Kronecker Product Correlation Model and Limited Feedback Codebook Design in a 3D Channel Model

A 2D antenna array introduces a new level of control and additional degrees of freedom in multiple-input-multiple-output (MIMO) systems particularly for the so-called "massive MIMO" systems. To accurately assess the performance gains of these large arrays, existing azimuth-only channel models have been extended to handle 3D channels by modeling both the elevation and azimuth dimensions. In this paper, we study the channel correlation matrix of a generic ray-based 3D channel model, and our analysis and simulation results demonstrate that the 3D correlation matrix can be well approximated by a Kronecker production of azimuth and elevation correlations. This finding lays the theoretical support for the usage of a product codebook for reduced complexity feedback from the receiver to the transmitter. We also present the design of a product codebook based on Grassmannian line packing.Comment: 6 pages, 5 figures, to appear at IEEE ICC 201

Limited Feedback Design for Interference Alignment on MIMO Interference Networks with Heterogeneous Path Loss and Spatial Correlations

Interference alignment is degree of freedom optimal in K -user MIMO interference channels and many previous works have studied the transceiver designs. However, these works predominantly focus on networks with perfect channel state information at the transmitters and symmetrical interference topology. In this paper, we consider a limited feedback system with heterogeneous path loss and spatial correlations, and investigate how the dynamics of the interference topology can be exploited to improve the feedback efficiency. We propose a novel spatial codebook design, and perform dynamic quantization via bit allocations to adapt to the asymmetry of the interference topology. We bound the system throughput under the proposed dynamic scheme in terms of the transmit SNR, feedback bits and the interference topology parameters. It is shown that when the number of feedback bits scales with SNR as C_{s}\cdot\log\textrm{SNR}, the sum degrees of freedom of the network are preserved. Moreover, the value of scaling coefficient C_{s} can be significantly reduced in networks with asymmetric interference topology.Comment: 30 pages, 6 figures, accepted by IEEE transactions on signal processing in Feb. 201

High-Dimensional Stochastic Gradient Quantization for Communication-Efficient Edge Learning

Edge machine learning involves the deployment of learning algorithms at the wireless network edge so as to leverage massive mobile data for enabling intelligent applications. The mainstream edge learning approach, federated learning, has been developed based on distributed gradient descent. Based on the approach, stochastic gradients are computed at edge devices and then transmitted to an edge server for updating a global AI model. Since each stochastic gradient is typically high-dimensional (with millions to billions of coefficients), communication overhead becomes a bottleneck for edge learning. To address this issue, we propose in this work a novel framework of hierarchical stochastic gradient quantization and study its effect on the learning performance. First, the framework features a practical hierarchical architecture for decomposing the stochastic gradient into its norm and normalized block gradients, and efficiently quantizes them using a uniform quantizer and a low-dimensional codebook on a Grassmann manifold, respectively. Subsequently, the quantized normalized block gradients are scaled and cascaded to yield the quantized normalized stochastic gradient using a so-called hinge vector designed under the criterion of minimum distortion. The hinge vector is also efficiently compressed using another low-dimensional Grassmannian quantizer. The other feature of the framework is a bit-allocation scheme for reducing the quantization error. The scheme determines the resolutions of the low-dimensional quantizers in the proposed framework. The framework is proved to guarantee model convergency by analyzing the convergence rate as a function of the quantization bits. Furthermore, by simulation, our design is shown to substantially reduce the communication overhead compared with the state-of-the-art signSGD scheme, while both achieve similar learning accuracies