Channel Feedback Overhead Research Articles

Deep learning-based channel estimation with application to 5G and beyond networks

Channel state information (CSI) feedback estimation for a downlink medium in a massive multiple input multiple output (MIMO) system is an essential and critical task to improve channel capacity and performance yield, especially in a frequency division duplex (FDD) multiplexing system. However, spectral efficiency degradation is a massive issue due to high channel feedback overhead. This work proposes a deep learning-based channel estimation (DLCE) model to improve channel reconstruction efficiency and channel overhead reduction accuracy. The proposed deep learning (DL) mechanism consists of encoder and decoder network where encoder network is utilized to compress CSI matrices whereas decoder network is used to decompress obtained CSI matrices. Here, inverse discrete Fourier transform (IDFT) method is utilized to convert CSI matrices of frequency domain into CSI matrices of delay domain. Simulation results are evaluated between uplink and downlink medium in the massive MIMO system considering a co-operation in science and technology (COST) 2,100 model. Here, a significant improvement in correlation and normalized mean square error (NMSE) results is observed. The proposed DLCE model shows superior performance against varied channel estimation techniques in terms of NMSE and correlation efficiency.

Downlink Precoding for DP-UPA FDD Massive MIMO via Multi-Dimensional Active Channel Sparsification

In this paper, we consider user selection and downlink precoding for an over-loaded single-cell massive multiple-input multiple-output (MIMO) system in frequency division duplexing (FDD) mode, where the base station is equipped with a dual-polarized uniform planar array (DP-UPA) and serves a large number of single-antenna users. Due to the absence of uplink-downlink channel reciprocity and the high-dimensionality of channel matrices, it is extremely challenging to design downlink precoders using closed-loop channel probing and feedback with limited spectrum resource. To address these issues, a novel methodology – active channel sparsification (ACS) – has been proposed recently in the literature for uniform linear array (ULA) to design sparsifying precoders, which substantially reduces channel feedback overhead. Pushing forward this line of research, we aim to facilitate the potential deployment of ACS in practical FDD massive MIMO systems, by extending it from ULA to DP-UPA with explicit user selection and making the current ACS implementation simplified. To this end, by leveraging Toeplitz matrix theory, we start with the spectral properties of channel covariance matrices from the lens of their matrix-valued spectral density function. Inspired by these properties, we extend the original ACS using scalar-weight bipartite graph representation to the matrix-weight counterpart. Building upon such matrix-weight bipartite graph representation, we propose a multi-dimensional ACS (MD-ACS) method, which is a generalization of original ACS formulation and is more suitable for DP-UPA antenna configurations. The nonlinear integer program formulation of MD-ACS can be classified as a generalized multi-assignment problem (GMAP), for which we propose a simple yet efficient greedy algorithm to solve it. Simulation results demonstrate the performance improvement of the proposed MD-ACS with greedy algorithm over the state-of-the-art methods based on the QuaDRiGa channel models.

Channel Feedback in TDD Massive MIMO Systems With Partial Reciprocity

It is widely believed that the channel reciprocity holds in time division duplexing (TDD) massive multiple-input multiple-output (MIMO) systems, so the uplink channel feedback is unnecessary. However, due to the constraint of transmission power and hardware complexity, users may use more receiving antennas than transmitting antennas in practical wireless communication systems. In this practical yet important scenario, only partial channel reciprocity holds, and thus channel feedback is still required in TDD massive MIMO systems. Unfortunately, this important topic has not been investigated in the literature. To fill in this gap, we propose an angle-domain support (ADS) based channel feedback scheme for TDD massive MIMO systems with unequal number of receiving and transmitting antennas. Firstly, by utilizing the angle-domain channel sparsity, we illustrate that a small number of elements in angle-domain channel, which are indexed by ADS, can capture the most power of the channel. Then, we propose the base station (BS) can obtain full downlink channel by decomposing the channel into two parts: the ADS and the low-dimensional angle-domain representation indexed by the ADS. At first, due to the partial channel reciprocity, the ADS is obtained by an angle-domain windows based support detection method at the BS without channel feedback. Then, the low-dimensional angle-domain representation indexed by the ADS is quantized and fed back to the BS. Theoretical analysis and simulation results demonstrate that the proposed scheme can achieve the near-optimal achievable sum-rate performance with low channel feedback overhead.

Dimension Reduced Channel Feedback for Reconfigurable Intelligent Surface Aided Wireless Communications

Reconfigurable intelligent surface (RIS) has recently received extensive research interest due to its capability to intelligently change the wireless propagation environment. For RIS-aided wireless communications in frequency division duplex (FDD) mode, channel feedback at the user equipment (UE) is essential for the base station (BS) to acquire the downlink channel state information (CSI). In this paper, a dimension reduced channel feedback scheme is proposed to reduce the channel feedback overhead by exploiting the single-structured sparsity of BS-RIS-UE cascaded channel. Since different UEs share the same sparse BS-RIS channel but have their respective RIS-UE channels, there are only limited non-zero column vectors in the BS-RIS-UE cascaded channel matrix, and different UEs share the same indexes of the non-zero columns. Thus, the downlink CSI can be decomposed into <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">user-independent</i> channel information (i.e., the indexes of non-zero columns) and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">user-specific</i> channel information (i.e., the non-zero column vectors), where the former for all UEs can be fed back by only one UE, while the latter can be fed back with a fairly low overhead by different UEs, respectively. Simulation results show that, compared with the conventional method, the proposed scheme can reduce channel feedback overhead by more than 80% for RIS-aided wireless communications.

Model-Driven Deep Learning Based Channel Estimation and Feedback for Millimeter-Wave Massive Hybrid MIMO Systems

This paper proposes a model-driven deep learning (MDDL)-based channel estimation and feedback scheme for wideband millimeter-wave (mmWave) massive hybrid multiple-input multiple-output (MIMO) systems, where the angle-delay domain channels' sparsity is exploited for reducing the overhead. First, we consider the uplink channel estimation for time-division duplexing systems. To reduce the uplink pilot overhead for estimating high-dimensional channels from a limited number of radio frequency (RF) chains at the base station (BS), we propose to jointly train the phase shift network and the channel estimator as an auto-encoder. Particularly, by exploiting the channels' structured sparsity from an a priori model and learning the integrated trainable parameters from the data samples, the proposed multiple-measurement-vectors learned approximate message passing (MMV-LAMP) network with the devised redundant dictionary can jointly recover multiple subcarriers' channels with significantly enhanced performance. Moreover, we consider the downlink channel estimation and feedback for frequency-division duplexing systems. Similarly, the pilots at the BS and channel estimator at the users can be jointly trained as an encoder and a decoder, respectively. Besides, to further reduce the channel feedback overhead, only the received pilots on part of the subcarriers are fed back to the BS, which can exploit the MMV-LAMP network to reconstruct the spatial-frequency channel matrix. Numerical results show that the proposed MDDL-based channel estimation and feedback scheme outperforms state-of-the-art approaches.

Geometric Analysis-Based Cluster Head Selection for Sectorized Wireless Powered Sensor Networks

In this letter, we consider a sectorized wireless powered sensor network (WPSN), wherein sensor nodes, which are clustered based on sectors, transmit data to the cluster head (CH) using energy harvested from a hybrid access point. We construct a system model for this sectorized WPSN and formulate an optimization problem to obtain an optimal CH that maximizes the achievable transmission rate of sensing data. To obtain the optimal CH with low overhead and complexity, we perform an asymptotic geometric analysis (GA) that determines the optimal coordinates of the CH in the considered area of the sector such that only a small number of sensor nodes near this optimal coordinates need to be investigated. Simulation results show that the performance of the proposed GA-based CH selection method is close to the optimal performance exhibited by exhaustive search; moreover, the proposed method substantially reduces the channel feedback overhead.

Two Timescale Robust Energy-Efficient Precoding for Dual-Polarized MIMO Systems

In this work, we investigate in depth the two timescale robust system energy efficiency (EE) precoding design for the multiuser dual-polarized multiple-input multiple-output (MIMO) system. To achieve good performance, low feedback overhead as well as low implementation complexity, the dual-structured linear precoding scheme is adopted, which is based on the two timescale channel state information (CSI) and the dual-polarized antenna structure. The subgrouping technique, which is based on polarization, is also utilized to divide spatially grouped users into co-polarized subgroups to further reduce channel feedback overhead. The proposed robust system EE precoding design can achieve the maximization of the worst-case system EE, with the norm-bounded channel errors of all users. This robust EE optimization is naturally decomposed into two parts. In the first part, based on the polarized spatial correlation information, the block diagonalization is utilized to design the preprocessing matrix. In the second part, based on the relationship between the mean square error and the signal-to-interference-plus-noise ratio, the linear precoding matrix can be optimized by utilizing the sign-definiteness lemma and the fractional programming technique. Specifically, the corresponding nonconvex EE fractional optimization problem is converted to a series of semidefinite programming problems, which are solved by the convex optimization method efficiently. Simulation results indicate that the proposed two timescale based dual-structured precoding has many advantages on the robust system EE performance in the dual-polarized multiuser MIMO system.

Statistically-Aided Codebook-Based Hybrid Precoding for Millimeter Wave Channels

In this paper, we propose practical yet effective statistically-aided codebook-based hybrid precoding schemes for massive multiple-input multiple-output systems in millimeter wave bands. Particularly, we develop novel low-overhead hybrid precoding algorithms for selecting the baseband digital and radio frequency analog precoders from statistically skewed DFT-based codebooks. The proposed algorithms aim at maximizing the spectral efficiency based on minimizing the chordal distance between the optimal unconstrained precoder and the hybrid beamformer and maximizing the signal to the interference noise ratio for the single-user and multi-user cases, respectively. We investigate the performance of the proposed algorithms by considering the mutual information of the analog beamforming procedure (the common stage among the proposed algorithms) as a performance evaluation metric. We derive lower and upper bounds on the mutual information of the channel given the proposed algorithms. Moreover, we show that the performance gap between the lower and upper bounds depends heavily on how many DFT columns are aligned to the largest eigenvectors of the transmit antenna array response of the millimeter wave channel or equivalently the transmit channel covariance matrix when only statistical channel knowledge is available at the transmitter. Then, we show that the proposed algorithms are asymptotically optimal as the number of transmit antennas M goes to infinity and the millimeter wave channel has a limited number of paths P, i.e., P <; M. Further, we verify the performance of the proposed algorithms numerically where results illustrate that the spectral efficiency of the proposed algorithms can approach that of the optimal precoder in certain scenarios. Furthermore, these results show that the proposed hybrid precoding schemes have superior spectral efficiency performance while requiring lower (or at most comparable) channel feedback overhead in comparison with the prior art.

Overhead-Performance Tradeoff for MISO Broadcast Channels With Zero-Forcing Precoder

By applying a rate-distortion approach, we investigate the relationship between the amount of overhead and the system performance from an information-theoretic point of view. Though the purpose of rate-distortion theory is to find a lower bound on lossy source coding problems, the concepts of distortion and rate can be extended to communication performance measures and the quality of feedback overhead, respectively. In this article, we study the overhead-performance tradeoff for a downlink MU-MISO channel system with limited feedback. The required feedback bits for characterizing the channel state information is represented as a function of tolerable rate loss. The proposed method to derive this tradeoff is valid for any number of transmit antennas and users, and can help in designing practical systems where the impact of channel feedback overhead cannot be neglected. Comparing the obtained rate-distortion curves with vector quantization, it can be concluded that, for each user, by feeding back different numbers of bits for different channel power gains, the optimal performance can be achieved.

Machine Learning-Based Dimension Optimization for Two-Stage Precoder in Massive MIMO Systems with Limited Feedback

A two-stage precoder is widely considered in frequency division duplex massive multiple-input and multiple-output (MIMO) systems to resolve the channel feedback overhead problem. In massive MIMO systems, users on a network can be divided into several user groups of similar spatial antenna correlations. Using the two-stage precoder, the outer precoder reduces the channel dimensions mitigating inter-group interferences at the first stage, while the inner precoder eliminates the smaller dimensions of intra-group interferences at the second stage. In this case, the dimension of effective channel reduced by outer precoder is important as it leverages the inter-group interference, the intra-group interference, and the performance loss from the quantized channel feedback. In this paper, we propose the machine learning framework to find the optimal dimensions reduced by the outer precoder that maximizes the average sum rate, where the original problem is an NP-hard problem. Our machine learning framework considers the deep neural network, where the inputs are channel statistics, and the outputs are the effective channel dimensions after outer precoding. The numerical result shows that our proposed machine learning-based dimension optimization achieves the average sum rate comparable to the optimal performance using brute-forcing searching, which is not feasible in practice.

Wireless Multicast of Virtual Reality Videos With MPEG-I Format

Deploying virtual reality (VR) streaming systems over wireless networks can provide an immersive environment for users without behavioral restrictions, and thus has drawn considerable attentions recently. MPEG-I as a new panorama video standard just targets such immersive multimedia applications. Although multiple VR delivery schemes have been proposed, MPEG-I has not been sufficiently researched, especially for multicast scenarios. Therefore, in this paper, we would like to design a multicast scheme to deliver 360 VR videos with MPEG-I format. Specifically, based on the prediction of users' viewports, we formulate an optimization problem of user grouping and bandwidth allocation to maximize user utilities. To solve the problem, we first propose a method which is composed of an optimal bandwidth allocation algorithm and a two-level hierarchical user grouping scheme. Furthermore, we consider the channel feedback overhead in multicast scenarios with a large number of users. Based on a reasonable assumption, we propose a simplified grouping method with low feedback overhead. Simulation results demonstrate the effectiveness of our proposed method, which yields similar performance compared to an exhausting search method when serving a large number of users with high SNRs.

Sparsity-aided codebook for limited feedback in FDD massive MIMO system

Channel state information at transmitter (CSIT) is vital for massive multiple-input-multiple-output (MIMO) system to achieve unprecedented improvement in capacity and spectral efficiency. Unfortunately, CSIT is acquired via channel feedback in frequency-division duplexing (FDD) system, which suffers from large volume of feedback overhead and size of codebook, since they increase with the number of antennas at transmitter. In this paper, by exploiting the channel sparsity in virtual angular domain, a sparsity-aided codebook is proposed for FDD massive MIMO system to alleviate the channel feedback overhead and codebook size. Specifically, a sparsity aided limited channel feedback model is proposed, where the high dimensional channel is decomposed to the limited linear combination with channel coefficients in virtual angular domain. Then, the high dimensional channel can be quantized by the proposed codebook in a more precise way with significantly small codebook size and fed back in low overhead within virtual coherence time. Furthermore, the upper bound of inter-user interference and the per user rate loss incurred by the proposed sparsity-aided codebook are theoretically analyzed, in which the required quantization bits only increase linearly with the channel sparsity level rather than number of BS antennas when the rate loss is limited to a constant level.

Spectral and Energy Efficient Low-Overhead Uplink and Downlink Channel Estimation for 5G Massive MIMO Systems.

Uplink and Downlink channel estimation in massive Multiple Input Multiple Output (MIMO) systems is an intricate issue because of the increasing channel matrix dimensions. The channel feedback overhead using traditional codebook schemes is very large, which consumes more bandwidth and decreases the overall system efficiency. The purpose of this paper is to decrease the channel estimation overhead by taking the advantage of sparse attributes and also to optimize the Energy Efficiency (EE) of the system. To cope with this issue, we propose a novel approach by using Compressed-Sensing (CS), Block Iterative-Support-Detection (Block-ISD), Angle-of-Departure (AoD) and Structured Compressive Sampling Matching Pursuit (S-CoSaMP) algorithms to reduce the channel estimation overhead and compare them with the traditional algorithms. The CS uses temporal-correlation of time-varying channels to produce Differential-Channel Impulse Response (DCIR) among two CIRs that are adjacent in time-slots. DCIR has greater sparsity than the conventional CIRs as it can be easily compressed. The Block-ISD uses spatial-correlation of the channels to obtain the block-sparsity which results in lower pilot-overhead. AoD quantizes the channels whose path-AoDs variation is slower than path-gains and such information is utilized for reducing the overhead. S-CoSaMP deploys structured-sparsity to obtain reliable Channel-State-Information (CSI). MATLAB simulation results show that the proposed CS based algorithms reduce the feedback and pilot-overhead by a significant percentage and also improve the system capacity as compared with the traditional algorithms. Moreover, the EE level increases with increasing Base Station (BS) density, UE density and lowering hardware impairments level.

On the Performance of Channel-Statistics-Based Codebook for Massive MIMO Channel Feedback

The channel feedback overhead for massive multiple-input multiple-output systems with a large number of base station (BS) antennas is very high since the number of feedback bits of traditional codebooks scales linearly with the number of BS antennas. To reduce the feedback overhead, an effective codebook based on channel statistics has been designed, where the required number of feedback bits only scales linearly with the rank of the channel correlation matrix. However, this attractive conclusion was only proved under a particular channel assumption in the literature. To provide a rigorous theoretical proof under a general channel assumption, in this paper, we quantitatively analyze the performance of the channel-statistics-based codebook. Specifically, we first introduce the rate gap between the ideal case of perfect channel state information at the transmitter and the practical case of limited channel feedback, where we find that the rate gap depends on the quantization error of the codebook. Then, we derive an upper bound of the quantization error, based on which we prove that the required number of feedback bits to ensure a constant rate gap only scales linearly with the rank of the channel correlation matrix. Finally, numerical results are provided to verify this conclusion.

Joint Channel Training and Feedback for FDD Massive MIMO Systems

Massive multiple-input multiple-output (MIMO) is widely recognized as a promising technology for future 5G wireless communication systems. To achieve the theoretical performance gains in massive MIMO systems, accurate channel state information at the transmitter (CSIT) is crucial. Due to the overwhelming pilot signaling and channel feedback overhead, however, conventional downlink channel estimation and uplink channel feedback schemes might not be suitable for frequency-division duplexing (FDD) massive MIMO systems. In addition, these two topics are usually separately considered in the literature. In this paper, we propose a joint channel training and feedback scheme for FDD massive MIMO systems. Specifically, we firstly exploit the temporal correlation of time-varying channels to propose a differential channel training and feedback scheme, which simultaneously reduces the overhead for downlink training and uplink feedback. We next propose a structured compressive sampling matching pursuit (S-CoSaMP) algorithm to acquire a reliable CSIT by exploiting the structured sparsity of wireless MIMO channels. Simulation results demonstrate that the proposed scheme can achieve substantial reduction in the training and feedback overhead.

Power Allocation in Nonselfish Symbiotic Cognitive Relaying with Partial Channel State Information

We first address the problem of power allocation at cognitive users (CUs) to maximize the throughput of a nonselfish symbiotic cognitive radio scheme, in which the CUs may assist the data transmission of primary users (PUs) via nonorthogonal amplify-and-forward (AF) cognitive relaying and obtain an incentive time for their own data transmission in a nonselfish manner. Then, an optimal power allocation algorithm is proposed based on the full channel state information (CSI) among PUs, CUs, and base station (BS). In order to reduce the feedback overhead, another power allocation algorithm is devised based only on the partial CSI, that is, the CSI of BS-PU and the CSI of BS-CUs. Simulation results demonstrate that, compared with the optimal power allocation algorithm, the power allocation algorithm with only the partial CSI can achieve a similar performance with a smaller channel feedback overhead.

Decentralized User-Centric Scheduling with Low Rate Feedback for Mobile Small Cells

Small cells with wireless backhaul are promising, whereas challenges of severe overlapping coverage and strong interference are yet to be addressed. Coordinating small cells could resolve the challenges; however, existing multicell coordinated beamforming techniques involve high cost of communication overhead, synchronization and backhaul. Such problems may deteriorate in practical cellular applications, where there could be many users, each generating high channel feedback overhead to compete for an opportunity of being scheduled, and the downlink data signals of the coordinated cells need to be precisely synchronized at each of the users. We propose a new scheme, which cuts the overhead by 80% and enables the coordination to be practically implemented in a decentralized manner. Our scheme is a user-centric downlink scheduling approach, where mobile terminals trigger and participate in the scheduling decisions of small cells. We also develop a new recursive algorithm to optimize the quantization levels of mobile terminals' feedback, minimizing the feedback requirement. Analysis, confirmed by simulations, shows that our scheme is able to achieve 94.4% of the sum-rate upper-bound which can only be approached by idealized centralized coordination. In terms of throughput, given the 80% reduced overhead, our scheme is 139.5% better than the idealized centralized coordination approach.

Exploiting Spatial, Frequency, and Multiuser Diversity in 3GPP LTE Cellular Networks

This paper addresses the problem of frequency domain packet scheduling (FDPS) incorporating spatial division multiplexing (SDM) multiple input multiple output (MIMO) techniques on the 3GPP Long-Term Evolution (LTE) downlink. We impose the LTE MIMO constraint of selecting only one MIMO mode (spatial multiplexing or transmit diversity) per user per transmission time interval (TTI). First, we address the optimal MIMO mode selection (multiplexing or diversity) per user in each TTI in order to maximize the proportional fair (PF) criterion adapted to the additional frequency and spatial domains. We prove that both single-user (SU-) and multi-user (MU-) MIMO FDPS problems under the LTE requirement are NP-hard. We therefore develop two types of approximation algorithms (ones with full channel feedback and the others with partial channel feedback), all of which guarantee provable performance bounds for both SU- and MU-MIMO cases. Based on 3GPP LTE system model simulations, our approximation algorithms that take into account both spatial and frequency diversity gains outperform the exact algorithms that do not exploit the potential spatial diversity gain. Moreover, the approximation algorithms with partial channel feedback achieve comparable performance (with only 1-6 percent performance degradation) to the ones with full channel feedback, while significantly reducing the channel feedback overhead by nearly 50 percent.