RFDA Frequency Offset Synthesis Given Specified Range Resolution of the Spot-Like Beampattern

Random frequency diverse arrays (RFDAs) yield spot-like beampatterns in both angle and range dimensions. As a result of random frequency offsets, direct estimation of range and angle extension is not feasible. In this communication, the half power beamlength (HPBL) of the fundamental harmonic of the radiation pattern is utilized to design appropriate random frequency offsets to ensure that the RFDA exhibits a specified range resolution. For symmetric probability density functions (PDFs) of the frequency offsets, the problem is cast into a convex quadratic optimization program with linear constraints. In contrast, for general PDFs, the problem is primarily non-convex which is transformed into an iterative quadratic problem with linear constraints exploiting a Lagrange multiplier. Finally, a PDF-weighted random number generator is used to generate several RFDAs with the desired HPBLs. The proposed PDFs generate radiation patterns with desired range resolutions for arbitrary frequency offset coefficients, while enjoying acceptable side lobe levels.