Three‐state time‐modulated array‐enabled directional modulation for secure orthogonal frequency‐division multiplexing wireless transmission

Recent works have shown that by using time-modulated arrays (TMAs), directional modulation (DM) physical-layer secured transmitters for orthogonal frequency-division multiplexing (OFDM) wireless data transfer can be constructed. In this paper, three-state TMAs are introduced for OFDM DM systems which allow more ﬂexible manipulation of the injected orthogonal artiﬁcial noise and hence improve security. In particular, this paper presents for the ﬁrst time both static and dynamic three-state time-modulated OFDM DM systems. Simulated bit error rate (BER) spatial distributions are shown for various sys-tem conﬁgurations in order to illustrate representative examples of secrecy performance enhancement that can be achieved by the proposed transmitter arrangement.


INTRODUCTION
Directional modulation (DM) technology, originally associated with physical-layer secure wireless communications in free space, has been rapidly developing in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].Unlike the classical cryptographic method, in which the mathematical encryption and decryption are applied at higher protocol layers, in DM systems the digitally encoded information is projected into a pre-specified spatial direction while radiation in all other directions is distorted, thereby gaining fundamental information theoretical security [1,2].DM originated from the concept of near-field direct antenna modulation (NFDAM) that was first introduced in [3], wherein the genuine information and the scrambled waveforms were respectively sent along the desired and undesired directions by way of changing the nearfield electromagnetic boundary conditions hence its far-field radiation patterns at the transmission symbol rate.This DM method with pattern-reconfigurable array elements was further studied and demonstrated in [4,5].On the other hand, DM architectures constructed by reconfiguring array excitations at the radio frequency (RF) frontends were proposed in [6][7][8], with the DM essence revealed later in [2].Meanwhile, the orthogonal vector concept was first described, and then employed for DM synthesis to achieve multiple independent secure beam transmissions in [9,10].In order to achieve secure wireless communications in practical scenarios, synthesis-free DM architectures which enable the DM functionality by purposely designing the DM transmitter hardware were presented in [11][12][13][14].More recently, some other synthesis methods have been reported.A sparse linear array driven convex optimisationassisted approach was presented in [15], and a synthesis method using chaotic scrambling and artificial noise was put forward in [16].
The above-mentioned DM transmitters are confined to narrow band signal transmissions, while the first attempt for multi-carrier, more specifically orthogonal frequency-division multiplexing (OFDM), secure signal transmissions was achieved by exploiting the time-modulated array (TMA) concept [17].In TMA another dimension, time is introduced to the array design, which, in its original form, is able to obtain antenna radiation patterns with ultra-low sidelobes by way of utilising on-off RF switches to control the antenna element excitations [18].The TMA was exploited for steering beams in [19], and for generating multiple beams in [20].This multi-beam characteristic endows TMA transmitters with the ability to achieve space division multiple access [21].Specifically, as we have mentioned, in [17], the TMA enables OFDM DM transmitter to achieve physical-layer secure wireless communications.However, since there is little freedom to design the orthogonal artificial noise, it is not able to span the entire null-space of the legitimate channel.This ultimately leads to security performance reduction along some spatial directions.It is noteworthy that the excitation of each antenna element in the TMAs in the above-reported works can only be set as '1′ and '0′, namely with and without excitation, which we term as On-Off TMA.While in [22], an improved TMA concept was described which added '−1′ as an extra state, where '−1′ denotes a phase shift of π.In this paper, we term this type of TMA as three-state TMA to distinguish with the conventional two-state systems, that is, On-Off TMA.It is noted that these three-state and two-state are the description of the switch functions in TMAs, and they are not related to the DM states, namely static DM and dynamic DM [2].
In this paper, we utilise and extend the three-state TMA concept in order to simulate, for the first time, the operating characteristics of static and dynamic OFDM DM transmitters.The resulting systems exhibit promising features which are summarised as below • The positive properties of the previously reported On-Off time-modulated OFDM DM are well preserved in our scheme.In other words, the proposed OFDM DM systems here enjoy single RF-chain, inverse fast Fourier transform (IFFT) compatibility and are DM synthesis-free [17]; • Unlike earlier schemes the distribution (in spatial domain or in null-space of the legitimate channels) of the orthogonal artificial noise can be fully manipulated; • Narrower bit error rate (BER) main beam and suppressed BER sidelobes can be achieved in the static OFDM DM system variant through injecting more interference power, which can be further enhanced in the dynamic counterpart.
The paper is organised as follows.In Section 2, the three-state time-modulated OFDM DM transmitter architecture and the associated system assumptions are firstly described, followed by elaboration of its design principle.In Section 3, the BER simu- lations of the proposed OFDM DM systems are presented and compared with those in the previously reported On-Off timemodulated OFDM DM systems.Finally, Section 4 concludes the paper.

Three-state time-modulated OFDM DM transmitter architecture
The proposed architecture of the three-state time-modulated OFDM DM transmitter is illustrated using a one-dimensional (1D) N-element linear array in Figure 1.Here, a 1-to-N power splitter is used to divide the input standard OFDM signals into N identical copies.Then each signal copy goes through a corresponding phase shifter ϕ n followed by a single-pole triple-throw (SP3T) RF switch, setting its excitation as 'On', 'Off' and 'Flipping', represented as '1′, '0′ and '−1′ respectively.It is assumed that the array elements are uniformly spaced, see d in Figure 1, and d = λ 0 /2 where λ 0 is the wavelength corresponding to the lowest OFDM sub-carrier f 0 .The active element patterns of each element in the array are assumed to be isotropic and identical in our analysis.The input OFDM signal S(t) here can be written mathematically as where D k denotes the complex modulated symbol applied upon the kth sub-carrier (out of a total of K subcarriers) and f p is the sub-carrier frequency spacing.The factor 1/ √ K is included for power normalisation.It is noted that here only one single OFDM symbol transmission period is considered since the  following analysis is independent of each symbol transmitted.
The far-field radiation patterns of the proposed OFDM TMA in free space can thus be expressed as where θ is the spatial direction, θ ϵ [0, π], seen in Figure 1.ϕ n is the phase delay in the nth antenna branch used for beam steering, designed as in (3) to steer the main radiation beam along the legitimate user' direction θ 0 .Here the legitimate user refers to the user/receiver that the transmitter intends to convey the information to.In the DM system context, the legitimate user is the receiver that locates along the desired secure communication direction θ 0 .
U n (t) in (2) refers to the periodic sequence function in the time domain of the nth SP3T RF switch, see three cases in Figure 2. T p is the OFDM symbol period and f p = 1/T p .U n (t) in one period can be expressed as in (4).n ) represent the switch (On, Off) time instants for the positive and negative cycles respectively, as seen in Figure 2, and we define

Operating principle of the proposed three-state OFDM DM system
Here, the design principle of the proposed OFDM DM is first introduced, then the static and dynamic variants are described.The periodic function U n (t) can be represented by the Fourier series as In (6), C mn is the mth Fourier coefficient for the nth time sequence function, which can be expressed as ) m e (7) can be re-written as Substituting ( 1), ( 3), ( 6) and ( 9) into (2), we get n ,Δ n ,,t , )) ⋅ e j (n−1)(cos −cos  0 ) In order to secure the pre-selected direction θ 0 , the following conditions have to be met in order to guarantee the orthogonality in subcarrier domain, that is, m, and in spatial domain, that is, θ, between the artificial noise and genuine information S(t). V n , Δ n , , t ,  =  0 Considering ( 11), ( 12), a practical solution set is shown in (13).
q , when p ≠ q (13) The first condition in ( 13) is to guarantee (11) and the remaining two ensure that the condition in ( 12) is met.
When θ ≠ θ 0 the transmitted signal waveforms that fall into the xth (x = 1, 2, …, K) OFDM sub-carrier can be expressed as n , Δ n , , t ,  )] . ( The signal waveforms are distorted by the random data D k that are modulated onto all the sub-carriers, that is, k = 1, 2,…, K.These are synthesised artificial noise that is injected in all other directions.While when ( 13) is satisfied and Δ n are set to be independent of n, denoted as ∆τ (1) , ∆τ (2) , the received OFDM signals along the pre-selected θ 0 can be derived as From ( 15), it can be observed that the transmit beamforming gain is determined by N·|∆τ (1) -∆τ (2) | 2 , where '|•|' denotes the absolute value operator.
Based on the proposed three-state TMA concept, the static and dynamic OFDM DM array syntheses are now described.
• To construct static OFDM DM transmitters, both ∆τ (1) and ∆τ (2) are kept constant for each OFDM symbol.The difference between the proposed three-state time-modulated OFDM DM and the previous On-Off counterpart is now highlighted.In the On-Off time-modulated OFDM DM system, when the transmission gain for the legitimate user is defined, that is, proportionate to the duration of the 'On' state, the power of the generated artificial noise along other directions cannot be changed.Whereas in the proposed three-state time-modulated OFDM DM system, the gain for the legitimate user, seen in ( 15), is governed by '|∆τ (1) -∆τ (2) | 2′ and the power of the injected orthogonal artificial noise is determined by '(∆τ (1) ) 2 +(∆τ (2) ) 2 -|∆τ (1)  -∆τ (2) | 2 = 2∆τ (1) ∆τ (2) '.In other words, compared with the previous On-Off system, an extra degree of freedom is available to decouple the power of the genuine information projected along θ 0 and the artificial noise projected in all other directions.• Security can be further enhanced by dynamically assigning different ∆τ (1) and ∆τ (2) for each OFDM symbol, subject to keeping |∆τ (1) -∆τ (2) | as a constant.In such a fashion the distribution of the artificial noise in the spatial domain can be further randomised, resulting in, what is by definition, a dynamic OFDM DM array.• The properties of the static and dynamic three-state timemodulated OFDM DM transmitters will be discussed using the BER simulation metrics presented in Section 3.

SIMULATION RESULTS
In order to show the effect that the generated orthogonal (in the spatial domain) artificial noise has on the proposed three-state time-modulated OFDM DM transmitters, comparison examples depicting 1/ , ∆τ (2) , ρ, t, θ)| in dB, denoted as Γ m , are given in Figure 3 for various parameters that satisfy (13).In the examples in Figure 3, it is assumed that the linear transmit array has N = 7 equally spaced (λ 0 /2) elements and the desired communication direction θ 0 equals 60 • in both the proposed three-state DM systems and the On-Off time-modulated OFDM DM systems [17].It is noted that θ 0 is defined as the desired secure transmission direction, which can be selected among all spatial directions from 0 • to 180 • .Here we select θ 0 = 60 • only as an example to show the security benefit of our proposed DM system in the paper.In Figure 3, the 'proposed DM' refers to the proposed static OFDM DM system with ρ = 0. Since Γ m along directions other than θ 0 is non-zero for any integer m, the received xth sub-carrier by potential eavesdroppers is a summation of K terms with each magnitude of (1/ Here for better illustration, Γ m is depicted with m = -2, -1, 0, 1, 2 for the received third sub-carrier (x = 3) which is the vector summation of the five terms with magnitudes of (1/ For fair comparison, the determinants of achievable gain |∆τ (1) -∆τ (2) |•
To validate the efficacy of the proposed OFDM DM transmitters, the BER simulation results of the proposed static OFDM DM are depicted and compared with that in the On-Off time-modulated OFDM DM systems (see Figure 4).For comparison purposes, the BER simulation results of the non-DM systems are also shown (the gain along θ 0 is normalised to be identical).Here, it is assumed that K = 64 and each OFDM sub-carrier is binary phase shift keying (BPSK) or quadrature phase shift keying (QPSK) modulated.In all the BER simulations in this paper, we first generate a large number of modulated symbols for transmission, saying 10 + 7 , and free space transmission is assumed.Thus, the symbol streams are added with additive white Gaussian noise (AWGN) at the  receiver side, and for BER spatial distribution simulation purpose, the noise is assumed to be identical for receivers located along all directions.Here, the channel coding, for example, turbo codes [23,24], is not applied, as it will have a similar effect on the proposed three-state TMA DM systems and all other benchmark systems.Thus, it will not change the security performance comparison and the conclusion of this paper.In each BER simulation, a known preamble (or pilot sequence) is appended, which is correlated at the receiver end for synchronisation.After the synchronisation, the minimum Euclidean distance to ideal constellation symbols in the IQ space is used as demodulation criteria.This Monte Carlo simulation is used throughout in the paper for BER analysis.In Figures 4a and  4b, it can be observed that the information can be securely conveyed only along the spatial direction around 60 • , and the proposed three-state OFDM DM systems can achieve narrower BER main beam and suppressed BER sidelobes compared with the On-Off time-modulated OFDM DM systems.In contrast, the confidential information is vulnerable to interception in non-DM systems (see Figure 4c).In Figure 5, the compared BER results of On-Off TMA and three-state TMA BPSK modulated DM schemes are depicted at E b /N 0 of 15 dB.It can be observed that lower BER sidelobes can be achieved for both On-Off and three-state TMA DM schemes at level of 15 dB.Along the spatial direction around 60 • , the proposed three-state OFDM DM systems can still achieve narrower BER main beam compared with its counterparts.
In addition, the results show that the dynamic three-state time-modulated OFDM DM system is able to further narrow BER main beam and suppress sidelobes especially at high E b /N 0 (along θ 0 ) scenarios, that is, see the BER simulations in Figure 6 where E b /N 0 is increased to 50 dB.

CONCLUSION
In this paper, we propose the three-state TMA as a route to the construction of static and dynamic OFDM DM transmitters.With the advantage that by switching 'On' and 'Flipping' time period parameters the designer can flexibly decouple the power associated with genuine information being transmitted and the

FIGURE 6
Comparison of simulated BER in the proposed static and dynamic OFDM DM arrays when E b /N 0 along θ 0 of 60 • is set to be 50 dB.It is assumed that each sub-carrier is BPSK modulated and N = 7, K = 64, Δ = ∆τ (1) -∆τ (2) , ρ = 0 power of injected orthogonal artificial noise.This enables narrowing of the BER main beam and suppression of BER sidelobe levels while keeping the gain for legitimate users constant.It is noted that adding more states does not necessarily contribute to better OFDM-DM systems.Some aspects should be carefully analysed before reaching a conclusion.For example, more states usually associated with higher insertion loss, which will negatively contribute to the system performance.And more states inevitably provide the system more design flexibility but, in the meantime, they increase the design complexity.Those trade-offs are interesting topics for future research.

FIGURE 1
FIGURE 1 Proposed three-state time-modulated OFDM DM transmitter architecture.DM, directional modulation; OFDM, physical-layer secured transmitters for orthogonal frequency-division multiplexing.

FIGURE 2
FIGURE 2 Illustration of the switch function U n (t) in time domain

FIGURE 4
FIGURE 4 Comparison of simulated BER in the proposed static three-state time-modulated OFDM DM arrays, the On-Off counterpart and the non-DM arrays.E b /N 0 along θ 0 of 60 • is set to be 35 dB.Here N = 7, K = 64, ρ = 0 and G θ0 refers to the achievable gain along direction θ 0 .It is assumed that each sub-carrier is (a) BPSK, (b) QPSK and (c) BPSK and QPSK respectively modulated.BER, bit error rate; BPSK, binary phase shift keying; QPSK, quadrature phase shift keying.

FIGURE 5
FIGURE 5 Comparison of simulated BER spatial distributions in the proposed static three-state time-modulated OFDM DM arrays and the On-Off counterpart both with BPSK-modulated schemes.E b /N 0 along θ 0 of 60 • is set to 15 dB 17518636, 2022, 19, Downloaded from https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/cmu2.12485 by Queen'S University Belfast, Wiley Online Library on [25/01/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License