Channel estimation is a difficult problem in MIMO systems. Using a physical model allows to ease the problem, injecting a priori information based on the physics of propagation. However, such models rest on simplifying assumptions and require to know precisely the system configuration, which is unrealistic.In this paper, we propose to perform online learning for channel estimation in a massive MIMO context, adding flexibility to physical models by unfolding a channel estimation algorithm (matching pursuit) as a neural network. This leads to a computationally efficient neural network that can be trained online when initialized with an imperfect model. The method allows a base station to automatically correct its channel estimation algorithm based on incoming data, without the need for a separate offline training phase.It is applied to realistic channels and shows great performance, achieving channel estimation error almost as low as one would get with a perfectly calibrated system.
In wideband millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, channel estimation is challenging due to the hybrid analog-digital architecture, which compresses the received pilot signal and makes channel estimation a compressive sensing (CS) problem. However, existing high-performance CS algorithms usually suffer from high complexity. On the other hand, the beam squint effect caused by huge bandwidth and massive antennas will deteriorate estimation performance. In this paper, frequency-dependent angular dictionaries are first adopted to compensate for beam squint.…
Massive arrays deployed in millimeter-wave systems enable high angular resolution performance, which in turn facilitates sub-meter localization services. Albeit suboptimal, up to now the most popular localization approach has been based on a so-called two-step procedure, where triangulation is applied upon aggregation of the angle-of-arrival (AoA) measurements from the collaborative base stations. This is mainly due to the prohibitive computational cost of the existing direct localization approaches in large-scale systems. To address this issue, we propose a deep unfolding based fast direct lo…
In limited feedback multi-user multiple-input multiple-output (MU-MIMO) cellular networks, users send quantized information about the channel conditions to the associated base station (BS) for downlink beamforming. However, channel quantization and beamforming have been treated as two separate tasks conventionally, which makes it difficult to achieve global system optimality. In this paper, we propose an augmented deep unfolding (ADU) approach that jointly optimizes the beamforming scheme at the BSs and the channel quantization scheme at the users. In particular, the classic WMMSE beamformer i…
Zhejiang University（浙江大学）；Tongji University（同济大学）；University of California, Davis（加州大学戴维斯分校）
Optimization theory assisted algorithms have received great attention for precoding design in multiuser multiple-input multiple-output (MU-MIMO) systems. Although the resultant optimization algorithms are able to provide excellent performance, they generally require considerable computational complexity, which gets in the way of their practical application in real-time systems. In this work, in order to address this issue, we first propose a framework for deep-unfolding, where a general form of iterative algorithm induced deep-unfolding neural network (IAIDNN) is developed in matrix form to be…
Zhejiang University（浙江大学）；University of California, Davis（加州大学戴维斯分校）
The millimeter wave (mmWave) multiuser multiple-input multiple-output (MU-MIMO) systems with discrete lens arrays (DLA) have received great attention due to their simple hardware implementation and excellent performance. In this work, we investigate the joint design of beam selection and digital precoding matrices for mmWave MU-MIMO systems with DLA to maximize the sum-rate subject to the transmit power constraint and the constraints of the selection matrix structure. The investigated non-convex problem with discrete variables and coupled constraints is challenging to solve and an efficient fr…
The slice-wise multiplication of two tensors is required in a variety of tensor decompositions (including PARAFAC2 and PARATUCK2) and is encountered in many applications, including the analysis of multidimensional biomedical data (EEG, MEG, etc.) or multi-carrier MIMO systems. In this paper, we propose a new tensor representation that is not based on a slice-wise (matrix) description, but can be represented by a double contraction of two tensors. Such a double contraction of two tensors can be efficiently calculated via generalized unfoldings. It leads to new tensor models of the investigated …
Symbol Level Precoding (SLP) has attracted significant research interest due to its ability to exploit interference for energy-efficient transmission. This paper proposes an unsupervised deep-neural network (DNN) based SLP framework. Instead of naively training a DNN architecture for SLP without considering the specifics of the optimization objective of the SLP domain, our proposal unfolds a power minimization SLP formulation based on the interior point method (IPM) proximal `log' barrier function. Furthermore, we extend our proposal to a robust precoding design under channel state information…
Hybrid beamforming (HBF) is a key enabler for wideband terahertz (THz) massive multiple-input multiple-output (mMIMO) communications systems. A core challenge with designing HBF systems stems from the fact their application often involves a non-convex, highly complex optimization of large dimensions. In this paper, we propose HBF schemes that leverage data to enable efficient designs for both the fully-connected HBF (FC-HBF) and dynamic sub-connected HBF (SC-HBF) architectures. We develop a deep unfolding framework based on factorizing the optimal fully digital beamformer into analog and digit…
We propose a novel soft-output joint channel estimation and data detection (JED) algorithm for multiuser (MU) multiple-input multiple-output (MIMO) wireless communication systems. Our algorithm approximately solves a maximum a-posteriori JED optimization problem using deep unfolding and generates soft-output information for the transmitted bits in every iteration. The parameters of the unfolded algorithm are computed by a hyper-network that is trained with a binary cross entropy (BCE) loss. We evaluate the performance of our algorithm in a coded MU-MIMO system with 8 basestation antennas and 4…
In massive multiple-input multiple-output (MIMO) systems, hybrid analog-digital (AD) beamforming can be used to attain a high directional gain without requiring a dedicated radio frequency (RF) chain for each antenna element, which substantially reduces both the hardware costs and power consumption. While massive MIMO transceiver design typically relies on the conventional mean-square error (MSE) criterion, directly minimizing the symbol error rate (SER) can lead to a superior performance. In this paper, we first mathematically formulate the problem of hybrid transceiver design under the minim…
Coordinated weighted sum-rate maximization in multicell MIMO networks with intra- and intercell interference and local channel state at the base stations is recognized as an important yet difficult problem. A classical, locally optimal solution is obtained by the weighted minimum mean squared error (WMMSE) algorithm which facilitates a distributed implementation in multicell networks. However, it often suffers from slow convergence and therefore large communication overhead. To obtain more practical solutions, the unrolling/unfolding of traditional iterative algorithms gained significant atten…
The WMMSE beamforming algorithm is a popular approach to address the NP-hard weighted sum rate (WSR) maximization beamforming problem. Although it efficiently finds a local optimum, it requires matrix inverses, eigendecompositions, and bisection searches, operations that are problematic for real-time implementation. In our previous work, we considered the MU-MISO case and effectively replaced such operations by resorting to a first-order method. Here, we consider the more general and challenging MU-MIMO case. Our earlier approach does not generalize to this scenario and cannot be applied to re…
An alternate direction method of multipliers (ADMM)-based detectors can achieve good performance in both small and large-scale multiple-input multiple-output (MIMO) systems. However, due to the difficulty of choosing the optimal penalty parameters, their performance is limited. This paper presents a deep neural network (DNN)-based massive MIMO detection method which can overcome the above limitation. It exploits the unfolding technique and learns to estimate the penalty parameters. Additionally, a computationally cheaper detector is also proposed. The proposed methods can handle the higher-ord…
Cell-free massive MIMO (CF-mMIMO) systems represent a promising approach to increase the spectral efficiency of wireless communication systems. However, near-optimal beamforming solutions require a large amount of signaling exchange between access points (APs) and the network controller (NC). In this letter, we propose two unsupervised deep neural networks (DNN) architectures, fully and partially distributed, that can perform decentralized coordinated beamforming with zero or limited communication overhead between APs and NC, for both fully digital and hybrid precoding. The proposed DNNs achie…
MIMO systems in the context of 6G Vehicle-to-Everything (V2X) will require an accurate channel knowledge to enable efficient communication. Standard channel estimation techniques, such as Unconstrained Maximum Likelihood (U-ML), are extremely noisy in massive MIMO settings, while structured approaches, e.g., compressed sensing, are suited to low-mobility scenarios and are sensitive to hardware impairments. We propose a novel Multi-Vehicular algebraic channel estimation method for 6G V2X based on unsupervised learning which exploits recurrent vehicle passages in typical urban settings. Multiple…
Deep unfolding is a method of growing popularity that fuses iterative optimization algorithms with tools from neural networks to efficiently solve a range of tasks in machine learning, signal and image processing, and communication systems. This survey summarizes the principle of deep unfolding and discusses its recent use for communication systems with focus on detection and precoding in multi-antenna (MIMO) wireless systems and belief propagation decoding of error-correcting codes. To showcase the efficacy and generality of deep unfolding, we describe a range of other tasks relevant to commu…
In massive multiple-input multiple-output (MIMO) systems, hybrid analog-digital beamforming is an essential technique for exploiting the potential array gain without using a dedicated radio frequency chain for each antenna. However, due to the large number of antennas, the conventional channel estimation and hybrid beamforming algorithms generally require high computational complexity and signaling overhead. In this work, we propose an end-to-end deep-unfolding neural network (NN) joint channel estimation and hybrid beamforming (JCEHB) algorithm to maximize the system sum rate in time-division…
Hybrid beamforming is a promising technique to reduce the complexity and cost of massive multiple-input multiple-output (MIMO) systems while providing high data rate. However, the hybrid precoder design is a challenging task requiring channel state information (CSI) feedback and solving a complex optimization problem. This paper proposes a novel RSSI-based unsupervised deep learning method to design the hybrid beamforming in massive MIMO systems. Furthermore, we propose i) a method to design the synchronization signal (SS) in initial access (IA); and ii) a method to design the codebook for the…
Unsupervised Learning for Scalable Downlink Power Control in Cell-Free Massive MIMO
ENEA（意大利国家新能源、可再生能源和可持续发展局）；University of Cassino and Southern Lazio（卡西诺与拉齐奥南部大学）；Consorzio Nazionale Interuniversitario per le Telecomunicazioni（意大利大学电信联合体）
Department of Electrical Engineering, National Tsing Hua University（国立清华大学电机工程学系）；Research Center for Information Technology Innovation, Academia Sinica（中央研究院资讯科技创新研究中心）
Millimeter wave (mmWave) is a key technology for fifth-generation (5G) and beyond communications. Hybrid beamforming has been proposed for large-scale antenna systems in mmWave communications. Existing hybrid beamforming designs based on infinite-resolution phase shifters (PSs) are impractical due to hardware cost and power consumption. In this paper, we propose an unsupervised-learning-based scheme to jointly design the analog precoder and combiner with low-resolution PSs for multiuser multiple-input multiple-output (MU-MIMO) systems. We transform the analog precoder and combiner design probl…
Hybrid beamforming is a promising technology to improve the energy efficiency of massive MIMO systems. In particular, subarray hybrid beamforming can further decrease power consumption by reducing the number of phase-shifters. However, designing the hybrid beamforming vectors is a complex task due to the discrete nature of the subarray connections and the phase-shift amounts. Finding the optimal connections between RF chains and antennas requires solving a non-convex problem in a large search space. In addition, conventional solutions assume that perfect CSI is available, which is not the case…
In this paper, deep neural network (DNN) is utilized to improve the belief propagation (BP) detection for massive multiple-input multiple-output (MIMO) systems. A neural network architecture suitable for detection task is firstly introduced by unfolding BP algorithms. DNN MIMO detectors are then proposed based on two modified BP detectors, damped BP and max-sum BP. The correction factors in these algorithms are optimized through deep learning techniques, aiming at improved detection performance. Numerical results are presented to demonstrate the performance of the DNN detectors in comparison w…
Massive multiuser multiple-input multiple-output (MU-MIMO) has been the mainstream technology in fifth-generation wireless systems. To reduce high hardware costs and power consumption in massive MU-MIMO, low-resolution digital-to-analog converters (DAC) for each antenna and radio frequency (RF) chain in downlink transmission is used, which brings challenges for precoding design. To circumvent these obstacles, we develop a model-driven deep learning (DL) network for massive MU-MIMO with finite-alphabet precoding in this article. The architecture of the network is specially designed by unfolding…
Hybrid Knowledge-Data Driven Channel Semantic Acquisition and Beamforming for Cell-Free Massive MIMO
Beijing Institute of Technology（北京理工大学）；Yangtze Delta Region Academy, Beijing Institute of Technology (Jiaxing)（北京理工大学长三角研究院（嘉兴））；Advanced Technology Research Institute, Beijing Institute of Technology（北京理工大学前沿技术研究院）；China Mobile (Chengdu) Institute of Research and Development（中国移动（成都）研究院）
Efficient massive/ultra-massive multiple-input multiple-output (MIMO) detection algorithms with satisfactory performance and low complexity are critical to meet the high throughput and ultra-low latency requirements in 5G and beyond communications, given the extremely large number of antennas. In this paper, we propose a low-complexity graph neural network (GNN) enhanced approximate message passing (AMP) algorithm, AMP-GNN, for massive/ultra-massive MIMO detection. The structure of the neural network is customized by unfolding the AMP algorithm and introducing the GNN module for multiuser inte…
Millimeter-wave (mmWave) communications have been one of the promising technologies for future wireless networks that integrate a wide range of data-demanding applications. To compensate for the large channel attenuation in mmWave band and avoid high hardware cost, a lens-based beamspace massive multiple-input multiple-output (MIMO) system is considered. However, the beam squint effect in wideband mmWave systems makes channel estimation very challenging, especially when the receiver is equipped with a limited number of radio-frequency (RF) chains. Furthermore, the real channel data cannot be o…
Southeast University（东南大学）；National Sun Yat-sen University（国立中山大学）；Georgia Institute of Technology（佐治亚理工学院）
In this paper, we investigate the model-driven deep learning (DL) for MIMO detection. In particular, the MIMO detector is specially designed by unfolding an iterative algorithm and adding some trainable parameters. Since the number of trainable parameters is much fewer than the data-driven DL based signal detector, the model-driven DL based MIMO detector can be rapidly trained with a much smaller data set. The proposed MIMO detector can be extended to soft-input soft-output detection easily. Furthermore, we investigate joint MIMO channel estimation and signal detection (JCESD), where the detec…
In this letter, a novel nested PARAFAC algorithm was proposed to improve the 8D parameters estimation performance for the bistatic EMVS-MIMO radar. Firstly, the outer part PARAFAC algorithm was carried out to estimate the receive spatial response matrix and its first way factor matrix. For the estimated first way factor matrix, a theory is given to rearrange its data into an new matrix, which is the mode-1 unfolding matrix of a three-way tensor. Then, the inner part PARAFAC algorithm was used to estimate the transmit steering vector matrix, the transmit spatial response matrix and the receive …
In this paper, we investigate an intelligent reflecting surface (IRS) assisted multi-user multiple-input multiple-output (MIMO) full-duplex (FD) system. We jointly optimize the active beamforming matrices at the access point (AP) and uplink users, and the passive beamforming matrix at the IRS to maximize the weighted sum-rate of the system. Since it is practically difficult to acquire the channel state information (CSI) for IRS-related links due to its passive operation and large number of elements, we conceive a mixed-timescale beamforming scheme. Specifically, the high-dimensional passive be…
Pennsylvania State University（宾夕法尼亚州立大学）；InterDigital Communications（交互数字通信公司）
Reference signals overhead reduction has recently evolved as an effective solution for improving the system spectral efficiency. This paper introduces a new downlink data structure that is free from demodulation reference signals (DM-RS), and hence does not require any channel estimation at the receiver. The new proposed data transmission structure involves a simple repetition step of part of the user data across the different sub-bands. Exploiting the repetition structure at the user side, it is shown that reliable recovery is possible via canonical correlation analysis. This paper also propo…
Incorporating deep learning (DL) into multiple-input multiple-output (MIMO) detection has been deemed as a promising technique for future wireless communications. However, most DL-based detection algorithms are lack of theoretical interpretation on internal mechanisms and could not provide general guidance on network design. In this paper, we analyze the performance of DL-based MIMO detection to better understand its strengths and weaknesses. We investigate two different architectures: a data-driven DL detector with a neural network activated by rectifier linear unit (ReLU) function and a mode…
This paper proposes an unsupervised learning-based precoding framework that trains deep neural networks (DNNs) with no target labels by unfolding an interior point method (IPM) proximal `log' barrier function. The proximal `log' barrier function is derived from the strict power minimization formulation subject to signal-to-interference-plus-noise ratio (SINR) constraint. The proposed scheme exploits the known interference via symbol-level precoding (SLP) to minimize the transmit power and is named strict Symbol-Level-Precoding deep network (SLP-SDNet). The results show that SLP-SDNet outperfor…
In order to achieve reliable communication with a high data rate of massive multiple-input multiple-output (MIMO) systems in frequency division duplex (FDD) mode, the estimated channel state information (CSI) at the receiver needs to be fed back to the transmitter. However, the feedback overhead becomes exorbitant with the increasing number of antennas. In this paper, a two stages low rank (TSLR) CSI feedback scheme for millimeter wave (mmWave) massive MIMO systems is proposed to reduce the feedback overhead based on model-driven deep learning. Besides, we design a deep iterative neural networ…
Spatial wideband effects are known to affect channel estimation and localization performance in millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems. Based on perturbation analysis, we show that the spatial wideband effect is in fact more pronounced than previously thought and significantly degrades performance, even at moderate bandwidths, if it is not properly considered in the algorithm design. We propose a novel channel estimation method based on multidimensional ESPRIT per subcarrier, combined with unsupervised learning for pairing across subcarriers, which shows…
In this paper we consider maximum-likelihood (ML) MIMO detection under one-bit quantized observations and binary symbol constellations. This problem is motivated by the recent interest in adopting coarse quantization in massive MIMO systems--as an effective way to scale down the hardware complexity and energy consumption. Classical MIMO detection techniques consider unquantized observations, and many of them are not applicable to the one-bit MIMO case. We develop a new non-convex optimization algorithm for the one-bit ML MIMO detection problem, using a strategy called homotopy optimization. Th…
Non-negative matrix factorization (NMF) is a fundamental matrix decomposition technique that is used primarily for dimensionality reduction and is increasing in popularity in the biological domain. Although finding a unique NMF is generally not possible, there are various iterative algorithms for NMF optimization that converge to locally optimal solutions. Such techniques can also serve as a starting point for deep learning methods that unroll the algorithmic iterations into layers of a deep network. Here we develop unfolded deep networks for NMF and several regularized variants in both a supe…
We develop a two-stage deep learning pipeline architecture to estimate the uplink massive MIMO channel with one-bit ADCs. This deep learning pipeline is composed of two separate generative deep learning models. The first one is a supervised learning model and designed to compensate for the quantization loss. The second one is an unsupervised learning model and optimized for denoising. Our results show that the proposed deep learning-based channel estimator can significantly outperform other state-of-the-art channel estimators for one-bit quantized massive MIMO systems. In particular, our desig…
Ruhr University Bochum（波鸿鲁尔大学）；Technical University Berlin（柏林工业大学）；Technical University of Munich（慕尼黑工业大学）
We address the detection of material defects, which are inside a layered material structure using compressive sensing based multiple-input and multiple-output (MIMO) wireless radar. Here, the strong clutter due to the reflection of the layered structure's surface often makes the detection of the defects challenging. Thus, sophisticated signal separation methods are required for improved defect detection. In many scenarios, the number of defects that we are interested in is limited and the signaling response of the layered structure can be modeled as a low-rank structure. Therefore, we propose …
Iterative detection and decoding (IDD) is known to achieve near-capacity performance in multi-antenna wireless systems. We propose deep-unfolded interleaved detection and decoding (DUIDD), a new paradigm that reduces the complexity of IDD while achieving even lower error rates. DUIDD interleaves the inner stages of the data detector and channel decoder, which expedites convergence and reduces complexity. Furthermore, DUIDD applies deep unfolding to automatically optimize algorithmic hyperparameters, soft-information exchange, message damping, and state forwarding. We demonstrate the efficacy o…
For massive multiple-input multiple-output (MIMO) systems operating in frequency-division duplex mode, downlink channel state information (CSI) acquisition will incur large overhead. This overhead is substantially reduced when sparse channel estimation techniques are employed, owing to the channel sparsity in the angular domain. When a sparse channel estimation method is implemented, the measurement matrix, which is related to the pilot matrix, is essential to the channel estimation performance. Existing sparse channel estimation schemes widely adopt random measurement matrices, which have bee…
Centre for Wireless Communications, University of Oulu（奥卢大学无线通信中心）
A deep learning (DL)-based power control algorithm that solves the max-min user fairness problem in a cell-free massive multiple-input multiple-output (MIMO) system is proposed. Max-min rate optimization problem in a cell-free massive MIMO uplink setup is formulated, where user power allocations are optimized in order to maximize the minimum user rate. Instead of modeling the problem using mathematical optimization theory, and solving it with iterative algorithms, our proposed solution approach is using DL. Specifically, we model a deep neural network (DNN) and train it in an unsupervised mann…
Dalian Maritime University（大连海事大学）；Dalian Neusoft University of Information（大连东软信息学院）
In this paper, we consider an intelligent reflecting surface (IRS)-aided cell-free massive multiple-input multiple-output system, where the beamforming at access points and the phase shifts at IRSs are jointly optimized to maximize energy efficiency (EE). To solve EE maximization problem, we propose an iterative optimization algorithm by using quadratic transform and Lagrangian dual transform to find the optimum beamforming and phase shifts. However, the proposed algorithm suffers from high computational complexity, which hinders its application in some practical scenarios. Responding to this,…
