Generalized Approximate Message Passing Algorithm Research Articles

Joint Activity Detection and Channel Estimation for Intelligent-Reflecting-Surface-Assisted Wireless IoT Networks

Intelligent reflecting surfaces (IRSs) provide the ability to tune the wireless environments by introducing passive scattering elements between the base station (BS) or access points (APs) and users, and it is a promising technology for next generation wireless networks. In this paper, we consider joint activity detection and channel estimation in both centralized and distributed IRS assisted IoT networks. We determine the explicit distribution for the equivalent channel coefficients from the BS or APs to the users. It is shown that this distribution can be equivalently represented with a Gaussian scale mixture (GSM) model. With generalized approximate message passing (GAMP) algorithm, the received pilot signals at the BS or APs are decoupled into scalar Gaussian noise corrupted versions of the effective channel coefficients. Subsequently, minimum mean square error (MMSE) estimate of the effective channel coefficients and threshold detection rules are acquired. Finally, the optimal fusion rule is used to obtain the activity detection results of each user. As an additional low-complexity approach, we approximate the equivalent channel coefficients with a Gaussian approximation (GA) model. We derive the theoretical mean square error for the MMSE estimate of the effective channel coefficients using the GA model and the state evolution equations of the GAMP algorithm, under the assumption that the direct links from the BS to the users can be neglected due to unfavorable propagation conditions. Numerical results show that the Gaussian approximation for the distribution of the equivalent channel coefficients is accurate even for moderate number of elements at the IRS. And the theoretical mean square error for the MMSE estimate of the effective channel coefficients under the assumption that direct link is negligible is shown to overlap with the corresponding numerical simulations.

On Robust Millimeter Wave Line-of-Sight MIMO Communications With Few-Bit ADCs

This work focuses on providing robust line-of-sight (LoS) spatial multiplexing at flexible communications distances and directions. Considering oblique LoS uniform linear arrays, we first derive the rank-deficient and orthogonal conditions for the LoS MIMO channel matrices. With this discovery, the topology of high spatial-resolution on one side of the link is shown with a wide full-rank-channel guarantee interval over distance and direction variations. Additionally, to reduce the implementation costs and power consumption, we propose to use low amplitude-resolution quantizers at the side of high spatial-resolution. With numerical evaluations on systems having few-bit analog-to-digital converters (ADCs), the proposed system design is shown to simultaneously achieve a higher spectrum efficiency and higher energy efficiency compared to a conventional single-stream high-amplitude-resolution over a wide signal-to-noise-ratio (SNR) range. Furthermore, we investigate channel equalization under the extreme case of using 1-bit ADCs. After providing a new viewpoint on the generalized approximate message passing (GAMP) algorithm from constrained Bethe free energy minimization, our simulations on bit-error-rates show that the GAMP algorithm can significantly reduce the performance degradation due to coarse quantization and can significantly outperform the Bussgang decomposition based linear minimum-mean-square-error estimator, especially at high SNRs.

Massive MIMO Precoding and Spectral Shaping With Low Resolution Phase-Only DACs and Active Constellation Extension

Nonlinear precoding and pulse shaping are jointly considered in multi-user massive multiple-input multiple-output (MIMO) systems with low resolution D/A-converters (DACs) in terms of algorithmic approach as well as large system performance. Two design criteria are investigated: the mean squared error (MSE) with active constellation extension (ACE) and the symbol error rate (SER). Both formulations are solved based on a modified version of the generalized approximate message passing (GAMP) algorithm. Furthermore, theoretical performance results are derived based on the state evolution analysis of the GAMP algorithm. The MSE based technique is extended to jointly perform over-the-air (OTA) spectral shaping and precoding for frequency-selective channels, in which the spectral performance is characterized at the transmitter and at the receiver. Simulation and analytical results demonstrate that the MSE based approach yields the same performance as the SER based formulation in terms of uncoded SER. The analytical results provide good performance predictions up to medium SNR. Substantial improvements in detection, as well as spectral performance, are obtained from the proposed combined pulse shaping and precoding approach compared to standard linear methods.

A Computational Efficient 2-D Block-Sparse ISAR Imaging Method Based on PCSBL-GAMP-Net

Sparse aperture inverse synthesis aperture radar (SA-ISAR) imaging is generally solved by compressed sensing (CS) methods or sparse signal recovery (SSR). Many SSR methods focus on the sparsity of radar images only, which achieves unsatisfactory results on structural data. In addition, most of the traditional CS algorithms suffer from a heavy computational burden. In this article, a new deep unfolding network called pattern-coupled sparse Bayesian learning (PCSBL)-generalized approximate message passing (GAMP)-Net is proposed. The proposed network structure can learn the model of block-sparse information from data to reconstruct images of better quality via fewer iteration steps. First, a complex-valued pattern-coupled hierarchical Gaussian prior model is established. Then, the GAMP algorithm is applied for computational Bayesian inference. Based on the previous PCSBL-GAMP framework, the iterative procedure is unrolled to be a deep network structure. A complex-valued backpropagation (BP) algorithm is derived for network training. Experiment results based on simulated and measured data validate the superiority of the proposed method over the traditional PCSBL-GAMP algorithm. Also, the proposed algorithm is ten times faster than the traditional PCSBL-GAMP algorithm.

An Energy-Efficient Signal Detection Scheme for a Radar-Communication System Based on the Generalized Approximate Message-Passing Algorithm and Low-Precision Quantization

Integrated radar-communication systems will play an important role in the future battlefield scenarios by decreasing the interference, volume, weight, and power consumption of equipment and promoting information fusion with an enhanced network. An active electronically scanned array radar system is ideal for such scenarios. However, a few studies have focused on the modeling and detection of communication signals for such integrated systems. In this paper, an array division strategy is developed, and a low-complexity signal detection scheme based on the generalized approximate message-passing (GAMP) algorithm is implemented. Furthermore, a quantization model is introduced into the output function of the GAMP algorithm. The method effectively provides communication signal detection with low-precision quantization and outperforms the linear minimum mean square error-based algorithm at the same precision levels. Overall, an energy-efficient radar-communication strategy is developed to promote the application of such systems in the future battlefield scenarios.

FDD Downlink Channel Estimation Solution With Common Sparsity Learning Algorithm and Zero-Partition Enhanced GAMP Algorithm

To acquire precise channel state information in the forthcoming 5G frequency division duplexing (FDD) communication system, we study the virtual angular domain channel common sparsity in the massive multiple-input multiple-output orthogonal frequency division multiplexing downlink transmission system. Here, we propose an off-line learning algorithm, which is based on expectation maximization and generalized approximate message passing (GAMP) algorithms. Besides, the learning algorithm utilizes the common sparsity to obtain the support information of the sparse channel vectors. This process is defined as zero partition. With this learned information, the sparse channel vectors are estimated using GAMP again. We prove that when the learned support information is correct, the zero partition-enhanced GAMP algorithm will achieve better sparsity and indeterminacy trade-off performance when compared with the original GAMP algorithm. Based on these results, our proposed channel estimation (CE) solution has two stages. In the first stage, because of the practical propagation characteristics, the zero partition learning algorithm is amended to ensure the correctness of the learned result. In the second stage, channel vectors on the virtual angular domain are estimated with the proposed zero partition-enhanced GAMP algorithm. Analysis and numerical results prove that our CE solution will consume less pilots to ensure the estimation accuracy, when compared with other existed FDD downlink CE solution.

FDD massive MIMO downlink channel estimation with complex hybrid generalized approximate message passing algorithm

Precise channel state information (CSI) is essential for the massive multiple-input multiple-output (MIMO) system to achieve high spectrum and energy efficiency performance in the forthcoming 5G communication. Combined with angular domain channel sparsity, compressive sensing (CS) technique is introduced to estimate downlink CSI because it can help the frequency division duplex massive MIMO system to overcome the restriction of the limited pilot overhead. Conventional CS techniques consider different entries of the sparse signal as equivalent random variables. However, some scatters around the base station are fixed during practical propagation. Consequently, some propagation beams are more likely to locate within certain angular spread and the corresponding entries of the angular domain channel response vector are more likely to be non-zero valued. While this non-zero probability of a certain entry can be acquired offline by learning and analyzing the historical CSI, it is unnecessary to be estimated again during the sparse reconstruction process. When we describe the non-zero probability of a certain entry with the probabilistic density manner, hybrid prior probabilistic settings are used because of the practical propagation property. Combined with the complex generalized approximated message passing (GAMP) algorithm, a new channel estimation method is introduced in this paper. We define the GAMP algorithm with its intrinsic architecture and amended hybrid probability node settings as hybrid GAMP algorithm. A definite improvement of the pilot consumption as well as the estimation accuracy are simultaneously achieved through our proposed channel estimation method with complex hybrid GAMP algorithm and accurate hybrid settings. By further simulation, the influence of the inaccurate hybrid settings of the sparse channel response vector is drawn that the negative effect is proved to be quite small for the proposed channel estimation method.

Fixed Points of Generalized Approximate Message Passing With Arbitrary Matrices

The estimation of a random vector with independent components passed through a linear transform followed by a componentwise (possibly nonlinear) output map arises in a range of applications. Approximate message passing (AMP) methods, based on Gaussian approximations of loopy belief propagation, have recently attracted considerable attention for such problems. For large random transforms, these methods exhibit fast convergence and admit precise analytic characterizations with testable conditions for optimality, even for certain non-convex problem instances. However, the behavior of AMP under general transforms is not fully understood. In this paper, we consider the generalized AMP (GAMP) algorithm and relate the method to more common optimization techniques. This analysis enables a precise characterization of the GAMP algorithm fixed points that applies to arbitrary transforms. In particular, we show that the fixed points of the so-called max-sum GAMP algorithm for MAP estimation are critical points of a constrained maximization of the posterior density. The fixed points of the sum-product GAMP algorithm for estimation of the posterior marginals can be interpreted as critical points of a certain free energy.

Bilinear Generalized Approximate Message Passing—Part II: Applications

In this paper, we extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case. In Part I of this two-part paper, we derived our Bilinear G-AMP (BiG-AMP) algorithm as an approximation of the sum-product belief propagation algorithm in the high-dimensional limit, and proposed an adaptive damping mechanism that aids convergence under finite problem sizes, an expectation-maximization (EM)-based method to automatically tune the parameters of the assumed priors, and two rank-selection strategies. Here, in Part II, we discuss the specializations of BiG-AMP to the problems of matrix completion, robust PCA, and dictionary learning, and present the results of an extensive empirical study comparing BiG-AMP to state-of-the-art algorithms on each problem. Our numerical results, using both synthetic and real-world datasets, demonstrate that EM-BiG-AMP yields excellent reconstruction accuracy (often best in class) while maintaining competitive runtimes.

Bilinear Generalized Approximate Message Passing—Part I: Derivation

We extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case, which enables its application to matrix completion, robust PCA, dictionary learning, and related matrix-factorization problems. In the first part of the paper, we derive our Bilinear G-AMP (BiG-AMP) algorithm as an approximation of the sum-product belief propagation algorithm in the high-dimensional limit, where central-limit theorem arguments and Taylor-series approximations apply, and under the assumption of statistically independent matrix entries with known priors. In addition, we propose an adaptive damping mechanism that aids convergence under finite problem sizes, an expectation-maximization (EM)-based method to automatically tune the parameters of the assumed priors, and two rank-selection strategies. In the second part of the paper, we discuss the specializations of EM-BiG-AMP to the problems of matrix completion, robust PCA, and dictionary learning, and present the results of an extensive empirical study comparing EM-BiG-AMP to state-of-the-art algorithms on each problem. Our numerical results, using both synthetic and real-world datasets, demonstrate that EM-BiG-AMP yields excellent reconstruction accuracy (often best in class) while maintaining competitive runtimes and avoiding the need to tune algorithmic parameters.

An Empirical-Bayes Approach to Recovering Linearly Constrained Non-Negative Sparse Signals

We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex signals. This problem arises in, e.g., hyperspectral imaging, portfolio optimization, density estimation, and certain cases of compressive imaging. Our first approach solves a linearly constrained non-negative version of LASSO using the max-sum version of the generalized approximate message passing (GAMP) algorithm, where we consider both quadratic and absolute loss, and where we propose a novel approach to tuning the LASSO regularization parameter via the expectation maximization (EM) algorithm. Our second approach is based on the sum-product version of the GAMP algorithm, where we propose the use of a Bernoulli non-negative Gaussian-mixture signal prior and a Laplacian likelihood, and propose an EM-based approach to learning the underlying statistical parameters. In both approaches, the linear equality constraints are enforced by augmenting GAMP's generalized-linear observation model with noiseless pseudo-measurements. Extensive numerical experiments demonstrate the state-of-the-art performance of our proposed approaches.