In this paper, we propose a low-complexity method to approximately solve the SINR-constrained optimization problem of symbol-level precoding (SLP). First, assuming a generic modulation scheme, the precoding optimization problem is recast as a standard non-negative least squares (NNLS). Then, we improve an existing closed-form SLP (CF-SLP) scheme using the conditions for nearly perfect recovery of the optimal solution support, followed by solving a reduced system of linear equations. We show through simulation results that in comparison with the CF-SLP method, the improved approximate solution of this paper, referred to as ICF-SLP, significantly enhances the performance with a negligible increase in complexity. We also provide comparisons with a fast-converging iterative NNLS algorithm, where it is shown that the ICF-SLP method is comparable in performance to the iterative algorithm with a limited maximum number of iterations. Analytic discussions on the complexities of different methods are provided, verifying the computational efficiency of the proposed method. Our results further indicate that the ICF-SLP scheme performs quite close to the optimal SLP, particularly in the large system regime.
Constant envelope (CE) precoding design is of great interest for massive multiuser multi-input multi-output systems because it can significantly reduce hardware cost and power consumption. However, existing CE precoding algorithms are hindered by excessive computational overhead. In this letter, a novel model-driven deep learning (DL)-based network that combines DL with conjugate gradient algorithm is proposed for CE precoding. Specifically, the original iterative algorithm is unfolded and parameterized by trainable variables. With the proposed architecture, the variables can be learned effici…
In this work, we propose an iterative scheme for computing a linear precoder that takes into account the impact of hardware impairments in the multiuser multiple-input single-output downlink. We particularly focus on the case when the transmitter is equipped with nonlinear power amplifiers. Using Bussgang's theorem, we formulate a lower bound on the achievable sum rate in the presence of hardware impairments, and maximize it using projected gradient ascent. We provide numerical examples that demonstrate the efficacy of the proposed distortion-aware scheme for precoding over a millimeter-wave~c…
Considering the expensive radio frequency (RF) chain, huge training overhead and feedback burden issues in massive MIMO, in this letter, we propose a mixed-timescale per-group hybrid precoding (MPHP) scheme under an adaptive partially-connected RF precoding structure (PRPS), where the RF precoder is implemented using an adaptive connection network (ACN) and M analog phase shifters (APSs), where M is the number of antennas at the base station (BS). Exploiting the mixed-time stage channel state information (CSI) structure, the joint-design of ACN and APSs is formulated as a statistical signal-to…
The long-term average performance of the MISO downlink channel, with a large number of users compared to transmit antennas of the BS, depends on the interference management which necessitates the joint design problem of scheduling and precoding. Unlike the previous works which do not offer a truly joint design, this paper focuses on formulating a problem amenable for the joint update of scheduling and precoding. Novel optimization formulations are investigated to reveal the hidden difference of convex/ concave structure for three classical criteria (weighted sum rate, max-min SINR, and power m…
In this correspondence, we propose a space domain index modulation (IM) scheme for the downlink of multiuser multiple-input multiple-output (MU-MIMO) systems. Instead of the most common approach where spatial bits select active receiver antennas, in the presented scheme the spatial information is mapped onto the transmitter side. This allows IM to better exploit large dimensional antenna settings which are typically easier to deploy at the base station. In order to mitigate inter-user interference and allow single user detection, a precoder is adopted at the BS. Furthermore two alternative enh…
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…
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. …
Millimeter-wave and terahertz technologies have been attracting attention from the wireless research community since they can offer large underutilized bandwidths which can enable the support of ultra-high-speed connections in future wireless communication systems. While the high signal attenuation occurring at these frequencies requires the adoption of very large (or the so-called ultra-massive) antenna arrays, in order to accomplish low complexity and low power consumption, hybrid analog/digital designs must be adopted. In this paper we present a hybrid design algorithm suitable for both mmW…
Microwave Linear Analog Computers Aided Multiuser Communication: General Impedance Matching and Precoding Optimization
The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Shenzhen Future Network of Intelligence Institute（深圳未来网络智能研究院）；National University of Singapore（新加坡国立大学）
Intelligent reflecting surfaces (IRSs) have emerged as a revolutionary solution to enhance wireless communications by changing propagation environment in a cost-effective and hardware-efficient fashion. In addition, symbol-level precoding (SLP) has attracted considerable attention recently due to its advantages in converting multiuser interference (MUI) into useful signal energy. Therefore, it is of interest to investigate the employment of IRS in symbol-level precoding systems to exploit MUI in a more effective way by manipulating the multiuser channels. In this paper, we focus on joint symbo…
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 …
This study proposes a symbol-level precoding algorithm based on the minimum mean squared error design objective under a strict per antenna power constraint for PSK modulation. The proposed design is then formulated in the standard form of a second-order cone program, allowing for an optimal solution via the interior point method. Numerical results indicate that the proposed design is superior to the existing approaches in terms of bit-error-rate for the low and intermediate SNR regime.
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…
Aiming at maximizing the energy efficiency (EE) of multicast multibeam satellite communications, we consider the precoding design under the total power and quality of service (QoS) constraints. Since the original EE maximization problem is nonconvex, it is sequentially converted into a concave-convex fractional programming problem by introducing some variables and using the first-order Taylor low bound approximation. Based on the Charnes-Cooper transformation, it is further converted into a convex problem. Then an iterative algorithm is presented to design the energy efficient precoding. To fi…
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…
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…
In this paper, we address the symbol level precoding (SLP) design problem under max-min SINR criterion in the downlink of multiuser multiple-input single-output (MISO) channels. First, we show that the distance preserving constructive interference regions (DPCIR) are always polyhedral angles (shifted pointed cones) for any given constellation point with unbounded decision region. Then we prove that any signal in a given unbounded DPCIR has a norm larger than the norm of the corresponding vertex if and only if the convex hull of the constellation contains the origin. Using these properties, we …
Most recently, there has been a flurry of research activities on studying how massive MIMO precoding should be designed when the digital-to-analog conversion at the transmitter side is operated by cheap one-bit digital-to-analog converters (DACs). Such research is motivated by the desire to substantially cut down the hardware cost and power consumption of the radio-frequency chain, which is unaffordable in massive MIMO if high-resolution DACs are still used. One-bit MIMO precoding design problems are much harder to solve than their high-resolution DAC counterparts. In our previous work, we dev…
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 qu…
The practical utilization of the symbol-level precoding in MIMO systems is challenging since the implementation of the sophisticated optimization algorithms must be done with reasonable computational resources. In the real implementation of MIMO precoding systems, the processing time for each set of symbols is a crucial parameter, especially in the high-throughput mode. In this work, a symbol-level optimization algorithm with reduced complexity is devised. Performance of a symbol-level precoder is shown to improve in terms of the processing times per set of symbols.
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…
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…
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…
We consider a downlink multiuser massive MIMO system comprising multiple heterogeneous base stations with hybrid precoding architectures. To enhance the energy efficiency of the network, we propose a novel coordinated hybrid precoding technique, where the coordination between the base stations is aimed at exploiting interference as opposed to mitigating it as per conventional approaches. We formulate an optimization problem to compute the coordinated hybrid precoders that minimize the total transmit power while fulfilling the required quality of service at each user. Furthermore, we devise a l…
Conventional symbol-level precoding (SLP) designs assume fixed modulations and detection rules at the receivers for simplifying the transmit precoding optimizations, which greatly limits the flexibility of SLP and the communication quality-of-service (QoS). To overcome the performance bottleneck of these approaches, in this letter we propose an end-to-end learning based approach to jointly optimize the modulation orders, the transmit precoding and the receive detection for an SLP communication system. A neural network composed of the modulation order prediction (MOP-NN) module and the symbol-l…
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…
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…
Quantized constant envelope (QCE) precoding, a new transmission scheme that only discrete QCE transmit signals are allowed at each antenna, has gained growing research interests due to its ability of reducing the hardware cost and the energy consumption of massive multiple-input multiple-output (MIMO) systems. However, the discrete nature of QCE transmit signals greatly complicates the precoding design. In this paper, we consider the QCE precoding problem for a massive MIMO system with phase shift keying (PSK) modulation and develop an efficient approach for solving the constructive interferen…
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…
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…
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…
Low-cost passive intelligent reflecting surfaces (IRSs) have recently been envisioned as a revolutionary technology capable of reconfiguring the wireless propagation environment through carefully tuning reflection elements. This paper proposes deploying an IRS to cover the dead zone of cellular multiuser full-duplex (FD) two-way communication links while suppressing user-side self-interference (SI) and co-channel interference (CI). Based on information exchanged by the base station (BS) and all users, this approach can potentially double the spectral efficiency. To ensure network fairness, we …
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…
Symbol level precoding (SLP) has been proven to be an effective means of managing the interference in a multiuser downlink transmission and also enhancing the received signal power. This paper proposes an unsupervised learning based SLP that applies to quantized deep neural networks (DNNs). Rather than simply training a DNN in a supervised mode, our proposal unfolds a power minimization SLP formulation in an imperfect channel scenario using the interior point method (IPM) proximal `log' barrier function. We use binary and ternary quantizations to compress the DNN's weight values. The results s…
Hybrid analog-digital (A/D) transceivers designed for millimeter wave (mmWave) systems have received substantial research attention, as a benefit of their lower cost and modest energy consumption compared to their fully-digital counterparts. We further improve their performance by conceiving a Tomlinson-Harashima precoding (THP) based nonlinear joint design for the downlink of multiuser multiple-input multiple-output (MIMO) mmWave systems. Our optimization criterion is that of minimizing the mean square error (MSE) of the system under channel uncertainties subject both to realistic transmit po…
This paper proposes a memory-efficient deep neural network (DNN) framework-based symbol level precoding (SLP). We focus on a DNN with realistic finite precision weights and adopt an unsupervised deep learning (DL) based SLP model (SLP-DNet). We apply a stochastic quantization (SQ) technique to obtain its corresponding quantized version called SLP-SQDNet. The proposed scheme offers a scalable performance vs memory tradeoff, by quantizing a scale-able percentage of the DNN weights, and we explore binary and ternary quantizations. Our results show that while SLP-DNet provides near-optimal perform…
This paper considers symbol-level precoding (SLP) for multiuser multi-input single-output (MISO) downlink transmission with the aid of intelligent reflecting surface (IRS). Specifically, by assuming one-bit transmitted signals at the base station (BS), which arises from the use of low-resolution DACs in the regime of massive transmit antennas, a joint design of one-bit SLP at the BS and the phase shifts at the IRS is proposed with a goal of minimizing the worst-case symbol error probability (SEP) of the users under the PSK modulation. This joint design problem is essentially a mixed integer no…
Deep Reinforcement Learning-Based Precoding for Multi-RIS-Aided Multiuser Downlink Systems with Practical Phase Shift
Research Center for Information Technology Innovation (CITI), Academia Sinica（信息科技创新研究中心（CITI），学术院）；Institute of Communications Engineering, National Sun Yat-sen University（通讯工程研究所，国立中山大学）；Bradley Department of Electrical and Computer Engineering, Virginia Tech（电气与计算机工程系，弗吉尼亚理工大学）
In this letter, we propose a sphere bounding scheme for probabilistic robust constructive interference (CI) power minimizing precoding, to address the imperfect channel state information (CSI) caused by the channel error (CE), which satisfies the known distribution in single-cell multiuser multipleinput single-output (MISO) downlink transmission. In the proposed scheme, we transform the probabilistic quality of service (QoS) constraints into tractable sphere bounding second-order cone (SOC) constraints through taking two-step tightening, and then we model tightened CI max-min signal-to-noise r…
Intelligent reflecting surface (IRS) has emerged as a promising solution to enhance wireless information transmissions by adaptively controlling prorogation environment. Recently, the brand-new concept of utilizing IRS to implement a passive transmitter attracts researchers' attention since it potentially realizes low-complexity and hardware-efficient transmitters of multiple-input single/multiple-output (MISO/MIMO) systems. In this paper we investigate the problem of precoder design for a low-resolution IRS-based transmitter to implement multi-user MISO/MIMO wireless communications. Particula…
Bit error rate (BER) performance of impulse radio Ultra-Wideband (UWB) systems in the presence of intrasymbol interference, inter-symbol interference, multiuser interference and addictive white Gaussian noise (AWGN) is presented in this paper. By analyzing the indoor office LOS channel model defined by IEEE 802.15.4a Task Group and deducing the variance for intra-symbol interference (IASI), inter-symbol interference (ISI) and multiuser interference (MUI), the system BER expression is obtained and verified by MATLAB simulations. Through comparing the simulation results with and without intra-sy…
