A new Modified Iterative Fourier Technique (MIFT) is proposed for the design of interleaved linear antenna arrays which operate at different frequencies with no grating lobes, lowsidelobe levels, and wide bandwidths. In view of the Fourier transform mapping between the element excitations and array factor of uniform linear antenna array, the spectrum of the array factor is first acquired with FFT and its energy distributions are investigated thoroughly. The relationship between the carrier frequency and the element excitation is obtained by the densityweighting theory. In the following steps, the element excitations of interleaved subarrays are carefully selected in an alternate manner, which ensures that similar patterns can be achieved for interleaved subarrays. The Peak Sidelobe Levels (PSLs) of the interleaved subarrays are further reduced by the iterative Fourier transform algorithm. Numerical simulation results show that favorable design of the interleaved linear antenna arrays with different carrier frequencies can be obtained by the proposed method with favorable pattern similarity, low PSL, and wide bandwidths.
Wideband multifunction antenna arrays are given a distinctive attention, in particular for applications involving radar tracking, biomedical imaging, wireless communications, location and remote sensing, and so forth. A popular solution for assuring the necessary bandwidth of the multifunction array is to use radiators with a very large bandwidth [
In order to address these challenges, several deterministic methods have been proposed in the literature. Multiple interleaved subarrays are obtained by means of the difference sets (DS) [
To address these challenging problems effectively, a Modified Iterative Fourier Technique (MIFT) for interleaving linear antenna array with different carrier frequencies is proposed in this paper. The Iterative Fourier Technique (IFT), which was earlier presented by Carroll for synthesizing array patterns [
The rest of the paper is organized as follows. In order to convey the technical approach in a clear manner, the densityweighting theory was briefly described and the description of the MIFT algorithm was presented in Section
In this section, the densityweighting theory is first briefly reviewed. Densityweighting method developed by Skolnik is a statistic technique for the design of an equally weighted thinned antenna array (i.e., the excitations are equal to 1 or 0) [
Since the interleaved subarrays operate at different frequency, the interelement spaces and subarray aperture sizes are different. Without loss of generality, considering a shared aperture linear antenna array consisting of
In the traditional iterative Fourier transform algorithm [
In this study, by changing the selection of element excitations, a new interleaving method is proposed for the design of interleaved linear antenna array with different carrier frequencies. To achieve an efficient design of the interleaved linear antenna array, the expected value of the array factor AF for each interleaved subarray should be kept the same as much as possible, which ensures that the performancesimilarity of the interleaved subarrays can be obtained. In every iteration of our proposed method, the PSLs of the interleaved subarrays are decreased by an adaptation of the sidelobe region of AF to the sidelobe level threshold (SLT). The SLT plays a key role in obtaining a lowsidelobe interleaved array by MIFT method, and a high or low value of SLT can largely raise PSLs of interleaved subarrays. To get an interleaved array with the minimum PSL, the MIFT should be performed with a suitable SLT. However, the SLT value that fits the method best is difficult to find because the considerable computational burden is required by repeatedly adjusting the value of SLT. According to many synthesis trials, a good value of the SLT suitable for the MIFT can be confined in a small interval
The flowchart of the MIFT algorithm for the design of interleaved linear antenna array with different carrier frequencies is shown in Figure
Flowchart of the MIFT algorithm.
To convey the proposed method in a clear manner, suppose that
Set the values of the initial element excitations as 1 with a probability of
Compute AF from element excitation vector using a
Adjust the values of AF to adapt to the constraint of the SLT. In more detail, only the samples of AF that exceed the SLTs are corrected, and the rest of the samples of AF are left unchanged.
Calculate the updated element excitation
Truncate
Sort the truncated excitation to get a new excitation vector
Take the excitations of the first subarray to be the updated input for the next iteration.
Repeat Steps (2)–(7) until the prescribed sidelobe requirements for AF are unchanged or the allowed number of iterations is reached.
Set the element excitations of all the interleaved subarrays equal to “1” and output the results.
The schematic diagram of the element excitations selecting process for the interleaved subarrays (
This section is aimed at assessing the performance of multiple interleaved subarrays with different carrier frequencies based on MIFT method. An interleaved linear antenna array consisting of 100 elements spaced half wavelength apart is concerned. In the iterations, the value of the sidelobe level threshold is set as −20 dB, and the 1024point direct and inverse FFT are utilized. Without loss of generality, the MIFT method is exploited to interleave four subarrays (i.e.,
Performance parameters for the interleaved subarrays.
Type  Aperture occupancy ratio  Carrier frequency  Mainbeam width  PSL 

Subarray 1  89% 

2.4°  −7.29 dB 
Subarray 2  93% 

2.8°  −8.17 dB 
Subarray 3  96% 

5.6°  −7.96 dB 
Subarray 4  99% 

8°  −8.96 dB 
(a) Normalized power pattern for the subarrays. (b) Magnification of the pattern for the interleaved subarrays.
The next simulation is to assess the performance of the bandwidth and mainbeam width when the carrier frequency of interleaved subarrays is increased. The curve of the relationship between the carrier frequency and mainbeam lobe width is shown in Figure
The curve of the relation between the carrier frequency and mainbeam width.
The curve of the relation between the carrier frequency and PSL.
In this paper a new method is demonstrated to interleave multiple subarrays which share a common aperture with different carrier frequencies. Through MIFT algorithm, lowsidelobe levels and similar radiation patterns for multiinterleaved subarrays can be achieved and the available aperture space is efficiently utilized. Some numerical simulations are presented to assess the performance of the MIFT method for the design of interleaved antenna array with different carrier frequencies. The performance of the bandwidth and mainbeam width with the increased carrier frequencies is also evaluated. The broadband widths of the interleaved subarrays with different carrier frequencies is stacked and the wideband multifunction antenna array based on multiple interleaved subarrays with different carrier frequencies can be designed by MIFT algorithm. Future efforts will be devoted to extending the proposed method to twodimensional planar antenna array in the presence of mutual coupling effect.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China under Grant no. 61172148.