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.
The spatial covariance exploits the relatively stationary long-term statistics of the propagation channel, and it can be leveraged for precoder design in mmWave networks @cite_37 @cite_17 @cite_2 @cite_25 @cite_33 . The rationale behind the use of spatial covariance matrix are two-fold. Firstly, in many cases, the angular coherence time (several seconds or more) is much longer than the channel coherence time (several milliseconds) @cite_18 @cite_37 . As a result, the angular and average power features of the channel can be assumed to be time-invariant, resulting in the spatial covariance matrix to be constant across many channel coherence intervals. Secondly, the spatial covariance matrix is frequency invariant, due to the significant angular congruence across the frequency bands @cite_36 @cite_27 , which is important for a wideband system where a common analog precoder can be shared across different sub-carriers. These reasons make the spatial covariance based precoding particularly attractive: once the RF beamformer is designed based on the channel covariance, it need not be updated every time instant. We would like to refer the reader to the works @cite_25 @cite_17 @cite_37 @cite_33 for a comprehensive discussion on the spatial covariance estimation for mmWave HADB MIMO architectures.
@cite_37 @cite_18 @cite_33 @cite_36 @cite_27 @cite_2 @cite_25 @cite_17
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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. 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. Spatial channel covariance information can replace instantaneous full channel state information for designing hybrid analog digital precoders. Estimating the spatial channel covariance is challenging due to the inherent limitation of the hybrid architecture, i.e., much fewer radio frequency (RF) chains than antennas. In this paper, we propose a spatial channel covariance estimation method for spatially sparse time-varying frequency-selective channels. The proposed method leverages the fact that the channel can be represented as a low-rank higher-order tensor. Numerical results demonstrate that the proposed approach achieves higher estimation accuracy in comparison with existing covariance estimation methods.