Impacts of frequency increment errors on frequency diverse array beampattern

Different from conventional phased array, which provides only angle-dependent beampattern, frequency diverse array (FDA) employs a small frequency increment across the antenna elements and thus results in a range angle-dependent beampattern. However, due to imperfect electronic devices, it is difficult to ensure accurate frequency increments, and consequently, the array performance will be degraded by unavoidable frequency increment errors. In this paper, we investigate the impacts of frequency increment errors on FDA beampattern. We derive the beampattern errors caused by deterministic frequency increment errors. For stochastic frequency increment errors, the corresponding upper and lower bounds of FDA beampattern error are derived. They are verified by numerical results. Furthermore, the statistical characteristics of FDA beampattern with random frequency increment errors, which obey Gaussian distribution and uniform distribution, are also investigated.