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Large intelligent surfaces arise as an emerging technology and critical building block for sixth-generation (6G) wireless networks. Reconfigurable holographic surfaces (RHSs) have been attracting significant attention recently as active antenna arrays with the capability of forming narrow beams at low cost and complexity. This paper introduces the directional modulation (DM) concept for RHS, where a large number of elements are exploited to control not only the signal's power at the receiver but also its phase. Thus, a novel DM algorithm is proposed for RHS enables modulating a carrier wave to transmit information toward specific directions while broadcasting arbitrary signals toward other directions. Error vector magnitude results are reported for multiple users, where the directions of two users with respect to the RHS are varied. Mutual information result is also provided for 6 users to demonstrate the application of RHS for the physical layer security. Results are highly promising for future low-cost and secure spatially multiplexed communications. [ABSTRACT FROM AUTHOR]

For any parameter vector (r , t , ω) in ℍ : = ℝ × ℝ n × ℝ n , the representation matrix S (r , t , ω) of the Heisenberg group (ℍ , ∗) is extended to a new form S B , W , A (r , t , ω) with nonsingular matrices B , W , A which are related to the directional translation B t : f → f (⋅ − B t) , directional modulation ℳ W ω : f (x) → e i x ′ W ω and dilation A : f → | det (A) | − 1 2 f (A − 1 ⋅) if B ′ W = I n , the identity matrix of order n. In the case B ′ W ≠ I n , an intrinsic group structure under the matrix S B , W , A (r , t , ω) is investigated and a unitary operator representation is offered. [ABSTRACT FROM AUTHOR]

Abstract Large intelligent surfaces arise as an emerging technology and critical building block for sixth-generation (6G) wireless networks. Reconfigurable holographic surfaces (RHSs) have been attracting significant attention recently as active antenna arrays with the capability of forming narrow beams at low cost and complexity. This paper introduces the directional modulation (DM) concept for RHS, where a large number of elements are exploited to control not only the signal’s power at the receiver but also its phase. Thus, a novel DM algorithm is proposed for RHS enables modulating a carrier wave to transmit information toward specific directions while broadcasting arbitrary signals toward other directions. Error vector magnitude results are reported for multiple users, where the directions of two users with respect to the RHS are varied. Mutual information result is also provided for 6 users to demonstrate the application of RHS for the physical layer security. Results are highly promising for future low-cost and secure spatially multiplexed communications.

The advancement of future large‐scale wireless networks necessitates the development of cost‐effective and scalable security solutions. Specifically, physical layer (PHY) security has been put forth as a cost‐effective alternative to cryptographic mechanisms that can circumvent the need for explicit key exchange between communication devices. Herein, a space–time‐modulated digitally‐coded metamaterial (MTM) leaky wave antenna (LWA) is proposed that can enable PHY security by achieving the functionalities of directional modulation (DM) using a machine learning‐aided branch‐and‐bound (B&B) optimized coding sequence. Theoretically, it is first shown that the proposed space–time MTM antenna can achieve DM through both the spatial and spectral manipulation of the orthogonal frequency division multiplexing signal. Simulation results are then provided as proof‐of‐principle, demonstrating the applicability of the approach for achieving DM in various communication settings. Furthermore, a prototype of the proposed architecture controlled by a field‐programmable gate array is realized, which achieves DM via an optimized coding sequence carried out by the learning‐aided B&B algorithm corresponding to the states of the MTM LWA's unit cells. Experimental results confirm the theory behind the space–time‐modulated MTM LWA in achieving DM, which is observed via both the spectral harmonic patterns and bit error rate measurements. [ABSTRACT FROM AUTHOR]

Abstract For integrated sensing and communication, one important research direction is to employ various beamforming techniques to avoid interference between the two functions. In this work, based on a hybrid beamforming antenna array structure, a physical layer security technique called directional modulation (DM) is studied for multi-beam multiplexing applications. The proposed design can form a more effective directional transmission through both beamforming and DM, while multiplexing multiple user beams through a common set of analog coefficients. In this hybrid beamforming structure, only one digital-to-analog converter (DAC) is connected to each subarray, and finite-precision phase shifters are further considered. Design examples for dual-beam multiplexing with an interleaved subarray structure and a localized subarray structure, respectively, are provided, which show that the interleaved subarray structure can form narrower mainlobe and a lower sidelobe level than the localized structure and has an overall better performance.

The advancement of future large‐scale wireless networks necessitates the development of cost‐effective and scalable security solutions. Specifically, physical layer (PHY) security has been put forth as a cost‐effective alternative to cryptographic mechanisms that can circumvent the need for explicit key exchange between communication devices. Herein, a space–time‐modulated digitally‐coded metamaterial (MTM) leaky wave antenna (LWA) is proposed that can enable PHY security by achieving the functionalities of directional modulation (DM) using a machine learning‐aided branch‐and‐bound (B&B) optimized coding sequence. Theoretically, it is first shown that the proposed space–time MTM antenna can achieve DM through both the spatial and spectral manipulation of the orthogonal frequency division multiplexing signal. Simulation results are then provided as proof‐of‐principle, demonstrating the applicability of the approach for achieving DM in various communication settings. Furthermore, a prototype of the proposed architecture controlled by a field‐programmable gate array is realized, which achieves DM via an optimized coding sequence carried out by the learning‐aided B&B algorithm corresponding to the states of the MTM LWA's unit cells. Experimental results confirm the theory behind the space–time‐modulated MTM LWA in achieving DM, which is observed via both the spectral harmonic patterns and bit error rate measurements.

In Non-orthogonal multiple access, a user with a weaker channel gain is assigned more power than a user with a stronger channel. This type of power allocation allows the strong user (SU) to apply the successive interference cancellation (SIC) method that first detects the symbols of the weak user (WU) before detecting its data. The SIC method makes the WU data vulnerable to eavesdropping at the SU and so increases the detection complexity. This paper studies the physical layer security of the data against eavesdropping. The proposed scheme uses directional modulation that distorts the symbols transmitted in an undesired direction therefore the external eavesdroppers receive different symbols. It becomes complicated for an external eavesdropper to track and detect the signal of legitimate users. This scheme eliminates the WU data on the location of the SU so the strong user does not need the SIC. We analyze the impacts of various factors on security, such as the number of antennas and the secrecy rate.

For integrated sensing and communication, one important research direction is to employ various beamforming techniques to avoid interference between the two functions. In this work, based on a hybrid beamforming antenna array structure, a physical layer security technique called directional modulation (DM) is studied for multi-beam multiplexing applications. The proposed design can form a more effective directional transmission through both beamforming and DM, while multiplexing multiple user beams through a common set of analog coefficients. In this hybrid beamforming structure, only one digital-to-analog converter (DAC) is connected to each subarray, and finite-precision phase shifters are further considered. Design examples for dual-beam multiplexing with an interleaved subarray structure and a localized subarray structure, respectively, are provided, which show that the interleaved subarray structure can form narrower mainlobe and a lower sidelobe level than the localized structure and has an overall better performance. [ABSTRACT FROM AUTHOR]

In Non-orthogonal multiple access, a user with a weaker channel gain is assigned more power than a user with a stronger channel. This type of power allocation allows the strong user (SU) to apply the successive interference cancellation (SIC) method that first detects the symbols of the weak user (WU) before detecting its data. The SIC method makes the WU data vulnerable to eavesdropping at the SU and so increases the detection complexity. This paper studies the physical layer security of the data against eavesdropping. The proposed scheme uses directional modulation that distorts the symbols transmitted in an undesired direction therefore the external eavesdroppers receive different symbols. It becomes complicated for an external eavesdropper to track and detect the signal of legitimate users. This scheme eliminates the WU data on the location of the SU so the strong user does not need the SIC. We analyze the impacts of various factors on security, such as the number of antennas and the secrecy rate. [ABSTRACT FROM AUTHOR]

Novel transmission schemes, enabled by recent advances in the fields of metamaterial (MTM), leaky-wave antenna (LWA) and directional modulation (DM), are proposed for enhancing the physical layer (PHY) security. MTM-LWAs, which offer compact, integrated, and cost-effective alternatives to the classic phased-array architectures, are particularly of interest for emerging wireless communication systems including Internet-of-Things. The proposed secure schemes are devised to accomplish the functionalities of directional modulation (DM) transmitters for orthogonal frequency-division multiplexing (OFDM) and non-contiguous OFDM transmissions, while enjoying the implementation benefits of MTM-LWAs. Specifically, transmitter architectures based on the idea of time-modulated MTM-LWA have been put forth as a promising solution for PHY security for the first time. The PHY security for the proposed schemes are investigated from the point of view of both passive and active attacks where an adversary aims to decode secret information and feed spurious data to the legitimate receiver, respectively. Numerical simulations reveal that even when the adversary employs sophisticated state-of-the-art deep learning based attacks, the proposed transmission schemes are resistant to these attacks and reliably guarantee system security. [ABSTRACT FROM AUTHOR]

Intelligent reflecting surface (IRS) is a revolutionary and low-cost technology for boosting the spectrum and energy efficiencies in future wireless communication network. In order to create controllable multipath transmission in the conventional line-of-sight (LOS) wireless communication environment, an IRS-aided directional modulation (DM) network is considered. In this paper, to improve the transmission security of the system and maximize the receive power sum (Max-RPS), two alternately optimizing schemes of jointly designing receive beamforming (RBF) vectors and IRS phase shift matrix (PSM) are proposed: Max-RPS using general alternating optimization (Max-RPS-GAO) algorithm and Max-RPS using zero-forcing (Max-RPS-ZF) algorithm. Simulation results show that, compared with the no-IRSassisted scheme and no-PSM optimization scheme, the proposed IRS-assisted Max-RPS-GAO method and Max-RPS-ZF method can significantly improve the secrecy rate (SR) performance of the DM system. Moreover, compared with the Max-RPS-GAO method, the proposed Max-RPS-ZF method has a faster convergence speed and a certain lower computational complexity.

As excellent tools for aiding communication, an intelligent reflecting surface (IRS) and an unmanned aerial vehicle (UAV) can extend the coverage area, remove the blind area, and achieve a dramatic rate improvement. In this paper, we improve the secrecy rate (SR) performance of directional modulation (DM) networks using an IRS and UAV in combination. To fully explore the benefits of the IRS and UAV, two efficient methods are proposed to enhance the SR performance. The first approach computes the confidential message (CM) beamforming vector by maximizing the SR, and the signal-to-leakage-noise ratio (SLNR) method is used to optimize the IRS phase shift matrix (PSM), which is called Max-SR-SLNR. To reduce the computational complexity, the CM, artificial noise (AN) beamforming, and IRS phase shift design are independently designed in the following method. The CM beamforming vector is constructed based on the maximum ratio transmission (MRT) criteria along the channel from Alice-to-IRS, the AN beamforming vector is designed by null-space projection (NSP) on the remaining two channels, and the PSM of the IRS is directly given by the phase alignment (PA) method. This method is called the MRT-NSP-PA. The simulation results show that the SR performance of the Max-SR-SLNR method outperforms the MRT-NSP-PA method in the cases of small-scale and medium-scale IRSs, and the latter approaches the former in performance as the IRS tends to a larger scale.

In this paper, we investigate the anti-jamming problem of a directional modulation (DM) system with the aid of intelligent reflecting surface (IRS). As an efficient tool to combat malicious jamming, receive beamforming (RBF) is usually designed by using the statistical properties of the jamming received by Bob. Thus, it is very necessary to estimate the receive jamming covariance matrix (JCM) at Bob. To achieve a precise JCM estimation, three JCM estimation methods, including eigenvalue decomposition (EVD), parametric estimation method by gradient descend (PEM-GD) and parametric estimation method by alternating optimization (PEM-AO), are proposed. Here, the proposed EVD is derived according to the rank-2 constraint of JCM. The PEM-GD method fully explores the structure features of JCM and the PEM-AO is proposed to decrease the computational complexity of the former via dimensionality reduction. The simulation results show that the proposed three methods perform better than directly using sample covariance matrix. Additionally, the proposed PEM-GD and PEM-AO outperform EVD method and the clutter and disturbance covariance estimator RCML. [ABSTRACT FROM AUTHOR]

A direction-range-time dependent vortex wave directional modulation (DM) scheme based on the frequency diverse array (FDA) is proposed for secure transmission. We design the random frequency offset for the array element in a circular arc FDA, which generates the quasi-helical phase front and the irregular phase front at the specific range. In order that the time-variance phase front can maintain the helical phase characteristics at the desired range, according to the designed frequency offset function, we design a DM excitation signal with the specific time-variance phase offset for each array element. The direction-range-time dependent phase pattern is modulated into the vortex signal constellation for the desired transmission. Theoretical analyses and numerical simulations validate the effectiveness of our proposed approach with no artificial noise. [ABSTRACT FROM AUTHOR]

Recently, intelligent reflecting surfaces (IRSs) and unmanned aerial vehicles (UAVs) have been integrated into wireless communication systems to enhance the performance of air–ground transmission. To balance performance, cost, and power consumption well, a hybrid IRS and UAV-assisted directional modulation (DM) network is investigated in this paper in which the hybrid IRS consisted of passive and active reflecting elements. We aimed to maximize the achievable rate by jointly designing the beamforming and phase shift matrix (PSM) of the hybrid IRS subject to the power and unit-modulus constraints of passive IRS phase shifts. To solve the non-convex optimization problem, a high-performance scheme based on successive convex approximation and fractional programming (FP) called the maximal signal-to-noise ratio (SNR)-FP (Max-SNR-FP) is proposed. Given its high complexity, we propose a low-complexity maximal SNR-equal amplitude reflecting (EAR) (Max-SNR-EAR) scheme based on the maximal signal-to-leakage-noise ratio method, and the criteria of phase alignment and EAR. Given that the active and passive IRS phase shift matrices of both schemes are optimized separately, to investigate the effect of jointly optimizing them to improve the achievable rate, a maximal SNR majorization-minimization (MM) (Max-SNR-MM) scheme using the MM criterion to design the IRS PSM is proposed. Simulation results show that the rates harvested by the three proposed methods were slightly lower than those of the active IRS with higher power consumption, which were 35% higher than those of no IRS and random phase IRS, while passive IRS achieved only about a 17% rate gain over the latter. Moreover, compared with the Max-SNR-FP, the proposed Max-SNR-EAR and Max-SNR-MM methods caused obvious complexity degradation at the price of slight performance loss.

To reduce the signal-to-interference-plus-noise ratio (SINR) loss of analog directional modulation (DM) with finite radio frequency (RF) phase shifters (PSs), a hybrid analog and digital (HAD) DM with mixed PSs is proposed. Using the law of large numbers, the closed-form expressions of SINR performance loss (PL), secrecy rate (SR), and bit error rate (BER) are derived. In accordance with the closed-form expression of SINR loss, it is clear that the SINR PL at desired receiver (Bob) gradually decreases as the fraction $\eta$ of the low-resolution phase shifter decreases, where $\eta$ is defined as the ratio of the number of low-resolution shifters to the total number of shifters. The simulation results show that the SINR PL, SR PL, and BER gradually decrease as the number of quantization bits increases. When the fraction of low-resolution shifters is equal to 50%, 2 bits is sufficient for low-resolution shifters to achieve a SINR PL less than 0.5 dB and a negligible BER degradation. Also, when the number of quantization bits of low-resolution shifters is equal to 2, the SR PL is about 0.3 bits/s/Hz. Thus, compared with analog DM, the HAD DM structure strikes a good balance between PL and circuit cost. [ABSTRACT FROM AUTHOR]

Abstract In this paper, two regional robust secure precise wireless transmission (SPWT) schemes for multi-user unmanned aerial vehicle (UAV), (1)regional signal-to-leakage-and-noise ratio (SLNR) and artificial-noise-to-leakage-and-noise ratio (ANLNR) (R-SLNR-ANLNR) maximization and (2) point SLNR and ANLNR (P-SLNR-ANLNR) maximization, are proposed to tackle with the estimation errors of the target users’ location. In the SPWT system, the estimation error for SPWT cannot be ignored. However, the conventional robust methods in secure wireless communications optimize the beamforming vector in the desired positions only in statistical means and cannot guarantee the security for each symbol. The proposed regional robust schemes are designed for optimizing the secrecy performance in the whole error region around the estimated location. Specifically, with the known maximal estimation error, we define the target region and wiretap region. Then, we design an optimal beamforming vector and an artificial noise projection matrix, which achieve the confidential signal in the target area having the maximal power while only few signal power is conserved in the potential wiretap region. Instead of considering the statistical distributions of the estimated errors into optimization, we optimize the SLNR and ANLNR of the whole target area, which significantly decreases the complexity. Moreover, the proposed schemes can ensure that the desired users are located in the optimized region, which are more practical than the conventional methods. Simulation results show that our proposed regional robust SPWT design is capable of substantially improving the secrecy rate compared to the conventional non-robust method. The P-SLNR-ANLNR maximization-based method has the comparable secrecy performance with lower complexity than that of the R-SLNR-ANLNR maximization-based method.

Intelligent reflecting surface (IRS) is of low-cost and energy-efficiency and will be a promising technology for the future wireless communications like sixth generation. To address the problem of conventional directional modulation (DM) that Alice only transmits single confidential bit stream (CBS) to Bob with multiple antennas in a line-of-sight channel, IRS is proposed to create friendly multipaths for DM such that two CBSs can be transmitted from Alice to Bob. This will significantly enhance the secrecy rate (SR) of DM. To maximize the SR (Max-SR), a general non-convex optimization problem is formulated with the unit-modulus constraint of IRS phase-shift matrix (PSM), and the general alternating iterative (GAI) algorithm is proposed to jointly obtain the transmit beamforming vectors (TBVs) and PSM by alternately optimizing one and fixing another. To reduce its high complexity, a low-complexity iterative algorithm for Max-SR is proposed by placing the constraint of null-space (NS) on the TBVs, called NS projection (NSP). Here, each CBS is transmitted separately in the NSs of other CBS and AN channels. Simulation results show that the SRs of the proposed GAI and NSP can approximately double that of IRS-based DM with single CBS for massive IRS in the high signal-to-noise ratio region. [ABSTRACT FROM AUTHOR]

In this paper, a novel directional modulation with distributed receiver selection (DM-DRS) scheme is proposed for secure wireless communications. In DM-DRS, a particular subset of receivers is activated and part of the information bits are modulated by the index of the activation pattern, in addition to traditional digital modulation. Especially, the scrambling matrix is introduced for the sake of preventing the eavesdropping. Moreover, the performances of bit error rate (BER) in terms of the union bound for both the legitimate user and eavesdropper are respectively derived in the context of an optimal joint maximum likelihood (ML) detector, and the theoretical BER upper bounds are demonstrated to be tight by the numerical results. In the context of the discrete-input and continuous-output system, the ergodic secrecy rates of the legitimate user and the eavesdropper are obtained, the secrecy rate is also quantified. Furthermore, our numerical results exhibit that DM-DRS can achieve an increased transmission rate compared to its traditional directional modulation with cooperative receivers (DM-CR) and spatial and direction modulation (SDM) counterparts, while guaranteeing an improved BER performance. [ABSTRACT FROM AUTHOR]

An orbital angular momentum directional modulation (OAM-DM) signal is proposed for communication and guidance integration. This signal is transmitted by a uniform circular antenna array (UCA). We divide the array into odd and even antenna groups. Each group is excited by differential coded digital modulation waveform to send different signal constellations in different directions. In order to improve the performance of angle estimation, we have designed specific phase shift sequences to obtain the different OAM modes. Mode detection can eliminate multiple value ambiguity of elevation and azimuth angles. The single antenna receiver can demodulate the OAM-DM signal to communicate, detect OAM modes and estimate angles in different directions. Finally, we assess the effectiveness of the proposed approach via numerical simulation.

In this paper, the concept and recent development of exploiting frequency diverse array (FDA) and its variants for the physical-layer wireless security have been revisited and carefully examined. Following rigorous analytical derivation and illustrative simulations, the authors realize that the investigations performed in some recent works overlooked one critical issue facing the real-world applications, and system models established and used before were based on a limited assumption, i.e. that the legitimate and eavesdropping users at different ranges sample the signal waveforms at the same time instant. The limitation of this assumption results in their studies inconclusive. The authors aim to take the first step to divert research efforts and rectify the previous incomplete analyses. The authors argue that in the current technology base the FDA cannot secure a free-space wireless transmission in range domain, because the previously claimed `secure reception region' propagates in range domain as time elapses.

Directional modulation (DM) can transmit information to the desired direction or directions with known constellation mappings, but with scrambled ones in other directions. However, one problem of the design is that when desired receivers and eavesdroppers are in the same transmission direction, their beam responses cannot be distinguished, as steering vectors for these locations are the same. To solve the problem, positional modulation (PM) is introduced where a given modulation pattern can only be received at certain desired positions. In this work, the multi-path effect is exploited for positional modulation with the aid of metasurface acting as a low-cost flexible reflecting surface. Design examples are provided to show the effectiveness of the proposed design.

Robot swarms, which constitute typical multi-user systems, have played more and more important roles in many areas. In this paper, a directional modulation (DM) scheme for frequency diverse array (FDA) based on the leakage power minimization criterion is proposed, which can be used in a robot swarm system as well as other multi-user scenarios. Based on this scheme, location-dependent secure transmission can be obtained in the multi-user downlink channels under certain circumstances, where independent data streams can be sent to different legitimate users safely. Meanwhile, the difficulty for perfect eavesdropping is significantly increased compared with phased-array-based DM. We also use the block successive upper-bound minimization algorithm to optimize the frequency offsets of the array, and the algorithm can be effectively performed. This scheme utilizes the baseband model of the FDA, which is another contribution of this paper. It solves the problems brought by the time-varying nature of the FDA and reveals the distance-angle correlation of the FDA more fundamentally. Based on that, besides the proposed FDA-DM scheme, a novel multiple access technique, named as link division multiple access, is also preliminarily proposed. It allows the transmitter to distinguish multiple users in the same or proximal locations without the help of time division, frequency division, or code division. At last, numerical results are presented to verify the superiorities of LDMA and the proposed FDA-DM scheme.

Positional modulation (PM) has been introduced recently where a given modulation pattern can only be received at certain desired positions. To achieve it, the multi-path effect is exploited for positional modulation with the aid of metasurface acting as a low-cost flexible reflecting surface. In this paper, sparse antenna array based positional modulation design is proposed for the first time; to reduce the implementation complexity of the metasurface, the number of active units is also minimised for a given PM design requirement. Design examples are provided to show the effectiveness of the proposed design.

The physical layer security techniques have made great progress in the past few years. The essential idea of physical layer transmission is to maximize the randomness of undesired channels. The 4-D antenna arrays formed by introducing time as the fourth controlling degree of freedom can be used to regulate the radiated fields in space, time, and frequency domains simultaneously. Thus, 4-D antenna arrays are an effective carrier for achieving physical layer secure transmission. However, the traditional secure transmission approach based on 4-D antenna arrays always inevitably leads to high sidelobe levels (SLLs) of radiated power or less channel randomness. Aimed at this problem, a novel physical layer secure transmission approach based on 4-D antenna arrays is proposed, which combines the advantages of traditional phased arrays and 4-D arrays. The approach can be used to reduce the SLL of radiated power and improve the channel randomness by optimizing the time sequences and static amplitude weighting. Moreover, the signal distortion caused by time modulation can be compensated in the desired direction by premodulating the transmitted signals. Both the numerical and experimental results demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The frequency diverse array (FDA)-based directional modulation (DM) technology plays an important role in the physical-layer security (PLS) transmission of 5G and beyond communications. In order to meet the tremendous increase in mobile data traffic, a new memory-efficient design for the FDA-DM-based PLS transmission is urgently demanded. In this article, an analytical symmetrical multi-carrier FDA model is proposed in three dimensions, namely, range, azimuth angle, and elevation angle, differing from the conventional analytical approach with only range and azimuth angle considered. Then, a single-point (SP) artificial noise (AN) aided FDA-DM scheme is proposed, which reduces the memory consumption significantly compared with the conventional zero-forcing (ZF) and singular value decomposition (SVD) approaches. Moreover, the PLS performance of the proposed FDA-DM scheme is analyzed in fluctuating two-ray (FTR) fading channels for the first time, including the average secrecy capacity (ASC) and the secrecy outage probability (SOP). More importantly, the closed-form expressions for the lower bound on ASC and the upper bound on SOP are derived, respectively. The effectiveness of the analytical expressions is verified by numerical simulations. This work opens a way to lower the memory requirements for DM-based PLS transmission of 5G and beyond communications. [ABSTRACT FROM AUTHOR]

In this paper, we propose to use self-sustained jammers to generate artificial noise with the aim of enhancing the physical layer security of a directional modulation (DM) relay system. To this end, we specifically tackle an optimization problem of designing beamforming vectors at the source, relay, and jammers to maximize a lower bound on the average secrecy rate of the considered system. Due to that the optimization problem is non-convex and the optimization variables are coupled, and so we cannot directly solve this problem. As such, we first develop a centralized scheme to achieve the near-optimal beamforming vectors with the aid of semidefinite relaxation, successive convex approximation, and an alternating iterative algorithm. The tightness of the incurred relaxation and the convergence of the involved algorithm are proved. To reduce the overhead and complexity of the centralized scheme, we also develop two decentralized schemes with partial cooperation and without cooperation among devices to obtain suboptimal beamforming vectors. Our examination shows that the developed centralized scheme can achieve similar performance as the optimal beamforming vectors, which can only be obtained through exhaustive numerical search. Our examination also specifies the conditions under which the decentralized schemes can achieve similar or significantly worse performance relative to the centralized scheme. Furthermore, our examination demonstrates that the developed three schemes are robust to the angle estimation errors in practical DM systems.

Multi-carrier-based waveform design for directional modulation (DM) is studied, where simultaneous data transmission over multiple frequencies can be achieved, with given phase distribution at the main lobe and as random as possible over sidelobe regions for each frequency. The design can be implemented efficiently by the inverse discrete Fourier transform (IDFT) structure. However, the problem of multi-carrier design is the high peak-to-average-power ratio (PAPR) of the resultant signals, leading to non-linear distortion when signal peaks pass through saturation regions of a power amplifier. To solve the problem, the $\text {PAPR}\leq \rho ~(\rho \geq 1)$ constraint is considered in the design, and a solution called wideband beam and phase pattern formation by Newton's method (WBPFN) is proposed. The resultant beam patterns, phase patterns, and complementary cumulative distribution function (CCDF) of PAPR are presented to demonstrate the effectiveness of the proposed design.

Directional modulation (DM) as a physical layer security technique has been studied based on the traditional antenna arrays; however, in most of the designs, only one signal is transmitted at one carrier frequency. In this paper, signal polarization information is exploited, and a new DM scheme is designed, which can transmit a pair of orthogonally polarized signals to the same direction at the same frequency simultaneously, resulting in doubled channel capacity. These two signals can also be considered as one composite signal using a four-dimensional (4-D) modulation scheme across the two polarization diversity channels. Moreover, compressive sensing (CS)-based formulations for designing sparse crossed-dipole arrays in this context are proposed to exploit the degrees of freedom in the spatial domain for further improved performance, as demonstrated by various design examples.

Traditional directional modulation designs are normally based on a single phased array, with the assumption that eavesdroppers and desired users are in different directions. However, it is not always the case, as it is possible that they are in the same direction. As a result, signals received by eavesdroppers will be approximately the same as desired users. To solve the problem, a multiple antenna array model is introduced, and the principle of the design is that the eavesdropper located in the same direction as the desired user for one antenna array may not be in the same direction for another antenna array. Based on such a model, in this paper, a power minimization constraint for the design is proposed, and an artificial noise component is included, resulting in a scrambled phase response for eavesdroppers. Beam pattern, phase pattern, and bit error rate are used as metrics to show the effectiveness of the designs based on multiple fixed antenna arrays and location optimized antenna arrays, respectively.

Directional modulation (DM) as a physical layer security technique has been studied from many different aspects recently. Normally all existing designs based on antenna arrays lead to varying weight coefficients for different antennas and for different signal symbols, which poses a particular challenge for feed circuits design in analogue implementation. In this paper, to reduce the implementation complexity, a constant magnitude constraint is proposed for the first time, and the resultant non-convex constraint can be modified to a convex form so that the problem can be solved conveniently by existing convex optimisation toolboxes. Design examples are provided to show the effectiveness of the proposed design.

The radio frequency (RF) phase shifter with finite quantization bits in analog beamforming (AB) structure forms quantization error (QE) and causes a performance loss of received signal to interference plus noise ratio (SINR) at the receiver (called Bob). By using the law of large numbers in probability theory, the closed-form expression of the SINR performance loss is derived to be inversely proportional to the square of Sinc (or sin(x)/x) function. Here, a phase alignment method is applied in the directional modulation transmitter with the AB structure. Also, the secrecy rate (SR) expression is derived with the QE. From the numerical simulation results, we find that the SINR performance loss gradually decreases as the number L of quantization bits increases. This loss is less than 0.3 dB when L is larger than or equal to three. As L exceeds five, the SINR performance loss at Bob can be approximately trivial. Similarly, the SR performance loss gradually reduces as L increases. In particular, the SR performance loss is about 0.1 bits/s/Hz for L = 3 at signal-to-noise ratio of 15 dB.

In this paper, directional modulation (DM) is investigated to enhance physical layer security. Practical transmitter designs are exploited under imperfect channel state information (CSI) and hardware constraints, such as finite-resolution phase shifters (PSs) and per-antenna power budget. Tailored for the practical issues in realizing DM, a series of practical scenarios are investigated. Starting from the scenario where eavesdroppers (Eve)s’ information is completely unknown, corresponding designs are proposed to optimize legitimate users (LU)s’ receiving performance while randomizing the Eves’ received signal. When the Eves’ CSI is imperfectly known, in the second scenario, the Eves’ receiving performance is further deteriorated by imposing destructive interference to the Eves. For each scenario, three algorithms are proposed under hardware constraints and imperfect CSI, i.e., one direct-mapping algorithm suitable for high/moderate number of bits in PSs, one heuristic algorithm with improved receiving performance at the cost of complexity, and one iterative-closed-form algorithm with enhanced practicality of symbol-level based DM. Simulation demonstrates that the algorithms achieve lower symbol error rate (SER) at the LUs while significantly deteriorating the Eves’ SER, leading to an improved secrecy throughput over the benchmarks. [ABSTRACT FROM AUTHOR]

Directional modulation (DM) refers to a class of efficient techniques for enhancing the physical layer security of wireless communications. However, conventional DM approaches cannot guarantee the transmission security when eavesdroppers are located close to the legitimate user. In this paper, to mitigate this problem, a new DM scheme with cooperative receivers (DM-CR) is proposed for secrecy communications. Specifically, the legitimate user employs multiple cooperative receivers, and a predefined distortion factor set is introduced to the beamforming vector. The proposed DM-CR scheme is able to guarantee transmission security regardless of the direction or location of the eavesdroppers. Furthermore, the average bit error probability of the proposed DM-CR scheme is investigated. Both analytical and simulation results are presented to show that the proposed DM-CR scheme significantly outperforms the benchmark in terms of the bit error rate, so as to provide secure transmission toward future wireless communications.