We consider a channel with discrete binary input X that is corrupted by a given continuous noise to produce a continuous-valued output Y. A quantizer is then used to quantize the continuous-valued output Y to the final binary output Z. The goal is to design an optimal quantizer Q* and also find the optimal input distribution p*(X) that maximizes the mutual information I(X; Z) between the binary input and the binary quantized output. A linear time complexity searching procedure is proposed. Based on the properties of the optimal quantizer and the optimal input distribution, we reduced the searching range that results in a faster implementation algorithm. Both theoretical and numerical results are provided to illustrate our method.
Quantized channel state information (CSI) plays a critical role in precoding design which helps reap the merits of multiple-input multiple-output (MIMO) technology. In order to reduce the overhead of CSI feedback, we propose a deep learning based CSI quantization method by developing a joint convolutional residual network (JCResNet) which benefits MIMO channel feature extraction and recovery from the perspective of bit-level quantization performance. Experiments show that our proposed method substantially improves the performance.
We develop a direction of arrival (DoA) and channel estimation algorithm for the one-bit quantized millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) system. By formulating the estimation problem as a noisy one-bit compressed sensing problem, we propose a computationally efficient gridless solution based on the expectation-maximization generalized approximate message passing (EMGAMP) approach. The proposed algorithm does not need the prior knowledge about the number of DoAs and outperforms the existing methods in distinguishing extremely close DoAs for the case of one-bit q…
Low-resolution devices are promising for systems that demand low energy consumption and low complexity as required in IoT systems. In this study, we propose a novel waveform for bandlimited channels with 1-bit quantization and oversampling at the receivers. The proposed method implies that the information is conveyed within the time instances of zero-crossings which is then utilized in combination with a Gray-coding scheme. Unlike the existing method, the proposed method does not require optimization and transmission of a dynamic codebook. The proposed approach outperforms the state-of-the-art…
It is known that the estimated energy consumption of digital-to analog converters (DACs) is around 30\% of the energy consumed by analog-to-digital converters (ADCs) keeping fixed the sampling rate and bit resolution. Assuming that similarly to ADC, DAC dissipation doubles with every extra bit of resolution, a decrease in two resolution bits, for instance from 4 to 2 bits, represents a 75$\% $ lower dissipation. The current limitations in sum-rates of 1-bit quantization have motivated researchers to consider extra bits in resolution to obtain higher levels of sum-rates. Following this, we devi…
Over-the-air federated edge learning (Air-FEEL) is a communication-efficient framework for distributed machine learning using training data distributed at edge devices. This framework enables all edge devices to transmit model updates simultaneously over the entire available bandwidth, allowing for over-the-air aggregation. A one-bit digital over-the-air aggregation (OBDA) scheme has been recently proposed, featuring one-bit gradient quantization at edge devices and majority-voting based decoding at the edge server. However, the low-resolution one-bit gradient quantization slows down the model…
Today's communication systems typically use high resolution analog-to-digital converters (ADCs). However, considering future communication systems with data rates in the order of 100Gbit/s the ADC power consumption becomes a major factor due to the high sampling rates. A promising alternative are receivers based on 1-bit quantization and oversampling w.r.t. the signal bandwidth. Such an approach requires a redesign of modulation, receiver synchronization, and demapping. A zero crossing modulation is a natural choice as the information needs to be carried in the zero crossing time instants. The…
We derive an expression for the capacity of massive multiple-input multiple-output Millimeter wave (mmWave) channel where the receiver is equipped with a variable-resolution Analog to Digital Converter (ADC) and a hybrid combiner. The capacity is shown to be a function of Cramer-Rao Lower Bound (CRLB) for a given bit-allocation matrix and hybrid combiner. The condition for optimal ADC bit-allocation under a receiver power constraint is derived. This is derived based on the maximization of capacity with respect to bit-allocation matrix for a given channel, hybrid precoder, and hybrid combiner. …
Deep learning has been recently applied to physical layer processing in digital communication systems in order to improve end-to-end performance. In this work, we introduce a novel deep learning solution for soft bit quantization across wideband channels. Our method is trained end-to-end with quantization- and entropy-aware augmentations to the loss function and is used at inference in conjunction with source coding to achieve near-optimal compression gains over wideband channels. To efficiently train our method, we prove and verify that a fixed feature space quantization scheme is sufficient …
We present optimal sample complexity estimates for one-bit compressed sensing problems in a realistic scenario: the procedure uses a structured matrix (a randomly sub-sampled circulant matrix) and is robust to analog pre-quantization noise as well as to adversarial bit corruptions in the quantization process. Our results imply that quantization is not a statistically expensive procedure in the presence of nontrivial analog noise: recovery requires the same sample size one would have needed had the measurement matrix been Gaussian and the noisy analog measurements been given as data.
A neural network is quantized for the mitigation of nonlinear and components distortions in a 16-QAM 9x50km dual-polarization fiber transmission experiment. Post-training additive power-of-two quantization at 6 bits incurs a negligible Q-factor penalty. At 5 bits, the model size is reduced by 85%, with 0.8 dB penalty.
We present a novel sub-8-bit quantization-aware training (S8BQAT) scheme for 8-bit neural network accelerators. Our method is inspired from Lloyd-Max compression theory with practical adaptations for a feasible computational overhead during training. With the quantization centroids derived from a 32-bit baseline, we augment training loss with a Multi-Regional Absolute Cosine (MRACos) regularizer that aggregates weights towards their nearest centroid, effectively acting as a pseudo compressor. Additionally, a periodically invoked hard compressor is introduced to improve the convergence rate by …
We consider the weak target detection problem with unknown parameter in colocated multiple-input multiple-output (MIMO) radar. To cope with the sheer amount of data for large-size systems, a multi-bit quantizer is utilized in the sampling process. As a low-complexity alternative to classic generalized likelihood ratio test (GLRT) for quantized data, we propose the multi-bit detector on Rao test with a closed-form test statistic, whose theoretical asymptotic distribution is provided to generalize the actual detection performance. Besides, we refine the design of quantizer by optimized quantizat…
This paper considers the problem of estimating the sparse mmWave massive multiple input - multiple output (MIMO) OFDM channel from one-bit quantized measurements. Unlike previous grid-based one-bit compressive sensing approaches, we present a gridless convex method to recover sparse channel form one-bit measurements via Binary Atomic Norm Minimization (BiANM) and Reweighted Binary Atomic Norm Minimization (ReBiANM). Simulation results verify the accuracy of the binary and reweighted binary atomic norm minimization techniques.
Systems with 1-bit quantization and oversampling are promising for the Internet of Things (IoT) devices in order to reduce the power consumption of the analog-to-digital-converters. The novel time-instance zero-crossing (TI ZX) modulation is a promising approach for this kind of channels but existing studies rely on optimization problems with high computational complexity and delay. In this work, we propose a practical waveform design based on the established TI ZX modulation for a multiuser multi-input multi-output (MIMO) downlink scenario with 1-bit quantization and temporal oversampling at …
One-bit quantization has recently become an attractive option for data acquisition in cutting edge applications, due to the increasing demand for low power and higher sampling rates. Subsequently, the rejuvenated one-bit array processing field is now receiving more attention, as "classical" array processing techniques are adapted / modified accordingly. However, array calibration, often an instrumental preliminary stage in array processing, has so far received little attention in its one-bit form. In this paper, we present a novel solution approach for the blind calibration problem, namely, wi…
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
In this paper, we propose a uniformly dithered 1-bit quantization scheme for high-dimensional statistical estimation. The scheme contains truncation, dithering, and quantization as typical steps. As canonical examples, the quantization scheme is applied to the estimation problems of sparse covariance matrix estimation, sparse linear regression (i.e., compressed sensing), and matrix completion. We study both sub-Gaussian and heavy-tailed regimes, where the underlying distribution of heavy-tailed data is assumed to have bounded moments of some order. We propose new estimators based on 1-bit quan…
