Hybrid Message Passing Algorithm for Downlink FDD Massive MIMO-OFDM Channel Estimation

The design of message passing algorithms on factor graphs has been proven to be an effective manner to implement channel estimation in wireless communication systems. In Bayesian approaches, a prior probability model that accurately matches the channel characteristics can effectively improve estimation performance. In this work, we study the channel estimation problem in a frequency division duplexing (FDD) downlink massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system. As the prior probability, we propose the Markov chain two-state Gaussian mixture with large variance difference (TSGM-LVD) model to exploit the structured sparsity in the angle-frequency domain of the massive MIMO-OFDM channel. In addition, we present a new method to derive the hybrid message passing (HMP) rule, which can calculate the message with mixed linear and non-linear model. To the best of the authors' knowledge, we are the first to apply the HMP rule to practical communication systems, designing the HMP-TSGM-LVD algorithm under the structured turbo-compressed sensing (STCS) framework. Simulation results demonstrate that the proposed HMP-TSGM-LVD algorithm converges faster and outperforms its counterparts under a wide range of simulation settings

Successive Linear Approximation VBI for Joint Sparse Signal Recovery and Dynamic Grid Parameters Estimation

For many practical applications in wireless communications, we need to recover a structured sparse signal from a linear observation model with dynamic grid parameters in the sensing matrix. Conventional expectation maximization (EM)-based compressed sensing (CS) methods, such as turbo compressed sensing (Turbo-CS) and turbo variational Bayesian inference (Turbo-VBI), have double-loop iterations, where the inner loop (E-step) obtains a Bayesian estimation of sparse signals and the outer loop (M-step) obtains a point estimation of dynamic grid parameters. This leads to a slow convergence rate. Furthermore, each iteration of the E-step involves a complicated matrix inverse in general. To overcome these drawbacks, we first propose a successive linear approximation VBI (SLA-VBI) algorithm that can provide Bayesian estimation of both sparse signals and dynamic grid parameters. Besides, we simplify the matrix inverse operation based on the majorization-minimization (MM) algorithmic framework. In addition, we extend our proposed algorithm from an independent sparse prior to more complicated structured sparse priors, which can exploit structured sparsity in specific applications to further enhance the performance. Finally, we apply our proposed algorithm to solve two practical application problems in wireless communications and verify that the proposed algorithm can achieve faster convergence, lower complexity, and better performance compared to the state-of-the-art EM-based methods.Comment: 13 pages, 17 figures, submitted to IEEE Transactions on Wireless Communication

Hybrid approximate message passing

Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper presents a systematic framework for incorporating such approximate message passing (AMP) methods in general graphical models. The key concept is a partition of dependencies of a general graphical model into strong and weak edges, with the weak edges representing interactions through aggregates of small, linearizable couplings of variables. AMP approximations based on the Central Limit Theorem can be readily applied to aggregates of many weak edges and integrated with standard message passing updates on the strong edges. The resulting algorithm, which we call hybrid generalized approximate message passing (HyGAMP), can yield significantly simpler implementations of sum-product and max-sum loopy belief propagation. By varying the partition of strong and weak edges, a performance--complexity trade-off can be achieved. Group sparsity and multinomial logistic regression problems are studied as examples of the proposed methodology.The work of S. Rangan was supported in part by the National Science Foundation under Grants 1116589, 1302336, and 1547332, and in part by the industrial affiliates of NYU WIRELESS. The work of A. K. Fletcher was supported in part by the National Science Foundation under Grants 1254204 and 1738286 and in part by the Office of Naval Research under Grant N00014-15-1-2677. The work of V. K. Goyal was supported in part by the National Science Foundation under Grant 1422034. The work of E. Byrne and P. Schniter was supported in part by the National Science Foundation under Grant CCF-1527162. (1116589 - National Science Foundation; 1302336 - National Science Foundation; 1547332 - National Science Foundation; 1254204 - National Science Foundation; 1738286 - National Science Foundation; 1422034 - National Science Foundation; CCF-1527162 - National Science Foundation; NYU WIRELESS; N00014-15-1-2677 - Office of Naval Research

Joint Scattering Environment Sensing and Channel Estimation Based on Non-stationary Markov Random Field

This paper considers an integrated sensing and communication system, where some radar targets also serve as communication scatterers. A location domain channel modeling method is proposed based on the position of targets and scatterers in the scattering environment, and the resulting radar and communication channels exhibit a two-dimensional (2-D) joint burst sparsity. We propose a joint scattering environment sensing and channel estimation scheme to enhance the target/scatterer localization and channel estimation performance simultaneously, where a spatially non-stationary Markov random field (MRF) model is proposed to capture the 2-D joint burst sparsity. An expectation maximization (EM) based method is designed to solve the joint estimation problem, where the E-step obtains the Bayesian estimation of the radar and communication channels and the M-step automatically learns the dynamic position grid and prior parameters in the MRF. However, the existing sparse Bayesian inference methods used in the E-step involve a high-complexity matrix inverse per iteration. Moreover, due to the complicated non-stationary MRF prior, the complexity of M-step is exponentially large. To address these difficulties, we propose an inverse-free variational Bayesian inference algorithm for the E-step and a low-complexity method based on pseudo-likelihood approximation for the M-step. In the simulations, the proposed scheme can achieve a better performance than the state-of-the-art method while reducing the computational overhead significantly.Comment: 15 pages, 13 figures, submitted to IEEE Transactions on Wireless Communication

A Two-Stage 2D Channel Extrapolation Scheme for TDD 5G NR Systems

Recently, channel extrapolation has been widely investigated in frequency division duplex (FDD) massive MIMO systems. However, in time division duplex (TDD) fifth generation (5G) new radio (NR) systems, the channel extrapolation problem also arises due to the hopping uplink pilot pattern, which has not been fully researched yet. This paper addresses this gap by formulating a channel extrapolation problem in TDD massive MIMO-OFDM systems for 5G NR, incorporating imperfection factors. A novel two-stage two-dimensional (2D) channel extrapolation scheme in both frequency and time domain is proposed, designed to mitigate the negative effects of imperfection factors and ensure high-accuracy channel estimation. Specifically, in the channel estimation stage, we propose a novel multi-band and multi-timeslot based high-resolution parameter estimation algorithm to achieve 2D channel extrapolation in the presence of imperfection factors. Then, to avoid repeated multi-timeslot based channel estimation, a channel tracking stage is designed during the subsequent time instants, in which a sparse Markov channel model is formulated to capture the dynamic sparsity of massive MIMO-OFDM channels under the influence of imperfection factors. Next, an expectation-maximization (EM) based compressive channel tracking algorithm is designed to jointly estimate unknown imperfection and channel parameters by exploiting the high-resolution prior information of the delay/angle parameters from the previous timeslots. Simulation results underscore the superior performance of our proposed channel extrapolation scheme over baselines

Channel Estimation in Multi-user Massive MIMO Systems by Expectation Propagation based Algorithms

Massive multiple input multiple output (MIMO) technology uses large antenna arrays with tens or hundreds of antennas at the base station (BS) to achieve high spectral efficiency, high diversity, and high capacity. These benefits, however, rely on obtaining accurate channel state information (CSI) at the receiver for both uplink and downlink channels. Traditionally, pilot sequences are transmitted and used at the receiver to estimate the CSI. Since the length of the pilot sequences scale with the number of transmit antennas, for massive MIMO systems downlink channel estimation requires long pilot sequences resulting in reduced spectral efficiency and the so-called pilot contamination due to sharing of the pilots in adjacent cells. In this dissertation we first review the problem of channel estimation in massive MIMO systems. Next, we study the problem of semi-blind channel estimation in the uplink in the case of spatially correlated time-varying channels. The proposed method uses the transmitted data symbols as virtual pilots to enhance channel estimation. An expectation propagation (EP) algorithm is developed to iteratively approximate the joint a posterior distribution of the unknown channel matrix and the transmitted data symbols with a distribution from an exponential family. The distribution is then used for direct estimation of the channel matrix and detection of the data symbols. A modified version of Kalman filtering algorithm referred to as KF-M emerges from our EP derivation and it is used to initialize our algorithm. Simulation results demonstrate that channel estimation error and the symbol error rate of the proposed algorithm improve with the increase in the number of BS antennas or the number of data symbols in the transmitted frame. Moreover, the proposed algorithms can mitigate the effects of pilot contamination as well as time-variations of the channel. Next, we study the problem of downlink channel estimation in multi-user massive MIMO systems. Our approach is based on Bayesian compressive sensing in which the clustered sparse structure of the channel in the angular domain is exploited to reduce the pilot overhead. To capture the clustered structure, we employ a conditionally independent identically distributed Bernoulli-Gaussian prior on the sparse vector representing the channel, and a Markov prior on its support vector. An EP algorithm is developed to approximate the intractable joint distribution on the sparse vector and its support with a distribution from an exponential family. This distribution is then used for direct estimation of the channel. The EP algorithm requires the model parameters which are unknown. We estimate these parameters using the expectation maximization (EM) algorithm. Simulation results show that the proposed combination of EM and EP referred to as EM-EP algorithm outperforms several recently-proposed algorithms in the literature