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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

This paper develops schemes for block-sparse channel estimation in millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems that exploit the spatial sparsity inherent in such channels. Initially, a novel sparse Bayesian learning (SBL) based block-sparse channel estimation technique is developed for a mmWave hybrid MIMO system with multiple measurement vectors, which overcomes the shortcomings of the existing orthogonal matching pursuit-based framework. This is subsequently extended to a temporally correlated block-sparse mmWave MIMO channel. Further, an online recursive hierarchical Bayesian Kalman Filter is developed for the estimation of a time-selective mmWave MIMO channel. Bayesian Cramér–Rao bounds are also derived for the proposed static and time-selective mmWave MIMO channel estimation schemes followed by precoder/combiner design employing the SBL-based imperfect channel estimates. Simulation results are presented to demonstrate the improved performance of the proposed SBL-based channel estimation techniques in comparison to the popular OMP-based scheme proposed recently. [ABSTRACT FROM AUTHOR]

Trajectory estimation of moving targets is examined; in particular, quasi-linear trajectories are considered. Background subtraction methods, exploiting low-rank backgrounds, and sparse features of interest are extended to incorporate linear constraints. The line constraint is enforced via a rotation that yields an additional low rank condition. The proposed method is applied to single object tracking in video, wherein the trajectory can be parameterized as a line. The optimization is solved via the augmented Lagrange multiplier method. An average performance improvement of 4 dB is observed over previous background subtraction methods for estimating the position and velocity of the target. Furthermore, about a 6.2 dB gain is seen over previous target tracking methods that do not exploit the linear nature of the trajectory. The Cramér–Rao bound (CRB) for background subtraction with a linear constraint is derived and numerical results show that the proposed method achieves near optimal performance via comparison to the CRB. An aggregated error is shown to converge to zero and a boundedness analysis is conducted which suggests that the iterative algorithm is convergent as confirmed by simulations. Finally, the proposed technique is applied to real video data and is shown to be effective in estimating quasi-linear trajectories. [ABSTRACT FROM AUTHOR]

In this paper, the estimation of a narrowband time-varying channel under the practical assumptions of finite block length and finite transmission bandwidth is investigated. It is shown that the signal, after passing through a time-varying narrowband channel reveals a useful parametric low-rank structure that can be represented as a bilinear form. To estimate the channel, two strategies are developed. The first method exploits the low-rank bilinear structure of the channel via a non-convex strategy based on an alternating direction optimization between the delay and Doppler directions. While prior Wirtinger flow methods have exhibited good performance with proper initialization, this is not true in the current scenario. Due to the non-convex nature of this approach, this first approach is sensitive to local minima. Furthermore, the convergence rate of the Wirtinger flow method is shown to be provably modest. Thus, a novel convex approach based on the minimization of the atomic norm using measurements of the signal at the time domain is proposed based on a second bilinear parametrization of the channel. For the convex approach, optimality and uniqueness conditions, and a theoretical guarantee for noiseless channel estimation with small number of measurements are characterized. Numerical results show that the performance of the proposed algorithm is independent of the leakage effect and the new methods can achieve a 5–12 dB improvement, on average, compared to a classical $l_1$ -based sparse approximation method that does not consider the leakage effect, and 2 dB improvement over a basis expansion method that considers the leakage effect. [ABSTRACT FROM AUTHOR]

In millimeter-wave channels, most of the received energy is carried by a few paths. Traditional precoders sweep the angle-of-departure (AoD) and angle-of-arrival (AoA) space with directional precoders to identify directions with largest power. Such precoders are heuristic and lead to suboptimal AoD/AoA estimation. We derive optimal precoders, minimizing the Cramér–Rao bound (CRB) of the AoD/AoA under a given uncertainty range, assuming a fully digital architecture at the transmitter and spatial filtering of a single path. The precoders are found by solving a suitable convex optimization problem. We demonstrate that the accuracy can be improved by at least a factor of two over traditional precoders, and show that there is an optimal number of distinct precoders beyond which the CRB does not improve. [ABSTRACT FROM AUTHOR]

This paper presents two novel approaches for joint carrier frequency offset (CFO) and doubly selective channel estimation in the uplink of multiple-input multiple-output orthogonal frequency division multiple access (MIMO-OFDMA) systems. Considering high-mobility situations, where channels change within one OFDMA symbol interval, and the time varying nature of CFOs, basis expansion modeling (BEM) is employed to represent the time variations of the channel. Two new approaches are then proposed based on Schmidt–Kalman filtering (SKF). The first approach utilizes Schmidt-extended Kalman filtering for each user to estimate CFO and BEM coefficients. The second approach uses Gaussian particle filtering along with SKF to estimate CFO and BEM coefficients of each user. The Bayesian Cramér–Rao bound is derived, and the performances of the new schemes are evaluated using the mean square errors. It is demonstrated that the new approaches can significantly improve the mean-square error performance in comparison with the existing methods. [ABSTRACT FROM AUTHOR]

A set-membership affine projection algorithm is proposed that can estimate a complex-valued channel matrix using a set of complex-valued pilots in the presence of additive white Gaussian noise. It is shown that the algorithm converges faster than the well-known set-membership normalized least mean square algorithm (SM-NLMS) while it resolves the high steady-state error value and the complexity issues in the regular affine projection algorithm. The fast convergence of the proposed algorithm means that a shorter training sequence inside each data block is required, which in turn improves the effective bit rate. This fast convergence is more pronounced when the pilot vectors are highly correlated. We incorporated the set-membership filtering framework into our study to reduce the computational complexity of the algorithm and preserve energy in the WSNs. Other studies have shown the superiority of the adaptive filtering algorithms, and in particular the NLMS algorithm, over other alternatives in various signal processing areas in WSNs, therefore, our proposed algorithm is a powerful substitute for a variety of algorithms. In other words, the implementation of various signal processing algorithms for different purposes can be replaced with the implementation of the proposed multipurpose algorithm. In this paper, we combine the results of our previous studies and prove the convergence of the algorithm. Furthermore, the steady-state analysis in the output mean square error is presented for two cases of pilot signals, and in the conducted simulations, the MSE performance of the algorithm is compared with the regular affine projection algorithm and the SM-NLMS algorithm. [ABSTRACT FROM AUTHOR]

Estimation of both cascaded and residual self-interference (RSI) channels and a new training frame structure are considered for full-duplex (FD) amplify-and-forward (AF) one-way relay networks with rapidly time-varying individual channels. To estimate the RSI and the rapidly time-varying cascaded channels, we propose a new training frame structure in which orthogonal training blocks are sent by the source node and delivered to the destination over an FD-AF relay. Exploiting the orthogonality of the training blocks, we obtain two decoupled training signal models for the estimation of the RSI and the cascaded channels. We apply linear minimum mean square error (MMSE) based estimators to the cascaded channel as well as RSI channel. In order to investigate the mean square error (MSE) performance of the system, we also derive the Bayesian Cramer–Rao lower bound. As another performance benchmark, we also assess the symbol error rate (SER) performances corresponding to the estimated and the perfect channel state information available at the receiver side. Computer simulations exhibit the proposed training frame structure and the linear MMSE estimator MSE and SER performances are shown. [ABSTRACT FROM AUTHOR]

In this work, the problem of signal parameter estimation from measurements acquired by a low-complexity analog-to-digital converter (ADC) with 1-bit output resolution and an unknown quantization threshold is considered. Single-comparator ADCs are energy-efficient and can be operated at ultrahigh sampling rates. For analysis of such systems, a fixed and known quantization threshold is usually assumed. In the symmetric case, i.e., zero hard-limiting offset, it is known that in the low signal-to-noise ratio (SNR) regime the signal processing performance degrades moderately by ${2}/{\pi }$ ( $-\text{1.96}$ dB) when comparing to an ideal $\infty$ -bit converter. Due to hardware imperfections, low-complexity 1-bit ADCs will, in practice, exhibit an unknown threshold different from zero. Therefore, we study the accuracy that can be obtained with received data processed by a hard-limiter with unknown quantization level by using asymptotically optimal channel estimation algorithms. To characterize the estimation performance of these nonlinear algorithms, we employ analytic error expressions for different setups while modeling the offset as a nuisance parameter. In the low SNR regime, we establish the necessary condition for a vanishing loss due to missing offset knowledge at the receiver. As an application, we consider the estimation of single-input single-output wireless channels with intersymbol interference and validate our analysis by comparing the analytic and experimental performance of the studied estimation algorithms. Finally, we comment on the extension to multiple-input multiple-output channel models. [ABSTRACT FROM AUTHOR]

We propose a novel soft-input soft-output equalizer for single-carrier transmissions over unknown frequency-selective block-fading channels. Our equalizer leverages the recently proposed parametric bilinear generalized approximate message passing algorithm for joint channel-estimation and symbol-detection, and exploits fast Fourier transform (FFT)-processing to achieve a per-symbol complexity that grows only logarithmically in the channel delay-spread. Furthermore, it supports the use of Gaussian mixture models to support the approximately sparse nature of wideband wireless channel responses. Numerical experiments, conducted using physically motivated Saleh–Valenzuela channel models, show that the proposed approach achieves channel normalized mean square error and bit error rate that are significant improved over existing turbo frequency-domain equalization approaches for unknown channels. Additional experiments show that the proposed scheme facilitates much higher spectral efficiencies than sparse deconvolution methods based on convex relaxation. [ABSTRACT FROM AUTHOR]

Time-division duplex (TDD)-based massive MIMO systems rely on the reciprocity of the wireless propagation channels when calculating the downlink precoders based on uplink pilots. However, the effective uplink and downlink channels incorporating the analog radio front-ends of the base station (BS) and user equipments (UEs) exhibit non-reciprocity due to non-identical behavior of the individual transmit and receive chains. When the downlink precoder is not aware of such channel non-reciprocity (NRC), system performance can be significantly degraded due to the NRC-induced interference terms. In this paper, we consider a general TDD-based massive MIMO system where frequency-response mismatches at both the BS and UEs, as well as the mutual coupling mismatches at the BS large-antenna system all coexist and induce channel NRC. Based on the NRC-impaired signal models, we first propose a novel iterative estimation method for acquiring both the BS and UE side NRC matrices and then also propose an efficient NRC-aware downlink precoder design which utilizes the obtained estimates. Furthermore, an efficient pilot signaling scheme between the BS and UEs is introduced in order to facilitate executing the proposed estimation method and the NRC-aware precoding technique in practical systems. Comprehensive numerical results indicate substantially improved spectral efficiency performance when the proposed NRC estimation and NRC-aware precoding methods are adopted, compared to the existing state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Large-scale antenna systems are considered as a viable technology to compensate for huge path loss in millimeter-wave (mmWave) communications. However, due to the massive antennas, the channel state information (CSI) acquisition is costly and challenging. In this paper, we develop a novel compressive channel estimation framework based on multiple measurement vectors (MMV). Compared with conventional single measurement vector (SMV)-based approach, the proposed framework exploits structural sparsity exhibited in the relatively rich local scattering mmWave channels to greatly reduce the training and computational overheads. Moreover, we propose a channel subspace matching pursuit (CSMP) algorithm based on the MUltiple SIgnal Classification (MUSIC) as an MMV solver. By leveraging the benefits of MUSIC, the proposed CSMP can properly exploit the diversity gain from structural sparsity, and further improve the estimation quality via the superresolution capability. Meanwhile, an efficient implementation method of the proposed CSMP is also presented. Compared to the conventional MMV solver, the proposed CSMP exhibits much lower complexity. Finally, several simulation results show that the MMV-based CSMP achieves significant performance gains over other estimation algorithms, especially when the angular resolutions are high. Regarding the computational cost, the simulation result shows that the MMV-based estimation algorithms are approximately two orders of magnitude smaller than the SMV-based estimation algorithms. [ABSTRACT FROM AUTHOR]

We present novel lower bounds on the mean square error (MSE) of the location estimation of an emitting source via a network where the sensors are deployed randomly. The sensor locations are modeled as a homogenous Poisson point process. In contrast to previous bounds that are a function of the specific locations of all the sensors, we present Cramér-Rao bound (CRB) type bounds on the expected mean square error; that is, we first derive the CRB on the MSE as a function of the sensors' location, and then take expectation with respect to the distribution of the sensors' location. Thus, these bounds are not a function of a particular sensor configuration, but rather of the sensor statistics. Hence, these novel bounds can be evaluated prior to sensor deployment and provide insights into design issues such as the necessary sensor density, the effect of the channel model, the effect of the signal power, and others. The derived bounds are simple to evaluate and provide a good prediction of the actual network performance. Numerical results show that the novel bounds give a good approximation even in other deployment scenarios such as a square or a triangular grid. [ABSTRACT FROM AUTHOR]

We consider the problem of downlink training sequence design for frequency-division-duplex multiuser massive multiple-input multiple-output systems in the general case where users have distinct spatial correlations. The training sequences leverage spatial correlations and are designed to minimize the channel estimation weighted sum mean square error (MSE) under the assumption that users employ minimum MSE estimators. Noting that the weighted sum MSE function is invariant to unitary rotations of its argument, a solution is obtained using a steepest descent method on the Grassmannian manifold. We extend the proposed design to scenarios with temporal correlations combined with Kalman filters at the users, and design sequences exploiting the multiuser spatio-temporal channel structure. Finally, we consider scenarios where only a limited number of bits $B$ are available at the base station (BS) to inform the users of each chosen sequence, e.g., sequences are chosen from a set of $2^B$ vectors known to the BS and users, and develop a subspace version of matching pursuit techniques to choose the desired sequences. Simulation results using realistic channel models show that the proposed solutions improve user fairness with a proper choice of weights, lead to accurate channel estimates with training durations that can be much smaller than the number of BS antennas, and show substantial gains over randomly chosen sequences for even small values of $B$. [ABSTRACT FROM PUBLISHER]

Phase noise correction is crucial to exploit full advantage of orthogonal frequency-division multiplexing (OFDM) in modern high-data-rate communications. OFDM channel estimation with simultaneous phase noise compensation has therefore drawn much attention and stimulated continuing efforts. Existing methods, however, either have not taken into account the fundamental properties of phase noise or are only able to provide estimates of limited applicability owing to considerable computational complexity. In this paper, we have reformulated the joint phase noise and channel estimation problem in the time domain as opposed to existing frequency-domain approaches, which enables us to develop much more efficient algorithms using the majorization–minimization technique. In addition, we propose two methods based on dimensionality reduction and regularization, respectively, that can adapt to various phase noise levels and signal-to-noise ratio and achieve much lower estimation errors than the benchmarks without incurring much additional computational cost. Several numerical examples with phase noise generated by free-running oscillators or phase-locked loops demonstrate that our proposed algorithms outperform existing methods with respect to both computational efficiency and mean squared error within a large range of SNRs. [ABSTRACT FROM PUBLISHER]

Channel estimation in multicarrier systems employing filter banks with offset quadrature amplitude modulation (FBMC/OQAM) is far less easy compared to orthogonal frequency division multiplexing (OFDM). Challenges come from the interference effect, inherent in this type of FBMC systems, and the (generally) nonnegligible frequency selectivity of their subchannels, due to the nature of this modulation and the cyclic prefix (CP)-free transmission. Most of the FBMC/OQAM channel estimation methods rely on the assumption of a low frequency selective channel (thus implying (almost) flat subchannels) in order to more easily (i.e., in a manner analogous to CP-OFDM) tackle this problem. However, they perform quite poorly when applied in more demanding propagation conditions. Others, more recent ones, relax the assumption of low frequency selectivity but they either depend on a parametric model for the channel or they concentrate on persubchannel estimation and often require long training sequences. This paper revisits this problem through a formulation that does not rely on any simplifying assumption about the channel. This gives rise to a new estimation method, applicable to channels of any frequency selectivity, which relies on a very short preamble for training. The latter is optimized with respect to the channel estimation mean squared error and is shown to result in a very significant simplification of the estimation procedure. Both full (block-type) and sparse (comb-type) preambles are considered. Applying these results in low-dispersion channels yields, as special cases, existing and new preamble-based estimation schemes for such scenarios. The superiority of the proposed method over classical ones is demonstrated via simulation results for both mildly and highly frequency selective channels. [ABSTRACT FROM PUBLISHER]

The performance of the recently proposed high-resolution direct position determination method is analyzed. The method is based on minimum-variance-distortionless-response considerations to create a high-resolution spectrum (heat map) that enables single-step localization of multiple radio frequency emitters. Under the assumption of independent, identically distributed, circular, complex Gaussian snapshots, we derive an approximation to the estimation mean square error matrix. The approximation is an analytical expression, composed of variance and bias due to finite sample effects and asymptotic bias. Some of the obtained closed-form results are also relevant for other estimation techniques that combine independent minimum-variance-distortionless-response spectrums. Simulations are used to verify the usefulness of the theoretical expressions. [ABSTRACT FROM AUTHOR]

We consider mean squared estimation with lookahead of a continuous-time signal corrupted by additive white Gaussian noise. We show that the mutual information rate function, i.e., the mutual information rate as function of the signal-to-noise ratio (SNR), does not, in general, determine the minimum mean squared error (MMSE) with fixed finite lookahead, in contrast to the special cases with 0 and infinite lookahead (filtering and smoothing errors), respectively, which were previously established in the literature. Further, we investigate the simple class of continuous-time stationary Gauss-Markov processes (Ornstein-Uhlenbeck processes) as channel inputs, and explicitly characterize the behavior of the minimum mean squared error (MMSE) with finite lookahead and signal-to-noise ratio (SNR). We extend our results to mixtures of Ornstein–Uhlenbeck processes, and use the insight gained to present lower and upper bounds on the MMSE with lookahead for a class of stationary Gaussian input processes, whose spectrum can be expressed as a mixture of Ornstein–Uhlenbeck spectra. [ABSTRACT FROM AUTHOR]

The recent trends of densification and centralized signal processing in radio access networks suggest that future networks may comprise ubiquitous antennas coordinated to form a network-wide gigantic array, referred to as the ubiquitous array (UA). In this paper, the UA communication techniques are designed and analyzed based on a geometric model. Specifically, the UA is modeled as a continuous circular/spherical array enclosing target users and free-space propagation is assumed. First, consider the estimation of multiuser UA channels induced by user locations. Given single pilot symbols, a novel channel estimation scheme is proposed that decomposes training signals into Fourier/Laplace series and thereby translates multiuser channel estimation into peak detection of a derive function of location. The process is shown to suppress noise. Moreover, it is proved that estimation error due to interference diminishes with the increasing minimum user-separation distance following the power law, where the exponent is 1/3 and 1 for the circular and spherical UA, respectively. If orthogonal pilot sequences are used, channel estimation is found to be perfect. Next, consider channel-conjugate data transmission that maximizes received signal power. The power of interference between two users is shown to decay with the increasing user-separation distance sub-linearly and super-linearly for the circular and spherical UA, respectively. Furthermore, a novel multiuser precoding design is proposed by exciting different phase modes of the UA and controlling the mode weight factors to null interference. The number of available degrees of freedom for interference nulling using the UA is proved to be proportional to the minimum user-separation distance. [ABSTRACT FROM AUTHOR]

This paper considers a multiple-input multiple-output (MIMO) receiver with very low-precision analog-to-digital convertors (ADCs) with the goal of developing massive MIMO antenna systems that require minimal cost and power. Previous studies demonstrated that the training duration should be relatively long to obtain acceptable channel state information. To address this requirement, we adopt a joint channel-and-data (JCD) estimation method based on Bayes-optimal inference. This method yields minimal mean square errors with respect to the channels and payload data. We develop a Bayes-optimal JCD estimator using a recent technique based on approximate message passing. We then present an analytical framework to study the theoretical performance of the estimator in the large-system limit. Simulation results confirm our analytical results, which allow the efficient evaluation of the performance of quantized massive MIMO systems and provide insights into effective system design. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new blind frequency synchronization scheme for multiuser orthogonal-frequency-division multiplexing (OFDM) uplink transmissions. The spatial multiplexing is supported in the considered model that allows the subcarriers to be simultaneously occupied by multiple users, while the orthogonal frequency division multiple access (OFDMA) can serve as a special case of our discussion. We propose to assign different null subcarriers to different users and design algorithm that can perform blind carrier frequency offset (CFO) estimation for each individual user with the aid of large number of receive antennas, which then removes the necessity of multidimensional searching. After estimating CFO for one user, the orthogonal complement space of the other users can be obtained which could be further utilized for multiuser interference cancelation. Hence, the multiuser OFDM uplink model reduces to an equivalent single user signal model, where the blind channel estimation with scalar ambiguity can be designed and the conventional single-user data detection can be peformed. To make the proposed study complete, the closed-form performance analysis for mean square error (MSE) of the CFO estimation is derived, based on which the discussion about optimal null subcarrier assignment scheme is further provided. Finally, the Cramer–Rao bound (CRB) is derived, and the numerical results are provided to corroborate the proposed studies. [ABSTRACT FROM PUBLISHER]

In this paper, we develop frequency-domain phase noise estimation schemes for an orthogonal frequency division multiplexing (OFDM) system that utilize the geometrical structure associated with the spectral components of the complex exponential of the phase noise process. This geometry can be expressed as a set of non-convex quadratic equality constraints that involve permutation matrices. Since the oscillator power spectral density is typically a low-pass process, we can reduce the dimensionality of the phase noise spectral vector. In particular, we propose a new dimensionality reduction model that preserves the phase noise spectral geometry when moving from smaller to larger dimensional spaces. Using this new model and building upon existing works, the phase noise estimation problem is posed as an optimization problem. We show, using the S-procedure, that the optimization problem has an optimal solution that is attained and can be solved using semidefinite programming. In order to reduce the computational complexity of the aforementioned optimization problem, we consider sub-optimal schemes that provide an estimate satisfying this geometry. Through numerical simulations, we demonstrate superior bit-error-rate performance when the proposed model used in conjunction with the phase noise spectral geometry is incorporated in the estimation process. [ABSTRACT FROM PUBLISHER]

Carrier frequency offset (CFO) introduces spectrum misalignment of the transmit and receive filters, causing energy loss and distortion of received signal. A recent study presents an accurate signal model that incorporates these characteristics. However, CFO estimators in the existing literature were developed based on the signal models without these characteristics. This paper generalizes the accurate signal model with CFO to include timing offset and sampling offset and then studies what effects the accurate signal model bring to the CFO estimation and how to address them. We investigate different existing CFO estimators and find some of them lose their optimality under the accurate signal model. We also develop two new integer normalized CFO (ICFO) estimators under the accurate signal model using only one OFDM symbol; one of them is a pilot-aided estimator using both pilot and data and the other one is a blind estimator using data only. Compared with the existing approaches, both of the new estimators make better use of channel and energy loss information, thus yielding more accurate estimation. Furthermore, the proposed methods overcome the existing approaches’ limitation to phase shift keying modulation. Simulation results corroborate the advantages of the new estimators. Analytical performance results are also provided for the proposed estimators. [ABSTRACT FROM PUBLISHER]

In this paper, we derive the maximum a posteriori (MAP) symbol detector for a multiple-input multiple-output system in the presence of Wiener phase noise due to noisy local oscillators, and quasi-static fading channels. As in single-antenna systems, the computation of the optimum receiver is an analytically intractable problem and is unimplementable in practice. In this purview, we propose three suboptimal, low-complexity algorithms for approximately implementing the MAP symbol detector, which involve joint phase noise estimation and data detection. Our first algorithm is obtained by means of the sum-product algorithm, where we use the multivariate Tikhonov canonical distribution approach. In our next algorithm, we derive an approximate MAP symbol detector based on the smoother-detector framework, wherein the detector is properly designed by incorporating the phase noise statistics from the smoother. The third algorithm is derived based on the variational Bayesian framework. By simulations, we evaluate the performance of the proposed algorithms for both uncoded and coded data transmissions and observe that the proposed techniques significantly outperform the other important algorithms from prior works, which are considered herein. [ABSTRACT FROM PUBLISHER]

We consider the detection and estimation of a zero-mean Gaussian signal in a wireless sensor network with a coherent multiple access channel, when the fusion center (FC) is configured with a large number of antennas and the wireless channels between the sensor nodes and FC experience Rayleigh fading. For the detection problem, we study the Neyman–Pearson (NP) detector and energy detector (ED) and find optimal values for the sensor transmission gains. For the NP detector, which requires channel state information (CSI), we show that detection performance remains asymptotically constant with the number of FC antennas if the sensor transmit power decreases proportionally with the increase in the number of antennas. Performance bounds show that the benefit of multiple antennas at the FC disappears as the transmit power grows. The results of the NP detector are also generalized to the linear minimum mean-squared error estimator. For the ED, which does not require CSI, we derive optimal gains that maximize the deflection coefficient of the detector, and we show that a constant deflection can be asymptotically achieved if the sensor transmit power scales as the inverse square root of the number of FC antennas. Unlike the NP detector, for high sensor power, the multi-antenna ED is observed to empirically have significantly better performance than the single-antenna implementation. A number of simulation results are included to validate the analysis. [ABSTRACT FROM PUBLISHER]

In this paper, we examine the Bayesian Cramér–Rao lower bounds (BCRBs) for the channel estimation in an amplify-and-forward (AF) one-way relay network (OWRN) under the time-selective flat-fading scenario, where the superimposed training is adopted at the relay node in order to achieve the individual channel estimation. We formulate the nonlinear dynamic state space for the individual channels and derive the online/offline BCRBs for the fully data-aided (FDA) channel estimator and the partially data-aided (PDA) estimator. The former estimator has full knowledge about the symbols from both the source and the relay, while the latter one has imperfect statistical information about the data of the source, and possesses full information of the symbols superimposed by the relay. For the FDA scenario, we calculate the closed-form online/offline BCRBs and analyze the effect of the nodes' mobility on the BCRB performance, while for the PDA case, with the assumption of square QAM constellation set at the source, we design one framework to numerically evaluate online/offline BCRBs and analyze the asymptotic BCRBs at high SNRs particularly for the 4-QAM constellation set. Finally, numerical results are provided to corroborate the proposed studies. [ABSTRACT FROM PUBLISHER]

This work addresses channel estimation in multiple antenna multicell interference-limited networks. Channel state information (CSI) acquisition is vital for interference mitigation. Wireless networks often suffer from multicell interference, which can be mitigated by deploying beamforming to spatially direct the transmissions. The accuracy of the estimated CSI plays an important role in designing accurate beamformers that can control the amount of interference created from simultaneous spatial transmissions to mobile users. Therefore, a new technique based on the structure of the spatial covariance matrix and the discrete cosine transform (DCT) is proposed to enhance channel estimation in the presence of interference. Bayesian estimation and least squares estimation frameworks are introduced by utilizing the DCT to separate the overlapping spatial paths that create the interference. The spatial domain is thus exploited to mitigate the contamination which is able to discriminate across interfering users. Gains over conventional channel estimation techniques are presented in our simulations which are also valid for a small number of antennas. [ABSTRACT FROM PUBLISHER]

Channel state feedback is a serious burden that limits deployment of transmit beamforming systems with many antennas in frequency-division duplex (FDD) mode. Transmit beamforming with limited feedback systems estimate the channel at the receiver and send quantized channel state or beamformer information to the transmitter. A different approach that exploits the spatio-temporal correlation of the channel is proposed here. The transmitter periodically sends a beamformed pilot signal in the downlink, while the receiver quantizes the corresponding received signal and feeds back the bits to the transmitter. Assuming an autoregressive (AR) channel model, Kalman filtering (KF) based on the sign of innovations (SOI) is proposed for channel tracking, and closed-form expressions for the channel estimation mean-squared error (MSE) are derived under certain conditions. For more general channel models, a novel tracking approach is proposed that exploits the quantization bits in a maximum a posteriori (MAP) formulation. Simulations show that close to optimum performance can be attained with only 2 bits per channel dwell time block, even for systems with many transmit antennas. This clears a hurdle for transmit beamforming with many antennas in FDD mode—which was almost impossible with the prior state-of-art. [ABSTRACT FROM PUBLISHER]

Vector orthogonal frequency division multiplexing (V-OFDM) for single transmit antenna systems is a generalization of OFDM where single-carrier frequency domain equalization (SC-FDE) and OFDM are just two special cases. It has been shown to be able to collect multipath diversity and thus generally outperforms OFDM. The performance of OFDM under phase noise has been extensively studied in the literature. These effects can be summarized as introducing a common phase error (CPE) and inter carrier interference (ICI) resulting in poor performance. The performance of V-OFDM under phase noise still remains uninvestigated and in this paper it is shown that phase noise in V-OFDM systems leads to a common vector block phase error (CVBPE) as well as an inter vector block carrier interference (IVBCI) effect. An expression for the signal plus interference noise ratio (SINR) for a V-OFDM system is derived and found to agree closely with simulation results. A pilot vector CVBPE based phase noise estimation technique is derived, and then combined with the maximum likelihood (ML) and the linear minimum mean square error (LMMSE) estimators to estimate the phase noise. It turns out that compared with OFDM, V-OFDM systems can perform phase noise estimation with lower complexity. The decorrelation and cancellation techniques are then used to compensate for the phase noise impairment. Numerical results for both coded and uncoded systems with perfect and practical channel estimation are provided to validate the analysis and effectiveness of the proposed phase noise estimation and compensation methods. [ABSTRACT FROM AUTHOR]

This paper investigates pilot-aided channel estimation for two-way relay networks (TWRNs) in the presence of synchronization errors between the two sources. The unpredictable synchronization error leads to time domain offset and signal arriving order (SAO) ambiguity when two signals sent from two sources are superimposed at the relay. A two-step channel estimation algorithm is first proposed, in which the linear minimum mean-square-error (LMMSE) estimator is used to obtain initial channel estimates based on pilot symbols and a linear minimum error probability (LMEP) estimator is then developed to update these estimates. Optimal training sequences and power allocation at the relay are designed to further improve the performance for LMMSE based initial channel estimation. To tackle the SAO ambiguity problem, the generalized likelihood ratio testing method is applied and an upper bound on the SAO detection error probability is derived. By using the SAO information, a scaled LMEP estimation algorithm is proposed to compensate for the performance degradation caused by SAO detection error. Simulation results show that the proposed estimation algorithms can effectively mitigate the negative effects caused by asynchronous transmissions in TWRNs, thus significantly outperforming the existing channel estimation algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we design a new blind joint carrier frequency offset (CFO) and channel estimation method for orthogonal frequency-division multiplexing (OFDM) with multiantenna receiver. The proposed algorithm requires only one received OFDM block and thus belongs to the category of one-shot estimation methods. Other advantages of the proposed algorithm include 1) it supports fully loaded data carriers and is thus spectral efficient; 2) the channel from the transmitter to each receive antenna can be blindly estimated with only a scaling ambiguity; and 3) the algorithms outperforms the existing methods. Moreover, we derive the Cramér–Rao Bounds (CRB) of joint CFO and channel estimation in closed forms. Numeral results not only show the effectiveness of the proposed algorithm but also demonstrate its closed performance to CRB. [ABSTRACT FROM PUBLISHER]

It is well known that the impulse response of a wideband wireless channel is approximately sparse, in the sense that it has a small number of significant components relative to the channel delay spread. In this paper, we consider the estimation of the unknown channel coefficients and its support in OFDM systems using a sparse Bayesian learning (SBL) framework for exact inference. In a quasi-static, block-fading scenario, we employ the SBL algorithm for channel estimation and propose a joint SBL (J-SBL) and a low-complexity recursive J-SBL algorithm for joint channel estimation and data detection. In a time-varying scenario, we use a first-order autoregressive model for the wireless channel and propose a novel, recursive, low-complexity Kalman filtering-based SBL (KSBL) algorithm for channel estimation. We generalize the KSBL algorithm to obtain the recursive joint KSBL algorithm that performs joint channel estimation and data detection. Our algorithms can efficiently recover a group of approximately sparse vectors even when the measurement matrix is partially unknown due to the presence of unknown data symbols. Moreover, the algorithms can fully exploit the correlation structure in the multiple measurements. Monte Carlo simulations illustrate the efficacy of the proposed techniques in terms of the mean-square error and bit error rate performance. [ABSTRACT FROM AUTHOR]

A distributed inference scheme which uses bounded transmission functions over a Gaussian multiple access channel is considered. When the sensor measurements are decreasingly reliable as a function of the sensor index, the conditions on the transmission functions under which consistent estimation and reliable detection are possible is characterized. For the distributed estimation problem, an estimation scheme that uses bounded transmission functions is proved to be strongly consistent provided that the variances of the noise samples are bounded and that the transmission function is one-to-one. The proposed estimation scheme is compared with the amplify-and-forward technique and its robustness to impulsive sensing noise distributions is highlighted. In contrast to amplify-and-forward schemes, it is also shown that bounded transmissions suffer from inconsistent estimates if the sensing noise variance goes to infinity. For the distributed detection problem, similar results are obtained by studying the deflection coefficient. Simulations corroborate our analytical results. [ABSTRACT FROM PUBLISHER]

To fully utilize the spatial multiplexing gains or array gains of massive MIMO, the channel state information must be obtained at the transmitter side (CSIT). However, conventional CSIT estimation approaches are not suitable for FDD massive MIMO systems because of the overwhelming training and feedback overhead. In this paper, we consider multi-user massive MIMO systems and deploy the compressive sensing (CS) technique to reduce the training as well as the feedback overhead in the CSIT estimation. The multi-user massive MIMO systems exhibits a hidden joint sparsity structure in the user channel matrices due to the shared local scatterers in the physical propagation environment. As such, instead of naively applying the conventional CS to the CSIT estimation, we propose a distributed compressive CSIT estimation scheme so that the compressed measurements are observed at the users locally, while the CSIT recovery is performed at the base station jointly. A joint orthogonal matching pursuit recovery algorithm is proposed to perform the CSIT recovery, with the capability of exploiting the hidden joint sparsity in the user channel matrices. We analyze the obtained CSIT quality in terms of the normalized mean absolute error, and through the closed-form expressions, we obtain simple insights into how the joint channel sparsity can be exploited to improve the CSIT recovery performance. [ABSTRACT FROM PUBLISHER]

Suppose a linear model \bf y=\bf H\bf x+\bf n, where inputs \bf x,n are independent Gaussian mixtures. The problem is to design the transfer matrix \bf H so as to minimize the mean square error (MSE) when estimating \bf x from \bf y. This problem has important applications, but faces at least three hurdles. Firstly, even for a fixed \bf H, the minimum MSE (MMSE) has no analytical form. Secondly, the MMSE is generally not convex in \bf H. Thirdly, derivatives of the MMSE w.r.t. \bf H are hard to obtain. This paper casts the problem as a stochastic program and invokes gradient methods. The study is motivated by two applications in signal processing. One concerns the choice of error-reducing precoders; the other deals with selection of pilot matrices for channel estimation. In either setting, our numerical results indicate improved estimation accuracy—markedly better than those obtained by optimal design based on standard linear estimators. Some implications of the non-convexities of the MMSE are noteworthy, yet, to our knowledge, not well known. For example, there are cases in which more pilot power is detrimental for channel estimation. This paper explains why. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of estimating time varying phase noise caused by imperfect oscillators in multiple-input multiple-output (MIMO) systems. The estimation problem is parameterized in detail and based on an equivalent signal model its dimensionality is reduced to minimize the overhead associated with phase noise estimation. New exact and closed-form expressions for the Bayesian Cramér–Rao lower bounds (BCRLBs) and soft-input maximum a posteriori (MAP) estimators for online, i.e., filtering, and offline, i.e., smoothing, estimation of phase noise over the length of a frame are derived. Simulations demonstrate that the proposed MAP estimators' mean-square error (MSE) performances are very close to the derived BCRLBs at moderate-to-high signal-to-noise ratios. To reduce the overhead and complexity associated with tracking the phase noise processes over the length of a frame, a novel soft-input extended Kalman filter (EKF) and extended Kalman smoother (EKS) that use soft statistics of the transmitted symbols given the current observations are proposed. Numerical results indicate that by employing the proposed phase tracking approach, the bit-error rate performance of a MIMO system affected by phase noise can be significantly improved. In addition, simulation results indicate that the proposed phase noise estimation scheme allows for application of higher order modulations and larger numbers of antennas in MIMO systems that employ imperfect oscillators. [ABSTRACT FROM PUBLISHER]

It is proved that in a non-Bayesian parametric estimation problem, if the Fisher information matrix (FIM) is singular, unbiased estimators for the unknown parameter will not exist. Cramér-Rao bound (CRB), a popular tool to lower bound the variances of unbiased estimators, seems inapplicable in such situations. In this correspondence, we show that the Moore-Penrose generalized inverse of a singular FIM can be interpreted as the CRB corresponding to the minimum variance among all choices of minimum constraint functions. This result ensures the logical validity of applying the Moore-Penrose generalized inverse of an FIM as the covariance lower bound when the FIM is singular. Furthermore, the result can be applied as a performance bound on the joint design of constraint functions and unbiased estimators. [ABSTRACT FROM PUBLISHER]

In this two-part paper, the problem of channel estimation in Ultra Wide-Band (UWB) systems is investigated. In Part I, a novel Hybrid Sparse/Diffuse (HSD) model is proposed for the UWB channel, and new channel estimation strategies are designed for this model. In this paper (Part II), a Mean-Squared Error (MSE) analysis of the Generalized MMSE and Generalized Thresholding Estimators developed in Part I is performed, for the asymptotic regimes of low and high SNR. The analysis quantifies the achievable MSE performance of these schemes over unstructured estimators. Specifically, we prove that it is beneficial to be conservative in the estimation of the sparse component, i.e., to assume that the sparse component is sparser than it actually is. Moreover, we analyze the scenario with a non-orthogonal pilot sequence, and establish a connection between the Generalized Thresholding estimator and conventional sparse approximation algorithms proposed in the literature. In addition to the theoretical analysis, these channel estimation schemes are evaluated in a more realistic geometry-based channel emulator, for which the HSD model developed in Part I is an approximation. The numerical results are shown to match the expected asymptotic MSE behavior. Moreover, the proposed estimation techniques are shown to outperform conventional unstructured and purely sparse estimators, from both an MSE and a bit error rate perspectives, even for the realistic geometry-based channel model. [ABSTRACT FROM PUBLISHER]

In this two-part paper, the problem of channel estimation in Ultra Wide-Band (UWB) systems is investigated. Due to the large transmission bandwidth, the channel has been traditionally modeled as sparse. However, some propagation phenomena, e.g., scattering from rough surfaces and frequency distortion, are better modeled by a diffuse channel. Herein, a novel Hybrid Sparse/Diffuse (HSD) channel model is proposed. Tailored to the HSD model, channel estimators are designed for different scenarios that vary in the amount of side information available at the receiver. An Expectation-Maximization algorithm to estimate the power delay profile of the diffuse component is also designed. The proposed methods are compared to unstructured and purely sparse estimators. The numerical results show that the HSD estimation schemes considerably improve the estimation accuracy and the bit error rate performance over conventional channel estimators. In Part II, the new channel estimators are evaluated with more realistic geometry-based channel emulators. The numerical results show that, even when the channel is generated in this manner, the new estimation strategies achieve high performance. Moreover, a Mean-Squared Error analysis of the proposed estimators is performed, in the high and low Signal to Noise Ratio regimes, thus quantifying, in closed form, the achievable performance gains. [ABSTRACT FROM PUBLISHER]

Oscillator phase noise limits the performance of high speed communication systems since it results in time varying channels and rotation of the signal constellation from symbol to symbol. In this paper, joint estimation of channel gains and Wiener phase noise in multi-input multi-output (MIMO) systems is analyzed. The signal model for the estimation problem is outlined in detail and new expressions for the Cramér-Rao lower bounds (CRLBs) for the multi-parameter estimation problem are derived. A data-aided least-squares (LS) estimator for jointly obtaining the channel gains and phase noise parameters is derived. Next, a decision-directed weighted least-squares (WLS) estimator is proposed, where pilots and estimated data symbols are employed to track the time-varying phase noise parameters over a frame. In order to reduce the overhead and delay associated with the estimation process, a new decision-directed extended Kalman filter (EKF) is proposed for tracking the MIMO phase noise throughout a frame. Numerical results show that the proposed LS, WLS, and EKF estimators' performances are close to the CRLB. Finally, simulation results demonstrate that by employing the proposed channel and time-varying phase noise estimators the bit-error rate performance of a MIMO system can be significantly improved. [ABSTRACT FROM PUBLISHER]