## 2 Directional Modulation Background and Practical Challenges  
In a DM PA, phase shifts are applied at each element such that the complex summation of the far-field plane waves produces an altered constellation when sampled by a single channel receiver (see [13, 14]). The alteration of the constellation, in turn, leads to the increased probability of bit errors. By appropriately designing the applied phase shifts, BERs can be controlled across the angle dimension.  
In a DM FDA, it is common that the diverse radiated frequencies are processed on independent receive channels, and the complex summation of the synchronized channels achieves an altered constellation (see [9]). Increasing the number of elements yields more degrees of freedom when altering the constellation (i.e., more complex exponentials can be summed at the receiver, providing more control of the resultant amplitude and angle). The trade-off for the increased number of elements is an increase in the hardware channels required for the receiver.  
The frequency diversity employed by the FDA allows for BER control in both range and angle, improving upon the PA which can only control BER in angle. It is clear that these approaches differ in concept and channel requirements at the receiver, incurring a trade-off with respect to the DM PA receiver simplicity and the DM FDA ability to control BER in range and angle. Alternative approaches to secure FDA DM exist in the literature. For example, the approach taken in [8] uses artificial noise sequences on transmit. However, we choose to start with the techniques described in [9] for the ease of practical implementation.  
In [9], DM is modeled for an \(N\)-element linear FDA using quadrature phase-shift keying (QPSK). The signal model in Equation (5) in [9] sets up a vector-valued optimization of an additive length-\(N\) phase offset vector, wherein a genetic algorithm is used to iteratively refine the phase values for DM. The goal of such vector-valued optimization is that the coherent sum of the complex exponentials corresponding to the antenna elements should have very large amplitudes near the correct constellation points for desired range-angle locations and small amplitudes for incorrect constellation points for undesired range-angle locations. This idea is visually highlighted in Figure 8a,b in [9]. Here, we desire to undertake and address the practical considerations of building such a system.  
The use of frequency diversity is key for range dimension beamforming; however, it also presents a practical challenge with respect to coherent, multi-frequency signal generation and reception. In this work, we test the multi-frequency phase synchronicity of a multi-frequency transmitter using a single channel SDR receiver to capture the radiated field behavior. The collected data allow us to test the analytical signal model and phase coherency of the transmit hardware. This test also serves as the first step in designing and actualizing a coherent multi-channel transmit-receive testbed required to implement the conceptual DM FDA architectures discussed in the academic literature.  
In addition to testing the phase coherency of multi-frequency signal generation, we implement fast-time coefficients programmed on digital waveforms imported to a Keysight M8190A arbitrary waveform generator (AWG). The AWG is operated in uncoupled channel mode, allowing each transmit channel to operate independently while pulling from a common sample clock. To start sample streaming, the trigger condition is set as a positive-edge 0.5 V minimum waveform input. After the triggering event occurs, the samples on each respective channel are fed into their respective DACs and radiated into free-space via antennas. Sample synchronization is achieved via commonly clocked DACs. To generate a high-fidelity output signal from the AWG, we select an output frequency of 720 MHz, which is within the operational bandwidth given by the AWG baseband sample rate of 8 Gs/s.