Hybrid Beamforming for Millimeter Wave Systems Using the MMSE Criterion

Abstract

Hybrid analog and digital beamforming (HBF) has recently emerged as an attractive technique for millimeter-wave (mmWave) communication systems. It well balances the demand for sufficient beamforming gains to overcome the propagation loss and the desire to reduce the hardware cost and power consumption. In this paper, the mean square error (MSE) is chosen as the performance metric to characterize the transmission reliability. Using the minimum sum-MSE criterion, we investigate the HBF design for broadband mmWave transmissions. To overcome the difficulty of solving the multi-variable design problem, the alternating minimization method is adopted to optimize the hybrid transmit and receive beamformers alternatively. Specifically, a manifold optimization based HBF algorithm is firstly proposed, which directly handles the constant modulus constraint of the analog component. Its convergence is then proved. To reduce the computational complexity, we then propose a low-complexity general eigenvalue decomposition based HBF algorithm in the narrowband scenario and three algorithms via the eigenvalue decomposition and orthogonal matching pursuit methods in the broadband scenario. A particular innovation in our proposed alternating minimization algorithms is a carefully designed initialization method, which leads to faster convergence. Furthermore, we extend the sum-MSE based design to that with weighted sum-MSE, which is then connected to the spectral efficiency based design. Simulation results show that the proposed HBF algorithms achieve significant performance improvement over existing ones, and perform close to full-digital beamforming.Index Terms-Millimeter-wave (mmWave) communications, Minimum mean square error (MMSE), Hybrid analog and digital beamforming (HBF), Alternating optimization, Manifold optimization (MO)

Beamforming Design for Large-Scale Antenna Arrays Using Deep Learning

“…For example, in the broadband scenario, by concatenating the multi-tap channel vectors as the input and redefining the loss function to the one related to the broadband SE [4], the BFNN can be extended to optimize the analog beamformer for broadband mmWave channels. For another example, considering the HBF problem with multiple RF chains, while the optimal digital beamformer can be solved with a closed-form solution [3], [5], a simple extension of the current BFNN is to increase the output dimensions from N t to N RF N t for the N t × N RF analog BF matrix with a new loss function. Following the similar idea, the BFNN can also be considered in the joint transmit and receive BF design or the multi-user BF design.…”

“…However, the analog beamformer is limited to a pre-defined codebook. To enhance the performance of OMP, the manifold optimization method was applied in [3], [4] for the analog BF optimization. An element wise iterative algorithm was proposed in [5] to optimize the analog beamformer.…”

“…• Second, through a large number of training iterations with a lot of samples, the DL-based schemes have been shown to have the ability to understand the complicated characteristics of wireless channels [6]. Compared with the conventional works assuming perfect CSI [1], [3]- [5], the DL based approach is expected to possess strong robustness to imperfect CSI. • Most efficient traditional BF algorithms require timeconsuming serial iterations with high-complexity [4], [5].…”

“…By doing so, in the second online deployment stage, the BFNN can adapt itself to imperfect CSI and achieve robust performance to channel estimation errors. Since in the mmWave HBF design the optimal digital beamformer normally has a closed-form solution [3]- [5], as an initial work and for the easy of presentation, in this letter we focus on the analog BF design and consider the scenario of a large-scale antenna array with only one radio frequency (RF) chain. Fig.…”

Hybrid Precoding Design for Reconfigurable Intelligent Surface Aided mmWave Communication Systems

“…While mmWave suffers from severe path loss, their small wavelength allows the deployment of a large-scale antenna array to provide the high array gain and improve the link quality. Nevertheless, unlike sub-6 GHz communications where fully-digital (FD) processing is employed, the prohibitive cost and power consumption of the hardware components in mmWave bands make the analog-digital hybrid processing a viable solution to reduce the number of power-hungry radio frequency (RF) chains at the mmWave base-station (BS) [1].…”