LoRD-Net: Unfolded Deep Detection Network With Low-Resolution Receivers

The need to recover high-dimensional signals from their noisy low-resolution quantized measurements is widely encountered in communications and sensing. In this paper, we focus on the extreme case of one-bit quantizers, and propose a deep detector entitled LoRD-Net for recovering information symbols from one-bit measurements. Our method is a model-aware data-driven architecture based on deep unfolding of first-order optimization iterations. LoRD-Net has a task-based architecture dedicated to recovering the underlying signal of interest from the one-bit noisy measurements without requiring prior knowledge of the channel matrix through which the one-bit measurements are obtained. The proposed deep detector has much fewer parameters compared to black-box deep networks due to the incorporation of domain-knowledge in the design of its architecture, allowing it to operate in a data-driven fashion while benefiting from the flexibility, versatility, and reliability of model-based optimization methods. LoRD-Net operates in a blind fashion, which requires addressing both the non-linear nature of the data-acquisition system as well as identifying a proper optimization objective for signal recovery. Accordingly, we propose a two-stage training method for LoRD-Net, in which the first stage is dedicated to identifying the proper form of the optimization process to unfold, while the latter trains the resulting model in an end-to-end manner. We numerically evaluate the proposed receiver architecture for one-bit signal recovery in wireless communications and demonstrate that the proposed hybrid methodology outperforms both data-driven and model-based state-of-the-art methods, while utilizing small datasets, on the order of merely $\sim 500$ samples, for training.

I. Introduction

Analog-To-Digital conversion plays an important role in digital signal processing systems. While physical signals take values in continuous-time over continuous sets, they must be represented using a finite number of bits in order to be processed in digital hardware [2]. This operation is carried out using analog-to-digital converters (ADCs), which typically perform uniform sampling followed by a uniform quantization of the discrete-time samples. When using high-resolution ADCs, this conversion induces a minimal distortion, allowing to effectively process the signal using methods derived assuming access to the continuous-amplitude samples. However, the cost, power consumption and memory requirements of ADCs grow with the sampling rate and the number of bits assigned to each sample [3]. Consequently, recent years have witnessed an increasing interest in digital signal processing systems operating with low-resolution ADCs. Particularly, in multiple-input multiple-output (MIMO) communication receivers, which are required to simultaneously capture multiple analog signals with high bandwidth, there is a growing need to operate reliably with low-resolution ADCs [4]. The most coarse form of quantization is reduction of the signal to a single bit per sample, which may be accomplished via comparing the sample to some reference level, and recording whether the signal is above or below the reference. One-bit acquisition allows using high sampling rates at a low cost and low energy consumption. Due to such favorable properties of one-bit ADCs, they have been employed in a wide array of applications, including in wireless communications [1], [5], [6], radar signal processing [7]–[9], and sparse signal recovery [10], [11].