[Paper Review] Large-Scale Beamforming for Massive MIMO via Randomized Sketching

Hayoung Choi, Tao Jiang+3 more|arXiv (Cornell University)|Mar 14, 2019

Advanced MIMO Systems Optimization34 references4 citations

TL;DR

This paper proposes a randomized sketching-based regularized zero-forcing (RZF) beamforming method for massive MIMO systems to reduce the high computational complexity of matrix inversion. By leveraging preconditioned Richardson iteration with randomized sketching, the method achieves linear convergence to the optimal RZF beamformer with complexity proportional to $LK^2$ ($L \ll 2M$), significantly reducing computation while maintaining sum-rate performance close to the exact RZF solution.

ABSTRACT

Massive MIMO system yields significant improvements in spectral and energy efficiency for future wireless communication systems. The regularized zero-forcing (RZF) beamforming is able to provide good performance with the capability of achieving numerical stability and robustness to the channel uncertainty. However, in massive MIMO systems, the matrix inversion operation in RZF beamforming becomes computationally expensive. To address this computational issue, we shall propose a novel randomized sketching based RZF beamforming approach with low computational complexity. This is achieved by solving a linear system via randomized sketching based on the preconditioned Richard iteration, which guarantees high quality approximations to the optimal solution. We theoretically prove that the sequence of approximations obtained iteratively converges to the exact RZF beamforming matrix linearly fast as the number of iterations increases. Also, it turns out that the system sum-rate for such sequence of approximations converges to the exact one at a linear convergence rate. Our simulation results verify our theoretical findings.

Motivation & Objective

• To address the high computational complexity of matrix inversion in regularized zero-forcing (RZF) beamforming for massive MIMO systems.
• To develop a scalable beamforming solution that maintains high spectral efficiency and robustness to channel uncertainty.
• To achieve linear convergence in beamforming matrix approximation and system sum-rate using randomized sketching techniques.
• To reduce computational complexity from $\mathcal{O}(MK^2)$ to $\mathcal{O}(LK^2)$ with $L \ll 2M$.
• To theoretically prove convergence rates for both beamformer approximation and system sum-rate.

Proposed method

• Uses randomized sketching to compress the large-scale beamforming matrix into a smaller sketch, reducing computational load.
• Applies preconditioned Richardson iteration to solve the linear system for RZF beamforming efficiently.
• Employs a sketching matrix with specific random properties to preserve structural information of the original matrix.
• Derives iterative approximations to the RZF beamformer matrix through low-rank projections and randomized compression.
• The method ensures that the beamformer approximation converges linearly to the exact RZF solution.
• The sum-rate performance of the approximated beamformer converges linearly to the optimal RZF sum-rate.

Experimental results

Research questions

• RQ1 Can randomized sketching techniques be effectively applied to reduce the computational complexity of RZF beamforming in massive MIMO?
• RQ2 Does the proposed sketching-based beamforming method achieve linear convergence in approximating the optimal RZF beamformer?
• RQ3 What is the convergence rate of the system sum-rate when using the randomized sketching beamforming approximation?
• RQ4 How does the computational complexity scale with system dimensions compared to conventional RZF?
• RQ5 Can the method maintain robustness and spectral efficiency close to the exact RZF beamforming?

Key findings

• The proposed randomized sketching RZF beamforming method achieves a computational complexity of $\mathcal{O}(LK^2)$ with $L \ll 2M$, significantly reducing the $\mathcal{O}(MK^2)$ complexity of standard RZF.
• The sequence of beamformer approximations converges linearly to the exact RZF beamformer as the number of iterations increases.
• The system sum-rate of the approximated beamformer converges linearly to the optimal RZF sum-rate with increasing iterations.
• Theoretical analysis proves that the beamformer approximation error and sum-rate error both decrease linearly with iteration count.
• Numerical results confirm the linear convergence of both beamformer approximation and sum-rate performance, validating the theoretical findings.
• The method maintains high spectral efficiency and robustness to channel uncertainty, closely matching the performance of the exact RZF beamformer.