[Paper Review] Max-Min Rate of Cell-Free Massive MIMO Uplink with Optimal Uniform Quantization

Manijeh Bashar, Kanapathippillai Cumanan+4 more|View|Jul 7, 2019

Advanced MIMO Systems Optimization44 references4 citations

TL;DR

This paper proposes an optimal power allocation and receiver filter design for cell-free Massive MIMO uplink with limited fronthaul, using geometric programming and generalized eigenvalue problems to maximize the minimum user rate under power and fronthaul constraints. The proposed iterative algorithm achieves sum-rate and fairness gains through optimal quantization and receiver filtering, with proven optimality via uplink-downlink duality.

ABSTRACT

Cell-free Massive multiple-input multiple-output (MIMO) is considered, where distributed access points (APs) multiply the received signal by the conjugate of the estimated channel, and send back a quantized version of this weighted signal to a central processing unit (CPU). For the first time, we present a performance comparison between the case of perfect fronthaul links, the case when the quantized version of the estimated channel and the quantized signal are available at the CPU, and the case when only the quantized weighted signal is available at the CPU. The Bussgang decomposition is used to model the effect of quantization. The max-min problem is studied, where the minimum rate is maximized with the power and fronthaul capacity constraints. To deal with the non-convex problem, the original problem is decomposed into two sub-problems (referred to as receiver filter design and power allocation). Geometric programming (GP) is exploited to solve the power allocation problem whereas a generalized eigenvalue problem is solved to design the receiver filter. An iterative scheme is developed and the optimality of the proposed algorithm is proved through uplink-downlink duality. A user assignment algorithm is proposed which significantly improves the performance. Numerical results demonstrate the superiority of the proposed schemes.

Motivation & Objective

• To address the challenge of limited fronthaul capacity in cell-free Massive MIMO systems, which restricts practical deployment despite theoretical performance gains.
• To improve spectral efficiency and fairness by jointly optimizing power allocation and receiver filter design under fronthaul and power constraints.
• To model the impact of uniform quantization on system performance using the Bussgang decomposition, enabling accurate analysis of quantization noise effects.
• To develop an iterative algorithm that maximizes the minimum user rate (max-min fairness) through optimal receiver filtering and power allocation.
• To prove the optimality of the proposed algorithm using uplink-downlink duality, ensuring convergence to the global optimum.

Proposed method

• The system models uplink transmission where distributed access points (APs) perform channel estimation, apply conjugate beamforming, and quantize the weighted signal before sending it to a central CPU over limited-capacity fronthaul links.
• The Bussgang decomposition is used to model the distortion introduced by uniform quantization, enabling tractable analysis of the quantization noise in the signal model.
• The max-min rate problem is decomposed into two subproblems: receiver filter design via generalized eigenvalue problem and power allocation via geometric programming (GP).
• An iterative algorithm alternates between updating the receiver filter and power allocation, with scaling steps to satisfy total and per-user power constraints.
• The algorithm's optimality is proven using uplink-downlink duality, showing equivalence between the uplink max-min problem and a corresponding virtual downlink problem.
• A user assignment algorithm is proposed to further enhance performance by optimizing which APs serve each user.

Experimental results

Research questions

• RQ1 How does the performance of cell-free Massive MIMO vary under different fronthaul configurations, particularly when only quantized signals are available at the CPU versus when both quantized channel estimates and signals are available?
• RQ2 What is the optimal power allocation strategy that maximizes the minimum user rate under fronthaul and transmit power constraints?
• RQ3 Can the proposed receiver filter design, based on channel statistics, significantly improve performance compared to conventional local linear receivers at APs?
• RQ4 How does the combination of geometric programming and generalized eigenvalue problems enable optimal and provably optimal solutions to the non-convex max-min rate problem?
• RQ5 What is the impact of user assignment on system fairness and spectral efficiency in quantized cell-free Massive MIMO?

Key findings

• The proposed iterative algorithm achieves optimal max-min fairness by jointly solving power allocation and receiver filter design, with convergence guaranteed via uplink-downlink duality.
• The use of a centralized receiver filter based on channel statistics provides significant performance gain over conventional local beamforming at APs.
• Geometric programming enables optimal power allocation under total and per-user power constraints, with scaling techniques ensuring constraint satisfaction.
• Numerical results demonstrate that the proposed scheme outperforms conventional schemes, especially in terms of fairness and sum rate, under limited fronthaul conditions.
• The performance gain is most pronounced when the number of APs and antennas per AP are large, and when the fronthaul capacity is constrained.
• The user assignment algorithm significantly improves system performance by optimizing AP-user associations, leading to better rate fairness and higher spectral efficiency.