Symbol-level Precoding Research Articles

Energy Efficiency Maximization for Downlink NOMA Designs via Symbol-Level Precoding

Energy Efficiency Maximization for Downlink NOMA Designs via Symbol-Level Precoding

Interference Exploitation in IRS-Aided Heterogeneous Networks: Joint Symbol Level Precoding and Reflecting Design

Interference Exploitation in IRS-Aided Heterogeneous Networks: Joint Symbol Level Precoding and Reflecting Design

Symbol-Level Precoding for MU-MIMO System With RIRC Receiver

Symbol-Level Precoding for MU-MIMO System With RIRC Receiver

Efficient symbol level precoding design for full-duplex integrated sensing and communication systems

Full-duplex (FD) integrated sensing and communication (ISAC) system attracts much attention because adopting the FD mode can enhance the transmission efficiency and reduce the transmission time of the ISAC system. However, the inevitable self-interference (SI) in FD mode would result in severe performance degradation. This paper considers the FD ISAC system and investigates a symbol-level precoding (SLP) design, which minimizes the Cramér-Rao Bound of target angle estimation while considering the constant-envelope power restraint, SI suppression and the quality of service requirement. Due to the non-convex fractional problem and the unit-modulus constraint, the optimization problem is reformulated by implementing the Schur complement, where the optimal waveform is obtained via the semidefinite programming algorithm. The SLP design that optimizes each symbol vector for all users may suffer high computational complexity of matrix multiplication with high numbers of users. A grouped SLP strategy in which the communication users are divided into several groups on the basis of channel correlation is proposed to reduce the complexity. The proposed grouped SLP design only suppresses group-to-group interference and converts the intra-group interference into a constructive interference, which can reduce the dimension of each precoded signal significantly, resulting in a low computational complexity. Simulation results illustrate that the proposed SLP design can effectively mitigate SI, which can improve the accuracy of target detection. Moreover, the proposed grouped-SLP design can further reduce computational complexity without dramatic performance degradation.

Robust Symbol-Level Precoding and Secondary Information Transmission in RIS-Aided Communications

Robust Symbol-Level Precoding and Secondary Information Transmission in RIS-Aided Communications

Symbol-level precoding scheme robust to channel estimation errors in wireless fading channels

Most studies on symbol-level (SL) precoding have assumed that channel estimation is perfect. However, because interference signals or additive white Gaussian noise exist in the received signal for channel estimation, channel estimation errors always exist. In this paper, we propose an SL precoding scheme that is robust to channel estimation errors. First, using the characteristics of the channel estimation errors, we derive an equation for the worst-case mean squared error (MSE) which is the maximum of the MSE. Then by designing the SL precoding to minimize the worst-case MSE, it has robust characteristics against channel estimation errors.

Hybrid Precoding Design for Wireless Fading Channels

Precoding techniques are widely used to eliminate interference between multiple user signals in a wireless fading channel environment. The linear MMSE precoding technique, one of the most widely used techniques so far, has low computational complexity but has the disadvantage of relatively poor symbol error rate (SER) performance. The symbol-level precoding (SLP) technique, on which much research has been conducted recently, has excellent SER performance but has the disadvantage of being too computationally complex. In this paper, we propose a hybrid precoding technique that simultaneously applies SLP and MMSE precoding to appropriately adjust SER performance and computational complexity performance. If two different types of precoding techniques are applied simultaneously, interference may occur between signals to which different types of precoding are applied, which can significantly deteriorate SER performance. Therefore, in this paper, precoding is designed to prevent interference between the two signals using the null space of the channel matrices. Through computer simulation, the proposed scheme showed that its SER performance was superior to that of the linear MMSE scheme, and the computational complexity was much lower than that of the SLP scheme.

Low-Complexity Hybrid Beamforming for MMSE-Based Symbol-Level Precoding in Multi-User MISO System

Low-Complexity Hybrid Beamforming for MMSE-Based Symbol-Level Precoding in Multi-User MISO System

Symbol-Level Precoding for Integrated Sensing and Communications: A Faster-Than-Nyquist Approach

Symbol-Level Precoding for Integrated Sensing and Communications: A Faster-Than-Nyquist Approach

Joint Precoding and CSI Dimensionality Reduction: An Efficient Deep Unfolding Approach

A recently proposed unified precoding and pilot design optimization (UPPiDO) framework offers a reduction in both training and feedback overhead of acquiring channel state information (CSI) and an enhancement in robustness (to CSI uncertainties) at the expense of a more computationally demanding precoding optimization. To address this increased complexity, in this paper we first propose an unfolding-friendly iterative algorithm, which can efficiently address a family of non-convex and non-smooth problems. Then, we develop an efficient approach to unfold the iterative algorithm designed. Besides being applicable to important and typical iterative optimization algorithms, a pivotal advantage of the proposed unfolding approach is that the trainable parameters are scalars (rather than matrices). This, in turn, reduces the number of training samples required and makes it suitable for rapidly fluctuating wireless environments. We apply the algorithm unfolding (AU) techniques developed to our UPPiDO-based symbol-level precoding and block-level precoding. Our complexity analysis indicates that the computational complexity is scalable both with the numbers of served users and antennas. Our simulation results demonstrate that the number of outer iterations (or layers) required is about 1/3 of that of the original iterative algorithms.

A Robust Symbol-Level Precoding Method for Multibeam Satellite Systems

Compared to interference mitigating precoding, interference exploiting symbol-level precoding (SLP) requires less transmit power to guarantee the quality of service in a multibeam satellite system. However, due to the large roundtrip time (RTT), it is impractical to obtain real-time channel state information on the satellite side. The random channel state information (CSI) phase error of outdated CSI could cause serious performance deterioration of SLP. To compensate the CSI phase error, we propose an outdated CSI-based robust SLP (RSLP) method, which optimizes the transmit power under outage probability constraints. The central limit theorem (CLT) and second-order Taylor expansion are used to relax the outage probability constraints into convex ones. In addition, because only outdated CSI-based robust block-level precoding exists, we present two comparative RSLP methods accordingly. Without violating outrage probability constraints, the proposed RSLP method requires much lower transmit power than comparative RSLP and existing robust block-level precoding methods. The complexity of the proposed RSLP method is also lower than that of two comparative RSLP methods.

Minimum Symbol Error Probability Discrete Symbol Level Precoding for MU-MIMO Systems With PSK Modulation

Minimum Symbol Error Probability Discrete Symbol Level Precoding for MU-MIMO Systems With PSK Modulation

Practical Interference Exploitation Precoding Without Symbol-by-Symbol Optimization: A Block-Level Approach

In this paper, we propose a constructive interference (CI)-based block-level precoding (CI-BLP) approach for the downlink of a multi-user multiple-input single-output (MU-MISO) communication system. Contrary to existing CI precoding approaches which have to be designed on a symbol-by-symbol level, here a constant precoding matrix is applied to a collection of symbols within a given transmission block, thus significantly reducing the computational costs over traditional CI-based symbol-level precoding (CI-SLP) as the CI-BLP optimization problem only needs to be solved once per block. For both PSK and QAM modulation, we formulate an optimization problem to maximize the minimum CI effect over the block subject to a block-rather than symbol-level power budget. We mathematically derive the optimal precoding matrix for CI-BLP as a function of the Lagrange multipliers in closed form. By formulating the dual problem, the original CI-BLP optimization problem is further shown to be equivalent to a quadratic programming (QP) optimization. Numerical results validate our derivations, and show that the proposed CI-BLP scheme achieves improved performance over the traditional CI-SLP method, thanks to the relaxed power constraint over the considered block of symbol slots.

Phase Rotation Assisted Interference Exploitation Precoding With Finite Block Length for MU-MIMO Systems

The interference exploitation precoding (IEP) leverages the harmful interference to align at the constructive interference (CI) region via symbol level precoding (SLP), which greatly improves the conventional zero forcing precoding with QPSK modulation or even higher modulations. This letter firstly develops a joint phase rotation structure, considering both the outer phase rotation for multiple layers and the inner phase alignment for IEP with finite block length in multi-user multiple-input multiple-output (MU-MIMO) systems, termed as JPR-IEP. To tackle the problem, a decoupling scheme is presented, which breaks JPR-IEP into two independent steps as DPR-IEP, thus converting the non-convex JPR-IEP to a solvable problem with low complexity. At last, a codebook-assisted DPR-IEP, namely CB-DPR-IEP with less computational complexity and feed-forward overhead is further investigated, which is approved to be the optimal choice considering the performance, the feed-forward and the complexity for practical MU-MIMO systems.

A Memory-Efficient Learning Framework for Symbol Level Precoding With Quantized NN Weights

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 trade-off, by quantizing a scalable percentage of the DNN weights, and we explore binary and ternary quantizations. Our results show that while SLP-DNet provides near-optimal performance, its quantized versions through SQ yield ~3.46× and ~2.64× model compression for binary-based and ternary-based SLP-SQDNets, respectively. We also find that our proposals offer ~20× and ~10× computational complexity reductions compared to SLP optimization-based and SLP-DNet, respectively.

End-to-End Learning for Symbol-Level Precoding and Detection With Adaptive Modulation

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-level precoding and detection (SLPD-NN) module is developed to solve this mathematically intractable problem. Simulations verify the notable performance improvement brought by the proposed end-to-end learning approach.

Multiuser-MISO Precoding Under Channel Phase Uncertainty in Satellite Communication Systems

Linear and symbol-level precoding in satellite communications have received increasing research attention thanks to their ability to tackle inter-beam interference, allowing the use of spectral resources more efficiently. However, there are still challenges and open questions regarding the implementation of practical precoding systems taking the phase uncertainties in estimating the channel state information into account. This work assesses the impact of phase variations and uncertainties inherent to the satellite communication system operating a precoded forward link. Specifically, we address the inability to measure at the user terminal, the absolute phase rotation introduced by the channel, and the transponder local oscillator phase noise effects on the precoding operations considering the use of frequency division multiplexing in the forward-uplink transmission. We formally demonstrate that the system performance for linear and non-linear precoding operations is not affected by the uncertainty in the phase measurements at the user terminal. Additionally, we show that using a single frequency reference for all the local oscillators at the transponder does not avoid the phase variations related to the frequency division multiplexing in the forward-uplink. This work demonstrates that these phase variations would not affect the system performance for an ideal zero-delay precoding loop. However, this is not feasible in practical scenarios, where the phase noise of the frequency reference at the transponder and the loop delay determine the impact on the system performance. We validate our results by simulations considering three frequency references with different stability levels in a typical geosynchronous orbit (GEO) satellite system. Our results suggest that practical implementations of multiuser-MISO precoding systems must include a differential phase synchronization loop to compensate for this performance degradation.

Weighted MMSE Precoding for Constructive Interference Region

In this letter, we propose a symbol-level precoding (SLP) design that aims to minimize the weighted mean square error between the received signal and the constellation point located in the constructive interference region (CIR). Unlike most existing SLP schemes that rely on channel state information (CSI) only, the proposed scheme exploits both CSI and the distribution information of the noise to achieve improved performance. We firstly propose a simple generic description of CIR that facilitates the subsequent SLP design. Such an objective can further be formulated as a nonnegative least squares (NNLS) problem, which can be solved efficiently by the active-set algorithm. Furthermore, the weighted minimum mean square error (WMMSE) precoding and the existing SLP can be easily verified as special cases of the proposed scheme. Finally, simulation results show that the proposed precoding outperforms the state-of-the-art SLP schemes in full signal-to-noise ratio ranges in both uncoded and coded systems without additional complexity over conventional SLP.

ADMM Based Symbol-Level Precoding for MU-MISO Downlink With Low-Resolution DACs

In this letter, we investigate the problem of symbol-level precoder design with low-resolution digital-to-analog converters (DACs) to implement wireless multiuser multiple-input single-output (MISO) downlink communications. Specifically, we aim to maximize the minimum distance between the noise-free received signal and its decision boundaries via a min-max fairness design. Due to the nondifferentiable objective and finite-alphabet constraint, the problem is NP-hard and difficult to tackle. To handle this problem, we first reduce the dimension of the variables by solving a relaxed problem. Then, the problem is transformed to a smoothed form which can be efficiently solved using the alternative direction method of multipliers (ADMM)-based framework. In addition, we propose a closed-from solution based on majorization-minimization method to provide a low-complexity near-optimal solution. We further provide the convergence and computational complexity analyses, and validate the performance by simulations.

Symbol-Level Precoding Design in IRS-Aided Secure Wireless Communication Systems

This letter investigates an intelligent reflective surface (IRS) aided secure wireless communication system, in which a multi-antenna base station (BS) transmits confidential messages to multiple users via symbol-level precoding (SLP). We consider the two cases where the eavesdropper (Eve) has no channel state information (CSI) and global CSI, respectively, to investigate the possible worst and best eavesdropping performance, and the security improvement brought by the joint SLP-IRS design. For the former, we consider the user-receive signal-to-interference-noise ratio (SINR) balancing problem under the constraints of transmission power and security, and prove that SLP is inherently safe. For the latter, we assume that a smart Eve can intercept signals using brute-force and maximum likelihood detection methods. First, its received SINR is derived under the artificial noise framework, and then a two-step design scheme for SLP and IRS is proposed. In particular, an iterative penalty method is proposed for the IRS design step. Simulation results verify the analysis and show that IRS can significantly enhance the security of system.