a semi blind channel estimation technique based on second order blind method for cdma systems this paper aims at studying a semi blind channel estimation scheme based on the subspace method or a carefully weighted linear prediction approach the corresponding composite semi blind cost functions result from a linear combination of the training based cost function and a blind cost function for each blind method we show how to calculate the asymptotic estimation error therefore by minimizing this error we can properly tune the k dimensional regularizing vector introduced in the composite semi blind criterion for k active users in the uplink the asymptotic estimation error minimization is a k variable minimization problem which is a complex issue with which to deal we explicitly show under what conditions this problem boils down to k single variable minimization problems our discussion is not limited to theoretical analyses simulation results performed in a realistic context universal mobile telecommunication system time division duplex umts tdd mode are provided in particular we conclude about the potential of the proposed approach in real communication systems

a new approach to multipath correction of constant modulus signals an adaptive digital filtering algorithm that can compensate for both frequency selective multipath and interference on constant envelope modulated signals is presented the method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal a class of so called constant modulus performance functions is developed which sense this am term but are insensitive to the angle modulation simple adaptive algorithms for finite impulse response fir digital filters are developed which employ a gradient search of the performance function one of the resulting algorithms is simulated for the example of an fm signal degraded by specular multipath propagation substantial improvements in noise power ratio npr are observed e g 25 db with moderately rapid convergence time these results are then extended to include tonal interference on a fm signal and intersymbol interference on a qpsk data signal

random walks on combs we develop techniques to obtain rigorous bounds on the behaviour of random walks on combs using these bounds we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but finite length we also calculate exactly the spectral dimension of some fixed non translationally invariant combs we relate the spectral dimension to the critical exponent of the mass of the two point function for random walks on random combs and compute mean displacements as a function of walk duration we prove that the mean first passage time is generally infinite for combs with anomalous spectral dimension

adaptive learning in complex reproducing kernel hilbert spaces employing wirtinger s subgradients this paper presents a wide framework for non linear online supervised learning tasks in the context of complex valued signal processing the complex input data are mapped into a complex reproducing kernel hilbert space rkhs where the learning phase is taking place both pure complex kernels and real kernels via the complexification trick can be employed moreover any convex continuous and not necessarily differentiable function can be used to measure the loss between the output of the specific system and the desired response the only requirement is the subgradient of the adopted loss function to be available in an analytic form in order to derive analytically the subgradients the principles of the recently developed wirtinger s calculus in complex rkhs are exploited furthermore both linear and widely linear in rkhs estimation filters are considered to cope with the problem of increasing memory requirements which is present in almost all online schemes in rkhs the sparsification scheme based on projection onto closed balls has been adopted we demonstrate the effectiveness of the proposed framework in a non linear channel identification task a non linear channel equalization problem and a quadrature phase shift keying equalization scheme using both circular and non circular synthetic signal sources

performance of blind and group blind multiuser detectors in blind or group blind linear multiuser detection the detector is estimated from the received signals with the prior knowledge of only the signature waveform of the desired user or the signature waveforms of some but not all users the performance of a number of such estimated linear detectors including the direct matrix inversion dmi blind linear minimum mean square error mmse detector the subspace blind linear mmse detector and the form i and form ii group blind linear hybrid detectors are analyzed asymptotic limit theorems for each of the estimates of these detectors when the signal sample size is large are established based on which approximate expressions for the average output signal to interference plus noise ratios sinrs and bit error rates bers are given to gain insights on these analytical results the performance of these detectors in an equicorrelated code division multiple acces cdma system is compared examples are provided to demonstrate the excellent match between the theory developed here and the simulation results

lagrange vandermonde mui eliminating user codes for quasi synchronous cdma in unknown multipath a family of codes for low complexity quasi synchronous code division multiple access cdma systems is developed in order to eliminate multiuser interference mui completely in the presence of unknown and even rapidly varying multipath judiciously designed precomputable symbol periodic user codes which we term lagrange or vandermonde and the corresponding linear receivers offer a generalization of orthogonal frequency division multiplexing ofdm which are especially valuable when deep fading carrier frequency errors and doppler effects are present the flexibility inherent to the designed transceivers is exploited to derive transmission strategies that cope with major impairments of wireless cdma channels the symbol periodic code design is also generalized to include the class of aperiodic spreading and orthogonal multirate codes for variable bit rate users performance analysis and simulations results illustrate the advantages of the proposed scheme over competing alternatives

widely linear estimation with complex data mean square estimation of complex and normal data is not linear as in the real case but widely linear the purpose of the paper is to calculate the optimum widely linear mean square estimate and to present its main properties the advantage with respect to the linear procedure is especially analyzed

performance analysis of the minimum variance beamformer we present an analysis of the signal to interference plus noise ratio sinr at the output of the minimum variance beamformer the analysis is based on the assumption that the signals and noise are gaussian and that the number of samples is large compared to the array size and it yields an explicit expression for the sinr in terms of the different parameters affecting the performance including signal to noise ratio snr interference to noise ratio inr signal to interference ratio sir angular separation between the desired signal and the interference array size and shape correlation between the desired signal and the interference and finite sample size

a subspace method for signature waveform estimation in synchronous cdma systems synchronous code division multiple access cdma techniques possess intrinsic protection against co channel interference due to orthogonal codes employed and thus offers higher capacity than existing frequency division multiple access fdma or time division multiple access tdma systems in the presence of multipath however each signal is subject to frequency selective fading and the orthogonality condition does not necessarily hold leading to increased cross correlation in these scenarios multiuser detection need to be performed to suppress interference and recover the message symbols to implement such a technique explicit knowledge of the nonorthogonal signature waveforms of all users is required we propose a blind estimation scheme that provides closed form estimates of the signature waveforms by exploiting the structure information of the data output in particular we show that the subspace of the data matrix contains sufficient information for unique determination of the signature waveforms based on this observation a multiple signal classification music like algorithm is derived performance analysis of the new approach is also presented

extension of wirtinger s calculus to reproducing kernel hilbert spaces and the complex kernel lms over the last decade kernel methods for nonlinear processing have successfully been used in the machine learning community the primary mathematical tool employed in these methods is the notion of the reproducing kernel hilbert space rkhs however so far the emphasis has been on batch techniques it is only recently that online techniques have been considered in the context of adaptive signal processing tasks moreover these efforts have only been focussed on real valued data sequences to the best of our knowledge no adaptive kernel based strategy has been developed so far for complex valued signals furthermore although the real reproducing kernels are used in an increasing number of machine learning problems complex kernels have not yet been used in spite of their potential interest in applications that deal with complex signals with communications being a typical example in this paper we present a general framework to attack the problem of adaptive filtering of complex signals using either real reproducing kernels taking advantage of a technique called complexification of real rkhss or complex reproducing kernels highlighting the use of the complex gaussian kernel in order to derive gradients of operators that need to be defined on the associated complex rkhss we employ the powerful tool of wirtinger s calculus which has recently attracted attention in the signal processing community wirtinger s calculus simplifies computations and offers an elegant tool for treating complex signals to this end in this paper the notion of wirtinger s calculus is extended for the first time to include complex rkhss and use it to derive several realizations of the complex kernel least mean square cklms algorithm experiments verify that the cklms offers significant performance improvements over several linear and nonlinear algorithms when dealing with nonlinearities

qr factorization based blind channel identification with second order statistics most eigenstructure based blind channel identification and equalization algorithms with second order statistics need svd or evd of the correlation matrix of the received signal in this paper we address new algorithms based on qr factorization of the received signal directly without calculating the correlation matrix this renders the qr factorization based algorithms more robust against ill conditioned channels i e those channels with almost common zeros among the subchannels first we present a block algorithm that performs the qr factorization of the received data matrix as a whole then a recursive algorithm is developed based on the qr factorization by updating a rank revealing ulv decomposition compared with existing algorithms in the same category our algorithms are computationally more efficient the computation in each recursion of the recursive algorithm is on the order of o m sup 2 if only equalization is required where m is the dimension of the received signal vector our recursive algorithm preserves the fast convergence property of the subspace algorithms thus converging faster than other adaptive algorithms such as the super exponential algorithm with comparable computational complexities moreover our proposed algorithms do not require noise variance estimation numerical simulations demonstrate the good performance of the proposed algorithms

the spectral dimension of random trees we present a simple yet rigorous approach to the determination of the spectral dimension of random trees based on the study of the massless limit of the gaussian model on such trees as a by product we obtain evidence in favour of a new scaling hypothesis for the gaussian model on generic bounded graphs and in favour of a previously conjectured exact relation between spectral and connectivity dimensions on more general tree like structures

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

scale free random branching trees in supercritical phase we study the size and the lifetime distributions of scale free random branching trees in which k branches are generated from a node at each time step with probability qk k in particular we focus on finite size trees in a supercritical phase where the mean branching number c k kqk is larger than 1 the tree size distribution p s exhibits a crossover behaviour when 2 3 a characteristic tree size sc exists such that for

on the growth of bounded trees bounded infinite graphs are defined on the basis of natural physical requirements when specialized to trees this definition leads to a natural conjecture that the average connectivity dimension of bounded trees cannot exceed two we verify that this bound is saturated by a class of random trees in which case we also derive explicit expressions for the growth probabilities

robust blind multiuser detection based on the worst case performance optimization of the mmse receiver the conventional minimum mean square error mmse multiuser receiver requires that each particular user transmits a sequence of training symbols known to the receiver and the receiver estimates the user signatures using this knowledge however in the presence of multiaccess interference mai during the training period and or in scenarios with short training sequence length the signature estimates can be erroneous and the performance of the mmse multiuser receiver can degrade substantially in this paper we propose a new blind multiuser receiver that is robust against the effects of erroneously presumed desired user signature and short data length our approach is based on the explicit modeling of possible mismatches in the mean square error cost function and worst case performance optimization we show that this approach leads to a multiuser receiver which uses the data covariance matrix with an adaptive diagonal loading the proposed method has simple implementation with a computational complexity comparable with that of the fixed diagonal loading based multiuser receiver simulation results show performance improvements achieved by our approach relative to existing techniques

the statistical geometry of scale free random trees the properties of random trees galton watson trees with scale free power like probability distribution of coordinations are investigated in the thermodynamic limit the scaling form of volume probability is found and the connectivity dimensions are determined and compared with other exponents which describe the growth the local spectral dimension is also determined through the study of the massless limit of the gaussian model on such trees

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

new user identification in a cdma system we present three detector estimators des which allow multiuser detection and parameter estimation without a side channel in a dynamic asynchronous code division multiple access cdma system in which users are entering and leaving the system these des optimally detect a new user given only the chip rate and the spreading factor of the new user two of these des the maximum likelihood detector estimator mlde and the generalized maximum likelihood detector estimator gmlde produce maximum likelihood estimates of the new user s signature sequence delay and amplitude which are then incorporated into a multiuser detector the third de the cyclic detector estimator cde is the most computationally efficient of the three processors this de detects the new user by testing for cyclostationarity and then uses suboptimal schemes to estimate the new user s signature sequence delay and amplitude simulations indicate that all three des reliably detect a new user for an e sub s spl sigma sup 2 symbol energy to noise ratio of 5 db the mlde and gmlde produce signature sequence and delay estimates with probability of error less than 0 07 for an e sub s spl sigma sup 2 of 10 db and the cde produces signature sequence and delay estimates with probability of error less than 0 13 for an e sub s spl sigma sup 2 of 15 db

data aided and blind stochastic gradient algorithms for widely linear mmse mai suppression for ds cdma in this paper three novel stochastic gradient algorithms for adjustment of the widely linear wl minimum mean squared error mmse filter for multiple access interference mai suppression for direct sequence code division multiple access ds cdma are introduced and analyzed in particular we derive a data aided wl least mean square lms algorithm a blind wl minimum output energy moe algorithm and a wl blind lms blms algorithm we give analytical expressions for the steady state signal to interference plus noise ratios sinrs of the proposed wl algorithms and we also investigate their speed of convergence wherever possible comparisons with the corresponding linear adaptive algorithms are made both analytical considerations and simulations show in good agreement the superiority of the novel wl adaptive algorithms nevertheless all proposed wl algorithms require a slightly lower computational complexity than their linear counterparts

blind adaptive multiuser detection in multipath cdma channels based on subspace tracking a blind adaptive technique for signal demodulation in multipath code division multiple access cdma communication channels is proposed this technique is based on signal subspace estimation the receiver employs a bank of linear filters decorrelating filters or linear mmse filters at the front end to mitigate the multiple access interference and the multipath interference a channel estimator is used to estimate the channel state for diversity combining it is shown that through the use of signal subspace estimation both the decorrelating filterbank and the linear mmse filterbank can be obtained blindly i e they can be estimated from the received signal with the prior knowledge of only the signature waveform of the desired user two forms of the subspace based linear filterbanks are developed and their equivalence in terms of the interference suppression capability is established these subspace based blind adaptive interference suppression techniques require at each symbol epoch the eigenvalues and the eigenvectors of an appropriate signal subspace which ran be obtained using computationally efficient sequential adaptive eigendecomposition subspace tracking algorithms moreover a blind adaptive method for estimating the channel state is developed which also produces the postcombining decision statistic as a byproduct

blind adaptive multiuser detection the decorrelating detector and the linear minimum mean square error mmse detector are known to be effective strategies to counter the presence of multiuser interference in code division multiple access channels in particular those multiuser detectors provide optimum near far resistance when training data sequences are available the mmse multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes this paper introduces an adaptive multiuser detector which converges for any initialization to the mmse detector without requiring training sequences this blind multiuser detector requires no more knowledge than does the conventional single user receiver the desired user s signature waveform and its timing the proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest

finitary simple lie algebras abstract an algebra is called finitary if it consists of finite rank transformations of a vector space we classify finitary simple lie algebras over a field of characteristic 0 we also describe finitary irreducible lie algebras

an analysis of the projection method for robust adaptive beamforming two causes of performance degradation in adaptive beamforming are perturbation error and sample covariance error these causes were discussed by feldman and griffihs see ieee trans signal processing vol 42 p 867 april 1994 which proposed an approach termed the projection method to reduce the sensitivity of the beamformer performance to both types of error this paper contains an analysis of the expected performance of the beamformer when it is implemented either with or without using the projection method based on a second order taylor series expansion of an approximate expression for the signal to interference plus noise ratio sinr at the beamformer output the analysis provides accurate results when either perturbation error or sample covariance error occurs a less accurate analysis based on a zeroth order taylor series expansion includes results presented by jablon 1986 and chang and yeh see ibid vol 40 no 11 p 1336 1992 as special cases

the blind widely linear minimum output energy algorithm for ds cdma systems a novel blind widely linear wl minimum output energy moe algorithm is proposed for the code division multiple access cdma receiver whereas the recently proposed wl moe algorithm is only applicable to real valued modulation the proposed receiver is applicable to complex valued modulation as well in this correspondence the blind wl moe filter is analyzed and the convergence properties of an adaptive implementation are derived the proposed algorithm dramatically outperforms nonwidely linear moe algorithms when at least one of the signals desired or interference is improper i e real valued while there is a small performance and complexity penalty relative to the previous wl moe algorithm when only real valued modulation is employed the great advantage of the proposed algorithm in being able to handle complex valued modulation such as the popular qam in most cases should outweigh this slight penalty

inner ideals of simple locally finite lie algebras abstract inner ideals of simple locally finite dimensional lie algebras over an algebraically closed field of characteristic 0 are described in particular it is shown that a simple locally finite dimensional lie algebra has a non zero proper inner ideal if and only if it is of diagonal type regular inner ideals of diagonal type lie algebras are characterized in terms of left and right ideals of the enveloping algebra regular inner ideals of finitary simple lie algebras are described

widely linear versus conventional subspace based estimation of simo flat fading channels mean squared error analysis we analyze the mean squared error mse performance of widely linear wl and conventional subspace based channel estimation for single input multiple output simo flat fading channels employing binary phase shift keying bpsk modulation when the covariance matrix is estimated using a finite number of samples the conventional estimator suffers from a phase ambiguity that reduces to a sign ambiguity for the wl estimator we derive accurate closed form expressions for the mse of the two estimators under four ambiguity resolution scenarios in the first three scenarios the receiver resolves the ambiguity using some clairvoyant knowledge about the channel the first scenario used as a reference is the ideal case of optimal resolution the second scenario assumes that one of the channel coefficients is known and the third assumes knowledge of the coefficient with the largest magnitude the fourth scenario considers the more realistic case where pilot symbols are employed for ambiguity resolution our work demonstrates that there is a strong relationship between the accuracy of ambiguity resolution and the relative performance of wl and conventional subspace based estimators showing that the wl estimator performs better when partial or inaccurate channel information is employed for ambiguity resolution

blind subspace based signature waveform estimation in bpsk modulated ds cdma systems with circular noise a new blind subspace based algorithm for signature waveform estimation in binary phase shift keying bpsk modulated direct sequence code division multiple access ds cdma systems is proposed our approach can be viewed as a modification of the popular blind technique by liu and xu lx which additionally exploits noncircularity of the transmitted signals and circularity of noise to increase the dimension of the observation space twice while keeping the dimension of the signal subspace unchanged this enables us to improve the performance substantially and to apply the proposed algorithm to scenarios with an increased number of active users and lengthier user channels as compared with the original lx algorithm the theoretical analysis of the identifiability of the proposed technique is provided which shows that it enjoys more relaxed identifiability conditions than the lx algorithm analytical expressions for the mean square error mse of the proposed algorithm are also derived numerical examples verify the advantages of the proposed algorithm over the lx technique and validate our analytical results

widely linear versus linear blind multiuser detection with subspace based channel estimation finite sample size effects in a recent paper a s cacciapuoti et al ldquofinite sample performance analysis of widely linear multiuser receivers in ds cdma systems ieee transactions on signal processing vol 56 no 4 pp 1572 1588 apr 2008 we presented the finite sample theoretical performance comparison between linear l and widely linear wl minimum output energy moe receivers for direct sequence code division multiple access ds cdma systems worked out under the assumption that the channel impulse response of the desired user is exactly known the main scope of this paper is to extend such an analysis taking into account not only autocorrelation matrix acm estimation effects but also the accuracy of subspace based blind channel estimation ce we aim to answer the two following questions which of the two estimation processes acm or ce is the main source of degradation when implementing the receivers on the basis of a finite sample size compared with the l moe one is the finite sample wl moe receiver with blind ce capable of achieving the performance gains predicted by the theory to this goal simple and easily interpretable formulas are developed for the signal to interference plus noise ratio sinr at the output of the l and wl moe receivers with blind ce when they are implemented using either the sample acm or its eigendecomposition in addition the derived formulas which are validated by simulations allow one to recognize and discuss interesting tradeoffs between the main parameters of the ds cdma system

blind identification of fir systems excited by discrete alphabet inputs an algorithm for the identification of finite impulse response fir system parameters from output measurements for systems excited by discrete alphabet inputs is described the approach taken is algebraic it does not rely directly on the statistical properties of the measurements but rather it essentially solves the nonlinear equations appearing in the problem by converting them to equivalent linear equations using the discrete alphabet property of the input signal the proposed algorithm was tested by computer simulations and some of these simulations are illustrated

spectral dimension of fractal trees we present in detail a calculation of the spectral dimension for a class of fractal trees called mathrm nt mathit d i e nice trees of dimension d defined as trees whose branches are splitting in r every time the distance from the origin is doubled where r is an integer greater than 1 which presents nonanomalous diffusion this is performed by an analytical technique related to an exact rescaling of the time variable which can be extended to more general geometrical structures

an artinian theory for lie algebras abstract complemented lie algebras are introduced in this paper a notion similar to that studied by o loos and e neher in jordan pairs we prove that a lie algebra is complemented if and only if it is a direct sum of simple nondegenerate artinian lie algebras moreover we classify simple nondegenerate artinian lie algebras over a field of characteristic 0 or greater than 7 and describe the lie inner ideal structure of simple lie algebras arising from simple associative algebras with nonzero socle

mmse interference suppression for direct sequence spread spectrum cdma we consider interference suppression for direct sequence spread spectrum code division multiple access cdma systems using the minimum mean squared error mmse performance criterion the conventional matched filter receiver suffers from the near far problem and requires strict power control typically involving feedback from receiver to transmitter for acceptable performance multiuser detection schemes previously proposed mitigate the near far problem but are complex and require explicit knowledge or estimates of the interference parameters in this paper we present and analyze several new mmse interference suppression schemes which have the advantage of being near far resistant to varying degrees depending on their complexity and can be implemented adaptively when interference parameters are unknown and or time varying numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver we conclude that mmse detectors can alleviate the need for stringent power control in cdma systems and may be a practical alternative to the matched filter receiver

linear multiuser detectors for synchronous code division multiple access channels under the assumptions of symbol synchronous transmissions and white gaussian noise the authors analyze the detection mechanism at the receiver comparing different detectors by their bit error rates in the low background noise region and by their worst case behavior in a near far environment where the received energies of the users are not necessarily similar optimum multiuser detection achieves important performance gains over conventional single user detection at the expense of computational complexity that grows exponentially with the number of users it is shown that in the synchronous case the performance achieved by linear multiuser detectors is similar to that of optimum multiuser detection attention is focused on detectors whose linear memoryless transformation is a generalized inverse of the matrix of signature waveform crosscorrelations and on the optimum linear detector it is shown that the generalized inverse detectors exhibit the same degree of near far resistance as the optimum multiuser detectors the optimum linear detector is obtained

an elemental characterization of strong primeness in lie algebras abstract in this paper we prove that a lie algebra l is strongly prime if and only if x y l 0 for every nonzero elements x y l as a consequence we give an elementary proof without the classification theorem of strongly prime jordan algebras of the fact that a linear jordan algebra or jordan pair t is strongly prime if and only if x t y 0 for every x y t moreover we prove that the jordan algebras at nonzero jordan elements of strongly prime lie algebras are strongly prime

asymptotic analysis of blind multiuser detection with blind channel estimation the analytical performance of the subspace based blind linear minimum mean square error mmse multiuser detection algorithm in general multipath multi antenna code division multiple access cdma systems is investigated in blind multiuser detection the linear mmse detector of a given user is estimated from the received signals based on the knowledge of only the spreading sequence of that user typically the channel of that user must be estimated first based on the orthogonality between the signal and noise subspaces an asymptotic limit theorem for the estimate of the blind linear detector when the received signal sample size is large is obtained based on which approximate expressions of the average output signal to inference plus noise ratios sinrs and bit error rates bers for both binary phase shift keying bpsk and quaternary phase shift keying qpsk modulations are given corresponding results for group blind multiuser detectors are also obtained examples are provided to demonstrate the excellent match between the theory developed in this paper and the simulation results

large sample performance of blind and group blind multiuser detectors a perturbation perspective in blind and group blind multiuser detection different detectors can be designed using either the sample data covariance matrix directly or its eigencomponents due to finite sample effect in practice their performance deviates from the corresponding optimum a perturbation technique is developed rigorously and systematically to analyze those detectors in this work subject to the assumption that the first order perturbation dominates corresponding results can be applied to a practical system of a given sample size in particular performance of the following typical detectors is studied for either flat or estimated multipath channels direct matrix inversion dmi blind minimum mean square error mmse detector subspace blind mmse detector direct zero forcing zf detector subspace zf detector and group blind hybrid detector simulation examples further verify various analytical results

partially blind adaptive mmse interference rejection in asynchronous ds cdma networks over frequency selective fading channels in this work the problem of joint suppression of multiple access and narrow band interference nbi for an asynchronous direct sequence code division multiple access cdma system operating on a frequency selective fading channel is addressed the receiver structure we consider can be deemed as a two stage one the first stage consists of a bank of minimum mean square error mmse filters each keyed to a given replica of the useful signal and aimed at suppressing the overall interference the second stage assuming knowledge of the fading channel coefficients realizations combines the mmse filters outputs according to a maximal ratio combining rule due to the presence of the nbi the resulting structure is in general time varying and becomes periodically time varying if the nbi bit rate has a rational ratio to that of the cdma system moreover enlarging the observation window beyond the signaling interval and oversampling the signal space may yield a noticeable performance improvement for the relevant case that the said ratio is rational a new cyclic blind recursive least squares rls based algorithm is introduced capable of tracking the periodically time varying receiver structure and allowing adaptive interference cancellation with a moderate complexity increase we also come up with a closed form expression for the conditional bit error rate ber which is useful both to evaluate semi analytical methods to assess the unconditional ber and to derive bounds on the system near far resistance the results indicate that the receiver achieves very satisfactory performance in comparison to previously known structures computer simulations also demonstrate that the cyclic blind rls algorithm exhibits quite fast convergence dynamics

blind subspace based signature estimation in ds cdma systems with unknown wide sense stationary interference in this paper we propose a new blind subspace based signature waveform estimation technique for direct sequence code division multiple access ds cdma communication systems operating in the presence of unknown wide sense stationary interference unlike the existing algorithms the proposed technique requires just a single receive antenna and is applicable to the case of arbitrary transmitted symbol constellations necessary and sufficient conditions for identifiability of the proposed technique are derived for practical scenarios where the data covariance matrix is estimated using a finite number of samples a closed form expression for the mean squared error mse of the estimated channel is obtained for the high signal to interference ratio sir regime and gaussian interference an approximation of the mse expression is also derived and the effects of different parameters on the performance of the proposed algorithm are analyzed numerical examples validate our analytical results

widely linear equalization and blind channel identification for interference contaminated multicarrier systems this work addresses the problem of designing efficient detection techniques for multicarrier transmission systems operating in the presence of narrowband interference nbi in this case conventional linear receivers such as the zero forcing zf or the minimum mean square error mmse ones usually perform poorly since they are not capable of suppressing satisfactorily the nbi to synthesize interference resistant detection algorithms we resort to widely linear wl filtering which allows one to exploit the noncircularity property of the desired signal constellation by jointly processing the received signal and its complex conjugate version in particular we synthesize new wl zf receivers for multicarrier systems which mitigate in the minimum output energy moe sense the nbi contribution at the receiver output without requiring knowledge of the nbi statistics by exploiting the noncircularity property we also propose a new subspace based blind channel identification algorithm and derive the channel identifiability condition blind identification can be performed satisfactorily also in the presence of nbi requiring only an approximate rank determination of the nbi autocorrelation matrix the performance analysis shows that the proposed moe wl zf receiver even when implemented blindly assures a substantial improvement over the conventional linear zf and mmse ones particularly when the nbi bandwidth is very small in comparison with the intercarrier spacing and the nbi is not exactly located on a subcarrier

the socle of a nondegenerate lie algebra we define the socle of a nondegenerate lie algebra as the sum of all its minimal inner ideals the socle turns out to be an ideal which is a direct sum of simple ideals and satisfies the descending chain condition on principal inner ideals every classical finite dimensional lie algebra coincides with its socle while relevant examples of infinite dimensional lie algebras with nonzero socle are the simple finitary lie algebras and the classical banach lie algebras of compact operators on an infinite dimensional hilbert space this notion of socle for lie algebras is compatible with the previous ones for associative algebras and jordan systems we conclude with a structure theorem for simple nondegenerate lie algebras containing abelian minimal inner ideals and as a consequence we obtain that a simple lie algebra over an algebraically closed field of characteristic 0 is finitary if and only if it is nondegenerate and contains a rank one element

exact and approximate maximum likelihood parameter estimation for quasi synchronous cdma signals in order to construct the optimal decorrelator for a quasi synchronous qs code division multiple access receiver it is necessary to estimate the user delays however in a qs system it is shown that delay estimation is equivalent to estimating a parameter vector which is related linearly to the received signal an exact maximum likelihood ml solution using alternating maximization is first developed for joint estimation of the user delay vectors and amplitudes suboptimal recursive least squares rls and least mean square algorithms are then presented which approximate the true ml solution it is shown that the optimal decorrelator and demodulated symbols are also generated by the rls algorithm simulation and analytical results are presented for the bit error rate performance of the adaptive receiver and the average squared error of the estimated delay vectors is compared with the cramer rao bound

chip interleaved block spread code division multiple access a novel multiuser interference mui free code division multiple access cdma transceiver for frequency selective multipath channels is developed relying on chip interleaving and zero padded transmissions orthogonality among different users spreading codes is maintained at the receiver even after frequency selective propagation as a result deterministic multiuser separation with low complexity code matched filtering becomes possible without loss of maximum likelihood optimality in addition to mui free reception the proposed system guarantees channel irrespective symbol detection and achieves high bandwidth efficiency by increasing the symbol block size filling the zero gaps with known symbols allows for perfectly constant modulus transmissions important variants of the proposed transceivers are derived to include cyclic prefixed transmissions and various redundant or nonredundant precoding alternatives semi blind channel estimation algorithms are also discussed simulation results demonstrate improved performance of the proposed system relative to competing alternatives

blind multiuser detection a subspace approach a new multiuser detection scheme based on signal subspace estimation is proposed it is shown that under this scheme both the decorrelating detector and the linear minimum mean square error mmse detector can be obtained blindly i e they can be estimated from the received signal with the prior knowledge of only the signature waveform and timing of the user of interest the consistency and asymptotic variance of the estimates of the two linear detectors are examined a blind adaptive implementation based on a signal subspace tracking algorithm is also developed it is seen that compared with the previous minimum output energy blind adaptive multiuser detector the proposed subspace based blind adaptive detector offers lower computational complexity better performance and robustness against signature waveform mismatch two extensions are made within the framework of signal subspace estimation first a blind adaptive method is developed for estimating the effective user signature waveform in the multipath channel secondly a multiuser detection scheme using spatial diversity in the form of an antenna array is considered a blind adaptive technique for estimating the array response for diversity combining is proposed it is seen that under the proposed subspace approach blind adaptive channel estimation and blind adaptive array response estimation can be integrated with blind adaptive multiuser detection with little attendant increase in complexity

detecting the number of signals in wireless ds cdma networks in this paper a new information theoretic algorithm is proposed for signal enumeration in ds cdma networks the approach is based on the predictive description length pdl of the observation vector the pdl is the length of a predictive code of observations for signal detection the pdl criterion is computed for the candidate models and is minimized to determine the number of signals the proposed technique uses the maximum likelihood ml estimate of the correlation matrix the only information used in the ml estimation of the correlation matrix is the multiplicity of the smallest eigenvalue the pdl algorithm has a signal to noise ratio resolution threshold that is smaller than that of the minimum description length mdl the proposed method can be used on line and can be applied to time varying and non stationary systems

the jordan socle and finitary lie algebras in this paper we introduce the notion of jordan socle for nondegenerate lie algebras which extends the definition of socle given in a fernandez lopez et al 3 graded lie algebras with jordan finiteness conditions comm algebra in press for 3 graded lie algebras any nondegenerate lie algebra with essential jordan socle is an essential subdirect product of strongly prime ones having nonzero jordan socle these last algebras are described up to exceptional cases in terms of simple lie algebras of finite rank operators and their algebras of derivations when working with lie algebras which are infinite dimensional over an algebraically closed field of characteristic 0 the exceptions disappear and the algebras of derivations are computed

a moment based blind method for identification of fir down link ds cdma channels in order to achieve lower bit error rates bers multiuser detection techniques have been proposed generally multiuser detectors can provide excellent performance only when channel parameters are precisely known in this paper we propose a moment based blind method to estimate down link channels precisely the mean square error mse expression of the channel vector estimate has been derived through simulations we show the effect of the channel estimation error on the performance of a multiuser detector in this paper we also show that finite impulse response fir channels can be blindly identified by using the proposed method and the spreading operation since the spreading operation of the code division multiple access cdma can induce cyclostationarity any fir channel can be identified by the proposed method of course in order to guarantee identifiability some conditions on the spreading codes will be satisfied in this paper these conditions are also found

blind channel estimation for long code multiuser cdma systems in cdma systems with long codes the users signatures change in each bit period impeding the estimation of the time invariant multipath parameters in this paper correlation matching methods are employed to blindly estimate those multipath parameters for given code sequences the output correlation matrix parameterized by the unknown channel coefficients is compared with its instantaneous approximation by minimizing the frobenius norm of the resulting error matrix the channel parameters can be estimated up to a complex scalar ambiguity both batch and adaptive algorithms are derived under the assumption of i i d code sequences identifiability up to a complex scalar ambiguity for each channel is guaranteed and the asymptotic convergence of the proposed algorithm is established furthermore step size selection for the adaptive version is investigated when only the code sequence of the user of interest is available a single user receiver is also derived simulation results verify those claims and provide comparisons with other methods

statistical ensemble of scale free random graphs a thorough discussion of the statistical ensemble of scale free connected random tree graphs is presented methods borrowed from field theory are used to define the ensemble and to study analytically its properties the ensemble is characterized by two global parameters the fractal and the spectral dimensions which are explicitly calculated it is discussed in detail how the geometry of the graphs varies when the weights of the nodes are modified the stability of the scale free regime is also considered when it breaks down either a scale is spontaneously generated or else a singular node appears and the graphs become crumpled a new computer algorithm to generate these random graphs is proposed possible generalizations are also discussed in particular more general ensembles are defined along the same lines and the computer algorithm is extended to arbitrary degenerate scale free random graphs

fractality in complex networks critical and supercritical skeletons fractal scaling char22 a power law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box char22 is studied we introduce a box covering algorithm that is a modified version of the original algorithm introduced by song et al nature london 433 392 2005 this algorithm enables easy implementation fractal networks are viewed as comprising a skeleton and shortcuts the skeleton embedded underneath the original network is a special type of spanning tree based on the edge betweenness centrality it provides a scaffold for the fractality of the network when the skeleton is regarded as a branching tree it exhibits a plateau in the mean branching number as a function of the distance from a root for nonfractal networks on the other hand the mean branching number decays to zero without forming a plateau based on these observations we construct a fractal network model by combining a random branching tree and local shortcuts the scaffold branching tree can be either critical or supercritical depending on the small worldness of a given network for the network constructed from the critical supercritical branching tree the average number of vertices within a given box grows with the lateral size of the box according to a power law an exponential form in the cluster growing method the critical and supercritical skeletons are observed in protein interaction networks and the world wide web respectively the distribution of box masses i e the number of vertices within each box follows a power law p m m ensuremath sim m ensuremath ensuremath eta the exponent ensuremath eta depends on the box lateral size ensuremath ell b for small values of ensuremath ell b ensuremath eta is equal to the degree exponent ensuremath gamma of a given scale free network whereas ensuremath eta approaches the exponent ensuremath tau ensuremath gamma ensuremath gamma ensuremath 1 as ensuremath ell b increases which is the exponent of the cluster size distribution of the random branching tree finally we study the perimeter h ensuremath alpha of a given box ensuremath alpha i e the number of edges connected to different boxes from a given box ensuremath alpha as a function of the box mass m b ensuremath alpha it is obtained that the average perimeter over the boxes with box mass m b is likely to scale as h m b ensuremath sim m b irrespective of the box size ensuremath ell b

performance analysis of the minimum variance beamformer in the presence of steering vector errors we present an analysis of the signal to interference plus noise ratio sinr at the output of the minimum variance beamformer in the presence of steering vector errors the analysis yields an explicit expression for the sinr in terms of the variance of the steering vector errors and the other parameters affecting performance including signal to noise ratio snr interference to noise ratio inr signal to interference ratio sir angular separation between desired signal and interference array size and shape correlation between desired signal and interference and finite sample size

a projection approach for robust adaptive beamforming it is well known that calibration errors can seriously degrade performance in adaptive arrays particularly when the input signal to noise ratio is large the effect is caused by the perturbation of the presumed steering vector from its optimal value although it is not as widely known similar degradation occurs in sampled matrix inversion processing when the covariance matrix is estimated while the desired signal is present in the snapshot data under these conditions performance loss is due to errors in the estimated covariance matrix and occurs even when the steering vector is known exactly in the paper a new method based of modification of the steering vector is proposed to overcome both the problems of perturbation and of sample covariance errors the method involves projection of the presumed steering vector onto the observed signal plus interference subspace an analysis is also presented illustrating that the sample covariance errors can be viewed as a particular type of perturbation error and a simple approximation is derived for the expected beamformer performance as a function of the number of data snapshots both analytical and experimental results are presented that illustrate the advantages of the proposed method

blind channel identification subspace tracking method without rank estimation subspace ss methods are an effective approach for blind channel identification however these methods also have two major disadvantages 1 they require accurate channel length estimation and or rank estimation of the correlation matrix which is difficult with noisy channels and 2 they require a large amount of computation for the singular value decomposition svd which makes it inconvenient for adaptive implementation although many adaptive subspace tracking algorithms can be applied the computational complexity is still o m sup 3 where m is the data vector length in this paper we introduce new recursive subspace algorithms using ulv updating and successive cancellation techniques the new algorithms do not need to estimate the rank of the correlation matrix furthermore the channel length can be overestimated initially and be recovered at the end by a successive cancellation procedure which leads to more convenient implementations the adaptive algorithm has computations of o m sup 2 in each recursion the new methods can be applied to either the single user or the multiuser cases simulations demonstrate their good performance

complexity reduction in subspace based blind channel identification for ds cdma systems direct sequence code division multiple access is emerging as a potential multiple access communication scheme for future digital wireless communications systems such wide band systems usually operate in a frequency selective fading channel that introduces intersymbol interference and thus potential performance degradation previously proposed subspace based blind channel identification algorithms which provide estimates of channel parameters for effective equalization suffer from high numerical complexity for systems with large spreading gains in this paper it is shown that through the use of matched filter outputs reduction in numerical complexity can be obtained the complexity reduction is considerable when the channel length is small and the system is moderately loaded the results show that the new algorithm suffers a slight performance loss although the employed matched filter outputs do not form a set of sufficient statistics for the unknown channels the difference between the matched filter outputs and the sufficient statistics becomes negligible for large observation lengths and the asymptotic normalized fisher information does not change performance is evaluated through simulations the derivation of a tight approximation of the mean squared channel estimation error and through comparisons to the cramer rao bound for the estimation error variance it is shown that the approximation of the mean squared error can be obtained in terms of the correlation of the spreading codes and the channels this representation of the error supplies a tool for investigating the relationship between performance and spreading sequence correlations

lie algebras graded by 3 graded root systems and jordan pairs covered by grids let r be an irreducible root system a lie algebra l is called graded by r if l is graded with grading group the root lattice of r such that the only nonzero homogeneous subspaces of l have degree 0 or a root in r the grading is induced by the adjoint action of a split cartan subalgebra of a finite dimensional simple lie subalgebra of l with root system r and l is generated by the homogeneous subspaces of nonzero degree this class of lie algebras was introduced and studied by s berman and r moody in invent math 108 1992 where in particular a classification up to central equivalence is given in the simply laced case the doubly laced cases have recently been classified by g benkart and e zelmanov let r be a 3 graded root system i e r is not of type e 8 f 4 or g 2 in this paper lie algebras graded by r are described in a unified way without case by case considerations namely it is shown that a lie algebra l is 3 graded if and only if l is a central extension of the tits kantor koecher algebra of a jordan pair covered by a grid whose associated 3 graded root system is isomorphic to r this result is then used to classify lie algebras graded by r we give the classification of jordan pairs covered by a grid and describe their tits kantor koecher algebras one of the advantages of this approach is that it works over rings containing 1 2 and 1 3 and also for infinite root systems another application is the description of slodowy s intersection matrix algebras arising from multiply affinized cartan matrices

fast subspace decomposition many recent signal processing techniques in various areas e g array signal processing system identification and spectrum estimation require a step of extracting the low dimensional subspace from a large space this step is usually called subspace decomposition which is conventionally accomplished by an eigendecomposition ed since an ed requires o m sup 3 flops for an m spl times m matrix it may represent a barrier to the real time implementation of these algorithms the authors present a fast algorithm for signal subspace decomposition which is termed fsd that exploits the special matrix structure low rank plus identity associated with signal subspace algorithms and requires only o m sup 2 d flops where d often spl lt m denotes the signal subspace dimension unlike most of alternatives the dimension of the signal subspace is not assumed known apriori and is estimated as part of the procedure moreover theoretical analysis has been conducted and its results show the strong consistency of the new detection scheme and the asymptotic equivalence between fsd and ed in estimating the signal subspace their new approach can also exploit other matrix structure common in signal processing areas e g toeplitz or hankel and thus achieve another order of computational reduction moreover it can be easily implemented in parallel to reduce further the computation time to as little as o md using o m simple processors

joint channel and carrier offset estimation in cdma communications this paper addresses the problem of cdma multiuser detection in the presence of unknown multipath channels and residual carriers an analytic algorithm that provides closed form channel and carrier offset estimates is proposed the algorithm first converts the multiuser estimation problem into single user problems and then analytically solves the resulting nonlinear multivariate optimization problems using a polynomial matrix projection property the performance of the proposed algorithm is investigated through first order perturbation analysis we also calculate the cramer rao bound crb to illustrate the efficiency of the new algorithm the analyzes are supported by computer simulations

on blind multiuser forward link channel estimation by the subspace method identifiability results blind channel estimation for periodic sequence ds cdma systems can be cast into the framework of structured blind estimation of multi input multi output mimo fir systems where the structure is imposed by the user s signatures a possible approach to tackle this problem consists in looking for a structured solution to one of the blind mimo fir systems proposed previously this is the approach undertaken by several authors however most of them did not address identifiability issues in this paper we first recall and reformulate some general mimo fir identification results of meraim loubaton and moulines see ieee trans inform theory vol 43 p 499 511 1997 and point out some difficulties posed by the subspace approach next we use the above material in order to analyze the behavior of the subspace forward link channel estimate of cdma systems we derive new results showing that the subspace method is not robust to an over determination of the channel order greater than the spreading factor if however the over determination error is less than the spreading factor we show that the subspace estimate is consistent if the codes of the users are properly designed