In massive MIMO systems, the knowledge of channel covariance matrix is crucial for MMSE channel estimation in the uplink and plays an important role in several downlink multiuser beamforming schemes. Due to the large number of base station antennas in massive MIMO, accurate covariance estimation is challenging especially in the case where the number of samples is limited and thus comparable to the channel vector dimension. As a result, the standard sample covariance estimator yields high estimation error which may yield significant system performance degradation with respect to the ideal channel knowledge case. To address such covariance estimation problem, we propose a method based on a parametric representation of the channel angular scattering function. The proposed parametric representation includes a discrete specular component which is addressed using the well-known MUltiple SIgnal Classification (MUSIC) method, and a diffuse scattering component, which is modeled as the superposition of suitable dictionary functions. To obtain the representation parameters we propose two methods, where the first solves a non-negative least-squares problem and the second maximizes the likelihood function using expectation-maximization. Our simulation results show that the proposed methods outperform the state of the art with respect to various estimation quality metrics and different sample sizes.
相關內容
Hybrid analog and digital beamforming transceivers are instrumental in addressing the challenge of expensive hardware and high training overheads in the next generation millimeter-wave (mm-Wave) massive MIMO (multiple-input multiple-output) systems. However, lack of fully digital beamforming in hybrid architectures and short coherence times at mm-Wave impose additional constraints on the channel estimation. Prior works on addressing these challenges have focused largely on narrowband channels wherein optimization-based or greedy algorithms were employed to derive hybrid beamformers. In this paper, we introduce a deep learning (DL) approach for channel estimation and hybrid beamforming for frequency-selective, wideband mm-Wave systems. In particular, we consider a massive MIMO Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system and propose three different DL frameworks comprising convolutional neural networks (CNNs), which accept the raw data of received signal as input and yield channel estimates and the hybrid beamformers at the output. We also introduce both offline and online prediction schemes. Numerical experiments demonstrate that, compared to the current state-of-the-art optimization and DL methods, our approach provides higher spectral efficiency, lesser computational cost and fewer number of pilot signals, and higher tolerance against the deviations in the received pilot data, corrupted channel matrix, and propagation environment.
Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This regularizer removes the penalties on a few large-magnitude elements from the conventional l1-norm regularizer, and thus it only forces penalties on the remaining elements that are expected to be zeros. Accurate and fast reconstructions can be achieved by performing gradient projection updates within the framework of difference of convex functions (DC) programming. A double-loop algorithm and a single-loop algorithm are proposed via different DC decompositions, and these two algorithms have distinct computation complexities and convergence rates. Then, an extension algorithm is further proposed by designing the step sizes of the single-loop algorithm. The extension algorithm has a faster convergence rate and can achieve approximately the same level of accuracy as the proposed double-loop algorithm. Numerical results show significant advantages of the proposed algorithms over existing reconstruction algorithms in terms of reconstruction accuracies and runtimes. Compared to the benchmark channel estimation techniques, the proposed algorithms also achieve smaller mean squared error and higher achievable spectral efficiency.
There are several challenges associated with inverse problems in which we seek to reconstruct a piecewise constant field, and which we model using multiple level sets. Adopting a Bayesian viewpoint, we impose prior distributions on both the level set functions that determine the piecewise constant regions as well as the parameters that determine their magnitudes. We develop a Gauss-Newton approach with a backtracking line search to efficiently compute the maximum a priori (MAP) estimate as a solution to the inverse problem. We use the Gauss-Newton Laplace approximation to construct a Gaussian approximation of the posterior distribution and use preconditioned Krylov subspace methods to sample from the resulting approximation. To visualize the uncertainty associated with the parameter reconstructions we compute the approximate posterior variance using a matrix-free Monte Carlo diagonal estimator, which we develop in this paper. We will demonstrate the benefits of our approach and solvers on synthetic test problems (photoacoustic and hydraulic tomography, respectively a linear and nonlinear inverse problem) as well as an application to X-ray imaging with real data.
Data in non-Euclidean spaces are commonly encountered in many fields of Science and Engineering. For instance, in Robotics, attitude sensors capture orientation which is an element of a Lie group. In the recent past, several researchers have reported methods that take into account the geometry of Lie Groups in designing parameter estimation algorithms in nonlinear spaces. Maximum likelihood estimators (MLE) are quite commonly used for such tasks and it is well known in the field of statistics that Stein's shrinkage estimators dominate the MLE in a mean-squared sense assuming the observations are from a normal population. In this paper, we present a novel shrinkage estimator for data residing in Lie groups, specifically, abelian or compact Lie groups. The key theoretical results presented in this paper are: (i) Stein's Lemma and its proof for Lie groups and, (ii) proof of dominance of the proposed shrinkage estimator over MLE for abelian and compact Lie groups. We present examples of simulation studies of the dominance of the proposed shrinkage estimator and an application of shrinkage estimation to multiple-robot localization.
Estimation of User Terminals' (UTs') Angle of Arrival (AoA) plays a significant role in the next generation of wireless systems. Due to high demands, energy efficiency concerns, and scarcity of available resources, it is pivotal how these resources are used. Installed antennas and their corresponding hardware at the Base Station (BS) are of these resources. In this paper, we address the problem of antenna selection to minimize Cramer-Rao Lower Bound (CRLB) of a planar antenna array when fewer antennas than total available antennas have to be used for a UT. First, the optimal antenna selection strategy to minimize the expected CRLB in a planar antenna array is proposed. Then, using this strategy as a preliminary step, we present a two-step antenna selection method whose goal is to minimize the instantaneous CRLB. Minimizing instantaneous CRLB through antenna selection is a combinatorial optimization problem for which we utilize a greedy algorithm. The optimal start point of the greedy algorithm is presented alongside some methods to reduce the computational complexity of the selection procedure. Numerical results confirm the accuracy of the proposed solutions and highlight the benefits of using antenna selection in the localization phase in a wireless system.
We study the non-parametric estimation of the value ${\theta}(f )$ of a linear functional evaluated at an unknown density function f with support on $R_+$ based on an i.i.d. sample with multiplicative measurement errors. The proposed estimation procedure combines the estimation of the Mellin transform of the density $f$ and a regularisation of the inverse of the Mellin transform by a spectral cut-off. In order to bound the mean squared error we distinguish several scenarios characterised through different decays of the upcoming Mellin transforms and the smoothnes of the linear functional. In fact, we identify scenarios, where a non-trivial choice of the upcoming tuning parameter is necessary and propose a data-driven choice based on a Goldenshluger-Lepski method. Additionally, we show minimax-optimality over Mellin-Sobolev spaces of the estimator.
We study downlink channel estimation in a multi-cell Massive multiple-input multiple-output (MIMO) system operating in time-division duplex. The users must know their effective channel gains to decode their received downlink data. Previous works have used the mean value as the estimate, motivated by channel hardening. However, this is associated with a performance loss in non-isotropic scattering environments. We propose two novel estimation methods that can be applied without downlink pilots. The first method is model-based and asymptotic arguments are utilized to identify a connection between the effective channel gain and the average received power during a coherence interval. The second method is data-driven and trains a neural network to identify a mapping between the available information and the effective channel gain. Both methods can be utilized for any channel distribution and precoding. For the model-aided method, we derive all expressions in closed form for the case when maximum ratio or zero-forcing precoding is used. We compare the proposed methods with the state-of-the-art using the normalized mean-squared error and spectral efficiency (SE). The results suggest that the two proposed methods provide better SE than the state-of-the-art when there is a low level of channel hardening, while the performance difference is relatively small with the uncorrelated channel model.
Cell-free massive MIMO is one of the core technologies for future wireless networks. It is expected to bring enormous benefits, including ultra-high reliability, data throughput, energy efficiency, and uniform coverage. As a radically distributed system, the performance of cell-free massive MIMO critically relies on efficient distributed processing algorithms. In this paper, we propose a distributed expectation propagation (EP) detector for cell-free massive MIMO, which consists of two modules: a nonlinear module at the central processing unit (CPU) and a linear module at each access point (AP). The turbo principle in iterative channel decoding is utilized to compute and pass the extrinsic information between the two modules. An analytical framework is provided to characterize the asymptotic performance of the proposed EP detector with a large number of antennas. Furthermore, a distributed joint channel estimation and data detection (JCD) algorithm is developed to handle the practical setting with imperfect channel state information (CSI). Simulation results will show that the proposed method outperforms existing detectors for cell-free massive MIMO systems in terms of the bit-error rate and demonstrate that the developed theoretical analysis accurately predicts system performance. Finally, it is shown that with imperfect CSI, the proposed JCD algorithm improves the system performance significantly and enables non-orthogonal pilots to reduce the pilot overhead.
The simultaneous estimation of many parameters based on data collected from corresponding studies is a key research problem that has received renewed attention in the high-dimensional setting. Many practical situations involve heterogeneous data where heterogeneity is captured by a nuisance parameter. Effectively pooling information across samples while correctly accounting for heterogeneity presents a significant challenge in large-scale estimation problems. We address this issue by introducing the "Nonparametric Empirical Bayes Structural Tweedie" (NEST) estimator, which efficiently estimates the unknown effect sizes and properly adjusts for heterogeneity via a generalized version of Tweedie's formula. For the normal means problem, NEST simultaneously handles the two main selection biases introduced by heterogeneity: one, the selection bias in the mean, which cannot be effectively corrected without also correcting for, two, selection bias in the variance. Our theoretical results show that NEST has strong asymptotic properties without requiring explicit assumptions about the prior. Extensions to other two-parameter members of the exponential family are discussed. Simulation studies show that NEST outperforms competing methods, with much efficiency gains in many settings. The proposed method is demonstrated on estimating the batting averages of baseball players and Sharpe ratios of mutual fund returns.
Detailed derivations of two bounds of the minimum mean-square error (MMSE) of complex-valued multiple-input multiple-output (MIMO) systems are proposed for performance evaluation. Particularly, the lower bound is derived based on a genie-aided MMSE estimator, whereas the upper bound is derived based on a maximum-likelihood (ML) estimator. Using the famous relationship between the mutual information (MI) and MMSE, two bounds for the MI are also derived, based on which we discuss the asymptotic behaviours of the average MI in the high-signal-to-noise ratio (SNR) regime. Theoretical analyses suggest that the average MI will converge its maximum as the SNR increases and the diversity order is the same as receive antenna number.
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