Joint Beamforming Design and Bit Allocation in Massive MIMO with Resolution-Adaptive ADCs

Low-resolution analog-to-digital converters (ADCs) have emerged as a promising technology for reducing power consumption and complexity in massive multiple-input multiple-output (MIMO) systems while maintaining satisfactory spectral and energy efficiencies (SE/EE). In this work, we first identify the essential properties of optimal quantization and leverage them to derive a closed-form approximation of the covariance matrix of the quantization distortion. The theoretical finding facilitates the system SE analysis in the presence of low-resolution ADCs. We then focus on the joint optimization of the transmit-receive beamforming and bit allocation to maximize the SE under constraints on the transmit power and the total number of active ADC bits. To solve the resulting mixed-integer problem, we first develop an efficient beamforming design for fixed ADC resolutions. Then, we propose a low-complexity heuristic algorithm to iteratively optimize the ADC resolutions and beamforming matrices. Numerical results for a $64 \times 64$ MIMO system demonstrate that the proposed design offers $6\%$ improvement in both SE and EE with $40\%$ fewer active ADC bits compared with the uniform bit allocation. Furthermore, we numerically show that receiving more data streams with low-resolution ADCs can achieve higher SE and EE compared to receiving fewer data streams with high-resolution ADCs.