The use of low-resolution Analog-to-Digital Converters (ADCs) is a practical solution for reducing cost and power consumption for massive Multiple-Input-Multiple-Output (MIMO) systems. However, the severe nonlinearity of low-resolution ADCs causes significant distortions in the received signals and makes the channel estimation and data detection tasks much more challenging. In this paper, we show how \textit{Support Vector Machine} (\textit{SVM}), a well-known supervised-learning technique in machine learning, can be exploited to provide efficient and robust channel estimation and data detection in massive MIMO systems with one-bit ADCs. First, the problem of channel estimation for uncorrelated channels is formulated as a conventional SVM problem. The objective function of this SVM problem is then modified for estimating spatially correlated channels. Next, a two-stage detection algorithm is proposed where SVM is further exploited in the first stage. The performance of the proposed data detection method is very close to that of Maximum-Likelihood (ML) data detection when the channel is perfectly known. We also propose an SVM-based joint Channel Estimation and Data Detection (CE-DD) method, which makes use of both the to-be-decoded data vectors and the pilot data vectors to improve the estimation and detection performance. Finally, an extension of the proposed methods to OFDM systems with frequency-selective fading channels is presented. Simulation results show that the proposed methods are efficient and robust, and also outperform existing ones.
Distributed MIMO radar is known to achieve superior sensing performance by employing widely separated antennas. However, it is challenging to implement a low-complexity distributed MIMO radar due to the complex operations at both the receivers and the fusion center. This work proposed a low-bit quantized distributed MIMO (LiQuiD-MIMO) radar to significantly reduce the burden of signal acquisition and data transmission. In the LiQuiD-MIMO radar, the widely-separated receivers are restricted to operating with low-resolution ADCs and deliver the low-bit quantized data to the fusion center. At the…
We investigate the one-bit MIMO (1b-MIMO) radar that performs one-bit sampling with a time-varying threshold in the temporal domain and employs compressive sensing in the spatial and Doppler domains. The goals are to significantly reduce the hardware cost, energy consumption, and amount of stored data. The joint angle and Doppler frequency estimations from noisy one-bit data are studied. By showing that the effect of noise on one-bit sampling is equivalent to that of sparse impulsive perturbations, we formulate the one-bit $\ell_1$-regularized atomic-norm minimization (1b-ANM-L1) problem to ac…
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.
This paper considers the problem of estimating the sparse mmWave massive multiple input - multiple output (MIMO) OFDM channel from one-bit quantized measurements. Unlike previous grid-based one-bit compressive sensing approaches, we present a gridless convex method to recover sparse channel form one-bit measurements via Binary Atomic Norm Minimization (BiANM) and Reweighted Binary Atomic Norm Minimization (ReBiANM). Simulation results verify the accuracy of the binary and reweighted binary atomic norm minimization techniques.
We develop a two-stage deep learning pipeline architecture to estimate the uplink massive MIMO channel with one-bit ADCs. This deep learning pipeline is composed of two separate generative deep learning models. The first one is a supervised learning model and designed to compensate for the quantization loss. The second one is an unsupervised learning model and optimized for denoising. Our results show that the proposed deep learning-based channel estimator can significantly outperform other state-of-the-art channel estimators for one-bit quantized massive MIMO systems. In particular, our desig…
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…
Recent years have witnessed growing interest in reduced cost radar systems operating with low power. Multiple-input multiple-output (MIMO) radar technology is known to achieve high performance sensing by probing with multiple orthogonal waveforms. However, implementing a low cost low power MIMO radar is challenging. One of the reasons for this difficulty stems from the increased cost and power consumption required by analog-to-digital convertors (ADCs) in acquiring the multiple waveforms at the radar receiver. In this work we study reduced cost MIMO radar receivers restricted to operate with l…
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, whi…
Channel estimation is a challenging task, especially in a massive multiple-input multiple-output (MIMO) system with one-bit analog-to-digital converters (ADC). Traditional deep learning (DL) methods, that learn the mapping from inputs to real channels, have significant difficulties in estimating accurate channels because their loss functions are not well designed and investigated. In this paper, a conditional generative adversarial networks (cGAN) is developed to predict more realistic channels by adversarially training two DL networks. cGANs not only learn the mapping from quantized observati…
Having lower quantization resolution, has been introduced in the literature, as a solution to reduce the power consumption of massive MIMO and millimeter wave MIMO systems. In this paper, we analyze bit error rate (BER) performance of quantized uplink massive MIMO employing a few-bit resolution ADCs. Considering Zero-Forcing (ZF) detection, we derive a closed-form quantized signal-to-interference-plus-noise ratio (SINR) to achieve an analytical BER approximation for coarse quantized M-QAM massive MIMO systems, by using a linear quantization model. The proposed expression is a function of quant…
This article presents a differential detection scheme for the uplink of a massive MIMO system that employs one-bit quantizers on each receive antenna. We focus on the detection of differential amplitude and phase shift keying symbols and we use the Bussgang theorem to express the quantized received signal in terms of quantized signals received during previous channel uses. Subsequently, we derive the maximum likelihood detector for the differentially encoded amplitude and phase information symbols. We note that while the one-bit detector can decode the differentially encoded phase information …
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 MI…
Receivers with one-bit analog-to-digital converters (ADCs) are promising for high bandwidth millimeter wave (mmWave) systems as they consume less power than their full resolution counterparts. The extreme quantization in one-bit receivers and the use of large antenna arrays at mmWave make channel estimation challenging. In this paper, we develop channel estimation algorithms that exploit the low-rank property of mmWave channels. We also propose a novel training solution that results in a low complexity implementation of our algorithms. Simulation results indicate that the proposed methods achi…
Hybrid beamforming is key to achieving energy-efficient 5G wireless networks equipped with massive amount of antennas. Low-resolution data converters bring yet another degree of freedom to energy efficiency for the state-of-the-art 5G transceivers. In this work, we consider the design of hybrid precoders for massive multiple-input multiple-output (MIMO) channels in millimeter-wave (mmWave) spectrum along with one-bit digital-to-analog converters (DACs) and finite-quantized phase shifters. In particular, we propose an alternating-optimization-based precoder design which recursively computes the…
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 estimat…
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…
This paper considers the problem of estimating the sparse millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) OFDM channel from 1-bit quantized measurements. Unlike previous quantized on-grid approaches to compressive sensing, we introduce an off-grid convex scheme which uses binary atomic norm minimization (BiANM) to estimate sparse channel form 1-bit measurements. Moreover, in this paper, we propose a decoupled angle-delay version of BiANM called decoupled binary atomic norm minimization (DeBiANM) in order to reduce complexity. Further, for improving the accuracy of the es…
One-bit digital-to-analog converters (DACs) are a practical and promising solution for reducing cost and power consumption in massive multiple-input multiple-output (MIMO) systems. However, the one-bit precoding problem is NP-hard and even more challenging in frequency-selective fading channels compared to the flat-fading scenario. While block-wise processing (BWP) can effectively address the inter-symbol-interference (ISI) in frequency-selective fading channels, its computational complexity and processing delay can be too high for practical implementation. An alternative solution to alleviate…
In this paper, we aim to design highly energy efficient end-to-end communication for millimeter wave multiple-input multiple-output systems. This is done by jointly optimizing the digital-to-analog converter (DAC)/analog-to-digital converter (ADC) bit resolutions and hybrid beamforming matrices. The novel decomposition of the hybrid precoder and the hybrid combiner to three parts is introduced at the transmitter (TX) and the receiver (RX), respectively, representing the analog precoder/combiner matrix, the DAC/ADC bit resolution matrix and the baseband precoder/combiner matrix. The unknown mat…
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…
Estimation in few-bit MIMO systems is challenging, since the received signals are nonlinearly distorted by the low-resolution ADCs. In this paper, we propose a deep learning framework for channel estimation, data detection, and pilot signal design to address the nonlinearity in such systems. The proposed channel estimation and data detection networks are model-driven and have special structures that take advantage of the domain knowledge in the few-bit quantization process. While the first data detection network, namely B-DetNet, is based on a linearized model obtained from the Bussgang decomp…
Low resolution analog-to-digital converters (ADCs) can be employed to improve the energy efficiency (EE) of a wireless receiver since the power consumption of each ADC is exponentially related to its sampling resolution and the hardware complexity. In this paper, we aim to jointly optimize the sampling resolution, i.e., the number of ADC bits, and analog/digital hybrid combiner matrices which provides highly energy efficient solutions for millimeter wave multiple-input multiple output systems. A novel decomposition of the hybrid combiner to three parts is introduced: the analog combiner matrix…
We propose sparsity-adaptive beamspace channel estimation algorithms that improve accuracy for 1-bit data converters in all-digital millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) basestations. Our algorithms include a tuning stage based on Stein's unbiased risk estimate (SURE) that automatically selects optimal denoising parameters depending on the instantaneous channel conditions. Simulation results with line-of-sight (LoS) and non-LoS mmWave massive MIMO channel models show that our algorithms improve channel estimation accuracy with 1-bit measurements in a computatio…
Adopting one-bit analog-to-digital convertors (ADCs) for massive multiple-input multiple-output (MIMO) implementations has great potential in reducing the hardware cost and power consumption. However, distortions caused by quantization raise great challenges. In MIMO orthogonal frequency-division modulation (OFDM) detection, coarse quantization renders the orthogonal separation among subcarriers inapplicable, forcing us to deal with a problem that has a very large problem size. In this paper we study the expectation-maximization (EM) approach for one-bit MIMO-OFDM detection. The idea is to ite…
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…
We consider timing and frequency synchronization for the massive multiuser (MU) multiple-input multiple-output (MIMO) downlink where 1-bit digital-to-analog converters (DACs) are used at the base station (BS). We focus on the practically relevant scenario in which orthogonal-frequency division multiplexing (OFDM) is used to communicate over frequency-selective channels. Our contributions are twofold. First, we use Bussgang's theorem to analyze the impact on performance caused by timing and frequency offsets in the presence of 1-bit DACs at the BS. Second, we demonstrate the efficacy of the wid…
In this paper, we have analyzed the performance-complexity tradeoff of {a selective} likelihood ascent search (LAS) algorithm initialized by a linear detector, such as matched filtering (MF), zero forcing (ZF) and minimum mean square error (MMSE), {and considering an optimization factor $ρ$ from the bit flipping rule}. The scenario is the uplink of a massive MIMO (M-MIMO) system, and the {analysis has }been developed by means of computer simulations. With the increasing number of base station (BS) antennas, the classical detectors become inefficient. Therefore, the LAS is employed for performa…
In a cell-free cloud radio access network (C-RAN) architecture, uplink channel estimation is carried out by a centralized baseband processing unit (BBU) connected to distributed remote radio heads (RRHs). When the RRHs have multiple antennas and limited radio front-end resources, the design of uplink channel estimation is faced with the challenges posed by reduced radio frequency (RF) chains and one-bit analog-to-digital converters (ADCs) at the RRHs. This work tackles the problem of jointly optimizing the pilot sequences and the pre-RF chains analog combiners with the goal of minimizing the s…
We consider the weak target detection problem with unknown parameter in colocated multiple-input multiple-output (MIMO) radar. To cope with the sheer amount of data for large-size systems, a multi-bit quantizer is utilized in the sampling process. As a low-complexity alternative to classic generalized likelihood ratio test (GLRT) for quantized data, we propose the multi-bit detector on Rao test with a closed-form test statistic, whose theoretical asymptotic distribution is provided to generalize the actual detection performance. Besides, we refine the design of quantizer by optimized quantizat…
This paper focuses on channel estimation for mmWave MIMO systems with 1-bit spatial sigma-delta analog-to-digital converters (ADCs). The channel estimation performance with 1-bit spatial sigma-delta ADCs depends on the quantization noise modeling. Therefore, we present a new method for modeling the quantization noise by leveraging the deterministic input-output relation of the 1-bit spatial sigma-delta ADC. Using this new noise model, we propose an algorithm for channel estimation for a narrowband single-user mmWave line-of-sight MIMO system by determining the unknown angles and path attenuati…
Modern communication systems organize receivers in blocks in order to simplify their analysis and design. However, an approach that considers the receiver design from a wider perspective rather than treating it block-by-block may take advantage of the impacts of these blocks on each other and provide better performance. Herein, we can benefit from machine learning and compose a receiver model implementing supervised learning techniques. With this motivation, we consider a one-to-one transmission system over a flat fast fading wireless channel and propose a support vector machines (SVM)-based r…
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…
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…
Coarsely quantized MIMO signalling methods have gained popularity in the recent developments of massive MIMO as they open up opportunities for massive MIMO implementation using cheap and power-efficient radio-frequency front-ends. This paper presents a new one-bit MIMO precoding approach using spatial Sigma-Delta ($ΣΔ$) modulation. In previous one-bit MIMO precoding research, one mainly focuses on using optimization to tackle the difficult binary signal optimization problem that arises from the precoding design. Our approach attempts a different route. Assuming angular MIMO channels, we apply …
The use of low-resolution data converters in the radio-frequency (RF) chains of all-digital massive multiple-input multiple-output (MIMO) basestations promises significant reductions in power consumption, hardware costs, and interconnect bandwidth. We propose a quantization-aware data-detection algorithm which mitigates the performance loss of 1-bit quantized massive MIMO orthogonal frequency-division multiplexing (OFDM) systems. Since the system performance heavily depends on the quality of channel estimates, we also develop a nonlinear 1-bit channel estimation algorithm that builds upon the …
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…
We consider the problem of jointly optimizing ADC bit resolution and analog beamforming over a frequency-selective massive MIMO uplink. We build upon a popular model to incorporate the impact of low bit resolution ADCs, that hitherto has mostly been employed over flat-fading systems. We adopt weighted sum rate (WSR) as our objective and show that WSR maximization under finite buffer limits and important practical constraints on choices of beams and ADC bit resolutions can equivalently be posed as constrained submodular set function maximization. This enables us to design a constant-factor appr…
We develop a direction of arrival (DoA) and channel estimation algorithm for the one-bit quantized millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) system. By formulating the estimation problem as a noisy one-bit compressed sensing problem, we propose a computationally efficient gridless solution based on the expectation-maximization generalized approximate message passing (EMGAMP) approach. The proposed algorithm does not need the prior knowledge about the number of DoAs and outperforms the existing methods in distinguishing extremely close DoAs for the case of one-bit q…
In this paper, we focus on 1-bit precoding approaches for downlink massive multiple-input multiple-output (MIMO) systems, where we exploit the concept of constructive interference (CI). For both PSK and QAM signaling, we firstly formulate the optimization problem that maximizes the CI effect subject to the requirement of the 1-bit transmit signals. We then mathematically prove that, when employing the CI formulation and relaxing the 1-bit constraint, the majority of the transmit signals already satisfy the 1-bit formulation. Building upon this important observation, we propose a 1-bit precodin…
Most recently, there has been a flurry of research activities on studying how massive MIMO precoding should be designed when the digital-to-analog conversion at the transmitter side is operated by cheap one-bit digital-to-analog converters (DACs). Such research is motivated by the desire to substantially cut down the hardware cost and power consumption of the radio-frequency chain, which is unaffordable in massive MIMO if high-resolution DACs are still used. One-bit MIMO precoding design problems are much harder to solve than their high-resolution DAC counterparts. In our previous work, we dev…
In this paper, we focus on the multiuser massive multiple-input single-output (MISO) downlink with low-cost 1-bit digital-to-analog converters (DACs) for PSK modulation, and propose a low-complexity refinement process that is applicable to any existing 1-bit precoding approaches based on the constructive interference (CI) formulation. With the decomposition of the signals along the detection thresholds, we first formulate a simple symbol-scaling method as the performance metric. The low-complexity refinement approach is subsequently introduced, where we aim to improve the introduced symbol-sca…
Fifth-generation (5G) cellular systems will build on massive multi-user (MU) multiple-input multiple-output (MIMO) technology to attain high spectral efficiency. However, having hundreds of antennas and radio-frequency (RF) chains at the base station (BS) entails prohibitively high hardware costs and power consumption. This paper proposes a novel nonlinear precoding algorithm for the massive MU-MIMO downlink in which each RF chain contains an 8-phase (3-bit) constant-modulus transmitter, enabling the use of low-cost and power-efficient analog hardware. We present a high-throughput VLSI archite…
