# Experimental Test of Continuous Wave Frequency Diverse Array Doppler Radar +
## 1 Introduction  
The frequency diverse array (FDA) was first introduced in a series of works by [PERSON] and collaborators [1, 2, 3]. In such an array, linearly progressive frequency offsets were applied between uniformly spaced elements, generating range-angle coupled beampatterns with periodic modulations in range, angle, and time [4, 5]. The resulting auto-scanning behavior is accomplished without the use of any other electronics or external phase-shifting hardware. Multi-mission, multi-mode applications have also been proposed in [1, 2, 3], including simultaneous synthetic aperture and moving target indication. The frequency diversity of the array introduces range-angle beamforming, which improves upon the angle-only beamforming from a phased array (PA) radiating a single carrier frequency. By decoupling the range and angle dimensions, steerable localizations in energy can be created in the far-field pattern. Work in this area includes the random FDA [6], FDA sub-array architectures [7, 8, 9], non-linear frequency offsets [10, 11, 12, 13, 14, 15], algorithmic optimizations of the FDA beampattern [16, 17], multiple input multiple output (MIMO) [18], false target generation [19], electronic counter-counter measures (ECCM) [20], and FDA wireless power transfer architectures [21, 22, 23], among others. Although much theoretical work has been conducted in the area of FDAs, only a limited number of array builds have been reported in the open academic literature. The current list of builds known to the authors includes the following:  
* [PERSON] [24]: \(3\times 5\) planar array with a \(3\times 1\) sub-array structure with 5 distinct frequencies. The transmit array had a designed carrier frequency of 3  GHz, and [24] features several narrowband far-field collections. The signal generation was accomplished by signal generators. * [PERSON] [25]: two element FDA waveform testbed with a (typical) carrier frequency of 10  GHz. Signal generation was accomplished by an arbitrary waveform generator (AWG). * [PERSON] [26]: \(1\times 10\) linear frequency modulated (LFM) FDA. Carrier frequency of 3  GHz with signal generation accomplished by a single LFM-CW source and a delay network. * [PERSON] [27]: re-built and improved the \(1\times 10\) LFM FDA in [26]. The build had a carrier frequency of 3  GHz and used a single LFM-continuous wave (CW) source and a delay network to generate the transmit signals. * [PERSON] and [PERSON] [28; 29]: MISO LFM FDA with a \(1\times 8\) transmit array. The transmit array had a designed carrier frequency of 3.3  GHz and used an RFSoC as the transceiver. * [PERSON] [30]: \(1\times 3\) linear FDA using Ettus Universal Software Radio Peripheral (USRP) x310 software defined radios (SDR) as the transceivers. The array had a designed carrier frequency of 2.4 GHz. * [PERSON] [31]: \(1\times 2\) linear FDA with binary phase-shift keying modulations using an AWG. The array had a designed carrier frequency of 720 MHz. There also exists one hardware implementation by [PERSON] [32; 33] but with no array build. The initial setup, we show the results of the first experimental FDA data collections using SDR platforms, which have recently seen increasing use in the academic literature (AOA/DOA [34; 35; 36; 37; 38], phased arrays [39], communications systems [40; 41; 42; 43], and FMCW radars [44]). These collections are designed to demonstrate the FDA as a low-complexity perimeter surveillance system with an auto-scanning mainbeam feature, with an emphasis placed on validating the signal model-level behavior of the system. The collections feature moving targets, including cars and drones, commonly found in perimeter surveillance applications. We document the system evolution from initial far-field pattern measurements to time-frequency analysis of micro-Doppler features generated by a rotating blade. Using linear CW FDA radar, the following are our contributions to FDA research:  
1. We experimentally demonstrate both the temporal periodicity and angular scanning behavior of the FDA far-field pattern. 2.