Frequency-division Duplexing Massive Massive Multiple-input Multiple-output Research Articles

AcsiNet: Attention-Based Deep Learning Network for CSI Prediction in FDD MIMO Systems

In 5G frequency division duplex (FDD) systems, the user equipment needs to feedback the measured downlink channel state information (CSI) to the base station to improve the throughput. For massive multiple-input-multiple-output (MIMO) systems, each antenna in base station needs its CSI feedback, which results in significant transmission overhead and latency. We propose an attention-based deep learning network to directly predict the downlink CSI from the corresponding uplink one, eliminating the feedback overhead completely. Specifically, the uplink CSI is first compressed based on the 3D inverse discrete Fourier transform, then is fed into an attention-based deep learning network which can focus on key CSI characteristics. The simulation results show that the proposed method achieves high prediction accuracy and low complexity, indicating prospective applications in FDD massive MIMO systems.

Deep learning for joint channel estimation and feedback in massive MIMO systems

The great potentials of massive Multiple-Input Multiple-Output (MIMO) in Frequency Division Duplex (FDD) mode can be fully exploited when the downlink Channel State Information (CSI) is available at base stations. However, the accurate CSI is difficult to obtain due to the large amount of feedback overhead caused by massive antennas. In this paper, we propose a deep learning based joint channel estimation and feedback framework, which comprehensively realizes the estimation, compression, and reconstruction of downlink channels in FDD massive MIMO systems. Two networks are constructed to perform estimation and feedback explicitly and implicitly. The explicit network adopts a multi-Signal-to-Noise-Ratios (SNRs) technique to obtain a single trained channel estimation subnet that works well with different SNRs and employs a deep residual network to reconstruct the channels, while the implicit network directly compresses pilots and sends them back to reduce network parameters. Quantization module is also designed to generate data-bearing bitstreams. Simulation results show that the two proposed networks exhibit excellent performance of reconstruction and are robust to different environments and quantization errors.

Downlink Channel Estimation for FDD Massive MIMO Using Conditional Generative Adversarial Networks

For implementation of massive multiple-input multiple-output (MIMO) cellular systems in frequency division duplex (FDD) mode, accurate estimation of downlink channel state information (CSI) is necessary, but full radio channel reciprocity between the uplink and downlink does not exist in that mode. Existing work on estimating downlink CSI in FDD massive MIMO systems has considered such approaches as angle-of-arrival reciprocity, compressive sensing, using second-order channel statistics (particularly the channel covariance matrix (CCM)), and machine learning using deep neural networks (DNNs). Typical DNN-based approaches are unsuitable for this problem because DNNs require large datasets, thousands of training epochs, and are susceptible to environmental variations. To overcome these shortcomings, we develop a conditional generative adversarial network (CGAN) approach to uplink-to-downlink mapping of both CCMs and CSI. To apply this method, we convert the uplink and downlink CCMs/CSI to images and employ CGAN techniques previously applied to image translation. The normalized mean square error performance of the proposed CGAN is evaluated for several array sizes for both CCM and CSI mapping. For uplink-to-downlink CSI mapping, we also examine the spectral efficiency performance of our CGAN-based method, as well as the impact of pilot reuse; both simulated and measured CSI data are considered. Our results demonstrate performance improvement over existing algorithms.

A Partial Reciprocity-Based Channel Prediction Framework for FDD Massive MIMO With High Mobility

Massive multiple-input multiple-output (MIMO) is believed to deliver unrepresented spectral efficiency gains for 5G and beyond. However, a practical challenge arises during its commercial deployment, which is known as the “curse of mobility”. The performance of massive MIMO drops alarmingly when the velocity level of user increases. In this paper, we tackle the problem in frequency division duplex (FDD) massive MIMO with a novel Channel State Information (CSI) acquisition framework. A joint angle-delay-Doppler (JADD) wideband precoder is proposed for channel training. Our idea consists in the exploitation of the partial channel reciprocity of FDD and the angle-delay-Doppler channel structure. More precisely, the base station (BS) estimates the angle-delay-Doppler information of the UL channel based on UL pilots using Matrix Pencil (MP) method. It then computes the wideband JADD precoders according to the extracted parameters. Afterwards, the user estimates and feeds back some scalar coefficients for the BS to reconstruct the predicted DL channel. Asymptotic analysis shows that the CSI prediction error converges to zero when the number of BS antennas and the bandwidth increases. Numerical results with industrial channel model demonstrate that our framework can well adapt to high speed (350 km/h), large CSI delay (10 ms) and channel sample noise.

Learning How to Transfer From Uplink to Downlink via Hyper-Recurrent Neural Network for FDD Massive MIMO

In order to unlock the full advantages of massive multiple-input multiple-output (MIMO) in the downlink, the base station (BS) must leverage information about the downlink fading channels. However, in frequency division duplex (FDD) systems, full channel reciprocity does not hold, and acquiring information about the downlink channels generally requires downlink pilot transmission followed by uplink feedback. Prior work proposed to design pilot transmission, feedback, and channel state information (CSI) estimation, or directly downlink beamforming, via deep learning in an end-to-end manner. While previous work only used downlink pilots in a single slot, in this work, we introduce an enhanced end-to-end design that leverages partial uplink-downlink reciprocity and temporal correlation of the fading processes by utilizing jointly downlink and uplink pilots across multiple time slots. The proposed method is based on a novel deep learning architecture – HyperRNN – that combines hypernetworks and recurrent neural networks (RNNs) to optimize the transfer of long-term invariant channel features from uplink to downlink. Simulation results demonstrate that the HyperRNN achieves a lower normalized mean square error (NMSE) performance in terms of channel estimation, and that it attains a larger achievable sum-rate when applied to multi-user beamforming, as compared to the state of the art.

A Compressive Sensing and Deep Learning-Based Time-Varying Channel Estimation for FDD Massive MIMO Systems

To achieve the performance gains of massive multiple-input multiple-output (MIMO) systems, the downlink channel state information (CSI) must be acquired at the base station (BS). In frequency division duplexing (FDD) massive MIMO systems, the BS always first transmits downlink pilot symbols so that the user equipment (UE) can estimate CSI and then feedback to the BS. However, the huge number of antennas at the BS will lead to overwhelming feedback overhead. Moreover, time-varying caused by high mobility of user terminals makes the priori channel knowledge of the channels to change from one slot to another so that CSI aquisition is hard. To simultaneously reduce the overhead of overwhelming downlink pilot signaling and uplink feedback in time-varying massive MIMO systems, we propose a channel estimation scheme based on compressive sensing (CS) and deep learning (DL) in frequency division duplexing (FDD) massive MIMO systems. Specifically, we first develop a new CS-based algorithm for sparse channel estimation, which requires no priori knowledge of channel statistics. After obtaining the innitial channel estimation, we utilize two DL-based networks, named DnNet and DnLSTM respectively for denoising. Simulation results demonstrate that the proposed method can considerably reduce the training and feedback overhead and outperform the existing classical algorithms.

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.

A low complexity burst channel estimation algorithm for FDD massive MIMO systems

To fully attain array gains of massive multiple-input multiple-output (MIMO) and its energy and spectral efficiency, deriving channel state information (CSI) at the base station (BS) side is essential. However, CSI estimation of frequency-division duplex (FDD) based massive MIMO is a challenging task owning to the required pilots, which are proportional to the number of antennas at the BS side. Therefore, the pilot overhead should be inevitably mitigated in the process of downlink channel estimation of FDD technique. In this paper, we propose a novel compressed sensing (CS) algorithm which takes advantage of correlation between the received and transmitted signals to estimate the channel with high precision, and moreover, to reduce the computational complexity imposed on the BS side. The main idea behind the proposed algorithm is to sort the specific number of maximum correlations as a common support in each iteration of the algorithm. Simulation results indicate that the proposed algorithm is capable of estimating downlink channel better than the counterpart algorithms in terms of mean square error (MSE) and the computational complexity. Meanwhile, the complexity of the proposed method linearly grows up when the number of BS antennas increases.

Dual-Polarized FDD Massive MIMO: A Comprehensive Framework

We propose a comprehensive scheme for realizing a massive multiple-input multiple-output (MIMO) system with dual-polarized antennas in frequency division duplexing (FDD) mode. Dual-polarized arrays are commonly employed due to the favorable property that, in principle, they can double the number of channel spatial degrees of freedom with a less-than-proportional increase in array size. However, processing a dual-polarized massive MIMO channel is demanding due to the high channel dimension and the lack of Uplink-Downlink (UL-DL) channel reciprocity in FDD mode. In particular, the difficulty arises in common channel training and DL precoding in a multi-user setup. To address this, we develop a unified framework consisting of three steps: (1) covariance estimation to efficiently estimate the UL covariance from noisy UL pilots; (2) a UL-DL covariance transformation method that obtains the DL covariance from the estimated UL covariance, eliminating the need for DL channel covariance training via pilot transmission; <xref ref-type="disp-formula" rid="deqn3a-deqn3b" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(3)</xref> a joint multi-user DL channel training method, which enables the BS to estimate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">effective DL channels</i> given any protocol-specific pilot dimension and to use them for interference-free DL beamforming and data transmission. Through extensive simulations, we show that our scheme is applicable to a variety of communication scenarios in terms of the number of antennas, UL and DL pilot dimensions, and angular scattering properties. Unlike the common trend in the literature, we do <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">not</i> make strong structural assumptions about the wireless channel (such as angular sparsity), ensuring a general treatment of the problem.

AoD-Adaptive Channel Feedback for FDD Massive MIMO Systems With Multiple-Antenna Users

In this paper, we propose an efficient feedback scheme for an angle of departure (AoD) based channel estimation in frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems with multiple antennas at the users. The channel feedback scheme is based on zero-forcing block diagonalization (BD) and it is proposed for two distinct design cases; in case I, the number of streams intended for a user equals the number of antennas at that user; in case II, the number of streams is less than the number of receive antennas. Case I is applicable in scenarios where high data rate requirements are needed as it transmits data symbols over all of the available degrees of freedom of the system. Diversely, case II is applicable when reliability is a priority in the system as it uses the additional <i>receive</i> antennas at the user to achieve spatial diversity to enhance the link performance. The proposed scheme is analyzed for the two cases by quantifying the downlink rate gap from the case of perfect channel state information (CSI). Moreover, we design structured feedback codebooks based on optimal subspace packing in the Grassmannian manifold and show that these codes achieve close performance to the perfect CSI case. Additionally, a vector quantization scheme is proposed to quantize the user&#x2019;s channel matrix when optimal power allocation across multiple streams is adopted in the low signal-to-noise ratio (SNR) region. The feedback codebooks are based on optimal line packing in the Grassmannian manifold, where every vector of the user&#x2019;s channel matrix is quantized and sent to the BaseStation. The results demonstrate a fundamental trade-off between vector quantization, with power optimization across the data streams, and subspace quantization. Specifically, vector quantization codebooks outperform subspace-based codebooks in the low SNR region, while the situation is reversed in the high SNR region.

SALDR: Joint Self-Attention Learning and Dense Refine for Massive MIMO CSI Feedback With Multiple Compression Ratio

The advantages of massive multiple-input multiple-output (MIMO) techniques depend heavily on the accuracy of channel state information (CSI). In frequency division duplexing (FDD) massive MIMO systems, the user equipment (UE) needs to feed downlink CSI back to the base station (BS) through the feedback link. The excessive feedback overheads and low reconstruction accuracy are the main obstacles for actual deployment of FDD massive MIMO systems. In recent years, deep learning (DL) has been widely used to address the above problems. In this letter, we propose a neural network by utilizing the self-attention learning and dense refine (SALDR), which improves the accuracy of CSI feedback. Furthermore, a unified decoder named SALDR-U is designed to realize different compression ratios for CSI feedback without changing any parameter. Simulation results show that the proposed SALDR and SALDR-U outperform the state-of-the-art network in terms of accuracy and overhead of CSI feedback. The source code for all the experiments is available at GitHub.The code of this letter can be downloaded from GitHub link: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/XS96/SALDR</uri> .

Compressive Sampled CSI Feedback Method Based on Deep Learning for FDD Massive MIMO Systems

Accurate downlink channel state information (CSI) is required to be fed back to the base station (BS) in frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems in order to achieve maximum antenna diversity and multiplexing. However, downlink CSI feedback overhead scales with the number of transceiver antennas, a major hurdle for practical deployment of FDD massive MIMO systems. To solve this problem, we propose a compressive sampled CSI feedback method based on deep learning (SampleDL). In SampleDL, the massive MIMO channel matrix is sampled uniformly in time/frequency dimension before being fed into neural networks (NNs), which will reduce the computational resource/time at user equipment (UE) as well as enhance the CSI recovery accuracy at the BS. Both theoretical analysis and normalized mean square errors (NMSE) results confirm the advantages of the proposed method in terms of time complexity and recovery accuracy. Besides, a suitable CSI feedback period is explored by link level simulations, which aims to further reduce the overhead of CSI feedback without degrading the communication quality.

Federated Learning for DL-CSI Prediction in FDD Massive MIMO Systems

In frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems, deep learning for predicting the downlink channel state information (DL-CSI) has been extensively studied. However, in some small cellular base stations (SBSs), a small amount of training data is insufficient to produce an excellent model for CSI prediction. Traditional centralized learning (CL) based method brings all the data together for training, which can lead to overwhelming communication overheads. In this work, we introduce a federated learning (FL) based framework for DL-CSI prediction, where the global model is trained at the macro base station (MBS) by collecting the local models from the edge SBSs. We propose a novel model aggregation algorithm, which updates the global model twice by considering the local model weights and the local gradients, respectively. Numerical simulations show that the proposed aggregation algorithm can make the global model converge faster and perform better than the compared schemes. The performance of the FL architecture is close to that of the CL-based method, and the transmission overheads are much fewer.

Deep Learning and Compressive Sensing-Based CSI Feedback in FDD Massive MIMO Systems

To fully utilize multiplexing and array gains of massive multiple-input multiple-output (MIMO), the downlink channel state information (CSI) must be acquired at the base station (BS). In frequency division duplexing (FDD) massive MIMO systems, the downlink CSI is generally estimated at the user equipment (UE) and then fed back to the BS. The huge number of antennas at the BS leads to overwhelming feedback overhead. To address this issue, we propose a framework, named CS-ReNet. In this framework, the CSI is first compressed at the UE based on the compressive sensing (CS) technology and then reconstructed at the BS using a deep learning (DL)-based signal recovery solver, named ReNet. We analyze the CSI quality at the BS in terms of the normalized mean-squared error (NMSE) and cosine similarity. Simulation results demonstrate that the proposed method outperforms the existing CS-based and some DL-based methods.

Randomized Channel Sparsifying Hybrid Precoding for FDD Massive MIMO Systems

We propose a novel randomized channel sparsifying hybrid precoding (RCSHP) design to reduce the signaling overhead of channel estimation and the hardware cost and power consumption at the base station (BS), in order to fully harvest benefits of frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems. RCSHP allows time-sharing among multiple analog precoders, each serving a compatible user group. The analog precoder is adapted to the channel statistics to properly sparsify the channel for the associated user group, such that the resulting effective channel (product of channel and analog precoder) not only has enough spatial degrees of freedom (DoF) to serve this group of users, but also can be accurately estimated under the limited pilot budget. The digital precoder is adapted to the effective channel based on the duality theory to facilitate the power allocation and exploit the spatial multiplexing gain. We formulate the joint optimization of the time-sharing factors and the associated sets of analog precoders and power allocations as a general utility optimization problem, which considers the impact of effective channel estimation error on the system performance. Then we propose an efficient stochastic successive convex approximation algorithm to provably obtain Karush-Kuhn-Tucker (KKT) points of this problem.

Energy efficiency maximization in FDD massive MIMO systems with channel aging

In this paper, energy efficiency (EE) of the frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems in the downlink transmission is investigated by considering the channel aging effect. First, we present a model for channel aging in the FDD massive MIMO systems and study its effect on the EE of the system. We assume that the channel aging exists in the entire transmission frame of the FDD systems which includes both pilot and data transmission phases. Then, we propose methods for compensating for this effect and increasing the EE. These methods include channel prediction method in the pilot transmission phase, system’s parameters optimization for maximizing the EE and a hybrid method. By numerical simulations, we compare the performance of the proposed methods and their abilities to combat the channel aging effect in the massive MIMO systems and EE improvement.

Performance Analysis of Channel Extrapolation in FDD Massive MIMO Systems

Channel estimation for the downlink of frequency division duplex (FDD) massive multiple-input-multiple output (MIMO) systems is well known to generate a large overhead as the amount of training generally scales with the number of transmit antennas in a MIMO system. In this paper, we consider the solution of extrapolating the channel frequency response from uplink pilot estimates to the downlink frequency band. This drastically reduces the downlink pilot overhead and completely removes the need for a feedback from the users. The price to pay is a degradation in the quality of the channel estimates, which reduces the downlink spectral efficiency. We first show that conventional estimators fail to achieve reasonable accuracy. We propose instead to use high-resolution channel estimation. We derive the Cramer-Rao lower bound (CRLB) of the mean squared error (MSE) of the extrapolated channel. Furthermore, a relationship between the imperfect channel state information (CSI) and the downlink user performance is derived. The extrapolation-based FDD massive MIMO performance is validated through numerical simulations and compared to a corresponding time division duplex (TDD) system. Considered figures of merit for extrapolation performance include channel MSE, beamforming efficiency, extrapolation range, spectral efficiency and uncoded symbol error rate. Our main conclusion is that channel extrapolation is a viable solution for FDD massive MIMO systems.

A Comparison of TDD and FDD Massive MIMO Systems Against Smart Jamming

Frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems introduce a large overhead in downlink channel estimation in contrast to the time division duplex (TDD) mode. This overhead results in a considerable spectral efficiency (SE) gap between the FDD and TDD modes. In this paper, we consider the performance of the TDD and FDD massive MIMO systems with a spatially correlated channel in the presence of jamming in the network. We show how a smart jammer can effectively design its attack signal to degrade the network performance in terms of the downlink SE. Since the jammer can obtain different information about the channels in the TDD and FDD modes, two distinct jamming strategies are proposed for each mode. In the numerical results, the performance of both the TDD and FDD modes under the optimized jamming designs are evaluated and compared. Our results show that despite more attention to the TDD mode in current massive MIMO systems, it is more vulnerable to smart jamming attacks compared to the FDD mode which results in a smaller SE-gap between the modes. Furthermore, a countermeasure technique is proposed to combat this jamming attack in both the TDD and FDD modes by estimating the jamming power, grouping users, and allocating power among them. The numerical results demonstrate the effectiveness of the proposed countermeasure techniques in both the TDD and FDD modes.

ELM-Based Superimposed CSI Feedback for FDD Massive MIMO System

In frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO), deep learning (DL)-based superimposed channel state information (CSI) feedback has presented promising performance. However, it is still facing many challenges, such as the high complexity of parameter tuning, large number of training parameters, and long training time, etc. To overcome these challenges, an extreme learning machine (ELM)-based superimposed CSI feedback is proposed in this paper, in which the downlink CSI is spread and then superimposed on uplink user data sequence (UL-US) to feed back to base station (BS). At the BS, an ELM-based network is constructed to recover both downlink CSI and UL-US. In the constructed ELM-based network, we employ the simplified versions of ELM-based subnets to replace the subnets of DL-based superimposed feedback, yielding less training parameters. Besides, the input weights and hidden biases of each ELM-based subnet are loaded from the same matrix by using its full or partial entries, which significantly reduces the memory requirement. With similar or better recovery performances of downlink CSI and UL-US, the proposed ELM-based method has less training parameters, storage space, offline training and online running time than those of DL-based superimposed CSI feedback.

Low-Complexity Compressed Sensing Downlink Channel Estimation for Multi-Antenna Terminals in FDD Massive MIMO Systems

In frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems, the overhead of downlink channel estimation is complex in terms of the pilot overhead, the calculation cost and the estimation process. In this paper, we propose a low-complexity downlink channel estimation scheme based on compressed sensing for mobile multi-antenna terminals. In the scheme, the mobile terminal estimates the downlink massive MIMO channel and utilises the characteristics of the spatial sparsity of the massive MIMO channel to reduce the feedback overhead by feeding back the nonzero value of the sparse channel. Specifically, we propose a low-complexity estimation algorithm based on compressive sensing for multi-antenna terminals to reduce the computational overhead of the terminal. Since different antennas of a terminal share the same support set, the algorithm estimates multiple indices per iteration, collecting the estimated indices of different antennas at the end of each iteration, thereby reducing the total number of iterations of the algorithm. Then, we derive a halting condition for a greedy algorithm that stops the iteration process according to the residual energy. The simulation results illustrate the efficiency of the halting condition for the greedy algorithm and the low complexity of the proposed algorithm. In contrast to different greedy algorithms and the Bayesian algorithm, the proposed algorithm has a complexity that decreases as the number of terminal antennas.