on the capacity achieving distribution of the discrete time noncoherent and partially coherent awgn channels we investigate the communication limits over rapid phase varying channels and consider the capacity of a discrete time noncoherent additive white gaussian noise ncawgn channel under the average power constraint we obtain necessary and sufficient conditions for the capacity achieving input distribution and show that this distribution is discrete and possesses an infinite number of mass points using this characterization of the capacity achieving distribution we compute a tight lower bound on the capacity of the channel based on examining suboptimal input distributions in addition we provide some easily computable lower and upper bounds on the channel capacity finally we extend some of these results to the partially coherent channel where it is assumed that a phase locked loop pll is used to track the carrier phase at the receiver and that an ideal interleaver and de interleaver are employed rendering the tikhonov distributed residual phase errors statistically independent from one symbol interval to another

noncoherent detection of coherent lightwave signals corrupted by phase noise waves are treated that modulate by either on off keying ook or binary frequency shift keying fsk and are further impaired by additive gaussian noise heterodyne detection of such a waveform produces an electronic bandpass signal which to ease demodulation in the presence of phase noise is noncoherently demodulated to extract the baseband pulse stream the treatment goes beyond previous bit error rate ber analyses of optical heterodyne receivers for ook and fsk first there is full adherence to the standard brownian motion model of phase noise also the receiver structure is formulated in such a way that the probability density function of the receiver output samples can be accurately determined this permits calculations of the additive noise and phase noise tolerable when achieving bit error rates as small as 10 sup 9 finally the study is comprehensive regarding the range of parameters explored filtering at an intermediate frequency if alone as well as if filtering plus postdetection low pass filtering is considered when the receiver parameters decision threshold for ook and if filter bandwidth are optimized large amounts of phase noise can be accommodated with only minor increases in required signal to noise ratio this is especially important when the bit rate is moderate compared to the laser linewidth

entropy based tests of uniformity abstract the power properties of an entropy based test are investigated when used for testing uniformity on 0 1 percentage points and power against seven alternatives are reported compared with other tests of uniformity the entropy based test possesses good power properties for many alternatives some asymptotic null and alternative distributions are derived for sample sizes up to 100 the table of percentage points provides a practical guide for using this test a theory of entropy based tests of distributional hypotheses other than uniformity is outlined

calculation of mutual information for partially coherent gaussian channels with applications to fiber optics the mutual information between a complex valued channel input and its complex valued output is decomposed into four parts based on polar coordinates an amplitude term a phase term and two mixed terms numerical results for the additive white gaussian noise awgn channel with various inputs show that at high signal to noise ratio snr the amplitude and phase terms dominate the mixed terms for the awgn channel with a gaussian input analytical expressions are derived for high snr the decomposition method is applied to partially coherent channels and a property of such channels called spectral loss is developed spectral loss occurs in nonlinear fiber optic channels and it may be one effect that needs to be taken into account to explain the behavior of the capacity of nonlinear fiber optic channels

solving satisfiability problems by fluctuations the dynamics of stochastic local search algorithms stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems we give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random satisfiability problems we find two different dynamical regimes depending on the number of constraints per variable for low constraintness the problems are solved efficiently i e in linear time for higher constraintness the solution times become exponential we observe that the dynamical behavior is characterized by a fast equilibration and fluctuations around this equilibrium if the algorithm runs long enough an exponentially rare fluctuation towards a solution appears

a consistent nonparametric test for serial independence abstract we propose a nonparametric test for serial independence against serial dependence of fixed order that is consistent against all such alternatives the conditions required are weak the asymptotic distribution under the null is 1 2 and the test works regardless of the underlying distribution also included are a nuisance parameter result monte carlo simulations a theoretical efficiency study an empirical example and a review of possible extensions in addition we derive a similar consistent test for lack of serial dependence of order one against serial dependence of order one

hypothesis testing in time series via the empirical characteristic function a generalized spectral density approach abstract the standardized spectral density completely describes serial dependence of a gaussian process for non gaussian processes however it may become an inappropriate analytic tool because it misses the nonlinear processes with zero autocorrelation by generalizing the concept of the standardized spectral density i propose a new spectral tool suitable for both linear and nonlinear time series analysis the generalized spectral density is indexed by frequency and a pair of auxiliary parameters it is well defined for both continuous and discrete random variables and requires no moment condition introduction of the auxiliary parameters renders the spectrum able to capture all pairwise dependencies including those with zero autocorrelation the standardized spectral density can be derived by properly differentiating the generalized spectral density with respect to the auxiliary parameters at the origin the consistency of a class of parzen s kernel type estimators for the generalized spectral dens

exponential series estimator of multivariate densities abstract we present an exponential series estimator ese of multivariate densities which has an appealing information theoretic interpretation for a d dimensional random variable x with density p 0 the ese takes the form p x exp i 1 0 m 1 i d 0 m d i i x where i are some real valued linearly independent functions defined on the support of p 0 we derive the convergence rate of the ese in terms of the kullback leibler information criterion the integrated squared error and some other metrics we also derive its almost sure uniform convergence rate we then establish the asymptotic normality of p we undertake two sets of monte carlo experiments the first experiment examines the ese performance using mixtures of multivariate normal densities the second estimates copula density functions the results demonstrate the efficacy of the ese an empirical application on the joint distributions of stock returns is presented

asymptotic distribution theory for nonparametric entropy measures of serial dependence entropy is a classical statistical concept with appealing properties establishing asymptotic distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging in this paper we develop an asymptotic theory for a class of kernel based smoothed nonparametric entropy measures of serial dependence in a time series context we use this theory to derive the limiting distribution of granger and lin s 1994 normalized entropy measure of serial dependence which was previously not available in the literature we also apply our theory to construct a new entropy based test for serial dependence providing an alternative to robinson s 1991 approach to obtain accurate inferences we propose and justify a consistent smoothed bootstrap procedure the naive bootstrap is not consistent for our test our test is useful in for example testing the random walk hypothesis evaluating density forecasts and identifying important lags of a time series it is asymptotically locally more powerful than robinson s 1991 test as is confirmed in our simulation an application to the daily s p 500 stock price index illustrates our approach

a consistent characteristic function based test for conditional independence abstract y is conditionally independent of z given x if pr f y x z f y x 1 for all y on its support where f denotes the conditional density of y given x z or x this paper proposes a nonparametric test of conditional independence based on the notion that two conditional distributions are equal if and only if the corresponding conditional characteristic functions are equal we extend the test of su and white 2005 a hellinger metric nonparametric test for conditional independence discussion paper department of economics ucsd in two directions 1 our test is less sensitive to the choice of bandwidth sequences 2 our test has power against deviations on the full support of the density of x y z we establish asymptotic normality for our test statistic under weak data dependence conditions simulation results suggest that the test is well behaved in finite samples applications to stock market data indicate that our test can reveal some interesting nonlinear dependence that a traditional linear granger causality test fails to detect

conditions for a monotonic channel capacity motivated by results in optical communications where the performance can degrade dramatically if the transmit power is sufficiently increased the channel capacity is characterized for various kinds of memoryless vector channels it is proved that for all static point to point channels the channel capacity under an equal power constraint is a nondecreasing function of power as a consequence maximizing the mutual information over all input distributions with a certain power is for such channels equivalent to maximizing it over the larger set of input distributions with upperbounded power the channel coding theorem is formally proved for an equal power constraint for interference channels such as optical wavelength division multiplexing systems the primary channel capacity is always nondecreasing with power if all interferers transmit with identical distributions as the primary user also if all input distributions in an interference channel are optimized jointly then the achievable sum rate capacity is again nondecreasing the results generalize to the channel capacity as a function of a wide class of costs not only power

measure invariance of copula functions as tool for testing no arbitrage assumption abstract copulas which are invariant under margins transforms induced by some change of measure are investigated it is emphasized that this particular kind of transforms induced by some change of measure largely used in pricing techniques preserves the invariance of the aggregation operator and a sufficient condition to assure it is proved the discussion is extended to the time preserving of measure invariance a characterization of its stability in time for multivariate stationary processes based on the dynamic copula representation see cherubini et al 2011 is provided finally a measure invariance based statistical test for the absence of arbitrage opportunity assumption and its preservation in time is proposed and an empirical experiment based on quotes of s p 500 futures and options traded on the chicago mercantile exchange cme is discussed

testing for pairwise serial independence via the empirical distribution function built on skaug and tjostheim s approach this paper proposes a new test for serial independence by comparing the pairwise empirical distribution functions of a time series with the products of its marginals for various lags where the number of lags increases with the sample size and different lags are assigned different weights typically the more recent information receives a larger weight the test has some appealing attributes it is consistent against all pairwise dependences and is powerful against alternatives whose dependence decays to zero as the lag increases although the test statistic is a weighted sum of degenerate cramer von mises statistics it has a null asymptotic n 0 1 distribution the test statistic and its limit distribution are invariant to any order preserving transformation the test applies to time series whose distributions can be discrete or continuous with possibly infinite moments finally the test statistic only involves ranking the observations and is computationally simple it has the advantage of avoiding smoothed nonparametric estimation a simulation experiment is conducted to study the finite sample performance of the proposed test in comparison with some related tests

a non parametric independence test using permutation entropy in the present paper we construct a new simple consistent and powerful test for independence by using symbolic dynamics and permutation entropy as a measure of serial dependence we also give a standard asymptotic distribution of an affine transformation of the permutation entropy under the null hypothesis of independence the test statistic and its standard limit distribution are invariant to any monotonic transformation the test applies to time series with discrete or continuous distributions eventhough the test is based on entropy measures it avoids smoothed non parametric estimation an application to several daily financial time series illustrates our approach

entropy and predictability of stock market returns abstract we examine the predictability of stock market returns by employing a new metric entropy measure of dependence with several desirable properties we compare our results with a number of traditional measures the metric entropy is capable of detecting nonlinear dependence within the returns series and is also capable of detecting nonlinear affinity between the returns and their predictions obtained from various models thereby serving as a measure of out of sample goodness of fit or model adequacy several models are investigated including the linear and neural network models as well as nonparametric and recursive unconditional mean models we find significant evidence of small nonlinear unconditional serial dependence within the returns series but fragile evidence of superior conditional predictability profit opportunity when using market switching versus buy and hold strategies

envelope statistics for filtered optical signals corrupted by phase noise consideration is given to the case of an optical pulse containing phase noise which is passed through either an optical filter or following heterodyne lightwave detection an electrical filter because of the phase noise the envelope of the filter output at any instant is a random variable an analytical method is developed for estimating the probability density function pdf of this envelope for different kinds of filter responses and for realistic combinations of phase noise severity and filter bandwidth obvious applications are to detection analyses of coherent lightwave systems wherein finite laser linewidths constitute an important source of impairment for each of the several types of filters considered the envelope pdf can be accurately fitted by an exponential function approximation where the decay constant is related in a simple way to known system parameters

models and information rates for wiener phase noise channels a waveform channel is considered where the transmitted signal is corrupted by wiener phase noise and additive white gaussian noise a discrete time channel model that considers the effect of filtering on the phase noise is developed the model is based on a multi sample receiver i e an integrate and dump filter whose output is sampled at a rate higher than the signaling rate it is shown that at high signal to noise ratio snr the multi sample receiver achieves a rate that grows logarithmically with the snr if the number of samples per symbol oversampling factor grows with the cubic root of the snr moreover the pre log factor is at least 1 2 and can be achieved by amplitude modulation for an approximate discrete time model of the multi sample receiver the capacity pre log at high snr is shown to be at least 3 4 if the number of samples per symbol grows with the square root of the snr the analysis shows that phase modulation achieves a pre log of at least 1 4 while amplitude modulation still achieves a pre log of 1 2 this is strictly greater than the capacity pre log of the approximate discrete time wiener phase noise channel with only one sample per symbol which is 1 2 numerical simulations are used to compute lower bounds on the information rates achieved by the multi sample receiver the simulations show that oversampling is beneficial for both strong and weak phase noise at high snr in fact the information rates are sometimes substantially larger than when using commonly used approximate discrete time models

comparing nonparametric versus parametric regression fits in general there will be visible differences between a parametric and a nonparametric curve estimate it is therefore quite natural to compare these in order to decide whether the parametric model could be justified an asymptotic quantification is the distribution of the integrated squared difference between these curves we show that the standard way of bootstrapping this statistic fails we use and analyse a different form of bootstrapping for this task we call this method the wild bootstrap and apply it to fitting engel curves in expenditure data analysis

consistent model specification tests omitted variables and semiparametric functional forms in this paper we develop several consistent tests in the context of a nonparametric regression model these include tests for the significance of a subset of regressors and tests for the specification of the semiparametric functional form of the regression function where the latter covers tests for a partially linear and a single index specification against a general nonparametric alternative one common feature to the construction of all these tests is the use of the central limit theorem for degenerate u statistics of order higher than two as a result they share the same advantages over most of the corresponding existing tests in the literature a they do not depend on any ad hoc modifications such as sample splitting random weighting etc b under the alternative hypotheses the test statistics in this paper diverge to positive infinity at a faster rate than those based on ad hoc modifications

the channel capacity of discrete time phase modulation in awgn the capacity of a bandlimited phase only modulated system in additive white gaussian noise is calculated where the phase is not restricted to a finite alphabet and the demodulator supplies only phase measurements the results match a known asymptote at high signal to noise ratios and form an upper limit on the capacities of mpsk for finite m

optimizing constellations for single subcarrier intensity modulated optical systems we optimize modulation formats for the additive white gaussian noise channel with nonnegative input also known as the intensity modulated direct detection channel with and without confining them to a lattice structure our optimization criteria are the average electrical average optical and peak power the nonnegative constraint on the input to the channel is translated into a conical constraint in signal space and modulation formats are designed by sphere packing inside this cone some dense packings are found which yield more power efficient modulation formats than previously known for example at a spectral efficiency of 1 5 bit s hz the modulation format optimized for average electrical power has a 2 55 db average electrical power gain over the best known format to achieve a symbol error rate of 10 6 the corresponding gains for formats optimized for average and peak optical power are 1 35 and 1 72 db respectively using modulation formats optimized for peak power in average power limited systems results in a smaller power penalty than when using formats optimized for average power in peak power limited systems we also evaluate the modulation formats in terms of their mutual information to predict their performance in the presence of capacity achieving error correcting codes and finally show numerically and analytically that the optimal modulation formats for reliable transmission in the wideband regime have only one nonzero point

testing the markov property with high frequency data this paper develops a framework to nonparametrically test whether discrete valued irregularly spaced financial transactions data follow a markov process for that purpose we consider a specific optional sampling in which a continuous time markov process is observed only when it crosses some discrete level this framework is convenient for it accommodates the irregular spacing that characterizes transactions data under such an observation rule the current price duration is independent of a previous price duration given the previous price realization a simple nonparametric test then follows by examining whether this conditional independence property holds monte carlo simulations suggest that the asymptotic test has huge size distortions though a bootstrap based variant entails reasonable size and power properties in finite samples as for an empirical illustration we investigate whether bid ask spreads follow markov processes using transactions data from the new york stock exchange the motivation lies on the fact that asymmetric information models of market microstructures predict that the markov property does not hold for the bid ask spread we robustly reject the markov assumption for two out of the five stocks under scrutiny finally it is reassuring that our results are consistent with two alternative measures of asymmetric information

estimating the direction in which a data set is most interesting estimation of orientation is a key operation at each step in projection pursuit since projection pursuit is a nonparametric algorithm and since even low dimensional approximations to the target function must converge to their limits at rates considerably slower than n 1 2 where n is sample size then it might be thought that the same is true of orientation estimates it is shown in the present paper that this is not the case and that estimation of orientation is a parametric operation in the sense that under mild nonparametric assumptions correctly chosen kernel type orientation estimates converge to their limits at rate n 1 2 this property is not enjoyed by standard projection pursuit orientation estimates which converge at a slower rate than n 1 2 most attention in the present paper is focussed on the case of projection pursuit density approximation but it is pointed out that our arguments hold generally an important practical conclusion is that data should be smoothed less when estimating orientation than when constructing the final projection pursuit approximation

ml detection in phase noise impaired simo channels with uplink training the problem of maximum likelihood ml detection in training assisted single input multiple output simo systems with phase noise impairments is studied for two different scenarios i e the case when the channel is deterministic and known constant channel and the case when the channel is stochastic and unknown fading channel furthermore two different operations with respect to the phase noise sources are considered namely the case of identical phase noise sources and the case of independent phase noise sources over the antennas in all scenarios the optimal detector is derived for a very general parameterization of the phase noise distribution furthermore a high signal to noise ratio snr analysis is performed to show that symbol error rate ser floors appear in all cases the ser floor in the case of identical phase noise sources for both constant and fading channels is independent of the number of antenna elements in contrast the ser floor in the case of independent phase noise sources is reduced when increasing the number of antenna elements for both constant and fading channels finally the system model is extended to multiple data channel uses and it is shown that the conclusion is valid for these setups as well

polar decomposition of mutual information over complex valued channels a polar decomposition of mutual information between a complex valued channel s input and output is proposed for an input whose amplitude and phase are independent of each other the mutual information is symmetrically decomposed into three terms 1 an amplitude term 2 a phase term and 3 a cross term where the cross term is negligible theoretical bounds of the amplitude and phase terms are derived for additive white gaussian noise channels with gaussian inputs this decomposition is applied to amplitude phase shift keying with product constellation product apsk design and analysis it facilitates the product apsk to achieve a considerable shaping gain at some interesting rates over conventional quadrature amplitude modulation with a similar low complexity

soft metrics and their performance analysis for optimal data detection in the presence of strong oscillator phase noise in this paper we address the classical problem of maximum likelihood ml detection of data in the presence of random phase noise we consider a system where the random phase noise affecting the received signal is first compensated by a tracker estimator then the phase error and its statistics are used for deriving the ml detector specifically we derive an ml detector based on a gaussian assumption for the phase error probability density function pdf further without making any assumptions on the phase error pdf we show that the actual ml detector can be reformulated as a weighted sum of central moments of the phase error pdf we present a simple approximation of this new ml rule assuming that the phase error distribution is unknown the ml detectors derived are also the aposteriori probabilities of the transmitted symbols and are referred to as soft metrics then using the detector developed based on gaussian phase error assumption we derive the symbol error probability sep performance and error floor analytically for arbitrary constellations finally we compare sep performance of the various detectors metrics in this work and those from literature for different signal constellations phase noise scenarios and snr values

rank based extensions of the brock dechert and scheinkman test this article proposes new tests of randomness for innovations in a large class of time series models these tests are based on functionals of empirical processes constructed from either the model residuals or their associated ranks the asymptotic behavior of these processes is determined under the null hypothesis of randomness the limiting distributions are seen to be independent of estimation errors under appropriate regularity conditions several test statistics are derived from these processes the classical brock dechert and scheinkman statistic and a rank based analog are included as special cases because the limiting distributions of the rank based test statistics are margin free their finite sample p values can be easily calculated by simulation monte carlo experiments show that these statistics are quite powerful against several classes of alternatives

an upper bound on the error probability of quadratic detection in noisy phase channels a rigorous method to find the upper bound of the error probability of noncoherent quadratically detected signals in the presence of both additive white gaussian noise and brownian carrier phase noise is presented an analytical upper bound on the bit error probability is derived relying on a bivariate moment generating function of two bounded exponential functionals of the brownian phase path these functionals whose exact statistics are unknown yield the two basic impairments arising due to phase noise in band signal suppression and intersymbol crosstalk the classical theory of chebyshev systems is applied to obtain the limiting values of the involved generating function utilizing a multidimensional moment characterization of the involved functionals the impact of the incomplete statistical characterization used on the resultant upper bound tightness is addressed assessing the design and performance of lightwave heterodyned systems using this method is discussed the method enables the analysis of interchannel crosstalk effects in frequency division multiplexing systems

a nonparametric test of serial independence based on the empirical distribution function the blum kiefer rosenblatt 1961 statistic for testing independence is considered in a time series setting this test is under mild conditions shown to be consistent against lag one dependent alternatives the null distribution of the test statistic is established both when the marginal distribution is continuous and when it is discrete simulation results giving information on the size and the power of the test are provided and comparisons are made with other tests of serial dependence an extension of the test is made to detect higher lag dependence and finally the test is applied to a real data example

relative entropy measures of multivariate dependence abstract there has been a lot of work on measures of dependence or association for bivariate probability distributions or bivariate data these measures usually assume that the variables are both continuous or both categorical in comparison there is very little work on multivariate or conditional measures of dependence the purpose of this article is to discuss measures of multivariate dependence and measures of conditional dependence based on relative entropies these measures are conceptually very general as they can be used for a set of variables that can be a mixture of continuous ordinal categorical and nominal categorical variables for continuous or ordinal categorical variables a certain transformation of relative entropy to the interval 0 1 leads to generalizations of the correlation multiple correlation and partial correlation coefficients if all variables are nominal categorical the relative entropies are standardized to take a maximum of 1 and then transformed so that in the bivar

upper and lower bounds to the information rate transferred through first order markov channels with free running continuous state starting from the definition of mutual information one promptly realizes that the probabilities inferred by bayesian tracking can be used to compute the shannon information between the state and the measurement of a dynamic system in the gaussian and linear case the information rate can be evaluated from the probabilities computed by the kalman filter when the probability distributions inferred by bayesian tracking are nontractable one is forced to resort to approximated inference which gives only an approximation to the wanted probabilities we propose upper and lower bounds to the information rate between the hidden state and the measurement based on approximated inference application of these bounds to multiplicative communication channels is discussed and experimental results for the discrete time phase noise channel and for the gauss markov fading channel are presented

estimation of the entropy and information of absolutely continuous random variables a method is proposed for estimating the entropy and the mutual information of absolutely continuous random vectors and an upper bound of the mean risks for the proposed estimators under strong mixing conditions is given

lattice codes for amplified direct detection optical systems theories of shaping for lattice codes have been developed for systems optical or non optical using coherent detection with additive white gaussian noise awgn and for direct detection optical systems with awgn this paper considers shaping for amplified direct detection optical systems in which signal spontaneous beat noise a form of signal dependent noise is dominant an a dimensional a d signal is formed by modulating the intensities squares of field magnitudes of a sequence of n time disjoint pulses in field magnitude coordinates signal energy is represented by a l2 norm and the optimal constellation bounding region is the nonnegative orthant bounded by an n sphere under a continuous approximation as nrarrinfin the ultimate shape gain is 1 53 db and the induced signaling distribution on the constituent 1 d constellation becomes half gaussian in practice the ultimate shape gain can be approached when the 1 d constellation follows a truncated half gaussian distribution we investigate the tradeoffs between shape gain and increases in constellation expansion ratio or peak to average power ratio we compare our shaping results with those for coherent detection systems and direct detection optical systems with awgn