Low-resolution Analog-to-digital Converters Research Articles

Analysis and Optimization for Downlink Cell-Free Massive MIMO System with Mixed DACs.

This paper concentrates on the rate analysis and optimization for a downlink cell-free massive multi-input multi-output (MIMO) system with mixed digital-to-analog converters (DACs), where some of the access points (APs) use perfect-resolution DACs, while the others exploit low-resolution DACs to reduce hardware cost and power consumption. By using the additive quantization noise model (AQNM) and conjugate beamforming receiver, a tight closed-form rate expression is derived based on the standard minimum mean square error (MMSE) channel estimate technique. With the derived result, the effects of the number of APs, the downlink transmitted power, the number of DAC bits, and the proportion of the perfect DACs in the mixed-DAC architecture are conducted. We find that the achievable sum rate can be improved by increasing the proportion of the perfect DACs and deploying more APs. Besides, when the DAC resolution arrives at 5-bit, the system performance will invariably approach the case of perfect DACs, which indicates that we can use 5-bit DACs to substitute the perfect DACs. Thus, it can greatly reduce system hardware cost and power consumption. Finally, the weighted max–min power allocation scheme is proposed to guarantee that the users with high priority have a higher rate, while the others are served with the same rate. The simulation results prove the proposed scheme can be effectively solved by the bisection algorithm.

Bayesian Channel Estimation and Data Detection in Oversampled OFDM Receiver With Low-Resolution ADC

This paper focuses on a novel orthogonal frequency division multiplexing (OFDM) receiver architecture, which uses a low-resolution analog-to-digital converter (ADC) to oversample the received signal in time domain. Although attractive in terms of power consumption and hardware cost, low-resolution ADC incurs severe nonlinear quantization distortion and thus destroys the orthogonality between the OFDM subcarriers. The loss of orthogonality, together with the oversampling-caused correlation in noise samples, poses a great challenge to the OFDM receiver design. This paper aims to tackle this challenge. For the proposed receiver, we consider an often-used two-phase transmission protocol. In the first phase, training OFDM symbols are transmitted for channel estimation. In the second phase, information-conveying OFDM symbols are transmitted and detected using the previously obtained channel estimate. Therefore, the proposed receiver consists of two key components: channel estimator and data detector. These components are elaborately derived in the framework of Bayesian inference. Due to the diversity gain resulting from the oversampling operation, the proposed receiver can remarkably outperform the counterparts, including the conventional OFDM receiver with perfect infinite-precision quantization.

Variational Bayes’ Joint Channel Estimation and Soft Symbol Decoding for Uplink Massive MIMO Systems With Low Resolution ADCs

We consider the problem of joint channel estimation and data decoding in uplink massive multiple input multiple output systems with low resolution analog-to-digital converters (ADCs) at the base station. The nonlinearities introduced by the ADCs make the problem challenging: in particular, the existing linear detectors perform poorly. Also, the channel coding used in commercial wireless systems necessitates soft symbol detection to obtain satisfactory performance. In this paper, we present a low-complexity variational Bayesian (VB) inference procedure to jointly solve the (possibly correlated) channel estimation and soft symbol decoding problem. We present the approach in progressively more complex scenarios, including the case where even the channel statistics are not available at the receiver. Finally, we combine our proposed VB procedure with a belief propagation (BP) based channel decoder, which further enhances the performance without any additional complexity. We numerically evaluate the bit error rate (BER) and the normalized mean squared error (NMSE) in the channel estimates obtained by our algorithm as a function of various system parameters, and benchmark the performance against genie-aided and state-of-the-art receivers. The results show that VB procedure is a promising technique for the design of low-complexity advanced receivers in low resolution ADC based systems.

Is Multipath Channel Beneficial for Wideband Massive MIMO With Low-Resolution ADCs?

Coarse quantization by using low-resolution analog-to-digital converters (ADCs) is an attractive approach to relieve the burden of power consumption and hardware cost of implementing massive multiple-input multiple-output (MIMO) systems. In this article, we analyze the uplink spectral efficiency of a multiuser massive MIMO system with low-resolution ADCs in the context of orthogonal frequency division multiplexing (OFDM) under multipath channels. Firstly, we develop an efficient pilot scheme which results in a constant average power of the quantization noise for different channel delay power spectrums and also minimizes the mean squared error of channel estimation. Then a tight approximation of the uplink achievable rate is derived in a closed form considering both perfect channel state information (CSI) and estimated CSI. Then we analyze the impact of multipath channels on the system performance. Under perfect CSI, we discover that an increment of multipath taps has a positive impact on compensating the performance degradation due to the quantization noise. Under imperfect CSI, the most beneficial channel is uniformly distributed over a specific number of taps. Simulations are conducted to verify our analytical results.

Secrecy Rate Maximization for Reconfigurable Intelligent Surface Aided Millimeter Wave System With Low-Resolution DACs

In this letter, we investigate the secrecy rate of a reconfigurable intelligent surface (RIS)-aided millimeter-wave (mmWave) system with low-resolution digital-to-analog converters (LDACs). Compared to the RIS-aided systems in most existing works, we consider how to alleviate the hardware loss and improve the secrecy rate by using RIS. In particular, we formulate a secrecy rate maximization problem with hardware constraints. To handle the problem, an alternating optimization (AO)-based algorithm is proposed. Specifically, we first use the successive convex approximation (SCA) method to obtain the transmit beamforming. Then, the element-wise block coordinate descent (BCD) method is used to obtain the RIS phase shifts. Numerical results demonstrate that the RIS can mitigate the hardware loss, and the proposed AO-based algorithm with low complexity outperformances the baselines.

Spatial Wideband Channel Estimation for mmWave Massive MIMO Systems With Hybrid Architectures and Low-Resolution ADCs

In this article, a channel estimator for wideband millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems with hybrid architectures and low-resolution analog-to-digital converters (ADCs) is proposed. To account for the propagation delay across the antenna array, which cannot be neglected in wideband mmWave massive MIMO systems, the discrete time channel that models the spatial wideband effect is developed. Also, the training signal design that addresses inter-frame, inter-user, and inter-symbol interferences is investigated when the spatial wideband effect is not negligible. To estimate the channel parameters over the continuum based on the maximum a posteriori (MAP) criterion, the Newtonized fully corrective forward greedy selection-cross validation-based (NFCFGS-CV-based) channel estimator is proposed. NFCFGS-CV is a gridless compressed sensing (CS) algorithm, whose termination condition is determined by the CV technique. The CV-based termination condition is proved to achieve the minimum squared error (SE). The simulation results show that NFCFGS-CV outperforms state-of-the-art on-grid CS-based channel estimators.

Cell-Free Massive MIMO Systems With Low-Resolution ADCs: The Rician Fading Case

This article studies the uplink and downlink achievable rates of cell-free massive multi-input multi-output (MIMO) systems over Rician fading channels, assuming that each access point possesses multiple antennas that are connected with low-resolution analog-to-digital converters (ADCs). Achievable closed-form rate expressions for both uplink and downlink are derived, which enable us to explore the design issues surrounded by the key parameters, such as the number of total antennas, the transmit power, the ADC resolution, and the Rician <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {{\it K}}$</tex-math></inline-formula> -factor. Moreover, the weighted max–min fairness power optimization algorithms are proposed. Specifically, the proposed algorithms for uplink and downlink can be formulated as geometric programming and second-order-cone programming, respectively. All the theoretical analyses and the effectiveness of the proposed algorithms are verified by simulation experiments.

Deep Learning-Based Channel Estimation for Massive-MIMO With Mixed-Resolution ADCs and Low-Resolution Information Utilization

In this paper, we propose two deep-learning based uplink channel estimation approaches that can utilize not only high-resolution-ADC-quantized but also low-resolution-ADC-quantized received pilot signals to improve estimation performance for mixed analog-to-digital converters (ADCs) massive multiple-input multiple-output (MIMO) systems. In each approach, low-resolution-ADC-quantized received pilot signals are utilized with one of three different schemes, i.e., High-resolution quantized pilot + All low-resolution quantized pilot(High + All), High-resolution quantized pilot + Argument of low-resolution quantized pilot (High + Arg) or High-resolution quantized pilot + Modulus of low-resolution quantized pilot (High + Mod). All three schemes include the intact quantized pilot signals at high-resolution antennas, but the quantized pilot signals at low-resolution ADCs are exploited differently in each scheme. Modified selective-input prediction deep neural network (Modified SIP-DNN) is developed to predict more realistic channels and test the effectiveness of the utilization scheme. To achieve further performance improvement, a deep neural network (DNN) based two-stage network is proposed where the recovering DNN (RC-DNN) in the first stage forms a coarse estimation for channels at antennas with low-resolution ADCs and the refining DNN (Ref-DNN) in the second stage outputs a refined estimation for channels at all antennas. Simulation results show that our proposed approaches outperform state-of-the-art channel estimation method especially when most antennas are equipped with low-resolution ADCs.

Phase Loss Detection Using Current Signals: A Review

This paper discusses open phase faults, which can happen in a system grid-converter-motor drive, and measures to properly handle this type of fault. The authors of this paper provide classification of algorithms used for the detection of the loss of phase and explain the distinctive features of each group of methods. They review existing algorithms, which are based on the analysis of the current signals, discuss their pros and cons and suggest possible areas of usage for each group of methods. The authors also propose one novel method for detection of open phase, which was developed for low-cost systems with low resolution analog-to digital converters (ADC). This paper mainly considers methods for three-phase motors as the most popular machines, however some algorithms can be used in multiphase drives. The authors of the paper also share their more than 20 years’ experience combined, in this area, which was obtained by developing industrial and commercial drives, and focus on the requirements of the IEC/UL 60730 safety standard, where the phase-loss detection algorithm is one of the essential parts of control system.

Receiver Energy Efficiency and Transmission Latency Analysis of Outage-Constrained Differential PSK With a Finite Resolution ADC

We consider a power constrained downlink communication scenario where energy efficiency, reliability, and latency take precedence over rate, as in some Internet of Things (IoT) applications. To reduce its receiver power consumption and complexity, we assume that the IoT device has a single RF chain and investigate the finite-resolution analog-to-digital converter (ADC) operation with differential Phase Shift Keying (PSK) modulation. A lower ADC resolution leads to an exponential decrease in power consumption, while adopting differential PSK enables the use of a low-cost detector with no channel state information (CSI) or carrier phase recovery circuitry. Our main goal in this article is to compare, both analytically and numerically using representative IoT system design parameters, the receiver energy efficiency of the proposed differential PSK system with a coherent PSK system that uses estimated CSI under reliability and latency constraints in Rayleigh slow-fading and ADC quantization distortion conditions. To mitigate the ADC finite-resolution effects without requiring CSI at the receiver or transmitter, we propose and analyze a PSK differentially-modulated Alamouti space-time block transmission scheme with only two RF chains at the transmitter while still restricting the IoT device to have a single RF chain. Our results demonstrate that in the considered low-rate, and outage and latency-constrained scenario with stringent power consumption requirements, differentially-modulated Alamouti transmissions to a single RF-chain IoT device with a low-resolution ADC is an attractive choice in terms of receiver energy efficiency, reliability, and transmission latency.

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.

Massive MIMO as an Extreme Learning Machine

This work shows that a massive multiple-input multiple-output (MIMO) system with low-resolution analog-to-digital converters (ADCs) forms a natural extreme learning machine (ELM). The receive antennas at the base station serve as the hidden nodes of the ELM, and the low-resolution ADCs act as the ELM activation function. By adding random biases to the received signals and optimizing the ELM output weights, the system can effectively tackle hardware impairments, such as the nonlinearity of power amplifiers and the low-resolution ADCs. Moreover, the fast adaptive capability of ELM allows the design of an adaptive receiver to address time-varying effects of MIMO channels. Simulations demonstrate the promising performance of the ELM-based receiver compared to conventional receivers in dealing with hardware impairments.

Low-Latency Lattice-Reduction-Aided One-Bit Precoding Processor for 64-QAM 4×64 MU–MIMO Systems

Massive multi-user multiple-input multiple-output (MU-MIMO) communication is a crucial technique for next-generation wireless systems because it enables high-throughput and ultra-reliable data transmission. However, high power consumption is a challenging problem in conventional transceiver designs, where each RF chain at the transmitter requires a pair of high-resolution digital-to-analog converters (DACs), which are the primary power sources in front-end circuits. Therefore, quantized precoding algorithms were recently proposed to address this issue. They used low-resolution DACs at the transmitter and compensated for the distortion caused by the quantization effect at the baseband. This paper proposes a constellation-range gain-controlled lattice-reduction-aided (CR-GCLRA) one-bit precoding algorithm for massive MU-MIMO systems with high-order quadrature amplitude modulation (QAM) signaling. Lattice reduction (LR) preprocessing is adopted for performance enhancement. A novel gain-control mechanism is proposed to address the constellation range expansion problem in conventional LR preprocessing. We designed and implemented a CR-GCLRA one-bit precoding processor by using TSMC 40-nm CMOS technology to accelerate the one-bit precoding processing for 64-QAM 4 ×64 MU-MIMO system. The proposed one-bit precoding processor can achieve a throughput of 43.92 Mbits per second at a clock speed of 269 MHz with 271 mW power consumption and 0.51μs latency.

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.

Finite-Alphabet Symbol-Level Multiuser Precoding for Massive MU-MIMO Downlink

We propose a finite-alphabet symbol-level precoding technique for massive multiuser multiple-input multiple-output (MU-MIMO) downlink systems which are equipped with finite-resolution digital-to-analog converters (DACs) of any precision. Using the idea of constructive interference (CI), we adopt a max-min fair design criterion which aims to maximize the minimum instantaneous received signal-to-noise ratio (SNR) among the user equipments (UEs) while ensuring a CI constraint for each UE under the restriction that the output of the precoder is a vector with finite-alphabet discrete elements. Due to this latter constraint, the design problem is an NP-hard quadratic program with discrete variables, and hence, is difficult to solve. In this paper, we tackle this difficulty by reformulating the problem in several steps into an equivalent continuous-domain biconvex form, including equivalent representations for discrete and binary constraints. Our final biconvex reformulation is obtained via an exact penalty approach and can efficiently be solved using a standard cyclic block coordinate descent algorithm. We evaluate the performance of the proposed finite-alphabet precoding design for DACs with different resolutions, where it is shown that employing low-resolution DACs can lead to higher power efficiencies. In particular, we focus on a setup with one-bit DACs and show through simulation results that compared to the existing schemes, the proposed design can achieve SNR gains of up to 2 dB. We further provide analytic and numerical analyses of complexity and show that our proposed algorithm is computationally efficient as it typically needs only a few tens of iterations to converge.

Waveform Design for Collocated MIMO Radar With High-Mix-Low-Resolution ADCs

Adopting low-resolution analog-to-digital converters (ADCs) for receive antennas of a multiple-input multiple-output (MIMO) system can remarkably reduce the hardware cost, circuit power consumption as well as amount of data to be transferred from RF components and the baseband-processing unit. However, an obvious performance loss is also expected. Towards this end, in this work we introduce a new architecture which contains both high- and low-resolution ADCs (named as high-mix-low-resolution ADCs) for collocated MIMO radar, and the associated problem of waveform design is discussed in detail. Specifically, the problem jointly optimizes the waveform, ADC switch vector and receive filter, so as to maximize the signal-to-interference-plus-quantization-error-and-noise ratio (SIQENR). To tackle the resultant nonconvex problem, an alternating optimization method (AOM) is devised. To be more specific, the ADC switch vector and waveform matrix are optimized with the block successive upper-bound minimization (BSUM) framework based on the Dinkelback method. Furthermore, a continuous and concave function is introduced to approximate the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> norm to achieve a binary solution of the ADC switch vector. It is shown that the optimal solutions to the ADCs switch vector and waveform matrix can be efficiently attained by using the alternating direction method of multipliers (ADMM) approach and Karush-Kuhn-Tucher (KKT) conditions, respectively. Numerical simulations are provided to demonstrate the effectiveness of the proposed schemes.

Stochastic Hybrid Combining Design for Quantized Massive MIMO Systems

Both the power-dissipation and cost of massive multiple-input multiple-output (mMIMO) systems may be substantially reduced by using low-resolution analog-to-digital converters (LADCs) at the receivers. However, both the coarse quantization of LADCs and the inaccurate instantaneous channel state information (ICSI) degrade the performance of quantized mMIMO systems. To overcome these challenges, we propose a novel stochastic hybrid analog-digital combiner (SHC) scheme for adapting the hybrid combiner to the long-term statistics of the channel state information (SCSI). We seek to minimize the transmit power by jointly optimizing the SHC subject to average rate constraints. For the sake of solving the resultant nonconvex stochastic optimization problem, we develop a relaxed stochastic successive convex approximation (RSSCA) algorithm. Simulations are carried out to confirm the benefits of our proposed scheme over the benchmarkers.

Energy-Efficiency Maximization of Hybrid Massive MIMO Precoding With Random-Resolution DACs via RF Selection

Energy-efficiency (EE) is identified as a key 5G metric and will have a major impact on the hybrid beamforming system design. The most promising system designs include a reduced number of radio-frequency (RF) chains with digital-to-analog converters (DACs) of lower sampling resolution. However, naive reduction of beamformer components to reduce power consumption typically leads to significant loss of spectral-efficiency (SE). In this paper, we focus on the transmit beamforming (precoding) and we introduce an architecture with low-end components that maximizes the EE while minimizing the effects on SE. This is achieved by the novel design of the analog part of the precoder, where the number of the RF chains is not reduced a priori, but deactivated based on an optimization algorithm. Thus, the problem becomes a subset selection one, where only the RF chains with the optimal SE-EE performance are being activated. The selection algorithm not only determines the optimal number of RF chains to activate but also selects optimally between DACs of randomly-allocated resolution. Through simulations, we verify that the proposed architecture exhibits improved performance when compared with baseline precoding techniques which use a predefined number of RF chains with low-resolution DACs.

Analog Combining in Intelligent Reflecting Surface Assisted System with Low-Resolution ADCs

Intelligent Reflection Surface (IRS) and low-resolution analog-to-digital converters (ADCs) are proven to be efficient ways to release the burden of power consumption for future wireless systems. In this paper, the effect of IRS and quantization on the performance of multiple-input multiple-output (MDVIO) channels is investigated in terms of channel capacity. The reflection matrix of the IRS and analog combiner matrix are optimized jointly. To this end, the expression of capacity with low SNR is derived, and the optimization problem of the reflection matrix is converted to semidefinite programming (SDP). A gradient-based approach is proposed to optimize the analog combiner matrix and the reflection matrix in a general case. Simulation results are provided to assess the performance of proposed designs, it is shown that the IRS can improve the performance of the system where there is no line-of-sight channel to some extent, and a larger capacity could be obtained in low SNR expression than general expression under same conditions.

On the Performance of Massive MIMO Systems With Low-Resolution ADCs and MRC Receivers Over Rician Fading Channels

This article considers uplink massive multiple-input multiple-output (MIMO) systems with maximum-ratio-combining (MRC) receivers over Rician fading channels. Low-resolution analog-to-digital converters (ADCs) are considered for both data detection and channel estimation. Asymptotic approximations of the spectrum efficiency (SE) for large-scale MIMO systems are derived based on random matrix theory. With these closed-form expressions, we can provide insights into the tradeoffs between the SE and the ADC resolution and study the influence of the Rician K-factors on the performance. It is shown that a large value of K-factors may lead to a better performance and alleviate the influence of quantization noise on channel estimation. Moreover, we investigate the power-scaling laws for the system under imperfect channel state information and it shows that when the number of base station (BS) antennas is very large, without loss of the SE performance, the transmission power can be scaled by the number of BS antennas while the overall performance is limited by the resolution of ADCs. The asymptotic analysis is validated by numerical results. We also show that ADCs with intermediate resolutions lead to better energy efficiency than that with high-resolution or extremely low-resolution ADCs.