Comparative Analysis of Channel Estimation and Statistical Learning for MIMO Detection with Low-Resolution ADCs

Low-resolution analog-to-digital converters (ADCs) have been adopted in massive multiple-input multiple-output receivers, as their power consumption and hardware cost increase with the number of antennas. However, the resulting coarse quantization degrades the channel estimation (CE) and subsequent symbol detection, leading to the poor performance of the conventional CE-based maximum likelihood (ML) detector. To address this problem, this paper explains the preference for using a detector that directly learns output statistics with low-resolution ADCs by contrasting the two estimable quantities, i.e., the channel and output statistics, and the detection induced by each. For the channel, the Fisher information of B-bit observations is analyzed, and the error floor of the CE-based ML detection with linear channel estimation is characterized using a closed-form expression in the one-bit two-hypothesis case. For the output statistics, the estimation accuracy is derived as a function of the signal-to-noise ratio (SNR) for a fixed number of pilots, and the error exponent of statistical learning detection is determined. The two methods are then compared using a high-SNR error exponent. The simulation results reveal that statistical learning detection outperforms CE-based ML detection in the high-SNR regime at every finite resolution for which the channel is sign-ambiguous, provided that the noiseless codewords are distinct, and the two methods converge as the resolution increases. These results indicate that, under coarse quantization, learning the output statistics is more reliable than estimating the channel at high SNR. Therefore, statistical learning detection is recommended for operation with low-resolution ADCs, particularly in the high-SNR regime, where CE-based ML detection suffers from the error floor.