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.
A natural yet inefficient approach to reduce off-grid effects is to increase the number of discretized points, corresponding to increased grid resolution. This approach not only increases the mutual coherence of the dictionary matrix, leading to loss of the restricted isometric property, but also increases the problem dimension, which requires more computation @cite_8 . An alternative is to tackle off-grid effects upfront without increasing the grid size. For example, in the context of channel estimation, @cite_8 provide a controlled perturbation mechanism for spatial angular parameters based on orthogonal matching pursuit (OMP) @cite_6 . Other related works involve an improved off-grid sparse Bayesian algorithm @cite_15 , and a grid-less CS technique developed via atomic norm minimization @cite_3 . Although these methods all tackle off-grid issues, they are computationally prohibitive, which motivates us to develop and analyze robust low-complexity channel estimation algorithms that account for off-grid effects.
@cite_15 @cite_3 @cite_6 @cite_8
2339667469 2957141087 2151381597 2406740263
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. 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. We show that the maximization of the sum degrees-of-freedom for the static flat-fading multiple-input multiple-output (MIMO) interference channel is equivalent to a rank constrained rank minimization problem (RCRM), when the signal spaces span all available dimensions. The rank minimization corresponds to maximizing interference alignment (IA) so that interference spans the lowest dimensional subspace possible. The rank constraints account for the useful signal spaces spanning all available spatial dimensions. That way, we reformulate all IA requirements to requirements involving ranks. Then, we present a convex relaxation of the RCRM problem inspired by recent results in compressed sensing and low-rank matrix completion theory that rely on approximating rank with the nuclear norm. We show that the convex envelope of the sum of ranks of the interference matrices is the normalized sum of their corresponding nuclear norms and introduce tractable constraints that are asymptotically equivalent to the rank constraints for the initial problem. We also show that our heuristic relaxation can be tuned for the multi-cell interference channel. Furthermore, we experimentally show that in many cases the proposed algorithm attains perfect interference alignment and in some cases outperforms previous approaches for finding precoding and zero-forcing matrices for interference alignment. The goal of sparse recovery is to recover a k-sparse signal x e Rn from (possibly noisy) linear measurements of the form y = Ax, where A e Rmxn describes the measurement process. Standard results in compressive sensing show that it is possible to recover the signal x from m = O(k log(n k)) measurements, and that this bound is tight. The framework of model-based compressive sensing [BCDH10] overcomes the lower bound and reduces the number of measurements further to O(k) by limiting the supports of x to a subset M of the (nk) possible supports. This has led to many measurement-efficient algorithms for a wide variety of signal models, including block-sparsity and tree-sparsity. Unfortunately, extending the framework to other, more general models has been stymied by the following obstacle: for the framework to apply, one needs an algorithm that, given a signal x, solves the following optimization problem exactly: [EQUATION] (here x[n] denotes the projection of x on coordinates not in Ω). However, an approximation algorithm for this optimization task is not sufficient. Since many problems of this form are not known to have exact polynomial-time algorithms, this requirement poses an obstacle for extending the framework to a richer class of models. In this paper, we remove this obstacle and show how to extend the model-based compressive sensing framework so that it requires only approximate solutions to the aforementioned optimization problems. Interestingly, our extension requires the existence of approximation algorithms for both the maximization and the minimization variants of the optimization problem. Further, we apply our framework to the Constrained Earth Mover's Distance (CEMD) model introduced in [SHI13], obtaining a sparse recovery scheme that uses significantly less than O(k log(n k)) measurements. This is the first non-trivial theoretical bound for this model, since the validation of the approach presented in [SHI13] was purely empirical. The result is obtained by designing a novel approximation algorithm for the maximization version of the problem and proving approximation guarantees for the minimization algorithm described in [SHI13].