Deep Learning for Estimation and Pilot Signal Design in Few-Bit Massive MIMO Systems

Estimation in few-bit MIMO systems is challenging, since the received signals are nonlinearly distorted by the low-resolution ADCs. In this paper, we propose a deep learning framework for channel estimation, data detection, and pilot signal design to address the nonlinearity in such systems. The proposed channel estimation and data detection networks are model-driven and have special structures that take advantage of domain knowledge in the few-bit quantization process. While the first data detection network, B-DetNet, is based on a linearized model obtained from the Bussgang decomposition, the channel estimation network and the second data detection network, FBM-CENet and FBM-DetNet respectively, rely on the original quantized system model. To develop FBM-CENet and FBM-DetNet, the maximum-likelihood channel estimation and data detection problems are reformulated to overcome the indeterminant gradient issue. An important feature of the proposed FBM-CENet structure is that the pilot matrix is integrated into the weight matrices of its channel estimator. Thus, training the proposed FBM-CENet enables a joint optimization of both the channel estimator at the base station and the pilot signal transmitted from the users. Simulation results show significant performance gains in estimation accuracy by the proposed deep learning framework.

I. Introduction

One practical solution for reducing hardware cost and power consumption in massive MIMO systems is to use low-resolution (e.g., 1–3 bits) analog-to-digital converters (ADCs), due to their simple structure and very low power consumption. In particular, the number of comparators in a -bit ADC grows exponentially with , which means both the hardware complexity and the power consumption of an ADC scales exponentially with the resolution [1]. Therefore, the cost and power consumption of low-resolution ADCs are substantially lower than for high-resolution ADCs. Furthermore, the hardware structure of other components in an RF chain can also be simplified or removed when low-resolution ADCs are used. For example, the simplest architecture involving one-bit ADCs does not require an automatic gain control (AGC) since only the sign of the real and imaginary parts of the received signals is retained. The stringent linearity requirement of the low-noise amplifier (LNA) can be relaxed and a simpler low-cost amplifier can be used instead. These benefits on the hardware side make it possible to deploy low-resolution ADCs in practical massive MIMO systems. However, the lower-complexity and lower-power-consumption hardware necessitates special care in the subsequent signal processing. More specifically, the nonlinearities introduced by the low-resolution ADCs makes signal processing tasks such as channel estimation and data detection in few-bit MIMO systems much more challenging compared to those in unquantized systems. Therefore, it is crucial that efficient signal processing methods for channel estimation and data detection be developed for such systems so that they can be transitioned to commercial systems.