Thesis defences

PhD Oral Exam - Shahin Sheikh, Electrical and Computer Engineering

Noise Shaping for Antenna Beamforming

Tuesday, December 6, 2022 (all day)

This event is free


School of Graduate Studies


Daniela Ferrer



When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.


In analog beamforming (ABF), the digital phase shifters (DPSs) and digital attenuators (DAs) are expensive and power-hungry devices. The amount of insertion loss and costs can be substantially increased with respect to frequency and number of bits used, which is tricky for beamforming. The main problem stems from the limited number of bits of the DPSs contributing to a periodic error which yields a harmonic distortion in the beamspace domain called quantization lobs (QLs). However, such a limitation can also incur gain loss and beam point deviation. The periodicity of error can be trivially interrupted by inserting a portion of noise, an independent random signal with a specific distribution before the quantizer called dithering. Likewise, discretized space-fed antennas, such as reflectarray (RA) and transmitarray (TA) antennas, suffer from phase quantization. This problem even escalates at higher frequency bands as the physical pixel size gets scaled down; hence, it may fail to provide enough phase states.

For the case of digital beamforming (DBF), the number of bits used to quantify the data and the complex beamforming weights has a profound impact on the computational burdens and the system performance. For the case of a large aperture, multiple independent beams, and high data rate, a large number of bits might be impossible to use, which can lead to the distortion problem, somehow the same as one happens in the analog counterpart.

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 (FIR) filters are designed based on the discrete Hilbert transform method. In particular, the digital filter design for phase-only synthesis is comprehensively investigated, respecting the error spectra in the beamspace domain. 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. It is shown that the conventional dithering approaches are ineffective for restoring the null(s) embedded in the antenna radiation pattern to cancel the interference since random dither typically contributes to a flat noise that fills up the nulls; thus, those approaches that contribute to uniform error cannot be used for this purpose. However, the noise shaping approach, which is a spectrally shaped dither, can conveniently address such an issue.

Also, the method is implemented at the sub-array layer. Specifically, in one array architecture, all sub-arrays are assumed with the same complex weights in an overlapping configuration. The set of first layer sub-array outputs is introduced to a digital platform or further tiled to a third layer, and so on. Here, 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 QL 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.

Evidently, the space-fed antenna is of phase-only synthesis as the magnitude of the aperture field is imposed by the feed. Therefore, one may use real-valued noise shaping to address the quantization issue. One should note that the aperture efficiency drops in many applications due to beam shape loss, e.g., in contour beams and multi-focal antenna. In this regard, other error types, including fabrication, quantization, etc., should be managed to keep the antenna performance acceptable. Specifically, one method to generate multiple simultaneous beams is to use a feed chain in front of a reflector that might be designed multi-focal to compromise the extreme beams’ performances. We have presented a novel multi objective optimization based on Pareto dominance for the design of multi-focal RA (MF-RA). Also, we have investigated the quantization issue incurred by the practical pixel. This has been treated by using signal statistics and the noise shaping approach, which is used for space-fed antennas for the first time. This method can mitigate the quantization issue due to practical pixel response. 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 compared with each other. It is concluded that the noise shaping can somewhat relax the RA sidelobe level.

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