asymptotic statistical properties of ar spectral estimators for processes with mixed spectra the influence of a point spectrum on large sample statistics of the autoregressive ar spectral estimator is addressed in particular the asymptotic distributions of the ar coefficients the innovations variance and the spectral density estimator of a finite order ar p model to a mixed spectrum process are presented various asymptotic results regarding ar modeling of a regular process with a continuous spectrum are arrived at as special cases of the results for the mixed spectrum setting finally numerical simulations are performed to verify the analytical results

the cramer rao bound for training sequence design for burst mode cpm in this paper we study the cramer rao bound crb for continuous phase modulation cpm signals where frequency offset carrier phase and symbol timing are jointly estimated when transmitted over an additive white gaussian noise awgn channel we consider a data aided da estimation scenario in which the estimator takes advantage of a known training sequence at the start of each burst thus we first derive the joint crbs as functions of a known training sequence and cpm parameters by analyzing the crb expressions we propose the optimum training sequence for which the crb is minimized we show that the same training sequence is optimum for all three estimation parameters additionally we compare the performance of the optimum training sequence with a random one by providing a closed form expression for the unconditional crb ucrb for symbol timing estimation of cpm signals comparing the ucrb and the crb for the optimum training sequence reveals that a da estimator with the optimum training sequence leads to significant gains in terms of the mean square error of the estimation parameter when the underlying cpm scheme is non binary and or partial response

circulant approximations of the inverses of toeplitz matrices and related quantities with applications to stationary random processes the circulant approximation of vector and quadratic forms involving the inverse of a toeplitz covariance matrix r is addressed first a result is presented which increases the rate of convergence of the average matrix error under certain conditions on undertilde r the vector which defines r concerning vector and quadratic operations using r 1 it is noted that if undertilde x is ar p then the p banded near toeplitz structure of r 1results in an o 1 n type mean convergence of associated errors

maximum likelihood doppler frequency estimation under decorrelation noise for quantifying flow in optical coherence tomography recent hardware advances in optical coherence tomography oct have led to ever higher a scan rates however the estimation of blood flow axial velocities is limited by the presence and type of noise higher acquisition rates alone do not necessarily enable precise quantification of doppler velocities particularly if the estimator is suboptimal in previous work we have shown that the kasai autocorrelation estimator is statistically suboptimal under conditions of additive white gaussian noise in addition for practical oct measurements of flow decorrelation noise affects doppler frequency estimation by broadening the signal spectrum here we derive a general maximum likelihood estimator mle for doppler frequency estimation that takes into account additive white noise as well as signal decorrelation we compare the decorrelation mle with existing techniques using simulated and flow phantom data and find that it has better performance achieving the cramer rao lower bound by making an approximation we also provide an interpretation of this method in the fourier domain we anticipate that this estimator will be particularly suited for estimating blood flow in in vivo scenarios

on the use of cramer rao like bounds in the presence of random nuisance parameters we focus on the use of cramer rao like bounds for the estimation of a deterministic parameter in the presence of random nuisance parameters as a working example we consider the problem of estimating the carrier frequency offset affecting a linearly modulated waveform received through a rician fading channel we calculate the relevant cramer rao bound crb and also a set of cramer rao like bounds proposed in the literature among which we mention the hybrid crb the modified crb and the miller chang 1978 bound an extension of the latter bound is also provided the relative merits of these bounds are discussed both in terms of their tightness and ease of calculation a few useful inequalities involving the above bounds are also established

on lower bounds for nonstandard deterministic estimation we consider deterministic parameter estimation and the situation where the probability density function p d f parameterized by unknown deterministic parameters results from the marginalization of a joint p d f depending on random variables as well unfortunately in the general case this marginalization is mathematically intractable which prevents from using the known standard deterministic lower bounds lbs on the mean squared error mse actually the general case can be tackled by embedding the initial observation space in a hybrid one where any standard lb can be transformed into a modified one fitted to nonstandard deterministic estimation at the expense of tightness however furthermore these modified lbs mlbs appears to include the submatrix of hybrid lbs which is an lb for the deterministic parameters moreover since in the nonstandard estimation maximum likelihood estimators mles can be no longer derived suboptimal nonstandard mles nsmles are proposed as being a substitute we show that any standard lb on the mse of mles has a nonstandard version lower bounding the mse of nsmles we provide an analysis of the relative performance of the nsmles as well as a comparison with the mlbs for a large class of estimation problems last the general approach introduced is exemplified among other things with a new look at the well known gaussian complex observation models

on the convergence of the inverses of toeplitz matrices and its applications many issues in signal processing involve the inverses of toeplitz matrices one widely used technique is to replace toeplitz matrices with their associated circulant matrices based on the well known fact that toeplitz matrices asymptotically converge to their associated circulant matrices in the weak sense this often leads to considerable simplification however it is well known that such a weak convergence cannot be strengthened into strong convergence it is this fact that severely limits the usefulness of the close relation between toeplitz matrices and circulant matrices observing that communication receiver design often needs to seek optimality in regard to a data sequence transmitted within finite duration we define the finite term strong convergence regarding two families of matrices we present a condition under which the inverses of a toeplitz matrix converges in the strong sense to a circulant matrix for finite term quadratic forms this builds a critical link in the application of the convergence theorems for the inverses of toeplitz matrices since the weak convergence generally finds its usefulness in issues associated with minimum mean squared error and the finite term strong convergence is useful in issues associated with the maximum likelihood or maximum a posteriori principles

splittable traffic partition in wdm sonet rings to minimize sonet adms sonet adms are the dominant cost factor in the wdm sonet rings recently several articles belvaux et al european j oper res 108 1 1998 26 35 clinescu and wan traffic partition in wdm sonet rings to minimize sonet adms submitted for publication gerstel et al proc ieee infocom 98 vol 1 pp 94 101 liu et al proc infocom vol 2 2000 pp 1020 1025 sutter et al oper res 46 5 1998 719 728 proposed a number of heuristics for traffic partition so as to use as few sonet adms as possible most of these heuristics assumes wavelength continuity i e the same wavelength is allocated on all of the links in the path established for a traffic stream it was first observed and argued by gerstel et al that the number of adms can be potentially reduced by allowing a traffic stream to be locally transferred from one adm in a wavelength to another adm in a different wavelength at any intermediate node in other words the traffic streams are splittable in this paper we study two variations of this minimum adm problem with splittable traffic streams all traffic streams have prespecified routings and all traffic streams have no prespecified routings respectively both variations are shown to be np hard for the former variation a heuristic with approximation ratio at most 5 4 is proposed for the latter variation a similar heuristic with approximation ratio 3 2 is proposed

common nature of learning between back propagation and hopfield type neural networks for generalized matrix inversion with simplified models in this paper two simple structure neural networks based on the error back propagation bp algorithm i e bp type neural networks bpnns are proposed developed and investigated for online generalized matrix inversion specifically the bpnn l and bpnn r models are proposed and investigated for the left and right generalized matrix inversion respectively in addition for the same problem solving task two discrete time hopfield type neural networks hnns are developed and investigated in this paper similar to the classification of the presented bpnn l and bpnn r models the presented hnn l and hnn r models correspond to the left and right generalized matrix inversion respectively comparing the bpnn weight updating formula with the hnn state transition equation for the specific i e left or right generalized matrix inversion we show that such two derived learning expressions turn out to be the same in mathematics although the bp and hopfield type neural networks are evidently different from each other a great deal in terms of network architecture physical meaning and training patterns numerical results with different illustrative examples further demonstrate the efficacy of the presented bpnns and hnns for online generalized matrix inversion and more importantly their common natures of learning

moment based parameter estimation and blind spectrum sensing for quadrature amplitude modulation knowing accurate noise variance and signal power is crucial to most spectrum sensing algorithms such as energy detection matched filter detection and cyclostationary detection in this paper we consider a practical scenario when these two parameters are unknown and are needed to be estimated before the spectrum sensing this task is non trivial without knowing the status of the primary user and we categorize the related spectrum sensing as a blind one we develop the estimation algorithms for unknown parameters by exploiting the signal constellation of the primary user three different parameter estimators that do not require any training are then proposed based on the moments of the received signals since the secondary user may not know the primary user s signal constellation we develop a robust approach that approximates a finite quadrature amplitude modulation qam constellation by a continuous uniform distribution we also derive the modified cramer rao bound crb for noise variance estimation then the optimal moment pair is found from minimizing the mean squared error mse of the signal to noise ratio snr the method of choosing the spectrum sensing threshold by taking into consideration the estimation error is also discussed

frequency offset estimation for unknown qam constellations we introduce a novel both gain and signal to noise ratio independent constellation unaware blind frequency offset estimation procedure for qam signals asymptotic performance analysis and numerical simulations show that the herein presented method outperforms a selected state of the art blind constellation unaware estimator especially for cross constellations

lower bounds to the performance of bit synchronization for bandwidth efficient pulse shaping bandwidth efficient signaling requires using pulse shaping that inherently has intersymbol interference isi except when the timing is perfect several lower bounds to the mean square error mse of non data aided bit synchronizers are derived for this case the optimal lower bound is derived using the maximum likelihood ml criterion for a sequence of binary pulse amplitude modulated pulses in the presence of isi and gaussian noise this lower bound is used as a benchmark to evaluate the performance of other synchronizers in a practical scenario it is shown that a previous lower bound based on the isi free ml synchronizer cannot be used to lower bound the mse of bit synchronizers a detection theory bound dtb also called ziv zakai bound is applied to the symbol timing recovery problem in the presence of isi and it is shown that this bound is a tight lower bound on the mse of the ml synchronizer a simple lower bound on this dtb is derived and it is shown that the simple bound is almost as tight as the well known modified cramer rao bound mcrb at moderate values of snr while it does not suffer from the shortcomings of the mcrb at small values of snr

on dantzig wolfe decomposition in integer programming and ways to perform branching in a branch and price algorithm dantzig wolfe decomposition as applied to an integer program is a specific form of problem reformulation that aims at providing a tighter linear programming relaxation bound the reformulation gives rise to an integer master problem whose typically large number of variables is dealt with implicitly by using an integer programming column generation procedure also known as branch and price algorithm there is a large class of integer programs that are well suited for this solution technique in this paper we propose to base the dantzig wolfe decomposition of an integer program on the discretization of the integer polyhedron associated with a subsystem of constraints as opposed to its convexification this allows us to formulate the integrality restriction directly on the master variables and sets a theoretical framework for dealing with specific issues such as branching or the introduction of cutting planes in the master we discuss specific branching schemes and their effect on the structure of the column generation subproblem we give theoretical bounds on the complexity of the separation process and the extent of the modifications to the column generation subproblem our computational tests on the cutting stock problem and a generalisation the cutting strip problem show that in practice all fractional solutions can be eliminated using branching rules that preserve the tractability of the subproblem but there is a trade off between branching efficiency and subproblem tractability

on the use of extrinsic probabilities in the computation of non bayesian cramer rao bounds for coded linearly modulated signals this contribution considers the non bayesian cramer rao bound crb related to parameter estimation from a linearly modulated signal observed in additive white gaussian noise we compare the exact crb expression for coded modulation with two ad hoc crb acrb expressions the first acrb is obtained by substituting in the exact crb expression for uncoded modulation the a priori symbol probabilities by the extrinsic symbol probabilities the second acrb which has received some attention in recent scientific publications additionally assumes that the real and imaginary parts of the symbols are independent our exposition focuses on the particular case of phase shift estimation by means of examples we show that although for some coded modulation schemes the exact and acrbs yield virtually the same numerical result for other coded modulation schemes the acrbs differ considerably among themselves and from the exact crb we provide some explanations for this behavior we also argue that both acrbs are expected to virtually coincide with the exact crb in the case of bit interleaved coded modulation combined with a rectangular constellations with independent in phase and quadrature mapping and a binary code for which the factor graph does not contain short cycles

composite bound on the attainable mean square error in passive time delay estimation from ambiguity prone signals corresp the location of a radiating source can be determined by measuring the relative time delay of its signal wavefront to several spatially separated receivers a new technique is presented to investigate the performance of time delay measurement schemes based on a modified version of the ziv zakai lower bound this technique is shown to yield a tight bound on the attainable mean square measurement error for any prespecified signal to noise ratio conditions

the modified cramer rao bound and its application to synchronization problems we introduce the modified cramer rao bound crb which like the true crb is a lower bound to the error variance of any parameter estimator the modified crb proves useful when in addition to the parameter to be estimated the observed data also depend on other unwanted parameters the relationship between the modified and true crb is established and applications are discussed regarding the estimation of carrier frequency offset carrier phase and timing epoch in linearly modulated signals modified crbs for phase and timing estimation have been already discussed in previous works where it is shown that several practical carrier phase and clock recovery circuits do attain such bounds frequency discrimination instead is not so well represented in the literature and a significant contribution of this paper is the calculation of the modified crb for frequency estimation this bound is compared with the performance of some frequency detectors and it is concluded that further work is needed in search of more efficient frequency discrimination methods

sequence estimation and synchronization from nonsynchronized samples the authors study the problem of maximum likelihood sequence estimation and synchronization from samples of the output of a matched filter taken at integer multiples of the symbol rate which is assumed perfectly known by the receiver a general analysis is presented of sampled receivers that handle arbitrary baseband pulse shapes and arbitrary sampling rates it is observed that the optimal processing of the matched filter samples consists of digital interpolation followed by symbol by symbol decoding when sampling is at or above the nyquist rate or viterbi decoding when sampling is below the nyquist rate performance is studied through the cramer rao bound on mean square estimation error and a lower bound on error probability

extended ziv zakai lower bound for vector parameter estimation the bayesian ziv zakai bound on the mean square error mse in estimating a uniformly distributed continuous random variable is extended for arbitrarily distributed continuous random vectors and for distortion functions other than mse the extended bound is evaluated for some representative problems in time delay and bearing estimation the resulting bounds have simple closed form expressions and closely predict the simulated performance of the maximum likelihood estimator in all regions of operation

on the true and the modified cramer rao bounds for the estimation of a scalar parameter in the presence of nuisance parameters we consider the cramer rao bound crb for the estimation of a scalar parameter in the presence of nuisance parameters whereas this true crb is hard to evaluate in general we present a simple analytical expression for its high snr asymptote i e the asymptotic crb acrb we show that this acrb is related to the crb for the joint estimation of the scalar parameter and the nuisance parameters previously a modified crb mcrb for the estimation of a scalar parameter in the presence of nuisance parameters has been derived this mcrb is also simple to evaluate and is related to the crb for the estimation of the scalar parameter assuming that the value of the nuisance parameters is a priori known we show that the mcrb can be quite loose at high snr when the scalar parameter is coupled with the nuisance parameters in the case of synchronization parameter estimation we find that the acrb equals the mcrb whether or not some of the nuisance parameters are a priori known

improving discrete model representations via symmetry considerations in this paper we focus on a useful modeling concept that is frequently ignored while formu lating discrete optimization problems very often there exists a natural symmetry inherent in the problem itself that if propagated to the model can hopelessly mire a branch and bound solver by burdening it to explore and eliminate such alternative symmetric solutions we discuss three applications where such a symmetry arises a telecommunications network design problem a noise pollution problem and a machine procurement and operation problem for each case we identify the indistinguishable objects in the model that create the problem symmetry and show how imposing certain decision hierarchies within the model significantly enhances its solvability while using a popular modern day commercial branch and cut software cplex 6 5

snr and noise variance estimation for mimo systems accurate signal to noise ratio snr and noise variance estimation are extremely important aspects of receiver design in multiple input multiple output mimo systems typically these parameters are estimated using known pilot training symbols however significant improvements may be made by using both the known pilot symbols as well as the unknown data symbols in this paper we address snr and noise variance estimation of mimo systems for both a data aided da model a non data aided nda model as well as a mixed model that uses known and unknown data symbols the cramer rao lower bound crlb and modified cramer rao lower bound mcrlb for mimo snr and mimo noise variance estimation are determined for digital constellations such as bpsk qpsk 8psk and 16qam maximum likelihood estimators are derived in closed form for the da model for the nda model closed form approximations are derived in addition to iterative expectation maximization em algorithm based estimators all of which are demonstrated to perform very close to the crlb

optimal load balancing on sonet bidirectional rings in this paper we consider the ring loading problem which arises in the design of sonet bidirectional rings the issue of demand splitting divides the ring loading problem into the two kinds one allows a demand to be split and routed in two different directions and the other does not the former kind becomes a relaxation of the latter we present an efficient exact solution procedure for the case with demand splitting and a two approximation algorithm for the case without demand splitting computational results are also shown to prove the efficiency of the proposed procedures

computational study of a column generation algorithm for bin packing and cutting stock problems this paper reports on our attempt to design an efficient exact algorithm based on column generation for the cutting stock problem the main focus of the research is to study the extend to which standard branch and bound enhancement features such as variable fixing the tightening of the formulation with cutting planes early branching and rounding heuristics can be usefully incorporated in a branch and price algorithm we review and compare lower bounds for the cutting stock problem we propose a pseudo polynomial heuristic we discuss the implementation of the important features of the integer programming column generation algorithm and in particular the implementation of the branching scheme our computational results demonstrate the efficiency of the resulting algorithm for various classes of bin packing and cutting stock problems

symbol timing recovery for cpm with correlated data symbols we consider symbol timing recovery for continuous phase modulations cpms with correlated data symbols a popular example of such a scheme is shaped offset quadrature phase shift keying soqpsk we propose an extension to an existing non data aided blind timing error detector ted to make it compatible with such modulation schemes the merits of the modified ted are demonstrated by comparing its performance with and without taking the data correlation into account as a further modification we show that a quantization scheme can be used to yield an extremely low complexity version of the system with only negligible performance losses the s curve of the proposed quantized ted is given which rules out the existence of false lock points the proposed scheme shows great promise in a wide range of applications due to its low complexity its lack of false lock points and its blind nature such applications include timing recovery for noncoherent detection schemes and false lock detectors

preconditioned iterative methods for solving toeplitz plus hankel systems the use of preconditioned iterative methods to solve a system of equations with a toeplitz plus hankel coefficient matrix is studied a new preconditioner suitable for toeplitz plus hankel matrices is proposed and the spectral properties of reconditioned rational toeplitz plus hankel matrices are examined it is shown that the eigenvalues of the preconditioned matrix are clustered around unity except for a finite number of outliers depending on the orders of the rational generating functions and the clustering radius is proportional to the magnitude of the last elements in toeplitz and hankel matrices with the spectral regularities an n times n rational toeplitz plus hankel system can be solved by preconditioned iterative methods with o n log n operations numerical experiments are given to demonstrate the efficiency of the proposed preconditioner

optimum pilot sequences for data aided synchronization we compute the pilot sequences that minimize the cramer rao bound crb for carrier phase offset carrier frequency offset and symbol timing offset estimation if we require the pilot sequence to be drawn from a discrete set of constellation points then the alternating sequence is the crb minimizing sequence if we relax the constellation constraint and apply a total energy constraint we obtain three different sequences that minimize the crb for each of the synchronization parameters we show that the maximum likelihood ml estimator achieves the crb for any of the sequences presented we also explore the impact of using the pilot symbols in a preamble with unknown data symbols immediately following the interference caused by the unknown data symbols reduces the performance of the ml estimator beyond an snr threshold

closed form expressions for the exact cramer rao bounds of timing recovery estimators from bpsk msk and square qam transmissions in this paper we derive for the first time analytical expressions for the exact cramer rao lower bounds crlb for symbol timing recovery of binary phase shift keying bpsk minimum shift keying msk and square qam modulated signals it is assumed that the transmitted data are completely unknown at the receiver and that the shaping pulse verifies the first nyquist criterion moreover the carrier phase and frequency are considered as unknown nuisance parameters the time delay remains constant over the observation interval and the received signal is corrupted by additive white gaussian noise awgn our new expressions prove that the achievable performance holds irrespective of the true time delay value moreover they corroborate previous attempts to empirically compute the considered bounds thereby enabling their immediate evaluation

frequency domain analysis of a family of minimax signal estimators a minimax estimator of the mean of x approximately n theta r sub n is evaluated where r sub n is toeplitz the problem can be viewed as estimating a signal theta that has been corrupted by additive wide sense stationary noise the evaluation is carried out using a frequency domain approach that yields advantages in design and analysis in particular counterintuitive performance of an entire class of minimax forms is discovered when r sub n is not diagonal a numerical example is presented to demonstrate the performance

the risk unbiased cramer rao bound for non bayesian multivariate parameter estimation how accurately can one estimate a deterministic parameter subject to other unknown deterministic model nuisance parameters the most popular answer to this question is given by the cramer rao bound crb the main assumption behind the derivation of the crb is local unbiased estimation of all model parameters the foundations of this paper rely on doubting this assumption generally in multivariate parameter estimation each parameter in its turn can be treated as a single parameter of interest whereas the other model parameters are treated as nuisance as their misknowledge interferes with the estimation of the parameter of interest this approach is utilized in this paper to provide a fresh look at deterministic parameter estimation a new cramer rao cr type bound is derived without assuming unbiased estimation of the nuisance parameters rather than that we apply lehmann s concept of unbiasedness for a risk that measures the distance between the estimator and the locally best unbiased estimator which assumes perfect knowledge of the nuisance parameters the proposed risk unbiased crb rucrb is proven to be asymptotically attainable by the maximum likelihood estimator while being tighter than the conventional crb furthermore simulations verify the asymptotic achievability of the rucrb by the maximum likelihood estimator for an array processing problem

a fundamental lower bound to the performance of phase estimators over rician fading channels we present a fundamental lower bound to the mean square error of estimators of the phase of a sine wave passed through a rician fading channel explicit expressions for the bound with gaussian and rayleigh channels are provided the bound is derived by analyzing the performance of the bayes minimum mean square error phase estimator and therefore represents the best performance attainable by physically realizable phase estimators over a rician channel

the expectation maximization algorithm for symbol unsynchronized sequence detection the expectation maximization em algorithm for maximizing likelihood functions combined with the viterbi algorithm is applied to the problem of sequence detection when symbol timing information is not present although the em algorithm is noncausal results obtained using the algorithm on the problem of nonsynchronized sequence detection indicate that it converges most of the time in three iterations making it both of theoretical and of practical interest a practical algorithm based on the em algorithm is introduced it reduces the computational burden and improves performance by making use of timing estimates in previous observation windows

cramer rao bound on timing recovery of linearly modulated signals with no isi a new cramer rao lower bound for symbol timing recovery of linearly modulated quadrature amplitude modulation signals is presented contrary to some other works on the subject the transmitted data is assumed to be unknown at the receiver the bound is derived from a likelihood function that includes the symbol randomness for large number of symbols the bound is achievable at any signal to noise ratio the separation of symbol timing recovery and phase recovery schemes is investigated using the new results it is shown that the separation of these operations causes a degradation of less than 0 3 db compared to joint phase and timing recovery the bound is derived for symbol shaping limited to a single symbol length i e no intersymbol interference simulations for longer pulse shapes demonstrate that the new results provide better performance prediction than other known techniques

a cramer rao bound characterization of the em algorithm mean speed of convergence this paper deals with the mean speed of convergence of the expectation maximization em algorithm we show that the asymptotic behavior in terms of the number of observations of the em algorithm can be characterized as a function of the cramer rao bounds crbs associated to the so called incomplete and complete data sets defined within the em algorithm framework we particularize our result to the case of a complete data set defined as the concatenation of the observation vector and a vector of nuisance parameters independent of the parameter of interest in this particular case we show that the crb associated to the complete data set is nothing but the well known modified crb finally we show by simulation that the proposed expression enables to properly characterize the em algorithm mean speed of convergence from the crb behavior when the size of the observation set is large enough

a unifying approach to some old and new theorems on distribution and clustering abstract a unifying approach is proposed to studying the distributions of eigenvalues and singular values of toeplitz matrices associated with a fourier series and multilevel toeplitz matrices associated with a multidimensional fourier series obtained are the extensions of the szego and avram parter theorems where the generating function is now required to belong to l 2 and not necessarily to l analogous extensions are given for multilevel toeplitz matrices in particular it is proved that if f x 1 x p l 2 then the p level complex toeplitz matrices allied with f have their singular values distributed as f x 1 x p the distribution results for the cesaro optimal circulants hold even if f l 1 also suggested are new theorems on clustering that have to do with the preconditioning of multilevel toeplitz matrices by multilevel circulants

on relative property t and haagerup s property abstract consider the following three properties for countable discrete groups g 1 g has an infinite subgroup with relative property t 2 the group von neumann algebra l g has a diffuse von neumann subalgebra with relative property t and 3 g does not have haagerup s property it is clear that 1 implies 2 and 2 implies 3 i will prove that both of the converses are false this is joint work with ionut chifan

frequency domain interpretation of the cramer rao bound for carrier and clock synchronization the cramer rao bound is a fundamental lower bound on the variance of unbiased estimates applied to carrier phase and clock phase synchronization for digital communications it is shown that the corresponding bounds can be derived from the power density spectrum of the transmitted signal irrespective of the particular modulation scheme this allows the localization of the available information about the parameters in the frequency domain if the incoming signal is only partly exploited the resulting performance loss is now easily attainable

a useful form of the abel bound and its application to estimator threshold prediction this correspondence investigates the abel bound in order to predict the estimators mean square error mse threshold effect a tractable and computationally efficient form of this bound is derived this form combines the chapman robbins and the crameacuter rao bounds this bound is applied to a data aided carrier frequency estimation problem for which a closed form expression is provided an indicator of the signal to noise ratio threshold is proposed a comparison with recent results on the barankin bound chapman robbins version shows the superiority of the abel bound version to predict the mse threshold without increasing the computational complexity

rigidity results for wreath product ii1 factors abstract we consider ii 1 factors of the form m g b g where either i b is a non hyperfinite ii 1 factor and g is an icc amenable group or ii b is a weakly rigid ii 1 factor and g is icc group and where g acts on g b by bernoulli shifts we prove that isomorphism of two such factors implies cocycle conjugacy of the corresponding bernoulli shift actions in particular the groups acting must be isomorphic as a consequence we can distinguish between certain classes of group von neumann algebras associated to wreath product groups

optimizing regenerator cost in traffic grooming in optical networks regenerators have to be placed on lightpaths every d consecutive nodes in order to regenerate the signal in addition grooming enables the use of the same regenerator by several lightpaths up to g the grooming factor lightpaths can use the same regenerator in this work we consider the problem of minimizing the number of regenerators used in traffic grooming in optical networks starting from the 4 approximation algorithm of flammini et al 2010 10 for d 1 and a path topology we provide an approximation algorithm with the same approximation ratio for d 1and the ring and tree topologies we present also a technique based on matching that leads to the same approximation ratio in tree topology and can be used to obtain approximation algorithms in other topologies we provide an approximation algorithm for general topology that uses this technique finally all the results are extended to the case of general d

a lower bound on the mean square error of symbol timing recovery for nrz rectangular signals in this paper which is based on previous work see ibid vol 40 p 1635 1992 a closed form lower bound on the mean square error of symbol timing recovery is reported for nrz rectangular pulse sequences the bound is a function of the fundamental parameters e sub b the symbol energy and n sub 0 the noise power spectral density

bayesian estimation in the presence of deterministic nuisance parameters part i performance bounds how accurately can one estimate a random parameter subject to unknown deterministic nuisance parameters the hybrid cramer rao bound hcrb provides an answer to this question for a restricted class of estimators the hcrb is the most popular performance bound on the mean square error mse for random parameter estimation problems which involve deterministic parameters the hcrb is useful when one is interested in both the random and the deterministic parameters and in the coupling between their estimation errors this bound refers to locally weak sense unbiased estimators with respect to w r t the deterministic parameters however if these parameters are nuisance it is unnecessary to restrict their estimation as unbiased this paper is the first of a two part study of bayesian parameter estimation in the presence of deterministic nuisance parameters it begins with a study on order relations between existing cramer rao cr type bounds of mean unbiased bayesian estimators then a new cr type bound is developed with no assumption of unbiasedness on the nuisance parameters alternatively lehmann s concept of unbiasedness is employed rather than conventional mean unbiasedness it is imposed on a risk that measures the distance between the estimator and the minimum mse mmse estimator which assumes perfect knowledge of the nuisance parameters in the succeeding paper asymptotic performances of some bayesian estimators with maximum likelihood based estimates for the nuisance parameters are investigated the proposed risk unbiased bound rub is proved to be asymptotically achieved by the mmse estimator with maximum likelihood estimates for the nuisance parameters while the existing cr type bounds are not necessarily achievable

cramer rao lower bounds for frequency andphase nda estimation from arbitrary square qam modulated signals in this paper we derive for the first time the analytical expressions of the exact cramer rao lower bounds crlbs of the carrier frequency and the carrier phase from square quadrature amplitude modulated qam signals assuming the noise power and the signal amplitude to be completely unknown the signal is assumed to be corrupted by additive white gaussian noise awgn the main contribution of this paper consists in deriving the analytical expressions for the non data aided nda fisher information matrix fim for higher order square qam modulated signals we prove that the problem of estimating the synchronization parameters is separable from the one of estimating the signal and the noise powers by showing that the fim is block diagonal besides we show analytically that the phase crlb is higher than the frequency crlb implying that it is much easier to estimate the frequency than the distortion phase it will be seen that the crlbs differ widely from one modulation order to another in the medium snr range the newly derived expressions corroborate previous attempts to numerically or empirically compute the considered crlbs as well as their asymptotical expressions derived only in special snr regions

asymptotic and modified cramer rao bounds for frequency estimation in parallel fading channels modified and asymptotic cramer rao bounds mcrb and acrb respectively for frequency estimation in parallel fading channels are presented the bounds are derived for arbitrary correlation of fading processes in parallel channels and covariance of additive gaussian noise the results are specified for additive white noise numerical comparison with the true cramer rao bound crb for multipath rayleigh fading channels shows that the acrb is close to the true crb while the mcrb is not in a multiple input single output miso rician fading channel the acrb presents a tight lower bound for the maximum likelihood ml frequency estimation error in general the results obtained can be applied to scenarios with a signal of interest represented as an expansion in a basis of linear independent functions with random expansion coefficients specifically they are applicable to communications in multipath multiantenna and fast fading channels as well as any combination of these channel types

algorithms for distributing telecommunication traffic on a multiple ring sonet based network abstract we examine a problem arising in the assignment of telecommunication traffic to a set of synchronous optical network sonet rings prior sonet design algorithms determine node to ring assignments while concurrently prescribing an assignment of traffic to the rings however due to uncertain voice and data demand among client nodes it may become necessary to revise the planned routing scheme once the true values of this data are realized we develop a minimum cost flow algorithm for the case in which demands may be split across multiple rings and provide a transformation to a maximum flow problem for specially structured data the case in which each demand pair may be routed on only one ring is proven to be np hard and we accordingly provide a powerful heuristic and an effective standard valid inequality generation scheme to optimally solve this problem within reasonable computational limits the effectiveness of our approach is demonstrated on a set of randomly generated test data

edge disjoint routing in plane switch graphs in linear time by a switch graph we mean an undirected graph g p c w e such that all vertices in p the plugs have degree one and all vertices in w the switches have even degrees we call g plane if g is planar and can be embedded such that all plugs are in the outer face given a set s1 t1 sk tk of pairs of plugs the problem is to find edge disjoint paths p1 pk such that every pi connects si with ti the best asymptotic worst case complexity known so far is quadratic in the number of vertices in this article a linear and thus asymptotically optimal algorithm is introduced this result may be viewed as a concluding keystone for a number of previous results on various special cases of the problem

optimal placement of add drop multiplexers heuristic and exact algorithms we study a problem that has arisen recently in the design of telecommunications transmission networks at france telecom given a set of centers in a city or conglomeration linked together on a ring architecture given the expected demands between the centers and an essentially unlimited availability of rings of fixed capacity on the network assign demand pairs and corresponding add drop multiplexers to the rings so as to satisfy the demands and minimize the number of costly multiplexers installed heuristics based on simulated annealing have been developed for the basic problem and several variants france telecom is particularly interested in validating the effectiveness of the heuristics an exact algorithm based on integer column generation is shown to provide tight performance guarantees and in most cases to give provable minimum cost solutions column generation is used even though the subproblems are strongly np hard and are solved by standard mixed integer programming software in addition the master problems involve both integer columns and integer variables whereas these are 0 1 in most reported applications

true cramer rao bound for timing recovery from a bandlimited linearly modulated waveform with unknown carrier phase and frequency this paper derives the cramer rao bound crb related to the estimation of the time delay of a linearly modulated bandpass signal with unknown carrier phase and frequency we consider the following two scenarios joint estimation of the time delay the carrier phase and the carrier frequency and joint estimation of the time delay and the carrier frequency irrespective of the carrier phase the transmit pulse is a bandlimited square root nyquist pulse for each scenario the transmitted symbols constitute either an a priori known training sequence or an unknown random data sequence in spite of the presence of random data symbols and or a random carrier phase we obtain a relatively simple expression of the crb from which the effect of the constellation and the transmit pulse are easily derived we show that the penalty resulting from estimating the time delay irrespective of the carrier phase decreases with increasing observation interval however the penalty caused by not knowing the data symbols a priori cannot be reduced by increasing the observation interval comparison of the true crb to existing symbol synchronizer performance reveals that decision directed timing recovery is close to optimum for moderate to large signal to noise ratios

on the application of the cramer rao and detection theory bounds to mean square error of symbol timing recovery a modified cramer rao bound is derived that takes account of the fact that the symbol timing estimate is restricted to a finite interval of one symbol duration a detection theory bound is also applied to the symbol timing problem results obtained using the cramer rao and detection theory bounds are compared it is shown that the detection theory bound is superior to the traditionally used cramer rao bound in particular the detection theory bound gives useful results for sharp pulse shapes and shows a dependence of the mean square error on the data sequence it also yields meaningful results for small signal to noise ratios

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

the true cramer rao bound for carrier frequency estimation from a psk signal this paper considers the cramer rao bound crb related to estimating the carrier frequency of a noisy phase shift keying signal the following scenarios are discussed 1 carrier frequency estimation irrespective of the carrier phase based on either known or random data and 2 joint carrier phase and frequency estimation based on either known or random data ideal symbol timing is assumed we compare the results obtained from a commonly used simplified observation model against those resulting from the correct model because of the presence of nuisance parameters random data and or random carrier phase the analytical computation of the corresponding crbs is often not feasible here we present results that are based upon a combined analytical numerical approach our results show that the choice of the observation model has essentially no effect on the crbs at moderate and high signal to noise ratios we also show that of the two scenarios considered joint frequency and phase estimation yields the smaller crb the penalty resulting from frequency estimation irrespective of the carrier phase decreases with increasing observation interval

a bpsk qpsk timing error detector for sampled receivers a simple algorithm for detection of timing error of a synchronous band limited bpsk or qpsk data stream is proposed the algorithm requires only two samples per symbol for its operation one of the two samples is also used for the symbol decision derivation of the s curve reveals a sinusoidal shape

cramer rao bounds in the parametric estimation of fading radiotransmission channels the context of this paper is parameter estimation for linearly modulated digital data signals observed on a frequency flat time selective fading channel affected by additive white gaussian noise the aim is the derivation of cramer rao lower bounds for the joint estimation of all those channel parameters that impact signal detection namely carrier phase carrier frequency offset doppler shift frequency rate of change doppler rate signal amplitude fading power and gaussian noise power time selective frequency flat fading is modeled as a low pass autoregressive multiplicative distortion process in particular the important case of slow fading with the multiplicative process remaining constant over the whole data burst is specifically discussed asymptotic expressions of the bounds valid for a large observed sample or for high signal to noise ratio snr are also derived in closed form a few charts with numerical results are finally reported to highlight the dependence of the bounds on channel status snr fading bandwidth etc

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

a polynomial time algorithm for the weighted link ring loading problem with integer demand splitting we are given an n node undirected ring network in which each link of the ring is associated with a weight traffic demand is given for each pair of nodes in the ring each demand is allowed to be split into two integer parts which are then routed in different directions clockwise and counterclockwise respectively the load of a link is the sum of the flows routed through the link and the nonnegative weighted load of a link is the product of its weight and its load the objective is to find a routing scheme such that the maximum weighted load on the ring is minimized based on some useful structural properties of the decision version of the problem we design a polynomial time combinatorial algorithm for the optimization problem

on the performance limits of data aided synchronization this paper addresses data aided da synchronization in which the reference parameter acquisition is aided by a training sequence known to the receiver the cramer rao lower bound crb for the da timing and or carrier phase recovery is presented for da parameter estimation the crb typically varies with the training sequence this indicates that different training sequences offer fundamentally different performance in the literature the widely cited closed form crb for timing and carrier phase recovery was derived under the assumption that the training sequence is independent and identically distributed i i d and sufficiently long we derive a closed form crb for timing and carrier phase recovery with respect to an arbitrary training sequence and pulse shaping function for the over and under sampling cases it turns out that the crb is a weighted summation of the aperiodic correlation of the training sequence and the weighting factor is determined by the pulse shaping filter therefore this paper reveals the fundamental link between a training sequence and its corresponding performance limit

modified cramer rao bounds for continuous phase modulated signals we consider the estimation of signal amplitude time offset and the parameters of a polynomial phase signal from a continuous phase modulated cpm signal that contains both unknown data symbols and known pilot symbols transformation of the polynomial phase signal into an orthogonal basis allows us to derive the modified cramer rao bounds mcrb for the problem of vector parameter estimation in closed form numerical results demonstrate that the achievable estimation accuracy significantly depends on the burst structure and highlight the need for properly designed pilot sequences since our bounds are easy to evaluate they can aid the design of pilot and burst configuration for cpm systems

bayesian and hybrid cramer rao bounds for the carrier recovery under dynamic phase uncertain channels in this paper we study bayesian and hybrid cramer rao bounds bcrb and hcrb for the code aided ca the data aided da and the non data aided nda dynamical phase estimation of qam modulated signals we address the bounds derivation for both the offline scenario for which the whole observation frame is used and the online which only takes into account the current and the previous observations for the ca scenario we show that the computation of the bayesian information matrix bim and of the hybrid information matrix him is np hard we then resort to the belief propagation bp algorithm or to the bahl cocke jelinek raviv bcjr algorithm to obtain some approximate values moreover in order to avoid the calculus of the inverse of the bim and of the him we present some closed form expressions for the various crbs which greatly reduces the computation complexity finally some simulations allow us to compare the possible improvements enabled by the offline and the ca scenarios

phase and frequency estimation for psk packets bounds and algorithms new cramer rao lower bounds crbs are derived for the estimation of phase offset and frequency offset from a block of random bpsk or qpsk symbols at low signal to noise snr ratios these bounds are compared to existing bounds which apply to the unmodulated carrier or to known psk symbols and to the performance of some estimation algorithms

asymptotic performance evaluation of space frequency mmse filters for ofdm this paper proposes and analyzes two different linear space frequency architectures for the reception of ofdm modulated signals the classical sample matrix inversion smi algorithm and a new architecture that maximizes the output signal to interference plus noise ratio msinr the performance of these two linear receivers is compared in terms of asymptotic output sinr taking into account the finite sample size effect through the asymptotic covariance of the filter weights the analysis is asymptotic in the sense that the performance is analyzed assuming that both the number of carriers and the prefix length of the ofdm signal increase without bound at the same rate whereas their quotient remains constant assuming that the carrier frequencies become asymptotically close to one another we are able to derive explicit equations that shed some light on the influence of the frequency selectivity of channel and interference on the relative performance of the two approaches the results are useful in the sense that they provide first order approximations to the asymptotically optimum number of adjacent carriers to be processed by a single beamformer in a finite sample size situation

analytic and asymptotic analysis of bayesian cramer rao bound for dynamical phase offset estimation in this paper we present a closed form expression of a bayesian cramer rao lower bound for the estimation of a dynamical phase offset in a non data aided bpsk transmitting context this kind of bound is derived considering two different scenarios a first expression is obtained in an offline context and then a second expression in an online context logically follows the snr asymptotic expressions of this bound drive us to introduce a new asymptotic bound namely the asymptotic bayesian cramer rao bound this bound is close to the classical bayesian bound but is easier to evaluate

on the true cramer rao lower bound for data aided carrier phase independent frequency offset and symbol timing estimation in this letter we present new and simple closed form expressions for the true cramer rao lower bound crb for data aided da joint and individual carrier frequency offset and symbol timing estimation from a linearly modulated waveform transmitted over an awgn channel the bounds are derived under a carrier phase independent cpi estimation strategy wherein the carrier phase is viewed as a nuisance parameter and assumed to have a worst case noninformative uniform distribution over the computation of these crbs requires only a single numerical integration in addition computationally simpler yet highly accurate asymptotic lower bounds are presented as particularizations new bounds for individual cpi frequency estimation with known symbol timing from m psk and continuous wave cw signals are also reported

relative property t for the subequivalence relations induced by the action of sl2 z on t2 abstract let s be the equivalence relation induced by the action sl 2 z t 2 2 where 2 denotes the haar measure on the 2 torus t 2 we prove that any ergodic subequivalence relation r of s is either hyperfinite or rigid in the sense of s popa 41 the proof uses an ergodic theoretic criterion for rigidity of countable ergodic probability measure preserving equivalence relations moreover we give a purely ergodic theoretic formulation of rigidity for free ergodic probability measure preserving actions of countable groups

on the miller chang lower bound for nda carrier phase estimation in this letter we derive a new miller chang lower bound mcb for the variance of unbiased non data aided nda carrier phase estimates obtained from a block of n samples of a linearly modulated pulse amplitude modulation or quadrature amplitude modulation information signal transmitted through an additive white gaussian noise channel this bound is tighter than the corresponding crame spl acute r rao lower bound crb for data aided or continuous wave carrier phase estimation cw crb particularly when n is small for some given n and sufficiently high signal to noise ratios the mcb is tighter than the corresponding true nda crb the main limitation of this new mcb is that its application is restricted to carrier phase estimators which are unbiased for all possible values of the received symbol sequence

cramer rao lower bounds for qam phase and frequency estimation in this paper we present the true cramer rao lower bounds crlbs for the estimation of phase offset for common quadrature amplitude modulation qam psk and pam signals in awgn channels it is shown that the same analysis also applies to the qam fsk and pam crlbs for frequency offset estimation the ratio of the modulated to the unmodulated crlbs is derived for all qam psk and pam signals and calculated for specific cases of interest this is useful to determine the limiting performance of synchronization circuits for coherent receivers without the need to simulate particular algorithms the hounds are compared to the existing true crlbs for an unmodulated carrier wave cw bpsk and qpsk we investigated new and existing qam phase estimation algorithms in order to verify the new phase crlb this showed that new minimum distance estimator performs close to the qam bound and provides a large improvement over the power law estimator at moderate to high signal to noise ratios

a new bound and algorithm for star 16 qam carrier phase estimation the true cramer rao lower bound crlb is derived and evaluated for the estimation of carrier phase of star 16 quadrature amplitude modulation qam and can be simply applied to carrier frequency estimation different geometries are investigated by varying the ring ratio rr for signal to noise ratios snrs between 6 15 db the crlb with rr 3 is lower than that of square 16 qam a modified phase estimator is presented which closely follows the new crlb investigation of symbol error performance in short packet length reveals star 16 qam to be superior to square 16 qam for snr 13 db which is a reasonable operating range for a coded system although square 16 qam and star rr 1 8 are optimum for a perfect receiver when the effect of phase estimation is considered we find star rr 3 to be better for snr below 10 db

on the elementwise convergence of continuous functions of hermitian banded toeplitz matrices toeplitz matrices and functions of toeplitz matrices such as the inverse of a toeplitz matrix powers of a toeplitz matrix or the exponential of a toeplitz matrix arise in many different theoretical and applied fields they can be found in the mathematical modeling of problems where some kind of shift invariance occurs in terms of space or time r m gray s excellent tutorial monograph on toeplitz and circulant matrices has been and remains the best elementary introduction to the szegouml distribution theory on the asymptotic behavior of continuous functions of toeplitz matrices his asymptotic results widely used in engineering due to the simplicity of its mathematical proofs do not concern individual entries of these matrices but rather they describe an average behavior however there are important applications where the asymptotic expressions of interest are directly related to the convergence of a single entry of a continuous function of a toeplitz matrix using similar mathematical tools and to gain insight into the solutions of this sort of problems the present correspondence derives new theoretical results regarding the convergence of these entries

joint angular and delay domain mimo propagation parameter estimation using approximate ml method in this paper we derive an estimation method that jointly estimates the parameters of the concentrated propagation paths and the distributed scattering component that are frequently observed in multiple input multiple output mimo channel sounding measurements the joint angular delay domain model leads to a correlation matrix with high dimensionality which makes direct implementation of a maximum likelihood ml estimator unfeasible we derive low complexity methods for computing approximate ml estimates that exploit the structure of the covariance matrices we propose an iterative two step procedure that alternates between the estimation of the parameters of the concentrated propagation paths and the parameters of the distributed scattering for the distributed scattering the estimator first optimizes the parameters describing their time delay structure then using the estimated time delay parameters the parameters of the angular distributions are optimized we present simulation results and compare the estimated time delay and angular distributions to the actual distributions demonstrating that high quality estimates are obtained the large sample performance of the estimator is studied by establishing the cramer rao lower bound crlb and comparing it to the variances of the estimates the simulations show that the variance of the proposed estimation technique reaches the crlb for relatively small sample size for most parameters and no bias is observed

proper actions of wreath products and generalizations we study stability properties of the haagerup property and of coarse embeddability in a hilbert space under certain semidirect products in particular we prove that they are stable under taking standard wreath products our construction also allows for a characterization of subsets with relative property t in a standard wreath product

cramer rao lower bound and em algorithm for envelope based snr estimation of nonconstant modulus constellations signal to noise ratio snr estimation for linearly modulated signals is addressed in this letter focusing on envelope based estimators which are robust to carrier offsets and phase jitter and on the challenging case of nonconstant modulus constellations for comparison purposes the true cramer rao lower bound is numerically evaluated obtaining an analytical expression in closed form for the asymptotic case of high snr values which quantifies the performance loss with respect to coherent estimation as the maximum likelihood algorithm is too complex for practical implementation an expectation maximization em approach is proposed achieving a good tradeoff between complexity and performance for medium to high snrs finally a hybrid scheme based on em and moments based estimates is suggested which performs close to the theoretical limit over a wide snr range

inverse toeplitz preconditioners for ill posed problems abstract it has been shown recently that iterative regularization using conjugate gradient type methods for image restoration problems can be effectively preconditioned with circulant approximations here it is shown that the theoretical properties of this approach are not restricted to circulant matrices specifically a toeplitz approximate inverse preconditioning scheme for discrete ill posed problems is considered it is proved that the preconditioned system approximates the prolate matrix and that this property implies that fast convergence of conjugate gradient type methods can be expected in addition it is shown that these results can be generalized to two dimensional problems an image restoration application is used to demonstrate the properties of the preconditioner

a performance lower bound for quadratic timing recovery accounting for the symbol transition density the symbol transition density in a digitally modulated signal affects the performance of practical synchronization schemes designed for timing recovery this paper focuses on the derivation of simple performance limits for the estimation of the time delay of a noisy linearly modulated signal in the presence of various degrees of symbol correlation produced by the various transition densities in the symbol streams the paper develops high and low signal to noise ratio snr approximations of the so called gaussian unconditional crame spl acute r rao bound ucrb as well as general expressions that are applicable in all ranges of snr the derived bounds are valid only for the class of quadratic non data aided nda timing recovery schemes to illustrate the validity of the derived bounds they are compared with the actual performance achieved by some well known quadratic nda timing recovery schemes the impact of the symbol transition density on the classical threshold effect present in nda timing recovery schemes is also analyzed previous work on performance bounds for timing recovery from various authors is generalized and unified in this contribution

blind self noise free frequency detectors for a subclass of msk type signals frequency offset due to doppler shift and or oscillator instabilities degrade the receiver performance a family of frequency detectors for frequency offset estimation and compensation in digital receivers is introduced the proposed detectors are best suited for frequency offset compensation of a subclass of binary continuous phase modulation with h 1 2 that includes modulation schemes with nonnegative frequency pulses for the considered modulation schemes the modulation induced self noise term is absent from the variance of the frequency estimate the estimator is nondata and nontiming aided and its estimation range is either half or a quarter of the bit rate r with larger frequency offsets the estimators that have a spl plusmn r 2 estimation range introduce a frequency ambiguity of r that is of no relevance to the performance of a differential detection based receiver

graph decomposition is np complete a complete proof of holyer s conjecture an h decomposition of a graph g v e is a partition of e into subgraphs isomorphic to h given a fixed graph h the h decomposition problem is to determine whether an input graph g admits an h decomposition in 1980 holyer conjectured that h decomposition is np complete whenever h is connected and has three edges or more some partial results have been obtained since then a complete proof of holyer s conjecture is the content of this paper the characterization problem of all graphs h for which h decomposition is np complete is hence reduced to graphs where every connected component contains at most two edges

carrier phase and frequency estimation for pilot symbol assisted transmission bounds and algorithms in this paper we consider the cramer rao lower bound crb for the joint estimation of the carrier phase and the frequency offset from a noisy linearly modulated burst signal containing random data symbols dss as well as known pilot symbols pss we point out that the crb depends on the location of the pss in the burst the number of pss the number of dss the signal to noise ratio snr and the data modulation scheme distributing the pss symmetrically about the center of the burst and estimating the carrier phase in the center of the burst interval decouples the frequency and phase estimation making the crb for phase estimation independent of the specific location of the pss at low and moderate snr the crbs for both phase and frequency estimation decrease as the fraction of the pss in the burst increases in addition the crb for frequency estimation decreases as the pss are separated with more dss numerical evaluation of the crb indicates that the carrier phase and frequency of a hybrid burst i e containing pss and dss can be estimated more accurately when exploiting both the presence of the dss and the a priori knowledge about the pss instead of using only the knowledge about the pss and ignoring the dss or considering all the received symbols pss and dss as unknown and ignoring the knowledge about the pss comparison of the crb with the performance of existing carrier synchronizers shows that the iterative soft decision directed sdd estimator with data aided da initialization performs very closely to the crb and provides a large improvement over the classical non data aided nda estimator at lower snr