One-bit Analog-to-digital Converters Research Articles

Non-Orthogonal Multiple Access with One-Bit Analog-to-Digital Converters Using Threshold Adaptation.

In digital communication systems featuring high-resolution analog-to-digital converters (ADCs), the utilization of successive interference cancellation and detection can enhance the capacity of a Gaussian multiple access channel (MAC) by combining signals from multiple transmitters in a non-orthogonal manner. Conversely, in systems employing one-bit ADCs, it is exceedingly difficult to eliminate non-orthogonal interference using digital signal processing due to the considerable distortion present in the received signal when employing such ADCs. As a result, the Gaussian MAC does not yield significant capacity gains in such cases. To address this issue, we demonstrate that, under a given deterministic interference, the capacity of a one-bit-quantized channel becomes equivalent to the capacity without interference when an appropriate threshold value is chosen. This finding suggests the potential for indirect interference cancellation in the analog domain, facilitating the proposition of an efficient successive interference cancellation and detection scheme. We analyze the achievable rate of the proposed scheme by deriving the mutual information between the transmitted and received signals at each detection stage. The obtained results indicate that the sum rate of the proposed scheme generally outperforms conventional methods, with the achievable upper bound being twice as high as that of the conventional methods. Additionally, we have developed an optimal transmit power allocation algorithm to maximize the sum rate in fading channels.

Improved Likelihood Probability in MIMO Systems Using One-Bit ADCs

This study considers an improved likelihood probability in multi-input multi-output (MIMO) systems using one-bit analog-to-digital converters (ADCs). MIMO systems using one-bit ADCs are known to exhibit from performance degradation because of inaccurate likelihood probabilities. To overcome this degradation, the proposed method leverages the detected symbols to estimate the true likelihood probability by combining the initial likelihood probability. An optimization problem is formulated to minimize the mean-squared error between the true and combined likelihood probabilities, and a solution is derived using the least-squares method. Simulation results show that the proposed method obtains a signal-to-noise gain of approximately 0.3 dB to achieve a frame error rate of 10−1 compared to conventional methods. This improvement in performance is attributed to the enhanced reliability of the likelihood probability.

Joint Channel Estimation and Mixed-ADCs Allocation for Massive MIMO via Deep Learning

Millimeter wave (mmWave) multi-user massive multi-input multi-output (MIMO) is a promising technique for the next generation communication systems. However, the hardware cost and power consumption grow significantly as the number of radio frequency (RF) components increases, which hampers the deployment of practical massive MIMO systems. To address this issue and further facilitate the commercialization of massive MIMO, mixed analog-to-digital converters (ADCs) architecture has been considered, where parts of conventionally assumed full-resolution ADCs are replaced by one-bit ADCs. In this paper, we first propose a deep learning-based (DL) joint pilot design and channel estimation method for mixed-ADCs mmWave massive MIMO. Specifically, we devise a pilot design neural network whose weights directly represent the optimized pilots, and develop a Runge-Kutta model-driven densely connected network as the channel estimator. Instead of randomly assigning the mixed-ADCs, we then design a novel antenna selection network for mixed-ADCs allocation to further improve the channel estimation accuracy. Moreover, we adopt an autoencoder-inspired end-to-end architecture to jointly optimize the pilot design, channel estimation and mixed-ADCs allocation networks. Simulation results show that the proposed DL-based methods have advantages over the traditional channel estimators as well as the state-of-the-art networks.

Compressed Sensing Based Active User Detection in MIMO Systems With One-Bit ADC

We investigate an active user detection for massive machine-type communication systems, in which a massive number of users with sporadic transmission communicate with a base station (BS) with multiple antennas. Due to hardware cost and power consumption, it is assumed that each receiver antenna at the BS is equipped with one-bit analog-to-digital converter (ADC). This problem can be formulated as a new compressed sensing problem with one-bit quantized multiple measurement vectors (termed one-bit CS-MMV). In this paper, we propose a novel algorithm (named Turbo-QISTA) by properly incorporating Turbo principle into quantized iterative shrinkage threshold algorithm (QISTA). Our major contribution is to design two key metrics (i.e., extrinsic and a priori information) of Turbo principle suitable for one-bit CS-MMV problem. Via simulations, we demonstrate the superiority of the proposed Turbo-QISTA.

Convexity of the Capacity of One-Bit Quantized Additive White Gaussian Noise Channels

In this study, the maximum error-free transmission rate of an additive white Gaussian noise channel with a symmetric analog-to-digital converter (ADC) was derived as a composite function of the binary entropy function, Gaussian Q-function, and the square root function, assuming that the composite function was convex on the set of all non-negative real numbers. However, because mathematically proving this convexity near zero is difficult, studies in this field have only presented numerical results for small values in the domain. Because the low-signal-to-noise (SNR) regime is considered to be a major application area for one-bit ADCs in wireless communication, deriving a concrete proof of the convexity of the composite function on small SNR values (non-negative values near zero) is important. Therefore, this study proposes a novel proof for convexity, which is satisfied for all non-negative values, based on the continuity of the involved functions.

Cooperative DF Protocol for MIMO Systems Using One-Bit ADCs.

This study considers a detection scheme for cooperative multi-input–multi-output (MIMO) systems using one-bit analog-to-digital converters (ADCs) in a decode-and-forward (DF) relay protocol. The use of one-bit ADCs is a promising technique for reducing the power consumption, which is necessary for supporting future wireless systems comprising a large number of antennas. However, the use of a large number of antennas remains still limited to mobile devices owing to their size. Cooperative communication using a DF relay can resolve this limitation; however, detection errors at the relay make it difficult to employ cooperative communication directly. This difficulty is more severe in a MIMO system using one-bit ADCs due to its nonlinear nature. To efficiently address the difficulty, this paper proposes a detection scheme that mitigates the error propagation effect. The upper bound of the pairwise error probability (PEP) of one-bit ADCs is first derived in a weighted Hamming distance form. Then, using the derived PEP, the proposed detection for the DF relay protocol is derived as a single weighted Hamming distance. Finally, the complexity of the proposed detection is analyzed in terms of real multiplications. The simulation results show that the proposed detection method efficiently mitigates the error propagation effect but has a relatively low level of complexity when compared to conventional detection methods.

Learning Linear MMSE Precoder for Uplink Massive MIMO Systems With One-Bit ADCs

In this letter, we present a deep learning based linear precoder design to improve the performance for uplink multiuser multiple-input multiple-output (MU-MIMO) systems with one-bit analog-to-digital converters (ADCs). Specifically, by utilizing the Bussgang decomposition based linear minimum mean squared error (MMSE) receiver at the base station (BS), we aim to further minimize the system MSE by optimizing the precoder at each user equipment (UE). To address this problem efficiently, we propose a deep neural network based approach by unfolding the developed projected gradient descent (PGD) algorithm and treating the step size in each PGD iteration as trainable network parameters. Simulation results show that the proposed network design outperforms the conventional PGD algorithm under both perfect and estimated channel state information (CSI) and the improvement is achieved with reduced online complexity.

One-Bit Target Detection in Collocated MIMO Radar and Performance Degradation Analysis

Target detection is an important problem in multiple-input multiple-output (MIMO) radar. Many existing target detection algorithms were proposed without taking into consideration the quantization error caused by analog-to-digital converters (ADCs). This paper addresses the problem of target detection for MIMO radar with one-bit ADCs and derives a Rao’s test-based detector. The proposed method has several appealing features: 1) it is a closed-form detector; 2) it allows us to handle sign measurements straightforwardly; 3) there are closed-form approximations of the detector’s distributions, which allow us to theoretically evaluate its performance. Moreover, the closed-form distributions allow us to study the performance degradation due to the one-bit ADCs, yielding an approximate 2 dB loss in the low-signal-to-noise-ratio (SNR) regime compared to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\infty$</tex-math></inline-formula> -bit ADCs. Simulation results are included to showcase the advantage of the proposed detector and validate the accuracy of the theoretical results.

Performance Bound for MIMO Systems Using One-Bit ADCs Over Rayleigh Fading Channels

This study explores the performance of multiple-input multiple-output (MIMO) systems with one-bit analog-to-digital converters (ADCs) over Rayleigh fading channels. We particularly aim to characterize the pairwise error probability (PEP) achieved by maximum likelihood detection (MLD), which provides the optimal detection performance of the considered systems. First, the upper bound of the PEP is derived by leveraging Jensen’s inequality and the Chernoff bound. The asymptotic bounds of the PEP are then characterized to clarify the impact of the one-bit ADCs on the diversity order of the MIMO systems. Notably, the diversity order of the MIMO systems with one-bit ADCs is the same as the number of receive antennas only when transmitting two symbol vectors with the opposite sign. Except for this special case, the asymptotic bound of the PEP is saturated at a high signal-to-noise ratio due to the use of the one-bit ADCs. Using simulations, we verify that the analytical results coincide with the asymptotic behavior of the PEP of the MLD for MIMO systems with one-bit ADCs over Rayleigh fading channels.

Transmit Code and Receive Filter Design for PMCW Radars in the Presence of One-Bit ADC

Phase-modulated continuous-wave (PMCW) radar is an emerging technology in various civilian applications. Due to the high bandwidth of the PMCW signal, it needs high-speed analog-to-digital converters (ADCs). High-resolution ADCs supporting this high bandwidth are expensive, have a big size on the chip, and consume high power, which are significant challenges for radar. A solution to deal with the aforementioned challenges is to use low-resolution, or in the most extreme case, one-bit ADCs. In this article, we aim at designing the transmit code and the receive filter for the PMCW radar in the presence of one-bit ADC at the receiver side. To this end, we introduce the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mean</i> integrated sidelobe level metric, called MISL. MISL generalizes the well-known ISL metric for nonideal ADC usage at the receiver side and takes the effect of noise and target backscattering coefficient into account. For mathematical tractability, we employ the maximum likelihood estimation of the target backscattering coefficient. This leads to casting an optimization problem that does not need knowledge about noise and target characteristics. We utilize the cyclic optimization procedure to optimize the transmit code and the receive filter. The filter design subproblem admits a closed-form solution, whereas we obtain a solution to transmit code design subproblem via the coordinate descent framework. Numerical examples illustrate the superior performance of the proposed method compared to benchmarks that design sequences assuming ideal ADC at the receiver.

Differential Modulation in Massive MIMO With Low-Resolution ADCs

In this paper, we present a differential modulation and detection scheme for use in the uplink of a system with a large number of antennas at the base station, each equipped with low-resolution analog-to-digital converters (ADCs). We derive an expression for the maximum likelihood (ML) detector of a differentially encoded phase information symbol received by a base station operating in the low-resolution ADC regime. We also present an equal performing reduced complexity receiver for detecting the phase information. To increase the supported data rate, we also present a maximum likelihood expression to detect differential amplitude phase shift keying symbols with low-resolution ADCs. We note that the derived detectors are unable to detect the amplitude information. To overcome this limitation, we use the Bussgang Theorem and the Central Limit Theorem (CLT) to develop two detectors capable of detecting the amplitude information. We numerically show that while the first amplitude detector requires multiple quantization bits for acceptable performance, similar performance can be achieved using one-bit ADCs by grouping the receive antennas and employing variable quantization levels (VQL) across distinct antenna groups. We validate the performance of the proposed detectors through simulations and show a comparison with corresponding coherent detectors. Finally, we present a complexity analysis of the proposed low-resolution differential detectors

MIMO Networks With One-Bit ADCs: Receiver Design and Communication Strategies

High resolution analog to digital converters (ADCs) are conventionally used at the receiver terminals to store an accurate digital representation of the received signal, thereby allowing for reliable decoding of transmitted messages. However, in a wide range of applications, such as communication over millimeter wave and massive multiple-input multiple-output (MIMO) systems, the use of high resolution ADCs is not feasible due to power budget limitations. In the conventional fully digital receiver design, where each receiver antenna is connected to a distinct ADC, reducing the ADC resolution leads to performance loss in terms of achievable rates. One proposed method to mitigate the rate-loss is to use analog linear combiners leading to design of hybrid receivers. Here, the hybrid framework is augmented by the addition of delay elements to allow for temporal analog processing. Two new classes of receivers consisting of delay elements, analog linear combiners, and one-bit ADCs are proposed. The fundamental limits of communication in single and multi-user (uplink and downlink) MIMO systems employing the proposed receivers are investigated. In the high signal to noise ratio regime, it is shown that the proposed receivers achieve the maximum achievable rates among all receivers with the same number of one-bit ADCs.

Receive filter design for MIMO radar with one-bit ADCs

Low-resolution analog-to-digital converter (ADC), especially one-bit ADCs, is of great importance for large-scale systems due to its significant advantages, e.g., low hardware cost and low power consumption. In this paper, the problem of receive filter design for multiple-input multiple-output (MIMO) radar with one-bit ADCs is investigated. With deterministic noise distribution parameters and target scattering coefficient, the probabilities of detection and false-alarm for MIMO radar with one-bit ADCs are derived, and then the receive filter is obtained by maximizing the probability of detection subject to a fixed false-alarm. In addition, we define a quantized signal-to-noise ratio (QSNR) for MIMO radar with one-bit ADCs, and evaluate the performance difference between one-bit and infinite-bit quantizations from the SNR point of view. For imperfect scenario where the noise distribution parameters are unknown, a one-bit observation based method is devised to estimate the mean and variance of the noise. Moreover, we study the effect of unknown target scattering coefficient on the performance of the designed receive filter in terms of the QSNR, and propose robust methods to overcome this uncertainty. Finally, several representative simulations are presented to demonstrate the effectiveness of the proposed methods.

Secrecy Capacity of a Gaussian Wiretap Channel With ADCs is Always Positive

We consider a complex Gaussian wiretap channel with finite-resolution analog-to-digital converters (ADCs) at both the legitimate receiver and the eavesdropper. For this channel, we show that a positive secrecy rate is always achievable as long as the channel gains at the legitimate receiver and at the eavesdropper are different, regardless of the quantization levels of the ADCs. For the achievability, we first consider the case of the one-bit ADCs at the legitimate receiver and apply a binary input distribution where the two input points have the same phase when the channel gain at the legitimate receiver is less than that at the eavesdropper, and otherwise the opposite phase. Then the result is generalized for the case of arbitrary finite-resolution ADCs at the legitimate receiver by translating the input distribution appropriately. We also provide numerical lower bounds on the achievable secrecy rates, and analyze the tendency of the secrecy rates according to the channel difference, the power constraint, and the quantization levels for some cases. For the special case of the real Gaussian wiretap channel with one-bit ADCs at both the legitimate receiver and the eavesdropper, we show that our choice of phase does not lose any optimality for the Wyner code.

One-Bit ADCs/DACs Based MIMO Radar: Performance Analysis and Joint Design

Extremely low-resolution (e.g. one-bit) analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) can substantially reduce hardware cost and power consumption for MIMO radar especially with large scale antennas. In this paper, we focus on the detection performance analysis and joint design for the MIMO radar with one-bit ADCs and DACs. Specifically, under the assumption of low signal-to-noise ratio (SNR) and interference-to-noise ratio (INR), we derive the expressions of probability of detection ($\mathcal{P}_d$) and probability of false alarm ($\mathcal{P}_f$) for one-bit MIMO radar and also the theoretical performance gap to infinite-bit MIMO radars for the noise-only case. We further find that for a fixed $\mathcal{P}_f$, $\mathcal{P}_d$ depends on the defined quantized signal-to-interference-plus-noise ratio (QSINR), which is a function of the transmit waveform and receive filter. Thus, an optimization problem arises naturally to maximize the QSINR by joint designing the waveform and filter. For the formulated problem, we propose an alternatin\emph{g} wavefo\emph{r}m and filt\emph{e}r d\emph{e}sign for QSINR maximiza\emph{t}ion (GREET). At each iteration of GREET, the receive filter is upadted via the minimum variance distortionless response (MVDR) method, and the one-bit waveform is optimized based on the alternating direction method of multipliers (ADMM) algorithm where the closed-form solutions are obtained for both the primary and slack variables. Numerical simulations are consistent to the theoretical performance analysis and demonstrate the effectiveness of the proposed design algorithm.

One-Bit Phase Retrieval: More Samples Means Less Complexity?

The classical problem of phase retrieval has found a wide array of applications in optics, imaging and signal processing. In this paper, we consider the phase retrieval problem in a one-bit setting, where the signals are sampled using one-bit analog-to-digital converters (ADCs). A significant advantage of deploying one-bit ADCs in signal processing systems is their superior sampling rates as compared to their high-resolution counterparts. This leads to an enormous amount of one-bit samples gathered at the output of the ADC in a short period of time. We demonstrate that this advantage pays extraordinary dividends when it comes to convex phase retrieval formulations, namely that the often encountered matrix semi-definiteness constraints as well as rank constraints (that are computationally prohibitive to enforce), become redundant for phase retrieval in the face of a growing sample size. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.

Zero-Delay Joint Source Channel Coding for a Bivariate Gaussian Source over the Broadcast Channel with One-Bit ADC Front Ends.

In this work, we consider the zero-delay transmission of bivariate Gaussian sources over a Gaussian broadcast channel with one-bit analog-to-digital converter (ADC) front ends. An outer bound on the conditional distortion region is derived. Focusing on the minimization of the average distortion, two types of methods are proposed to design nonparametric mappings. The first one is based on the joint optimization between the encoder and decoder with the use of an iterative algorithm. In the second method, we derive the necessary conditions to develop the optimal encoder numerically. Using these necessary conditions, an algorithm based on gradient descent search is designed. Subsequently, the characteristics of the optimized encoding mapping structure are discussed, and inspired by which, several parametric mappings are proposed. Numerical results show that the proposed parametric mappings outperform the uncoded scheme and previous parametric mappings for broadcast channels with infinite resolution ADC front ends. The nonparametric mappings succeed in outperforming the parametric mappings. The causes for the differences between the performances of two nonparametric mappings are analyzed. The average distortions of the parametric and nonparametric mappings proposed here are close to the bound for the cases with one-bit ADC front ends in low channel signal-to-noise ratio regions.

Blind Federated Learning at the Wireless Edge With Low-Resolution ADC and DAC

We study collaborative machine learning systems where a massive dataset is distributed across independent workers which compute their local gradient estimates based on their own datasets. Workers send their estimates through a multipath fading multiple access channel with orthogonal frequency division multiplexing to mitigate the frequency selectivity of the channel. We assume that there is no channel state information (CSI) at the workers, and the parameter server (PS) employs multiple antennas to align the received signals. To reduce the power consumption and the hardware costs, we employ complex-valued low-resolution digital-to-analog converters (DACs) and analog-to-digital converters (ADCs), at the transmitter and the receiver sides, respectively, and study the effects of practical low-cost DACs and ADCs on the learning performance. Our theoretical analysis shows that the impairments caused by low-resolution DACs and ADCs, including those of one-bit DACs and ADCs, do not prevent the convergence of the federated learning algorithms, and the multipath channel effects vanish when a sufficient number of antennas are used at the PS. We also validate our theoretical results via simulations, and demonstrate that using low-resolution, even one-bit, DACs and ADCs causes only a slight decrease in the learning accuracy.

Linear and Deep Neural Network-Based Receivers for Massive MIMO Systems With One-Bit ADCs

The use of one-bit analog-to-digital converters (ADCs) is a practical solution for reducing cost and power consumption in massive Multiple-Input-Multiple-Output (MIMO) systems. However, the distortion caused by one-bit ADCs makes the data detection task much more challenging. In this paper, we propose a two-stage detection method for massive MIMO systems with one-bit ADCs. In the first stage, we present several linear receivers based on the Bussgang decomposition that show significant performance gains over conventional linear receivers. Next, we reformulate the maximum-likelihood (ML) detection problem to address its non-robustness. Based on the reformulated ML detection problem, we propose a model-driven deep neural network-based detector, namely OBMNet, whose performance is comparable with an existing support vector machine-based receiver, albeit with a much lower computational complexity. A nearest-neighbor search method is then proposed for the second stage to refine the first stage solution. Unlike existing search methods that typically perform the search over a large candidate set, the proposed search method generates a limited number of most likely candidates and thus limits the search complexity. Numerical results confirm the low complexity, efficiency, and robustness of the proposed two-stage detection method.

Training Length Adaptation for Reinforcement Learning-Based Detection in Time-Varying Massive MIMO Systems With One-Bit ADCs

This study elucidates a reinforcement learning (RL)-based detection with one-bit analog-to-digital converters (ADCs) in time-varying massive multiple-input and multiple-output channels. In one-bit ADCs, conventional channel estimation exhibits poor performance owing to nonlinear quantization. The RL-based detection alleviates this degradation by learning the true likelihood probability during data transmission. However, in time-varying channels, the learned likelihood probability is inconsistent with the true likelihood probability due to temporal channel variations. This inconsistency can cause severe performance degradation. To effectively exploit the learned likelihood probability, we propose a training length adaptation method that determines an appropriate training length based on the channel conditions. To achieve this, we consider an optimization problem that minimizes the training length while guaranteeing the performance of RL-based detection. The solution of the optimization problem is obtained by an explicit form based on simple approximations, and it reveals that the optimal training length depends on the change in the likelihood probability. Simulation results demonstrate that the proposed method efficiently reduces the training length when a rapid change in likelihood probability is produced in fading channels. Moreover, this reduction contributes to improving the spectral efficiency by an avoiding undesirable learning process. Consequently, the spectral efficiency of the proposed method can be significantly increased compared to that of conventional RL-based detection. For instance, the proposed method achieves 1.76 times higher spectral efficiency than the conventional method at 30 km/h.