Statistical CSI-Based Distributed Precoding Design for OFDM-Cooperative Multi-Satellite Systems
National Mobile Communications Research Laboratory, Southeast University（东南大学国家移动通信重点实验室）；Purple Mountain Laboratories（紫金山实验室）；University of Luxembourg（卢森堡大学）；Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg（卢森堡大学安全、可靠与信任跨学科中心）；Shanghai Satellite Network Research Institute Co., Ltd.（上海卫星网络研究院有限公司）；Shanghai Key Laboratory of Satellite Network（上海市卫星网络重点实验室）；State Key Laboratory of Satellite Network（卫星网络国家重点实验室）
Yafei Wang, Vu Nguyen Ha, Konstantinos Ntontin, Hong Yan, Wenjin Wang, Symeon Chatzinotas, Björn Ottersten
发表信息：
IEEE Journal on Selected Areas in Communications, Early Access, 05 Jan. 2026
This paper investigates the design of distributed precoding for multi-satellite massive MIMO transmissions. We first conduct a detailed analysis of the transceiver model, in which delay and Doppler precompensation is introduced to ensure coherent transmission. In this analysis, we examine the impact of precompensation errors on the transmission model, emphasize the near-independence of inter-satellite interference, and ultimately derive the received signal model. Based on such signal model, we formulate an approximate expected rate maximization problem that considers both statistical channel state information (sCSI) and compensation errors. Unlike conventional approaches that recast such problems as weighted minimum mean square error (WMMSE) minimization, we demonstrate that this transformation fails to maintain equivalence in the considered scenario. To address this, we introduce an equivalent covariance decomposition-based WMMSE (CDWMMSE) formulation derived based on channel covariance matrix decomposition. Taking advantage of the channel characteristics, we develop a low-complexity decomposition method and propose an optimization algorithm. To further reduce computational complexity, we introduce a model-driven scalable deep learning (DL) approach that leverages the equivariance of the mapping from sCSI to the unknown variables in the optimal closed-form solution, enhancing performance through novel dense Transformer network and scaling-invariant loss function design. Simulation results validate the effectiveness and robustness of the proposed method in some practical scenarios. We also demonstrate that the DL approach can adapt to dynamic settings with varying numbers of users and satellites.
Unique Word Orthogonal Frequency Division multiplexing (UW-OFDM) is a variant of the multicarrier technique that has shown better bit error performance compared to cyclic prefixed (CP-)OFDM. Like other multicarrier techniques, UW-OFDM suffers from the high peak-to-average-power ratio (PAPR) problem, which is an obstacle ahead of practical implementation of UW-OFDM. In this paper, the generator matrix, which is inherent to UW-OFDM, is not only used to create the specific UW-OFDM system, but also to reduce the PAPR. To do so, a suitable optimization problem is developed, and solved using the Pro…
Cell densification is a key driver to increase area spectral efficiencies in multi-antenna cellular systems. As increasing the densities of base stations (BSs) and users that share the same spectrum, however, both inter-user-interference (IUI) and inter-cell interference (ICI) problems give rise to a significant loss in spectral efficiencies in such systems. To resolve this problem under the constraint of local channel state information per BS, in this paper, we present a novel noncooperative multi-user multiple-input multiple-output (MIMO) precoding technique, called signal-to-interference-pu…
Time reversal (TR) recently emerged as an interesting communication technology capable of providing a good spatio-temporal signal focusing effect. New generations of large-bandwidth devices with reduced cost leverage the use of TR wideband communication systems. While TR is usually implemented in the time domain, the same benefit can be obtained in an orthogonal frequency division multiplexing (OFDM) system by precoding the information in the frequency domain. Besides using multiple antennas, the focusing effect of TR also comes from the use of a high rate back-off factor (BOF), which is the s…
Massive MIMO requires a large number of antennas and the same amount of power amplifiers (PAs), one per antenna. As opposed to 4G base stations, which could afford highly linear PAs, next-generation base stations will need to use inexpensive PAs, which have a limited region of linear amplification. One of the research challenges is effectively handling signals which have high peak-to-average power ratios (PAPRs), such as orthogonal frequency division multiplexing (OFDM). This paper introduces a PAPR-aware precoding scheme that exploits the excessive spatial degrees-of-freedom of large scale mu…
Spectral precoding is a promising technique to suppress out-of-band emissions and comply with leakage constraints over adjacent frequency channels and with mask requirements on the unwanted emissions. However, spectral precoding may distort the original data vector, which is formally expressed as the error vector magnitude (EVM) between the precoded and original data vectors. Notably, EVM has a deleterious impact on the performance of multiple-input multiple-output orthogonal frequency division multiplexing-based systems. In this paper we propose a novel spectral precoding approach which const…
This work considers the precoding problem in massive multiuser multiple-input multiple-output (MU-MIMO) systems equipped with low-resolution digital-to-analog converters (DACs). In previous literature on this topic, it is commonly assumed that the channel state information (CSI) is perfectly known. However, in practical applications the CSI is inevitably contaminated by noise. In this paper, we propose, for the first time, an eigen-inference (EI) precoding scheme to improve the error performance of the coarsely quantized massive MU-MIMO systems under imperfect CSI, which is mathematically mode…
This paper proposes a new large-scale mask-compliant spectral precoder (LS-MSP) for orthogonal frequency division multiplexing systems. In this paper, we first consider a previously proposed mask-compliant spectral precoding scheme that utilizes a generic convex optimization solver which suffers from high computational complexity, notably in large-scale systems. To mitigate the complexity of computing the LS-MSP, we propose a divide-and-conquer approach that breaks the original problem into smaller rank 1 quadratic-constraint problems and each small problem yields closed-form solution. Based o…
Hybrid precoding plays a key role in realizing massive multiple-input multiple-output (MIMO) transmitters with controllable cost. MIMO precoders are required to frequently adapt based on the variations in the channel conditions. In hybrid MIMO, here precoding is comprised of digital and analog beamforming, such an adaptation involves lengthy optimization and depends on accurate channel state information (CSI). This affects the spectral efficiency when the channel varies rapidly and when operating with noisy CSI. In this work we employ deep learning techniques to learn how to rapidly and robust…
In this paper we first derived the mathematical expression for lower bound spectral efficiency (SE) calculation for zero-force (ZF), and minimum mean square error (MMSE). Secondly, we calculated the simulation SE with three algorithms for ZF and MMSE precoding. We compared the simulation and theoretical results and found that the theoretical results are 1 to 1.5 bits less than the simulation values which implied that the theoretical lower bounds are actually the lower bounds. To achieve the maximum spectral efficiency in downlink massive MIMO systems we assumed perfect CSI, ZF and MMSE precodi…
Most of the non-linear transceivers, which are based on Tomlinson Harashima (TH) precoding and have been proposed in the literature for two-way relay networks, assume perfect channel state information (CSI). In this paper, we propose a novel and robust TH precoding scheme for two-way relay networks with multiple antennas at the transceiver and the relay nodes. We assume imperfect CSI and that the channel uncertainty is bounded by a spherical region. Furthermore, we consider the sum of the mean square error as the objective function, under a limited power constraint for transceiver and relay no…
Digital Twin Enabled Site Specific Channel Precoding: Over the Air CIR Inference
Department of EECS, Howard University（霍华德大学电子工程与计算机科学系）；Department of Electrical and Computer Engineering, Université Laval（拉瓦尔大学电子与计算机工程系）；DeepSig Inc.（DeepSig公司）
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 …
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…
Classical antenna selection schemes require instantaneous channel state information (CSI). This leads to high signaling overhead in the system. This work proposes a novel joint receive antenna selection and precoding scheme for multiuser multiple-input multiple-output uplink transmission that relies only on the long-term statistics of the CSI. The proposed scheme designs the switching network and the uplink precoders, such that the expected throughput of the system in the long term is maximized. Invoking results from the random matrix theory, we derive a closed-form expression for the expected…
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 …
This paper analyzes the bit error rate (BER) of multicarrier index keying - orthogonal frequency division multiplexing (MCIK-OFDM) with selection combining (SC) diversity reception. Particularly, we propose a generalized framework to derive the BER for both the low-complexity greedy detector (GD) and maximum likelihood (ML) detector. Based on this, closedform expressions for the BERs of MCIK-OFDM with the SC using either the ML or the GD are derived in presence of the channel state information (CSI) imperfection. The asymptotic analysis is presented to gain helpful insights into effects of dif…
We address physical layer security in distributed antenna (DA) systems, where eavesdroppers (Eves) can intercept the information transmitted for the intended receiver (IR). To realize a user-centric, power-efficient and physical layer security-addressing system, we aim at minimizing total power consumption by jointly designing DA selection and secure precoding. Different from the conventional artificial noise (AN)-aided secure transmission, where AN is treated as an undesired element for the IR, we design AN such that it is constructive to the IR while keeping destructive to the Eves. Importan…
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…
In this paper, we address robust design of symbol-level precoding for the downlink of multiuser multiple-input multiple-output wireless channels, in the presence of imperfect channel state information (CSI) at the transmitter. In particular, we consider two common uncertainty models for the CSI imperfection, namely, spherical (bounded) and stochastic (Gaussian). Our design objective is to minimize the total (per-symbol) transmission power subject to constructive interference (CI) constraints as well as users' quality-of-service requirements in terms of signal-to-interference-plus-noise ratio. …
We consider a scalable user-centric wireless network with dynamic cluster formation as defined by Björnsson and Sanguinetti. After having shown the importance of dominant channel subspace information for uplink (UL) pilot decontamination and having examined different UL combining schemes in our previous work, here we investigate precoding strategies for the downlink (DL). Distributed scalable DL precoding and power allocation methods are evaluated for different antenna distributions, user densities and UL pilot dimensions. We compare distributed power allocation methods to a scheme based on a …
In this letter, we consider linear precoding for downlink massive multi-user (MU) multiple-input multiple-output (MIMO) systems. We propose the novel successively-regularized zero forcing (SRZF) precoding, which exploits successive null spaces of the MIMO channels of the users, along with regularization, to control the inter-user interference (IUI) and to enhance performance and robustness to imperfect channel state information (CSI) at the base station (BS). We study the IUI characteristics of the proposed SRZF precoding for perfect and imperfect CSI at the BS. Furthermore, via computer simul…
Robust Multi-Stream Massive MIMO Satellite Systems Based on Statistical CSI
Hangzhou Institute of Technology, Xidian University（西安电子科技大学杭州研究院）；Department of Mathematics and Algorithms Research, Nokia Bell Labs（诺基亚贝尔实验室数学与算法研究部）；School of Information Science and Electronic Engineering, Shanghai Jiao Tong University（上海交通大学信息科学与工程学院）
In this paper, we adopt a multiobjective optimization approach to jointly optimize the rate and power in OFDM-based cognitive radio (CR) systems. We propose a novel algorithm that jointly maximizes the OFDM-based CR system throughput and minimizes its transmit power, while guaranteeing a target bit error rate per subcarrier and a total transmit power threshold for the secondary user (SU), and restricting both co-channel and adjacent channel interferences to existing primary users (PUs) in a statistical manner. Since the interference constraints are met statistically, the SU transmitter does no…
ReFLEX: Length-Generalizable CSI Denoising for MIMO-OFDM via Relative-Frequency Bias
Moscow Institute of Physics and Technology (State University)（莫斯科物理技术学院（国家大学））；Yangtze Delta Region Academy（长江三角洲地区研究院）；Beijing Institute of Technology（北京理工大学）；School of Interdisciplinary Science（交叉科学学院）
Beamforming and precoding/combining are techniques aimed at processing multiantenna signals at the transmitter and/or at the receiver of a wireless communication system. While they have been routinely used to improve performance in current and previous generations of mobile communications systems, they are expected to play a more fundamental role in 5th Generation (5G) New Radio (NR) cellular systems, whose functionalities have been defined in the first phase of 3GPP 5G standardization process. Besides operating in traditional cellular sub-6 GHz frequency band, 5G NR has been natively designed…
