The spectrum scarcity at sub-6 GHz spectrum has made millimeter-wave (mmWave) frequency band a key component of the next-generation wireless networks. While mmWave spectrum offers extremely large transmission bandwidths to accommodate ever-increasing data rates, unique characteristics of this new spectrum need special consideration to achieve the promised network throughput. In this work, we consider the off-grid problem for mmWave communications, which has a significant impact on basic network functionalities involving beam steering and tracking. The off-grid effect naturally appears in compressed sensing (CS) techniques adopting a discretization approach for representing the angular domain. This approach yields a finite set of discrete angle points, which are an approximation to the continuous angular space, and hence degrade the accuracy of related parameter estimation. In order to cope with the off-grid effect, we present a novel parameter-perturbation framework to efficiently estimate the channel and the covariance for mmWave networks. The proposed algorithms employ a smart perturbation mechanism in conjunction with a low-complexity greedy framework of simultaneous orthogonal matching pursuit (SOMP), and jointly solve for the off-grid parameters and weights. Numerical results show a significant performance improvement through our novel framework as a result of handling the off-grid effects, which is totally ignored in the conventional sparse mmWave channel or covariance estimation algorithms.
Estimating the covariance is complicated due to the fact that only the signals pre-combined by the analog precombiner are available at the baseband. Based on the way the covariance matrix is estimated, it can be broadly categorized into two methods: 1) which we will refer as the indirect method, and 2) which we will refer as the direct method hereafter. The central idea in the indirect approach is to solve for the channel estimates for every successive snapshot and use these estimates to calculate the covariance matrix. Upon obtaining the channel estimates for every snapshot, the covariance calculation is relatively straightforward. However, in cases when the channel estimates are not required, then one can explicitly operate on the covariance of measurements directly to estimate the covariance matrix which is central to the latter approach. Both the and the problems can be posed as a compressed sensing (CS) problem leveraging the sparse nature of mmWave channels @cite_4 @cite_9 @cite_35 @cite_6 @cite_27 .
@cite_35 @cite_4 @cite_9 @cite_6 @cite_27
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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. 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. The tremendous bandwidth available in the millimeter wave frequencies above 10 GHz have made these bands an attractive candidate for next-generation cellular systems. However, reliable communication at these frequencies depends critically on beamforming with very high-dimensional antenna arrays. Estimating the channel sufficiently accurately to perform beamforming can be challenging due to both low coherence time and a large number of antennas. Also, the measurements used for channel estimation may need to be made with analog beamforming, where the receiver can “look” in only one direction at a time. This paper presents a novel method for estimation of the receive-side spatial covariance matrix of a channel from a sequence of power measurements made in different angular directions. It is shown that maximum likelihood estimation of the covariance matrix reduces to a non-negative matrix completion problem. We show that the non-negative nature of the covariance matrix reduces the number of measurements required when the matrix is low-rank. The fast iterative methods are presented to solve the problem. Simulations are presented for both single-path and multi-path channels using models derived from real measurements in New York City at 28 GHz. In high mobility applications of millimeter wave (mmWave) communications, e.g., vehicle-to-everything communication and next-generation cellular communication, frequent link configuration can be a source of significant overhead. We use the sub-6 GHz channel covariance as an out-of-band side information for mmWave link configuration. Assuming: (i) a fully digital architecture at sub-6GHz; and (ii) a hybrid analog-digital architecture at mmWave, we propose an out-of-band covariance translation approach and an out-of-band aided compressed covariance estimation approach. For covariance translation, we estimate the parameters of sub-6 GHz covariance and use them in theoretical expressions of covariance matrices to predict the mmWave covariance. For out-of-band aided covariance estimation, we use weighted sparse signal recovery to incorporate out-ofband information in compressed covariance estimation. The outof-band covariance translation eliminates the in-band training completely, whereas out-of-band aided covariance estimation relies on in-band as well as out-of-band training. We also analyze the loss in the signal-to-noise ratio due to an imperfect estimate of the covariance. The simulation results show that the proposed covariance estimation strategies can reduce the training overhead compared to the in-band only covariance estimation.