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.
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…
In this article, we investigate channel estimation for wideband millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) under hybrid architecture with lowprecision analog-to-digital converters (ADCs). To design channel estimation for the hybrid structure, both analog processing components and frequency-selective digital combiners need to be optimized. The proposed channel estimator follows the typical linear-minimum-mean-square-error (LMMSE) structure and applies for an arbitrary channel model. Moreover, for sparsity channels as in mmWave, the proposed estimator performs more ef…
Advances in analog-to-digital converter (ADC) technology have opened up the possibility to directly digitize wideband radio frequency (RF) signals, avoiding the need for analog down-conversion. In this work, we consider an orthogonal frequency-division multiplexing (OFDM)-based massive multi-user (MU) multiple-input multiple-output (MIMO) uplink system that relies on direct RF-sampling at the base station and digitizes the received RF signals with 1-bit ADCs. Using Bussgang's theorem, we provide an analytical expression for the error-vector magnitude (EVM) achieved by digital down-conversion a…
Analog to Digital Converters (ADCs) are a major contributor to the energy consumption on the receiver side of millimeter-wave multiple-input multiple-output (MIMO) systems with large antenna arrays. Consequently, there has been significant interest in using low-resolution ADCs along with hybrid beam-forming at MIMO receivers for energy efficiency. However, decreasing the ADC resolution results in performance loss -- in terms of achievable rates -- due to increased quantization error. In this work, we study the application of practically implementable nonlinear analog operations, prior to sampl…
This paper considers the channel estimation problem for massive multiple-input multiple-output (MIMO) systems that use one-bit analog-to-digital converters (ADCs). Previous channel estimation techniques for massive MIMO using one-bit ADCs are all based on single-shot estimation without exploiting the inherent temporal correlation in wireless channels. In this paper, we propose an adaptive channel estimation technique taking the spatial and temporal correlations into account for massive MIMO with one-bit ADCs. We first use the Bussgang decomposition to linearize the one-bit quantized received s…
Use of low resolution analog to digital converters (ADCs) is an effective way to reduce the high power consumption of millimeter wave (mmWave) receivers. In this paper, a receiver with low resolution ADCs based on adaptive thresholds is considered in downlink mmWave communications in which the channel state information is not known a-priori and acquired through channel estimation. A performance comparison of low-complexity algorithms for power and ADC allocation among transmit and receive terminals, respectively, is provided. Through simulation of practical mmWave cellular networks, it is show…
In this article, deep learning is applied to estimate the uplink channels for mixed analog-to-digital converters (ADCs) massive multiple-input multiple-output (MIMO) systems, where a portion of antennas are equipped with high-resolution ADCs while others employ low-resolution ones at the base station. A direct-input deep neural network (DI-DNN) is first proposed to estimate channels by using the received signals of all antennas. To eliminate the adverse impact of the coarsely quantized signals, a selective-input prediction DNN (SIP-DNN) is developed, where only the signals received by the high…
Millimeter wave (mmWave) massive multiple-input multiple-output (massive MIMO) is one of the most promising technologies for the fifth generation and beyond wireless communication system. However, a large number of antennas incur high power consumption and hardware costs, and high-frequency communications place a heavy burden on the analog-to-digital converters (ADCs) at the base station (BS). Furthermore, it is too costly to equipping each antenna with a high-precision ADC in a large antenna array system. It is promising to adopt low-resolution ADCs to address this problem. In this paper, we …
This paper proposes the Newtonized fully corrective forward greedy selection-cross validation-based (NFCFGS-CV-based) channel estimator for millimeter (mmWave) hybrid massive multiple-input multiple-output (MIMO) systems with low-resolution analog-to-digital converters (ADCs). The proposed NFCFGS algorithm is a gridless compressed sensing (CS) technique that combines the FCFGS and Newtonized orthogonal matching pursuit (NOMP) algorithms. In particular, NFCFGS performs single path estimation over the continuum at each iteration based on the previously estimated paths. The CV technique is adopte…
In this paper, the fully corrective forward greedy selection-cross validation-based (FCFGS-CV-based) channel estimator is proposed for wideband millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems with low-resolution analog-to-digital converters (ADCs). The sparse nature of the mmWave virtual channel in the angular and delay domains is exploited to convert the maximum a posteriori (MAP) channel estimation problem to an optimization problem with a concave objective function and sparsity constraint. The FCFGS algorithm, which is the generalized orthogonal matching pursu…
The combination of orthogonal frequency modulation (OFDM) and multiple-input multiple-output (MIMO) systems plays an important role in modern communication systems. In order to meet the growing throughput demands, future MIMO-OFDM receivers are expected to utilize a massive number of antennas, operate in dynamic environments, and explore high frequency bands, while satisfying strict constraints in terms of cost, power, and size. An emerging technology to realize massive MIMO receivers of reduced cost and power consumption is based on dynamic metasurface antennas (DMAs), which inherently implem…
High hardware cost and high power consumption of massive multiple-input and multiple output (MIMO) are two challenges for the future wireless communications including beyond fifth generation (B5G) and sixth generation (6G). Adopting the low-resolution analog-to-digital converter (ADC) is viewed as a promising solution. Additionally, the direction of arrival (DOA) estimation is an indispensable technology for beam alignment and tracking in massive MIMO systems. Thus, in this paper, the performance of DOA estimation with mixed-ADC structure is firstly investigated. The Cramer-Rao lower bound (CR…
We consider channel estimation for an uplink massive multiple-input multiple-output (MIMO) system where the base station (BS) uses an array with low-resolution (1-2 bit) analog-to-digital converters and a spatial Sigma-Delta ($ΣΔ$) architecture to shape the quantization noise away from users in some angular sector. We develop a linear minimum mean squared error (LMMSE) channel estimator based on the Bussgang decomposition that reformulates the nonlinear quantizer model using an equivalent linear model plus quantization noise. We also analyze the uplink achievable rate with maximal ratio combin…
This paper considers uplink massive MIMO systems with 1-bit analog-to-digital converters (ADCs) and develops a deep-learning based channel estimation framework. In this framework, the prior channel estimation observations and deep neural network models are leveraged to learn the non-trivial mapping from quantized received measurements to channels. For that, we derive the sufficient length and structure of the pilot sequence to guarantee the existence of this mapping function. This leads to the interesting, and \textit{counter-intuitive}, observation that when more antennas are employed by the …
In this paper, 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 negligibl…
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 c…
In this paper, channel estimation for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems with one-bit analog-to-digital converters (ADCs) is considered. In the mmWave band, the number of propagation paths is small, which results in sparse virtual channels. To estimate sparse virtual channels based on the maximum a posteriori (MAP) criterion, sparsity-constrained optimization comes into play. In general, optimizing objective functions with sparsity constraints is NP-hard because of their combinatorial complexity. Furthermore, the coarse quantization of one-bit ADCs m…
In this paper, we derive a closed-form expression for the combiner of a multiple-input-multiple-output (MIMO) receiver equipped with a minimum-mean-square-error (MMSE) estimator. We propose using variable-bit-resolution analog-to- digital converters (ADC) across radio frequency (RF) paths. The combiner designed is a function of the quantization errors across each RF path. Using very low bit resolution ADCs (1-2bits) is a popular approach with massive MIMO receiver architectures to mitigate large power demands. We show that for certain channel conditions, adopting unequal bit resolution ADCs (e…
The uplink performance of massive multiple-input-multiple-output (MIMO) systems where the base stations (BS) employ low-resolution analog-to-digital converters (ADCs) is analyzed. A high performance MMSE receiver that takes both additive white Gaussian noise (AWGN) and quantization noise into consideration is designed, which works well for both cases of uniform resolution ADCs and non-uniform resolution ADCs. With the proposed MMSE receiver, we then employ the random matrix theory to derive the asymptotic equivalent of the uplink spectral efficiency (SE) of the system. Numerical results show t…
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. …
Massive multiple-input multiple-output (MIMO) is a promising technology for next generation wireless communication systems (5G). In this technology, Base Station (BS) is equipped with a large number of antennas. Employing high resolution analog-to-digital converters (ADCs) for all antennas may cause high costs and high power consumption for the BS. By performing numerical results, we evaluate the use of low-resolution ADCs for uplink massive MIMO by analyzing Bit Error Rate (BER) performance for different detection techniques (MMSE, ZF) and different modulations (QPSK, 16-QAM) to find an optim…
In order to reduce hardware complexity and power consumption, massive multiple-input multiple-output (MIMO) systems employ low-resolution analog-to-digital converters (ADCs) to acquire quantized measurements $\boldsymbol y$. This poses new challenges to the channel estimation problem, and the sparse prior on the channel coefficient vector $\boldsymbol x$ in the angle domain is often used to compensate for the information lost during quantization. By interpreting the sparse prior from a probabilistic perspective, we can assume $\boldsymbol x$ follows certain sparse prior distribution and recove…
In this paper, we present a new scenario of direction of arrival (DOA) estimation using massive multiple-input multiple-output (MIMO) receive array with low-resolution analog-to-digital convertors (ADCs), which can strike a good balance between performance and circuit cost. Based on the linear additive quantization noise model (AQNM), the effect of low-resolution ADCs on the methods, such as Root-MUSIC method, is analyzed. Also, the closed-form expression of Cramer-Rao lower bound (CRLB) is derived to evaluate the performance loss caused by the low-resolution ADCs. The simulation results show …
In this letter, we propose three linear receivers including Bussgang-based Maximal Ratio Combining (BMRC), Bussgang-based Zero-Forcing (BZF), and Bussgang-based Minimum Mean Squared Error (BMMSE) for massive MIMO systems with one-bit analog-to-digital converters (ADCs). Closed-form expressions of the proposed receivers are obtained by using the Bussgang decomposition to cope with the non-linear effect of the one-bit ADCs. Simulation results show significantly lower bit error rate floors obtained by the proposed receivers than those of conventional linear receivers.
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 pap…
In millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, one-bit analog-to-digital converters (ADCs) are employed to reduce the impractically high power consumption, which is incurred by the wide bandwidth and large arrays. In practice, the mmWave band consists of a small number of paths, thereby rendering sparse virtual channels. Then, the resulting maximum a posteriori (MAP) channel estimation problem is a sparsity-constrained optimization problem, which is NP-hard to solve. In this paper, iterative approximate MAP channel estimators for mmWave massive MIMO systems …
This paper considers uplink massive multiple-input multiple-output (MIMO) systems with lowresolution analog-to-digital converters (ADCs) over Rician fading channels. Maximum-ratio-combining (MRC) and zero-forcing (ZF) receivers are considered under the assumption of perfect and imperfect channel state information (CSI). Low-resolution ADCs are considered for both data detection and channel estimation, and the resulting performance is analyzed. Asymptotic approximations of the spectrum efficiency (SE) for large systems are derived based on random matrix theory. With these results, we can provid…
Institut National de la Recherche Scientifique (INRS-EMT)（加拿大魁北克大学国家科学研究院（电磁与电信研究所））
In this paper, we propose a multi-layer artificial neural network (ANN) that is trained with the Levenberg-Marquardt algorithm for use in signal detection over multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems, particularly those with low-resolution analog-to-digital converters (LR-ADCs). We consider a blind detection scheme where data symbol estimation is carried out without knowing the channel state information at the receiver (CSIR)---in contrast to classical algorithms. The main power of the proposed ANN-based detector (ANND) lies in its versatil…
Low-resolution analog-to-digital converters (ADCs) have been considered as a practical and promising solution for reducing cost and power consumption in massive Multiple-Input-Multiple-Output (MIMO) systems. Unfortunately, low-resolution ADCs significantly distort the received signals, and thus make data detection much more challenging. In this paper, we develop a new deep neural network (DNN) framework for efficient and low-complexity data detection in low-resolution massive MIMO systems. Based on reformulated maximum likelihood detection problems, we propose two model-driven DNN-based detect…
Leveraging the available millimeter wave spectrum will be important for 5G. In this work, we investigate the performance of digital beamforming with low resolution ADCs based on link level simulations including channel estimation, MIMO equalization and channel decoding. We consider the recently agreed 3GPP NR type 1 OFDM reference signals. The comparison shows sequential DCD outperforms MMSE-based MIMO equalization both in terms of detection performance and complexity. We also show that the DCD based algorithm is more robust to channel estimation errors. In contrast to the common believe we al…
This paper considers channel estimation and uplink achievable rate of the coarsely quantized massive multiple-input multiple-output (MIMO) system with radio frequency (RF) impairments. We utilize additive quantization noise model (AQNM) and extended error vector magnitude (EEVM) model to analyze the impacts of low-resolution analog-to-digital converters (ADCs) and RF impairments respectively. We show that hardware impairments cause a nonzero floor on the channel estimation error, which contraries to the conventional case with ideal hardware. The maximal-ratio combining (MRC) technique is then …
Achieving high channel estimation accuracy and reducing hardware cost as well as power dissipation constitute substantial challenges in the design of massive multiple-input multiple-output (MIMO) systems. To resolve these difficulties, sophisticated pilot designs have been conceived for the family of energy-efficient hybrid analog-digital (HAD) beamforming architecture relying on adaptive-resolution analog-to-digital converters (RADCs). In this paper, we jointly optimize the pilot sequences, the number of RADC quantization bits and the hybrid receiver combiner in the uplink of multiuser massiv…
Department of Electrical Engineering, Princeton University（普林斯顿大学电气工程系）；Department of Electrical Engineering, POSTECH（浦项科技大学电气工程系）
The use of one-bit analog-to-digital converters (ADCs) at a receiver is a power-efficient solution for future wireless systems operating with a large signal bandwidth and/or a massive number of receive radio frequency chains. This solution, however, induces a high channel estimation error and therefore makes it difficult to perform the optimal data detection that requires perfect knowledge of likelihood functions at the receiver. In this paper, we propose a likelihood function learning method for multiple-input multiple-output (MIMO) systems with one-bit ADCs using a reinforcement learning app…
Millimeter-wave (mmWave) massive multi-user multiple-input multiple-output (MU-MIMO) technology promises unprecedentedly high data rates for next-generation wireless systems. To be practically viable, mmWave massive MU-MIMO basestations (BS) must (i) rely on low-resolution data-conversion and (ii) be robust to jammer interference. This paper considers the problem of mitigating the impact of a permanently transmitting jammer during uplink transmission to a BS equipped with low-resolution analog-to-digital converters (ADCs). To this end, we propose SNIPS, short for Soft-Nulling of Interferers wi…
We consider a fully digital massive multiple-input multiple-output architecture with low-resolution analog-to-digital/digital-to-analog converters (ADCs/DACs) at the base station (BS) and analyze the performance trade-off between the number of BS antennas, the resolution of the ADCs/DACs, and the bandwidth. Assuming a hardware power consumption constraint, we determine the relationship between these design parameters by using a realistic model for the power consumption of the ADCs/DACs and the radio frequency chains. Considering uplink pilot-aided channel estimation, we build on the Bussgang d…
Multiple-input multiple-output (MIMO) systems exploit spatial diversity to facilitate multi-user communications with high spectral efficiency by beamforming. As MIMO systems utilize multiple antennas and radio frequency (RF) chains, they are typically costly to implement and consume high power. A common method to reduce the cost of MIMO receivers is utilizing less RF chains than antennas by employing hybrid analog/digital beamforming (HBF). However, the added analog circuitry involves active components whose consumed power may surpass that saved in RF chain reduction. An additional method to r…
In this work, we investigate dynamic oversampling techniques for large-scale multiple-antenna systems equipped with low-cost and low-power 1-bit analog-to-digital converters at the base stations. To compensate for the performance loss caused by the coarse quantization, oversampling is applied at the receiver. Unlike existing works that use uniform oversampling, which samples the signal at a constant rate, a novel dynamic oversampling scheme is proposed. The basic idea is to perform time-varying nonuniform oversampling, which selects samples with nonuniform patterns that vary over time. We cons…
This letter revisits the channel estimation problem for MIMO systems with one-bit analog-to-digital converters (ADCs) through a novel algorithm--Amplitude Retrieval (AR). Unlike the state-of-the-art methods such as those based on one-bit compressive sensing, AR takes a different approach. It accounts for the lost amplitudes of the one-bit quantized measurements, and performs channel estimation and amplitude completion jointly. This way, the direction information of the propagation paths can be estimated via accurate direction finding algorithms in array processing, e.g., maximum likelihood. Th…
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 propose several linear receivers based on the Bussgang decomposition, that show significant performance gain over existing linear receivers. Next, we reformulate the maximum-likelihood (ML) detection p…
Cramér-Rao Bound Optimization for Massive MIMO DFRC Systems with 1-Bit DACs and ADCs
State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；Ministry of Education Key Laboratory of Mathematics and Information Networks, School of Mathematical Sciences, Beijing University of Posts and Telecommunications（北京邮电大学数学科学与技术学院）
Hybrid analog/digital architectures and receivers with low-resolution analog-to-digital converters (ADCs) are two low power solutions for wireless systems with large antenna arrays. Most prior work represents two extreme cases in which either a small number of radio frequency (RF) chains with full-resolution ADCs, or low-resolution ADC with a number of RF chains equal to the number of antennas is assumed. In this paper, a generalized hybrid architecture with a small number of RF chains and a finite number of ADC bits is proposed. In such a system, the received signal suffers from two compressi…
The high path loss associated with millimeter wave (mmWave) frequency communication can be compensated by large scale antenna arrays such as multiple-input multiple-output (MIMO) systems. The hybrid beamforming architecture which uses fewer radio frequency chains is implemented to reduce power consumption and hardware complexity, while still supporting multi-stream communication. We propose an efficient expectation-maximization (EM)-based mmWave channel estimator for a lens-based hybrid MIMO system with low resolution sampling at the receiver. The lens-based beamformer is investigated to provi…
Massive multiple-input multiple-output (MIMO) communications using low-resolution analog-to-digital converters (ADCs) is a promising technology for providing high spectral and energy efficiency with affordable hardware cost and power consumption. However, the use of low-resolution ADCs requires special signal processing methods for channel estimation and data detection since the resulting system is severely non-linear. This paper proposes joint channel estimation and data detection methods for massive MIMO systems with low-resolution ADCs based on the variational Bayes (VB) inference framework…
