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 block of symbol slots within a channel coherence interval, 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.
In this paper, we study closed-form interference-exploitation precoding for multi-level modulations in the downlink of multi-user multiple-input single-output (MU-MISO) systems. We consider two distinct cases: first, for the case where the number of served users is not larger than the number of transmit antennas at the base station (BS), we mathematically derive the optimal precoding structure based on the Karush-Kuhn-Tucker (KKT) conditions. By formulating the dual problem, the precoding problem for multi-level modulations is transformed into a pre-scaling operation using quadratic programmin…
Interference is traditionally viewed as a performance limiting factor in wireless communication systems, which is to be minimized or mitigated. Nevertheless, a recent line of work has shown that by manipulating the interfering signals such that they add up constructively at the receiver side, known interference can be made beneficial and further improve the system performance in a variety of wireless scenarios, achieved by symbol-level precoding (SLP). This paper aims to provide a tutorial on interference exploitation techniques from the perspective of precoding design in a multi-antenna wirel…
We study the multi-user massive multiple-input-single-output (MISO) and focus on the downlink systems where the base station (BS) employs hybrid analog-digital precoding with low-cost 1-bit digital-to-analog converters (DACs). In this paper, we propose a hybrid downlink transmission scheme where the analog precoder is formed based on the SVD decomposition. In the digital domain, instead of designing a linear transmit precoding matrix, we directly design the transmit signals by exploiting the concept of constructive interference. The optimization problem is then formulated based on the geometry…
In this paper, we focus on 1-bit precoding for large-scale antenna systems in the downlink based on the concept of constructive interference (CI). By formulating the optimization problem that aims to maximize the CI effect subject to the 1-bit constraint on the transmit signals, we mathematically prove that, when relaxing the 1-bit constraint, the majority of the obtained transmit signals already satisfy the 1-bit constraint. Based on this important observation, we propose a 1-bit precoding method via a partial branch-and-bound (P-BB) approach, where the BB procedure is only performed for the …
Symbol-level precoding (SLP) based on the concept of constructive interference (CI) is shown to be superior to traditional block-level precoding (BLP), however at the cost of a symbol-by-symbol optimization during the precoding design. In this paper, we propose a CI-based block-level precoding (CI-BLP) scheme for the downlink transmission of a multi-user multiple-input single-output (MU-MISO) communication system, where we design a constant precoding matrix to a block of symbol slots to exploit CI for each symbol slot simultaneously. A single optimization problem is formulated to maximize the …
In this paper, we focus on 1-bit precoding approaches for downlink massive multiple-input multiple-output (MIMO) systems, where we exploit the concept of constructive interference (CI). For both PSK and QAM signaling, we firstly formulate the optimization problem that maximizes the CI effect subject to the requirement of the 1-bit transmit signals. We then mathematically prove that, when employing the CI formulation and relaxing the 1-bit constraint, the majority of the transmit signals already satisfy the 1-bit formulation. Building upon this important observation, we propose a 1-bit precodin…
In this paper, we focus on the physical layer security for a K-user multiple-input-single-output (MISO) wiretap channel in the presence of a malicious eavesdropper, where we propose several interference exploitation (IE) precoding schemes for different types of the eavesdropper. Specifically, in the case where a common eavesdropper decodes the signal directly and Eve's full channel state information (CSI) is available at the transmitter, we show that the required transmit power can be further reduced by re-designing the `destructive region' of the constellations for symbol-level precoding and …
We propose an optimal low-resolution precoding technique that minimizes the symbol error probability of the users. Unlike existing approaches that rely on QPSK modulation, for the derivation of the minimum symbol error probability objective function the current approach allows for any PSK modulation order. Moreover, the proposed method solves the corresponding discrete optimization problem optimally via a sophisticated branch-and-bound method. Moreover, we propose different approaches based on the greedy search method to compute practical solutions. Numerical simulations confirm the superiorit…
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.
The recently emerged symbol-level precoding (SLP) technique has been regarded as a promising solution in multi-user wireless communication systems, since it can convert harmful multi-user interference (MUI) into beneficial signals for enhancing system performance. However, the tremendous computational complexity of conventional symbol-level precoding designs severely hinders the practical implementations. In order to tackle this difficulty, we propose a novel deep learning (DL) based approach to efficiently design the symbol-level precoders. Particularly, in this correspondence, we consider a …
Symbol-level precoding (SLP) has recently emerged as a new paradigm for physical-layer transmit precoding in multiuser multi-input-multi-output (MIMO) channels. It exploits the underlying symbol constellation structure, which the conventional paradigm of linear precoding does not, to enhance symbol-level performance such as symbol error probability (SEP). It also allows the precoder to take a more general form than linear precoding. This paper aims to better understand the relationships between SLP and linear precoding, subsequent design implications, and further connections beyond the existin…
Recently, the use of intelligent reflecting surface (IRS) has gained considerable attention in wireless communications. By intelligently adjusting the passive reflection angle, IRS is able to assist the base station (BS) to extend the coverage and improve spectral efficiency. This paper considers a joint symbol-level precoding (SLP) and IRS reflecting design to minimize the symbol-error probability (SEP) of the intended users in an IRS-aided multiuser MISO downlink. We formulate the SEP minimization problems to pursue uniformly good performance for all users for both QAM and PSK constellations…
Rate-Splitting (RS) has been proposed recently to enhance the performance of multi-user multiple-input multiple-output (MU-MIMO) systems. In RS, a user message is split into a common and a private part, where the common part is decoded by all users, while the private part is decoded only by the intended user. In this paper, we study RS under a phase-shift keying (PSK) input alphabet for multi-user multi-antenna system and propose a constructive interference (CI) exploitation approach to further enhance the sum-rate achieved by RS under PSK signaling. To that end, new analytical expressions for…
This paper considers symbol-level precoding (SLP) for multiuser multiple-input single-output (MISO) downlink. SLP is a nonlinear precoding scheme that utilizes symbol constellation structures. It has been shown that SLP can outperform the popular linear beamforming scheme. In this work we reveal a hidden connection between SLP and linear beamforming. We show that under an energy minimization design, SLP is equivalent to a zero-forcing (ZF) beamforming scheme with perturbations on symbols. This identity gives new insights and they are discussed in the paper. As a side contribution, this work al…
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 propose an interference exploitation symbol-level precoding (SLP) method for multi-level modulations via an in-block power allocation scheme to greatly reduce the signaling overhead. Existing SLP approaches require the symbol-level broadcast of the rescaling factor to the users for correct demodulation, which hinders the practical implementation of SLP. The proposed approach allows a block-level broadcast of the rescaling factor as done in traditional block-level precoding, greatly reducing the signaling overhead for SLP without sacrificing the performance. Our derivations fu…
Precoding has been conventionally considered as an effective means of mitigating the interference and efficiently exploiting the available in the multiantenna downlink channel, where multiple users are simultaneously served with independent information over the same channel resources. The early works in this area were focused on transmitting an individual information stream to each user by constructing weighted linear combinations of symbol blocks (codewords). However, more recent works have moved beyond this traditional view by: i) transmitting distinct data streams to groups of users and ii)…
In this paper, we propose closed-form precoding schemes with optimal performance for constructive interference (CI) exploitation in the multiuser multiple-input single-output (MU-MISO) downlink. We first consider an optimization where we maximize the distance between the constructive region and the detection thresholds. The cases of both strict and non-strict phase rotation are considered and can further be formulated as convex optimization problems. For optimization with strict phase rotation, we mathematically derive the optimal beamforming structure with Lagrangian and Karush-Kuhn-Tucker (K…
Symbol-level precoding (SLP), which converts the harmful multi-user interference (MUI) into beneficial signals, can significantly improve symbol-error-rate (SER) performance in multi-user communication systems. While enjoying symbolic gain, however, the complicated non-linear symbol-by-symbol precoder design suffers high computational complexity exponential with the number of users, which is unaffordable in realistic systems. In this paper, we propose a novel low-complexity grouped SLP (G-SLP) approach and develop efficient design algorithms for typical max-min fairness and power minimization …
This paper proposes symbol level precoding in the downlink of a MISO cognitive system. The new scheme tries to jointly utilize the data and channel information to design a precoding that minimizes the transmit power at a cognitive base station (CBS); without violating the interference temperature constraint imposed by the primary system. In this framework, the data information is handled at symbol level which enables the characterization the intra-user interference among the cognitive users as an additional source of useful energy that should be exploited. A relation between the constructive m…
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 …
Based on the concept of constructive interference (CI), multiuser interference (MUI) has recently been shown to be beneficial for communication secrecy. A few CI-based secure precoding algorithms have been proposed that use both the channel state information (CSI) and knowledge of the instantaneous transmit symbols. In this paper, we examine the CI-based secure precoding problem with a focus on smart eavesdroppers that exploit statistical information gleaned from the precoded data for symbol detection. Moreover, the impact of correlation between the main and eavesdropper channels is taken into…
This paper investigates the idea of exploiting interference among the simultaneous multiuser transmissions in the downlink of multiple antennas 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). In this direction, the interference among the data streams is transformed under certain conditions to useful signal that can improve the signal to interference noise ratio (SINR) of the downlink transmissions. In this context, new constructive interferen…
In this letter, we study the optimal solution of the multiuser symbol-level precoding (SLP) for minimization of the total transmit power under given signal-to-interference-plus-noise ratio (SINR) constraints. Adopting the distance preserving constructive interference regions (DPCIR), we first derive a simplified reformulation of the problem. Then, we analyze the structure of the optimal solution using the Karush-Kuhn-Tucker (KKT) optimality conditions, thereby we obtain the necessary and sufficient condition under which the power minimizer SLP is equivalent to the conventional zero-forcing bea…
The constructive interference concept in the downlink of multiple-antenna systems is addressed in this paper. The concept of the joint exploitation of the channel state information (CSI) and data information (DI) is discussed. Using symbol-level precoding, the interference between data streams is transformed Under certain conditions into useful signal that can improve the signal to interference noise ratio (SINR) of the downlink transmissions. In the previous work, different constructive interference precoding techniques have been proposed for the MPSK scenario. In this context, a novel constr…
In this work, we consider secure communications in wireless multi-user (MU) multiple-input single-output (MISO) systems with channel coding in the presence of a multi-antenna eavesdropper (Eve). In this setting, we exploit machine learning (ML) tools to design soft and hard decoding schemes by using precoded pilot symbols as training data. In this context, we propose ML frameworks for decoders that allow an Eve to determine the transmitted message with high accuracy. We thereby show that MU-MISO systems are vulnerable to such eavesdropping attacks even when relatively secure transmission techn…
Symbol-level precoding is a new paradigm for multiuser downlink systems which aims at creating constructive interference among the transmitted data streams. This can be enabled by designing the precoded signal of the multiantenna transmitter on a symbol level, taking into account both channel state information and data symbols. Previous literature has studied this paradigm for MPSK modulations by addressing various performance metrics, such as power minimization and maximization of the minimum rate. In this paper, we extend this to generic multi-level modulations i.e. MQAM and APSK by establis…
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…
This work addresses the issue of interference generated by co-channel users in downlink multi-antenna multicarrier systems with frequency-packed faster-than-Nyquist (FTN) signaling. The resulting interference stems from an aggressive strategy for enhancing the throughput via frequency reuse across different users and the squeezing of signals in the time-frequency plane beyond the Nyquist limit. The error-free spectral efficiency is proved to be increasing with the frequency packing and FTN acceleration factors. The lower bound for the FTN sampling period that guarantees information losslesness…
This study proposes the construction of a transmit signal for large-scale antenna systems with cost-effective 1-bit digital-to-analog converters in the downlink. Under quadrature-amplitude-modulation constellations, it is still an open problem to overcome a severe error floor problem caused by its nature property. To this end, we first present a feasibility condition which guarantees that each user's noiseless signal is placed in the desired decision region. For robustness to additive noise, we formulate an optimization problem, we then transform the feasibility conditions to cascaded matrix f…
This paper investigates a joint beamforming design in a multiuser multiple-input single-output (MISO) communication network aided with an intelligent reflecting surface (IRS) panel. The symbol-level precoding (SLP) is adopted to enhance the system performance by exploiting the multiuser interference (MUI) with consideration of bounded channel uncertainty. The joint beamforming design is formulated into a nonconvex worst-case robust programming to minimize the transmit power subject to single-to-noise ratio (SNR) requirements. To address the challenges due to the constant modulus and the coupli…
This paper considers the problem of constant envelope (CE) precoder designs for multiuser massive MISO downlink channels. The use of CE signals allows one to employ low-cost radio frequency chains and thereby facilitates the implementation of massive MIMO. However, the subsequent CE precoder designs are usually challenging owing to the non-convex CE constraints. The existing CE precoder designs consider minimization of some measures on the distortion levels of the received symbols, and they usually aim at improving the symbol-error rate (SER) performances. In this paper we formulate a minimum …
Modern wireless channels are increasingly dense and mobile making the channel highly non-stationary. The time-varying distribution and the existence of joint interference across multiple degrees of freedom (e.g., users, antennas, frequency and symbols) in such channels render conventional precoding sub-optimal in practice, and have led to historically poor characterization of their statistics. The core of our work is the derivation of a high-order generalization of Mercer's Theorem to decompose the non-stationary channel into constituent fading sub-channels (2-D eigenfunctions) that are jointl…
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) has the potential to substantially improve the spectral efficiency, robustness and coverage of mobile networks. However, such potential is limited by hardware cost and power consumption associated with a large number of RF chains. Recently, one-bit quantization is proposed to address this issue by replacing high-resolution digital-to-analog converters (DACs) with one-bit DACs, thereby simplifying the RF chains. Despite low system cost, advanced signal processing techniques are needed to compensate for quantization distortions caused by low resoluti…
Coarsely quantized MIMO signalling methods have gained popularity in the recent developments of massive MIMO as they open up opportunities for massive MIMO implementation using cheap and power-efficient radio-frequency front-ends. This paper presents a new one-bit MIMO precoding approach using spatial Sigma-Delta ($ΣΔ$) modulation. In previous one-bit MIMO precoding research, one mainly focuses on using optimization to tackle the difficult binary signal optimization problem that arises from the precoding design. Our approach attempts a different route. Assuming angular MIMO channels, we apply …
We investigate Gaussian widely linear precoding known as improper Gaussian signaling for the cellular uplink with inter-cell interference, known as interference multiple access channel (IMAC). This transmission scheme provides extra degrees of freedom by treating the real and imaginary components of the complex Gaussian signal differently. Since current standards mainly utilize linear beamforming for waveform generation, we highlight the benefits of widely linear beamforming over multiple temporal dimensions (symbol extension in time) in the IMAC. This scheme achieves significantly higher info…
Symbol-level precoding (SLP) manipulates the transmitted signals to accurately exploit the multi-user interference (MUI) in the multi-user downlink. This enables that all the resultant interference contributes to correct detection, which is the so-called constructive interference (CI). Its performance superiority comes at the cost of solving a nonlinear optimization problem on a symbol-by-symbol basis, for which the resulting complexity becomes prohibitive in realistic wireless communication systems. In this paper, we investigate low-complexity SLP algorithms for both phase-shift keying (PSK) …
In this paper, we investigate the symbol-level precoding (SLP) design problem in the downlink of a multiuser multiple-input single-output (MISO) channel. We consider generic constellations with any arbitrary shape and size, and confine ourselves to one of the main categories of constructive interference regions (CIR), namely, distance preserving CIR (DPCIR). We provide a comprehensive study of DPCIRs and derive some properties for these regions. Using these properties, we first show that any signal in a given DPCIR has a norm greater than or equal to the norm of the corresponding constellation…
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…
$M$-ary signal transmission over AWGN channel with additive $Q$-ary interference where the sequence of i.i.d. interference symbols is known causally at the transmitter is considered. Shannon's theorem for channels with side information at the transmitter is used to formulate the capacity of the channel. It is shown that by using at most $MQ-Q+1$ out of $M^Q$ input symbols of the \emph{associated} channel, the capacity is achievable. For the special case where the Gaussian noise power is zero, a sufficient condition, which is independent of interference, is given for the capacity to be $\log_2 …
The exploitation of interference in a constructive manner has recently been proposed for the downlink of multiuser, multi-antenna transmitters. This novel linear precoding technique, herein referred to as constructive interference zero forcing (CIZF) precoding, has exhibited substantial gains over conventional approaches; the concept is to cancel, on a symbol-by-symbol basis, only the interfering users that do not add to the intended signal power. In this paper, the power allocation problem towards maximizing the performance of a CIZF system with respect to some metric (throughput or fairness)…
Wireless communication provides a wide coverage at the cost of exposing information to unintended users. As an information-theoretic paradigm, secrecy rate derives bounds for secure transmission when the channel to the eavesdropper is known. However, such bounds are shown to be restrictive in practice and may require exploitation of specialized coding schemes. In this paper, we employ the concept of directional modulation and follow a signal processing approach to enhance the security of multi-user MIMO communication systems when a multi-antenna eavesdropper is present. Enhancing the security …
The high mobility, density and multi-path evident in modern wireless systems makes the channel highly non-stationary. This causes temporal variation in the channel distribution that leads to the existence of time-varying joint interference across multiple degrees of freedom (DoF, e.g., users, antennas, frequency and symbols), which renders conventional precoding sub-optimal in practice. In this work, we derive a High-Order Generalization of Mercer's Theorem (HOGMT), which decomposes the multi-user non-stationary channel into two (dual) sets of jointly orthogonal subchannels (eigenfunctions), t…
A channel delay spread larger than the cyclic prefix (CP) creates inter-carrier/symbol interference (ISI/ICI) in orthogonal frequency-division multiplexing (OFDM). Recent interests in low-latency applications have motivated the usage of shorter OFDM symbols where one can either downscale the CP at the cost of interference, or maintain it but with larger overhead. Alternatively, this paper studies channel shortening methods exploiting the properties of large multi-antenna precoding in order to steer the transmitted signal energy toward channel paths inside an insufficient CP. It is shown that I…
In this letter, we propose a novel manifold-based algorithm to solve the constant envelope (CE) precoding problem with interference exploitation. For a given power budget, we design the precoded symbols subject to the CE constraints, such that the constructive effect of the multi-user interference (MUI) is maximized. While the objective for the original problem is non-differentiable on the complex plane, we consider the smooth approximation of its real representation, and map it onto a Riemannian manifold. By using the Riemmanian conjugate gradient (RCG) algorithm, a local minimizer can be eff…
Raptor codes are the first class of fountain codes with linear time encoding and decoding. These codes are recommended in standards such as Third Generation Partnership Project (3GPP) and digital video broadcasting. RaptorQ codes are an extension to Raptor codes, having better coding efficiency and flexibility. Standard Raptor and RaptorQ codes are systematic with equal error protection of the data. However, in many applications such as MPEG transmission, there is a need for Unequal Error Protection (UEP): namely, some data symbols require higher error correction capabilities compared to other…
In this paper, 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 squar…
For a state-dependent DMC with input alphabet $\mathcal{X}$ and state alphabet $\mathcal{S}$ where the i.i.d. state sequence is known causally at the transmitter, it is shown that by using at most $|\mathcal{X}||\mathcal{S}|-|\mathcal{S}|+1$ out of $|\mathcal{X}|^{|\mathcal{S}|}$ input symbols of the Shannon's \emph{associated} channel, the capacity is achievable. As an example of state-dependent channels with side information at the transmitter, $M$-ary signal transmission over AWGN channel with additive $Q$-ary interference where the sequence of i.i.d. interference symbols is known causally …
Conventionally, interference and noise are treated as catastrophic elements in wireless communications. However, it has been shown recently that exploiting known interference constructively can even contribute to signal detection ability at the receiving end. This paper exploits this concept to design artificial noise (AN) beamformers constructive to the intended receiver (IR) yet keeping AN disruptive to possible eavesdroppers (Eves). The scenario considered here is a multiple-input single-output (MISO) wiretap channel with multiple eavesdroppers. Both perfect and imperfect channel informatio…
The algebraic formulation for linear network coding in acyclic networks with the links having integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes, at any given time instant, is a $\mathbb{F}_{p^m}$-linear combination of the input symbols across different generations where, $\mathbb{F}_{p^m}$ denotes the field over which the network operates ($p$ is prime and $m$ is a positive integer). We use finite-field discrete fourier transform (DFT) to convert…
