Antenna Element Index Modulation for Frequency Diverse Array

. In this paper, we propose a new architecture and provide performance analysis for frequency diverse array (FDA) Radar combined with the index modulation (IM) techniques. Here, the IM concept is applied upon frequency oﬀsets in an FDA. Information is transmitted by a dynamically selected subset of antenna element indices applying predeﬁned carrier frequency oﬀsets, which generate diﬀerent radiation patterns. It is shown that this enables the capability for simultaneous wireless communication and FDA Radar that has the range-angle coupling issue resolved.

is FDA beampattern feature was mathematically derived and examined through simulation in [7,8].And they were further studied from a design perspective using in [9,10].In [11,12], the FDA was exploited to reject range dependent interference, which endows FDA potential number of important applications on Radar and navigation [13][14][15][16].However, for Radar applications, the range of the detection target cannot be directly obtained from the beamforming output peaks due to the inherent coupling of range and angle traditionally associated with FDA.In [17], a decoupled range-angle beampattern was proposed using logarithmically increased frequency offsets with compromised beamforming performance in range domain.Square and cubic increasing frequency offsets were also developed for decoupling in [18], which, however, require a large bandwidth.In [19], an FDA Radar using two pulses with zero and nonzero frequency increments was introduced to locate targets' range-angle coordinates, but it was only for Radar sensing.
In this paper, the authors attempt to establish a link between the IM technique and FDA Radar.e proposed antenna element IM FDA transmitters are constructed for the purpose of concurrent wireless communication and Radar sensing.e paper is organized as follows.In Section 2, the proposed antenna element IM FDA transmitter architecture is first described, followed by the elaboration of its operation principle.In Section 3, the approach to address the range-angle entanglement is introduced, leaving simulation results and discussion presented in Section 4. Finally, conclusions are drawn in Section 5.

Antenna Element IM FDA Transmitter
Considering a one-dimensional (1D) N-element array with uniform element spacing d, the n th element is excited with a signal of frequency: ( here, f 0 is a reference carrier frequency, and Δf is set to be several orders smaller than f 0 .U n,q (t) refers to the on-off function in time domain of the n th single-pole single-throw switch in the q th symbol slot of duration T s , U n,q (t) � 1, qT s ≤ t ≤ (q + 1)T s for selected antennas, 0, otherwise for other unselected antennas.
In (2), qT s and (q + 1)T s refer to the switch-on and switch-off time instants, respectively."1" represents "on" of the switch and "0" represents "off."For one period T(T > T s ), U n,q (t) is shown in Figure 1. Figure 2 depicts the antenna element IM FDA transmitter architecture.Information bit steam of p bits determines the indices of antenna elements whose RF carrier frequencies are shifted.
e mapping between bits and antenna indices is performed by the "Index Selector" module depicted in Figure 2. Afterwards, the selected antenna element index sequences are divided into two parts, i.e., H J1 and H J2 , respectively, corresponding to a smaller and a larger number of selected antenna elements.
e closing single-pole single-throw switches of S 1 and S 2 have a duration T. ϕ n denotes the phase shift of the n th RF carrier and ϕ n � nϕ 1 .
In the proposed antenna element IM FDA transmitter, the indices of antennas with carrier frequency offsets applied are dynamically updated in each transmitted symbol period.For each bit frame of p bits, K out of N antenna elements are selected.e selected antenna indices are grouped as where i g ∈ {1, 2, . .., N} and i a ≠ i b when a ≠ b.I G is determined by the baseband data of p bits, indicating where C(N, K) refers to the number of K-combinations out of a set of N elements.Generally, K ≤ N. Operator " • " denotes integer floor function.e mapping procedures, from p bits to K-antennas with applied carrier frequency offsets, are presented as follows: (i) e p bits are converted to a decimal number c, using where V (m) denotes the m th bit in the p-bit sequence D. Here, 0 ≤ c ≤ C(N, K)− 1. (ii) Map the decimal number c to a strictly decreasing sequence {j K , j K− 1 , . .., j 1 }, j c ∈ {0, 1, 2, . .., N -1}, and (iii) e sequence {j K + 1, j K− 1 + 1, . .., j 1 + 1}, termed as J hereafter, contains the indices of the selected antenna elements.
A one-to-one mapping between the p-bit sequences and the selected antenna indices J is guaranteed with a known K by this mapping rule [2].To better explain the mapping procedure, a flow chart is illustrated in Figure 3.An example of N � 16 and p � 6 is discussed here.Since p � log 2 [C(N, k)], we have K � 2 and 14, respectively, corresponding sequence H J1 and H J2 shown in Figure 2. If we assume a p-bit (6 bit) sequence of "110001" for K � 2, then using (5) we get the corresponding decimal number c � 49.Seen from Figure 3, j 2 starts at 15, as C(10, 2) � 45 < c � 49 < C(11, 2) � 55; thus, 10 is the largest number that satisfies the combinational numbers smaller than c, i.e., Similarly, via iteration, j 1 can be obtained, i.e., 4. erefore, the sequence H J1 of {11, 5} contains the selected antenna indices, which uniquely represents the binary information "110001."And for K � 14, H J2 can be obtained in an analogous manner.Using H J1 or H J2 is determined by the status of the corresponding switches of S 1 and S 2 .When the used element index sequence in the antenna array are known, the carrier frequency offsets are applied by closing the corresponding switches in the switch array, i.e., U J,q (t) � 1. 2 International Journal of Antennas and Propagation

Resolve the Range-Angle Entanglement
In the conventional FDA (CFDA), i.e., all antenna elements are applied with their corresponding carrier frequency o sets, the radiated eld in the far-eld region at a location A (R 1 , θ) can be expressed as where T is transmitted pulse duration that is further divided into h equal subpulses of duration T s .λ n is the wavelength corresponding to the operation frequency f n , i.e., λ n c 0 /f n , where c 0 is the speed of light.R n is the receiver displacement in free space with respect to the n th element that is given by θ is the spatial angle away o the array boresight.Since (N -1)Δf << f 1 and R n ≈ R 1 , the far eld pattern can be approximated as where φ − 2πf 1 (t − R 1 /c 0 ).e maximum values of P are obtained when Given N and p-bit sequence D Obtain c, K and Figure 3: e ow chart of mapping procedures.

International Journal of Antennas and Propagation
Δft − From ( 10), it can be observed that the range and angle of far field location A are coupled when the time variable t and M are fixed.It is noted that when none of the antenna elements are selected for frequency offsets, i.e., K � 0, the farfield pattern becomes that is, the classical phased array (PA) beampattern.In a specific region, the coupled range-angle beampattern issue can be resolved by hybridizing the properties of a PA, and an FDA in the proposed antenna element IM FDA through setting different numbers of antenna elements with applied frequency offsets.e operation can be summarized as follows: (1) Estimate θ by using the obtained quasi-PA beampattern.In one period of duration T, select fewer antenna elements, i.e., close the switch S 1 .Meanwhile, close the switches of antenna branches with indices identified in H J1 .According to the mapping rules described above for the continuous p-bit streams, a beampattern which has quasi-PA characteristics is obtained to evaluate the azimuth angle θ in (10) and binary information is conveyed by the selected antenna element indices.
(2) Obtain range information from the range-angle dependant beampattern with the aid of estimated θ obtained in the first step.In another T, increase the number of selected antenna elements through opening the switch S 1 and closing the switch S 2 .Also, close the switches in the switch array in accordance with H J2 . is operation forms a range-angle dependant beampattern with the transmitted bits.Since θ is known, R 1 in (10) can be derived.

Simulation Results and Analysis
To validate the efficacy of the proposed antenna element IM FDA transmitter, the radiated patterns are simulated that carrier bit streams for transmission.e parameters of the linear antenna element IM FDA transmitter used in the simulation are listed in Table 1.In a single duration T with closing the switch S 1 , assume a bit sequence comprising 80 bits is to be transmitted.e bit sequence is equally divided into 20 sections, and each part has 4 bits.If assume one of the 20 sections to be "0001," and it is conveyed with K � 1.Using the mapping rule described earlier, the selected antenna element index sequence H J1 is calculated to be {2}.
en, remaining bits, as blocks of 4 bit, are transmitted in the same manner.Similarly, when assuming 120 bits to be transmitted, K is set to 2. In the next duration T, if the bit stream contains 80 bits or 120 bits, each of the divided 20 sections respectively corresponds to 15 or 14 selected antenna elements for H J2 as log 2 [C (16,15)] � 4 bits and log 2 [C (16,14)] � 6 bits.Here, the average radiation pattern of 20 (T/T s ) randomly generated shapes (each radiation pattern shape corresponds to one transmitted data symbol which is mapped upon the selected antenna element indices) is considered.
In Figure 4, the proposed antenna element IM FDA radiation patterns in the range-angle dimension are simulated for different values of K.
e sample results in Figures 4(a) and 4(c) validate that the pattern characteristics of the phased array are well preserved with smaller K of antenna element IM FDA.While in Figures 4(b) and 4(d) with larger K, the "S"-shaped patterns are obtained, i.e., CFDA radiated patterns.In Figure 5, the target responses using the proposed scheme are depicted.Seen from Figure 5(a), in the angle domain, when compared with the first sidelobe level of the phased array (K � 0), i.e., around − 13 dB, the proposed scheme (K � 1, 2) can achieve the same level.In addition, it is shown that similar peak of first sidelobe levels as CFDA are obtained for K � 14, 15 at a fixed range.While in the range domain, Figure 5(b) shows that the same peak-to-sidelobe ratios (PSLs) can be achieved in the proposed scheme by comparison with the CFDA scheme.It is noted that for K � 14, the sidelobe levels are higher.is is because that with decreased number K, a PA radiation pattern characteristic at the sidelobe level about − 18 dB at 50 km range occurs, see Figure 4(d).Meanwhile, in Figure 4(c), the characteristics of CFDA radiation pattern occur at low energy level with increasing K. ese features are validated in Figure 6.When K ≤ 8, a PA radiation pattern is dominated, and the peak of first sidelobes are directly proportional to the selected K, indicating that the characteristics of the CFDA pattern are becoming obvious with increased K, and when K > 8, a CFDA radiation pattern is dominated.Hence, to achieve better PSLs, only smaller K and larger K are selected in the proposed scheme.is selected value of K also affects the bit rate which is described in Figure 7, showing that a tradeoff exists between Radar detection performance and communication bit rate when N is fixed.In Figure 8, the range and angle of the target locations are estimated by the proposed scheme using the multiple signal classification (MUSIC) algorithm.In Figure 8(a), integrating two settings of K 1 � 1 and K 2 � 15, at the direction θ � 30 °, two target locations that 5 km away from each other can be identified in range domain.And these two ranges can also be successfully estimated with setting K 1 � 2 and K 2 � 14 at the direction θ � 60 °, shown in Figure 8(b).Figures 9(a)-9(c)

6
International Journal of Antennas and Propagation because of the compromised resolution in the range domain.

Conclusions
Inspired by the IM concept, an antenna element IM FDA transmitter was proposed that has the ability to simultaneously deliver data wirelessly and Radar sensing.Also, the inherent range-angle coupling issue associated with an FDA system can be addressed in a speci c area by varying the number of antenna elements with applied frequency o sets.e proposed transmission scheme can be further extended with the support of experimental veri cation in the indoor environment.is is planned in the near future.e phaselocked loop (PLL) frequency synthesizers sharing the same reference signal are considered to be t for FDA frequency generations.
is antenna element IM FDA transmitter concept introduced in the paper should be useful in applications where there is a need for a communication link in addition to the Radar sensing.

Figure 2 :
Figure 2: Architecture of proposed antenna element IM FDA transmitter.
) and 9(b) that the two targets can be detected along with some other fake targets.

Figure 7 :Figure 8 :
Figure 7: Bit rate of the proposed scheme for various K with N 16, ∆f 3 kHz, and T s 0.1 ms.

Table 1 :
Parameters for linear antenna element IM FDA simulation.