Research On Parameter Estimation Method For Noncircular Signals

Noncircular signals are usually encountered in radio communications, such as AM,MASK, UQPSK, BPSK, MSK, GMSK and OQPSK signals. This dissertation addressesthe parameter estimation issue for noncircular signals, including time difference ofarrival (TDOA) estimation for noncircular signals, direction of arrival (DOA)estimation for noncircular signals with multiple noncoherent subarrays, and robustCapon beamforming for noncircular signals. Compared to utilizing only thecross-correlation statistics of a signal in the case of circular signals, the key point of theresearch on parameter estimation for noncircular signals is how to jointly utilize thecross-correlation and conjugate cross-correlation statistics of a noncircular singal toimprove the estimation perforamce. The main work and contibutions of this dissertationare as follows.1. The maximum likelihood (ML) estimator and the Cramer–Rao lower bound(CRB) of TDOA estimation for Gaussian noncircular signals in Gaussian circular noiseis derived. Compared to the cross-correlation and conjugate cross-correlation estimators,the ML estimator utilizes the second-order statistics (SOS) information of a noncircularsignal more comprehensively and thus has better performance. Then, based on thecyclostationarity of man-made signals, a scheme to modify the traditionalsignal-selective TDOA methods for noncircular signals is proposed. This schemeexploits simultaneously the information contained in both the cyclic cross-correlation(CCC) and the conjugate CCC of a noncircular signal.2. For real-valued Gaussian and Laplacian signal models, the TDOA estimatorsusing the two information-theoretic measures, joint entropy and mutual information(MI), have been compared. Then, a method employing the MI to exploit thesecond-order (SO) noncircularity of noncircular signals has been proposed.3. The asymptotically-minimum-variance (AMV) SO estimation of DOA fornoncircular sources with multiple noncoherent subarrays has been addressed. First, theML estimator and the closed-form CRB for this problem are derived for noncircularGaussian complex signals and circular Gaussian complex noise. Subsequently, themodified generalized least-squre estimator is proposed, which is anasymptotically-minimum-variance (AMV) SO estimator for both Gaussian and non-Gaussian circular sources. Then, an AMV SO estimator for noncircular sources ispresented.4. The MUSIC-like DOA estimation algorithms for multiple noncoherent subarrayshave been studied. A weighted MUSIC (w-MUSIC) algorithm for noncoherentsubarrays using only the first covariance matrix is proposed, and it is subsequentlyextended for noncircular sources. The asymptotic performance of the w-MUSICalgorithm and a previously introduced MUSIC algorithm in [85] for noncoherentsubarrays are analyzed and compared.5. A robust Capon beamformer for noncircular signals (termed NC-RCB) has beenproposed for the generalized case with possibly noncircular signal-of-interesting (SOI)and/or noncircular interferences. The NC-RCB exploits the SO noncircularity of theSOI and interferences simultaneously and is robust against the errors in the steeringvector, sample covariance matrix and noncircular parameter of the SOI. For noncircularSOI, the NC-RCB shows distinctly better performance than the robust Caponbeamformer using only the first covariance matrix.