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The problem of jointly estimating the number, the identities, and the data of active users in a time-varying multiuser environment was examined in a companion paper (IEEE Trans. Information Theory, vol. 53, no. 9, September 2007), at whose core was the use of the theory of finite random sets on countable spaces. Here we extend that theory to encompass the more general problem of estimating unknown continuous parameters of the active-user signals. This problem is solved here by applying the theory of random finite sets constructed on hybrid spaces. We do so deriving Bayesian recursions that describe the evolution with time of a posteriori densities of the unknown parameters and data. Unlike in the above cited paper, wherein one could evaluate the exact multiuser set posterior density, here the continuous-parameter Bayesian recursions do not admit closed-form expressions. To circumvent this difficulty, we develop numerical approximations for the receivers that are based on Sequential Monte Carlo (SMC) methods ("particle filtering"). Simulation results, referring to a code-divisin multiple-access (CDMA) system, are presented to illustrate the theory. Index Terms--Bayesian recursions, multiuser detection, particle filtering, random-set theory.

The interplay among the rank of optimized space-time code, the number of transmit diversity paths generated in the signal space and the amount of energy integrated along each path were explored to gain insight into a multiple-input multiple-output (MIMO) detection problem. The results confirmed the existence of an inherent tradeoff between diversity and integration and absence of uniformly optimum waveform design strategy.

The problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered. Assuming a Markov evolution of the system (in particular, the pair signal-observation forms a hidden Markov model (HMM)), a sequential procedure is proposed, wherein the detection part is a sequential probability ratio test (SPRT) and the estimation part relies upon a maximum a posteriori probability (MAP) criterion, gated by the detection stage (the parameter to be estimated is the trajectory of the state evolution of the system itself). A thorough analysis of the asymptotic behavior of the test in this new scenario is given, and sufficient conditions for its asymptotic optimality are stated, i.e., for almost sure minimization of the stopping time and for (first-order) minimization of any moment of its distribution. An application to radar surveillance problems is also examined. Index Terms--Asymptotic optimality, hidden Markov models (HMM), sequential detection and estimation, sequential probability ratio test (SPRT).

The general problem of joint sequential target detection and estimation is considered for multiframe surveillance radar systems. Numerical experiments are performed in order to understand the interplay between sensor-target parameters and system performances and also to quantify the gain with respect to other fixed-sample procedures.

This paper addresses the problem of early detection of K [greater than or equal to] 1 multiple moving targets in radar systems through the use of track-before-detect (TBD) techniques. At first, assuming prior knowledge of K, a binary generalized likelihood ratio test (GLRT) is derived, which shows that the multi-target TBD problem can be regarded as a K-path trellis search. Since optimal implementation of the GLRT has a nonlinear complexity either in the number of targets or in the number of integrated frames, suboptimum algorithms are investigated which allow to trade better estimation and tracking accuracy for a much lower implementation complexity. Next, the TBD problem with K unknown is discussed and a novel multi-hypothesis test strategy is derived as the solution to a constrained optimization problem, which subsumes the conventional binary GLRT as the special case of known K. Finally, numerical examples are provided to assess and compare the performances of the proposed TBD procedures.

In random-access communication systems, the number of active users varies with time, and has considerable bearing on receiver's performance. Thus, techniques aimed at identifying not only the information transmitted, but also that number, play a central role in those systems. An example of application of these techniques can be found in multiuser detection (MUD). In typical MUD analyses, receivers are based on the assumption that the number of active users is constant and known at the receiver, and coincides with the maximum number of users entitled to access the system. This assumption is often overly pessimistic, since many users might be inactive at any given time, and detection under the assumption of a number of users larger than the real one may impair performance. The main goal of this paper is to introduce a general approach to the problem of identifying active users and estimating their parameters and data in a random-access system where users are continuously entering and leaving the system. The tool whose use we advocate is Random-Set Theory (RST): applying this, we derive optimum receivers in an environment where the set of transmitters comprises an unknown number of elements. In addition, we can derive Bayesian-filter equations which describe the evolution with ti me of the a posteriori probability (APP) density of the unknown user parameters, and use this density to derive optimum detectors. In this paper, we restrict ourselves to interferer identification and data detection, while in a companion paper we shall examine the more complex problem of estimating users' parameters. Index Terms--Multiuser detection, random set theory, Bayesian recursions.

This paper considers the problem of multiple-input multiple-output (MIMO) radars employing space-time coding (STC) to achieve diversity. To this end, after briefly outlining the model of the received echo, a suitable detection structure is derived, and its performance is expressed in closed form as a function of the clutter statistical properties and of the space-time code matrix. Interestingly, this receiver requires prior knowledge of the clutter covariance, but the detection threshold is functionally independent thereof. At the transmitter design stage, we give two criteria for code construction: the first is based on the classical Chernoff bound, the second is an information-theoretic criterion. Interestingly, the two criteria lead to the same condition for code optimality, which in turn specializes, under the assumption of uncorrelated clutter and square code matrix, in some well-known full-rate space-time codes. A thorough performance assessment is also given, so as to establish the optimum achievable performance for MIMO radar systems.

The performance of user cooperation in the uplink of a synchronous direct-sequence (DS) code-division multiple-access (CDMA) cellular network is analyzed by using nonorthogonal spreading codes. A performance assessment is undertaken to analyze the impact of the multiple-access interference on the proposed cooperative strategies under different scenarios and system assumptions.

A new class of receivers based on widely linear data processing is proposed for data detection in communication systems affected by improper complex noise. It is shown that the improved receivers outperform the conventional ones both in terms of the error probability and of the capacity to cope with the power disparities that the fading channel induces on the data streams transmitted by different antennas.

We focus on the synthesis and the analysis of recursive receivers for direct-sequence code-division multiple-access systems aimed at achieving satisfactory performance at the price of a moderate computational complexity. At the analysis stage, some interesting properties shared by the proposed procedures are proven. Finally, the performance assessment shows that the new schemes are superior to the linear detectors, and some of them achieve a bit-error rate close to that of the optimum receiver. Index Terms--Direct-sequence code-division multiple-access (DS-CDMA) systems, iterative detection, multiuser detection.

In this paper we present a family of track-before-detect (TBD) procedures for early detection of moving targets from airborne radars. Upon a sectorization of the coverage area, the received echoes are jointly processed in the azimuth-range-Doppler domain and in the time domain through a Viterbi-like algorithm that exploits the physically admissible target transitions between successive illuminations, in order to collect all of the energy back-scattered during the time on target (TOT). A reduced-complexity implementation is derived assuming, at the design stage, that the target does not change resolution cell during the TOT in each scan. The constant false alarm rate (CFAR) constraint is also englobed in the proposed procedures as well as the possibility of working with quantized data. Simulation results show that the proposed algorithms have good detection and tracking capabilities even for high target velocities and low quantization rates.

Formulas for the modified Cramer-Rao bounds (CRBs) are obtained under the assumption that the spreading codes can be modeled as random nuisance parameters. Numerical examples showing the impact of the training length, signal-to-noise ratio (SNR) and the number of active users on the CRB are also reported and commented upon.

The problem of blind multiuser detection in a direct sequence code division multiple access (DS/CDMA) multiantenna systems is discussed. The design strategy and performance evaluation technique to space-time coded system are proposed.

In iterative data-detection and channel-estimation algorithms, the channel estimator and the data detector recursively exchange information in order to improve the system performance. While a vast bulk of the available literature demonstrates the merits of iterative schemes through computer simulations, in this paper analytical results on the performance of an iterative detection/estimation scheme are presented. In particular, this paper focus is on uncoded systems and both the situations that the receiver and the transmitter are equlpped with either a single antenna or multiple antennas are considered. With regard to the channel estimator, the analysis considers both the minimum mean square error and the maximum likelihood channel estimate, while, with regard to the data detector, linear receiver interfaces are considered. Closed-form formulas are given for the channel-estimation mean-square error and for its Cramer-Rao bound, as well as for the error probability of the data detector. Moreover, the problem of the optimal choice of the length of the training sequence is also addressed. Overall, results show that the considered iterative strategy achieves excellent performance and permits, at the price of some complexity increase, the use of very short training sequences without incurring any performance loss. Finally, computer simulations reveal that the experimental results are in perfect agreement with those predicted by the theoretical analysis. Index Terms--Channel estimation, Cramer-Rao bound (CRB), data detection, multiantenna systems, wireless communication.

In this paper, the problem of subspace-based blind adaptive multi-user detection in multi-rate direct-sequence code-division multiple-access (DS.CDMA) systems adopting short (periodic) spreading codes is considered. The solution that we propose is based on the well-known formulation of the linear minimum mean-squared error and decorrelating detectors in terms of signal subspace parameters. Since in a multi-rate scenario the correlation properties of the observable (and, hence, the signal subspace parameters) are periodically time-varying, classical subspace tracking algorithms, which assume that the subspace to be tracked is time-invariant or slowly time-varying, are shown to be not useful in this situation. A new recursive cyclic subspace tracking algorithm is thus developed. This procedure, which is based on a generalization of the PASTd algorithm, is able to capture the periodical variations of the signal subspace, and thus enables subspace-based blind adaptive multi-user detection in multi-rate CDMA systems. The proposed algorithm has a smaller computational complexity than the recently developed cyclic recursive-least-squares procedure, and, as numerical results confirm, is capable of providing very satisfactory performance. Index Terms--Blind adaptive multi-user detection, cyclic algorithms, direct-sequence code-division multiple-access (DS-CDMA) systems, multi-rate CDMA, subspace tracking.

The problem of blind adaptive joint multiuser detection and equalization in direct-sequence code division multiple access (DS/CDMA) systems operating on fading dispersive channels is examined and discussed.

Recently, a new class of linear multiuser receivers for direct-sequence code-division multiple-access (CDMA) systems employing binary phase-shift keying modulation has been introduced. Unlike classical decorrelating and minimum mean-square error linear multiuser detectors, the new receivers exploit the information contained in the pseudoautocorrelation of the observables, and are, thus, capable of achieving much better performance. In this letter, we present new results on the performance analysis of this class of new receivers. In particular, with reference to a CDMA system with deterministic spreading codes, we show that the new receivers outperform the classical ones in terms of both error probability and near-far resistance. With regard, instead, to CDMA systems with random spreading, we compute the average system near-far resistance, showing that the new receivers can accommodate twice the number of users accommodated by the classical linear multiuser receivers. Index Terms--Code-division multiple access (CDMA), improper random access, multiuser detection, performance analysis, random code-division multiple access (CDMA).

It has been recently shown that in a direct-sequence/code-division multiple-access (DS/CDMA) system employing binary phase-shift keying (BPSK) modulation the baseband equivalent of the CDMA multiplex is, under very mild assumptions, an improper complex random process, i.e., it has a nonzero pseudoautocorrelation function. In this correspondence, the problem of linear multiuser detection for asynchronous DS/CDMA systems with improper multiaccess interference (MAI) is considered. A new mean-output-energy (MOE) cost function is introduced, whose constrained minimization leads to two new linear multiuser detectors, exploiting the information contained in the pseudoautocorrelation of the observables, and which generalize the classical decorrelating and minimum mean-square error (MMSE) receivers. The problem of blind adaptive receiver implementation based on subspace tracking is also briefly tackled. Finally, the superiority of the new detectors with respect to the classical linear detection structures present in the literature is demonstrated through both theoretical considerations and computer simulations. Index Terms--Code division multiple access (CDMA), decorrelating detector, improper complex noise, minimum mean-square error (MMSE) detector, multiuser detection, subspace tracking.

In this paper, we handle the problem of joint suppression of multiple-access interference (MAI) and narrowband interference (NBI) in fading, dispersive channels. The detectors we consider are linear, one-shot structures, which allow for possible window enlargement and signal-space oversampling to improve performance. We focus on both zero-forcing and minimum-mean square-error design strategies, showing that the presence of NBI generally requires a time-varying processing of the observables, no matter what the optimization criterion. A thorough performance assessment of the proposed detectors is also presented, either through analytical formulas or through computer simulations. We finally deal with the problem of blind suppression of both MAI and NBI, introducing batch-estimation procedures to be implemented offline, which require very little and sometimes no prior knowledge as to the interference structure. Index Terms: DS/CDMA, interference suppression, selective fading.

This paper addresses the problem of narrow-band interference (NBI) cancellation in direct-sequence spread-spectrum systems. The proposed procedure amounts to a preliminary nonlinear processing, wherein, upon projection of the received signal onto a Fourier basis, a number of samples having the largest modula are excluded from further processing. The structure of the optimum detector operating on censored observations is obtained, showing that the optimum detector performs matched filtering on the censored data. The performance assessment demonstrates that this receiver is able to suppress narrow-band interferers, no matter what their structure, provided that the censoring depth is properly chosen. A blind version of such a receiver is presented also, and a comparative performance assessment demonstrates that, unlike other suppression procedures, the proposed system allows suppression of NBI with no prior knowledge on its structure. Index Terms - Interference suppression, order statistics, spread-spectrum communication.

Radar detection of coherent pulse trains embedded in compound-Gaussian disturbance with partially known statistics is discussed. We first give a thorough derivation of two recently proposed adaptive detection structures. Next, we derive a different detection scheme exploiting the assumption that the clutter is wide-sense stationary. Resorting to the theory of circulant matrices, in fact, we demonstrate that the estimation of the structure of the clutter covariance matrix can be reduced to the estimation of its eigenvalues, which in turn can be (efficiently) done via fast Fourier transform codes. After a thorough performance assessment, mostly carried on via computer simulations, the results show that the newly proposed detector achieves better performance than the two previously introduced adaptive detectors. Moreover, a sensitivity analysis shows that, even though this detector does not strictly guarantee the constant false alarm rate property with respect to the clutter covariance matrix, it is robust, in the sense that its performance is only slightly affected by variations in the clutter temporal correlation.

This paper handles the simultaneous suppression of narrow-band and multiaccess interference in code-division multiple-access (CDMA) direct-sequence spread-spectrum (DSSS) systems. The basic structure we refer to is reminiscent of the decorrelating detector, but here the design strategy relies on the concept of combating jointly the two interference sources - precisely, a decision as to the bit transmitted by each user is made based on the projection of the observables onto the orthogonal complement to the subspace spanned by the other users' signatures and the narrow-band interference. We focus on several different implementations of such a strategy, assuming a different degree of prior knowledge as to the narrow-hand interference. An important side result of the proposed approach is that, in general, complete suppression of data-like interference may be achieved through periodically time-varying processing. An adaptive version of such a receiver is also presented, wherein the projection direction is estimated based on suitable estimates of the covariance properties of the observables. The value of this method is also assessed by studying the rate of convergence of the estimated direction to the true projection direction.

This 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. Index Terms - Detection, fading channels, non-Gaussian noise, SIRP.

The problem of constant false-alarm rate (CFAR) detection of possibly range-spread targets in clutter-dominated environment, whether Weibull or lognormal is presented. The proposed scheme is a member of the clutter-map CFAR family, which relies on a combination of space and time processing as well as on the relevant properties of the location-scale distributions; it ensures CFAR against noise with biparametric variations without incurring masking effects from slow, extended targets or multiple interferers. We also give guidelines for designing the system parameters, along with approximate formulas for setting the appropriate threshold multipliers to achieve a given false-alarm rate (FAR) under Weibull and lognormal clutter.

The performance assessment of the clutter map constant false-alarm rate (CFAR) procedure presented in Part I [1] is introduced. At first, the performance in the presence of point targets is investigated, subject to both Weibull and lognormal clutter, so as to elicit the influence of the system parameters. The study essentially relies on Monte-Carlo simulations, but approximations for the detection rate are also developed. Admittedly, a global figure of performance, the Average Threshold Deviation (ATD), is introduced and its worth as a design tool is validated. Next, the effect of extended as well as multiple targets is considered, showing that the system can be designed so as to avoid self-masking from either range-spread targets persisting on the same map cell, or spurious targets in close spatial proximity to the cell under test. Finally, the system robustness is demonstrated through a sensitivity study, aimed at investigating the effect of a possible mismatch between the design and the actual clutter distribution, that of the clutter correlation and of a thermal noise component in the overall disturbance.

In a decentralized detection scheme, several sensors perform a binary (hard) decision and send the resulting data to a fusion center for the final decision. If each local decision has a constant false alarm rate (CFAR), the final decision is ensured to be CFAR. We consider the case that each local decision is a threshold decision, and the threshold is proportional, through a suitable multiplier, to a linear combination of order statistics (OS) from a reference set (a generalization of the concept of OS thresholding). We address the following problem: given the fusion rule and the relevant system parameters, select each threshold multiplier and the coefficients of each linear combination so as to maximize the overall probability of detection for constrained probability of false alarm. By a Lagrangian maximization approach, we obtain a general solution to this problem and closed-form solutions for the AND and OR fusion logics. A performance assessment is carried on, showing a global superiority of the OR fusion rule in terms of detection probability (for operating conditions matching the design assumptions) and of robustness (when these do not match). We also investigate the effect of the hard quantization performed at the local sensors, by comparing the said performance to those achievable by the same fusion rule in the limiting case of no quantization.

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.

A new family of constant false alarm rate (CFAR) processors is introduced. An Ll-CFAR forms its noise power estimate by linearly filtering ranked samples from the reference set; the weights of this combination, however, depend not only on the rank, but also on the relative proximity of the sample to the cell under test. From the class of Ll-CFARs may be chosen members which effectively censor spurious targets; members which exhibit impressive control of false alarm in the presence of a clutter edge; and members which are robust against both such inhomogeneities. While the design of such schemes is involved, their implementation is not significantly more burdensome than that of plain ordered statistic CFAR (OS- CFAR). After a discussion of the stochastic training of Ll-CFAR, the performance is thoroughly assessed under the most commonly encountered instances of environmental conditions, and compared with those of classical CFAR techniques.

We consider procedures for constant false alarm rate in Lognormal clutter, accounting for variations of both a scale and a shape parameter of the clutter. Adaptivity to both parameters is obtained through biparametric estimation based on a sliding window surrounding the radar cell under test. We present some new procedures exploiting best linear unbiased estimation (BLUE) and compare them to a previous procedure called Log-t which uses maximum likelihood estimation. The comparison is carried on under homogeneous clutter environment and under instances of inhomogeneous environment (clutter edges and spurious targets). In the latter instances, some advantages of BLUE procedures are highlighted which stem from the opportunity of censoring.

In this paper, we deal with interference suppression in asynchronous direct-sequence code-division multiple-access (CDMA) systems employing binary phase-shill keying modulation. Such an interference may arise from other users of the network, from external iow-rate systems, as well as from a CDMA network coexisting with the primary network to form a dual-rate network. We derive, for all of these cases, a new family of minimum mean-square-error detectors, which differ from their conventional counterparts in that they minimize a modified cost function. Since the resulting structure is not implementable with acceptable complexity, we also propose some suboptimum systems. The statistical analysis reveals that both the optimum and the suboptimum receivers are near-far resistant, not only with respect to the other users, but also with respect to the external interference. We also present a blind and a recursive least squares-based, decision-directed implementation of the receivers wherein only the signature and the timing of the user to be decoded and the signaling time and the frequency offset of the external interferer are assumed known. Finally, computer simulations show that the proposed adaptive algorithm outperforms the classical decision-directed RLS algorithm. Index Terms--Code-division multiple access, interference suppression, minimum-mean-square-error, multiple-access interference, multirate systems, multiuser detection, narrow-band interference.

In this work, the problem of joint suppression of multiple-access and narrow-band interference (NBI) for an asynchronous direct-sequence code-division multiple-access (CDMA) system operating on a frequency-selective fading channel is addressed. The receiver structure we consider can be deemed as a two-stage one: the first stage consists of a bank of minimum mean-square-error (MMSE) filters, each keyed to a given replica of the useful signal, and aimed at suppressing the overall interference; the second stage, assuming knowledge of the fading channel coefficients realizations, combines the MMSE filters outputs according to a maximal-ratio combining rule. Due to the presence of the NBI, the resulting structure is in general time-varying, and becomes periodically time-varying if the NBI bit-rate has a rational ratio to that of the CDMA system. Moreover, enlarging the observation window beyond the signaling interval and over-sampling the signal space may yield a noticeable performance improvement. For the relevant case that the said ratio is rational, a new cyclic blind recursive least squares (RLS)-based algorithm is introduced, capable of tracking the periodically time-varying receiver structure, and allowing adaptive interference cancellation with a moderate complexity increase. We also come up with a closed-form expression for the conditional bit-error rate (BER), which is useful both to evaluate semi-analytical methods to assess the unconditional BER and to derive bounds on the system near-far resistance. The results indicate that the receiver achieves very satisfactory performance in comparison to previously known structures. Computer simulations also demonstrate that the cyclic blind RLS algorithm exhibits quite fast convergence dynamics. Index Terms--DS-CDMA, frequency-selective fading, multiple-access interference, multiuser detection, narrow-band interference, recursive-least-squares, recursive-least-squares.

This paper handles the simultaneous suppression of narrow-band and multiaccess interference in asynchronous CDMA networks. We consider both linear one-shot detection and block-detection, showing that, in both cases, the presence of an external narrow-band interferer generally results in the need for time-varying processing. As to the linear one-shot detectors, we derive both a zero-forcing and a minimum mean square error detector, showing that they are members of an only family, wherein the optimization criterion is the constrained minimization of a suitably defined output interference energy. We also present a comparative performance assessment between the various detection strategies, studying the impact of both the optimization criterion and other system parameters, such as the oversampling ratio and the length of the observation window. We also handle the problem of blind and adaptive detection. At first we show that the linear one-shot receivers are readily amenable to a blind implementation, upon off-line estimation of the covariance matrix of the observables. Next, we consider the problem of an adaptive implementation of a periodically time-varying minimum mean square error receiver, introducing and assessing a new cyclic recursive least squares (RLS) algorithm: we show that, unlike the conventional RLS algorithms, the new algorithm is capable of tracking the periodically time-varying variation of the receiver structure, induced by the presence of a data-like narrow-band interferer. Index Terms--Blind receiver, interference suppression, recursive least squares (RLS) algorithm, spread spectrum.

The problem of M signal detection over a single input multiple output channel affected by fading dispersive is examined.

The detection of incoherent pulse trains in compound-Gaussian disturbance with known spectral density is dealt with here. Two alternative approaches are investigated. The first, assuming perfect knowledge of the signal fluctuation law and implementing the Neyman-Pearson test on the observed waveform, turns out to be not applicable to the radar problem. The second, instead, relying on the generalized likelihood ratio optimization strategy, leads to a canonical detector, whose structure is independent of the clutter amplitude probability density function. Interestingly, this detector turns out to be constant false-alarm rate in the sense that threshold setting does not require any knowledge as to the clutter distribution. Moreover, since such a processor is not implementable in real situations, we also present an FFT-based (fast Fourier transform) suboptimum structure. Finally, we give closed-form formulas for the detection performance of both receivers, showing that both of them largely outperform the square-law detector, especially in the presence of very spiky clutter.