Fast, Phase-Only Synthesis of Aperiodic Reflectarrays Using Nuffts and Cuda

Abstract

Abstract-We deal with one of the computationally most critical steps of the Phase-Only synthesis of aperiodic reflectarrays, namely the fast evaluation of the radiation operator. We present an approach exploiting the use of a fast numerical algorithm using 2D Non-Uniform FFTs (NUFFTs) of NED (NonEquispaced Data) and NER (Non-Equispaced Results) type and of parallel processing on Graphics Processing Units (GPUs). We extend the approach in K. Fourmont, J. Fourier Anal. Appl., Vol. 9, No. 5, 431-540, 2013 for implementing NUFFT routines to the 2D case and illustrate the parallel strategies to accelerate the approach. In particular, we show how the two levels of parallelism intrinsic in the interpolation step of the 2D NED-NUFFT can be fruitfully exploited by adopting dynamic parallelism, a feature made available in one of the latest architecture of NVIDIA cards. The presented synthesis results show that the introduction of further degrees of freedom (positions) allows improving the performance with respect to periodic reflectarrays. Also, the possibility of adopting aperiodic reflectarrays of reduced number of elements for fixed performance is demonstrated.

General Near Field Synthesis of Reflectarray Antennas for Their Use as Probes in Catr

“…Reflectarray antennas are most commonly used in far field applications [1], such as Direct Broadcast Satellite (DBS) [2][3][4][5], Local Multipoint Distribution Service (LMDS) [6][7][8] or radar interferometers [9,10]; while near field applications are less conventional. Nevertheless, in recent years reflectarrays have been proposed in near field for Radio-Frequency IDentification (RFID) reader applications [11], imaging [12] or microwave virus sanitizer [13].…”

Improved Reflectarray Phase-Only Synthesis Using the Generalized Intersection Approach with Dielectric Frame and First Principle of Equivalence

“…This time is independent of the number of reflectarray elements and is slightly larger than the time which could be obtained with the algorithm described in [3], since four more FFT are employed per iteration in [21]. Here, for = 7 and 900 optimizing variables, the mean time per iteration was 1.79 s and, for = 8, was 7.82 s. However, the improved convergence properties of the generalized IA guarantee better results in less iterations [13,22].…”

“…In addition to accelerating the algorithm, by doing the synthesis in several steps, optimizing a few variables at the beginning and increasing their number in following steps as the copolar pattern is shaped, convergence is improved [12,13], since the number of local minima is reduced in the first steps of the synthesis. Finally, if the desired shaped pattern is symmetric, only half of the variables need to be optimized, further reducing computing time and memory.…”

“…Reducing the number of optimizing variables has more impact in absolute terms for larger values of . In addition, reducing the number of variables not only reduces computing time but also improves convergence of the overall synthesis process [12,13]. In any case, since any synthesis process may take tens or even hundreds of iterations, a modest improvement per iteration may have a significant impact in the whole procedure.…”

“…However, this algorithm suffers from the problem of traps or local minima [12], although some strategies have been developed to minimize this issue [3]. Convergence of the IA can be improved by employing the generalized IA [12][13][14] working with the squared field amplitude (or equivalently, with the directivity or gain), although at the cost of greatly reducing its computational efficiency, since in that case a general minimization algorithm must be employed.…”