Physical waveform optimization for multiple beam multifunction digital arrays

Description (excerpt)

CROSS-REFERENCE TO RELATED APPLICATIONS The present application claims the benefit of U.S. Provisional Application No. 62/928,307 filed Oct. 30, 2019 and entitled “PHYSICAL WAVEFORM OPTIMIZATION FOR MULTIPLE BEAM MULTIFUNCTION DIGITAL ARRAYS,” the disclosure of which is incorporated by reference herein its entirety. TECHNICAL FIELD The present disclosure relates to generation of radio frequency (RF) waveforms and more specifically to generation of RF waveforms facilitating multiple different functionalities. BACKGROUND The radio spectrum is a fixed resource with an exponentially increasing demand from commercial communication applications. To meet the increased demand for commercial communication application, the radar spectrum has been eroded, which has created additional strain on defense applications that must already operate in congested and contested environments. As such, improving spectral efficiency (e.g., dynamic spectrum access) or developing methods to share spectrum between multiple functions (e.g., radar and communication sharing spectrum) has been the subject of ongoing research. Generally speaking, spectrum sharing can take two forms: cohabitation or co-design. The former tends primarily to address the interference that separately operated systems could cause to one another and the latter involves cooperative control within the same system. However, designing RF waveforms that are suited for sharing of the radio spectrum between both radar and communication functions has proved challenging. One solution that has been proposed includes transmitting radar and communication waveforms from an antenna aperture that includes a plurality of antenna elements by transmitting the radar waveforms and the communication waveforms in different time segments. For example, the antenna aperture may transmit the radar waveforms for a first time period and transmit the communication waveforms for a second time period that is non-overlapping with respect to the first time period. While this solution does allow radar and communications to share the spectrum it is not an efficient inefficient solution since the two different modes of operation (e.g., radar and communications) cannot be used simultaneously. It has been previously shown that a set of physically realizable frequency-modulated (FM) waveforms can be optimized using the Error Reduction Algorithm to emit simultaneous, pulsed radar and communications signals in different spatial directions using a technique referred to as Far-Field Radiated Emission Design (FFRED). The FFRED approach considers the transmission of multiple signals (e.g., radar and/or communications signals) simultaneously from a digital array while considering practical waveform attributes (e.g., constant amplitude, power efficiency). The FFRED approach has shown that optimized waveforms can be constrained to be constant amplitude by utilizing the spatial orthogonal complement to the desired transmission directions. While the FFRED approach described above has been demonstrated in theory, several challenges remain. For example, the transmitted waveforms may change from pulse to pulse, requiring a new set of waveforms to be determined for each pulse. Previous approaches for FFRED are unable to determine sets of waveforms suitable for simultaneous transmission of radar and communication signals when changes occur on a pulse-to-pulse basis. Thus, while the FFRED approach has been demonstrated in theory, real-world implementations remain impractical because the rapidly changing nature of the transmitted signals cannot be accounted for by existing FFRED implementations. SUMMARY Systems and methods are disclosed that provide a feasible implementation of FFRED algorithms suitable for real-world applications involving simultaneous transmission of radar and communication signals or other use cases. A set of signals for transmission and a transmission direction for each signal of the set of signals may be determined. The set of signals includes at least a first signal associated with a first transmission direction and a second signal associated with a second transmission direction that is different from the first direction. An optimization problem is configured based on characteristics of an antenna array and the set of signals and then solved to identify a set of waveforms suitable for transmitting the signals. To overcome the problems associated with previous FFRED approaches, a relaxed optimization problem is disclosed that enables the set of waveforms to be determined more rapidly, thereby accommodating the need to identify different waveforms when at least one of the transmitted signals (e.g., the radar signal or the communication signal) changes rapidly, such as from pulse-to-pulse. Solving the optimization problem may identify a set of waveform that exhibit high power efficiency, such as constant amplitude continuous waveforms, but may also seek to minimize wasted energy (e.g., transmitted waveform energy that is dispersed in directions other than those intended for a waveform). The set of waveforms may be coherent in the far-field, resulting in waveforms that are suitable for radar d