Adaptive detection of multidimensional signals in the presence of interference with unknown covariance matrix is an expanding topic in a variety of scenarios ranging from radar/sonar to digital communication systems. We attack the problem of detecting a multidimensional radar signal, modeled as an unknown N/spl times/H matrix, embedded in Gaussian noise with unknown covariance matrix, with the ambition of devising receivers which yield the constant false alarm rate (CFAR) property. We show that this aim can be achieved by resorting to the principle of invariance, namely restricting our attention to hypothesis testing problems which remain unaltered under a proper group of transformations. Several detectors based on the maximal invariant statistic are studied and, in particular, the generalized likelihood ratio test (GLRT) is shown to belong to the class of invariant tests.

In this work we consider the problem of M-ary signal detection over a single-input-multiple-output channel affected by time- and/or frequency-dispersive Rayleigh-distributed fading and in the presence of non-Gaussian noise, modeled as a spherically invariant random process (SIRP). We derive the optimum (minimum error-probability) detector, and show that its structure is canonical, i.e. it is independent of the actual noise statistics. Finally, the performance analysis of the receiver highlights that the adoption of diversity represents a suitable means to restore performance also in the presence of dispersive fading and impulsive non-Gaussian noise.

An adaptive detector of range-spread targets embedded in Gaussian noise with unknown covariance matrix is developed and assessed. The proposed receiver requires no prior knowledge about the target strength and its scattering geometry and achieves constant false alarm rate with respect to the noise covariance matrix.

We present a fully adaptive detector of coherent pulse trains embedded in compound-Gaussian clutter, whose covariance matrix is a circulant one. Remarkably, the proposed receiver ensures CFAR-ness with respect to the non-Gaussian noise distribution as well as to its temporal correlation. It also exhibits an acceptable loss with respect to previously proposed nonadaptive structures, even for small sizes of the estimation sample.

The paper discusses the problem of detecting one out of M Gaussian correlated signals in impulsive noise, modeled as a compound-Gaussian, possibly correlated process. We first show that, for uncorrelated noise, the detection problem admits one and the same optimum-in the sense of attaining minimum error probability-solution, independent of the noise statistics: the optimum detector, in fact, amounts to an estimation block, aimed at measuring the short-time noise power spectral density (PSD), whose output is fed to a bank of estimators-correlators, each keyed to one of the M admissible waveforms and to the estimated noise PSD. We also give suggestions for realizing a suboptimum receiver, with reduced complexity, which again is canonical in its structure. As for the performance analysis, we focus on binary frequency-shift keying (BFSK) signaling: we provide numerical results for two particular channel correlations and for Cauchy-distributed noise. These results indicate that, like for the general Gauss-Gauss case, the performance depends on the energy contrast, as well as on the "time-bandwidth" product of the useful signal. Moreover, noise spikiness seems to negatively affect the performance, in the sense that heavier and heavier high-amplitude tails of the noise marginal distribution give rise to higher and higher error probabilities for fixed energy contrast and time-bandwidth signal product.

The article addresses radar detection of coherent pulse trains embedded in spherically invariant noise with unknown statistics. Starting upon a newly proposed detector, which assumes knowledge of the structure of the clutter covariance matrix, we substitute the actual matrix by a proper estimate based on a set of secondary data vectors. Interestingly, the resulting detector achieves a constant false alarm rate with respect to the texture component of the clutter, and incurs an acceptable loss with respect to the case of a known covariance matrix.

This paper deals with the synthesis and the analysis of optimum receivers to detect one out of M equally likely, equi-energy, fading signals in impulsive noise, modelled as a compound Gaussian, possibly correlated process. We show that the conventional coherent and incoherent detectors are still optimum, independent of the noise as well as the fading probability density functions. The performance analysis has been carried on with reference to the general case of arbitrarily distributed disturbance: in order to simplify the analysis, asymptotical expressions have been developed for high signal-to-noise ratios as well as high signal space dimensionality. Interestingly enough, this allows separating the effect of the noise spikyness from that of the fading law. Results indicate that, for deep fading, the noise marginal distribution does not dramatically affect the error probability, nor is it influential on the limit operating characteristics corresponding to infinite signal space dimensions. For non-fluctuating signals, instead, the noise distribution plays a primary role: spiky noise usually produces performance impairment; moreover, the limit performance in impulsive disturbance may exhibit marked deviations from the well-known stepwise shape which is typical of Gaussian channels.>

The paper deals with the detection of signals with unknown parameters in impulsive noise, modeled as a spherically symmetric random process. The proposed model subsumes several interesting families of noise amplitude distributions: generalized Cauchy, generalized Laplace, generalized Gaussian, contaminated normal. It also allows handling of the case of correlated noise by a whitening approach. The generalized maximum likelihood decision strategy is adopted, resulting in a canonical detector, which is independent of the amplitude distribution of the noise. A general method for performance evaluation is outlined, and a comprehensive performance analysis is carried out for the case of M-ary equal-energy orthogonal signals under several distributional assumptions for the noise. The performance is contrasted with that of the maximum likelihood receiver for completely known signals, so as to assess the loss due to the a-priori uncertainty as to the signal parameters.>

The signal design problem for FSK communication via fading dispersive channels is considered. The channel is modeled as a linear filter whose time-varying impulse response is a sample function from a zero-mean Gaussian random field of arbitrary WSSUS type. The additive noise component in the received waveforms is supposed to be a zero-mean white Gaussian random process, and maximum likelihood demodulation is assumed. The signal design procedure here adopted consists of minimizing a known upper bound on the error probability, whereas the previous similar design method by Daly intended maximizing an upper bound on the detection probability for radar-astronomy targets. Though with slightly different optimal numerical values, here, as in Daly's problem, the signal design depends on a single parameter which is a simple functional of the channel timefrequency covariance function and of the signal envelope ambiguity function. A detailed example shows how the results of this concise paper can be used to optimize signal parameters and to predict the performance loss due to nonoptimal signal envelopes.