Extreme Beam Broadening using Phase Only Pattern Synthesis

This paper describes methods for broadening the beam of a phased array antenna using phase-only element weights. This type of broadening can be valuable for improving the search occupancy and/or reducing the search frame time for large phased arrays, when transmit beam broadening is combined with multiple simultaneous receive beams. Phase-only broadening is required for typical solid-state (active phased) arrays because control of the transmit amplitude at each element is not practical. A notable result is that there is a relationship between the amount of beam broadening and the efficiency (directivity) of the resulting beam. In particular it is shown that broadening less than ~2.5:1 results in reduced beam efficiency for both linear and circular arrays, while a broadening of greater than ~2.5:1 results in improved beam efficiency, and that, therefore, certain broadening configurations will be preferable to the radar designer (e.g. 4:1 in one plane rather than 2:1 in two planes, due to a large difference in efficiency). The algorithms used to achieve the broadening patterns presented here are based on a combination of homotopy from known optimality with a stochastic gradient descent approach using a carefully constructed one parameter family of penalty functions