Remarks on Noise Shaping for Phased Array Analog Beamforming

This article comprises three parts, which exhaustively investigates the noise-shaping approach in analog beamforming of phased array (PA) antenna. Specifically, the impact of digital filter design on different PA applications is studied. In the first part, an overview of noise shaping in a hexagonal lattice PA is investigated for the first time. Compared with the Nyquist square lattice, the hexagonal counterpart yields a much smaller invisible region which is a challenge for pushing the error out of the visible region. Nevertheless, it has been shown that the method suppresses the quantization lobes (QLs), realigns the point deviation, and may promote antenna gain. For those with critically large array pitch, the digital filter stopband may become prohibitively wide, contributing to a negligible antenna gain loss. The second part uses the method for restoring null(s). It is shown that the noise-shaping approach is quite effective in enhancing the fidelity of the system in nulling the spatially localized interferences. However, considering the discrepancy between addressing the QLs as a harmonic error and nulls buried beneath the quantization residue, the digital filter design is challenging and needs high attenuation level. Specifically, the number of nulls is an essential criterion for the method’s success. The computations are double-checked with full-wave simulations. The results verify the viability of the approach with a minor deflection from the computation. The third part investigates the noise-shaping approach in PA of the sparse element spacing. The complication of digital filter design with respect to antenna gain loss is investigated for different scenarios. Optimization is used for complicated cases to find an optimal filter to minimize the antenna gain loss.