functions corresponding to spatial angles within a finite discrete dictionary. In other words, the continuous parameter space of spatial angular features is discretized into a finite set of pre-defined spatial angles, which emphasizes the sparse representation of the MIMO channels. The estimation accuracy of CS methods based on this discretization is limited by the number of points in the dictionary. Although this discretization procedure yields state-of-art performance, it has several intrinsic disadvantages @cite_11 , including the .
@cite_11
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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. Spatial channel covariance information can replace full knowledge of the entire channel matrix for designing analog precoders in hybrid multiple-input-multiple-output (MIMO) architecture. Spatial channel covariance estimation, however, is challenging for the hybrid MIMO architecture because the estimator operating at baseband can only obtain a lower dimensional pre-combined signal through fewer radio frequency chains than antennas. In this paper, we propose two approaches to covariance estimation based on compressive sensing techniques. One is to apply a time-varying sensing matrix, and the other is to exploit the prior knowledge that the covariance matrix is Hermitian. We present the rationale behind the two ideas and validate the superiority of the proposed methods by theoretical analysis and numerical simulations. We conclude the paper by extending the proposed algorithms from narrowband MIMO systems with a single receive antenna to wideband systems with multiple receive antennas. Spatial channel covariance information can replace full channel state information for designing analog precoders in millimeter wave (mmWave) hybrid MIMO systems. Hybrid MIMO architectures, however, make it challenging to estimate the spatial channel covariance matrix because the estimator in baseband can only see the low-dimensional projections of the original channel. In this paper, we propose two key ideas for developing the covariance estimation techniques based on compressive sensing techniques. One is to use the Hermitian property of the covariance matrix, and the other is to use a time-varying analog combining matrix to effectively extend the measurement size. Millimeter (mm) wave massive MIMO has the potential for delivering orders of magnitude increases in mobile data rates, with compact antenna arrays providing narrow steerable beams for unprecedented levels of spatial reuse. A fundamental technical bottleneck, however, is rapid spatial channel estimation and beam adaptation in the face of mobility and blockage. Recently proposed compressive techniques which exploit the sparsity of mm wave channels are a promising approach to this problem, with overhead scaling linearly with the number of dominant paths and logarithmically with the number of array elements. Further, they can be implemented with RF beamforming with low-precision phase control. However, these methods make implicit assumptions on long-term phase coherence that are not satisfied by existing hardware. In this paper, we propose and evaluate a noncoherent compressive channel estimation technique which can estimate a sparse spatial channel based on received signal strength (RSS) alone, and is compatible with off-the-shelf hardware. The approach is based on cascading phase retrieval (i.e., recovery of complex-valued measurements from RSS measurements, up to a scalar multiple) with coherent compressive estimation. While a conventional cascade scheme would multiply two measurement matrices to obtain an overall matrix whose entries are in a continuum, a key novelty in our scheme is that we constrain the overall measurement matrix to be implementable using coarsely quantized pseudorandom phases, employing a virtual decomposition of the matrix into a product of measurement matrices for phase retrieval and compressive estimation. Theoretical and simulation results show that our noncoherent method scales almost as well with array size as its coherent counterpart, thus inheriting the scalability and low overhead of the latter.