Directional Modulation With Artificial-Noise Injection Into Time-Modulated Arrays

We propose a novel approach to directional modulation (DM) in time-modulated arrays (TMAs) that simultaneously radiates the information signal over a sum pattern and artificial noise over a difference pattern. Unlike other DM-TMA solutions, our technique achieves high-performance DM without the need for time-consuming optimization algorithms, preserving TMA efficiency. This versatility makes it suitable for high-mobility, low-latency applications.


I. INTRODUCTION
T HE conventional way of performing directional modu- lation (DM) with time-modulated arrays (TMAs) entails the intentional aliasing of the signal transmitted at the carrier frequency (or a useful harmonic) with signals transmitted at the remaining harmonics for specific directions.Spectral aliasing only happens when the signal bandwidth (B) exceeds the time modulation frequency (f 0 ).This lack of frequency orthogonality allows for the transmission of direction-dependent signals in time-varying scenarios provided that the instrumental parameters of the TMA modulating periodic sequences (i.e., the time delay and/or the duration time in ON-state) are optimized [1], [2], [3].Therefore, in the existing TMA techniques, time-sensitive optimization algorithms are indispensable to ensure a twofold objective: 1) to guarantee spatial orthogonality in the desired direction between the exploited harmonic pattern and those of the remaining harmonics, thus ensuring null or negligible sideband signal levels in the desired direction; and 2) to sufficiently distort (thanks to spectral aliasing) the information signal (IS) in all other directions but the desired one.Optimization is necessary for multicarrier TMA-DM and direct antenna phase-shift keying (PSK) modulation [4], [5], whereas advanced optimization algorithms are required in non-TMA-DM techniques based on the injection of artificial noise (AN) into all spatial directions except the IS transmission direction [6], [7].
Digital Object Identifier delays it introduces.This limitation of existing methods is the main motivation for this work.
This letter proposes a novel DM technique using AN injection within the context of TMAs.Unlike conventional DM-TMA approaches that exploit frequency nonorthogonality between signal replicas across different harmonics (B < f 0 ), our method avoids the need for optimization.This is achieved by generating two distinct radiation patterns simultaneously: a sum pattern for IS and a difference pattern for AN injection.Since the AN power is significantly lower than the IS power, it only needs to be injected in a limited number of antennas, resulting in a balance between TMA efficiency and hardware complexity (which is influenced by the number of antennas needed for noise injection and directly impacts DM performance).As a result, our approach offers competitive DM performance and TMA efficiency compared with optimization-based techniques, while simplifying TMA hardware requirements.

II. DM-TMA WITH AN: SIGNAL MODEL
Consider a uniformly excited linear array comprising 2 N isotropic elements (see the example in Fig. 1) where each antenna element is fed with a passband IS of the form u(t)e j2πf s t , i.e., a baseband signal u(t) centered at the radio frequency f s .This IS is time-modulated in the kth element by a periodic signal a T 0 k (t) with fundamental period T 0 .In addition, only a subset of 2 M elements (M ≤N ), in particular, those with indexes k∈Θ⊆{1, . . ., 2N }, are fed with AN of the form n(t)e j2πf n t where n(t) is band-limited Gaussian noise and f n is the AN center frequency.This AN is time-modulated at the corresponding kth element (k∈Θ) by another periodic signal b T 0 k (t), also with fundamental period T 0 .In the example of Fig. 1, 2 N = 16, 2 M = 6, and Θ = {6, 7, 8, 9, 10, 11}.
Accordingly, the radiated signal can be expressed as follows: where z k represents the position of the kth array element along the z-axis, θ is the angle with respect to the z-axis, and β s = 2π/λ s and β n = 2π/λ n denote the wavenumbers for the carrier wavelengths λ s = c/f s and λ n = c/f n , respectively.Fig. 2 shows the TMA modulating signals and how they are applied in each single-antenna element.We use simple bipolar squared periodic sequences, such as c(t) in Fig. 2(a), which can be applied by means of the low-complexity circuitry in Fig. 2(b), where the single-pole dual-throw (SPDT) is controlled by g(t), a unipolar version of c(t), i.e., g(t) = c(t) if c(t) = 1, and 0 otherwise.
The time-modulated feeding network (TM-FN) in each antenna combines two structures, as in Fig. 2(b), to form the IQ time modulator of Fig. 2(c) [9], [10], whose representing symbols are in Fig. 2(d) when TM-FN is used to time-modulate the IS or the AN (as outlined in Fig. 1).The IQ time-modulator in Fig. 2(c) is governed by time-delayed versions of c(t).Specifically, the I and Q branches of the modulator are controlled by g(t−τ k ) and g(t−τ k ), respectively, where τ k and τ k are time-delays instrumental in achieving the following benefits.
1) The simultaneous generation of sum and difference power patterns to radiate the IS and the AN, respectively.
2) The beamsteering capability of such patterns.
3) The elimination of the frequency-mirrored harmonics in both patterns generated by the TMA.In the following, the periodic modulating signals a T 0 k (t) and b T 0 k (t) are designed to simultaneously generate a sum and a difference radiated pattern with the TMA, respectively.We use IQ modulators, such as the one in Fig. 2(c).For the sum pattern, we set τ k = D k and τ k = T 0 /4 + D k , where D k is a variable time-delay, and to synthesize a T 0 k (t) (2) For the difference pattern, where Λ k is another variable timedelay.This leads to ( Recall that a T 0 k (t) is periodic (T 0 ).Hence, it can be represented by its exponential Fourier series expansion where G q , the Fourier series coefficients of g(t), are given by G q = 2/(jπq) if q is odd, and 0 if q is even.Ψ = {q = 4Γ −3; Γ ∈Z} = {. . ., −7, −3, 1, 5, . . .} is the set of nonzero harmonics in the first sum in (4) [10], and f 0 = 1/T 0 is the fundamental frequency.Moreover, since e −ji2πf 0 3T 0 /4 = j i and e −ji2πf 0 T 0 /2 = (−1) i , we readily arrive at the following expression for the exponential Fourier series expansion of b where Ξ = {i = 4Υ−5; Υ∈Z} = {. . ., −5, −1, 3, 7, . . .} is the set of nonzero harmonics of b T 0 k (t).By substituting (4) and ( 5) into (1), the signal radiated is rewritten as Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
Here, we identify the terms as the spatial signatures (or array factors) provided to the IS (at frequencies f s + qf 0 , q ∈ Ψ) and the AN (at frequencies f n + if 0 , i ∈ Ξ), respectively, and ( 6) is rewritten as follows: x(θ, t) If we assume that AN is injected into symmetric elements with respect to the center of the array, then M = card(θ 1 ) = card(θ 2 ), where card(A) denotes the cardinal of the set A. Under this circumstances, in view of ( 7), the selection of the time-delays τ k and τ k in ( 2) and ( 3) allows for the synthesis of a sum pattern F s q (θ) for each q∈Ψ, and a difference pattern F n i (θ) for each i∈Ξ.
Nevertheless, the only radiation patterns in (8) useful to perform DM are those corresponding to q = 1 and i = −1.This is because the normalized Fourier series power spectra of a T 0 k (t) and b T 0 k (t) satisfy 20 log 10 |G −3 /G 1 | = −9.54dB, and 20 log 10 |G 3 /G −1 | = −9.54dB, respectively.Hence, the maxima of the radiated patterns of the corresponding most significant unexploited harmonics (i.e., q = −3 and i = 3, respectively) are 9.54 dB below the maxima of the corresponding exploited harmonics (q = 1 and i = −1, respectively).
In addition, the time-modulation efficiency, i.e., the ratio between the respective useful and total average power radiated by the TMA for each input IS and AN are given by (see [11, eq. ( 16)]) = 0.811, respectively.Therefore, more than 81% of the total power is transmitted over the useful harmonics.Furthermore, considering that the sideband radiation (SBR), which consists of the unexploited harmonics, is given by and by selecting f s = f c −f 0 and f n = f c +f 0 , where f c is a reference carrier frequency, we can rewrite (8) as x(θ, t) = F s 1 (θ)u(t) + F n −1 (θ)n(t) e j2πf c t + SBR (10) i.e., the signal radiated is the sum of the useful signal to perform DM, [F s 1 (θ)u(t) + F n −1 (θ)n(t)]e j2πf c t , which has more than 81% of the transmitted power, and the SBR.Moreover, since the separation between harmonics is 4f 0 , for both the IS (see index set Ψ) and AN (see index set Ξ), if the corresponding maximum bandwidths of IS and AN satisfy B s max = B n max = 4f 0 , there will be no aliasing with the useful signal to perform DM.Therefore, the following approximation for the signal radiated is pertinent Note that the block diagram of the TMA in Fig. 1 (and any other combination of N and M ) is valid for any TMA in which the TM-FN of its individual elements are SSB.
Hence, instead of corresponding to a simple structure as the one in Fig. 2(c), the generic IQ modulators in Fig. 2(d) could be more complex structures (e.g., the one presented in [9] or [12]) that achieve higher efficiencies (94.96% and 91.19%, respectively).In fact, these SSB TMAs with a higher number of switches per antenna will be considered (if they were potentially employed in the proposed scheme in Fig. 1) for an efficiency/complexity comparison study with existing DM-TMA architectures in the next section.
On the other hand, the typical performance metric for TMAs is the time-modulation efficiency, defined as the ratio of the useful power radiated by the TMA (P TM U ) to the total average power radiated (P TM R ).In the proposed DM technique, the timemodulation efficiency is given by where P s U is the IS useful power radiated, and P s R and P n R are the IS and AN total average power radiated, respectively.Since [11,16]) as follows: where P s and P n are the IS and AN output power per antenna, respectively.Notice that the total AN power (crucial in quality of the DM) is 2M P n .Hence, as 2M P n /2N P s = M P n /N P s increases, so does the negative impact on η DM TMA .

III. NUMERICAL RESULTS
As the number of antennas where AN is injected increases symmetrically from the center of the array, the main lobes of the difference pattern will elevate their level, worsening the signalto-noise ratio (SNR) in the directions of the main sidelobes of the sum pattern.Simultaneously, a deeper null is created in the desired direction.Conversely, injecting AN in elements farther away from the center allows for the creation of a larger number of secondary sidelobes in the difference diagram, enabling the adjustment of SNR degradation in other directions.To illustrate its performance, we considered the proposed DM-TMA transmitting a quadrature phase-shift keying (QPSK) signal with a bit rate R b = 2 Mbit/s, carrier frequency f c = 2.4 GHz, time-modulation frequency f 0 = 1 MHz, and SNR in the desired direction SNR = 25 dB.We considered a first scenario where DM performance has priority over η DM TMA [see Figs.(P n /P s = 0.25).The improvement in the 10 dB beamwidth (Ω 10dB ) when injecting AN is remarkable (from 10.6 • to 3.6 • , i.e., 66.2%), as is also evident in Fig. 4(a), which shows how the bit error ratio (BER) response improves as P n /P s increases.Fig. 5 shows the received constellations in the directions indicated in Fig. 3(a), demonstrating the effectiveness of the DM.However, according to (13), η DM TMA = 68.3%.We considered a second scenario where η DM  TMA has priority over DM performance [see   TMA /ΔM | = 2.3%, for each additional noise injection antenna, the main lobe width Ω 10dB narrows by 12.6%, while η DM TMA only decreases slightly, by 2.3%.Table I provides a comparison with existing DM-TMA schemes in terms of complexity (average number of SPDT switches per antenna) and DM-TMA efficiency.

IV. CONCLUSION
We proposed an innovative approach to DM-TMA based on the simultaneous radiation of the IS over a sum pattern and AN over a difference pattern.This method does not require time-consuming optimization algorithms to achieve an excellent compromise between DM performance and TMA efficiency.Therefore, it is a well-suited technique for high mobility-low latency environments.

Fig. 2 .
Fig. 2. (a) Bipolar squared periodic signal c(t) used as the modulating signal in the proposed TMA approach.(b) Single-pole dual-throw (SPDT) switched circuitry to time-modulate the input signal s i (t) with c(t) to generate s o (t), where g(t) is the unipolar version of c(t): g(t) = c(t) if c(t) = 1 and 0 otherwise.(c) IQ time modulator that enables the modulation of the kth antenna element excitation with an single sideband (SSB) periodic pulsed signal a T 0 k (t), for the case of synthesis of a sum pattern, or b T 0 k (t), for the case of synthesis of a difference pattern.The generation of a T 0 k (t) or b T 0 k (t) depends only on the selection of the time delays τ k and τ k .(d) Simplified symbols of the corresponding IQ time modulators.
3(a)  and4(a)].We set N = 8, M = 6, Θ 1 = {1, 4, 5, 6, 7, 8}, and select D k and Λ k to steer both the maximum of the sum pattern and the null of the difference pattern to θ 0 = −40 • .Fig.3(a)shows the plots of the power radiated pattern of the AN as well as the SNR at the receiver without AN (P n = 0) and with AN Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

Fig. 3 .
Fig. 3. SNR at the receiver without AN (P n = 0), with AN (P n /P s = 0.25), and power radiated pattern of AN: (a) scenario #1; (b) scenario #2; (c) narrowing of Ω 10dB (performance) and decline of η DM TMA (time-modulation efficiency) versus M with respect to a TMA architecture without AN.

Fig. 5 .
Fig. 5. Received QPSK constellations for scenarios #1 and #2: (a) in the desired direction; (b) in the direction of the first sidelobe of the radiated pattern when P n = 0 (highly vulnerable); (c) idem for the second sidelobe (also vulnerable); (d) in the direction of the highest-level sidelobe when P n /P s = 0.25 (secure).
[8, k (t), with k∈Θ, time-modulate the AN n(t)e j2πfnt .Supporting multiple users requires a dedicated switching network for each user, similar to the one shown in this figure (consistent with other approaches, as seen in[8, Fig. 10]).

TABLE I COMPARISON
WITH EXISTING DM-TMA SCHEMES