Noncircularity Exploitation In Roubst Adaptive Beamforming

Noncircular signals such as AM, BPSK, UQPSK, QPSK, and QAM signals are widelyused in many practical systems, and the purpose of this dissertation is to investigate thepotential of noncircularity exploitation in robust beamforming. The key contributions are:(1) The diagonal loading (DL) technique is one of the most popular methods to improvethe robustness of the Capon beamformer in the presence of imprecise knowledge of thesignal-of-interest (SOI) steering vector and/or the covariance matrix. However, theselection of an appropriate DL level is not a trivial task. In this dissertation, a class ofrobust beamformers is considered which determines the regularization parameter (i.e. DLlevel) based on the noncircularity restoral (NR) principle. The resulted NRDL beamformersdo not require the user to choose the hyperparameters (such as the size of the uncertaintyset of the SOI steering vector), and outperform the classic hyperparameter-included robustCapon beamformer (RCB) algorithm and the hyperparameter-free mid-way (MW) method.In addition, two extensions of the NRDL beamformers are designed. They are: a) thebeamspace projected NRDL (BP-NRDL) beamformer which pre-filters out theinterferences, and b) the azimuth searching NRDL (AS-NRDL) beamformer which utilizesan additional searching domain of incident angles. Both extensions have proved their meritsover the original methods, while the former is subject to noncircularity diversity betweenthe SOI and interferences.(2) A robust variant of the generalized sidelobe canceller (GSC), which imposesderivative constraints (DC) on the block matrix and is able to null the SOI completely, isproposed. The resulted adaptive array can be virtually extended to a larger aperture in thepresence of fully noncircular incident signals, and the corresponding algorithm is namedNCDC-GSC. Both DC-and NCDC-GSC beamformers have closed-form expressions,which are of much lower complexity yet better performance.(3) The ongoing research on the additional exploitation of the spatial spectrum of theinterferences in robust beamforming has attracted attentions. The relevant contributions ofthis dissertation are: a) the derivative constrained noncircularity rate maximization(DC-NORM) beamformer pre-filters the interferences based on the spatial spectrum, and b)the widely linear DC (WLDC) beamformer is an aperture extended variant ofDC-NORM.Both DC-NORM and WLDC have closed-form expressions and are of low complexity. They are very resistant to strong interferences with higher noncircularity rates(NCRs) than the SOI, and the inaccurate knowledge of the SOI’s NCR. Besides, bothalgorithms can be modified to tackle moving jammers (which are common in applicationssuch as array radar systems, wireless communication and sonar) in a training-free fashion.(4) All the aforementioned algorithms are related to noncircular signals in the sense ofsecond-order statistics (SOS), e.g., BPSK and UQPSK signals. The processing ofnoncircular signals in the sense of higher-order statistics (HOS), such as QPSK and QAMsignals, is discussed using higher-order NRDL (HNRDL) and azimuth searchinghigher-order NRDL (AS-HNRDL) as examples. It should be noted that the HOS methodsare suitable for both HOS and SOS cases, while the SOS methods are applicable in the SOScase only.