Joint Spatial Division and Multiplexing for FDD in Intelligent Reflecting Surface-assisted Massive MIMO Systems

© 2022 IEEE - All rights reserved. This is the accepted manuscript version of an article which has been published in final form at https://10.1109/TVT.2022.3187656Intelligent reflecting surface (IRS) is a promising technology to deliver the higher spectral and energy requirements in fifth-generation (5G) and beyond wireless networks while shaping the propagation environment. Such a design can be further enhanced with massive multiple-input-multiple-output (mMIMO) characteristics towards boosting the network performance. However, channel reciprocity, assumed in 5G systems such as mMIMO, appears to be questioned in practice by recent studies on IRS. Hence, contrary to previous works, we consider frequency division duplexing (FDD) to study the performance of an IRS-assisted mMIMO system. However, FDD is not suitable for large number of antennas architectures. For this reason we employ the joint spatial division and multiplexing (JSDM) approach exploiting the structure of the correlation of the channel vectors to reduce the channel state information (CSI) uplink feedback, and thus, allowing the use even of a large number of antennas at the base station. JSDM entails dual-structured precoding and clustering the user equipments (UEs) with the same covariance matrix into groups. Specifically, we derive the sum spectral efficiency (SE) based on statistical CSI in terms of large-scale statistics by using the deterministic equivalent (DE) analysis while accounting for correlated Rayleigh fading. Subsequently, we formulate the optimization problem concerning the sum SE with respect to the reflecting beamforming matrix (RBM) and the total transmit power, which can be performed at every several coherence intervals by taking advantage of the slow-time variation of the large-scale statistics. This notable property contributes further to the decrease of the feedback overhead. Numerical results, verified by Monte-Carlo (MC) simulations, enable interesting observations by elucidating how fundamental system parameters such as the rank of the covariance matrix and the number of groups of UEs affect the performance. For example, the selection of a high rank improves the channel conditioning but increases the feedback overhead.Peer reviewe

Interleaved Training for Massive MIMO Downlink via Exploring Spatial Correlation

Interleaved training has been studied for single-user and multi-user massive MIMO downlink with either fully-digital or hybrid beamforming. However, the impact of channel correlation on its average training overhead is rarely addressed. In this paper, we explore the channel correlation to improve the interleaved training for single-user massive MIMO downlink. For the beam-domain interleaved training, we propose a modified scheme by optimizing the beam training codebook. The basic antenna-domain interleaved training is also improved by dynamically adjusting the training order of the base station (BS) antennas during the training process based on the values of the already trained channels. Exact and simplified approximate expressions of the average training length are derived in closed-form for the basic and modified beam-domain schemes and the basic antenna-domain scheme in correlated channels. For the modified antenna-domain scheme, a deep neural network (DNN)-based approximation is provided for fast performance evaluation. Analytical results and simulations verify the accuracy of our derived training length expressions and explicitly reveal the impact of system parameters on the average training length. In addition, the modified beam/antenna-domain schemes are shown to have a shorter average training length compared to the basic schemes.Comment: 14 pages (double column), 8 figures. The paper has been accepted by IEEE Transactions on Wireless Communication

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