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
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In this letter, an angle domain off-grid channel estimation algorithm for the uplink millimeter wave (mmWave) massive multiple-input and multiple-output systems is proposed. By exploiting spatial sparse structure in mmWave channels, the proposed method is capable of identifying the angles and gains of the scatterer paths. Comparing the conventional channel estimation methods for mmWave systems, the proposed method achieves better performance in terms of mean square error. Numerical simulation results are provided to verify the superiority of the proposed algorithm. In millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems, channel estimation in the presence of sparse multipath fading boils down to two-dimensional (2D) direction-of-arrival (DOA) estimation followed by path gain estimation. To achieve super-resolution angle estimation at affordable complexity, this paper develops an efficient channel estimation approach by applying a truncated atomic norm minimization (T-ANM) technique, which is implemented via partial antenna activation during training-based channel estimation. This technique makes use of a key observation that the sparse scattering characteristics of mmWave MIMO channel gives rise to a low-rank two-level Toeplitz structure in the angular domain. Because of the low-rank property, only a subset of the transceiver antennas needs to be activated to save training resources. Meanwhile, the Toeplitz structure enables ANM-based gridless 2D DOA estimation via reduced-size semidefinite programming. Simulation results show that the proposed reduced-size method can achieve comparable spectral efficiency as the full-size benchmark method at much lower computational complexity and shorter sensing time. This paper demonstrates theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal. This is a massive improvement over previous results, which require O(m2) measurements. The new results for OMP are comparable with recent results for another approach called basis pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems. The millimeter-wave (mmWave) communications is a promising technology for next-generation wireless networks with its available broad spectrum. Along with massive number of antennas employed at both end of the transceiver, the number of unknown channel coefficients become extremely large. Thanks to sparse nature of mmWave links, this paper proposes a parameter perturbation based sparse recovery technique for mmWave channel estimation. Recently, classical compressive sensing (CS) based sparse recovery techniques have been applied in this area. However, CS based reconstructions are highly effected by basis mismatch problems such as off-the-grid targets, or, equivalently, scattering points. The proposed iterative algorithm called parameter perturbed orthogonal matching pursuit (PPOMP) jointly solves for both the sparse signal, which is the unknown mmWave channel itself, and the basis mismatch due to off-the-grid problem. We verify through extensive numerical results that the proposed PPOMP algorithm achieves significantly better channel estimation performance compared to the state of the art sparse reconstruction techniques.