Analysis of Beam Pattern Variation Due to Frequency Noise in Frequency Diverse Array Using Cramér–Rao Bound and FDTD

We investigate the influence of frequency noise on the beam pattern within a frequency diverse array (FDA) utilizing the Cramér-Rao lower bound (CRLB). FDA radar offers an ability to adjust the beam pattern with distance as well as angle. This technology has the potential to significantly enhance target detection capabilities by concentrating energy on a specific location. We focus on symmetrical FDA, where the frequency increment is symmetrically distributed across the array, to focus a beam on a specific region. To assess the effect of frequency noise on a FDA, we utilize the CRLB to estimate the variance of the energy-concentrated spot size. Simulations are conducted to model the size of energy spot based on the noise variance, and the CRLB is calculated. It is observed that as the standard deviation of frequency noise increases, the variation of beam size also increases. The resulting CRLB value can help establish a required noise level when implementing FDA hardware. On the other hand, it is also found that the frequency noise enhanced the capability of FDA on concentrating a beam, as the average size of the beam decreases with noise. This phenomenon can be harnessed to create a smaller energy spot in a specific region.