## 1 Introduction  
The frequency diverse array (FDA) was first introduced in a series of works by [PERSON] in [1, 2, 3] and applied linear frequency offsets 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 such as simultaneous synthetic aperture and moving target indication have been proposed in [1, 2, 3]. Additional potential applications include volumetric scanning, beacons, and low-cost perimeter surveillance [6, 7]. In contrast to the traditional phased arrays (PAs) that operate at a single carrier frequency, the FDA proposed in [1, 2, 3] radiates sinusoids, having small linear frequency offsets at each element of the array, creating a range dependence in the far-field pattern. The added pattern dependence on range allows for beamforming in both range and angle, improving upon the PA which can only perform beamforming in angle. Directional modulation (DM) techniques implemented on FDAs allow for bit error rate (BER) shaping in the range and angle dimensions [8, 9, 10, 11, 12], while DM using the PA can only reduce BER in angle [13, 14]. The FDA also addresses the high costs and complexity of PA systems [6, 7]. Although the 'S' shaped far-field patterns (see Figure 3a from [15]) produced by arrays with linear frequency offsets and uniform element spacing can eliminate clutter, far-field range periodicities result in range ambiguities [16]. By decoupling the range and angle dimensions, steerable localizations in energy can be created in the far-field pattern. Work in this area includes random FDA architectures [17, 18], FDA sub-array architectures [19, 20, 21], non-linear frequency offsets [6, 7, 22, 23, 24, 25, 26], algorithmic optimizations of the FDA beampattern [27, 28, 29, 30] and FDA wireless power transfer architectures [31, 32, 33]. In the literature, DM for FDAs has been well explored in quantitative studies [8, 9, 10, 11, 12], and techniques exist using fast-time coefficients to produce multiple point-like energy localizations in the FDA far-field pattern [27]. Although much theoretical work has been conducted, there exist no hardware implementations or builds (to the knowledge of the authors) in the area of FDA communications in the open literature, with the known array builds focused on radar functionality and pattern measurements. The current list of builds known to the authors includes the following:  
* [PERSON] [34] (\(3\times 5\) planar array using a \(3\times 1\) sub-array structure with five distinct frequencies);
* [PERSON] [35] (two-element FDA waveform testbed);
* [PERSON] [36] (\(1\times 10\) linear frequency-modulated (LFM) FDA);
* [PERSON] [37] (re-built and improved the \(1\times 10\) LFM FDA in [36]);
* [PERSON] and [PERSON] [38, 39] (MISO LFM FDA with a \(1\times 8\) transmit array);
* Our previous work [40] (\(1\times 3\) linear FDA using Ettus Universal Software Radio Peripheral (USRP) X310 software defined radios (SDR)). The builds in [34, 35, 36, 37, 38, 39, 40] focus on radar implementations of the FDA. There also exists one hardware implementation by [PERSON] [41, 42] but with no array build. In this paper, we continue the efforts in [34, 35, 36, 37, 38, 39, 40, 41, 42] and contribute to the experimental development of the FDA with a far-field test of a two-element linear FDA implementing binary phase-shift keying (BPSK) modulations on both elements with a 1 MHz data rate. The goal of this work is to illustrate the steps needed to design, build, and test an FDA communication system with fast-time modulation in support of a future build and test of a DM FDA. The contributions of this paper are as follows:  
1. We demonstrate the theoretical fast-time BPSK FDA signal model in practice, motivating further practical study of different FDA transmit-receive architectures. 2.