mrc performance for binary signals in nakagami fading with general branch correlation exact expressions are derived for the performance of predetection maximal ratio combiner diversity reception with l correlated branches in nakagami fading bit error rates are evaluated for both coherent and noncoherent binary phase shift keying and frequency shift keying signals starting from the l variate moment generating function of the random input power vector the new formulation presented for the bit error rate in which the covariance matrix of the fading at the l branches explicitly appears allows arbitrary branch correlation to be taken into account for any diversity order in the case of identical fading severity on the branches results are presented for evaluation of the outage probability for integer values of fading severity as well as for the effect of the presence of unbalanced channels with arbitrary correlation

variation inequalities for the fejer and poisson kernels in this paper we show that the g th order variation operator for both the fejer and poisson kernels are bounded from l p to l p 1 2 counterexamples are given if g 2

canonical detection in spherically invariant noise 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

weighted variation inequalities for differential operators and singular integrals abstract we prove weighted strong q variation inequalities with 2 q for differential and singular integral operators for the first family of operators the weights used can be either sawyer s one sided a p weights or muckenhoupt s a p weights according to whether the differential operators in consideration are one sided or symmetric we use only muckenhoupt s a p weights for the second family all these inequalities hold equally in the vector valued case that is for functions with values in l for 1 as application we show variation inequalities for mean bounded positive invertible operators on l p with positive inverses

optimum detection of fading signals in impulsive noise 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 modified cramer rao bound in vector parameter estimation in this paper we extend the scalar modified cramer rao bound mcrb to the estimation of a vector of nonrandom parameters in the presence of nuisance parameters the resulting bound is denoted with the acronym mcrvb where v stands for vector as with the scalar bound the mcrvb is generally looser than the conventional crvb but the two bounds are shown to coincide in some situations of practical interest the mcrvb is applied to the joint estimation of carrier frequency phase and symbol epoch of a linearly modulated waveform corrupted by correlated impulsive noise encompassing white gaussian noise as a particular case wherein data symbols and noise power are regarded as nuisance parameters in this situation calculation of the conventional crvb is infeasible while application of the mcrvb leads to simple useful expressions with moderate analytical effort when specialized to the case of white gaussian noise the mcrvb yields results already available in the literature in fragmentary form and simplified contexts

clairvoyant and adaptive signal detection in non gaussian clutter a data dependent threshold interpretation this paper addresses the problem of signal detection in correlated non gaussian clutter modeled as a spherically invariant random process the optimum strategy to detect a constant signal with either known or unknown complex amplitude embedded in correlated gaussian clutter is given by comparing the whitening matched filter output with a fixed threshold when the clutter is non gaussian the performance of the matched filter sensibly degrades the optimum strategy is the classical whitening matched filter output compared with a data dependent threshold this interpretation provides a deeper insight into the structure of the optimum detector and allows us to single out a family of suboptimum detectors based on a polynomial approximation of the data dependent threshold they are easy to implement and have performance that is really close to the optimal the adaptive implementation of the polynomial detectors is also investigated and their performance is analyzed by means of monte carlo simulation for various clutter scenarios

the strong p variation of martingales and orthogonal series let 1 p and letx x n n 0 be a sequence of scalars the strongp variation ofx denoted byw p x is defined as w p x sup left left x 0 p sum limits k 1 infty x n k x n k 1 p right 1 p right where the supremum runs over all increasing sequences of integers 0 n 0 n 1 n 2 let 1 p 2 and letm m n n 0 be a martingale inl p our main results are as follows if sigma mathbb e m n m n 1 p infty thenw p m is finite a s and we have mathbb e w p m p leqq c mathbb e m 0 p sum limits n geqq 1 mathbb e m n m n 1 p for some constantc depending only onp on the other hand let n be an arbitrary orthonormal system of functions inl 2 considerx x n n 0 inl 2 and lets n 0 x i i ands s n n 0 we prove that if x n p 1 p 2 thenw p s t for a e t and w p s 2 c x n p 1 p for some constantc each of these results is an extension of a result proved by bretagnolle for sums of independent mean zero r v s the casep 2 in also discussed our proofs use the real interpolation method of lions peetre they admit extensions in the banach space valued case provided suitable assumptions are imposed on the banach space

estimates for the square variation of partial sums of fourier series and their rearrangements we investigate the square variation operator v2 which majorizes the partial sum maximal operator on general orthonormal systems ons of size n we prove that the l2 norm of the v2 operator is bounded by o ln n on any ons this result is sharp and refines the classical rademacher menshov theorem we show that this can be improved to o ln n for the trigonometric system which is also sharp we show that for any choice of coefficients this truncation of the trigonometric system can be rearranged so that the l2 norm of the associated v2 operator is o lnln n we also show that for p 2 a bounded ons of size n can be rearranged so that the l2 norm of the vp operator is at most op lnln n uniformly for all choices of coefficients this refines bourgain s work on garsia s conjecture which is equivalent to the v case several other results on operators of this form are also obtained the proofs rely on combinatorial and probabilistic methods

interference modeling in a direct sequence spread spectrum packet radio network a technique for characterizing multiuser interference and background noise in a direct sequence spread spectrum network is introduced and packet error probabilities are calculated the multiuser interference over a packet in the network is modeled as a compound gaussian multivariate random variable for moderate to large values of the processing gain the conditional variance is dependent on the number of users and their interference powers the method works for any interference with statistics of the block interference having a spherically symmetric distribution the best performance results in terms of the expected total interference power are obtained for the case of a large number of interferers with comparable interference powers as the number of interferers approaches infinity the performance is the same as that for gaussian noise for a small number of interferers the block error probability curve is broader than that for gaussian noise for small values of snr the probability of error is smaller than that corresponding to gaussian noise and for large values of snr it is larger modifications to the basic direct sequence scheme that improve performance in the case of one strong interferer are suggested

weighted variation inequalities for singular integrals and commutators abstract in this paper we extend the mixed weak type inequalities of sawyer type for calderon zygmund operators to the variation operators of type calderon zygmund operators moreover the corresponding quantitative weighted bounds as well as the weighted estimates in the extreme case p are also obtained meanwhile we also present the quantitative bloom type estimate and c p estimates for variation operators of commutators

second order statistics of complex signals the second order statistical properties of complex signals are usually characterized by the covariance function however this is not sufficient for a complete second order description and it is necessary to introduce another moment called the relation function its properties and especially the conditions that it must satisfy are analyzed both for stationary and nonstationary signals this leads to a new perspective concerning the concept of complex white noise as well as the modeling of any signal as the output of a linear system driven by a white noise finally this is applied to complex autoregressive signals and it is shown that the classical prediction problem must be reformulated when the relation function is taken into consideration

weighted jump and variational inequalities for rough operators abstract in this paper we systematically study weighted jump and variational inequalities for rough operators more precisely we show some weighted jump and variational inequalities for the families t t e e 0 of truncated singular integrals and m m t t 0 of averaging operators with rough kernels which are defined respectively by t e f x y e y y n f x y d y and m t f x 1 t n y t y f x y d y where the kernel belongs to l q s n 1 for q 1

vector valued q variation for ergodic averages and analytic semigroups abstract in this paper we establish umd lattice valued variational inequalities for ergodic averages of contractively regular operators and analytic semigroups these results generalize on the one hand some scalar valued variational inequalities in ergodic theory on the other hand xu s very recent result on umd lattice valued maximal inequality as an application we deduce the jump estimates and obtain quantitative information on the rate of the pointwise convergence for semigroups acting on umd lattice valued functions

the p variation of partial sum processes and the empirical process the p variation of a function f is the supremum of the sums of the p th powers of absolute increments of f over nonoverlapping intervals let f be a continuous probability distribution function dudley has shown that the p variation of the empirical process is bounded in probability as n to infty if and only if p 2 and for 1 leq p leq 2 the p variation of the empirical process is at least n 1 p 2 and is at most of the order n 1 p 2 log log n p 2 in probability in this paper we prove that the exact order of the 2 variation of the empirical process is log log n in probability and for 1 leq p 2 the p variation of the empirical process is of exact order n 1 p 2 in expectation and almost surely let s j x 1 x 2 dots x j then the p variation of the partial sum process for x 1 x 2 dots x n is defined as that of f on 0 n where f t s j for j 1 t leq j j 1 2 dots n bretagnolle has shown that the expectation of the p variation for independent centered random variables x i with bounded p th moments is of order n for 1 leq p 2 we prove that for p 2 the 2 variation of the partial sum process of i i d centered nonconstant random variables with finite 2 delta moment for some delta 0 is of exact order n log log n in probability

one sided extrapolation at infinity and singular integrals in this paper we prove on one hand extrapolation from infinity for the one sided classes ap a p q a p q and on the other hand the bmo boundedness for one sided singular integrals we also provide several applications of our results

vector valued q variation for differential operators and semigroups i in this paper we establish mathcal b valued variational inequalities for differential operators ergodic averages and symmetric diffusion semigroups under the condition that banach space mathcal b has martingale cotype property these results generalize on the one hand pisier and xu s result on the variational inequalities for mathcal b valued martingales on the other hand many classical variational inequalities in harmonic analysis and ergodic theory moreover we show that rademacher cotype q is necessary for the mathcal b valued q variational inequalities as applications of the variational inequalities we deduce the jump estimates and obtain quantitative information on the rate of convergence it turns out the rate of convergence depends upon the geometry of the banach space under consideration while cowling and leinert have shown that convergence holds for all separable banach spaces

ambient noise statistics signal processing algorithms optimized for gaussian noise may degrade significantly in a non gaussian noise environment therefore it is important to characterize the noise accurately before including its structure in the formulation of algorithms a generic distribution suitable for modeling non gaussian ambient noise in the kurtosis range 1 8

oscillation and variation for singular integrals in higher dimensions in this paper we continue our investigations of square function inequalities in harmonic analysis here we investigate oscillation and variation inequalities for singular integral operators in dimensions d 1 our estimates give quantitative information on the speed of convergence of truncations of a singular integral operator including upcrossing and a jump inequalities

recent advances of stretched gaussian distribution underlying hausdorff fractal distance and its applications in fitting stretched gaussian noise abstract this paper summarizes the latest advances of the third author s research group on stretched gaussian distribution underlying the hausdorff fractal theory and its applications in fitting stretched gaussian noise firstly the hausdorff fractal metrics are introduced as an extension of non euclidean distance based on the fractal scaling the hausdorff derivative is derived which can describe the problems of interest to construct non integer differential equations secondly we introduce the hausdorff derivatives in tackling partial differential equations and the fundamental solution of hausdorff derivative diffusion equation is stretched gaussian distribution thirdly we analyze the feasibility of the least square method for stretched gaussian noise which obeys stretched gaussian distribution the least square method is inapplicable when the noise level is larger than 5 finally by using the hausdorff fractal distance we introduce the stretched least square method which improves the traditional least square method to fit stretched gaussian noise

spherically invariant vector random fields in space and time this paper is concerned with spherically invariant or elliptically contoured vector random fields in space and or time which are formulated as scale mixtures of vector gaussian random fields while a spherically invariant vector random field may or may not have second order moments a spherically invariant second order vector random field is determined by its mean and covariance matrix functions just like the gaussian one this paper explores basic properties of spherically invariant second order vector random fields and proposes an efficient approach to develop covariance matrix functions for such vector random fields

a matrix valued wavelet kl like expansion for wide sense stationary random processes matrix valued wavelet series expansions for wide sense stationary processes are studied in this paper the expansion coefficients a are uncorrelated matrix random process which is a property similar to that of a matrix karhunen loe spl grave ve mkl expansion unlike the mkl expansion however the matrix wavelet expansion does not require the solution of the eigen equation this expansion also has advantages over the fourier series which is often used as an approximation to the mkl expansion in that it completely eliminates correlation the basis functions of this expansion can be obtained easily from wavelets of the matrix valued lemarie spl acute meyer type and the power spectral density of the process

detection and estimation of improper complex random signals nonstationary complex random signals are in general improper not circularly symmetric which means that their complementary covariance is nonzero since the karhunen loeve k l expansion in its known form is only valid for proper processes we derive the improper version of this expansion it produces two sets of eigenvalues and improper observable coordinates we then use the k l expansion to solve the problems of detection and estimation of improper complex random signals in additive white gaussian noise we derive a general result comparing the performance of conventional processing which ignores complementary covariances with processing that takes these into account in particular for the detection and estimation problems considered we find that the performance gain as measured by deflection and mean squared error mse respectively can be as large as a factor of 2 in a communications example we show how this finding generalizes the result that coherent processing enjoys a 3 db gain over noncoherent processing

on convexity of error rates in digital communications convexity properties of error rates of a class of decoders including the maximum likelihood min distance one as a special case are studied for arbitrary constellations bit mapping and coding earlier results obtained for the additive white gaussian noise channel are extended to a wide class of noise densities including unimodal and spherically invariant noise under these broad conditions symbol and bit error rates are shown to be convex functions of the signal to noise ratio snr in the high snr regime with an explicitly determined threshold which depends only on the constellation dimensionality and minimum distance thus enabling an application of the powerful tools of convex optimization to such digital communication systems in a rigorous way it is the decreasing nature of the noise power density around the decision region boundaries that ensures the convexity of symbol error rates in the general case the known high low snr bounds of the convexity concavity regions are tightened and no further improvement is shown to be possible in general the high snr bound fits closely into the channel coding theorem all codes including capacity achieving ones whose decision regions include the hardened noise spheres from the noise sphere hardening argument in the channel coding theorem satisfy this high snr requirement and thus has convex error rates in both snr and noise power we conjecture that all capacity achieving codes have convex error rates convexity properties in signal amplitude and noise power are also investigated some applications of the results are discussed in particular it is shown that fading is convexity preserving and is never good in low dimensions under spherically invariant noise which may also include any linear diversity combining

a quaternion widely linear model for nonlinear gaussian estimation this paper deals with the nonlinear minimum mean squared error estimation problem by using a quaternion widely linear model on the basis of the information supplied by a gaussian signal and its square a quaternion observation process is defined and then by applying a widely linear processing an optimal estimator for the continuous time setting is provided the special structure of the estimator proves its superiority over the complex valued widely linear solution the continuous discrete version of the problem is also studied where the solution takes the form of a suboptimal estimator useful in practical applications in addition the particular case of signal plus noise is considered in which the suboptimal solution and its associated error can be implemented through an iterative algorithm two numerical simulation examples are presented showing the advantages of the proposed approach

performance of ds ssma communications in impulsive channels part i linear correlation receivers the performance of digital linear correlation receivers is studied in a multiuser environment there are assumed to be two types of sources interfering with data transmission multiple access interference and additive channel noise which is attributed to impulsive noise sources in the environment the contribution of multiple access interference is examined by considering k asynchronous users transmitting simultaneously over a linear channel using the binary psk direct sequence spreadspectrum multiple access ds ssma technique alternatively the effects of the non gaussian impulsive channel in such a system are studied by modeling the samples of noise after front end filtering errorprobability performance under these conditions is compared to that for additive white gaussian noise awgn channels due to computational complexity exact analysis is limited here to systems utilizing short spreading sequences computationally simple methods are proposed for approximating the average error probability when the length of the signature sequences is large furthermore some asymptotic results are obtained for the case of infinitely long sequences in all cases performance variation is examined as the shape of the noise density varies with snr held constant the results of this analysis indicate that the presence of impulsive noise can cause significant performance degradation over that predicted from an awgn model even when the total noise power does not increase

non gaussian clutter modeling with generalized spherically invariant random vectors this paper describes the modeling of non gaussian clutter with a set of generalized spherically invariant random vectors sirv s the generalization extends the traditional model to account for dependence between successive sirv realizations significant properties of generalized sirv s are derived as well as a closed form expression for a family of generalized sirv density functions the density underlying recorded sonar reverberation is approximated with this function through appropriate choice of a shape parameter given this reverberation model the optimum detector is derived from the generalized sirv density likelihood ratio this paper concludes by showing how applying this optimum detector to non gaussian data leads to a reduction in the false alarm rate when compared to processing with a matched filter alone

detection of weak random signals in iid non gaussian noise this paper considers the detection of weak random signals in circularly symmetric independent identically distributed noise locally optimum detectors and ad hoc nonlinearities are considered with asymptotic expressions provided for evaluation of detection performance the analytical expressions are used to evaluate the robustness of detectors to mismatch in the noise models finite sample monte carlo simulation results indicate the reliability of these asymptotic measures in cases of practical interest the results show that as has been found for detection of weak known signals in non gaussian noise reasonably configured ad hoc nonlinearities are nearly optimum and robust to modest errors in the noise statistics

on mimo detection under non gaussian target scattering in this paper we consider a multiple input multiple output mimo detection problem with m widely spaced transmit antennas and l widely spaced receive antennas and we study the problem of designing the signal waveforms transmitted by each source node under non gaussian target scattering and temporally correlated gaussian clutter two figures of merit are investigated for space time code stc optimization under a semidefinite rank constraint 1 the lower chernoff bound lcb to the detection probability for fixed probability of false alarm and 2 the mutual information mi between the observations available at the receive nodes and the channel response generated by a point like target assumed present tout court both receive and transmit power constraints are discussed if the scattering distribution possesses some suitably defined properties of unitary invariance see both mi optimal and lcb optimal stcs have a simple canonical structure the same set of clutter dependant temporal codewords are employed at the transmit nodes the only difference among the many solutions being the amount of power radiated by each antenna such a spatial power allocation critically depends upon the adopted figure of merit the specified power constraint and the underlying scattering model sufficient conditions to determine the optimal power allocation for all design criteria are provided asymptotic power distributions are also derived in the limit of vanishingly small and increasingly large signal to clutter ratios proving that assuming gaussian scattering at the design stage is a robust choice a case study of relevant practical interest is examined in depth so as to compare the proposed design criteria and to assess the impact of signal non gaussianity on the system performances

data adaptive algorithms for signal detection in sub gaussian impulsive interference we address the problem of coherent detection of a signal embedded in heavy tailed noise modeled as a sub gaussian alpha stable process we assume that the signal is a complex valued vector of length l known only within a multiplicative constant while the dependence structure of the noise i e the underlying matrix of the sub gaussian process is not known we implement a generalized likelihood ratio detector that employs robust estimates of the unknown noise underlying matrix and the unknown signal strength the performance of the proposed adaptive detector is compared with that of an adaptive matched filter that uses gaussian estimates of the noise underlying matrix and the signal strength and is found to be clearly superior the proposed new algorithms are theoretically analyzed and illustrated in a monte carlo simulation

weighted inequalities for the one sided hardy littlewood maximal functions let m f x suph 0 l h jx h t 1 idt denote the one sided maximal function of hardy and littlewood for w x 0 on r and 1 0 and a v ll p then m is bounded from lp v to lp w if and only if m x a w 0 the corresponding weak type inequality is also characterized further properties of a weights such as a a e and a p a a1 p are established

detection of narrow band signals in spherically invariant noise this paper deals with noncoherent discrete time detection of a narrow band signal subject to slow and nonselective fading and embedded in correlated non gaussian noise modeled as a spherically invariant random process whose modulating random variable is continuous at first an asymptotic sufficient statistic for an arbitrary fading law is derived then the asymptotically optimum detector for rayleigh distributed amplitude fluctuations is synthesized the detection structure implementation requires the knowledge but for a scale factor of the correlation function of the noise but is independent of the distribution function of the modulating random variable the performance of the asymptotically optimum detector synthesized for rayleigh fading is assessed via computer simulations the results show that the performance degradation with respect to the fully optimum performance is scarcely significant even for low values of the sample size moreover in highly non gaussian noise the proposed detector largely outperforms the fully optimum detector synthesized under the correlated gaussian noise assumption

performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha stable process impulsive noise bursts in communication systems are traditionally handled by incorporating in the receiver a limiter which clips the received signal before integration an empirical justification for this procedure is that it generally causes the signal to noise ratio to increase recently very accurate models of impulsive noise were presented based on the theory of symmetric spl alpha stable probability density functions we examine the performance of optimum receivers designed to detect signals embedded in impulsive noise which is modeled as an infinite variance symmetric spl alpha stable process and compare it against the performance of several suboptimum receivers as a measure of receiver performance we compute an asymptotic expression for the probability of error for each receiver and compare it to the probability of error calculated by extensive monte carlo simulation

l p estimates for the variation for singular integrals on uniformly rectifiable sets the l p 1 p infty and weak l 1 estimates for the variation for calderon zygmund operators with smooth odd kernel on uniformly rectifiable measures are proven the l 2 boundedness and the corona decomposition method are two key ingredients of the proof

multiplicities and a dimension inequality for unmixed modules abstract we prove the following result which is motivated by the recent work of kurano and roberts on serre s positivity conjecture assume that r m is a local ring with finitely generated module m such that r ann m is quasi unmixed and contains a field and that p and q are prime ideals in the support of m such that p is analytically unramified p q m and e m p e m then dim r p dim r q dim m we also prove a similar theorem in a special case of mixed characteristic finally we provide several examples to explain our assumptions as well as an example of a noncatenary local domain r with prime ideal p such that e rp e r 1

comments on a representation for the symbol error rate using completely monotone functions it was shown in the above titled paper by rajan and tepedelenlioglu see ibid vol 59 no 6 p 3922 31 june 2013 that the symbol error rate ser of an arbitrary multidimensional constellation subject to additive white gaussian noise is characterized as the product of a completely monotone function with a nonnegative power of signal to noise ratio snr under minimum distance detection in this comment it is proved that the probability of correct decision of an arbitrary constellation admits a similar representation as well based on this fact it is shown that the stochastic ordering g 0 proposed by the authors as an extension of the existing laplace transform order to compare the average sers over two different fading channels actually predicts that the average sers are equal for any constellation of dimensionality smaller than or equal to 2 furthermore it is noted that there are no positive random variables x1 and x2 such that the proposed stochastic ordering is satisfied in the strict sense i e x1 g x2 when n 2 for any positive integer n additional remarks are noted about the fading scenarios at low snr and the generalization to additive compound gaussian noise originally discussed in the subject paper

optimum diversity detection over fading dispersive channels with non gaussian noise we consider the problem of m ary signal detection over a single input multiple output simo channel affected by frequency dispersive rayleigh distributed fading and corrupted by additive non gaussian noise modeled as a spherically invariant random process we derive both the optimum detection structure and a suboptimal reduced complexity receiver based on the low energy coherence approach interestingly both detection structures are canonical i e they are independent of the actual noise statistics we also carry out a performance analysis of both receivers with reference to the case that the channel is affected by a frequency selective fading and for a binary frequency shift keying signaling format the results obtained through both a chernoff bounding technique and monte carlo simulations reveal that the adoption of diversity also represents a suitable means to restore performance in the presence of dispersive fading and impulsive non gaussian noise interestingly it is also shown that the suboptimal receiver incurs a limited loss with respect to the optimum unrealizable receiving structure

non gaussian noise models in signal processing for telecommunications new methods an results for class a and class b noise models the subject here is generalized i e non gaussian noise models and specifically their first order probability density functions pdfs attention is focused primarily on the author s canonical statistical physical class a and class b models in particular class a noise describes the type of electromagnetic interference emi often encountered in telecommunication applications where this ambient noise is largely due to other intelligent telecommunication operations on the other hand ambient class b noise usually represents man made or natural nonintelligent i e nonmessage bearing noise and is highly impulsive class a noise is not an spl alpha stable process nor is it reducible to such except in the limiting gaussian cases of high density noise by the central limit theorem class b noise is also asymptotically normal before model approximation under rather broad conditions principally governed by the source propagation and distribution scenarios the pdf of class b noise alone no gaussian component can usually be approximated by 1 a symmetric gaussian spl alpha stable s spl alpha s model in the case of narrowband reception or when the pdf spl omega sub 1 spl alpha of the amplitude is symmetric and 2 a nonsymmetric spl alpha stable ns spl alpha s model no gaussian component can be constructed in broadband regimes new results here include i counting functional methods for constructing the general qth order characteristic functions cfs of class a and class b noise from which all moments and in principle the pdfs follow ii the first order cfs pdfs and cumulative probabilities apds of nonsymmetric broadband class b noise extended to include additive gauss noise agn iii proof of the existence of all moments in the basic class a and class b models iv the key physical role of agn and the fact that agn removes spl alpha stability v the explicit roles of the propagation and distribution scenarios and vi extension to noise fields although telecommunication applications are emphasized class a and class b noise models apply selectively but equally well to other physical regimes e g underwater acoustics and em radar optics etc supportive empirical data are included

locally optimal detection in multivariate non gaussian noise the detection of a vanishingly small known signal in multi variate noise is considered efficacy is used as a criterion of detector performance and the locally optimal detector lod for multivariate noise is derived it is shown that this is a generalization of the well known lod for independent identically distributed i i d noise several characterizations of multivariate noise are used as examples these include specific examples and some general methods of density generation in particular the class of multivariate densities generated by a zero memory nonlinear transformation of a correlated gaussian source is discussed in some detail the detector structure is derived and practical aspects of obtaining detector subsystems are considered through the use of monte carlo simulations the performance of this system if compared to that of the matched filter and of the i i d lod finally the class of multivariate densities generated by a linear transformation of an i i d noise source is described and its lod is shown to be a form frequently suggested to deal with multivariate non gaussian noise a linear filter followed by a memoryless nonlinearity and a correlator

an adaptive spatial diversity receiver for non gaussian interference and noise standard linear diversity combining techniques are not effective in combating fading in the presence of non gaussian noise an adaptive spatial diversity receiver is developed for wireless communication channels with slow flat fading and additive non gaussian noise the noise is modeled as a mixture of gaussian distributions and the expectation maximization em algorithm is used to derive estimates for the model parameters the transmitted signals are detected using a likelihood ratio test based on the parameter estimates the new adaptive receiver converges rapidly its bit error rate performance is very close to optimum when relatively short training sequences are used and it appears to be relatively insensitive to mismatch between the noise model and the actual noise distribution simulation results are included that illustrate various aspects of the adaptive receiver performance

a numerical solution for multichannel detection a numerical approach to the vector signal detection problem is proposed by using an approximate series representation for vector complex valued random processes this technique allows us to provide computationally feasible suboptimum receivers for the problem of detecting an improper or proper complex signal in additive white noise its implementation requires the knowledge of the correlation matrix of the vector process involved the performance of the technique devised is assessed by some communication examples

optimum detection over rayleigh fading dispersive channels with non gaussian noise 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

a dimension inequality for cohen macaulay rings the recent work of kurano and roberts on serre s positivity conjecture suggests the following dimension inequality for prime ideals p and q in a local cohen macaulay ring a n such that e ap e a we have dim a p dim a q dim a we establish this dimension inequality for excellent local cohen macaulay rings which contain a field for certain low dimensional cases and when r p is regular

asymptotic performance of m ary orthogonal modulation in generalized fading channels the asymptotic m to infinity probability of symbol error p sub e sub m for m ary orthogonal modulation in a nakagami m fading channel is given by the incomplete gamma function p m mx where x in 2 e sub b n sub 0 and e sub b is the average energy per bit for large signal to noise ratio this leads to a channel where the probability of symbol error varies as the inverse mth power of e sub b n sub 0 these channels exist for all m or 1 2 the special case of m 1 corresponds to rayleigh fading an inverse linear channel

differential and ergodic transforms in this paper we consider weighted differences of ergodic averages and averages associated with differentiation these weighted differences are shown to converge a e as well as in l p 1 p infty these results have consequences for unconditional convergence of the series of differences and give some information about how the averages converge

jump estimates for operators associated with polynomials abstract in this study we prove the jump inequalities for singular integrals and averages of radon type with rough kernels