on the structure of specht modules in the principal block of fσ3p abstract let f be a field of characteristic p at least 5 we study the loewy structures of specht modules in the principal block of f 3 p we show that a specht module in the block has loewy length at most 4 and composition length at most 14 furthermore we classify which specht modules have loewy length 1 2 3 or 4 produce a specht module having 14 composition factors describe the second radical layer and the socle of the reducible specht modules and prove that if a specht module corresponds to a partition that is p regular and p restricted then the head of the specht module does not extend the socle

on scaling laws of diversity schemes in decentralized estimation this paper is concerned with decentralized estimation of a gaussian source using multiple sensors we consider a diversity scheme where only the sensor with the best channel sends their measurements over a fading channel to a fusion center using the analog amplify and forwarding technique the fusion centre reconstructs a minimum mean squared error mmse estimate of the source based on the received measurements a distributed version of the diversity scheme where sensors decide whether to transmit based only on their local channel information is also considered we derive asymptotic expressions for the expected distortion of the mmse estimate at the fusion centre of these schemes as the number of sensors becomes large for comparison asymptotic expressions for the expected distortion for a coherent multiaccess scheme and an orthogonal access scheme are derived it is seen that as opposed to the coherent multiaccess scheme and the orthogonal scheme where the expected distortion decays as 1 m m being the number of sensors the expected distortion decays only as 1 ln m for the diversity schemes this reduction of the decay rate can be seen as a tradeoff between the simplicity of the diversity schemes and the strict synchronization and large bandwidth requirements for the coherent multiaccess and the orthogonal schemes respectively we study for the diversity schemes the optimal power allocation for minimizing the expected distortion subject to average power constraints the effect of optimizing the probability of transmission on the expected distortion in the distributed scenario is also studied it is proved that for rayleigh fading optimal sensor transmit power allocation achieves the same asymptotic scaling law as the constant power allocation scheme whereas it is observed that optimizing the sensor transmission probability with or without optimal power allocation in the distributed case makes very little difference to the asymptotic scaling laws

asymptotic properties of high order yule walker estimates of the ar parameters of an arma time series the high order yule walker equations are used to estimate the autoregressive parameters of an autoregressive moving average time series the asymptotic statistical properties of these estimates are derived it is shown that they are asymptotically unbiased and normal the covariance matrix of the limit distribution is derived the special case of estimating the autoregressive parameters of a noise corrupted autoregressive series is also examined

3 2 pairs of symmetric group algebras and their intermediate defect 4 blocks abstract in this paper we study 3 2 pairs of symmetric group algebras and their intermediate block in detail the aim is to understand how one block of a 3 2 pair can inherit two properties the ext quiver being bipartite and the principal indecomposable modules having a common loewy length 7 from the other we establish some sufficient conditions for this inheritance and verify these conditions for some special blocks

consistency properties of least squares estimates of autoregressive parameters in arma models a unified treatment of the consistency properties of the ordinary least squares estimates in an autoregressive fitting of time series from nonstationary or stationary autoregressive moving average models is given for a given model the orders of autoregressions which produce consistent estimates are obtained and the limiting values hence the biases of the estimates of other autoregressions are investigated

the ordinary quiver of a weight three block of the symmetric group is bipartite abstract suppose f is a field of characteristic p 5 and that b is a p block of the symmetric group s n of defect 3 we prove that the ext 1 quiver of b is bipartite with the bipartition being described in a simple way using the leg lengths of p hooks of partitions

optimal instrumental variable estimation and approximate implementations the accuracy properties of instrumental variables iv methods are investigated extensions such as prefiltering of data and use of additional instruments are included in the analysis the parameter estimates are shown to be asymptotically gaussian distributed an explicit expression is given for the covariance matrix of their distribution the covariance matrix is then taken as a multivariable measure of accuracy it is shown how it can be optimized by an appropriate selection of instruments and prefilter the so obtained optimal instrumental variable estimates cannot be used directly since the true system and the statistical properties of the disturbance must be known in order to compute the optimal instruments and prefilters a multistep procedure consisting of three or four simple steps is then proposed as a way to overcome this difficulty this procedure includes modeling of the disturbance as an arma process using a statistically efficient method such as a prediction error method the statistical properties of the estimates obtained with the multistep procedure are also analyzed those estimates are shown to be asymptotically gaussian distributed as well the covariance matrix of the estimation errors is compared to that corresponding to a prediction error method for some model structures these two approaches give the same asymptotic accuracy the conclusion is that the multistep procedure which is quite easy to implement and also has nice uniqueness properties can be viewed as an interesting alternative to prediction error methods

use of canonical analysis in time series model identification summary the second order moment structure of time series models is used to derive a canonical analysis in time series modelling consistency properties of certain canonical correlations and the corresponding eigenvectors are shown based on these properties a canonical correlation approach for tentative order determination in building autoregressivemoving average models is proposed this approach can handle directly nonstationary as well as stationary processes and it also provides consistent estimates of the autoregressive parameters involved the asymptotic distribution of the identification statistic is discussed

the overdetermined recursive instrumental variable method a recursive instrumental variable algorithm is derived for the overdetermined case in which the number of instruments is greater than the number of estimated parameters in some applications the algorithm provides improved parameter estimation accuracy compared to the standard recursive instrumental variable method the performance of the algorithm is illustrated by simulation results

instrumental variable methods for arma spectral estimation the modified yule walker technique of arma spectral estimation is shown to be a special case of the instrumental variable method of system identification several recursive instrumental variable algorithms are proposed for adaptive spectral estimation including a new algorithm for the overdetermined case an efficient lattice algorithm is presented for solving the modified yule walker equations given the sample correlation coefficients the performance of some of the algorithms is illustrated by simulation results

on the asymptotic capacity of stationary gaussian fading channels we consider a peak power limited single antenna flat complex gaussian fading channel where the receiver and transmitter while fully cognizant of the distribution of the fading process have no knowledge of its realization upper and lower bounds on channel capacity are derived with special emphasis on tightness in the high signal to noise ratio snr regime necessary and sufficient conditions in terms of the autocorrelation of the fading process are derived for capacity to grow double logarithmically in the snr for cases in which capacity increases logarithmically in the snr we provide an expression for the pre log i e for the asymptotic ratio between channel capacity and the logarithm of the snr this ratio is given by the lebesgue measure of the set of harmonics where the spectral density of the fading process is zero we finally demonstrate that the asymptotic dependence of channel capacity on the snr need not be limited to logarithmic or double logarithmic behaviors we exhibit power spectra for which capacity grows as a fractional power of the logarithm of the snr

olriv a new fast adaptive algorithm for rectangular block toeplitz systems in this paper we propose a new algorithm for solving overdetermined systems when they are rectangular block toeplitz the blocks can have more rows than columns it is based on the expression of the matrix of the system to solve as the intercorrelation between two vectorial processes namely the original and the instrumental processes the instrumental process has generally more components than the original one therefore it takes the overdetermined character of the system into consideration the proposed algorithm known as the overdetermined lattice recursive instrumental variable olriv belongs to the fast rls family and lies on a double lattice structure where one lattice performs the prediction of the original process and the other one the prediction of the instrumental process the geometric complete derivation of the proposed algorithm is given in the paper afterwards we show how olriv can be applied to perform blind adaptive identification of ar channels using high order statistics where the systems to solve are often overdetermined to ensure identifiability both the scalar and the vectorial cases are investigated simulation results are finally given to show the performances of olriv

comments on the wong and polak minimax approach to accuracy optimization of instrumental variable methods optimizing the accuracy of instrumental variable iv estimates on a minimax basis is discussed some flaws in an earlier approach of this kind are pointed out it is indicated that the minimax approach to accuracy optimization of iv estimates although conceptually attractive will in general lead to intractable problems

ld sup 2 arma identification algorithm the authors present the ld sup 2 arma identifier a novel algorithm that solves the essentially nonlinear autoregressive moving averaged arma identification problem with a linear procedure in two steps an order selection algorithm followed by an arma parameter estimator the determination of the ar and ma coefficients involves the solution of two dual systems of linear equations these systems decouple the estimation of the autoregressive component from the estimation of the moving average component the selection of the number of poles and of the number of zeros is accomplished by a scheme that minimizes the mismatch of the data to each proposed model simulated experiments on the proposed order selection procedure are presented

improved methods for the blind system identification using higher order statistics it is demonstrated by a detailed analysis of blind system identification that under specific system configurations a recently published least squares algorithm shows a poor convergence behavior especially if the system order is overdetermined to overcome these problems a supplementary condition is introduced that guarantees proper convergence in most cases an alternative approach for the blind identification of mixed phase systems the so called cumulant zero matching method is presented in this approach the solution of a set of nonlinear equations which is necessary in the least squares method is replaced by the calculation of zeros of polynomials the main advantage over the least squares solution is that overdetermination of the system order is rather harmless since it only results in additional zeros in the origin of the z plane the different methods for system identification presented are illustrated by simulation results

a comparison of two linear methods of estimating the parameters of arma models a finite order stationary and minimum phase arma autoregressive moving average p q model is equivalent to an infinite order ar autoregressive model two methods of estimating the parameters of the arma p q model by solving only linear equations are based on or closely related to this equivalence relation one method was derived directly from the equivalence relation by d graupe et al ibid vol ac 20 p 104 107 feb 1975 the other was derived by s li and b w dickinson ibid vol ac 31 p 275 278 mar 1986 and ieee trans acoust speech signal process vol assp 36 p 502 512 apr 1988 based on an iterated least squares regression approach the end results bear close resemblance to those of graupe et al the two methods are compared and ways to improve the parameter estimates are suggested

asymptotic capacity analysis for adaptive transmission schemes under general fading distributions asymptotic comparisons of ergodic channel capacity at high and low snrs are provided for several adaptive transmission schemes over fading channels with general distributions including optimal power and rate adaptation rate adaptation only channel inversion and its variants analysis of the high snr pre log constants of the ergodic capacity reveals the existence of constant capacity difference gaps among the schemes with a pre log constant of 1 closed form expressions for these high snr capacity difference gaps are derived which are proportional to the snr loss between these schemes in db scale the largest one of these gaps is found to be between the optimal power and rate adaptation scheme and the channel inversion scheme based on these expressions it is shown that the presence of space diversity or multi user diversity makes channel inversion arbitrarily close to achieving optimal capacity at high snr with sufficiently large number of antennas or users a low snr analysis also reveals that the presence of fading provably always improves capacity at sufficiently low snr compared to the additive white gaussian noise awgn case numerical results are shown to corroborate our analytical results

optimal instrumental variable estimates of the ar parameters of an arma process the modified yule walker myw equations for estimating the ar parameters of an arma process are presented as a special case of an instrumental variable iv method the consistency and accuracy of the ar parameter estimates are studied it is shown that estimation accuracy increases monotonically with the number of myw equations for an optimal choice of the weighting matrix used in the least squares solution of these equations the asymptotic error covariance of the optimal iv method equals that of the prediction error method the results of this paper verify experimental results reported in the literature regarding the performance of the myw method and provide the necessary accuracy analysis furthermore they suggest several simple asymptotically efficient multistep algorithms for estimating the ar parameters which are presented in a companion paper

a new technique for arma system identification and rational approximation the fundamental problem of identifying a linear time invariant system from measured samples of its output response to a known input is addressed utilizing a new and simple deterministic theory founded on well established passive network concepts the analysis together with documented numerical results demonstrates that the proposed method achieves two goals stable rational minimum phase transfer functions can be identified with a priori knowledge of either numerator or denominator degrees and stable rational minimum phase pade like approximations appear to be generated automatically in the nonrational case to substantiate these claims a detailed theoretical exposition of the basic ideas an extensive discussion of numerical results and a summary of related results are given

martin s conjecture holds for weight 3 blocks of symmetric groups abstract we prove that martin s conjecture holds for weight 3 blocks of symmetric group algebras that if these blocks have abelian defect group then their projective indecomposable modules have a common radical length 7

filtrations in rouquier blocks of symmetric groups and schur algebras we study rouquier blocks of symmetric groups and schur algebras in detail and obtain explicit descriptions for the radical layers of the principal indecomposable weyl young and specht modules of these blocks at the same time the jantzen filtrations of the weyl modules are shown to coincide with their radical filtrations we also address the conjectures of martin lascoux leclerc thibon rouquier and james for these blocks

comparison of some instrumental variable methods consistency and accuracy aspects a general analysis of various instrumental variable methods is given the investigation includes methods for open loop operation as well as methods designed for closed loop operation the instrumental variables are formed as different combinations of inputs delayed inputs delayed outputs filtered inputs and external setpoint variations necessary conditions as well as sufficient conditions for consistency are explicitly derived and discussed the paper also includes some simple counter examples to general consistency for some common instrumental variable methods also asymptotic accuracy properties are reviewed it is e g studied how the use of filters will influence the covariance matrix of the parameter estimates

adaptive deconvolution and identification of nonminimum phase fir systems based on cumulants a novel adaptive deconvolution and system identification scheme is introduced for a linear non minimum phase finite impulse response fir system driven by non gaussian white noise the adaptive scheme is based on approximating the fir system by noncausal autoregressive ar models and using higher order cumulants of the system output as such it is a blind equalization deconvolution scheme the set of updated ar parameters is obtained by using a gradient type algorithm and by using higher order cumulants instead of time samples of the output signal it is demonstrated by means of extensive simulations that the adaptive scheme works well for both stationary and nonstationary cases as expected it outperforms the autocorrelation based gradient method for nonminimum phase system identification and deconvolution performance comparisons to existing methods are given using as figures of merit the probability of errors in the restored input sequence computational complexity and convergence rate

regression models with time series errors abstract the time series regression models in which the errors of regression equations follow stationary or nonstationary autoregressive moving average models are considered convergence properties of the sample autocorrelation function of observed series and the least squares estimates of the linear regression parameters are shown based upon these results a procedure for specifying the tentative order of the mixed arma errors is proposed two examples are given

irreducible specht modules for hecke algebras of type a abstract let f be a field n a non negative integer a partition of n and s the corresponding specht module for the iwahori hecke algebra h f q s n james and mathas conjecture a necessary and sufficient condition on for s to be irreducible we prove the sufficiency of this condition in the case where f has infinite characteristic and also in the case where q 1

channels with block interference a new class of channel models with memory is presented in order to study various kinds of interference phenomena it is shown among other things that when all other parameters are held fixed channel capacity c is an em increasing function of the memory length while the cutoff rate r 0 generally is a em decreasing function calculations with various explicit coding schemes indicate that c is better than r 0 as a performance measure for these channel models as a partial resolution of this c versus r 0 paradox the conjecture is offered that r 0 is more properly a measure of coding delay rather than of coding complexity

brief paper convergence analysis of instrumental variable recursive subspace identification algorithms the convergence properties of recently developed recursive subspace identification methods are investigated in this paper the algorithms operate on the basis of instrumental variable iv versions of the propagator method for signal subspace estimation it is proved that under suitable conditions on the input signal and the system the considered recursive subspace identification algorithms converge to a consistent estimate of the propagator and by extension to the state space system matrices

the averaged overdetermined and generalized lms algorithm this paper provides and exploits one possible formal framework in which to compare and contrast the two most important families of adaptive algorithms the least mean square lms family and the recursive least squares rls family existing and well known algorithms belonging to any of these two families like the lms algorithm and the rls algorithm have a natural position within the proposed formal framework the proposed formal framework also includes among others the lms overdetermined recursive instrumental variable oriv algorithm and the generalized lms glms algorithm which is an instrumental variable iv enable lms algorithm furthermore this formal framework allows a straightforward derivation of new algorithms with enhanced properties respect to the existing ones specifically the oriv algorithm is exported to the lms family resulting in the derivation of the averaged overdetermined and generalized lms aoglms algorithm an overdetermined lms algorithm able to work with an iv the proposed aoglms algorithm overcomes as we analytically show here the limitations of glms and possesses a much lower computational burden than lms oriv being in this way a better alternative to both algorithms simulations verify the analysis

capacity of multiple antenna systems with both receiver and transmitter channel state information the capacity of multiple antenna systems operating in rayleigh flat fading is considered under the assumptions that channel state information csi is available at both transmitter and receiver and that the transmitter is subjected to an average power constraint first the capacity of such systems is derived for the special case of multiple transmit antennas and a single receive antenna the optimal power allocation scheme for such a system is shown to be a water filling algorithm and the corresponding capacity is seen to be the same as that of a system having multiple receive antennas with a single transmitter antenna whose outputs are combined via maximal ratio combining a suboptimal adaptive transmission technique that transmits only over the antenna having the best channel is also proposed for this special case it is shown that the capacity of such a system under the proposed suboptimal adaptive transmission scheme is the same as the capacity of a system having multiple receiver antennas with a single transmitter antenna combined via selection combining next the capacity of a general system of multiple transmitter and receiver antennas is derived together with an equation that determines the cutoff value for such a system the optimal power allocation scheme for such a multiple antenna system is given by a matrix water filling algorithm in order to eliminate the need for cumbersome numerical techniques in solving the cutoff equation approximate expressions for the cutoff transmission value are also provided it is shown that compared to the case in which there is only receiver csi large capacity gains are available with optimal power and rate adaptation schemes the increased capacity is shown to come at the price of channel outage and bounds are derived for this outage probability

recursive least squares ladder estimation algorithms recursive least squares ladder estimation algorithms have attracted much attention recently because of their excellent convergence behavior and fast parameter tracking capability compared to gradient based algorithms we present some recently developed square root normalized exact least squares ladder form algorithms that have fewer storage requirements and lower computational requirements than the unnormalized ones a hilbert space approach to the derivations of magnitude normalized signal and gain recursions is presented the normalized forms are expected to have even better numerical properties than the unnormalized versions other normalized forms such as joint process estimators e g adaptive line enhancer and arma pole zero models will also be presented applications of these algorithms to fast or zero startup equalizers adaptive noise and echo cancellers non gaussian event detectors and inverse models for control problems are also mentioned

the square root overdetermined recursive instrumental variable algorithm a square root version of the overdetermined recursive instrumental variable oriv algorithm is derived this version improves the numerical stability of the algorithm and avoids the problem of positive definiteness of the inverse covariance matrix the algorithm uses square root arrays and both orthogonal and hyperbolic rotations as necessitated by the nature of the oriv algorithm

an efficient method to compute consistent estimates of the ar parameters of an arma model a computationally efficient method for consistent estimation of the ar parameters of an arma model is obtained based on an iterated least squares approach proposed by tsay and tiao the method is derived from the lattice filter structure which generates an orthogonal basis for the hilbert space of interest it is shown that for the arma p q model we can get consistent estimates of the ar parameters by using a least squares lattice estimation algorithm and solving a system of q linear equations

information tradeoffs in using the sample autocorrelation function in arma parameter estimation this paper considers bounds on the statistical efficiency of estimators of the poles and zeros of an arma process based on estimates of the process autocorrelation function acf special attention is paid to autoregressive ar and ar plus white noise processes it is seen that reducing the arma process data to a given set of consecutive lags of the popular lagged product acf estimates prior to parameter estimation increases cramer rao bounds on the generalized error covariance a parametric study of the bound deterioration for some illustrative signal and noise situations reveals some empirical strategies for choosing acf estimate lags to preserve statistical information analysis is based on the relative information index rii 2 and derivations of the large sample fisher s information matrix for the raw data and for the lagged product acf estimate of an arma process are included

instability detection of arma systems based on ar system identification the ability of parametric autoregressive ar system identification methods to detect the instability of an autoregressive moving average arma system of an unknown order is investigated the collection of least squares ar estimators of various orders is shown to have the capacity to detect the instability of the underlying system necessary information is not the order of the system but instead an upper bound of the number of unstable poles with the maximal magnitude outside the unit circle

defect 3 blocks of symmetric group algebras abstract in this paper we study if the following properties are present in defect 3 blocks of symmetric group algebras k g n where k has characteristic p 5 the ext quiver is bipartite the p i m s have a common loewy length 7 we obtain a criteria for a defect 3 block b of k g n to inherit these properties from a defect 3 block b of k g n 1 with which it forms a 3 1 pair we also verify that the principal blocks of k g n 3 p n 4 p 1 have these properties

cartan matrices and morita equivalence for blocks of the symmetric groups theorem 1 the blocks of the symmetric groups with a given weight w 0 over a field of characteristic p can be collected into families according to the shapes of their cores each family consists of morita equivalent blocks the number of such families is at most flf 1 i l w 1 11 and each family contains a block of some g where n is less than or equal to p2 p 1 2 w 1 2 4 wp

estimation of the parameters of an arma signal model based on an orthogonal search an iterative procedure for estimating the parameters of an arma signal model input not accessible is empirically compared to the results of several other algorithms the arma identifier reported includes inherent order estimation the empirical results indicate unbiased estimates with less variance than those obtained by the other methods

recursive least squares lattice algorithms a geometrical approach several time recursive least squares algorithms have been developed in recent years in this paper a geometrical formalism is defined which utilizes a nested family of metric spaces indexed by the data time interval this approach leads to a simplified derivation of the so called recursive least squares lattice algorithms recursive in time and order in particular it is found that the resulting structure provides a single framework which encompasses an entire family of fairly complex algorithms as well as providing geometrical insight into their behavior

application of the lattice filter to robust estimation of ar and arma models a method for estimating the parameters of an autoregressive moving average arma model is proposed a p q stage lattice whitening filter is used to obtained consistent estimates of the ar parameters of an arma p p model it is shown that a set of ma parameter estimates can also be obtained using this approach with little added computation the method is used for estimation of the ar parameters of an arma process in additive white noise it is shown that the lattice filter is also useful in robust estimation of the ar parameter on an arma process with additive outliers

adaptive iir algorithms based on high order statistics recursive estimation algorithms are derived for moving average and autoregressive moving average processes these algorithms can be used for adaptive infinite impulse response iir filtering of non gaussian processes the behavior of these algorithms is illustrated by extensive numerical examples

asymptotic properties of the high order yule walker estimates of sinusoidal frequencies the asymptotic properties of the high order yule walker hoyw estimator of sinusoidal frequencies are analyzed an explicit formula for the covariance matrix of the hoyw frequency estimation error is derived the effects on estimation accuracy of the number of yw equations the model order and a certain weighting matrix are investigated analytically the optimally weighted hoyw estimator is described the analysis presented together with the already existing empirical evidence provides enough motivation for the use of an overdetermined and high order yule walker estimator

decomposition numbers for weight three blocks of symmetric groups and iwahori hecke algebras let f be a field q a non zero element of f and h n h f q g n the iwahori hecke algebra of the symmetric group g n if b is a block of h n of e weight 3 and the characteristic of f is at least 5 we prove that the decomposition numbers for b are all at most 1 in particular the decomposition numbers for a p block of g n of defect 3 are all at most 1

comparison of total least squares and instrumental variable methods for parameter estimation of transfer function models the estimation of the parameters of a transfer function model is considered relationships between the total least squares tls and instrumental variable iv approaches are outlined both methods

a new method for adaptive time delay estimation for non gaussian signals a novel adaptive scheme for time delay estimation is introduced for signal environments where the signal is non gaussian and the additive noise sources are spatially correlated gaussian with unknown power spectrum characteristics this scheme is based on parametric modeling between two sensor measurements and employs higher order statistics third or fourth order of the data it is demonstrated by means of extensive simulations that this scheme works well for both stationary and nonstationary cases as expected it outperforms the cross correlation based gradient method for time delay adaptation in spatially correlated gaussian noises the proposed scheme is compared to the overdetermined recursive instrumental variable method and is shown to exhibit substantially less computational complexity

a recursive procedure for arma modeling this paper presents a two part fast recursive algorithm for arma modeling the algorithm first obtains estimates of the p autoregressive coefficients from a set of p extended yule walker equations an exact recursive lattice algorithm for this estimator is then derived the q 1 numerator spectrum coefficients are then obtained by using one of the output data sequences of this lattice algorithm the complete recursive algorithm is fast in the sense that o p q computations are required for each update moreover an exponential forgetting factor is incorporated to facilitate tracking of time variations in the time series

instrumental variable subspace tracking using projection approximation subspace estimation plays an important role in for example sensor array signal processing recursive methods for subspace tracking with application to nonstationary environments have also drawn considerable interest in this paper instrumental variable iv extensions of the projection approximation subspace tracking past algorithm are presented the iv approach is motivated by the fact that past gives biased estimates when the noise is not spatially white the proposed algorithms are based on a projection like unconstrained criterion with a resulting computational complexity of 3ml o mn where m is the dimension of the measurement vector l is the dimension of the iv vector and n is the subspace dimension in addition an extension to a second order iv algorithm is proposed which in certain scenarios is demonstrated to have better tracking properties than the basic iv past algorithms the performance of the algorithms is demonstrated with a simulation study of a time varying array processing scenario