Learning-Based One-Bit Maximum Likelihood Detection for Massive MIMO Systems: Dithering-Aided Adaptive Approach

TL;DR

A dither-and-learning technique to estimate likelihood functions from dithered signals by adding a dithering signal to artificially decrease the SNR and infer the likelihood function from the quantized dithered signals by using an SNR estimate derived from a deep neural network-based estimator which is trained offline.

Abstract

In this paper, we propose a learning-based detection framework for uplink massive multiple-input and multiple-output (MIMO) systems with one-bit analog-to-digital converters. The learning-based detection only requires counting the occurrences of the quantized outputs of -1 and +1 for estimating a likelihood probability at each antenna. Accordingly, the key advantage of this approach is to perform maximum likelihood detection without explicit channel estimation which has been one of the primary challenges of one-bit quantized systems. However, due to the quasi-deterministic reception in the high signal-to-noise ratio (SNR) regime, one-bit observations in the high SNR regime are biased to either +1 or -1, and thus, the learning requires excessive training to estimate the small likelihood probabilities. To address this drawback, we propose a dither-and-learning technique to estimate likelihood functions from dithered signals. First, we add a dithering signal to artificially decrease the SNR and then infer the likelihood function from the quantized dithered signals by using an SNR estimate derived from a deep neural network-based estimator which is trained offline. We extend our technique by developing an adaptive dither-and-learning method that updates the dithering power according to the patterns observed in the quantized dithered signals. The proposed framework is also applied to channel-coded MIMO systems by computing a bit-wise and user-wise log-likelihood ratio from the refined likelihood probabilities. Simulation results validate the performance of the proposed methods in both uncoded and coded systems.

Figures (11)

• Figure 1: Symbol error rate simulation results of the optimal one-bit ML detection with full CSI against naive learning-based one-bit ML detection for $N_r =32$ receive antennas, $N_u = 3$ users, 4-QAM, and $N_{\sf tr} \in \{10, 100, 1000\}$ pilot signals.
• Figure 2: Illustration of the base station architecture with one-bit ADCs for $t\in\{\left(k-1\right)N_{\sf tr}+1,\ldots,kN_{\sf tr}\}$ for the training the $k$th symbol vector. Signals after ADCs are in real-value representation. During the pilot transmission phase, dithering signals are added before the quantization block. Based on the feedback information, the statistics of the dithering signal is updated.
• Figure 3: A communication data frame with a pilot transmission and a data transmission phases.
• Figure 4: Illustration of the supervised offline training of the SNR using deep neural networks. The networks are updated in the direction of reducing estimation errors.
• Figure 5: The number of under-trained likelihood functions among $2N_r$ likelihood functions for $N_u = 4$ users, 4-QAM, $N_r = 32$ antennas, and $N_{\sf tr}=45$ pilot signals with Rayleigh channels. The proposed adaptive dither-and-learning (ADL) method divides the training period into $N_s\in \{1,3,5\}$ sub-blocks for the feedback-driven update of dithering power.

Theorems & Definitions (4)

• Remark 1
• Remark 2: Under-trained likelihood functions
• Remark 3: Dithering noise
• Remark 4: Dithering power