modified biserial correlation coefficients asymptotic distribution theory of brogden s form of biserial correlation coefficient is derived and large sample estimates of its standard error obtained its efficiency relative to the biserial correlation coefficient is examined other modifications of the statistic are evaluated and on the basis of these results recommendations for choice of estimator of biserial correlation are presented

optimal odd length binary z complementary pairs a pair of sequences is called a golay complementary pair gcp if their aperiodic auto correlation sums are zero for all out of phase time shifts existing known binary gcps only have even lengths in the form of 21026 where are non negative integers to fill the gap left by the odd lengths we investigate the optimal oddlength binary pairs which display the closest correlation property to that of gcps our criteria of closeness is that each pair has the maximum possible zero correlation zone zcz width and minimum possible out of zone aperiodic auto correlation sums such optimal pairs are called optimal odd length binary z complementary pairs ob zcp in this paper we show that each optimal ob zcp has maximum zcz width of n 1 2 and minimum out of zone aperiodic sum magnitude of 2 where n denotes the sequence length odd systematic constructions of such optimal op zcps are proposed by insertion and deletion of certain binary gcps which settle the 2011 li fan tang tu open problem positively the proposed optimal ob zcps may serve as a replacement for gcps in many engineering applications where odd sequence lengths are preferred in addition they give rise to a new family of base two almost difference families adf which are useful in studying partially balanced incomplete block design bibd index terms aperiodic correlation almost difference set ads almost difference families adf golay complementary pair gcp zero correlation zone zcz z complementary pair zcp

on the large sample distributions of modified sample biserial correlation coefficients the asymptotic distributions of brogden s and lord s modified sample biserial correlation coefficients are derived the asymptotic variances of these estimators are evaluated for bivariate normal populations and compared to the asymptotic variance of the maximum likelihood estimator

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

optimal linear mean square filter for continuous time jump linear systems we consider a class of hybrid systems which is modeled by continuous time linear systems with markovian jumps in the parameters lsmjp our aim is to derive the best linear mean square estimator for such systems the approach adopted here produces a filter which bears those desirable properties of the kalman filter a recursive scheme suitable for computer implementation which allows some offline computation that alleviates the computational burden apart from the intrinsic theoretical interest of the problem in its own right and the application oriented motivation of getting more easily implementable filters another compelling reason why the study here is pertinent has to do with the fact that the optimal nonlinear filter for our estimation problem is not computable via a finite computation the filter is infinite dimensional our filter has dimension nn with n denoting the dimension of the state vector and n the number of states of the markov chain

a comparison of generalized and modified sample biserial correlation estimators in a recent paper bedrick derived the asymptotic distribution of lord s modified sample biserial correlation estimator and studied its efficiency for bivariate normal populations we present a more detailed examination of the properties of lord s estimator and several competitors including brogden s estimator we show that lord s estimator is more efficient for three nonnormal distributions than a generalization of pearson s sample biserial estimator in addition lord s estimator is reasonably efficient relative to the maximum likelihood estimator for these distributions these conclusions are consistent with bedrick s results for the bivariate normal distribution we also study the small sample bias and variance of lord s estimator and the coverage properties of several confidence interval estimates

new complete complementary codes for peak to mean power control in multi carrier cdma owing to the zero non trivial aperiodic correlation sum properties complete complementary codes ccc have been applied to asynchronous multi carrier code division multiple access mc cdma communications in order to provide zero interference performance when each complementary code is arranged to be a matrix the peak to mean envelope power ratio pmepr of the ccc mc cdma system is determined by the column sequences of the complementary matrices the existing ccc have the column sequence pmepr of m where m denotes the number of subcarriers in a ccc mc cdma system in practice m is generally large and a pmepr approaching this value is unacceptable to solve this problem a new class of ccc using generalized boolean functions and with a column sequence pmepr of at most 2 is proposed in this paper

the polyserial correlation coefficient the polyserial and point polyserial correlations are discussed as generalizations of the biserial and point biserial correlations the relationship between the polyserial and point polyserial correlation is derived the maximum likelihood estimator of the polyserial correlation is compared with a two step estimator and with a computationally convenient ad hoc estimator all three estimators perform reasonably well in a monte carlo simulation some practical applications of the polyserial correlation are described

a construction of ofdm 16 qam sequences having low peak powers using a realization of 16 qam as set addition of two scaled versions of the 4 psk constellation we construct 16 qam sequences having low peak to mean envelope power ratios pmepr from 4 psk golay sequences various upper bounds on the peak envelope powers of these sequences are established transmission using these sequences provides twice as much rate as transmission using complementary golay sequences with a maximum pmepr of 3 6 5 56 db

new constructions of general qam golay complementary sequences a construction of general quadrature amplitude modulation qam golay complementary sequences based on quadrature phase shift keying golay davis jedwab sequences gdj sequences is described existing constructions of 16 and 64 qam golay sequences are extended to 4q qam sequences of length 2m for q 1 m 2 this construction gives m 1 42 q 1 m 1 4 q 1 2q 1 m 2 4 m 1 golay complementary sequences a previous offset pair enumeration conjecture for 64 qam golay sequences is proved as a special case of the enumeration for 4q qam golay sequences when used for orthogonal frequency division multiplexing signals the peak to mean envelope power ratio upper bound is shown to be 6 2q 1 2q 1 approaching 6 as the qam constellation size increases

estimating the polyserial correlation coefficient we develop simple noniterative estimators of the polyserial correlation coefficient a general relationship between the polyserial correlation and the point polyserial correlation is exploited to give extensions of pearson s brogden s and lord s biserial estimators to the multicategory setting the small sample and asmptotic properties of these estimators are studied in some detail a comparison with maximum likelihood estimates shows that lord s polyserial estimator is fairly efficient across three probability models

near complementary sequences with low pmepr for peak power control in multicarrier communications new families of near complementary sequences are presented for peak power control in multicarrier communications a framework for near complementary sequences is given by an explicit boolean expression and an equivalent matrix structure the framework transforms seed pairs to near complementary sequences by the aid of golay complementary sequences new families of near complementary sequences of various lengths and pmepr 4 are then presented where the sequences are constructed by the framework employing the seeds of shortened and extended golay complementary pairs the families present in a constructive way a large number of sequences of pmepr 4 for the lengths 100 of 24 28 30 34 36 48 56 60 62 66 68 72 and 96 where no golay pairs have been reported the sequence families can find potential applications for peak power control requiring codewords or sequences of various lengths as well as low peak to mean envelope power ratio pmepr

a new construction of 16 qam golay complementary sequences we present a new construction of 16 qam golay sequences of length n 2 sup m the number of constructed sequences is 14 12m m 2 4 sup m 1 when employed as a code in an orthogonal frequency division multiplexing ofdm system this set of sequences has a peak to mean envelope power ratio pmepr of 3 6 by considering two specific subsets of these sequences we obtain new codes with pmepr bounds of 2 0 and 2 8 and respective code sizes of 2 2m m 2 4 sup m 1 and 4 4m m 2 4 sup m 1 these are larger than previously known codes for the same pmepr bounds

linear minimum mean square error estimation for discrete time markovian jump linear systems the linear minimum mean square error estimator lmmse for discrete time linear systems subject to abrupt changes in the parameters modeled by a markov chain spl theta k spl epsiv 1 n is considered the filter equations are derived from geometric arguments in a recursive form resulting in an on line algorithm suitable for computer implementation the author s approach is based on estimating x k 1 sub spl theta k i instead of estimating directly x k the uncertainty introduced by the markovian jumps increases the dimension of the filter to n n 1 where n is the dimension of the state variable an example where the dimension of the filter can be reduced to n is presented as well as a numerical comparison with the imm filter

doppler resilient golay complementary waveforms we describe a method of constructing a sequence pulse train of phase coded waveforms for which the ambiguity function is free of range sidelobes along modest doppler shifts the constituent waveforms are golay complementary waveforms which have ideal ambiguity along the zero doppler axis but are sensitive to nonzero doppler shifts we extend this construction to multiple dimensions in particular to radar polarimetry where the two dimensions are realized by orthogonal polarizations here we determine a sequence of two by two alamouti matrices where the entries involve golay pairs and for which the range sidelobes associated with a matrix valued ambiguity function vanish at modest doppler shifts the prouhet thue morse sequence plays a key role in the construction of doppler resilient sequences of golay complementary waveforms

a unified approach for stochastic and mean square stability of continuous time linear systems with markovian jumping parameters and additive disturbances necessary and sufficient conditions for stochastic stability ss and mean square stability mss of continuous time linear systems subject to markovian jumps in the parameters and additive disturbances are established we consider two scenarios regarding the additive disturbances one in which the system is driven by a wiener process and one characterized by functions in l 2 m omega cal f mathbb p which is the usual scenario for the h infty approach the markov process is assumed to take values in an infinite countable set mathcal s it is shown that ss is equivalent to the spectrum of an augmented matrix lying in the open left half plane to the existence of a solution for a certain lyapunov equation and implies is equivalent for mathcal s finite asymptotic wide sense stationarity awss it is also shown that ss is equivalent to the state x t belonging to l 2 n omega cal f mathbb p whenever the disturbances are in l 2 m omega cal f mathbb p for the case in which mathcal s is finite ss and mss are equivalent and the lyapunov equation can be written down in two equivalent forms with each one providing an easier to check sufficient condition

synthesis of power efficient multitone signals with flat amplitude spectrum it is shown that generally any binary or polyphase sequence belonging to a pair of complementary sequences can be used to construct the initial phases of tones forming a multitone signal with the crest factor less than or equal to 6 db the previously proposed shapiro rudin sequences are representatives of a much larger family of binary golay complementary sequences numerical investigations show that the values of the crest factors obtained by applying complementary sequences binary or polyphase are between 5 and 6 db regardless of the number of tones

maximum likelihood estimation of multivariate polyserial and polychoric correlation coefficients the method of finding the maximum likelihood estimates of the parameters in a multivariate normal model with some of the component variables observable only in polytomous form is developed the main stratagem used is a reparameterization which converts the corresponding log likelihood function to an easily handled one the maximum likelihood estimates are found by a fletcher powell algorithm and their standard error estimates are obtained from the information matrix when the dimension of the random vector observable only in polytomous form is large obtaining the maximum likelihood estimates is computationally rather labor expensive therefore a more efficient method the partition maximum likelihood method is proposed these estimation methods are demonstrated by real and simulated data and are compared by means of a simulation study

on cosets of the generalized first order reed muller code with low pmepr golay sequences are well suited for use as codewords in orthogonal frequency division multiplexing ofdm since their peak to mean envelope power ratio pmepr in q ary phase shift keying psk modulation is at most 2 it is known that a family of polyphase golay sequences of length 2m organizes in m 2 cosets of a q ary generalization of the first order reed muller code rmq 1 m in this paper a more general construction technique for cosets of rm q 1 m with low pmepr is established these cosets contain so called near complementary sequences the application of this theory is then illustrated by providing some construction examples first it is shown that the m 2 cosets of rmq 1 m comprised of golay sequences just arise as a special case second further families of cosets of rmq 1 m with maximum pmepr between 2 and 4 are presented showing that some previously unexplained phenomena can now be understood within a unified framework a lower bound on the pmepr of cosets of rmq 1 m is proved as well and it is demonstrated that the upper bound on the pmepr is tight in many cases finally it is shown that all upper bounds on the pmepr of cosets of rmq 1 m also hold for the peak to average power ratio papr under the walsh hadamard transform wht

complementary sequences for isi channel estimation a merit factor based on the sequence autocorrelation function whose minimization leads to the reduction in the cramer rao lower bound crlb for the variance of two sided intersymbol interference isi channel estimation is introduced pairs of binary pilot symbol sequences a preamble and a postamble for channel estimation are jointly designed to minimize this merit factor given that the number of channel taps is l and the length of a pilot symbol sequence is n l 1 where n spl ges l we distinguish between the case when n is even and the case when it is odd for even n we show that complementary sequences not only minimize the merit factor but also the crlb for a subset of odd n we construct almost complementary periodic sequence pairs that minimize the merit factor the optimal pilot symbol block signaling requires alternating between two in most cases different binary sequences that form the merit minimizing pair

new 64 qam golay complementary sequences a construction of 64 qam golay complementary sequences was proposed by lee and golomb where three qpsk golay davis jedwab complementary sequences gdj sequences or standard golay sequences related by a pair of offsets were combined to form each 64 qam golay sequence feasible offset pairs were given as first order generalized boolean functions in algebraic normal form new offset pairs were described in a conjecture of li leading to new 64 qam golay complementary sequences the proof of the conjecture is presented

a new construction of 64 qam golay complementary sequences in this correspondence we present a new construction for 64 qam golay sequences of length n 2 sup m for integer m the peak envelope power pep of 64 qam golay sequences is shown to be bounded by 4 66n the new construction of 64 qam golay sequences of length n 2 sup m is based on our earlier construction of new offsets of 16 qam golay sequences which are also presented here the total number of offsets of 64 qam golay sequences is 496 for m 2 808 for m 3 and 976 for m 4 obtained by computer search we also computed the pep distribution for 64 qam golay sequences for m 2 m 3 and m 4

robust mode independent filtering for discrete time markov jump linear systems with multiplicative noises this paper deals with the robust mode independent linear filtering problem for discrete time markov jump linear systems with multiplicative noises it is assumed that the values of the markov chain are not available and that the parameters of the systems are subject to convex polytopic uncertainties the goal is to design a mode independent that is one that doesn t depend on the markov jump parameter dynamic linear filter such that the closed loop system is mean square stable and minimises an upper bound for the stationary expected value of the square error a linear matrix inequalities lmi formulation based on a parameter dependent lyapunov procedure is proposed to solve the problem the paper concludes with an illustrative example

maximum likelihood estimation of polyserial correlations this paper considers a multivariate normal model with one of the component variables observable only in polytomous form the maximum likelihood approach is used for estimation of the parameters in the model the newton raphson algorithm is implemented to obtain the solution of the problem examples based on real and simulated data are reported

a new construction of 16 qam near complementary sequences we present a new 16 qam near complementary sequence construction where the length of the sequences is n 2m the 16 qam near complementary sequences are constructed by nonlinear offsets but the peak to mean envelope power ratio bounds for these 16 qam near complementary sequences is as low as 2 4 the number of newly constructed 16 qam near complementary sequences is m 2 4m 1

16 qam almost complementary sequences with low pmepr a pair of sequences is said to be an almost complementary pair acp if they have zero aperiodic autocorrelation sums except at only one position over all the positive negative time shifts having correlation property very close to that of golay complementary pairs gcps acps may be used as an alternative to gcps in many applications in communications and radar for high rate code keying ofdm communication we construct novel 16 qam acps from three new classes of quadratic offsets leading to three large sets of 16 qam almost complementary sequences with maximum peak to mean envelope power ratio pmepr of 2 4