relations between the correlators of the topological sigma model coupled to gravity we prove a new recursive relation between the correlators which together with known relations allows one to express all of them through the full system of gromov witten invariants in the sense of kontsevich manin and the intersection indices of tautological classes on effectively calculable in view of earlier results due to mumford kontsevich getzler and faber this relation shows that a linear change of coordinates of the big phase space transforms the potential with gravitational descendants to another function defined completely in terms of the gromov witten correspondence and the intersection theory on we then extend the formalism of gravitational descendants from quantum cohomology to more general frobenius manifolds and cohomological field theories

iterative map equalization and decoding in wireless mobile coded ofdm orthogonal frequency division multiplexing ofdm system suffers extra performance degradation in fast fading channels due to intercarrier interference ici combining frequency domain equalization and bit interleaved coded modulation bicm the iterative receiver is able to harvest both temporal and frequency diversity realizing that ici channels are intrinsically isi channels this paper proposes a soft in soft out siso maximum a posteriori map equalizer by extending ungerboeck s maximum likelihood sequence estimator mlse formulation to ici channels the siso map equalizer employs bcjr algorithm and computes the bit log likelihood ratios llr for the entire received sequence by efficiently constructing a trellis that takes into account of the ici channel structure a reduced state rs formulation of the siso map equalizer which provides good performance complexity tradeoff is also described utilizing the fact that ici energy is clustered in adjacent subcarriers frequency domain equalization is made localized this paper further proposes two computational efficient linear minimum mean square error lmmse based equalization methods recursive q tap sic lmmse equalizer and recursive sliding window sw sic lmmse equalizer respectively simulations results demonstrate that the iterative siso rs map equalizer achieves the performance of no ici with normalized doppler frequency fdts up to 20 46 in realistic mobile wimax environment

on channel estimation and detection for multicarrier signals in fast and selective rayleigh fading channels time domain channel estimation and detection techniques are presented for multicarrier signals in a fast and frequency selective rayleigh fading channel as a consequence of the time varying channel the orthogonality between subcarriers is destroyed in conventional frequency domain approaches resulting in interchannel interference which increases an irreducible error floor in proportion to the normalized doppler frequency an important feature of the proposed technique is the ability to exploit the time selective channel as a provider of time diversity this enables us to achieve performance superior to any other structure without increasing bandwidth or incorporating redundancy in order to reduce the complexity of the estimator we apply the theory of optimal low rank approximation to a minimum mean squared error channel estimator and present a theoretical calculation of mean squared error and simulations to confirm that the estimator is robust to changes in channel characteristics

joint channel estimation equalization and data detection for ofdm systems in the presence of very high mobility this paper is concerned with the challenging and timely problem of joint channel estimation equalization and data detection for uplink orthogonal frequency division multiplexing ofdm systems in the presence of frequency selective and very rapidly time varying channels the resulting algorithm is based on the space alternating generalized expectation maximization sage technique which is particularly well suited to multicarrier signal formats leading to a receiver structure that also incorporates interchannel interference ici cancelation in order to reduce the computational complexity of the algorithm band limited discrete cosine orthogonal basis functions are employed to represent the rapidly time varying fading channel by the discrete cosine serial expansion coefficients it is shown that depending on the normalized doppler frequency only a small number of expansion coefficients is sufficient to approximate the channel perfectly and there is no need to know the correlation function of the input signal in this way the resulting reduced dimensional channel coefficients are estimated and the data symbols detected iteratively with tractable complexity the proposed sage joint detection algorithm updates the data sequences serially and the channel parameters are updated in parallel leading to a receiver structure that also incorporates ici cancelation computer simulations show that the cosine transformation represents the time varying channel very effectively and the proposed algorithm has excellent symbol error rate and channel estimation performance even with a very small number of channel expansion coefficients employed in the algorithm resulting in substantial reduction of the computational complexity

low complexity block turbo equalization for ofdm systems in time varying channels we propose low complexity block turbo equalizers for orthogonal frequency division multiplexing ofdm systems in time varying channels the presented work is based on a soft minimum mean squared error mmse block linear equalizer ble that exploits the banded structure of the frequency domain channel matrix as well as a receiver window that enforces this banded structure this equalization approach allows us to implement the proposed designs with a complexity that is only linear in the number of subcarriers three block turbo equalizers are discussed two are based on a biased mmse criterion while the third is based on the unbiased mmse criterion simulation results show that the proposed iterative mmse ble achieves a better bit error rate ber performance than a previously proposed iterative mmse serial linear equalizer sle the proposed equalization algorithms are also tested in the presence of channel estimation errors

schur agler and herglotz agler classes of functions positive kernel decompositions and transfer function realizations abstract we discuss transfer function realization for multivariable holomorphic functions mapping the unit polydisk or the right polyhalfplane into the operator analogue of either the unit disk or the right halfplane schur herglotz functions over either the unit polydisk or the right polyhalfplane which satisfy the appropriate stronger contractive positive real part condition for the values of these functions on commutative tuples of strict contractions strictly accretive operators schur agler herglotz agler functions over either the unit polydisk or the right polyhalfplane as originally shown by agler the first case polydisk to disk can be solved via unitary extensions of a partially defined isometry constructed in a canonical way from a kernel decomposition for the function the lurking isometry method we show how a geometric reformulation of the lurking isometry method embedding of a given isotropic subspace of a kre n space into a lagrangian subspace the lurking isotropic subspace method can be used to handle the second two cases polydisk to halfplane and polyhalfplane to disk as well as the last case polyhalfplane to halfplane if an additional growth condition at is imposed for the general fourth case we show how a linear fractional transformation change of variable can be used to arrive at the appropriate symmetrized nonhomogeneous bessmertny long resolvent realization we also indicate how this last result recovers the classical integral representation formula for scalar valued holomorphic functions mapping the right halfplane into itself

sumis near optimal soft in soft out mimo detection with low and fixed complexity the fundamental problem of interest here is soft input soft output multiple input multiple output mimo detection we propose a method referred to as subspace marginalization with interference suppression sumis that yields unprecedented performance at low and fixed deterministic complexity our method provides a well defined tradeoff between computational complexity and performance apart from an initial sorting step consisting of selecting channel matrix columns the algorithm involves no searching nor algorithmic branching hence the algorithm has a completely predictable run time and allows for a highly parallel implementation we numerically assess the performance of sumis in different practical settings full partial channel state information sequential iterative decoding and low high rate outer codes we also comment on how the sumis method performs in systems with a large number of transmit antennas

unitary colligations reproducing kernel hilbert spaces and nevanlinna pick interpolation in several variables abstract recently j agler studied the class s d of scalar valued analytic functions of d complex variables f for which f t 1 t d has norm at most 1 for any collection of d commuting contractions t 1 t d on a hilbert space h among other results he obtained a characterization of such functions in terms of a positivity property and in terms of a representation as the transfer function of a certain type of d variable linear system as well as a nevanlinna pick interpolation theorem for this class of functions in this note we examine the system theory aspects and uniqueness of the transfer function representation and give a simpler proof of the nevanlinna pick interpolation theorem for the class s d and obtain a d variable version of the toeplitz corona theorem by using ideas of arov and grossman introduced for 1 variable problems as a bonus we obtain a collection of linear fractional maps which parametrize the set of all s d solutions of an interpolation problem

low complexity equalization of ofdm in doubly selective channels orthogonal frequency division multiplexing ofdm systems may experience significant inter carrier interference ici when used in time and frequency selective or doubly selective channels in such cases the classical symbol estimation schemes e g minimum mean squared error mmse and zero forcing zf estimation require matrix inversion that is prohibitively complex for large symbol lengths an analysis of the ici generation mechanism leads us to propose a novel two stage equalizer whose complexity apart from the fft is linear in the ofdm symbol length the first stage applies optimal linear preprocessing to restrict ici support and the second stage uses iterative mmse estimation to estimate finite alphabet frequency domain symbols simulation results indicate that our equalizer has significant performance and complexity advantages over the classical linear mmse estimator in doubly selective channels

bounds on the interchannel interference of ofdm in time varying impairments in this article tight and universal bounds have been derived for the interchannel interference ici of an orthogonal frequency division multiplexing ofdm signal resulting from doppler spread the universal bound depends only on the product of the maximum doppler frequency and the ofdm symbol duration the tight bound also depends on the variance of the doppler spectrum compared with the exact ici expressions derived by other researchers these bounds are easier to evaluate and can provide useful insight

intersection theory on the moduli space of curves and the matrix airy function we show that two natural approaches to quantum gravity coincide this identity is nontrivial and relies on the equivalence of each approach to kdv equations we also investigate related mathematical problems

free pick functions representations asymptotic behavior and matrix monotonicity in several noncommuting variables r nevanlinna showed that elements of the pick class the set of complex analytic functions taking the upper half plane into itself have certain integral representations which reflect their asymptotic behavior at infinity later lowner connected the pick class to matrix monotone functions we generalize the nevanlinna representation theorems and lowner s theorem on matrix monotone functions to the free pick class the collection of functions that map tuples of matrices with positive imaginary part into the matrices with positive imaginary part which obey the free functional calculus

low complexity ici isi equalization in doubly dispersive multicarrier systems using a decision feedback lsqr algorithm we propose a low complexity intercarrier interference intersymbol interference ici isi equalizer for multicarrier transmissions over doubly dispersive channels decision feedback or interference cancellation is used with respect to both time and frequency the ici stage employs an extension of the iterative lsqr algorithm using groupwise interference cancellation with reliability based sorting of sets of subcarriers and a band approximation of the frequency domain channel matrix the lsqr algorithm is attractive because of its excellent numerical properties and low complexity optimal pulse design is optionally considered for shaping the ici isi simulation results demonstrate the excellent performance of the proposed ici isi equalizer

a generalization of schur functions applications to nevanlinna functions orthogonal polynomials random walks and unitary and open quantum walks abstract recent work on return properties of quantum walks the quantum analogue of random walks has identified their generating functions of first returns as schur functions this is connected with a representation of schur functions in terms of the operators governing the evolution of quantum walks i e the unitary operators on hilbert spaces in this paper we propose a generalization of schur functions by extending the above operator representation to arbitrary closed operators on banach spaces such generalized schur functions meet the formal structure of first return generating functions thus we call them fr functions we derive some general properties of fr functions among them a simple relation with an operator version of stieltjes functions which generalizes the renewal equation already known for random and quantum walks we also prove that fr functions satisfy splitting properties which extend useful factorizations of schur functions when specialized to self adjoint operators on hilbert spaces we show that fr functions become nevanlinna functions this allows us to obtain properties of nevanlinna functions which as far as we know seem to be new the fr function structure leads to a new operator representation of nevanlinna functions in terms of self adjoint operators whose spectral measures provide also new integral representations of such functions this allows us to characterize each nevanlinna function by a measure on the real line which we refer to as the measure of the nevanlinna function in contrast to standard operator and integral representations of nevanlinna functions these new ones are exact analogues of those already known for schur functions the above results are also the source of a very simple schur algorithm for nevanlinna functions based on interpolations at points on the real line which we refer to as the schur algorithm on the real line the paper is completed with several applications of fr functions to orthogonal polynomials and random and quantum walks which illustrate their wide interest an analogue for orthogonal polynomials on the real line of the khrushchev formula for orthogonal polynomials on the unit circle and the use of fr functions to study recurrence in random walks quantum walks and open quantum walks these applications provide numerous explicit examples of fr functions clarifying the meaning of these functions as first return generating functions and their splittings which become recurrence splitting rules they also show that these new tools despite being extensions of very classical ones play an important role in the study of physical problems of a highly topical nature

classical w algebras we reconsider the relation between classicalw algebras and deformations of differential operators emphasizing the consistency with diffeomorphisms generators of thew algebra that arek differentials are constructed by a systematic procedure the method extends following drinfeld and sokolov tow algebras based on arbitrary simple lie algebras

inverse methods for reconstruction of channel taps in ofdm systems we describe a novel pilot aided method for estimation of doubly selective wireless channels in ofdm systems we compute the first few fourier coefficients of each channel tap from the pilot information we then estimate the bem coefficients of the channel taps from their respective fourier coefficients using a recently developed inverse reconstruction method for a system with l channel taps the proposed method uses o l log l operations and o l memory per ofdm symbol we validate our method by simulating a system conforming to the ieee 802 16e standard

nondata aided joint channel estimation and equalization for ofdm systems in very rapidly varying mobile channels this paper is concerned with the challenging and timely problem of joint channel estimation and equalization for orthogonal frequency division multiplexing ofdm systems in the presence of frequency selective and very rapidly time varying channels the resulting algorithm is based on the space alternating generalized expectation maximization maximum a posteriori probability sage map technique which is particularly well suited to multicarrier signal formats the algorithm is implemented in the time domain which enables one to use the gaussian approximation of the transmitted ofdm samples consequently the averaging process of the nonpilot data symbols becomes analytically possible resulting in a feasible and computationally efficient channel estimation algorithm leading to a receiver structure that yields also an equalized output from which the data symbols are detected with excellent symbol error rate ser performance based on this gaussian approximation the exact bayesian cramer rao lower bound crlb as well as the convergence rate of the algorithm are derived analytically to reduce the computational complexity of the algorithm discrete legendre orthogonal basis functions are employed to represent the rapidly time varying fading channel it is shown that depending on the normalized doppler frequency only a small number of expansion coefficients is sufficient to approximate the channel very well and there is no need to know the correlation function of the input signal the computational complexity of the algorithm is shown to be o nl per detected data symbol and per sage map algorithm cycle where is the number of ofdm subcarriers and is the number of multipath components

contractive determinantal representations of stable polynomials on a matrix polyball we show that a polynomial p with no zeros on the closure of a matrix unit polyball a k a a cartesian product of cartan domains of type i and such that p 0 1 admits a strictly contractive determinantal representation i e p det i kz n where n n 1 ldots n k is a k tuple of nonnegative integers z n bigoplus r 1 k z r otimes i n r z r z r ij are complex matrices p is a polynomial in the matrix entries z r ij and k is a strictly contractive matrix this result is obtained via a noncommutative lifting and a theorem on the singularities of minimal noncommutative structured system realizations

low complexity affine mmse detector for iterative detection decoding mimo ofdm systems iterative turbo processing between detection and decoding shows near capacity performance on a multiple antenna system combining iterative processing with optimum front end detection is particularly challenging because the front end maximum a posteriori map algorithm has a computational complexity that is exponential sub optimum detector such as the soft interference cancellation linear minimum mean square error sic lmmse detector with near front end map performance has been proposed in the literature the asymptotic computational complexity of sic lmmse is o nt 2nr ntnr 3 ntmc2mc per detection decoding cycle where nt is number of transmit antenna nr is number of receive antenna and mc is modulation size a lower complexity detector is the hard interference cancellation lmmse hic lmmse detector hic lmmse has asymptotic complexity of o nt 2nr ntmc2mc but suffers extra performance degradation in this paper two front end detection algorithms are introduced that not only achieve asymptotic computational complexity of o nt 2nr ntnr 2 gamma beta 1 ntmc2mc where gamma beta is a function with discrete output 1 2 3 nt and o ntmc2mc respectively simulation results demonstrate that the proposed low complexity detection algorithms offer exactly same performance as their full complexity counterpart in an iterative receiver while being computational more efficient

bihamiltonian hierarchies in 2d topological field theory at one loop approximation we compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2d topological field theory the bihamiltonian structure of the hierarchy is given by a classical w algebra we compute the central charge of this algebra we also express the generating function of elliptic gromov witten invariants via tau function of the isomonodromy deformation problem arising in the theory of wdvv equations of associativity

optimum clustered pilot sequence for ofdm systems under rapidly time varying channel as channel time variation increases orthogonality among subcarriers in an orthogonal frequency division multiplexing ofdm symbol can be destroyed because of the relatively long symbol period whereupon intercarrier interference ici appears and hence an irreducible error floor occurs it was shown recently that grouping pilot tones into a number of equally spaced clusters can yield better channel estimation against the doubly selective channel than placing each pilot tone in an equally spaced manner however a random pilot sequence was used in the literature and an optimal sequence has not yet been studied this paper presents how to optimize the clustered pilot sequence first this paper a proves the existence of an optimum pilot sequence and b suggests a guideline for finding an optimum sequence second this paper shows that an optimum sequence is independent of the signal to noise ratio and doppler rate and the sequence is generally optimum for any channels third this paper verifies through analysis and simulation that the coded ofdm system with an optimized cluster pilot sequence can yield a smaller mean square channel estimation error and lower bit error rate than the system with an equidistance pilot or a random cluster pilot under a rapidly time varying channel

rational cayley inner herglotz agler functions positive kernel decompositions and transfer function realizations abstract the bessmertny class consists of rational matrix valued functions of d complex variables representable as the schur complement of a block of a linear pencil a z z 1 a 1 z d a d whose coefficients a k are positive semidefinite matrices we show that it coincides with the subclass of rational functions in the herglotz agler class over the right poly halfplane which are homogeneous of degree one and which are cayley inner the latter means that such a function is holomorphic on the right poly halfplane and takes skew hermitian matrix values on i r d or equivalently is the double cayley transform over the variables and over the matrix values of an inner function on the unit polydisk using agler knese s characterization of rational inner schur agler functions on the polydisk extended now to the matrix valued case and applying appropriate cayley transformations we obtain characterizations of matrix valued rational cayley inner herglotz agler functions both in the setting of the polydisk and of the right poly halfplane in terms of transfer function realizations and in terms of positive kernel decompositions in particular we extend bessmertny s representation to rational cayley inner herglotz agler functions on the right poly halfplane where a linear pencil a z is now in the form a z a 0 z 1 a 1 z d a d with a 0 skew hermitian and the other coefficients a k positive semidefinite matrices

matched filter bounds for wireless communication over rayleigh fading dispersive channels this letter extends the theory of the matched filter bound for fading dispersive channels we generalize to arbitrary fading as well as delay properties of the channel the channel model is a standard time varying linear filter and the calculation of the matched filter bound is based on a karhunen loeve expansion of the received pulse spectrum when an isolated pulse is transmitted results are presented illustrating the various diversity effects we conclude that in addition to the effect on probability of bit error of implicit delay diversity there is the less well known effect of implicit doppler diversity in fast fading the effect on probability of bit error of pulse shaping and explicit diversity is also illustrated

a spectral approach to inter carrier interference mitigation in ofdm systems in this paper we propose a new method for intercarrier interference ici mitigation in orthogonal frequency division multiplexing ofdm systems the proposed approach views the signal reconstruction problem at the receiver end as an integer least squares ils problem and uses a recently developed spectral approach called sequential probabilistic ils spils to solve it the proposed approach outperforms other state of the art approaches while having the same computational complexity in addition we present a novel extension to the spils scheme that allows the generation of soft decisions for communication systems which use soft decision decoding the use of soft decision decoding naturally brings significant improvement in the detection reliability and we show that the proposed method again outperforms other state of the art approaches to better address the tradeoff between performance and complexity we first suggest a novel method to reduce the number of matrix inversions required and hence to reduce the implementation complexity without any degradation in performance we also introduce a novel low complexity scheme termed quick spils qspils in which we lose a little in detection reliability but significantly reduce the implementation complexity index terms digital communications

low complexity equalization of time varying channels with precoding this correspondence deals with time varying tv single input multiple output simo channels which are both frequency selective due to high data rate and time selective due to mobility a complex exponential basis expansion model ce bem is used to model the channel we consider a block transmission system where on the transmit side a precoder is employed to enable the maximum available diversity for a ce bem channel after direct decoding on the receive side the resulting channel resembles a finite impulse response fir filter on both block and symbol level we therefore propose an equalizer that bears a structure analogous to the effective channel in comparison with a standard block minimum mean square error decision feedback equalizer bmmse dfe that involves the inversion of a large size matrix the proposed parametric equalizer renders a similar performance but at a lower computational cost if there are multiple outputs present another contribution of this correspondence is a semiblind algorithm to estimate this equalizer when the channel state information is not available the equalizer taps and the information symbol estimates are refined recursively by means of normalized least mean squares nlms adaptation

low complexity equalization for doubly selective channels modeled by a basis expansion we propose a novel equalization method for doubly selective wireless channels whose taps are represented by an arbitrary basis expansion model bem we view such a channel in the time domain as a sum of product convolution operators created from the basis functions and the bem coefficients equivalently a frequency domain channel can be represented as a sum of convolution products the product convolution representation provides a low complexity memory efficient way to apply the channel matrix to a vector we compute a regularized solution of a linear system involving the channel matrix by means of the gmres and the lsqr algorithms which utilize the product convolution structure without ever explicitly creating the channel matrix our method applies to all cyclic prefix transmissions in an ofdm transmission with k subcarriers each iteration of gmres or lsqr requires only o k k flops and o k memory additionally we further accelerate convergence of both gmres and lsqr by using the single tap equalizer as a preconditioner we validate our method with numerical simulations of a wimax like system ieee 802 16e in channels with significant delay and doppler spreads the proposed equalizer achieves bers comparable to those of mmse equalization and noticeably outperforms low complexity equalizers using an approximation by a banded matrix in the frequency domain with preconditioning the lowest bers are obtained within 3 16 iterations our approach does not use any statistical information about the wireless channel