1-bit Analog-to-digital Converters Research Articles

A 1-bit DACs precoding for MU-MIMO based on binary equilibrium constraint: An alternating direction method

High power consumption is one of the main problems in the practical application of massive multi-user multi-input-multi-output (MU-MIMO) systems, and using 1-bit digital-to-analog converters (DACs) instead of high-resolution DACs is an effective way to reduce the power consumption of massive MU-MIMO systems. How to design efficient precoding schemes to improve the performance of 1-bit MU-MIMO systems has become a hot research field. This paper mainly studies the precoding problem of 1-bit DACs based on minimum mean squared error (MMSE). We first transform the non-convex constraints of the traditional optimization problem using binary equilibrium constraints. Then, to solve the transformed objective problem, we establish a framework based on the alternating direction method (ADM), use the fast projection gradient (FPG) method, and propose an alternating maximum minimum (AMM) algorithm to solve the optimization variables alternately. We have verified the convergence of the proposed algorithm and analyzed the accuracy of the proposed ADM framework and the computational complexity of the proposed algorithm in detail. In the simulation section, we analyze the uncoded bit error rate (BER) performance of the proposed algorithm in phase-shift keying (PSK) modulation and quadrature amplitude modulation (QAM) modes. The simulation results show that compared with existing advanced algorithms, the proposed algorithm can achieve performance advantages of about 1 dB and 2 dB in QPSK modulation mode and 16QAM modulation mode, respectively.

High Order QAM Modulation in Massive MIMO Systems With Asymmetrically Quantized 1-Bit ADCs

Deploying 1-bit analog-to-digital converters (ADCs) in massive multiple-input multiple-output (MIMO) systems is promising to reduce the energy consumption. However, serious quantization errors limit the feasibility of high order quadrature amplitude modulation (QAM). This paper focuses on the performance analysis of 1-bit ADC massive MIMO systems with high order QAM. Firstly, we theoretically analyze the relationship between the quantization error and various quantization parameters. We reveal that there exists an overlapping of constellations at high signal to noise ratio (SNR) with symmetric quantization. This is because the amplitude information in the detected signal at high SNR is lost which is multiplied by the zero quantization threshold in the symmetric quantization. To overcome this problem, asymmetric quantization should be considered. Based on the analysis of the quantization error, we propose two approaches to recover the amplitude information. One is a near unbiased detection (NUD) by scaling the traditional linear detector and optimizing the quantization threshold. The other is a sub-array detection based on non-uniform quantization (SAD-NQ) to correct the deviation of the detection result by averaging over sub-arrays. Simulation results show that the proposed approaches can significantly improve the detection performance of high order QAM signal in the 1-bit ADC massive MIMO systems.

Quantization error for weak RF simultaneous signal estimation

In a congested signal environment, it is difficult to obtain estimates of weak RF signal parameters. Determining signal parameter estimates in real time is a challenge for electronic warfare receivers that aim to receive multiple simultaneous signals. Prior work provided estimates of weak signal parameters (weak signal frequency and weak signal amplitude) without taking into account any error introduced by analog-to-digital converters that are inherently part of digital signal processing systems. In order to obtain realistic estimates, we need to take error introduced by an ADC into account. The primary aim of this paper is to quantify error introduced by a single ideal ADC as a function of angle. This paper presents a method to estimate angle resolution and quantization levels in N-bit analog-to-digital converters (ADCs) for use in a weak radiofrequency (RF) simultaneous signal estimation process. The paper quantifies the error in the angle quantization of an N-bit ADC for an input complex signal that is the instantaneous frequency obtained for the situation in which there are two simultaneous signals (with one strong signal and one weak signal) in a weak RF simultaneous signal estimation process. The presented method describes the process to determine the angle quantization range, angle quantization uncertainty, and angle quantization error. This approach has potential applications in electronic warfare (EW) systems. The approach also has potential for assessing ADC performance for measurements that approach the quantum limit. Results are presented for 1-bit, 2-bit, 3-bit, and 10-bit ADCs.

Wireless Multi-Casting for Wideband Millimeter-Wave System With 1-bit DAC

Wireless multi-casting is an efficient transmission modality for downlink network control and content sharing. Conventional multi-casting amounts to finding an optimized beamforming vector under a specific performance metric and without the need of a dedicated treatment at the receiver. However, the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">one-fit-all</i> strategy is not directly applicable to mmWave systems equipped with 1-bit digital-to-analog converters (DAC), prompting us to develop a new multi-casting framework. The overarching design is built upon a vector-based instead of a scalar-based modulation, with which the multi-casting exhibits special features on both the transmitter and receiver. Specifically, we start by revealing the theoretical fundamentals for multi-casting under different 1-bit setups. Then, we design an iterative scheme to generate high-order constellations by establishing the equivalence between the codeword basis and low-order constellations. Finally, effective detection solutions are individually proposed for low-order and high-order constellations per their specific signal structures. Extensive analyses and simulations have been carried out to corroborate the decency of the proposed multi-casting strategy.

Multiuser-MIMO Systems Using Comparator Network-Aided Receivers With 1-Bit Quantization

Low-resolution analog-to-digital converters (ADCs) are promising for reducing energy consumption and costs of multiuser multiple-input multiple-output (MIMO) systems with many antennas. We propose low-resolution multiuser MIMO receivers where the signals are simultaneously processed by 1-bit ADCs and a comparator network, which can be interpreted as additional virtual channels with binary outputs. We distinguish the proposed comparator networks in fully and partially connected. For such receivers, we develop the low-resolution aware linear minimum mean-squared error (LRA-LMMSE) channel estimator and detector according to the Bussgang theorem. We also develop a robust detector which takes into account the channel state information (CSI) mismatch statistics. By exploiting knowledge of the channel coefficients we devise a mean-square error (MSE) greedy search and a sequential signal-to-interference-plus-noise ratio (SINR) search for optimization of partially connected networks. Numerical results show that a system with extra virtual channels can outperform a system with additional receive antennas, in terms of bit error rate (BER). Furthermore, by employing the proposed channel estimation with its error statistics, we construct a lower bound on the ergodic sum rate for a linear receiver. Simulation results confirm that the proposed approach outperforms the conventional 1-bit MIMO system in terms of BER, MSE and sum rate.

Enhanced Signal Detection and Constellation Design for Massive SIMO Communications With 1-Bit ADCs

In this paper, we investigate a transmitter and receiver design for a single-user massive SIMO (single-input multiple-output) system with 1-bit analog-to-digital converters (ADCs) at the base station (BS), where the user adopts higher-order modulation, e.g., 16-quadrature amplitude modulation (16-QAM), for the data transmission. For the channel estimation and the signal detection, linear least-squares (LS) estimation and maximum ratio combining (MRC) are respectively employed. In this context, we first introduce closed-form formulas for the mean of the estimated symbols and for the correlation matrix between their real and imaginary parts considering the effect of 1-bit quantization. The study of the distribution of the estimated symbols indicates that, in presence of 1-bit ADCs, the conventional 16-QAM detector and the typical square 16-QAM modulation are not adequate. In light of this, we propose three novel symbol detectors and re-design the 16-QAM modulation in order to improve the symbol error rate (SER). Furthermore, the upper bound on the SER is analyzed based on the pair-wise error probability and the boundary equation between two regions is also studied. Through numerical results, the proposed framework, i.e., the symbol detector and the transmit constellation design, shows a significant enhancement in the SER performance against the conventional detector and the typical square 16-QAM modulation.

On Robust Millimeter Wave Line-of-Sight MIMO Communications With Few-Bit ADCs

This work focuses on providing robust line-of-sight (LoS) spatial multiplexing at flexible communications distances and directions. Considering oblique LoS uniform linear arrays, we first derive the rank-deficient and orthogonal conditions for the LoS MIMO channel matrices. With this discovery, the topology of high spatial-resolution on one side of the link is shown with a wide full-rank-channel guarantee interval over distance and direction variations. Additionally, to reduce the implementation costs and power consumption, we propose to use low amplitude-resolution quantizers at the side of high spatial-resolution. With numerical evaluations on systems having few-bit analog-to-digital converters (ADCs), the proposed system design is shown to simultaneously achieve a higher spectrum efficiency and higher energy efficiency compared to a conventional single-stream high-amplitude-resolution over a wide signal-to-noise-ratio (SNR) range. Furthermore, we investigate channel equalization under the extreme case of using 1-bit ADCs. After providing a new viewpoint on the generalized approximate message passing (GAMP) algorithm from constrained Bethe free energy minimization, our simulations on bit-error-rates show that the GAMP algorithm can significantly reduce the performance degradation due to coarse quantization and can significantly outperform the Bussgang decomposition based linear minimum-mean-square-error estimator, especially at high SNRs.

Channel Estimation and Data Detection Analysis of Massive MIMO With 1-Bit ADCs

We present an analytical framework for the channel estimation and the data detection in massive multiple-input multiple-output uplink systems with 1-bit analog-to-digital converters (ADCs) and i.i.d. Rayleigh fading. First, we provide closed-form expressions of the mean squared error (MSE) of the channel estimation considering the state-of-the-art linear minimum MSE estimator and the class of scaled least-squares estimators. For the data detection, we provide closed-form expressions of the expected value and the variance of the estimated symbols when maximum ratio combining is adopted, which can be exploited to efficiently implement minimum distance detection and, potentially, to design the set of transmit symbols. Our analytical findings explicitly depend on key system parameters such as the signal-to-noise ratio (SNR), the number of user equipments, and the pilot length, thus enabling a precise characterization of the performance of the channel estimation and the data detection with 1-bit ADCs. The proposed analysis highlights a fundamental SNR trade-off, according to which operating at the right noise level significantly enhances the system performance.

Channel Estimation in MIMO Systems With One-Bit Spatial Sigma-Delta ADCs

This paper focuses on channel estimation in single-user and multi-user MIMO systems with multi-antenna base stations equipped with 1-bit spatial sigma-delta analog-to-digital converters (ADCs). A careful selection of the quantization voltage level and phase shift used in the feedback loop of 1-bit sigma-delta ADCs is critical to improve its effective resolution. We first develop a quantization noise model for 1-bit spatial sigma-delta ADCs. Using the developed noise model, we then present a two-step channel estimation algorithm to estimate a multipath channel parameterized by the gains, angles of arrival (AoAs), and angles of departure (AoDs). Specifically, in the first step, the AoAs are estimated using uplink pilots, which excite all the angles uniformly. Next, in the second step, the AoDs are estimated by progressively refining uplink beams through a recursive bisection procedure followed by a weighted least squares path gain estimator. For this algorithm, we propose a technique to select the quantization voltage level and phase shift. Through numerical simulations, we demonstrate that with the proposed parametric channel estimation algorithm, MIMO systems with 1-bit spatial sigma-delta ADCs perform significantly better than those with regular 1-bit ADCs and are on par with MIMO systems having high-resolution ADCs

1-Bit Massive MIMO Transmission: Embracing Interference with Symbol-Level Precoding

The deployment of large-scale antenna arrays for cellular base stations (BSs), termed as `Massive MIMO', has been a key enabler for meeting the ever-increasing capacity requirement for 5G communication systems and beyond. Despite their promising performance, fully-digital massive MIMO systems require a vast amount of hardware components including radio frequency chains, power amplifiers, digital-to-analog converters (DACs), etc., resulting in a huge increase in terms of the total power consumption and hardware costs for cellular BSs. Towards both spectrally-efficient and energy-efficient massive MIMO deployment, a number of hardware limited architectures have been proposed, including hybrid analog-digital structures, constant-envelope transmission, and use of low-resolution DACs. In this paper, we overview the recent interest in improving the error-rate performance of massive MIMO systems deployed with 1-bit DACs through precoding at the symbol level. This line of research goes beyond traditional interference suppression or cancellation techniques by managing interference on a symbol-by-symbol basis. This provides unique opportunities for interference-aware precoding tailored for practical massive MIMO systems. Firstly, we characterize constructive interference (CI) and elaborate on how CI can benefit the 1-bit signal design by exploiting the traditionally undesired multi-user interference as well as the interference from imperfect hardware components. Subsequently, we overview several solutions for 1-bit signal design to illustrate the gains achievable by exploiting CI. Finally, we identify some challenges and future research directions for 1-bit massive MIMO systems that are yet to be explored.

Improved CRB for Millimeter-Wave Radar With 1-Bit ADCs

Millimeter-wave is widely used for consumer radar applications like driver assistance systems in automated vehicles and gesture recognition in touch-free interfaces. To cope with the increased hardware complexity, higher costs and power consumption of wideband systems at millimeter-wave frequencies, we propose a fully digital architecture with low-resolution analog-to-digital converters (ADCs) on each radio-frequency chain. The effect of the low-resolution ADCs on radar parameter estimation is characterized by the Cramer-Rao bound (CRB) under the proposed hardware constraints. Prior work has shown that at low signal-to-noise ratio, a radar system with 1-bit ADCs suffers a performance loss of 2 dB in parameter estimation compared to a system with ideal infinite resolution ADCs. In this paper, we design an analog preprocessing unit that beamforms in a particular direction and improves the system performance in terms of the achievable CRB. We optimize the proposed preprocessing architecture and show that the optimized network is realizable through low-cost low-resolution phase-shifters. With the optimized preprocessor network in the system, we reduce the gap to 1.16 dB compared to a system with ideal ADCs. We demonstrate the potential of the proposed architecture to meet the requirements of high-resolution sensing through analytical derivation and numerical computation of an improved CRB and show its achievability through a correlation-based estimator.

Optimized Uniform Scalar Quantizers of Ternary ADCs for Large-Scale MIMO Communications

Large-scale multiple-input multiple-output (LS-MIMO), a promising technology for the future wireless networks to boost the network capacity, unavoidably faces hardware cost and power consumption issues due to a large number of high-resolution power-hungry analog-to-digital converters (ADCs) at the receiver side. The low-resolution ADCs have recently been proven to be an effective solution to cut down the system cost. This paper studies the LS-MIMO communication systems where three-level ADCs, so-called Ternary ADCs (T-ADCs), are employed to achieve better energy efficiency in some LS-MIMO configurations. The truncation limit of the uniform scalar quantizer of the T-ADCs is optimized to minimize the quantization distortion on the LS-MIMO received signal, and thus its performance approaches that of the well-known Lloyd-Max algorithm while offering lower complexity and better robustness. Furthermore, our proposed solution is independent of the number of antennas. The LS-MIMO systems' performance with the proposed T-ADCs is substantially improved over the conventional 3- σ uniform scalar quantizer in three different performance metrics - achievable rates, iterative decoding thresholds of pragmatic protograph low-density parity-check codes (LDPC), and the frame error rate (FER)/bit error rate (BER). Our energy efficiency investigation reveals that proposed T-ADCs attain better energy efficiency than that of the 1-bit ADCs and 2-bit ADCs when the ratio between the receiving antennas and the transmitting antennas is low and medium as the power consumption of ADCs and the transmission power are better balanced in comparison with one-bit ADCs and two-bit ADCs.

High Order PSK Modulation in Massive MIMO Systems With 1-Bit ADCs

Massive multiple-input multiple-output (MIMO) systems with 1-bit analog-to-digital converters (ADCs) are promising to reduce the energy consumption. However, the serious quantization error caused by 1-bit ADCs will potentially limit the feasibility of high order modulations. This paper focuses on the analysis of the high order phase-shift keying (PSK) signal transmission in the 1-bit ADC massive MIMO system. Firstly, assuming ideal channel estimation and a single mobile station (MS), we theoretically prove that with an asymptotically large number of antennas at the base station, PSK signals with arbitrary modulation order can be recovered in the 1-bit ADC massive MIMO system. Secondly, we analyze the impact of pilot based channel estimation on the recovery of the high order PSK signals, which leads to a periodic asymptotic detection phase error (ADPE) at high signal to noise ratio (SNR). Furthermore, we also propose to optimize the pilot sequence for minimizing the cumulative absolute ADPE. Finally, the analysis is extended to the multi-MS case and the performance with different pilot patterns is discussed. Simulation results validate our analysis and show that using our proposed optimized pilot sequence can significantly improve the detection performance for both single-MS and multi-MS 1-bit ADC massive MIMO systems.

On the Capacity-Achieving Scheme and Capacity of 1-Bit ADC Gaussian-Mixture Channels

This paper addresses the optimal signaling scheme and capacity of an additive Gaussian mixture (GM) noise channel using 1-bit analog-to-digital converters (ADCs). The consideration of GM noise provides a more realistic baseline for the analysis and design of co-channel interference links and networks. Towards that goal, we first show that the capacityachieving input signal is π/2 circularly symmetric. By examining a necessary and sufficient Kuhn–Tucker condition (KTC) for an input to be optimal, we demonstrate that the maximum number of optimal mass points is four. Our proof relies on Dubin’s theorem and the fact that the KTC coefficient is positive, i.e., the power constraint is active. By combining with the π/2 circularly symmetric property, it is then concluded the optimal input is unique, and it has exactly four mass points forming a square centered at the origin. By further checking the first and second derivatives of the modified KTC, it is then shown that the phase of the optimal mass point located in the first quadrant is π/4. Thus, the capacity-achieving input signal is QPSK. This result helps us obtain the channel capacity in closed-form.

Asymptotic Capacity of Massive MIMO With 1-Bit ADCs and 1-Bit DACs at the Receiver and at the Transmitter

In this paper, we investigate the capacity of massive multiple-input multiple-output (MIMO) systems corrupted by complex-valued additive white Gaussian noise (AWGN) when both the transmitter and the receiver employ 1-bit digital-to-analog converters (DACs) and 1-bit analog-to-digital-converters (ADCs). As a result of 1-bit DACs and ADCs, the transmitted and received symbols, as well as the transmitand receive-side noisy channel state information (CSI) are assumed to be quantized to 1-bit of information. The derived results, applicable to both single-user and multi-user MIMO, show that the capacity of the considered massive MIMO system is 2N and 2M bits per channel use when N is fixed and M goes to infinity and when M is fixed and N goes to infinity, respectively, where M and N denote the number of transmit and receive antennas, respectively. These coincide with the respective capacities with full and noise-free CSI at both the transmitter and the receiver. In both cases, we showed that the derived capacities can be achieved with noisy 1-bit CSI at the massive-side and without any CSI at the other end. Moreover, we showed that the capacity can be achieved in one channel use without employing channel coding, which results in a latency of one channel use.

Channel Estimation for Large-Scale Multiple-Antenna Systems Using 1-Bit ADCs and Oversampling

Large-scale multiple-antenna systems with large bandwidth are fundamental for future wireless communications, where the base station employs a large antenna array. In this scenario, one problem faced is the large energy consumption as the number of receive antennas scales up. Recently, low-resolution analog-to-digital converters (ADCs) have attracted much attention. Specifically, 1-bit ADCs are suitable for such systems due to their low cost and low energy consumption. This paper considers uplink large-scale multiple-antenna systems with 1-bit ADCs on each receive antenna. We investigate the benefits of using oversampling for channel estimation in terms of the mean square error and symbol error rate performance. In particular, low-resolution aware channel estimators are developed based on the Bussgang decomposition for 1-bit oversampled systems and analytical bounds on the mean square error are also investigated. Numerical results are provided to illustrate the performance of the proposed channel estimation algorithms and the derived theoretical bounds.

Massive MIMO With Ternary ADCs

Massive multiple-input-multiple-output (MIMO) system inevitably faces the hardware cost and energy efficiency problem due to its large number of antennas at the base station (BS). The use of low-resolution analog-to-digital converters (ADCs), e.g., typical 1-bit ADCs, can effectively reduce the system cost. In this paper, we consider a massive MIMO uplink with ternary/three level ADCs. The design of typical linear combiner based detectors is given along with their analytical symbol-error-rate (SER) performance results. Analytical and simulation results show that 1) ternary ADCs can effectively compensate the SER performance gap between 1-bit and full-resolution ADCs; 2) optimal design of ternary ADCs for SER minimization can be referred to the existing design for quantization error minimization; 3) ternary ADCs perform better than 2-bit ADCs in energy efficiency. Thus, for some low-cost scenarios where implementing 2-bit ADCs for each antenna in massive MIMO may be even unaffordable, ternary ADC can be a good choice.

Efficient Nonlinear Precoding for Massive MIMO Downlink Systems With 1-Bit DACs

The power consumption of digital-to-analog converters (DACs) constitutes a significant proportion of the total power consumption in a massive multiuser multiple-input multiple-output (MU-MIMO) base station (BS). Using 1-bit DACs can significantly reduce the power consumption. This paper addresses the precoding problem for the massive narrow-band MU-MIMO downlink system equipped with 1-bit DACs at each BS. In such a system, the precoding problem plays a central role as the precoded symbols are affected by extra distortion introduced by 1-bit DACs. In this paper, we develop a highly efficient nonlinear precoding algorithm based on the alternative direction method framework. Unlike the classic algorithms, such as the semidefinite relaxation (SDR) and squared-infinity norm Douglas-Rachford splitting (SQUID) algorithms, which solve convex relaxed versions of the original precoding problem, the new algorithm solves the original nonconvex problem directly. The new algorithm is guaranteed to globally converge under some mild conditions. A sufficient condition for its convergence has been derived. The experimental results in various conditions demonstrated that the new algorithm can achieve the state-of-the-art performance comparable with the SDR algorithm while being much more efficient (e.g., more than 300 times faster than the SDR algorithm).

Transmit Signal Design for Large-Scale MIMO System With 1-bit DACs

Deploying low-resolution (e.g. one-bit) digital-to-analog converters (DACs) is of great importance in the multiple-input multiple-output (MIMO) system equipped with a large-scale antenna array since such a hardware architecture brings low-cost and circuit power saving for each antenna. In this paper, the problem of transmit signal design in a large-scale MIMO system with 1-bit DACs is investigated. To ensure directional transmission, we propose to design the transmit signal by minimizing the weighted mean-squared error (MSE) between the formed beampattern and a given one. The resulting design problem, which involves a nonconvex fourth-order objective and a set of nonconvex discrete constraints, is NP-hard, and therefore, an alternating minimization (AM) method is devised. In order to obtain a high-quality 1-bit solution, we propose a continuous and differentiable function to approximate the 1-bit signal, such that the problem with discrete 1-bit constraint is recast to an unconstrained optimization problem with a penalty term, which can be effectively solved via the limited-memory Broyden, Fletcher, Goldfarb, and Shanno (L-BFGS) approach. Moreover, it is found that a closed-form solution can be obtained when equal weights are applied. In addition, low-complexity schemes are developed based on the fast Fourier transform (FFT). The numerical simulations are conducted to demonstrate the effectiveness and superiority of the proposed method.

Supervised and Semi-Supervised Learning for MIMO Blind Detection With Low-Resolution ADCs

The use of low-resolution analog-to-digital converters (ADCs) is considered to be an effective technique to reduce the power consumption and hardware complexity of wireless transceivers. However, in systems with low-resolution ADCs, obtaining channel state information (CSI) is difficult due to significant distortions in the received signals. The primary motivation of this paper is to show that learning techniques can mitigate the impact of CSI unavailability. We study the blind detection problem in multiple-input-multiple-output (MIMO) systems with low-resolution ADCs using learning approaches. Two methods, which employ a sequence of pilot symbol vectors as the initial training data, are proposed. The first method exploits the use of a cyclic redundancy check (CRC) to obtain more training data, which helps improve the detection accuracy. The second method is based on the perspective that the to-be-decoded data can itself assist the learning process, so no further training information is required except the pilot sequence. For the case of 1-bit ADCs, we provide a performance analysis of the vector error rate for the proposed methods. Based on the analytical results, a criterion for designing transmitted signals is also presented. Simulation results show that the proposed methods outperform existing techniques and are also more robust.