multiple primary user spectrum sensing in the low snr regime we consider multi antenna cooperative spectrum sensing in cognitive radio networks when there are multiple primary users and or multipath channels a noise uncertainty free detector that is optimal in the low signal to noise ratio regime is analyzed we derive the moments of the test statistics involved which lead to simple and accurate analytical formulae for the key performance metrics the approximative false alarm and detection probabilities as well as receiver operating characteristic are given in closed form from the considered simulation settings performance gain over several known detection algorithms is observed in scenarios with relatively low signal to noise ratio

multiantenna glr detection of rank one signals with known power spectrum in white noise with unknown spatial correlation multiple antenna detection of a gaussian signal with spatial rank one in temporally white gaussian noise with arbitrary and unknown spatial covariance is considered this is motivated by spectrum sensing problems in the context of dynamic spectrum access in which several secondary networks coexist but do not cooperate creating a background of spatially correlated broadband interference when the temporal correlation of the signal of interest is assumed known up to a scale factor the corresponding generalized likelihood ratio test is shown to yield a scalar optimization problem closed form expressions of the test are obtained for the general signal spectrum case in the low signal to noise ratio snr regime as well as for signals with binary valued power spectrum in arbitrary snr the two resulting detectors turn out to be equivalent an asymptotic approximation to the test distribution for the low snr regime is derived closely matching empirical results from spectrum sensing simulation experiments

the form of life i it is possible but not necessary however we deny naive realism it is difficult to describe the form of life in a newtonian paradigm because any formal descriptions of biological systems inevitably include the concept of function they entail the problem of self reference the description of function can be compared to that of meaning of a word and in philosophy we no longer understand that there exists meaning inherent in a word of a language as well as the problem of meaning we cannot describe the aspect resulting from the function because we cannot identify the specific function of a shape or morphology with the relationship between the shape itself and its environment therefore even if we construct a new formal language in which the self contradiction resulting from the self reference is alleviated that language is just one of various possible ones in this sense the form of life in formal description is possible but not necessary the phrase not necessary just refers to the outside of the formal description in this paper reference to the outside of a formal system is discussed in the context of time space complementarity and it is strongly related to the origin of irreversible time we have to introduce both forward and backward time as proposed previously by the author and coworkers even in this context

lattice computers for approximating euclidean space in the context of mesh like parallel processing computers for i approximating continuous space and ii analog simulation of the motion of objects and waves in continuous space the present paper is concerned with which mesh like interconnection of processors might be particularly suitable for the task and why processor interconnection schemes based on nearest neighbor connections in geometric lattices are presented along with motivation then two major threads are exploded regarding which lattices would be good the regular lattices for their symmetry and other properties in common with continuous space and the well known root lattices for being in a sense the lattices required for physically natural basic algorithms for motion the main theorem of the present paper implies that the well known lattice a n is the regular lattice having the maximum number of nearest neighbors among the n dimensional regular lattices it is noted that the only n dimensional lattices that are both regular and root are a n and z n z n is the lattice of n cubes the remainder of the paper specifies other desirable properties of a n including other ways it is superior to z n for our purposes

digital mechanics an informational process based on reversible universal cellular automata abstract this paper is written from the perspective of a computer scientist and addressed to theoretical physicists as a consequence it may seem somewhat unusual but rest assured everything is really quite simple the point of this paper is that the study of certain phenomena from computer science suggests that there are computer systems cellular automata that may be appropriate as models for microscopic physical phenomena cellular automata are now being used to model varied physical phenomena normally modelled by wave equations fluid dynamics ising models etc we hypothesize that there will be found a single cellular automaton rule that models all of microscopic physics and models it exactly we call this field dm for digital mechanics

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

multiple cumulants based spectrum sensing methods for cognitive radios in cognitive radios energy detector is considered for spectrum sensing in the literature however its performance deteriorates rapidly if the noise power is not known exactly moreover due to the presence of a colored channel interferer or some other reasons the conventional white gaussian noise may become colored in order to solve these problems this paper proposes several multicumulant based spectrum sensing methods generalized likelihood ratio test glrt based multicumulant glrtmc based detection method and multiantenna assisted multicumulant mamc based detection method glrtmc detection method is derived from generalized likelihood ratio test and assumed to be near optimum in theory mamc detection method on the other hand by using multiple antennas is a complexity reduced detector and allows us to make a compromise between performance and complexity it is well known that cumulants higher than second order are zero for gaussian distributions thus glrtmc detection method and mamc detection method can extract a non gaussian signal from gaussian noise even when the noise is colored in addition the proposed methods are nonparametric in the sense that they do not require any exact prior knowledge about the signal or the noise such as noise power or cyclic frequencies hence they are immune from noise uncertainty simulation experiments are provided to show the validity and the superiority over single cumulant based detector of the proposed multicumulant based detectors

a blind likelihood based approach for ofdm spectrum sensing in the presence of i q imbalance we investigate the spectrum sensing problem in orthogonal frequency division multiplexing based cognitive radio networks under i q imbalance we start by deriving the likelihood ratio test in the presence of i q imbalance at the analog front ends of both the primary and secondary users in addition we derive closed form expressions for the probabilities of detection and false alarm and the receiver operating characteristics and examine their dependence on both transmit and receive i q imbalance levels furthermore we compare the performance of the likelihood ratio test with that of the energy detector and demonstrate the superiority of the former over the latter next we generalize our analysis to the blind case where we derive simple closed form expressions for the generalized likelihood ratio test and its false alarm probability as a function of the received signal only i e without requiring any knowledge of the primary to secondary channel response noise statistics or i q imbalance parameters our results demonstrate that the correlation properties of the primary user s signal induced by transmit i q imbalance are signal features that can be exploited in a blind fashion at the secondary user to enhance the detection probability significantly compared to the conventional energy detector

when and how can a cellular automaton be rewritten as a lattice gas both cellular automata ca and lattice gas automata lg provide finite algorithmic presentations for certain classes of infinite dynamical systems studied by symbolic dynamics it is customary to use the terms cellular automaton and lattice gas for a dynamic system itself as well as for its presentation the two kinds of presentation share many traits but also display profound differences on issues ranging from decidability to modeling convenience and physical implementability following a conjecture by toffoli and margolus it had been proved by kari that any invertible ca at least up to two dimensions can be rewritten as an isomorphic lg but until now it was not known whether this is possible in general for noninvertible ca which comprise almost all ca and represent the bulk of examples in theory and applications even circumstantial evidence whether in favor or against was lacking here for noninvertible ca a we prove that an lg presentation is out of the question for the vanishingly small class of surjective ones we then turn our attention to all the rest noninvertible and nonsurjective which comprise all the typical ones including conway s game of life for these b we prove by explicit construction that all the one dimensional ones are representable as lg and c we present and motivate the conjecture that this result extends to any number of dimensions the tradeoff between dissipation rate and structural complexity implied by the above results have compelling implications for the thermodynamics of computation at a microscopic scale

time space trade offs for reversible computation a reversible turing machine is one whose transition function is 1 1 so that no instantaneous description id has more than one predecessor using a pebbling argument this paper shows that for any varepsilon 0 ordinary multitape turing machines using time t and space s can be simulated by reversible ones using time o t 1 varepsilon and space o s log t or in linear time and space o st varepsilon the former result implies in particular that reversible machines can simulate ordinary ones in quadratic space these results refer to reversible machines that save their input thereby insuring a global 1 1 relation between initial and final ids even when the function being computed is many to one reversible machines that instead erase their input can of course compute only 1 1 partial recursive functions and indeed provide a godel numbering of such functions the time space cost of computing a 1 1 function on such a machine is equal within a small polynomial to the cost of co

invertible cellular automata a review abstract in the light of recent developments in the theory of invertible cellular automata we attempt to give a unified presentation of the subject and discuss its relevance to computer science and mathematical physics

reversible simulation of one dimensional irreversible cellular automata abstract a cellular automaton ca is called reversible or injective iff its global function is one to one it has been shown by toffoli that any irreversible k dimensional ca is simulated by a k 1 dimensional rca in this paper we show that any one dimensional ca with finite configurations can be simulated by a one dimensional reversible ca this is proved by using the framework of partitioned ca pca

computing with distributed chaos we describe and discuss in detail some recent results by sinha and ditto phys rev lett 81 2156 1998 demonstrating the capacity of a lattice of threshold coupled chaotic maps to perform computations such systems are shown to emulate logic gates encode numbers and perform specific arithmetic operations such as addition and multiplication as well as yield more specialized operations such as the calculation of the least common multiplier of a sequence of numbers furthermore we extend the scheme to multidimensional continuous time dynamics in particular to a system relevant to chaotic lasers

physics like models of computation abstract reversible cellular automata are computer models that embody discrete analogues of the classical physics notions of space time locality and microscopic reversibility they are offered as a step towards models of computation that are closer to fundamental physics

generalized mean detector for collaborative spectrum sensing in this paper a unified generalized eigenvalue based spectrum sensing framework referred to as generalized mean detector gmd has been introduced the generalization of the detectors namely i the eigenvalue ratio detector erd involving the ratio of the largest and the smallest eigenvalues ii the geometric mean detector gemd involving the ratio of the largest eigenvalue and the geometric mean of the eigenvalues and iii the arithmetic mean detector armd involving the ratio of the largest and the arithmetic mean of the eigenvalues is explored the foundation of the proposed unified framework is based on the calculation of exact analytical moments of the random variables of test statistics of the respective detectors in this context we approximate the probability density function pdf of the test statistics of the respective detectors by gaussian gamma pdf using the moment matching method finally we derive closed form expressions to calculate the decision threshold of the eigenvalue based detectors by exchanging the derived exact moments of the random variables of test statistics with the moments of the gaussian gamma distribution function the performance of the eigenvalue based detectors is compared with the traditional detectors such as energy detector ed and cyclostationary detector csd and validate the importance of the eigenvalue based detectors particularly over realistic wireless cognitive environments analytical and simulation results show that the gemd and the armd yields considerable performance advantage in realistic spectrum sensing scenarios moreover our results based on proposed simple and tractable approximation approaches are in perfect agreement with the empirical results

fluctuation driven computing on number conserving cellular automata a number conserving cellular automaton ncca is a cellular automaton in which the states of cells are denoted by integers and the sum of all of the numbers in a configuration is conserved throughout its evolution nccas have been widely used to model physical systems that are ruled by conservation laws of mass or energy imai et al 13 showed that the local transition function of ncca can be effectively translated into the sum of a binary flow function over pairs of neighboring cells in this paper we explore the computability of nccas in which the pairwise number flows are performed at fully asynchronous timings despite the randomness that is associated with asynchronous transitions useful computation still can be accomplished efficiently in the cellular automata through the active exploitation of fluctuations 18 specifically certain numbers may flow randomly fluctuating between forward and backward directions in the cellular space as if they were subject to brownian motion because random fluctuations promise a powerful resource for searching through a computational state space the brownian like flow of the numbers allows for efficient embedding of logic circuits into our novel asynchronous ncca

emergence of universal global behavior from reversible local transitions in asynchronous systems reversible computing usually focuses on how to establish a valid equivalence between the global reversibility and local reversibility in computational systems hitherto the equivalence has been precisely developed in cellular automata combinational circuits and quantum computers but it implicitly assumes that the underlying systems are synchronously timed alternative systems include the delay insensitive di circuits and asynchronous cellular automata acas where the local operations of each component cell may be executed independently at random times despite the randomness associated with asynchronous timings equivalence between the global and local reversibility can be simply achieved in both di circuits morita 2001 and acas lee et al 2003 provided that their local operations transitions are thoroughly serialized the complete exclusion of concurrency in local behavior however will profoundly depress the parallel processing efficiency of di circuits as well as the intrinsic massive parallelism of acas this paper aims at exploring what kind of complex global behavior may arise from the concurrent operations that are invertible at local level to this end we show that di circuits composed of reversible elements can actually exhibit universal input and output behavior with the universality emerging from the concurrency in reversible local operations likewise by further embedding all circuits into the cellular space the emergence of universal global transitions from reversible local transitions can be exactly identified in an aca which due to the bijectivity of its local function has significantly lower complexity as compared to other models

on conservative and monotone one dimensional cellular automata and their particle representation number conserving or conservative cellular automata ca have been used in several contexts in particular traffic models where it is natural to think about them as systems of interacting particles in this article we consider several issues concerning one dimensional cellular automata which are conservative monotone specially non increasing or that allow a weaker kind of conservative dynamics we introduce a formalism of particle automata and discuss several properties that they may exhibit some of which like anticipation and momentum preservation happen to be intrinsic to the conservative ca they represent for monotone ca we give a characterization and then show that they too are equivalent to the corresponding class of particle automata finally we show how to determine for a given ca and a given integer b whether its states admit a b neighborhood dependent relabeling whose sum is conserved by the ca iteration this can be used to uncover conservative principles and particle like behavior underlying the dynamics of some ca compliments at http www dim uchile cl anmoreir ncca

multiantenna glr detection of rank one signals with known power spectral shape under spatially uncorrelated noise we establish the generalized likelihood ratio glr test for a gaussian signal of known power spectral shape and unknown rank one spatial signature in additive white gaussian noise with an unknown diagonal spatial correlation matrix this is motivated by spectrum sensing problems in dynamic spectrum access in which the temporal correlation of the primary signal can be assumed known up to a scaling and where the noise is due to an uncalibrated receive array for spatially independent identically distributed i i d noise the corresponding glr test reduces to a scalar optimization problem whereas the glr detector in the general non i i d case yields a more involved expression which can be computed via alternating optimization methods low signal to noise ratio snr approximations to the detectors are given together with an asymptotic analysis showing the influence on detection performance of the signal power spectrum and snr distribution across antennas under spatial rank p conditions we show that the rank one glr detectors are consistent with a statistical criterion that maximizes the output energy of a beamformer operating on filtered data simulation results support our theoretical findings in that exploiting prior knowledge on the signal power spectrum can result in significant performance improvement

nonuniform sampling walls in wideband signal detection this work shows the existence of sampling walls in detection of wideband signals from bernoulli nonuniform sampling bns in the presence of noise uncertainty a sampling wall is defined as the sampling density below which the target error probabilities i e the missed detection and false alarm probabilities cannot be guaranteed at a given signal to noise ratio snr regardless the number of acquired samples the bns is adopted because it exhibits good tradeoff properties between complexity and performance it is shown that bns suffers from noise enhancement which translates into a whitening effect in the correlation of the legacy signal contrarily to the existing literature the signal detection problem is addressed without having to reconstruct neither the signal nor its spectrum more specifically the optimal low snr detector is formulated as a generalized likelihood ratio test glrt to exploit the available side information of the problem i e the noise variance the sampling density and the legacy signal autocorrelation by deriving the asymptotic performance of the glrt in the presence of noise uncertainty explicit expressions for sampling walls are obtained as a function of the legacy signal occupancy the snr and the noise uncertainty further numerical results are provided to assess the behavior of the sampling walls and signal detection performance

decentralized eigenvalue algorithms for distributed signal detection in wireless networks in this paper we derive and analyze two algorithms referred to as decentralized power method dpm and decentralized lanczos algorithm dla for distributed computation of one the largest or multiple eigenvalues of a sample covariance matrix over a wireless network the proposed algorithms based on sequential average consensus steps for computations of matrix vector products and inner vector products are first shown to be equivalent to their centralized counterparts in the case of exact distributed consensus then closed form expressions of the error introduced by nonideal consensus are derived for both algorithms the error of the dpm is shown to vanish asymptotically under given conditions on the sequence of consensus errors finally we consider applications to spectrum sensing in cognitive radio networks and we show that virtually all eigenvalue based tests proposed in the literature can be implemented in a distributed setting using either the dpm or the dla simulation results are presented that validate the effectiveness of the proposed algorithms in conditions of practical interest large scale networks small number of samples and limited number of iterations

the structure of reversible one dimensional cellular automata abstract an algorithm is presented for determining reversibility characteristics of 1 dimensional cellular automaton laws the concept of local reversibility is defined each locally reversible automaton is shown to be isomorphic to a member of the class of center reversible automata algorithms are described for generating the set of center reversible laws and the set of center reversible additive laws

pre expansivity in cellular automata we introduce the property of pre expansivity for cellular automata ca it is the property of being expansive on asymptotic pairs of configurations i e configurations that differ in only finitely many positions pre expansivity therefore lies between expansivity and pre injectivity two important notions of ca theory we show that there exist one dimensional positively pre expansive cas which are not positively expansive and they can be chosen reversible while positive expansivity is impossible for reversible cas we show however that no bi dimensional ca which is linear over an abelian group can be pre expansive we also consider the finer notion of k expansivity expansivity over pairs of configurations with exactly k differences and show examples of linear ca in dimension 2 and on the free group that are k expansive depending on the value of k whereas no positively expansive ca exists in this setting

on multiple antenna spectrum sensing under noise variance uncertainty and flat fading we investigate a spectrum sensing method based on asymptotic analysis of the discrete fourier transform of the received multiantenna signal possibly non gaussian for flat fading primary user signals in white noise under noise variance uncertainty the proposed approach is based on the generalized likelihood ratio test glrt paradigm for a restricted version of the problem obtained by ignoring the spatial structure of the primary users received signals and it permits the noise variances to be different at different antennas without requiring knowledge of their values simulation examples show the efficacy of the proposed approach compared with the energy detector and some existing time domain glrt approaches a performance analysis of the proposed detector is carried out and verified via simulations it is also shown that the proposed test statistic is equivalent to an existing time domain glrt statistic except that the latter has been derived under the assumption that received signal is gaussian whereas we make no such assumption

characterization of random fluctuation based computation in cellular automata a brownian cellular automaton bca is an asynchronous cellular automaton aca in which the timing of the local cell state transitions approaches a poisson point process and the global transitions between cell configurations can be formulated as an irreducible and reversible markov chain bcas exploit fluctuations to find solutions of a computation via a stochastic search process this characteristic has been shown to contribute to a decreased complexity of bcas lee and peper 2008 as compared to non brownian acas with equivalent functionality this paper proposes a computationally universal bca that is based on a conventional aca rather than the previously employed block cellular automata which have transition rules that update each cell simultaneously with its neighboring cells the proposed allows for a more natural update model in which no need arises to locally synchronize the cells in a neighborhood the resulting bca is significantly less complex than equivalent non block non brownian acas which demonstrates that random fluctuations can serve as a powerful resource for efficient computation on cellular automata

on the performance of hadamard ratio detector based spectrum sensing for cognitive radios we consider the problem of multiantenna spectrum sensing ss in cognitive radios crs when the receivers are assumed to be uncalibrated across the antennas the performance of the hadamard ratio detector hrd is analyzed in such a scenario specifically we first derive the exact distribution of the hrd statistic under the null hypothesis which leads to an elaborate but closed form expression for the false alarm probability then we derive a simpler and tight closed form approximation for both the false alarm and detection probabilities by using a moment based approximation of the hrd statistical distribution under both hypotheses finally the accuracy of the obtained results is verified by simulations

optimal glrt based robust spectrum sensing for mimo cognitive radio networks with csi uncertainty in this paper we develop generalized likelihood ratio test glrt based detectors for robust spectrum sensing in multiple input multiple output mimo cognitive radio networks considering uncertainty in the available channel state information csi initially for a scenario with known csi uncertainty statistics we derive the novel robust estimator correlator detector recd and the robust generalized likelihood detector rgld which are robust against the uncertainty in the available estimates of the channel coefficients subsequently for a scenario with unknown csi uncertainty statistics we develop a generalized likelihood ratio test glrt based composite hypothesis robust detector chrd for spectrum sensing closed form expressions are presented for the probability of detection p d and the probability of false alarm p fa to characterize the detection performance of the proposed robust spectrum sensing schemes further a deflection coefficient based optimization framework is also developed and solved to derive closed form expressions for the optimal beacon sequences simulation results are presented to demonstrate the performance improvement achieved by the proposed robust spectrum sensing schemes and to verify the analytical results derived

cellular automata as a paradigm for ecological modeling we review cellular automata as a modeling formalism and discuss how it can be used for modeling spatial ecological processes the implications of this modeling paradigm for ecological observation are stressed finally we discuss some shortcomings of the cellular automaton formalism and mention some extensions and generalizations which may remedy these shortcomings

co evolving non uniform cellular automata to perform computations a major impediment of cellular automata ca stems from the difficulty of utilizing their complex behavior to perform useful computations recent studies by packard and mitchell et al have shown that cas can be evolved to perform a computational task in this paper non uniform cas are studied where each cell may contain a different rule in contrast to the original uniform model we describe experiments in which non uniform cas are evolved to perform the computational task using a local co evolutionary algorithm for radius r 3 we attain peak performance values of 0 92 comparable to those obtained for uniform cas 0 93 0 95 this is notable considering the huge search spaces involved much larger than the uniform case smaller radius cas previously unstudied in this context attain performance values of 0 93 0 94 for r 1 this is considerably higher than the maximal possible uniform ca performance of 0 83 suggesting that non uniformity reduces connectivity requirements we thus demonstrate that 1 non uniform cas can attain high computational performance and 2 such systems can be evolved rather than designed

multi source signal detection with arbitrary noise covariance detecting the presence of signals in noise from multiple sources is a fundamental problem in statistical signal processing in this paper we consider multi antenna signal detection when the noise covariance matrix is assumed to be arbitrary and unknown we address this problem in the context of cognitive radio where a multiple primary user detector is analyzed this detector is known as wilks detector in statistics literature which was derived under the generalized likelihood ratio criterion we calculate the moments of wilks detector which lead to simple and accurate approximate analytical formulae for the false alarm probability the detection probability and the receiver operating characteristic from the considered simulation settings performance gain over existing detection algorithms is observed in scenarios with arbitrary and unknown noise correlation and multiple primary users

knot invariants and cellular automata abstract there is a deep connection between the theory of invariants of knots in three dimensions and certain classes of solvable models in statistical mechanics we study the consequences of this for a class of cellular automaton systems knot invariants furnish both a non perturbative framework for the classification and analysis of such models and a primary tool with which to study the emergence of thermodynamic behavior in extended systems

reversible cellular automata with memory two dimensional patterns from a single site seed standard cellular automata ca are ahistoric memoryless i e the new state of a cell depends on its neighborhood configuration only at the preceding time step historic memory of all past iterations can be incorporated into ca by featuring each cell by a weighted mean of all its past states in this paper a new kind of reversible ca which incorporates memory is introduced in a two dimensional scenario

formal model of internal measurement alternate changing between recursive definition and domain equation abstract we sketch a paradox generally resulting from recursivity and propose a novel model to express evolutionary processes that requires identification of an interaction with internal measurement in this model a paradox is not resolved and the notion of relativity of any resolution is implicit in a dynamical system a certain transition rule is used recursively along time if one takes the foundation or context of recursivity into consideration one obtains a fixed point or one confronts a paradox in order to resolve this paradox we adopt scott s technical way to identify the form of a fixed point with a domain equation and to obtain a reflective domain however we simultaneously show that any resolution is destined to be relative in utilizing this notion we construct a model of dynamical process by embedding a measurement process in one time step any time transition involves the process of doubting the foundation of a transition rule leading to a fixed point solving it and obtaining a reflexive domain is used as a new transition rule also this process perpetually proceeds along time and then the system perpetually proceeds while any solution is destined to be relative we illustrate this type of model by using a dynamically changing contraction mapping as the interface of state and transition rule finally we show that one can formalize emergent properties by using this model and discuss the relationship between endo physics and internal measurement

general theory of fractal path integrals with applications to many body theories and statistical physics a general scheme of fractal decomposition of exponential operators is presented in any order m namely exp x a b sm x o xm 1 for any positive integer m where sm x et1a et2b et3a et4b etma with finite m depending on m a general recursive scheme of construction of tj is given explicitly it is proven that some of tj should be negative for m 3 and for any finite m nonexistence theorem of positive decomposition general systematic decomposition criterions based on a new type of time ordering are also formulated the decomposition exp x a b sm x n n o xm 1 nm yields a new efficient approach to quantum monte carlo simulations

theory of cellular automata a survey this article surveys some theoretical aspects of cellular automata ca research in particular we discuss classical and new results on reversibility conservation laws limit sets decidability questions universality and topological dynamics of ca the selection of topics is by no means comprehensive and reflects the research interests of the author the main goal is to provide a tutorial of ca theory to researchers in other branches of natural computing to give a compact collection of known results with references to their proofs and to suggest some open problems

locally most powerful invariant tests for correlation and sphericity of gaussian vectors in this paper we study the existence of locally most powerful invariant tests lmpit for the problem of testing the covariance structure of a set of gaussian random vectors the lmpit is the optimal test for the case of close hypotheses among those satisfying the invariances of the problem and in practical scenarios can provide better performance than the typically used generalized likelihood ratio test glrt the derivation of the lmpit usually requires one to find the maximal invariant statistic for the detection problem and then derive its distribution under both hypotheses which in general is a rather involved procedure as an alternative wijsman s theorem provides the ratio of the maximal invariant densities without even finding an explicit expression for the maximal invariant we first consider the problem of testing whether a set of n dimensional gaussian random vectors are uncorrelated or not and show that the lmpit is given by the frobenius norm of the sample coherence matrix second we study the case in which the vectors under the null hypothesis are uncorrelated and identically distributed that is the sphericity test for gaussian vectors for which we show that the lmpit is given by the frobenius norm of a normalized version of the sample covariance matrix finally some numerical examples illustrate the performance of the proposed tests which provide better results than their glrt counterparts

detection of rank p signals in cognitive radio networks with uncalibrated multiple antennas spectrum sensing is a key component of the cognitive radio paradigm primary signals are typically detected with uncalibrated receivers at signal to noise ratios snrs well below decodability levels multiantenna detectors exploit spatial independence of receiver thermal noise to boost detection performance and robustness we study the problem of detecting a gaussian signal with rank p unknown spatial covariance matrix in spatially uncorrelated gaussian noise with unknown covariance using multiple antennas the generalized likelihood ratio test glrt is derived for two scenarios in the first one the noises at all antennas are assumed to have the same unknown variance whereas in the second a generic diagonal noise covariance matrix is allowed in order to accommodate calibration uncertainties in the different antenna frontends in the latter case the glrt statistic must be obtained numerically for which an efficient method is presented furthermore for asymptotically low snr it is shown that the glrt does admit a closed form and the resulting detector performs well in practice extensions are presented in order to account for unknown temporal correlation in both signal and noise as well as frequency selective channels

artificial life with autonomously emerging boundaries the boundary conditions of biological systems are not controllable due to the perpetual disequilibration of force this means that the possibilities for the future are open i e one to many mapping however the future is uniquely determined a posteriori we argue that such an idea is a basic concept for biological and evolutionary systems and implies unprogrammable systems but it cannot be described only in a forward time description we propose a model in which the uncontrollable boundaries can be described in introducing a backward time dynamics a posteriori description with respect to the extent of the controllability of boundary conditions systems are classified into constant microscopic macroscopic and disequilibrium systems in the last the local transition rule is perpetually transformed as time progresses due to the uncontrollable microscopic boundary conditions our paradigm deviates from the newtonian paradigm i e the paradigm of prediction and its purpose is not to describe the physics of being but to describe that of becoming evolution

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

multi antenna based spectrum sensing for cognitive radios a glrt approach in this letter we propose multi antenna based spectrum sensing methods for cognitive radios crs using the generalized likelihood ratio test glrt paradigm the proposed methods utilize the eigenvalues of the sample covariance matrix of the received signal vector from multiple antennas taking advantage of the fact that in practice the primary user signals to be detected will either occupy a subspace of dimension strictly smaller than the dimension of the observation space or have a non white spatial spectrum these methods do not require prior knowledge of the primary user signals or the channels from the primary users to the cr by making different assumptions on the availability of the white noise power value at the cr receiver we derive two algorithms that are shown to outperform the standard energy detector

cellular automata for nanometer scale computation abstract cellular automata have recently been proposed as an architecture for dense locally interacting arrays of submicron devices however because conventional von neumann cellular automata do not correctly reflect the long range behavior of typical inter device interactions they do not provide a suitable theoretical model for the proposed device arrays in this paper we define replica cellular automata a class of cellular automata that can be generated from lattice gas cellular automata we show that for inter device interactions that have a well defined screening length d replica cellular automata provide a suitable formal model as an example of their applicability we exhibit a computation universal cellular automata architecture in which the cells consist of charge transfer quantum dot devices

frequency domain glr detection of a second order cyclostationary signal over fading channels cyclostationary processes exhibit a form of frequency diversity based on that we show that a digital waveform with symbol period t can be asymptotically represented as a rank 1 frequency domain vector process which exhibits uncorrelation at different frequencies inside the nyquist spectral support of 1 t by resorting to the fast fourier transform fft this formulation obviates the need of estimating a cumbersome covariance matrix to characterize the likelihood function we then derive the generalized likelihood ratio test glrt for the detection of a cyclostationary signal in unknown white noise without the need of a assuming a synchronized receiver this provides a sound theoretical basis for the exploitation of the cyclostationary feature and highlights an explicit link with classical square timing recovery schemes which appear implicitly in the core of the glrt moreover to avoid the well known sensitivity of cyclostationary based detection schemes to frequency selective fading channels a parametric channel model based on a lower bound on the coherence bandwidth is adopted and incorporated into the glrt by exploiting the rank 1 structure of small spectral covariance matrices the obtained detector outperforms the classical spectral correlation magnitude detector

spectrum sensing in the presence of multiple primary users we consider multi antenna cooperative spectrum sensing in cognitive radio networks when there may be multiple primary users a detector based on the spherical test is analyzed in such a scenario based on the moments of the distributions involved simple and accurate analytical formulae for the key performance metrics of the detector are derived the false alarm and the detection probabilities as well as the detection threshold and receiver operation characteristics are available in closed form simulations are provided to verify the accuracy of the derived results and to compare with other detectors in realistic sensing scenarios

robust spectrum sensing for noncircular signal in multiantenna cognitive receivers although noncircular nc signals are frequently encountered in wireless communications their statistical property has not yet been utilized in state of the art methods for spectrum sensing in this paper a variant of hadamard hdm ratio test is devised to exploit the nc property of the primary signals for spectrum sensing which is named the nc hdm algorithm as the nc hdm approach is able to exploit full statistical property of the nc signals and handle deviations from independent and identically distributed iid noise it is superior to the state of the art algorithms in detection accuracy and or robustness moreover performance analysis is conducted for the nc hdm approach including the invariant property false alarm probability and detection probability that is employing the moment matching box s chi square approximation the false alarm probability can be determined since the exact moments of the nc hdm test statistic under the signal absence hypothesis can be determined and all moments have been matched the derived false alarm probability is very accurate leading to simple and precise computation of the theoretical decision threshold on the other hand as the first two exact moments of the nc hdm test statistic under the signal presence hypothesis can be precisely calculated the detection probability based on moment matching beta approximation is quite accurate numerical results are included to demonstrate the superiority of the nc hdm approach and validate our theoretical calculations

passive detection of correlated subspace signals in two mimo channels in this paper we consider a two channel multiple input multiple output passive detection problem in which there is a surveillance array and a reference array the reference array is known to carry a linear combination of broadband noise and a subspace signal of known dimension but unknown basis the question is whether the surveillance channel carries a linear combination of broadband noise and a subspace signal of the same dimension but unknown basis which is correlated with the subspace signal in the reference channel we consider a second order detection problem where these subspace signals are structured by an unknown but common p dimensional random vector of symbols transmitted from sources of opportunity and then received through unknown m times p matrices at each of the m element arrays the noises in each channel have spatial correlation models ranging from arbitrarily correlated to independent with identical variances we provide a unified framework to derive the generalized likelihood ratio test for these different noise models in the most general case of arbitrary noise covariance matrices the test statistic is a monotone function of canonical correlations between the reference and surveillance channels