| The detection and filtering are basic contexts of statistical signal processing. Signal detection in noise is a typical problem of communication, radar, sonar, and other applications areas. To find an appropriate detection statistic is the key problem. Higher-order statistics are helpful to improve detection performance. CDMA system is widely used in civil. When it is used in military, for communication reconnaissance, the detection of DS-CDMA signal based on higher-order statistics is very important. Adaptive filtering algorithms are important technologies in such diverse fields as channel equalization, echo cancellation, system identification, parameter estimation, among others. In practical applications, many signals and noises often accompany spikes and impulsiveness, andα-stable distribution can preferably describe these signals and noises. Adaptive filtering algorithms based on fractional lower-order statistics(FLOS) show better performance inα-stable distribution environment.This dissertation deals with mainly concerned on the study of two aspects, which are DS-CDMA signal detection theory and methods based on higher-order statistics, and adaptive filtering algorithms based on fractional lower-order statistics, the main contributions are as follows.1)The fourth-order cumulants and moments of DS-CDMA signal are derived, which are fundament of detection methods. It is shown that the first-order to fourth-order cumulants and moments for synchronization DS-CDMA signal and asynchronous DS-CDMA signal are the same. Thus the detection performance using the same statistics for the synchronization DS-CDMA signal and the asynchronous DS-CDMA signal is the same. And it is also shown that the noise is useful to fourth-order moment slices, but useless to fourth-order cumulant slices. Thus, the detection performance of methods based on fourth-order moment slices is better than that of methods based on fourth-order cumulant slices. Different fourth-order moment slices have different noise cancellation capability. The fourth-order moment with slice (τ,τ,τ) is the same as that with slice (0,0,τ), and their noise cancellation capability is superior to the fourth-order moment with slice (0,0,0) and slice (0,τ,τ). Thus, the detection performance of methods based on the former two fourth-order moment slices for DS-CDMA signal is the same, and is better than that of methods based on the latter two fourth-order moment slices.2)Using above theories and hypothesis test theory detection methods based on fourth-order statistics in time domain and in frequency domain are proposed. It is shown that the performance of detection methods in time domain is dependent on the delayτ, and detection performance is difficult to ensure in communication blind reconnaissance. The performance of detection method in frequency domain is not dependent on the delayτ. To reduce the effect of estimation error of the fourth-order moment slice, de-noise processing is used. The performance of detection method in frequency domain is better than that of methods in time domain, and of the correlation method. The detection method in frequency domain can be used to blind reconnaissance for DS-CDMAsignals.3)The least mean P-norm type algorithms inα-stable distribution environment are studied. To improve the performance of adaptive filtering algorithms, adaptive data block filtering algorithms based on the least mean P-norm criterion are proposed, which are fixed step-sized data block least mean P-norm (DBLMP) algorithm and its normalized version (DBNLMP algorithm), variable step-sized data block normalized least mean P-norm (VDBNLMP) and generalized data block normalized least mean P-norm (GDBNLMP) algorithm. And the VDBNLMP algorithm retains the advantage of faster convergence speed which is achieved by the DBNLMP algorithm as compared to the NLMP algorithm. Furthermore, it also has the advantage of smaller steady misadjustment as compared to the NLMP algorithm. The GDBNLMP algorithm converges faster than the"Momentum"-type generalized NLMP (Mom-GNLMP) algorithm.4)Adaptive lattice filtering algorithms inα-stable distribution environment are studied. An adaptive generalized Burg algorithm (GBurgAL) based on the least mean p-norm criterion and an adaptive lattice filtering algorithm (LPL) based on the least p-norm criterion are proposed. GBurgAL has better steady misadjustment and stronger resisting impulse noise capability than least mean p-norm lattice(LMPL) algorithms and least mean square lattice(LMSL) algorithms. LPL has faster convergence rate and stronger resisting impulse noise capability than GBurgAL and least square lattice(LSL) algorithm. And the effect of parameters on the performance of LPL is less than that on the performance of GBurgAL, and parameters of LPL are easy to select. Therefore, LPL is the best lattice algorithm at present.
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