Deep Learning for Distributed Channel Feedback and Multiuser Precoding in FDD Massive MIMO
Foad Sohrabi, Kareem M. Attiah, Wei Yu
备注：
15 pages, 10 figures, This is the final version to be published in IEEE Transactions on Wireless Communications, The source code for this paper are available at: https://github.com/foadsohrabi/DL-DSC-FDD-Massive-MIMO
This paper shows that deep neural network (DNN) can be used for efficient and distributed channel estimation, quantization, feedback, and downlink multiuser precoding for a frequency-division duplex massive multiple-input multiple-output system in which a base station (BS) serves multiple mobile users, but with rate-limited feedback from the users to the BS. A key observation is that the multiuser channel estimation and feedback problem can be thought of as a distributed source coding problem. In contrast to the traditional approach where the channel state information (CSI) is estimated and quantized at each user independently, this paper shows that a joint design of pilots and a new DNN architecture, which maps the received pilots directly into feedback bits at the user side then maps the feedback bits from all the users directly into the precoding matrix at the BS, can significantly improve the overall performance. This paper further proposes robust design strategies with respect to channel parameters and also a generalizable DNN architecture for varying number of users and number of feedback bits. Numerical results show that the DNN-based approach with short pilot sequences and very limited feedback overhead can already approach the performance of conventional linear precoding schemes with full CSI.
When operating massive multiple-input multiple-output (MIMO) systems with uplink (UL) and downlink (DL) channels at different frequencies (frequency division duplex (FDD) operation), acquisition of channel state information (CSI) for downlink precoding is a major challenge. Since, barring transceiver impairments, both UL and DL CSI are determined by the physical environment surrounding transmitter and receiver, it stands to reason that, for a static environment, a mapping from UL CSI to DL CSI may exist. First, we propose to use various neural network (NN)-based approaches that learn this mapp…
A massive multiple-input multiple-output (MIMO) system, operating in Frequency Division Duplexing (FDD) mode of operation, suffers from prohibitively high overhead associated with downlink channel state information (CSI) acquisition and downlink precoding, due to the lack of uplink/downlink channel reciprocity. In this paper, a heuristic edge-weighted vertex-coloring based pattern division (EWVC-PD) scheme is proposed to alleviate the overhead of a two-layer precoding approach, in a practical scenario where the user clusters undergo serious angular-spreading-range (ASR) overlapping. Specifical…
We propose a method for channel training and precoding in FDD massive MIMO based on deep neural networks (DNNs), exploiting Downlink (DL) channel covariance knowledge. The DNN is optimized to maximize the DL multi-user sum-rate, by producing a pre-beamforming matrix based on user channel covariances that maps the original channel vectors to effective channels. Measurements of these effective channels are received at the users via common pilot transmission and sent back to the base station (BS) through analog feedback without further processing. The BS estimates the effective channels from rece…
In this letter, we study the performance of a downlink multiuser massive multiple-input multiple-output (MIMO) system with sub-connected structure over limited feedback channels. Tight rate approximations are theoretically analyzed for the system with pure analog precoding and hybrid precoding. The effect of quantized analog and digital precoding is characterized in the derived expressions. Furthermore, it is revealed that the pure analog precoding outperforms the hybrid precoding using maximal-ratio transmission (MRT) or zero forcing (ZF) under certain conditions, and we theoretically charact…
Massive MIMO systems can achieve high spectrum and energy efficiency in downlink (DL) based on accurate estimate of channel state information (CSI). Existing works have developed learning-based DL CSI estimation that lowers uplink feedback overhead. One often overlooked problem is the limited number of DL pilots available for CSI estimation. One proposed solution leverages temporal CSI coherence by utilizing past CSI estimates and only sending CSI-reference symbols (CSI-RS) for partial arrays to preserve CSI recovery performance. Exploiting CSI correlations, FDD channel reciprocity is helpful …
Aiming at maximizing the achievable sum-rate of wideband multiuser mmWave massive MIMO systems, the hybrid precoding is studied. Since each computation of the achievable sum-rate can be performed only after the analog precoder and digital precoder are both determined, the maximization of the achievable sum-rate has intractable computational complexity. By introducing the interference free (IF) achievable sum-rate, the design of the analog and digital precoders can be decoupled. To avoid the beam conflict and maximize the IF achievable sum-rate, a Hungarian-based codeword selection algorithm is…
Precoding design exploiting deep learning methods has been widely studied for multiuser multiple-input multiple-output (MU-MIMO) systems. However, conventional neural precoding design applies black-box-based neural networks which are less interpretable. In this paper, we propose a deep learning-based precoding method based on an interpretable design of a neural precoding network, namely iPNet. In particular, the iPNet mimics the classic minimum mean-squared error (MMSE) precoding and approximates the matrix inversion in the design of the neural network architecture. Specifically, the proposed …
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Transmitter channel state information (CSIT) is indispensable for the spectral efficiency gains offered by massive multiple-input multiple-output (MIMO) systems. In a frequency-division-duplexing (FDD) massive MIMO system, CSIT is typically acquired through downlink channel estimation and user feedback, but as the number of antennas increases, the overhead for CSI training and feedback per user grows, leading to a decrease in spectral efficiency. In this paper, we show that, using uplink pilots in FDD, the downlink sum spectral efficiency gain with perfect downlink CSIT is achievable when the …
Consider the following problem: A multi-antenna base station (BS) sends multiple symbol streams to multiple single-antenna users via precoding. However, unlike conventional multiuser precoding, the transmitted signals are subjected to binary, unit-modulus, or even discrete unit-modulus constraints. Such constraints arise in the one-bit and constant-envelope (CE) massive MIMO scenarios, wherein high-resolution digital-to-analog converters (DACs) are replaced by one-bit DACs and phase shifters, respectively, for cutting down hardware cost and energy consumption. Multiuser precoding under one-bit…
The high energy consumption of massive multi-input multi-out (MIMO) system has become a prominent problem in the millimeter wave(mm-Wave) communication scenario. The hybrid precoding technology greatly reduces the number of radio frequency(RF) chains by handing over part of the coding work to the phase shifting network, which can effectively improve energy efficiency. However, conventional hybrid precoding algorithms based on mathematical means often suffer from performance loss and high computational complexity. In this paper, a novel BP-neural-network-enabled hybrid precoding algorithm is pr…
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To enable user diversity and multiplexing gains, a fully digital precoding multiple input multiple output (MIMO) architecture is typically applied. However, a large number of radio frequency (RF) chains make the system unrealistic to low-cost communications. Therefore, a practical three-stage hybrid analogue-digital precoding architecture, occupying fewer RF chains, is proposed aiming for a non-orthogonal IoT signal in low-cost multiuser MIMO systems. The non-orthogonal waveform can flexibly save spectral resources for massive devices connections or improve data rate without consuming extra sp…
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Motivated by challenges to existing multiuser transmission methods in a low signal to noise ratio (SNR) regime, and emergence of massive numbers of low data rate ehealth and internet of things (IoT) devices, in this paper we show that it is beneficial to incorporate knowledge of modulation type into multiuser transmit precoder design. Particularly, we propose a transmit precoding (beamforming) specific to BPSK modulation, which has maximum power efficiency and capacity in poor channel conditions. To be more specific, in a multiuser scenario, an objective function is formulated based on the wei…
We propose a deep learning-based channel estimation, quantization, feedback, and precoding method for downlink multiuser multiple-input and multiple-output systems. In the proposed system, channel estimation and quantization for limited feedback are handled by a receiver deep neural network (DNN). Precoder selection is handled by a transmitter DNN. To emulate the traditional channel quantization, a binarization layer is adopted at each receiver DNN, and the binarization layer is also used to enable end-to-end learning. However, this can lead to inaccurate gradients, which can trap the receiver…
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Relay-aided transmission is envisioned as a key strategy to combat severe path loss and link blockages emerging as unique challenges in millimeter-wave (mmWave) communications. This work considers a relay-aided multiuser mmWave communications scenario aiming at maximizing the sum rate through optimal transmit and relay precoder design. We propose a novel joint precoder design strategy, which exploits weighted minimum mean-square error (WMMSE) using its equivalency to sum-rate maximization. We obtain closed form expressions of transmit and relay precoders, and propose to compute them through al…
Two-way relaying can improve spectral efficiency in two-user cooperative communications. It also has great potential in multiuser systems. A major problem of designing a multiuser two-way relay system (MU-TWRS) is transceiver or precoding design to suppress co-channel interference. This paper aims to study linear precoding designs for a cellular MU-TWRS where a multi-antenna base station (BS) conducts bi-directional communications with multiple mobile stations (MSs) via a multi-antenna relay station (RS) with amplify-and-forward relay strategy. The design goal is to optimize uplink performance…
In millimeter wave (mmWave) systems, antenna architecture limitations make it difficult to apply conventional fully digital precoding techniques but call for low cost analog radio-frequency (RF) and digital baseband hybrid precoding methods. This paper investigates joint RF-baseband hybrid precoding for the downlink of multiuser multi-antenna mmWave systems with a limited number of RF chains. Two performance measures, maximizing the spectral efficiency and the energy efficiency of the system, are considered. We propose a codebook based RF precoding design and obtain the channel state informati…
This paper studies the sum rate performance of a low complexity quantized CSI-based Tomlinson-Harashima (TH) precoding scheme for downlink multiuser MIMO tansmission, employing greedy user selection. The asymptotic distribution of the output signal to interference plus noise ratio of each selected user and the asymptotic sum rate as the number of users K grows large are derived by using extreme value theory. For fixed finite signal to noise ratios and a finite number of transmit antennas $n_T$, we prove that as K grows large, the proposed approach can achieve the optimal sum rate scaling of th…
Traditional approaches in the analysis of downlink systems decouple the precoding and the channel estimation problems. However, in cellular systems with mobile users, these two problems are in fact tightly coupled. In this paper, this coupling is explicitly studied by accounting for channel training overhead and estimation error while determining the overall system throughput. The paper studies the problem of utilizing imperfect channel estimates for efficient linear precoding and user selection. It presents precoding methods that take into account the degree of channel estimation error. Infor…
Tomlinson-Harashima precoding (THP) is considered as a prominent precoding scheme due to its capability to efficiently cancel out the known interference at the transmitter side. Therefore, the information rates achieved by THP are superior to those achieved by conventional linear precoding schemes. In this paper, a new lower bound on the achievable information rate for the regularized THP scheme under additive white Gaussian noise (AWGN) channel with multiuser interference is derived. Analytical results show that the lower bound derived in this paper is tighter than the original lower bound pa…
This paper tackles the problem of the simultaneous interference among the multiple users in the downlink of a wireless multiantenna system. In order to exploit the multiuser interference and transform it into useful power at the receiver side, symbol-level precoding is utilized through joint exploitation of the data from each individual user and the channel state information. This paper introduces a complexity reduction scheme that exploits the constellations symmetry to reduce the number of possible calculations and the number of constraints in the symbol-level optimization problem. This pape…
This study proposes a novel precoding scheme for multiuser multiple-input multiple-output (MIMO) relay systems in the presence of imperfect channel state information (CSI). The base station (BS) and the MIMO relay station (RS) are both equipped with the same codebook of unitary matrices. According to each element of the codebook, we create a latent precoding matrix pair, namely a BS precoding matrix and an RS precoding matrix. The RS precoding matrix is formed by multiplying the appropriate unitary matrix from the codebook by a power scaling factor. Based on the given CSI and a block of transm…
Low-resolution precoding techniques have gained considerable attention in the wireless communications area recently. Vital but hardly discussed in literature, discrete precoding in conjunction with channel coding is the subject of this study. Unlike prior studies, we propose three different soft detection methods and an iterative detection and decoding scheme that allow the utilization of channel coding in conjunction with low-resolution precoding. Besides an exact approach for computing the extrinsic information, we propose two approximations with reduced computational complexity. Numerical r…
In this paper, we consider a reconfigurable intelligence surface (RIS) aided uplink multiuser multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) system, where the receiver is assumed to conduct low-complexity iterative detection. We aim to minimize the total transmit power by jointly designing the precoder of the transmitter and the passive beamforming of the RIS. This problem can be tackled from the perspective of information theory. But this information-theoretic approach may involve prohibitively high complexity since the number of rate constraints that specif…
Block diagonalization (BD) based precoding techniques are well-known linear transmit strategies for multiuser MIMO (MU-MIMO) systems. By employing BD-type precoding algorithms at the transmit side, the MU-MIMO broadcast channel is decomposed into multiple independent parallel single user MIMO (SU-MIMO) channels and achieves the maximum diversity order at high data rates. The main computational complexity of BD-type precoding algorithms comes from two singular value decomposition (SVD) operations, which depend on the number of users and the dimensions of each user's channel matrix. In this work…
This paper considers the implementation of Tomlinson-Harashima (TH) precoding for multiuser MIMO systems based on quantized channel state information (CSI) at the transmitter side. Compared with the results in [1], our scheme applies to more general system setting where the number of users in the system can be less than or equal to the number of transmit antennas. We also study the achievable average sum rate of the proposed quantized CSI-based TH precoding scheme. The expressions of the upper bounds on both the average sum rate of the systems with quantized CSI and the mean loss in average su…
This paper investigates the problem of interference among the simultaneous multiuser transmissions in the downlink of multiple antennas systems. Using symbol level precoding, a new approach towards the multiuser interference is discussed along this paper. The concept of exploiting the interference between the spatial multiuser transmissions by jointly utilizing the data information (DI) and channel state information (CSI), in order to design symbol-level precoders, is proposed. In this direction, the interference among the data streams is transformed under certain conditions to useful signal t…
Massive multiple-input multiple-output (MIMO) is envisioned to offer considerable capacity improvement, but at the cost of high complexity of the hardware. In this paper, we propose a low-complexity hybrid precoding scheme to approach the performance of the traditional baseband zero-forcing (ZF) precoding (referred to as full-complexity ZF), which is considered a virtually optimal linear precoding scheme in massive MIMO systems. The proposed hybrid precoding scheme, named phased-ZF (PZF), essentially applies phase-only control at the RF domain and then performs a low-dimensional baseband ZF pr…
Lenstra-Lenstra-Lovasz (LLL) algorithm, which is one of the lattice reduction (LR) techniques, has been extensively used to obtain better basis of the channel matrix. In this paper, we jointly apply Seysen's lattice reduction algorithm (SA), instead of LLL, with the conventional linear precoding algorithms. Since SA obtains more orthogonal lattice basis compared to that obtained by LLL, lattice reduction aided (LRA) precoding based on SA algorithm outperforms the LRA precoding with LLL. Simulation results demonstrate that a gain of 0.5dB at target BER of 10^-5 is achieved when SA is used inste…
This paper considers minimum sum mean-squared error (sum-MSE) linear transceiver designs in multiuser downlink systems with imperfect channel state information. Specifically, we derive the optimal energy allocations for training and data phases for such a system. Under MMSE estimation of uncorrelated Rayleigh block fading channels with equal average powers, we prove the separability of the energy allocation and transceiver design optimization problems. A closed-form optimum energy allocation is derived and applied to existing transceiver designs. Analysis and simulation results demonstrate the…
User electromagnetic (EM) exposure is continuously being exacerbated by the evolution of multi-antenna portable devices. To mitigate the effects of EM radiation, portable devices must satisfy tight regulations on user exposure level, generally measured by specific absorption rate (SAR). To this end, we investigate the SAR-aware uplink precoder design for the energy efficiency (EE) maximization in multiuser multiple-input multiple-output transmission exploiting statistical channel state information (CSI). As the objective function of the design problem is computationally demanding in the absenc…
Massive MIMO is a promising technology in future wireless communication networks. However, it raises a lot of implementation challenges, for example, the huge pilot symbols and feedback overhead, requirement of real-time global CSI, large number of RF chains needed and high computational complexity. We consider a two-tier precoding strategy for multi-cell massive MIMO interference networks, with an outer precoder for inter-cell/inter-cluster interference cancellation, and an inner precoder for intra-cell multiplexing. In particular, to combat with the computational complexity issue of the oute…
We propose an optimal MMSE precoding technique using quantized signals with constant envelope. Unlike the existing MMSE design that relies on 1-bit resolution, the proposed approach employs uniform phase quantization and the bounding step in the branch-and-bound method is different in terms of considering the most restrictive relaxation of the nonconvex problem, which is then utilized for a suboptimal design also. Moreover, unlike prior studies, we propose three different soft detection methods and an iterative detection and decoding scheme that allow the utilization of channel coding in conju…
Millimeter wave (mmWave) is a practical solution to provide high data rate for the vehicle-to-everything (V2X) communications. This enables the future autonomous vehicles to exchange big data with the base stations (BSs) such as the velocity and the location to improve the awareness of the advanced driving assistance system (ADAS). In this context, we consider a single-cell multiuser doubly-selective system wherein the BS simultaneously serves multiple vehicles. To accomplish this requirement, the BS is implemented in hybrid architecture to support multiple spatial streams while the vehicles h…
We analytically approximate the expected sum capacity loss between the optimal downlink precoding technique of dirty paper coding (DPC), and the sub-optimal technique of zero-forcing precoding, for multiuser channels. We also consider the most general case of multi-stream transmission to multiple users, where we evaluate the expected sum capacity loss between DPC and block diagonalization precoding. Unlike previously, assuming heterogeneous Ricean fading, we utilize the well known affine approximation to predict the expected sum capacity difference between both precoder types (optimal and sub-…
A large majority of cellular networks deployed today make use of Frequency Division Duplexing (FDD) where, in contrast with Time Division Duplexing (TDD), the channel reciprocity does not hold and explicit downlink (DL) probing and uplink (UL) feedback are needed in order to achieve spatial multiplexing gain. To support massive MIMO, the overhead incurred by conventional DL probing and UL feedback schemes scales linearly with the number of BS antennas and, therefore, may be very large. In this paper, we present a new approach to achieve a very competitive trade-off between spatial multiplexing…
In this paper, we study the hybrid precoding structures over limited feedback channels for massive multiuser multiple-input multiple-output (MIMO) systems. We focus on the system performance of hybrid precoding under a more realistic hardware network model, particularly, with inevitable dissipation. The effect of quantized analog and digital precoding is characterized. We investigate the spectral efficiencies of two typical hybrid precoding structures, i.e., the sub-connected structure and the fully-connected structure. It is revealed that increasing signal power can compensate the performance…
Multiple-antenna systems is a key technique to serve multiple users in future wireless systems. For low energy consumption and hardware complexity we first consider transmit symbols with constant magnitude and then 1-bit digital-to-analog converters. We propose precoding designs which maximize the minimum distance to the decision threshold at the receiver. The precoding design with 1-bit DAC corresponds to a discrete optimization problem, which we solve exactly with a branch-and-bound strategy. We alternatively present an approximation based on relaxation. Our results show that the proposed br…
Cell-free system where a group of base stations (BSs) cooperatively serves users has received much attention as a promising technology for the future wireless systems. In order to maximize the cooperation gain in the cell-free systems, acquisition of downlink channel state information (CSI) at the BSs is crucial. While this task is relatively easy for the time division duplexing (TDD) systems due to the channel reciprocity, it is not easy for the frequency division duplexing (FDD) systems due to the CSI feedback overhead. This issue is even more pronounced in the cell-free systems since the us…
This paper proposes a novel nature-inspired $α$-fair hybrid precoding (NI-$α$HP) technique for millimeter-wave multi-user massive multiple-input multiple-output systems. Unlike the existing HP literature, we propose to apply $α$-fairness for maintaining various fairness expectations (e.g., sum-rate maximization, proportional fairness, max-min fairness, etc.). After developing the analog RF beamformer via slow time-varying angular information, the digital baseband (BB) precoder is designed via the reduced-dimensional effective channel matrix seen from the BB-stage. For the $α$-fairness, we deri…
MIMO systems are considered as most promising for wireless communications. However, with an increasing number of radio front ends the corresponding energy consumption and costs become an issue, which can be relieved by the utilization of low-resolution quantizers. In this study we propose an optimal precoding algorithm constrained to constant envelope signals and phase quantization that maximizes the minimum distance to the decision threshold at the receivers using a branch-and-bound strategy. The proposed algorithm is superior to the existing methods in terms of bit error rate. Numerical resu…
This paper addresses the problem of exploiting interference among simultaneous multiuser transmissions in the downlink of multiple-antenna systems. Using symbol-level precoding, a new approach towards addressing the multiuser interference is discussed through jointly utilizing the channel state information (CSI) and data information (DI). The interference among the data streams is transformed under certain conditions to a useful signal that can improve the signal-to-interference noise ratio (SINR) of the downlink transmissions and as a result the system's energy efficiency. In this context, ne…
We propose an algorithm to maximize the instantaneous sum data rate transmitted by a base station in the downlink of a multiuser multiple-input, multiple-output system. The transmitter and the receivers may each be equipped with multiple antennas and each user may receive more than one data stream. We show that maximizing the sum rate is closely linked to minimizing the product of mean squared errors (PMSE). The algorithm employs an uplink/downlink duality to iteratively design transmit-receive linear precoders, decoders, and power allocations that minimize the PMSE for all data streams under …
