Hybrid Precoding for Multiuser Millimeter Wave Massive MIMO Systems: A Deep Learning Approach

Abstract

In multi-user millimeter wave (mmWave) multipleinput-multiple-output (MIMO) systems, hybrid precoding is a crucial task to lower the complexity and cost while achieving a sufficient sum-rate. Previous works on hybrid precoding were usually based on optimization or greedy approaches. These methods either provide higher complexity or have sub-optimum performance. Moreover, the performance of these methods mostly relies on the quality of the channel data. In this work, we propose a deep learning (DL) framework to improve the performance and provide less computation time as compared to conventional techniques. In fact, we design a convolutional neural network for MIMO (CNN-MIMO) that accepts as input an imperfect channel matrix and gives the analog precoder and combiners at the output. The procedure includes two main stages. First, we develop an exhaustive search algorithm to select the analog precoder and combiners from a predefined codebook maximizing the achievable sum-rate. Then, the selected precoder and combiners are used as output labels in the training stage of CNN-MIMO where the input-output pairs are obtained. We evaluate the performance of the proposed method through numerous and extensive simulations and show that the proposed DL framework outperforms conventional techniques. Overall, CNN-MIMO provides a robust hybrid precoding scheme in the presence of imperfections regarding the channel matrix. On top of this, the proposed approach exhibits less computation time with comparison to the optimization and codebook based approaches.

A Stochastic Gradient Descent Approach for Hybrid mmWave Beamforming With Blockage and CSI-Error Robustness

“…In contrast with previously proposed solutions, in which perfect CSI is assumed [26]- [29], our method relies on conventional initial estimates of the channels' angles of departure and complex gains, and on statistical knowledge of the corresponding blockages [6]- [8], [10], [11] and estimation error probabilities [16]- [18]. The channel uncertainties, including path blockages and imperfect CSI, are captured jointly in a newly introduced Bernoulli-Gaussian model, which is used to generate the training data for the MSGD-based optimizer, altogether resulting in a stochastic learning beamforming solution that is robust to both types of impairments.…”

“…• In Subsection II-B, we incorporate into a Bernoulli-Gaussian probability density function (PDF) the statistical features of both path blockages [6]- [8], [10], [11] and CSI errors [16]- [18], resulting in an integrated stochastic mmWave channel model that enables both challenges to be addressed simultaneously. • In Subection IV, the designed learning rates to accelerate the convergence of the digital and analog beamforming problems are derived in closed-form, based on lower-bounds of the corresponding Lipschitz constants, and integrated with the results of the preceding subsection to compose the proposed scheme summarized in Algorithm 1.…”

“…Under the argument that accurate RF components at mmWave bands are expensive, cost reduction via the design of partially connected hybrid beamformers such as those in [14], [15] has been motivated. The same argument that lowercost RF components lead to various imperfections, which in turn can be counterweighted by robust hybrid designs, motivated works such as [16] in which the authors proposed that the alternating maximization of a smooth signal-tonoise-ratio (SNR)-driven optimization problem can be solved via orthogonal matching pursuit (OMP), for the realization of transceivers and amplify-and-forward (AF) relays with CSI uncertainty; in [17], a transmit beamforming scheme was designed via a fractional programming approach and was matched with a minimum mean square error (MMSE) receive beamformer to mitigate hardware and CSI imperfection; and [18] aimed to maximize the sum-rate under imperfect CSI feedback, employing a robust convolutional neural-network approach.…”

“…The first is that these methods are either digital or fully-connected hybrid radio architectures, which can be further extended to the partially-connected hybrid architecture 1 [12]- [16] owing to their lower costs and scalability advantages. The second is that these recent beamforming schemes, while assuming perfect knowledge of the channel coefficients when considering path blockages, deviate from earlier trends toward solutions that are robust against CSIerrors [16]- [18]. Therefore, it can be said that these first solutions have taken a well-justified scientific license for sacrificing CSI-error robustness and low-cost architectural premises in the design of mmWave beamforming schemes, with the goal of developing insights on combating the pathblockage problem.…”

Deep Channel Learning for Large Intelligent Surfaces Aided mm-Wave Massive MIMO Systems

“…In order to feed the deep network we use real, imaginary and the absolute value of each entry of the received signal. While the use of only real/imaginary components is still possible [10], it is shown in [17]- [20] that the use of "three-channel" data ameliorates the performance by enriching the features inherited in the input data. Let us define the input of the deep network as X DC and X CC for the direct and cascaded channel, respectively.…”