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An invariant testing approach for detecting multidimensional signals in unknown noise successfully models the space time steering vector of rank one waveforms as the Kronecker product of two unknown vectors lying in known subspaces. The model is useful for array detection in the presence of multipath and spectral/polarization diversity in both radar processing and wireless communication. Detectors constructed on the maximal invariant principles reveal the negligible effect of waveform uncertainty on the signal to noise ratio for achieving adequate detection probability.

We study the design of constant false-alarm rate (CFAR) tests for detecting a rank-one signal in the presence of background Gaussian noise with unknown spatial covariance. We look at invariant tests, i.e., those tests whose performance is Independent of the nuisance parameters, like the background noise covariance. Such tests are shown to have the desirable CFAR property. We characterize the class of all such tests by showing that any invariant decision statistic can be written as a function of two basic statistics which are in fact the adaptive matched filter (AMF) statistic and Kelly's generalized likelihood ratio statistic. Further, we establish an optimum test in the limit of low signal-to-noise ratio (SNR), the locally most powerful invariant (LMPI) test. We also derive the bound for the probability of detection of any invariant detector, at a fixed false-alarm rate, and compare the LMPI and the published detectors (Kelly and AMF) to it.

Novel validation tests of the uniform linear array (ULA) model use the centrosymmetry property of covariance matrices to decide spatial stationarity. These are constant size tests for assessing the significance level. Simulations based on an ideal ULA demonstrate near perfect performance of the tests. Heuristics enable separation of propagation effects from ULA deviations.

The maximal invariant function for array detection problems is more comprehensive than the generalized likelihood ratio (GLRT) method and can analyze optimality features along with invariant tests for the unstructured covariance case. Using the structured covariance matrices conforming to stochastic interferers in a given subspace with unknown GLRT, the maximal invariant is estimated and new invariant detectors are suggested. The invariance tests are robust to high-dimensional nuisance parameters.

Comparison of various cost functions for the mapping of digital signal processing (DSP) algorithms on multiprocessors by examining a recursive least squares problem indicates that the Min-Max + Idle cost function outperforms the other cost functions. Application of the Min-Max + Idle cost function to a QR decomposition problem on an iPSC 860 hypercube demonstrates that the mapping is concurrent and requires low execution times.

An inexpensive new method for detecting sinusoidal signals hidden in nonwhite noise works under general assumptions such as the very low rank of the noise component of the data. The conventional multiwindow method of spectrum estimation continuously yields a false alarm test for the existence of sinusoid in a time series when the noise is Gaussian. The new method is a generalized version of the conventional method to an array.

The probability of false alarm, P(sub FA), in the detection of a sinusoidal signal in white Gaussian noise by the multiwindow spectral analysis method is investigated. Proof is given concerning the higher value of the total P(sub FA), where the sinusoid's frequency is unknown, as opposed to the conditional P(sub FA), where a priori sinusoidal frequency is assumed. The method, which is especially suited to complex signals, requires careful computation and data interpretation when used with real signals.

Adaptive array algorithms based on sample matrix inversion (SMI) require the availability of a secondary data set to 'train' the adaptive filter. Numerous data-independent rules have been proposed for selecting this training data. However, such rules often perform poorly in inhomogeneous environments. We present data-adaptive methodologies for selecting the training data. The techniques, called 'Power Selected Training' and 'Power Selected Deemphasis', use measurements of the interference environment to select training data. This work describes these algorithms and their performance on recorded radar data.