Hybrid Beamforming for Millimeter Wave Systems Using the MMSE Criterion (1902.08343v1)

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.

• The paper proposes a series of hybrid beamforming algorithms for millimeter-wave systems based on the Minimum Mean Square Error (MMSE) criterion, offering an alternative to spectral efficiency maximization.
• It introduces manifold optimization and low-complexity eigenvalue decomposition methods to optimize hybrid transmit and receive beamformers, utilizing a novel initialization method to speed up convergence.
• Numerical results show the proposed algorithms achieve near-optimal performance compared to full-digital systems, significantly reducing Mean Square Error (MSE) and enhancing transmission reliability.

Hybrid Beamforming for Millimeter Wave Systems Using the MMSE Criterion

The paper "Hybrid Beamforming for Millimeter Wave Systems Using the MMSE Criterion" addresses the challenges of designing hybrid beamforming (HBF) systems for millimeter-wave (mmWave) communications, a crucial technology for the realization of 5G networks. The goal of HBF is to balance the increasing demand for beamforming gain with the need to limit hardware complexity and power consumption. To this end, the authors explore a design approach using the minimum mean square error (MMSE) criterion.

Summary and Numerical Results

The paper proposes a series of algorithms for HBF under the MMSE framework, distinguishing itself from the typically more employed spectral efficiency maximization. By leveraging the MMSE criterion, the work seeks to optimize both the transmit and receive ends of the communication system to ensure reliable data transmission in a broadband mmWave MIMO environment.

The authors introduce a manifold optimization-based algorithm for HBF, specifically designed to address the complex task of simultaneously optimizing hybrid transmit and receive beamformers under a non-convex constant modulus constraint for the analog components. The convergence of this algorithm is rigorously demonstrated.

In scenarios where computational complexity is a concern, the paper details several low-complexity alternative algorithms. These include a general eigenvalue decomposition-based algorithm for narrowband HBF and three different methods for broadband systems using eigen decomposition and orthogonal matching pursuit. A particular innovation across these algorithms is an initialization method that significantly speeds up convergence.

The numerical results indicate that the proposed HBF solutions demonstrate a marked improvement in performance compared to existing ones, showing close-to-optimal results relative to full-digital beamforming systems. This is quantified through significant reductions in mean square error (MSE), leading to enhanced transmission reliability.

Implications and Future Directions

The implications of this research are significant for practical mmWave communications, suggesting that systems can achieve near-optimal performance using hybrid designs that are computationally feasible and hardware efficient. This has potential impact not only in 5G implementations but also in future wireless standards where bandwidth demands will continue to grow.

Furthermore, by extending the proposed MMSE-based design to weighted MMSE (WMMSE) and relating it to spectral efficiency, the authors provide a versatile framework that can cater to different performance metrics based on system requirements. While this paper adeptly navigates the challenges of HBF for point-to-point mmWave systems, future research could explore solutions for multi-user and dynamic environments.

The paper opens several avenues for future work. The practical consideration of finite-resolution phase shifters, as well as real-time channel estimation and synchronization effects, are natural next steps for researchers aiming to move from theoretical insights to deployment-ready technologies. Additionally, the algorithms' adaptability to multi-user settings presents an exciting opportunity to further enhance system capacity and efficiency.

In conclusion, this paper contributes robustly to the ongoing conversation around efficient mmWave communications, presenting insightful solutions that are both innovative in their design and pragmatic in addressing real-world constraints.