Abstract

This thesis is an exhaustive investigation of a well-known signal processing approach called noise shaping for beamforming. We adopted the noise-shaping approach for phase-only and amplitude-phase synthesis for the first time. To do that, 1-D and 2-D, real- and complex-coefficient, minimum-phase digital finite impulse response filters are designed based on the discrete Hilbert transform method. It is shown for the first time that by pushing the error out of the so-called visible region, the decrease of antenna directivity due to the quantization can be compensated to some extent, which provides an advantage over the uniform distribution of error. In some cases, pushing the error out of the visible region might be impossible. For such cases, we proposed using the spaced-notches filter. Moreover, it has been shown that the method is of maximum efficacy when both the phase and amplitude of the excitation signal are controllable. Thus, complex-valued noise shaping can be exploited for the phase-amplitude synthesis of the phased array, showing quite promising performance. Furthermore, the superiority of noise shaping over conventional random methods for null restoration is brought to attention with several examples for the first time.
Also, the method is implemented at the sub-array layer. A concept study based on the noise shaping approach addressing the quantization error at the sub-array layer is presented for the first time. The noise shaping might be used for the last layer since it typically has enough elements. In this case, the noise shaping is exploited to push the distortion to where other layers' sub-array factors have enough attenuation, which is supposed to alleviate the quantization lobe level to some extent. To do that, a novel approach is proposed in which the sub-array factor, or composite sub-array factor, should be tiled with the periodicity of the ultimate-layer array factor, and subsequently, a contribution of all tiles yields the digital filter layout.
Moreover, we have investigated the quantization issue incurred by the practical pixel in reflectarray. The quantization error has been treated by using signal statistics and the noise shaping approach, which is used for space-fed antennas for the first time. For the space-fed antenna, we used real-valued noise shaping to address the quantization issue. Nevertheless, it is shown that the local periodicity assumption is an important limitation since increasing the depth of the stopband filter for noise shaping inserts a considerable portion of noise into the phase arrangement on the reflective surface, which is problematic for antenna performance. Also, the filter stopband should be designed for all extreme beams, limiting noise-shaping effectiveness for mechanical steering. Then, a resonant type element based on the delay line is chosen for better control of phase delay arrangement. Two prototypes are fabricated, one based on conventional design and the other based on spectrally shaped noise. The performance of the two antennas is compared with each other. It is concluded that the noise shaping can somewhat relax the reflectarray sidelobe level.