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.
In the literature, several CS approaches have been utilized to estimate the channel and the spatial covariance. For the indirect approach, the channel estimates can be obtained using the SMV CS techniques such as @cite_9 @cite_35 . However, these SMV techniques fail to exploit the common support of the channel estimates across different snapshots. The common support across multiple snapshots is due to the invariant angular domain features across multiple snapshots which is central to the use of spatial covariance matrix. The MMV techniques can exploit this common support structure; however, most of the MMV techniques are designed with sensing matrix fixed over all the snapshots making it inefficient for matrices. The statistical problem of covariance estimation can be approached by explicitly estimating the covariance using the measurement covariance space. Strategies such as MUSIC @cite_43 and ESPRIT @cite_8 algorithms can be adopted but these methods fail to leverage the channel sparsity. Recently, a CS MMV based covariance estimation for the time-varying sensing matrices has been proposed in @cite_6 and a tensor-based decomposition approach has been proposed in @cite_21 . Further CS algorithms for the direct approach of spatial covariance estimation can be found in @cite_33 @cite_6 @cite_27 @cite_12 @cite_21
@cite_35 @cite_33 @cite_8 @cite_9 @cite_21 @cite_6 @cite_43 @cite_27 @cite_12
2784857961 2963304087 2592085864 2601789736
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. 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. By stacking layers of convolution and nonlinearity, convolutional networks (ConvNets) effectively learn from lowlevel to high-level features and discriminative representations. Since the end goal of large-scale recognition is to delineate complex boundaries of thousands of classes, adequate exploration of feature distributions is important for realizing full potentials of ConvNets. However, state-of-theart works concentrate only on deeper or wider architecture design, while rarely exploring feature statistics higher than first-order. We take a step towards addressing this problem. Our method consists in covariance pooling, instead of the most commonly used first-order pooling, of highlevel convolutional features. The main challenges involved are robust covariance estimation given a small sample of large-dimensional features and usage of the manifold structure of covariance matrices. To address these challenges, we present a Matrix Power Normalized Covariance (MPNCOV) method. We develop forward and backward propagation formulas regarding the nonlinear matrix functions such that MPN-COV can be trained end-to-end. In addition, we analyze both qualitatively and quantitatively its advantage over the well-known Log-Euclidean metric. On the ImageNet 2012 validation set, by combining MPN-COV we achieve over 4 , 3 and 2.5 gains for AlexNet, VGG-M and VGG-16, respectively; integration of MPN-COV into 50-layer ResNet outperforms ResNet-101 and is comparable to ResNet-152. The source code will be available on the project page: http: www.peihuali.org MPN-COV.