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This paper considers channel estimation and system performance for the uplink of a single-cell massive multiple-input multiple-output system. Each receiver antenna of the base station is assumed to be equipped with a pair of one-bit analog-to-digital converters to quantize the real and imaginary part of the received signal. We first propose an approach for channel estimation that is applicable for both flat and frequency-selective fading, based on the Bussgang decomposition that reformulates the nonlinear quantizer as a linear function with identical first- and second-order statistics. The resulting channel estimator outperforms previously proposed approaches across all SNRs. We then derive closed-form expressions for the achievable rate in flat fading channels assuming low SNR and a large number of users for the maximal ratio and zero forcing receivers that takes channel estimation error due to both noise and one-bit quantization into account. The closed-form expressions, in turn, allow us to obtain insight into important system design issues such as optimal resource allocation, maximal sum spectral efficiency, overall energy efficiency, and number of antennas. Numerical results are presented to verify our analytical results and demonstrate the benefit of optimizing system performance accordingly.

In this paper, we propose a federated online training framework for deep neural network (DNN)-based channel estimation (CE) in frequency-division duplexing (FDD) multi-user massive multiple-input multiple-output (MU-MIMO) systems. The proposed DNN consists of two stages, where Stage-I explores the partial common sparsity structure among the users, while Stage-II estimates the channel state information (CSI) with reduced pilot overhead leveraging the common support information provided by Stage-I. To realize online training, we first propose three axioms for a legitimate online loss function, based on which we develop the federated online training algorithm with convergence analysis. The proposed two-tier DNN is trained online at the base station (BS) based on real-time pilot measurements distributively fed back from the users without the need of true channel labels, and the estimates for the CSI at the transmitter (CSIT) can be simultaneously generated in real-time. Meanwhile, the weights of Stage-II can be broadcasted to the users for real-time estimation of the CSI at the receiver (CSIR) at each user. Simulation shows that the proposed solution achieves higher CE performance than traditional compressive sensing (CS)-based algorithms while enjoying much faster computation. The solution is also robust to the channel model mismatches induced by the change of propagation environment, and is able to track the time-varying channel model. [ABSTRACT FROM AUTHOR]

Designing efficient sparse recovery algorithms that could handle noisy quantized measurements is important in a variety of applications – from radar to source localization, spectrum sensing and wireless networking. We take advantage of the approximate message passing (AMP) framework to achieve this goal given its high computational efficiency and state-of-the-art performance. In AMP, the signal of interest is assumed to follow certain prior distribution with unknown parameters. Previous works focused on finding the parameters that maximize the measurement likelihood via expectation maximization – an increasingly difficult problem to solve in cases involving complicated probability models. In this paper, we treat the parameters as unknown variables and compute their posteriors via AMP. The parameters and signal of interest can then be jointly recovered. Compared to previous methods, the proposed approach leads to a simple and elegant parameter estimation scheme, allowing us to directly work with 1-bit quantization noise model. We then further extend our approach to general multi-bit quantization noise model. Experimental results show that the proposed framework provides significant improvement over state-of-the-art methods across a wide range of sparsity and noise levels. [ABSTRACT FROM AUTHOR]

In this paper, we propose and implement blind multiuser carrier frequency offsets (CFOs) estimation for multi-input multi-output (MIMO) single carrier frequency division multiple access (SC-FDMA) uplink system using orthogonal propagator method (OPM) over a noisy frequency-selective channel. The performance of typical OPM is limited at low signal-to-noise ratio (SNR) due to its noise-free signal model. The additive white Gaussian noise mainly impacts the diagonal elements of the data covariance matrix (DCM) of the received signal. First, the proposed fractional CFOs estimator minimizes the noise effect by reconstructing the denoised diagonal elements of the DCM for the received signal through cubic Hermite interpolation. Therefore, we use modified OPM to estimate multiple CFOs for MIMO SC-FDMA systems. Second, we have used an iterative method based on the first-order Taylor series approximation of the CFO vector to avoid peak ambiguity and reduce the number of iterations required in the grid search. The mean square error of the proposed CFO estimator considerably improves compared with the existing methods at a low SNR regime. The bit error rate performance of the proposed method for MIMO SC-FDMA is also compared with the existing methods. Finally, the proposed estimator is validated by implementing it on radio frequency hardware testbed over an indoor propagation environment. [ABSTRACT FROM AUTHOR]

It is well accepted that acquiring downlink channel state information in frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems is challenging because of the large overhead in training and feedback. In this paper, we propose a deep generative model (DGM)-based technique to address this challenge. Exploiting the partial reciprocity of uplink and downlink channels, we first estimate the frequency-independent underlying channel parameters, i.e., the magnitudes of path gains, delays, angles-of-arrivals (AoAs) and angles-of-departures (AoDs), via uplink training, since these parameters are common in both uplink and downlink. Then, the frequency-specific underlying channel parameters, specifically, the phase of each propagation path, are estimated via downlink training using a very short training signal. In the first step, we incorporate the underlying distribution of the channel parameters as a prior into our channel estimation algorithm. We use DGMs to learn this distribution. Simulation results indicate that our proposed DGM-based channel estimation technique outperforms, by a large gap, the conventional channel estimation techniques in practical ranges of signal-to-noise ratio (SNR). In addition, a near-optimal performance is achieved using only few downlink pilot measurements. [ABSTRACT FROM AUTHOR]

We propose a new nonconvex framework for blind multiple signal demixing and recovery. The proposed Riemannian geometric approach extends the well known constant modulus algorithm to facilitate grant-free wireless access for simultaneous demixing and recovery of multiple signal demixing and recovery. We formulate the problem as non-convex problem optimization problem integrated with the signal orthogonality constraint in the form of Riemannian Orthogonal CMA (ROCMA). Unlike traditional stochastic gradient solutions that require large data samples, parameter tuning, and careful initialization, we leverage Riemannian geometry and transform the orthogonality requirement of recovered signals into a Riemannian manifold optimization. Our solution demonstrates full recovery of multiple access signals without large data sample size or special initialization with high probability of success. [ABSTRACT FROM AUTHOR]

In this paper, two types of linear estimators are considered for three related estimation set-ups involving set-theoretic uncertainty pertaining to $ \mathcal {H}_{2}$ and $ \mathcal {H}_{\infty }$ balls of frequency-responses. The problems at stake correspond to robust $ \mathcal {H}_{2}$ and $ \mathcal {H}_{\infty }$ estimation in the face of non-parametric “channel-model’ uncertainty and to a nominal $ \mathcal {H}_{\infty }$ estimation problem. The estimators considered here are defined by minimizing the worst-case estimation error magnitude over the “uncertainty set” or by minimizing an average cost under the constraint that the worst-case error of any admissible estimator does not exceed a prescribed value. The main point is to explore the derivation of estimators which may be viewed as less conservative alternatives to minimax estimators, or in other words, that allow for trade-offs between worst-case performance and better performance over “large” subsets of the uncertainty set. The “average costs” over $ \mathcal {H}_{2}-$ signal balls are obtained as limits of averages over sets of finite impulse responses, as their length grows unbounded. The estimator design problems for the two types of estimators and the three set-ups addressed here are recast as semi-definite programming problems (SDPs, for short). These SDPs are solved in the case of simple examples to illustrate the potential of the “average cost/worst-case constraint” estimators to mitigate the inherent conservatism of the minimax estimators. [ABSTRACT FROM AUTHOR]

In this paper, two different timing-mismatch compensation strategies for two-channel time-interleaved analog-to-digital converters are comprehensively analyzed and compared. In the first strategy (SA), one channel serves as a reference channel, and the other channel is compensated to match the reference channel using the timing mismatch between the channels. In the second strategy (SB), both channels are compensated to match each other, using half the value of the channel mismatch with different signs. For SB, the paper introduces a novel compensation structure that utilizes parallel differentiator-multiplier (PDM) branches. Expressions for the spurious-free dynamic range (SFDR) after compensation are derived for both strategies. These expressions reveal that the novel PDM structure achieves a remarkably greater SFDR than the existing cascaded differentiator-multiplier (CDM) compensation structure which can be used for both SA and SB. This is because, after compensation, the remaining aliasing distortion in the proposed PDM structure is shown to be of higher approximation order (in terms of the mismatch value) and thus substantially smaller than in the CDM structure. Simulations included in the paper validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, wepropose a novel two-stage transmission framework for an intelligent reflecting surface (IRS) assisted millimeter wave (mmWave) system in the presence of phase error caused by hardware impairments. Specifically, in Stage I, we introduce a pilot-based phase calibration task and reformulate it as an alternating optimization program. Building on this formulation, an efficient iterative algorithm is developed to jointly estimate the phase error, which needs to be calibrated, and the channels corresponding to the first user. Stage II consists of two blocks, channel estimation and data transmission. During the channel estimation block, by leveraging on the sparsity of mmWave channels, we propose a fast Fourier transform based scheme to estimate the IRS-BS channel and user-IRS channels. During the data transmission block, based on the estimated channel state information, base station precoders and IRS phase shifts are jointly optimized to maximize the sum signal-to-leakage-plus-noise ratio of all users. To handle this non-convex problem, we further develop a low-complexity joint beamforming algorithm by exploiting fractional programming techniques. Moreover, to examine the performance of the proposed phase calibration scheme, we derive the Cramer-Rao lower bound for the intended phase error estimation. Simulation results validate the effectiveness of our proposed transmission framework and the necessity of IRS phase calibration. [ABSTRACT FROM AUTHOR]

Anti-eavesdropping channel estimation (ANECE) is useful for a network of cooperative full-duplex radio devices/users. Using ANECE, a secret key can be generated by each pair of users, and additional secret information can be transmitted between a pair of users. This paper analyzes the capacity of the secret key based on ANECE, and compares it with the conventional method for channel training. The paper also analyzes the secrecy capacity of information transmission using an one-way scheme, and compares it with a two-way scheme. It is shown that the total amount of secrecy generated from ANECE can be substantially larger than that based on the conventional method especially when an eavesdropper may have an unlimited number of antennas. The paper also formulates a total secure degree of freedom (TSDoF) of the ANECE based scheme, and compares it with a prior scheme of secret information transmission from a multi-antenna node to another against a multi-antenna eavesdropper where channel state information is unknown everywhere initially. The comparison shows that there is a substantial gain of TSDoF by exploiting full-duplex radios and reciprocal channels via ANECE. Most of the key insights are highlighted in twelve proven properties. [ABSTRACT FROM AUTHOR]

In millimeter wave (mmWave) systems, it is challenging to ensure reliable communication links due to the high sensitivity to the presence of blockages. In order to improve the robustness of mmWave systems in the presence of random blockages, we consider the deployment of multiple reconfigurable intelligent surfaces (RISs) to enhance the spatial diversity gain, and the design of robust beamforming schemes based on stochastic optimization methods that minimize the maximum outage probability among multiple users so as to ensure fairness. Under the stochastic optimization framework, we adopt the stochastic majorization–minimization (SMM) method and the stochastic successive convex approximation (SSCA) method to construct deterministic surrogate problems at each iteration, and to obtain closed-form solutions of the precoding matrix at the base station (BS) and the beamforming vectors at the RISs. Both stochastic optimization methods are proved to converge to the set of stationary points of the original stochastic problems. Simulation results show that the proposed robust beamforming for RIS-aided systems can effectively compensate for the performance loss caused by the presence of random blockages, especially when the blockage probability is high. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surface (RIS) is a promising device that can reconfigure the electromagnetic propagation environment through adjustment of the phase shifts of its reflecting elements. However, channel estimation in RIS-aided multiuser multiple-input single-output (MU-MISO) wireless communication systems is challenging due to the passive nature of the RIS and the large number of reflecting elements that can lead to high channel estimation overhead. To address this issue, we propose a novel cascaded channel estimation strategy with low pilot overhead by exploiting the sparsity and the correlation of multiuser cascaded channels in millimeter-wave MISO systems. Based on the fact that the physical positions of the BS, the RIS and users do not appreciably change over multiple consecutive channel coherence blocks, we first estimate the full channel state information (CSI) including all the angle and gain information in the first coherence block, and then only re-estimate the channel gains in the remaining coherence blocks with much lower pilot overhead. In the first coherence block, we propose a two-phase channel estimation method, in which the cascaded channel of one typical user is estimated in Phase I based on the linear correlation among cascaded paths, while the cascaded channels of other users are estimated in Phase II by utilizing the reparameterized CSI of the common base station (BS)-RIS channel obtained in Phase I. The minimum pilot overhead is much less than the existing works. Simulation results show that the performance of the proposed method outperforms the existing methods in terms of the estimation accuracy when using the same amount of pilot overhead. [ABSTRACT FROM AUTHOR]

In this paper, we consider remote state estimation with simultaneous wireless information and power transfer (SWIPT). A remote estimator receives the state estimate transmitted by a sensor and sends an acknowledgment (ACK) signal to the sensor via a feedback wireless channel. The sensor has no other energy supply except that it can harvest wireless energy from the received ACK signal, which carries information and energy simultaneously. Since the symbol error rate of the state estimate transmitted by the sensor depends on the sensor’s transmission power allocation, there exists a tradeoff between the accuracy of the state estimate received by the remote estimator and the transmission power consumption of the sensor. Moreover, the sensor’s transmission power is restricted by the remaining energy level in its battery, which is decided by the amount of the harvested wireless energy. Therefore, we jointly optimize the transmission power allocation of the remote estimator and the sensor and formulate the optimization problem into an infinite time-horizon average cost Markov decision process (MDP). We first prove the existence of the optimal stationary power allocation policy, and then present the monotonic structures of the optimal policy. Simulation results are provided to verify and illustrate the main results. [ABSTRACT FROM AUTHOR]

The conventional direction of arrival (DOA) estimation methods are performed with multiple receiving channels. In this paper, a changeling DOA estimation problem is addressed in a different scenario with only one full-functional receiving channel. A new unmanned aerial vehicle (UAV) swarm system using multiple lifted reconfigurable intelligent surface (RIS) is proposed for the DOA estimation. The UAV movement degrades the DOA estimation performance significantly, and the existing atomic norm minimization (ANM) methods cannot be used in the scenario with array perturbation. Specifically, considering the position perturbation of UAVs, a new atomic norm-based DOA estimation method is proposed, where an atomic norm is defined with the parameter of the position perturbation. Then, a customized semi-definite programming (SDP) method is derived to solve the atomic norm-based method, where different from the traditional SDP method, an additional transforming matrix is formulated. Moreover, a gradient descent method is applied to refine the estimated DOA and the position perturbation further. Simulation results show that the proposed method achieves much better DOA estimation performance in the RIS-aided UAV swarm system with only one receiving channel than various benchmark schemes. [ABSTRACT FROM AUTHOR]

In wireless sensor networks, due to the bandwidth constraint, the distributed nodes (DNs) might only provide binary representatives of the source signal, and then transmit them to the central node (CN). In this paper, we consider the joint estimation of signal amplitude and background noise variance from binary observations over decentralized channels. We first analyze the Cramér–Rao lower bounds (CRLBs) of the parameters of interest and develop a quasilinear estimator (QLE), in which the desirable estimates can be obtained from several intermediate parameters linearly. Next, we consider a more realistic situation where the decentralized channel is noisy during the data transmission. Based on the error propagation model, the asymptotic analysis shows that the performance of the proposed QLE is mainly dominated by the thresholds of the quantizers, which encourages us to adopt a correlated quantization (CQ) scheme by exploiting the spatial correlation among background noises/channel noises. To ease the implementation of QLE in practice, an adaptive quantization (AQ) scheme is also proposed so as to obtain reasonable selections of the required thresholds. Finally, numerical simulations are provided to validate our theoretical findings. [ABSTRACT FROM AUTHOR]

The design of methods for inference from time sequences has traditionally relied on statistical models that describe the relation between a latent desired sequence and the observed one. A broad family of model-based algorithms have been derived to carry out inference at controllable complexity using recursive computations over the factor graph representing the underlying distribution. An alternative model-agnostic approach utilizes machine learning (ML) methods. Here we propose a framework that combines model-based algorithms and data-driven ML tools for stationary time sequences. In the proposed approach, neural networks are developed to separately learn specific components of a factor graph describing the distribution of the time sequence, rather than the complete inference task. By exploiting stationary properties of this distribution, the resulting approach can be applied to sequences of varying temporal duration. Learned factor graphs can be realized using compact neural networks that are trainable using small training sets, or alternatively, be used to improve upon existing deep inference systems. We present an inference algorithm based on learned stationary factor graphs, which learns to implement the sum-product scheme from labeled data, and can be applied to sequences of different lengths. Our experimental results demonstrate the ability of the proposed learned factor graphs to learn from small training sets to carry out accurate inference for sleep stage detection using the Sleep-EDF dataset, as well as for symbol detection in digital communications with unknown channels. [ABSTRACT FROM AUTHOR]

We address here the issue of jointly estimating the angle parameters of a single sinusoid with Wiener carrier phase noise and observed in additive, white, Gaussian noise (AWGN). We develop the theoretical foundation for time-domain, phase-based, joint maximum likelihood (ML) estimation of the unknown carrier frequency and the initial carrier phase, with simultaneous maximum a posteriori probability (MAP) estimation of the time-varying carrier phase noise. The derivation is based on the amplitude and phase-form of the noisy received signal model together with the use of the best, linearized, additive observation phase noise model due to AWGN. Our newly derived estimators are closed-form expressions, consisting of both the phase and the magnitude of all the received signal samples. More importantly, they all have a low-complexity, sample-by-sample iterative processing structure, which can be implemented iteratively in real-time. As a basis for comparison, the Cramer-Rao lower bound (CRLB) for the ML estimators and the Bayesian CRLB (BCRLB) for the MAP estimator are derived in the presence of carrier phase noise, and the results simply depend on the signal-to-noise ratio (SNR), the observation length and the phase noise variance. It is theoretically shown that the estimates obtained are unbiased, and the mean-square error (MSE) of the estimators attain the CRLB/BCRLB at high SNR. The MSE performance as a function of the SNR, the observation length and the phase noise variance is verified using Monte Carlo simulation, which shows a remarkable improvement in estimation accuracy in large phase noise. [ABSTRACT FROM AUTHOR]

The large antenna arrays with hybrid analog and digital (HAD) architectures can provide a large aperture with low cost and hardware complexity, resulting in enhanced direction-of-arrival (DOA) estimation and reduced power consumption. This paper investigates the trade-off between DOA estimation and power consumption in large antenna arrays with HAD architectures. Particularly, the DOA estimation problem of fully-connected, sub-connected (SC), and switches-based (SE) hybrid architectures is formulated into a unified expression, with the compression matrix in a time-varying form. Based on this model, we derive a dynamic maximum likelihood (D-ML) estimator that is suitable for both HAD and conventional fully digital (FD) structures, and the closed-form expression of Cramér-Rao bound (CRB) to evaluate the performance limit of the D-ML estimator for different HAD structures. The theoretical CRB analysis in the single-source case reveals that, the SC structure has the ability to achieve approximately the same performance as the FD structures at DOAs around zero, but suffers from the inherent angle ambiguity because of the antenna grouping. In addition, we propose a dynamic SC (D-SC) structure that is proved to eliminate the angle ambiguity with time-varying phase shifters, and a switch optimization (SWO) algorithm to minimize the CRB of SE structures. Finally, we introduce a new metric, DOA efficiency, to measure the trade-off between the DOA estimation performance and power consumption of different structures. Simulation results verify our theoretical analysis and the superiority of the proposed D-SC structure and the SWO algorithm. [ABSTRACT FROM AUTHOR]

Time-of-arrival (TOA) based localization plays a central role in current and future localization systems. Such systems, exploiting the fine delay resolution properties of wideband and ultra-wideband (UWB) signals, are particularly attractive for ranging under harsh propagation conditions in which significant multipath may be present. While multipath has been traditionally considered detrimental in the design of TOA estimators, it can be exploited to benefit ranging. This paper investigates the impact of a priori multipath information on TOA estimation. To this end, bounds on the performance of TOA estimation in dense multipath channels are provided and discussed under different operating conditions. The effects of channel dispersion and transmission bandwidth on ranging systems are investigated showing that, contrary to communication systems, diversity behavior is only exhibited in the medium signal-to-noise ratio regime. [ABSTRACT FROM AUTHOR]

We propose adjustable phase shift pilots (APSPs) for channel acquisition in wideband massive multiple-input multiple-output (MIMO) systems employing orthogonal frequency division multiplexing (OFDM) to reduce the pilot overhead. Based on a physically motivated channel model, we first establish a relationship between channel space-frequency correlations and the channel power angle-delay spectrum in the massive antenna array regime, which reveals the channel sparsity in massive MIMO-OFDM. With this channel model, we then investigate channel acquisition, including channel estimation and channel prediction, for massive MIMO-OFDM with APSPs. We show that channel acquisition performance in terms of sum mean square error can be minimized if the user terminals' channel power distributions in the angle-delay domain can be made nonoverlapping with proper pilot phase shift scheduling. A simplified pilot phase shift scheduling algorithm is developed based on this optimal channel acquisition condition. The performance of APSPs is investigated for both one symbol and multiple symbol data models. Simulations demonstrate that the proposed APSP approach can provide substantial performance gains in terms of achievable spectral efficiency over the conventional phase shift orthogonal pilot approach in typical mobility scenarios.

The temporal variations in the wireless propagation channel, referred to as channel aging, cause a mismatch between the estimated channel and the channel state at the time of data detection. This mismatch has been shown to severely impair the performance of massive MIMO systems. In this paper, we present data aided MSE-optimal channel tracking algorithms to decode the received symbols and update the channel estimates at the base station (BS) and the UEs. These algorithms combine ideas from Kalman filtering for channel tracking and deterministic equivalent analysis for symbol estimation. In the uplink case, we first develop a minimum mean squared error (MMSE) data estimator and the MSE-optimal channel predictor based on the Kalman filtering algorithm. We analytically show that the updated channel estimate obtained from the estimates of the data symbols leads to significantly larger signal to interference-plus-noise ratio (SINR), and hence achievable rate, compared to that obtained from the channel estimate based on pilot symbols. Following this, in the downlink case, we develop an algorithm to track the effective channel at the UEs and analyze its MSE, SINR and achievable rate performance. We show that tracking the effective downlink channel mitigates the effects of channel aging and leads to improved performance. However, since the beamforming matrices at the BS are not updated, downlink channel tracking is not as effective as uplink channel tracking. Finally, via Monte Carlo simulations, we validate our derived results, and demonstrate the gains achievable by tracking the time-varying channels in massive MIMO systems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate widely-linear channel estimation and data detection for the uplink of the massive multiple-input multiple-output (MIMO) with in-phase or quadrature-phase imbalance (IQI). We firstly investigate widely-linear minimum mean square error (WL-MMSE) estimation for the effective channel which is the product of the IQI coefficients and the wireless channel. We reuse pilots among different user terminals (UTs) to reduce pilot overhead and derive a lower bound of the estimation MSE. Based on the optimal condition under which the lower bound is achieved, we show that if we assign the same pilot for the UTs of which the covariance matrices are orthogonal, the pilot interference does not affect the MSE performance. Then according to the obtained estimates of the effective channel, we further propose WL-MMSE data detection that is robust to the estimation error. The proposed widely-linear approach can cope with the IQI and multi-user interference jointly. With some results of operator-valued free probability theory, we derive an asymptotic deterministic equivalent for the ergodic achievable sum rate of the proposed robust WL-MMSE data detection. The performance of the proposed widely-linear processing approach is verified by the numerical results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel channel estimation method and optimize the pilot symbols based on intrinsic interference utilization for offset quadrature amplitude modulation based filter-bank multicarrier (OQAM/FBMC) systems. Specifically, we firstly propose a line fitting based channel estimation method by analyzing and utilizing the distribution characteristics of the demodulated OQAM symbols, where no guard symbols are needed between pilot symbols and data symbols. Then, we formulate a pilot symbol optimization problem by utilizing the intrinsic interferences to improve the accuracy of the line fitting. Finally, we obtain the optimal solution of the optimization problem and present the corresponding pilot structure. Simulation results demonstrate that the proposed method with the optimized pilot structure performs the best among candidate pilot symbols and outperforms the traditional interference approximation method (IAM) with the optimal pilot structure. [ABSTRACT FROM AUTHOR]

In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as matrix-factorization problem arising in relay communication among others. Assuming statistically independent matrix entries with known priors, the new algorithm called ML-BiGAMP could approximate the general sum-product loopy belief propagation (LBP) in the high-dimensional limit enjoying a substantial reduction in computational complexity. We demonstrate that, in large system limit, the asymptotic MSE performance of ML-BiGAMP could be fully characterized via a set of simple one-dimensional equations termed state evolution (SE). We establish that the asymptotic MSE predicted by ML-BiGAMP’ SE matches perfectly the exact MMSE predicted by the replica method, which is well-known to be Bayes-optimal but infeasible in practice. This consistency indicates that the ML-BiGAMP may still retain the same Bayes-optimal performance as the MMSE estimator in high-dimensional applications, although ML-BiGAMP's computational burden is far lower. As an illustrative example of the general ML-BiGAMP, we provide a detector design that could estimate the channel fading and the data symbols jointly with high precision for the two-hop amplify-and-forward relay communication systems. [ABSTRACT FROM AUTHOR]

Carrier frequency offset (CFO) and channel estimation is a classic topic with a large body of prior work using the maximum likelihood (ML) approach together with the Cramér-Rao lower bound (CRLB) analysis. We give the maximum a posteriori probability (MAP) estimation solution, which is particularly useful for tracking. Unlike the ML cases, the corresponding Bayesian CRLB (BCRLB) shows a clear relation with parameters and low complexity algorithms are provided to achieve the BCRLB in almost all SNR range. Among them, the universal algorithm takes a new approach and avoids error floors of the traditional approach. We assume that the time invariant MIMO channel within a packet can have spatial correlation and nonzero mean. The estimation is based on pilot signals. An unexpected result is that the joint MAP estimation is equivalent to an individual MAP estimation of the frequency offset first, again different from the ML results. We provide insight on the pilot/training signal design based on the BCRLB. Unlike past algorithms that trade performance and/or complexity for the accommodation of time varying channels, the MAP solution provides a different route for dealing with time variation. Within a short enough (segment of) packet where the channel and CFO are approximately time invariant, the low complexity algorithm can be employed. Similar to the belief propagation, the estimation of the previous (segment of) packet can serve as the prior knowledge for the next (segment of) packet. [ABSTRACT FROM AUTHOR]

This work studies the problem of neighbor discovery for device-to-device (D2D) communications of LTE user equipments (UEs) in a modern cellular network. By listening to cellular uplink transmissions, UEs can detect potential D2D partners through a neighbor discovery process compatible with the standard LTE network protocol. We focus on neighbor discovery utilizing sounding reference signal (SRS) channel, which can be accessed by peer UEs that are LTE-compliant. Under the constraint of unknown channel statistics during uplink hearing, we propose joint neighbor detection and D2D channel estimation for listening UEs using the framework of sparse channel recovery. Composite hypothesis testing methods are further developed to refine neighbor detection accuracy. We evaluate the performance of our neighbor discovery methods under various network parameters to facilitate practical design and implementation of D2D in 4G cellular networks. © 2012 IEEE.

The estimation of mutual information (MI) or conditional mutual information (CMI) from a set of samples is a long-standing problem. A recent line of work in this area has leveraged the approximation power of artificial neural networks and has shown improvements over conventional methods. One important challenge in this new approach is the need to obtain, given the original dataset, a different set where the samples are distributed according to a specific product density function. This is particularly challenging when estimating CMI. In this paper, we introduce a new technique, based on k nearest neighbors (k-NN), to perform the resampling and derive high-confidence concentration bounds for the sample average. Then the technique is employed to train a neural network classifier and the CMI is estimated accordingly. We propose three estimators using this technique and prove their consistency, make a comparison between them and similar approaches in the literature, and experimentally show improvements in estimating the CMI in terms of accuracy and variance of the estimators. [ABSTRACT FROM AUTHOR]

Existing Orthogonal Frequency-Division Multiplexing (OFDM) variants based on cyclic prefix (CP) allow for efficient time synchronization, but suffer from lower power efficiency compared to zero-padded (ZP)-OFDM. Because of its power efficiency, ZP-OFDM is considered as an appealing solution for the emerging low-power wireless systems. However, in the absence of CP, time synchronization in ZP-OFDM is a challenging task. In this paper, the non-data-aided (NDA) maximum-likelihood (ML) time synchronization for ZP-OFDM is analytically derived. We show that the optimal NDA-ML synchronization algorithm offers a high lock-in probability and can be efficiently implemented using Monte Carlo sampling (MCS) technique in combination with golden-section search method in one dimension. To obtain the optimal NDA-ML time synchronization algorithm, we first derive a closed-form expression for the joint probability density function (PDF) of the received ZP-OFDM samples in frequency-selective fading channels. The derived expression is valid for doubly-selective fading channels with mobile users as well. The performance of the proposed synchronization algorithm is evaluated under various practical settings through simulation experiments. It is shown that the proposed optimal NDA-ML synchronization algorithm and its MCS implementation substantially outperforms existing NDA time synchronization algorithms in terms of lock-in probability and mean-squared error (MSE). [ABSTRACT FROM AUTHOR]

It is well-known that time-varying channels can provide time diversity and improve error rate performance compared to time-invariant fading channels. However, exploiting time diversity requires very accurate channel estimates at the receiver. In order to reduce the number of unknown channel coefficients while estimating the time-varying channel, basis expansion models can be used along with long transmission frames that contain multiple orthogonal frequency division multiplexing (OFDM) symbols that experience the channel variation. The design of these OFDM frames need to judiciously incorporate training and data insertions in the transmitted signal while maintaining orthogonality. In this work, we propose an inter channel interference (ICI)-free training model depending on pilot symbols only and provide a corresponding time-varying channel estimation method. This scheme relies on an algorithm to determine the number of OFDM symbols per frame and the number of basis functions per path with minimal information about the Doppler bandwidth. As a performance benchmark, Bayesian Cramér Rao lower bound (CRLB) and the corresponding MSE bound are derived analytically for the proposed training model. Theoretical MSE expressions of the proposed estimation scheme are also derived as well as the MSE expressions in the presence of Doppler frequency mismatch. Simulations exhibit substantial MSE improvement and the corresponding Symbol Error Rate (SER) performances of the low complexity estimation scheme. They also corroborate that, unlike the common results in the literature, an OFDM system can perform better as the Doppler frequency increases with judicious design of training and channel estimation schemes. [ABSTRACT FROM AUTHOR]

Matrix-monotonic optimization exploits the monotonic nature of positive semi-definite matrices to derive optimal diagonalizable structures for the matrix variables of matrix-variable optimization problems. Based on the optimal structures derived, the associated optimization problems can be substantially simplified and underlying physical insights can also be revealed. In our work, a comprehensive framework of the applications of matrix-monotonic optimization to multiple-input multiple-output (MIMO) transceiver design is provided for a series of specific performance metrics under various linear constraints. This framework consists of two parts, i.e., Part-I for single-variable optimization and Part-II for multi-variable optimization. In this paper, single-variable matrix-monotonic optimization is investigated under various power constraints and various types of channel state information (CSI) condition. Specifically, three cases are investigated: 1) both the transmitter and receiver have imperfect CSI; 2) perfect CSI is available at the receiver but the transmitter has no CSI; 3) perfect CSI is available at the receiver but the channel estimation error at the transmitter is norm-bounded. In all three cases, the matrix-monotonic optimization framework can be used for deriving the optimal structures of the optimal matrix variables. [ABSTRACT FROM AUTHOR]

In contrast to Part I of this treatise (Xing, 2021) that focuses on the optimization problems associated with single matrix variables, in this paper, we investigate the application of the matrix-monotonic optimization framework in the optimization problems associated with multiple matrix variables. It is revealed that matrix-monotonic optimization still works even for multiple matrix-variate based optimization problems, provided that certain conditions are satisfied. Using this framework, the optimal structures of the matrix variables can be derived and the associated multiple matrix-variate optimization problems can be substantially simplified. In this paper several specific examples are given, which are essentially open problems. Firstly, we investigate multi-user multiple-input multiple-output (MU-MIMO) uplink communications under various power constraints. Using the proposed framework, the optimal structures of the precoding matrices at each user under various power constraints can be derived. Secondly, we considered the optimization of the signal compression matrices at each sensor under various power constraints in distributed sensor networks. Finally, we investigate the transceiver optimization for multi-hop amplify-and-forward (AF) MIMO relaying networks with imperfect channel state information (CSI) under various power constraints. At the end of this paper, several simulation results are given to demonstrate the accuracy of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers massive access in massive multiple-input multiple-output (MIMO) systems and proposes an adaptive active user detection and channel estimation scheme based on compressive sensing. By exploiting the sporadic traffic of massive connected user equipments and the virtual angular domain sparsity of massive MIMO channels, the proposed scheme can support massive access with dramatically reduced access latency. Specifically, we design non-orthogonal pseudo-random pilots for uplink broadband massive access, and formulate the active user detection and channel estimation as a generalized multiple measurement vector compressive sensing problem. Furthermore, by leveraging the structured sparsity of the uplink channel matrix, we propose an efficient generalized multiple measurement vector approximate message passing (GMMV-AMP) algorithm to realize joint active user detection and channel estimation based on a spatial domain or an angular domain channel model. To jointly exploit the channel sparsity present in both the spatial and the angular domains for enhanced performance, a Turbo-GMMV-AMP algorithm is developed for detecting the active users and estimating their channels in an alternating manner. Finally, an adaptive access scheme is proposed, which adapts the access latency to guarantee reliable massive access for practical systems with unknown channel sparsity level. Additionally, the state evolution of the proposed GMMV-AMP algorithm is derived to predict its performance. Simulation results demonstrate the superiority of the proposed active user detection and channel estimation schemes compared to several baseline schemes. [ABSTRACT FROM AUTHOR]

Grant-free random access is a promising protocol to support massive access in beyond fifth-generation (B5G) cellular Internet-of-Things (IoT) with sporadic traffic. Specifically, in each coherence interval, the base station (BS) performs joint activity detection and channel estimation (JADCE) before data transmission. Due to the deployment of a large-scale antennas array and the existence of a huge number of IoT devices, JADCE usually has high computational complexity and needs long pilot sequences. To solve these challenges, this paper proposes a dimension reduction method, which projects the original device state matrix to a low-dimensional space by exploiting its sparse and low-rank structure. Then, we develop an optimized design framework with a coupled full column rank constraint for JADCE to reduce the size of the search space. However, the resulting problem is non-convex and highly intractable, for which the conventional convex relaxation approaches are inapplicable. To this end, we propose a logarithmic smoothing method for the non-smoothed objective function and transform the interested matrix to a positive semidefinite matrix, followed by giving a Riemannian trust-region algorithm to solve the problem in complex field. Simulation results show that the proposed algorithm is efficient to a large-scale JADCE problem and requires shorter pilot sequences than the state-of-art algorithms which only exploit the sparsity of device state matrix. [ABSTRACT FROM AUTHOR]

Spatial–temporal (ST) subspace-based channel estimation techniques formulated with $\ell 2$ minimum mean square error (MMSE) criterion alleviate the multi-access interference (MAI) problem when the interested signals exhibit low-rank property. However, the conventional $\ell 2$ ST subspace-based methods suffer from mean squared error (MSE) deterioration in unknown interference channels, due to the difficulty to separate the interested signals from the channel covariance matrices (CCMs) contaminated with unknown interference. As a solution to the problem, we propose a new $\ell 1$ regularized ST channel estimation algorithm by applying the expectation-maximization (EM) algorithm to iteratively examine the signal subspace and the corresponding sparse-supports. The new algorithm updates the CCM independently of the slot-dependent $\ell 1$ regularization, which enables it to correctly perform the sparse-independent component analysis (ICA) with a reasonable complexity order. Simulation results shown in this paper verify that the proposed technique significantly improves MSE performance in unknown interference MIMO channels, and hence, solves the BER floor problems from which the conventional receivers suffer. [ABSTRACT FROM AUTHOR]

Multiple-input multiple-output (MIMO) millimeter wave (mmWave) communication is a key technology for next generation wireless networks. One of the consequences of utilizing a large number of antennas with an increased bandwidth is that array steering vectors vary among different subcarriers. Due to this effect, known as beam squint, the conventional channel model is no longer applicable for mmWave massive MIMO systems. In this paper, we study channel estimation under the resulting non-standard model. To that aim, we first analyze the beam squint effect from an array signal processing perspective, resulting in a model which sheds light on the angle-delay sparsity of mmWave transmission. We next design a compressive sensing based channel estimation algorithm which utilizes the shift-invariant block-sparsity of this channel model. The proposed algorithm jointly computes the off-grid angles, the off-grid delays, and the complex gains of the multi-path channel. We show that the newly proposed scheme reflects the mmWave channel more accurately and results in improved performance compared to traditional approaches. We then demonstrate how this approach can be applied to recover both the uplink as well as the downlink channel in frequency division duplex (FDD) systems, by exploiting the angle-delay reciprocity of mmWave channels. [ABSTRACT FROM AUTHOR]

This work presents a generalization of classical factor analysis (FA). Each of $M$ channels carries measurements that share factors with all other channels, but also contains factors that are unique to the channel. Furthermore, each channel carries an additive noise whose covariance is diagonal, as is usual in factor analysis, but is otherwise unknown. This leads to a problem of multi-channel factor analysis with a specially structured covariance model consisting of shared low-rank components, unique low-rank components, and diagonal components. Under a multivariate normal model for the factors and the noises, a maximum likelihood (ML) method is presented for identifying the covariance model, thereby recovering the loading matrices and factors for the shared and unique components in each of the $M$ multiple-input multiple-output (MIMO) channels. The method consists of a three-step cyclic alternating optimization, which can be framed as a block minorization-maximization (BMM) algorithm. Interestingly, the three steps have closed-form solutions and the convergence of the algorithm to a stationary point is ensured. Numerical results demonstrate the performance of the proposed algorithm and its application to passive radar. [ABSTRACT FROM AUTHOR]

This paper presents secrecy analyses of a full-duplex MIMOME network which consists of two full-duplex multi-antenna users (Alice and Bob) and an arbitrarily located multi-antenna eavesdropper (Eve). The paper assumes that Eve's channel state information (CSI) is completely unknown to Alice and Bob except for a small radius of secured zone. The first part of this paper aims to optimize the powers of jamming noises from both users. To handle Eve's CSI being unknown to users, the focus is placed on Eve at the most harmful location, and the large matrix theory is applied to yield a hardened secrecy rate to work on. The performance gain of the power optimization in terms of maximum tolerable number of antennas on Eve is shown to be significant. The second part of this paper shows two analyses of anti-eavesdropping channel estimation (ANECE) that can better handle Eve with any number of antennas. One analysis assumes that Eve has a prior statistical knowledge of its CSI, which yields lower and upper bounds on secure degrees of freedom of the system as functions of the number (N) of antennas on Eve and the size (K) of information packet. The second analysis assumes that Eve does not have any prior knowledge of its CSI but performs blind detection of information, which yields an approximate secrecy rate for the case of K being larger than N. [ABSTRACT FROM AUTHOR]

With the increasing scale of antenna arrays in wideband millimeter-wave (mmWave) communications, the physical propagation delays of electromagnetic waves traveling across the whole array will become large and comparable to the time-domain sample period, which is known as the spatial-wideband effect. In this case, different subcarriers in an orthogonal frequency division multiplexing (OFDM) system will “see” distinct angles of arrival (AoAs) for the same path. This effect is known as beam squint, resulting from the spatial-wideband effect, and makes the approaches based on the conventional multiple-input multiple-output (MIMO) model, such as channel estimation and precoding, inapplicable. After discussing the relationship between beam squint and the spatial-wideband effect, we propose a channel estimation scheme for frequency-division duplex (FDD) mmWave massive MIMO-OFDM systems with hybrid analog/digital precoding, which takes the beam squint effect into consideration. A compressive sensing-based approach is developed to extract the frequency-insensitive parameters of each uplink channel path, i.e., the AoA and the time delay, and the frequency-sensitive parameter, i.e., the complex channel gain. With the help of the reciprocity of these frequency-insensitive parameters in FDD systems, the downlink channel estimation can be greatly simplified, where only limited pilots are needed to obtain downlink complex gains and reconstruct downlink channels. Furthermore, the uplink and downlink channel covariance matrices can be constructed from these frequency-insensitive channel parameters rather than through a long-term average, which enables the minimum mean-squared error (MMSE) channel estimation to further enhance performance. Numerical results demonstrate the superiority of the proposed scheme over the conventional methods under general system configurations in mmWave communications. [ABSTRACT FROM AUTHOR]

When the large antenna array and the large bandwidth are deployed in a massive multiple-input multiple-output (MIMO) system, the spatial-wideband effect and the related beam squint effect make the energy of each multipath component distributed mainly within a square area in angle-delay domain rather than distributed like an impulse. With the finite numbers of antennas and subcarriers in practical massive MIMO-OFDM systems, the power leakage of each path outside the corresponding square area is non-negligible. In this paper, we first derive the millimeter-wave (mmWave) massive MIMO channel model for OFDM transceivers and then design an optimal energy-focusing window, which shapes the channel in spatial-frequency domain to maximally concentrate the energy of each multipath component inside the corresponding square area in angle-delay domain. With the help of this window, the power leakage can be significantly reduced. As a result, the sparsity of mmWave channels can be primely preserved and the inter-user interference can be significantly alleviated for angle- and delay-based channel estimation and precoding. Simulation results demonstrate the effectiveness of the proposed window design. [ABSTRACT FROM AUTHOR]

Quantization plays a critical role in digital signal processing systems. Quantizers are typically designed to obtain an accurate digital representation of the input signal, operating independently of the system task, and are commonly implemented using serial scalar analog-to-digital converters (ADCs). In this work, we study hardware-limited task-based quantization, where a system utilizing a serial scalar ADC is designed to provide a suitable representation in order to allow the recovery of a parameter vector underlying the input signal. We propose hardware-limited task-based quantization systems for a fixed and finite quantization resolution, and characterize their achievable distortion. We then apply the analysis to the practical setups of channel estimation and eigen-spectrum recovery from quantized measurements. Our results illustrate that properly designed hardware-limited systems can approach the optimal performance achievable with vector quantizers, and that by taking the underlying task into account, the quantization error can be made negligible with a relatively small number of bits. [ABSTRACT FROM AUTHOR]

Beamspace channel estimation is indispensable for millimeter-wave MIMO systems relying on lens antenna arrays for achieving substantially increased data rates, despite using a small number of radio-frequency chains. However, most of the existing beamspace channel estimation schemes have been designed for narrowband systems, while the rather scarce wideband solutions tend to assume that the sparse beamspace channel exhibits a common support in the frequency domain, which has a limited validity owing to the effect of beam squint caused by the wide bandwidth in practice. In this paper, we investigate the wideband beamspace channel estimation problem without the common support assumption. Specifically, by exploiting the effect of beam squint, we first prove that each path component of the wideband beamspace channel exhibits a unique frequency-dependent sparse structure. Inspired by this structure, we then propose a successive support detection (SSD) based beamspace channel estimation scheme, which successively estimates all the sparse path components following the classical idea of successive interference cancellation. For each path component, its support at different frequencies is jointly estimated to improve the accuracy by utilizing the proved sparse structure, and its influence is removed to estimate the remaining path components. The performance analysis shows that the proposed SSD-based scheme can accurately estimate the wideband beamspace channel at a low complexity. Simulation results verify that the proposed SSD-based scheme enjoys a reduced pilot overhead, and yet achieves an improved channel estimation accuracy. [ABSTRACT FROM AUTHOR]

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the magnitude of its Fourier transform to enable the reconstruction of the original signal. Solving the phase retrieval problem is equivalent to recovering a signal from its auto-correlation function. In this paper, we assume the original signal to be sparse; this is a natural assumption in many applications, such as X-ray crystallography, speckle imaging and blind channel estimation. We propose an algorithm that resolves the phase retrieval problem in three stages, first, we leverage the finite rate of innovation sampling theory to super-resolve the auto-correlation function from a limited number of samples, second, we design a greedy algorithm that identifies the locations of a sparse solution given the super-resolved auto-correlation function, finally, we recover the amplitudes of the atoms given their locations and the measured auto-correlation function. Unlike traditional approaches that recover a discrete approximation of the underlying signal, our algorithm estimates the signal on a continuous domain, which makes it the first of its kind. Along with the algorithm, we derive its performance bound with a theoretical analysis and propose a set of enhancements to improve its computational complexity and noise resilience. Finally, we demonstrate the benefits of the proposed method via a comparison against Charge Flipping, a notable algorithm in crystallography. [ABSTRACT FROM AUTHOR]

A multistatic system uses a transmitter to illuminate the object of interest and collects the reflected signal by a number of receivers to determine its location. In some scenarios such as passive coherent localization or for gaining flexibility, the position of the transmitter is not known. This paper investigates the use of the indirect path measurements reflected off the object alone, or together with the direct path measurements from the transmitter to receivers for locating the object in the absence of the transmitter position. We show that joint estimation of the object and transmitter positions from both the indirect and direct measurements can yield a better object location estimate than using the indirect measurements only by eliminating the dependency of the transmitter position. An algebraic closed-form solution is developed for the nonlinear problem of joint estimation and is shown analytically to achieve the Cramér–Rao lower bound performance under Gaussian noise over the small error region. To complete the study and gain insight, the optimal receiver placement in the absence of transmitter position is derived by minimizing the estimation confidence region or the mean-square estimation error for the object location. The performance lost due to unknown transmitter position under the optimal geometries is quantified. Simulations confirm well with the theoretical developments. [ABSTRACT FROM AUTHOR]

This paper considers and analyzes the performance of semiblind, training, and data-aided channel estimation schemes for multiple-input multiple-output (MIMO) filter bank multicarrier (FBMC) systems with offset quadrature amplitude modulation. A semiblind MIMO-FBMC (SB-MF) channel estimator is developed that exploits both the training symbols and second-order statistical properties of the data symbols, which leads to a significant decrease in the mean squared error (MSE) with respect to its conventional training-based counterpart. Its performance is compared with that of the interference approximation method-based least squares MIMO-FBMC (LS-MF) channel estimator, wherein the channel is estimated using exclusively training symbols. The Cramér–Rao lower bounds are derived to characterize the MSE of the proposed and LS-MF estimators, which interestingly demonstrate that while the MSE per parameter of the proposed scheme decreases with the number of receive antennas, it remains constant for the training-based scheme. The resulting bit error rates are derived for the proposed SB-MF and LS-MF channel estimators. An expectation maximization-based data-aided MIMO-FBMC channel estimator is also investigated that performs iterative maximum a posteriori channel estimation in the E-step followed by data detection in the M-step. A comparative analysis is presented for the computational complexities of the various schemes. Simulation results with practical channel models demonstrate that the proposed semiblind scheme significantly outperforms the training-based and data-aided schemes. [ABSTRACT FROM AUTHOR]

In this paper, we study blind channel-and-signal estimation by exploiting the burst-sparse structure of angular-domain propagation channels in massive MIMO systems. The state-of-the-art approach utilizes the structured channel sparsity by sampling the angular-domain channel representation with a uniform angle-sampling grid, a.k.a. virtual channel representation. However, this approach is only applicable to uniform linear arrays and may cause a substantial performance loss due to the mismatch between the virtual representation and the true angle information. To tackle these challenges, we propose a sparse channel representation with a super-resolution sampling grid and a hidden Markovian support. Based on this, we develop a novel approximate inference based blind estimation algorithm to estimate the channel and the user signals simultaneously, with emphasis on the adoption of the expectation-maximization method to learn the angle information. Furthermore, we demonstrate the low-complexity implementation of our algorithm, making use of factor graph and message passing principles to compute the marginal posteriors. Numerical results show that our proposed method significantly reduces the estimation error compared to the state-of-the-art approach under various settings, which verifies the efficiency and robustness of our method. [ABSTRACT FROM AUTHOR]

Orthogonal time frequency space (OTFS) modulation outperforms orthogonal frequency division multiplexing (OFDM) in high-mobility scenarios. One challenge for OTFS massive MIMO is downlink channel estimation due to the large number of base station antennas. In this paper, we propose a 3D-structured orthogonal matching pursuit algorithm based channel estimation technique to solve this problem. First, we show that the OTFS MIMO channel exhibits 3D-structured sparsity: normal sparsity along the delay dimension, block sparsity along the Doppler dimension, and burst sparsity along the angle dimension. Based on the 3D-structured channel sparsity, we then formulate the downlink channel estimation problem as a sparse signal recovery problem. Simulation results show that the proposed algorithm can achieve accurate channel state information with low pilot overhead. [ABSTRACT FROM AUTHOR]

Quantizers take part in nearly every digital signal processing system that operates on physical signals. They are commonly designed to accurately represent the underlying signal, regardless of the specific task to be performed on the quantized data. In systems working with high-dimensional signals, such as massive multiple-input multiple-output (MIMO) systems, it is beneficial to utilize low-resolution quantizers, due to cost, power, and memory constraints. In this paper, we study quantization of high-dimensional inputs, aiming at improving performance under resolution constraints by accounting for the system task in the quantizers design. We focus on the task of recovering a desired signal statistically related to the high-dimensional input, and analyze two quantization approaches. We, first, consider vector quantization, which is typically computationally infeasible, and characterize the optimal performance achievable with this approach. Next, we focus on practical systems that utilize hardware-limited scalar uniform analog-to-digital converters (ADCs), and design a task-based quantizer under this model. The resulting system accounts for the task by linearly combining the observed signal into a lower dimension prior to quantization. We then apply our proposed technique to channel estimation in massive MIMO networks. Our results demonstrate that a system utilizing low-resolution scalar ADCs can approach the optimal channel estimation performance by properly accounting for the task in the system design. [ABSTRACT FROM AUTHOR]

We consider the problem of reconstructing two signals from the autocorrelation and cross-correlation measurements. This inverse problem is a fundamental one in signal processing, and arises in many applications, including phase retrieval and blind channel estimation. In a typical phase retrieval setup, only the autocorrelation measurements are obtainable. We show that, when the measurements are obtained using three simple “masks”, phase retrieval reduces to the aforementioned reconstruction problem. The classic solution to this problem is based on finding common factors between the $z$ -transforms of the autocorrelation and cross-correlation vectors. This solution has enjoyed limited practical success, mainly due to the fact that it is not sufficiently stable in the noisy setting. In this paper, inspired by the success of convex programming in provably and stably solving various quadratic constrained problems, we develop a semidefinite programming-based algorithm and provide theoretical guarantees. In particular, we show that almost all signals can be uniquely recovered by this algorithm (up to a global phase). Comparative numerical studies demonstrate that the proposed method significantly outperforms the classic method in the noisy setting. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of recovering a group sparse vector from a small number of linear measurements. In the past, the common approach has been to use various “group sparsity-inducing” norms such as the Group LASSO norm for this purpose. By using the theory of convex relaxations, we show that it is also possible to use $\ell _1$ -norm minimization for group sparse recovery. We introduce a new concept called group robust null space property (GRNSP), and show that, under suitable conditions, a group version of the restricted isometry property (GRIP) implies the GRNSP, and thus leads to group sparse recovery. When all groups are of equal size, our bounds are sometimes less conservative than known bounds. Moreover, our results apply even to situations where the groups have different sizes. When specialized to conventional sparsity, our bounds reduce to one of the well-known “best possible” conditions for sparse recovery. This relationship between GRNSP and GRIP is new even for conventional sparsity, and substantially streamlines the proofs of some known results. Using this relationship, we derive bounds on the $\ell _p$ -norm of the residual error vector for all $p \in [1,2]$ , and not just when $p = 2$. When the measurement matrix consists of random samples of a sub-Gaussian random variable, we present bounds on the number of measurements, which are sometimes less conservative than currently known bounds. [ABSTRACT FROM AUTHOR]