Signal detection and estimation using the multi-window method

Two important problems in array signal processing are the determination of the number of narrow band signals impinging on an array and the determination of their Directions Of Arrival (DOA). The array output is sampled over a period of time the observation interval and the number of signals present and their DOAs estimated. Most existing methods assure that the interference characteristics do not change during the observation interval. In this thesis this restriction is relaxed and a novel methodology developed that works even in a scenario where the interference changes very rapidly. The main assumptions made on the signals are that they are assumed point sources, they do not move over the observation interval, and they are in the far-field. The interference is assumed Gaussian.; A detection scheme is developed that works in the case of a known DOA; this is named a conditional detector, conditioned upon the known DOA. The statistics of the detector are derived and it is shown that this scheme is a constant false alarm rate (CFAR) detector. The main implication being that a meaningful, data invariant, threshold can be set for the detector. This scheme is developed for complex valued signals, and the effect of applying it to real valued signals is discussed. In particular it is shown that for real valued signals it may be unreliable for low grazing angles.; The conditional detector is extended to the case when the DOA is unknown; this is termed the unconditional detector. The unconditional detector estimates a potential DOA and then tests for the presence of a signal. This detector structure is shown to be asymptotically unbiased in the sense of increasing SNR. The effect of the DOA estimation on the probability of false alarm {dollar}(Psb{lcub}FA{rcub}){dollar} is discussed and lower bounds derived. These bounds are given in terms of the {dollar}Psb{lcub}FA{rcub}{dollar} for the conditional detector. We conclude the study of the unconditional detector by comparing its DOA estimation to MUSIC when the interference is severely nonstationary. It is shown how MUSIC fails even though the number of signals is known to the MUSIC algorithm.; As an a motivation for further study the problem of detection and DOA estimation in the case of random signals is formulated. The Maximum Likelihood (ML) estimates of the signal parameters are discussed and a known theorem that partially solves the ML problem is given.