Reduced complexity FPGA-based digital signal processing for adaptive beamforming

Advancements in FPGA technology have permitted near real-time signal processing. To achieve real-time signal processing one can consider reduced complexity algorithms. An important component of many modern signal processing algorithms is calculation of the signal autocorrelation matrix. Instead of calculating the conventional autocorrelation, we propose to use the complex hybrid-sign and the quadruplex algorithms introduced by Jacovitti (1987) and Sullivan et al. (1995), respectively. The accuracy of these algorithms is of concern especially in applications which are resolution sensitive. In particular, we consider the effect of the hybrid and quadruplex approximations on the direction of arrival (DOA) estimate produced by beamforming. We show that the variance of the DOA estimate approaches the theoretical estimate predicted by Sullivan for low S/N ratio. At high S/N ratio, the bias and variance of the quadruplex estimate are actually better than the conventional method