## 8 Summary, Future Work, and Discussion  
This paper documents the build and test of an FDA communication system, which we hope to extend to a simultaneous FDA radar/communications system. In this work, a two-element linear FDA is used to transmit messages on the range-angle plane using BPSK modulations on both elements. The collected data enable us to evaluate the analytical signal model and phase synchronicity of the transmit hardware. This test represents the first step in designing and implementing a coherent multi-channel transmit-receive testbed, which is essential for realizing the conceptual DM-FDA architectures found in the academic literature. The theoretical baseband behavior of the received waveform when down-converted at the carrier frequency \(f_{0}\) is characterized, then demonstrated via experimental results. The link between the transmitter and receiver is analyzed, and a transmit modulation scheme is developed with appropriate power considerations to achieve a desired BER. Figure 14: Experimental demonstration of Equations (24) and (25) (**left**) and length-11 Barker code correlation with 250 \(\upmu\)s worth of bit information from the synchronized waveform in Figure 12 (**right**). Figure 13: Simulated baseband BPSK FDA (**left**) and 100 \(\upmu\)s of the captured BPSK FDA data with receiver synchronization in Figure 12 (**right**). The modulated information is bookended using the length-11 Barker code, which marks both the beginning and ending of the encoded message. The received bitstream is validated with a discrete correlation of the received bitstream with the length-11 Barker code, as well as a cross-referencing of the received bitstream with the information bits programmed at the transmitter. The DM FDA analysis presented in the academic literature often relies on a set of principles, which typically includes some (or all) of the following:  
1. Phase-synchronous analysis that assumes the receiver is always frequency- and phase locked with the transmitter. 2. Neglecting spectrum spreading, with closely spaced spread spectrum signals that are assumed to be perfectly separable. 3. No use of training symbols. Orthogonal training symbols can be created via a time-division multiplexing approach. Thus, movement of the symbols on a constellation does not necessarily imply non-recoverability. To address the points above, we generate a list of research questions that we will address in our future work:  
1. What are the necessary requirements of the multi-channel coherent receive hardware? 2. What is the trade-off between the designed frequency offsets and tolerable spectrum spreading with respect to signal separability? 3. How can we measure the 'zone-of-security' generated by DM FDAs? Moreover, how can BER control be attributed to the DM FDA itself and not artifacts of practical analog signal conditioning, signal generation, and/or down conversion? Conceptualization, B.C.J. and R.M.N. ; methodology, B.C.J. ; software, N.R.M. ; validation, N.R.M. and J.K.A.H. ; formal analysis, B.C.J. and R.M.N. ; investigation, B.C.J. and N.R.M. ; resources, R.M.N. ; data curation, N.R.M. and J.K.A.H. ; writing--original draft preparation, N.R.M. and B.C.J. ; writing--review and editing, N.R.M., B.C.J., J.K.A.H., R.M.N. and T.D.B. ; visualization, N.R.M. ; supervision, B.C.J., R.M.N. and T.D.B. ; project administration, B.C.J. and R.M.N. ; funding acquisition, R.M.N. All authors have read and agreed to the published version of the manuscript. This research was funded by the US Office of Naval Research grant number N00014-20-1-2160. Not applicable. The datasets presented in this article are not readily available because of sponsor restrictions. Author [PERSON] was employed by the company Maxar Intelligence. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.