This paper considers a massive multiple-inputmultiple-output (MIMO) system with low-resolution analog-todigital converters (ADCs). In this system, inspired by supervised learning, we propose a novel communication framework that consists of channel training and data detection. The underlying idea of the proposed framework is to use the input-output relations of a nonlinear system, formed by a channel and a quantization at the ADCs, for data detection. Specifically, for the channel training, we develop implicit and explicit training methods that empirically learn the conditional probability mass functions (PMFs) of the nonlinear system. For the data detection, we propose three detection methods that map a received signal vector to one of the indexes of possible symbol vectors, according to the empirical conditional PMFs learned from the channel training. We also present a low-complexity version of the proposed framework that reduces a detection complexity by using a successive-interference-cancellation (SIC) approach. In this lowcomplexity version, a symbol vector is divided into two subvectors and then these two subvectors are successively detected using SIC. When employing the proposed framework with one-bit ADCs, we derive an analytical expression for the symbol-vectorerror probability. One major observation is that the symbolvector-error probability decreases exponentially with the inverse of the number of transmit antennas, the operating signal-tonoise ratio, and the minimum distance that can increase with the number of receive antennas. Simulations demonstrate the detection error reduction of the proposed framework compared to existing detection techniques.

This paper presents a low-complexity near-maximum-likelihood-detection (near-MLD) algorithm called one-bit-sphere-decoding for an uplink massive multiple-input multiple-output (MIMO) system with one-bit analog-to-digital converters (ADCs). The idea of the proposed algorithm is to estimate the transmitted symbol vector sent by uplink users (a codeword vector) by searching over a sphere, which contains a collection of codeword vectors close to the received signal vector at the base station in terms of a weighted Hamming distance. To reduce the computational complexity for the construction of the sphere, the proposed algorithm divides the received signal vector into multiple sub-vectors each with reduced dimension. Then, it generates multiple spheres in parallel, where each sphere is centered at the sub-vector and contains a list of sub-codeword vectors. The detection performance of the proposed algorithm is also analyzed by characterizing the probability that the proposed algorithm performs worse than the MLD. The analysis shows how the dimension of each sphere and the size of the sub-codeword list are related to the performance-complexity tradeoff achieved by the proposed algorithm. Simulation results demonstrate that the proposed algorithm achieves near-MLD performance, while reducing the computational complexity compared to the existing MLD method.

The use of one-bit analog-to-digital converters (ADCs) at a receiver is a power-efficient solution for future wireless systems operating with a large signal bandwidth and/or a massive number of receive radio frequency chains. This solution, however, induces a high channel estimation error and therefore makes it difficult to perform the optimal data detection that requires perfect knowledge of likelihood functions at the receiver. In this paper, we propose a likelihood function learning method for multiple-input multipleoutput (MIMO) systems with one-bit ADCs using a reinforcement learning approach. The key idea is to exploit input-output samples obtained from data detection, to compensate the mismatch in the likelihood function. The underlying difficulty of this idea is a label uncertainty in the samples caused by a data detection error. To resolve this problem, we define a Markov decision process (MDP) to maximize the accuracy of the likelihood function learned from the samples. We then develop a reinforcement learning algorithm that efficiently finds the optimal policy by approximating the transition function and the optimal state of the MDP. Simulation results demonstrate that the proposed method provides significant performance gains for the optimal data detection methods that suffer from the mismatch in the likelihood function. Index TermsMultiple-input-multiple-output (MIMO), one-bit analog-to-digital converter (ADC), reinforcement learning, robust data detection, likelihood function learning.

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