Performance Analysis And Application Research Of Adaptive Estimation Algorithm For Noncircular Complex-Valued Data

Complex-valued random signals are embedded into the very fabric of science and engi-neering,being essential to communications,radar,sonar,optics,acoustics,electromagnetics,oceanography,and other applied sciences,yet the usual circular assumptions made about their statistical behaviour are often a poor representation of the underlying physics.In this disserta-tion,we focus on the design,performance analysis as well as applications in communications of adaptive estimation algorithms with noncircular complex-valued signals.By exploiting the full second-order statistics of these signals,not only significant performance improvements can be achieved,but also deeper theoretical insights are provided for adaptive estimation algorithms,which further inspires their practical use in real-world applications.The main contributions of this work are as follows:Theoretical analyses and comparisons for both strictly linear(SL)and widely linear(WL)estimators using both the mean square error(MSE)and Gaussian entropy criteria with noncircu-lar Gaussian input data is provided.In particular,a novel complementary weight error variance analysis is first proposed to qualify the degree of noncircularity of their respective weight er-rors.The bounderness of complementary weight error variances in different estimators is next investigated,which is enabled through the strong uncorrelating transform(SUT)that jointly di-agonalizes both the input covariance matrix and its complementary counterpart.Furthermore,a joint consideration of both the standard and complementary weight error variance analyses is shown to exhibit sufficient degrees of freedom to qualify individual performance in real and imaginary data channels of these estimators.This reveals that the class of Gaussian entropy based SL estimators yields reduced or at very least equal weight error variances in both the real and imaginary channels,as compared with its MSE counterpart.The analysis also shows that when a WL estimator is applied to match a linear model,although it brings about an overall performance degradation,as compared with the MSE based SL estimator,there may exist a smaller weight error estimation variance locally in either the real or the imaginary data chan-nel.However,performance losses in both the data channels are expected when compared to the Gaussian entropy based SL estimator.Simulations in the system identification setting support the analysis.A full second-order performance analysis is introduced for the least stochastic entropy(LSE)adaptive estimation algorithm with correlated noncircular Gaussian inputs.This is achieved by considering the coupled evolution of both the weight error covariance matrix and comple-mentary covariance matrix.A mean square stability bound on the step-size is also established to guarantee convergence,and to allow for a closed-form evaluation of the weight error variance of the LSE at steady-state.The analysis also shows that during the recursive minimization of the weight error variance,the weight error of LSE becomes increasingly more circular.Simulations in a system identification setting support the analysis.A novel mean square analysis in the frequency domain is presented to rigorously inves-tigate how the full second-order statistics of the noncircular correlated complex-valued input signals influence the convergence of the weight error covariance matrix and the MSE of the un-constrained frequency domain block least mean square(UFBLMS)algorithm.Next,the com-plementary mean square analysis is also conducted to investigate how the noncircularity of the input and the system noise propagates into the error and the weight error vector.This is achieved by examining their complementary second-order statistics,namely,the complementary MSE(CMSE)and weight error complementary covariance matrix.By doing so,we establish a full second-order statistical framework to assess the error and the weight error vector of UFBLMS in both the transient and steady-state stages; intuitive closed-form relations between the steay-state MSE/CMSE and the input noncircularity are also provided.Simulations and real-world data set experiments support the analysis.A class of generalized complex-valued Kalman filter(GCKF)algorithms is proposed for the linear and nonlinear state space models with second-order circular or noncircular signals.This is established by first proposing a novel batch estimator which combines both linear mini-mum mean square error(LMMSE)estimator and conjugate linear minimum mean square error(CLMMSE)estimator for the estimation of general complex-valued signals.Theoretical analy-sis of the superiority of the proposed estimator over the traditional LMMSE estimator in terms of MSE is also provided,motivating the subsequent development of the GCKF algorithm in the sense that performance gains can be expected by incorporating both the innovation and its conjugate in the state update equation.Such a filter structure is then extended to the nonlinear filtering problem,yielding the generalized complex-valued extended KF(GCEKF)algorithm and generalized complex-valued unscented KF(GCUKF)algorithm,of which the derivation of the latter is achieved based on a new sigma points selection scheme that provides a sample esti-mate of the first two moments with a second-order accuracy.Simulations in both autoregressive process estimation and channel estimation support the analysis.A blind adaptive frequency-dependent(FD)inphase/quadrature(I/Q)imbalance compen-sator is proposed for wideband direct-conversion receivers.This is achieved by virtue of restor-ing the second-order circular nature of the desired signal,a property which is violated under I/Q imbalance.The full second-order performance analysis of the proposed compensator is made mathematically tractable via the weight error covariance and complementary covariance analyses.In this way,we illuminate the intrinsic physical insights underlying the proposed com-pensator in the sense that during the iterative I/Q imbalance compensation process,its weight error vector becomes,in theory,purely proper.For rigor,we also provide an accurate evalua-tion of its excellent mirror-frequency interference attenuation capability in terms of the image rejection ratio(IRR),which indicates that after compensation,FD I/Q distortions can be effec-tively eliminated over the whole bandwidth,i.e.,the IRR of the compensated receiver becomes frequency-independent.Simulation results in an orthogonal frequency division multiplexing(OFDM)transmission scheme support the analysis.