the bunch kaufman factorization of symmetric matrices signature similar to sign regular matrices abstract the bunch kaufman pivoting strategy is a most commonly used method in practice to factor symmetric indefinite matrices however this method in general may destroy the band structure of banded matrices and its growth factor bound of 2 57 n 1 can almost be attained in this paper we investigate the behavior of the method for factorizing symmetric indefinite matrices that are signature similar to sign regular matrices with signature the growth factor bound depending on flips in the signature is derived for factorizing such banded matrices if the bunch kaufman pivoting strategy is modified as suggested by sorensen and van loan then not only do the same growth factor bounds hold but also the bandwidth is nicely preserved

scalar product of bethe vectors from functional equations in this work the scalar product of bethe vectors for the six vertex model is studied by means of functional equations the scalar products are shown to obey a system of functional equations originated from the yang baxter algebra and its solution is given as a multiple contour integral

sequence set design with good correlation properties via majorization minimization sets of sequences with good correlation properties are desired in many active sensing and communication systems e g multiple input multiple output mimo radar systems and code division multiple access cdma cellular systems in this paper we consider the problems of designing complementary sets of sequences css and also sequence sets with both good auto and cross correlation properties algorithms based on the general majorization minimization method are developed to tackle the optimization problems arising from the sequence set design problems all the proposed algorithms can be implemented by means of the fast fourier transform fft and thus are computationally efficient and capable of designing sets of very long sequences a number of numerical examples are provided to demonstrate the performance of the proposed algorithms

complete mutually orthogonal golay complementary sets from reed muller codes recently golay complementary sets were shown to exist in the subsets of second order cosets of a q ary generalization of the first order reed muller rm code we show that mutually orthogonal golay complementary sets can also be directly constructed from second order cosets of a q ary generalization of the first order rm code this identification can be used to construct zero correlation zone zcz sequences directly and it also enables the construction of zcz sequences with special subsets

quasi ldu factorization of nonsingular totally nonpositive matrices abstract let a a ij r n n be a nonsingular totally nonpositive matrix in this paper we describe some properties of these matrices when a11 0 and obtain a characterization in terms of the quasi ldu factorization of a where l is a block lower triangular matrix d is a diagonal matrix and u is a unit upper triangular matrix

integrability in time dependent systems with one degree of freedom the notion of integrability is discussed for classical nonautonomous systems with one degree of freedom the analysis is focused on models which are linearly spanned by finite lie algebras by constructing the autonomous extension of the time dependent hamiltonian we prove the existence of two invariants in involution which are shown to obey the criterion of functional independence the implication of this result is that chaotic motion cannot exist in these systems in addition if the invariant manifold is compact then the system is liouville integrable as an application we discuss regimes of integrability in models of dynamical tunneling and parametric resonance and in the dynamics of two level systems under generic classical fields a corresponding quantum algebraic structure is shown to exist which satisfies analog conditions of liouville integrability and reproduces the classical dynamics in an appropriate limit within the weyl wigner formalism the quantum analog is then conjectured to be integrable as well

new constructions of zero correlation zone sequences in this paper we propose three classes of systematic approaches for constructing zero correlation zone zcz sequence families in most cases these approaches are capable of generating sequence families that achieve the upper bounds on the family size and the zcz width for a given sequence period our approaches can produce various binary and polyphase zcz families with desired parameters and alphabet size they also provide additional tradeoffs amongst the above four system parameters and are less constrained by the alphabet size furthermore the constructed families have nested like property that can be either decomposed or combined to constitute smaller or larger zcz sequence sets we make detailed comparisons with related works and present some extended properties for each approach we provide examples to numerically illustrate the proposed construction procedure

the peak sidelobe level of families of binary sequences a numerical investigation is presented for the peak sidelobe level psl of legendre sequences maximal length shift register sequences m sequences and rudin shapiro sequences the psl gives an alternative to the merit factor for measuring the collective smallness of the aperiodic autocorrelations of a binary sequence the growth of the psl of these infinite families of binary sequences is tested against the desired growth rate o spl radic nlnn for sequence length n the claim that the psl of m sequences grows like o spl radic n which appears frequently in the radar literature is concluded to be unproven and not currently supported by data notable similarities are uncovered between the psl and merit factor behavior under cyclic rotations of the sequences

simplified ranging systems using discrete wavelet decomposition we employ the concepts and tools of the discrete wavelet transform dwt to encapsulate a body of previous research on efficiently analyzable phase coded waveforms for use in ranging applications this dwt perspective enables the direct synthesis of half rate implementations which are suitable for high speed applications we introduce and study a set of sequences based on a classical welti construction which are both dwt decomposable and exhibit a zero autocorrelation zone property under cyclic extension we propose a general extension technique which extends the zero correlation width while retaining the same simple receiver filter and show that this technique is appropriate for many of the sequences in our construction finally we propose a transmit waveform construction which allows a further reduction of two in the receiver hardware complexity we discuss the resulting tradeoffs between receiver complexity and transmit power

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

a class of pseudonoise sequences over gf p with low correlation zone a new class of pseudonoise sequences over gf p based on gordon mills welch 1962 sequences is constructed the sequences have the property that in a specified zone the out of phase autocorrelation and cross correlation values are all equal to 1 such sequences with low correlation zone lcz are suitable for approximately synchronized code division multiple access cdma system

efficient generation and correlation of sequence pairs with three zero correlation zones this paper presents three novel methods to efficiently generate and correlate sequence pairs with three zero correlation zones in the sum of their aperiodic correlation functions these sequences have achieved great importance in communications systems when the maximum transmission delay is less than the length of these zones because the multiple access interference mai and the intersymbol interference isi can be removed the proposed algorithms are based on the properties of complementary sets of sequences css and they offer an efficient hardware implementation of the corresponding generators and correlators that reduces the total number of operations to be performed in comparison with straightforward implementations that makes possible real time operation as well as the use of very long sequences

total nonpositivity of nonsingular matrices in this paper nonsingular totally nonpositive matrices are studied and new characterizations are provided in terms of the signs of minors with consecutive initial rows or consecutive initial columns these characterizations extend an existing characterization that uses some restrictive hypotheses

quantum integrability in systems with finite number of levels we consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners we argue that if the matrices depend on a real parameter one can define quantum integrability from this feature alone leading to specific results such as exact solvability poissonian energy level statistics and to level crossings

rudin shapiro like sequences with maximum asymptotic merit factor borwein and mossinghoff investigated the rudin shapiro like sequences which are infinite families of binary sequences usually represented as polynomials each family of rudin shapiro like sequences is obtained from a starting sequence which we call the seed by a recursive construction that doubles the length of the sequence at each step and many sequences produced in this manner have exceptionally low aperiodic autocorrelation borwein and mossinghoff showed that the asymptotic autocorrelation merit factor for any such family is at most 3 and found the seeds of length 40 or less that produce the maximum asymptotic merit factor of 3 the definition of rudin shapiro like sequences was generalized by katz lee and trunov to include sequences with arbitrary complex coefficients among which are families of low autocorrelation polyphase sequences katz lee and trunov proved that the maximum asymptotic merit factor is also 3 for this larger class here we show that a family of such rudin shapiro like sequences achieves asymptotic merit factor 3 if and only if the seed is either of length 1 or is the interleaving of a pair of golay complementary sequences for small seed lengths where this is not possible the optimal seeds are interleavings of pairs that are as close as possible to being complementary pairs and the idea of an almost complementary pair makes sense of remarkable patterns in previously unexplained data on optimal seeds for binary rudin shapiro like sequences

paraunitary filter banks over finite fields in real and complex fields unitary and paraunitary pu matrices have found many applications in signal processing there has been interest in extending these ideas to the case of finite fields we study the theory of pu filter banks fbs in gf q with q prime various properties of unitary and pu matrices in finite fields are studied in particular a number of factorization theorems are given we show that i all unitary matrices in gf q are factorizable in terms of householder like matrices and permutation matrices and ii the class of first order pu matrices the lapped orthogonal transform in finite fields can always be expressed as a product of degree one or degree two building blocks if q 2 we do not need degree two building blocks while many properties of pu matrices in finite fields are similar to those of pu matrices in complex field there are a number of differences for example unlike the conventional pu systems in finite fields there are pu systems that are unfactorizable in terms of smaller building blocks in fact in the special case of 2 spl times 2 systems all pu matrices that are factorizable in terms of degree one building blocks are diagonal matrices we derive results for both the cases of gf 2 and gf q with q 2 even though they share some similarities there are many differences between these two cases

complementary sets of non power of two length for peak to average power ratio reduction in ofdm golay complementary sequences and complementary sets have been proposed to deal with the high peak to average power ratio papr problem in orthogonal frequency division multiplexing ofdm system the existing constructions of complementary sets based on generalized boolean functions are limited to lengths which are powers of two in this paper we propose novel constructions of binary and nonbinary complementary sets of non power of two length regardless of whether or not the length of the complementary set is a power of two its papr is still upper bounded by the size of the complementary set therefore the constructed complementary sets can be applied in practical ofdm systems where the number of used subcarriers is not a power of two in addition while the binary golay complementary pairs exist only for limited lengths the constructed binary complementary sets of size 4 exist for more lengths with papr at most 4

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

a new framework for constructing mutually orthogonal complementary sets and zcz sequences in this correspondence new characterizations for the construction of zero correlation zone zcz sequences from mutually orthogonal golay complementary sets mogcs is presented it is shown that the recursive construction of mogcs is inherent in these characterizations previously known constructions of zcz sequences and mogcs are shown to be special cases of this characterization the notion of mutually orthogonal zcz sequence sets is also introduced

ds cdma signature sequences based on pr qmf banks in this paper we propose two classes of multivalued signature sequences for direct sequence code division multiple access ds cdma systems the proposed classes are obtained from the coefficients of the subbands of perfect reconstruction quadrature mirror filterbanks pr qmf the first and second classes are derived from the tree and lattice structure pr qmf banks respectively and they both have perfect correlation properties for synchronous ds cdma systems the second class in addition has generally better correlation properties than other well known sequences in asynchronous ds cdma systems some numerical results for the performance of the asynchronous ds cdma systems with several sequences including the second class of sequences are obtained

theoretical issues on lti systems that preserve signal richness in this paper theoretical issues about linear time invariant lti systems that preserve signal richness are explored this paper considers two particular definitions of signal richness and finds the necessary and sufficient conditions under which an lti system preserves the richness property several examples are presented to clarify the issues involved in the problem paraunitary pu and unimodular matrices can be shown not to preserve richness unless they are constant matrices or a delayed version in the pu case some richness preserving properties of cascaded systems are also investigated a structured proof of the necessary and sufficient conditions is presented the relationship between persistent excitation pe and the proposed definitions of richness is also described

a systematic framework for the construction of optimal complete complementary codes the complete complementary code ccc that was proposed by suehiro and hatori is a sequence family that is a set of sequence sets with ideal correlation sums numerous studies in the literature show its applications to direct spread code division multiple access ds cdma systems for interchannel interference ici free communication with improved spectral efficiency in this paper we propose a systematic framework for the construction of cccs based on n shift cross orthogonal sequence families n co sfs we show theoretical bounds on the size of n co sfs and cccs and give a set of four algorithms for their generation and extension the algorithms are optimal in the sense that the size of the resultant sequence families achieves theoretical bounds and with the algorithms we can construct an optimal ccc consisting of sequences whose lengths are not only almost arbitrary but even variable between sequence sets we also discuss the family size alphabet size and length of constructible cccs based on the proposed algorithms

a new class of zero correlation zone sequences in this correspondence two new methods for constructing sets of zero correlation zone zcz sequences are proposed these methods are based on perfect sequences and unitary matrices compared with previous methods the proposed methods can generate sets of nonbinary zcz sequences having a longer zero correlation zone the sequences obtained by these methods are suitable for approximately synchronized code division multiple access as cdma systems

characterizations of jacobi sign regular matrices abstract several characterizations of jacobi nonsingular sign regular matrices are presented moreover a stable test of o n elementary operations is obtained to check if an n n jacobi nonsingular matrix is sign regular

new optimal z complementary code sets based on generalized paraunitary matrices the concept of paraunitary pu matrices arose in the early 1990 s in the study of multi rate filter banks these matrices have found wide applications in cryptography digital signal processing and wireless communications existing pu matrices are subject to certain constraints on their existence and hence their availability is not guaranteed in practice motivated by this for the first time we introduce a novel concept called z paraunitary zpu matrix whose orthogonality is defined over a matrix of polynomials with identical degree not necessarily taking the maximum value we show that there exists an equivalence between a zpu matrix and a z complementary code set when the latter is expressed as a matrix with polynomial entries furthermore we investigate some important properties of zpu matrices which are useful for the extension of matrix sizes and sequence lengths we propose a new construction framework for optimal zpu matrices which includes existing pu matrices as special cases finally we give the enumeration formula for the constructed z complementary sequences from the optimal zpu matrices

construction of orthogonal and nearly orthogonal designs for computer experiments this paper presents new infinite families of orthogonal designs for computer experiments in cases where orthogonal designs cannot exist we construct alternative nearly orthogonal designs our designs can accommodate many factors and a large set of levels no iterative computer search is required to build up the desired orthogonal designs we develop and use new infinite classes of periodic golay pairs

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

quantum integrability and nonintegrability in the spin boson model we study the spectral properties of a spin boson hamiltonian that depends on two continuous parameters 0 or lambda infinity interaction strength and 0 or alpha or pi 2 integrability switch in the classical limit this system has two distinct integrable regimes alpha 0 and alpha pi 2 for each integrable regime we can express the quantum hamiltonian as a function of two action operators their eigenvalues multiples of variant planck s over 2pi are the natural quantum numbers for the complete level spectrum this functional dependence cannot be extended into the nonintegrable regime 0 alpha pi 2 here level crossings are prohibited and the level spectrum is naturally described by a single energy sorting quantum number in consequence the tracking of individual eigenstates along closed paths through both regimes leads to conflicting assignments of quantum numbers this effect is a useful and reliable indicator of quantum chaos a diagnostic tool that is independent of any level statistical analysis

a complete description of golay pairs for lengths up to 100 in his 1961 paper marcel golay showed how the search for pairs of binary sequences of length n with complementary autocorrelation is at worst a 2 6 problem andres in his 1977 master s thesis developed an algorithm which reduced this to a 2 n 2 1 search and investigated lengths up to 58 for existence of pairs in this paper we describe refinements to this algorithm enabling a 2 n 2 5 search at length 82 we find no new pairs at the outstanding lengths 74 and 82 in extending the theory of composition we are able to obtain a closed formula for the number of pairs of length 2 k n generated by a primitive pair of length n combining this with the results of searches at all allowable lengths up to 100 we identify five primitive pairs all others pairs of lengths less than 100 may be derived using the methods outlined

polyphase codes for uplink ofdm cdma systems we propose a ofdm cdma system that employs polyphase codes to support variable spreading factors a systematic approach for constructing the polyphase code sequences of variable spreading factors is developed polyphase codes exhibit better auto and cross correlation properties than hadamard codes when employed in ofdm cdma systems polyphase codes result in certain structured multiple access interference mai caused by multipath analytical and numerical results show that ofdm cdma systems employing polyphase codes have better papr performance than those using hadamard codes the ber performance of the ofdm cdma system using polyphase codes is evaluated by numerical results and compared to that of the ofdm cdma system using hadamard codes with and without clipping

a test and bidiagonal factorization for certain sign regular matrices abstract it is well known that a totally nonnegative matrix can be characterized in terms of its bidiagonal factorization which is critical to perform accurate computations however there is no known such factorization of other sign regular matrices in this paper we provide a characterization and test for certain sign regular matrices with the same signature sequence as that of nonsingular jacobi sign regular matrices consequently a bidiagonal factorization is derived for such sign regular matrix which in turn provides an effective way to generate these sign regular matrices

total positivity and neville elimination abstract neville elimination is described in terms of schur complements of matrices and used to improve some well known characterizations of totally positive and strictly totally positive matrices

ber minimized ofdm systems with channel independent precoders we consider the minimization of uncoded bit error rate ber for the orthogonal frequency division multiplexing ofdm system with an orthogonal precoder we analyze the ber performance of precoded ofdm systems with zero forcing and minimum mean squared error mmse receivers in the case of mmse receivers we show that for quadrature phase shift keying qpsk there exists a class of optimal precoders that are channel independent examples of this class include the discrete fourier transform dft matrix and the hadamard matrix when the precoder is the dft matrix the resulting optimal transceiver becomes the single carrier system with cyclic prefix sc cp system we also show that the worst solution corresponds to the conventional ofdm system the conventional ofdm system has the largest ber in the case of zero forcing receivers the design of optimal transceiver depends on the signal to noise ratio snr for higher snr solutions of optimal precoders are the same as those of mmse receivers

integrability by separation of variables abstract we study the integrability in the jacobi sense integrability by separation of variables of the hamiltonian differential systems using the levi civita theorem in particular we solve the stark problem for n 3

on nonsingular sign regular matrices abstract an m n matrix a is sign regular if for each k 1 k min m n all k k submatrices of a have determinant with the same nonstrict sign the zero pattern of nonsingular sign regular matrices is analyzed it is proved that the number of zero entries which can appear in a nonsingular sign regular matrix depends on its signature a matrix is totally nonpositive if all its minors are nonpositive a test for recognizing nonsingular totally nonpositive matrices is also provided

antipodal paraunitary matrices and their application to ofdm systems paraunitary pu matrices and filterbanks have played an important role in many applications this paper studies a special class of pu matrices called antipodal paraunitary apu matrices apu matrices are pu matrices whose coefficient matrices consist of spl plusmn 1 only several new methods will be introduced for the construction of apu matrices in particular a new method based on the butterfly structure that has a low cost implementation is proposed moreover one application of apu matrices in precoded orthogonal frequency division multiplexing ofdm systems will be considered by using an apu precoding matrix the complexity will be very low and experiments show that the use of apu matrices can greatly enhance the performance

a remark on the notion of independence of quantum integrals of motion in the thermodynamic limit studies of integrable quantum many body systems have a long history with an impressive record of success however surprisingly enough an unambiguous definition of quantum integrability remains a matter of an ongoing debate we contribute to this debate by dwelling upon an important aspect of quantum integrability the notion of independence of quantum integrals of motion qims we point out that a widely accepted definition of functional independence of qims is flawed and suggest a new definition our study is motivated by the pxp model a model of n spins 1 2 possessing an extensive number of binary qims the number of qims which are independent according to the common definition turns out to be equal to the number of spins n a common wisdom would then suggest that the system is completely integrable which is not the case we discuss the origin of this conundrum and demonstrate how it is resolved when a new definition of independence of qims is employed

a construction of multiple optimal zcz sequence sets with good cross correlation zero correlation zone zcz sequences are a class of spreading sequences having ideal auto correlation and cross correlation in a zone around the origin they have been extensively studied in recent years due to their important applications in quasi synchronous code division multiple access systems in this paper a construction of zcz sequence sets is proposed based on perfect nonlinear functions it generates multiple zcz sequence sets with the properties 1 each sequence is perfect in the sense that its out of phase auto correlation is always zero 2 each zcz sequence set is optimal with respect to the tang fan matsufuji bound in which all the sequences are pairwise cyclically distinct and 3 the maximum inter set cross correlation of multiple sequence sets achieves the well known sarwate bound

sign regular matrices and neville elimination abstract a pivoting strategy of o n operations for the neville elimination of n n nonsingular sign regular matrices is introduced among other nice properties it is proved that it preserves sign regularity it is also shown its relationship with scaled partial pivoting strategies for neville elimination

componentwise error analysis for linear systems associated with sign regular matrices in this paper we present a componentwise error analysis of solving linear systems whose coefficient matrices are sign regular matrices with the same signature sequences as those of jacobi sign regular matrices associated with corner cutting algorithms in computer aided geometric design it is interesting to show that for such sign regular matrices in finite precision floating point arithmetic the computed factors by gaussian elimination with the last two row exchanges satisfy a small componentwise relative backward error consequently the computed solutions of linear systems associated with such matrices admit pleasantly small componentwise relative backward errors

paraunitary based boolean generator for qam complementary sequences of length 2 k a boolean generator for a large number of standard complementary qam sequences of length 2 k is proposed this boolean generator is derived from the authors earlier paraunitary generator which is based on matrix multiplications both generators are based on unitary matrices in contrast to previous boolean qam algorithms which represent complementary sequences as a weighted sum our algorithm has a multiplicative form any element of a sequence can be generated efficiently by indexing the entries of unitary matrices with the binary representation of the discrete time index which is easily implemented as a binary counter our 1qum based on one qam unitary matrix and 2qum based on two qam unitary matrices algorithms generate generalized case i iii sequences and generalized case iv and v sequences respectively as specified by liu et al in 2013 in addition to many new 2qum sequences the ratio of the numbers of sequences that are generated by our new construction and the previous construction increases with the constellation size for example for a 1024 qam sequence of length 1024 this ratio is 4 4 however if we compare only 2qum sequences to case iv and v sequences this ratio is 267

theory and design of m channel maximally decimated quadrature mirror filters with arbitrary m having the perfect reconstruction property based on the concept of losslessness in digital filter structures this paper derives a general class of maximally decimated m channel quadrature mirror filter banks that lead to perfect reconstruction the perfect reconstruction property guarantees that the reconstructed signal hat x n is a delayed version of the input signal x n i e hat x n x n n 0 it is shown that such a property can be satisfied if the alias component matrix ac matrix for short is unitary on the unit circle of the z plane the number of channels m is arbitrary and when m is two the results reduce to certain recently reported 2 channel perfect reconstruction qmf structures a procedure based on recently reported fir cascaded lattice structures is presented for optimal design of such fir m channel filter banks design examples are included

the problem of quantum integrability abstract the notion of integrability in quantum mechanics is investigated in order to prepare rigorous grounds for the study of regular and irregular behaviour of quantum systems its common sense definition turns out to have deficiencies which are illustrated by various explicit examples part of the ambiguities are shown to have their origin in the difficulty of transferring the concept of independent constants of motion into quantum mechanics due to a fundamental theorem on sets of commuting operators by von neumann taking into account the classical limit with coherent states does not resolve the problems as a result it is pointed out why the appealing phenomenological distinction between regular and chaotic quantum systems cannot be traced back to the present notion of quantum integrability in a mathematically rigorous way

minimum ber block precoders for zero forcing equalization we determine the linear precoder that minimizes the bit error rate ber at moderate to high signal to noise ratios snrs for block transmission systems with zero forcing zf equalization and threshold detection the design is developed for the two standard schemes for eliminating inter block interference viz zero padding zp and cyclic prefix cp we show that both the zp minimum ber precoder and the cp minimum ber precoder provide substantially lower error rates than standard block transmission schemes such as orthogonal frequency division multiplexing ofdm the corresponding snr gains can be on the order of several decibels we also show that the cp minimum ber precoder can be obtained by a two stage modification of the water filling discrete multitone modulation dmt scheme in which the diagonal water filling power loading is replaced by a full matrix consisting of a diagonal minimum mean square error power loading matrix post multiplied by a discrete fourier transform dft matrix

full rank factorization in quasi ldu form of totally nonpositive rectangular matrices abstract let a a i j r n m be a totally nonpositive matrix with rank a r min n m and a 11 0 in this paper we obtain a characterization in terms of the full rank factorization in quasi ldu form that is a l d u where l r n r is a block lower echelon matrix u r r m is a unit upper echelon totally positive matrix and d r r r is a diagonal matrix with rank l rank u rank d r we use this quasi ldu decomposition to construct the quasi bidiagonal factorization of a moreover some properties about these matrices are studied

stringent numerical test of the poisson distribution for finite quantum integrable hamiltonians using a class of exactly solvable models based on the pairing interaction we show that it is possible to construct integrable hamiltonians with a wigner distribution of nearest neighbor level spacings however these hamiltonians involve many body interactions and the addition of a small integrable perturbation very quickly leads the system to a poisson distribution besides this exceptional case we show that the accumulated distribution of an ensemble of random integrable two body pairing hamiltonians is in perfect agreement with the poisson limit these numerical results for quantum integrable hamiltonians provide a further empirical confirmation of the work of berry and tabor in the semiclassical limit

quantum integrability of quadratic killing tensors quantum integrability of classical integrable systems given by quadratic killing tensors on curved configuration spaces is investigated it is proven that using a minimal quantization scheme quantum integrability is ensured for a large class of classic examples

integrability and level crossing manifolds in a quantum hamiltonian system we consider a two spin model represented classically by a nonlinear autonomous hamiltonian system with two degrees of freedom and a nontrivial integrability condition and quantum mechanically by a real symmetric hamiltonian matrix with invariant blocks of dimensionalities k frac 1 2 l l 1 l 1 2 dots in the six dimensional parameter space of this model classical integrability is satisfied on a five dimensional hypersurface and level crossings occur on four dimensional manifolds that are completely embedded in the integrability hypersurface except for some lower dimensional submanifolds under mild assumptions the classical integrability condition can be reconstructed from a purely quantum mechanical study of level degeneracies in finite dimensional invariant blocks of the hamiltonian matrix our conclusions are based on rigorous results for k 3 and on numerical results for k 6 10

generation and correlation architectures of multilevel complementary sets of sequences complementary sets of sequences css are used extensively in many applications as channel estimation and synchronization preamble or as a basic block for the generation of generalized orthogonal go sequences nevertheless binary css exist for very limited lengths while for multilevel css there are fewer limitations in the sequence length this paper presents two modular architectures for the generation and correlation of k multilevel css an algorithm for k 2k k n 0 multilevel css and another for k 3 4 multilevel css in contrast to previous generation algorithms the proposed architectures reduce the number of computations needed to perform the correlation of k multilevel css when compared to those required with a straightforward architecture furthermore these architectures can be used as a starting point for the search of multilevel css with low peak to average power ratio papr and flexible length

a test for strict sign regularity a characterization of strict sign regular matrices is obtained it is given in an algorithmic form which allows the easy construction of a test to check if a matrix is strictly sign regular the test is based on the neville elimination of several submatrices of a and requires less computational work than those which can be derived from other previously known characterizations of these matrices

quantum chaos delocalization and entanglement in disordered heisenberg models we investigate disordered one and two dimensional heisenberg spin lattices across the transition from integrability to quantum chaos from both statistical many body and quantum information perspectives special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics delocalization and entanglement in the presence of nontrivial symmetries the implication of the basis dependence of state delocalization indicators such as the number of principal components is addressed and a measure of relative delocalization is proposed in order to robustly characterize the onset of chaos in the presence of disorder both standard multipartite and generalized entanglement are investigated in a wide parameter regime by using a family of spin and fermion purity measures their dependence on delocalization and on energy spectrum statistics being examined a distinctive correlation between entanglement delocalization and integrability is uncovered which may be generic to systems described by the two body random ensemble and may point to a new diagnostic tool for quantum chaos analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full hilbert space are also established and compared with random matrix theory predictions

classical versus quantum integrability classical integrability and quantum integrability are compared for two degrees of freedom hamiltonian systems we use c number representatives for quantum operators and the moyal bracket for the commutator three different cases are found i the c number representative of the quantum mechanical second invariant is identical to the classical second invariant ii o 2 corrections are needed in the classical second invariant to obtain the quantum invariant and iii also the potential must be deformed by an o 2 term several examples from the henon heiles and holt families of integrable potentials are included

hamiltonians separable in cartesian coordinates and third order integrals of motion we present in this article all hamiltonian systems in e 2 that are separable in cartesian coordinates and that admit a third order integral both in quantum and in classical mechanics many of these superintegrable systems are new and it is seen that there exists a relation between quantum superintegrable potentials invariant solutions of the korteweg de vries equation and the painleve transcendents

variation diminishing transformations a direct approach to total positivity and its statistical applications abstract karlin has shown that the variation diminishing property possessed by totally positive distributions allows a unified and straightforward presentation of many basic properties of hypothesis tests his work in fact reveals that total positivity is equivalent to a suitably formulated variation diminishing property this largely expository article begins with the latter concept and consequently gives a more direct account of the theory this approach avoids the extensive mathematical preliminaries previously required and isolates the more important statistical property

complementary set matrices satisfying a column correlation constraint motivated by the problem of reducing the peak to average power ratio papr of transmitted signals we consider a design of complementary set matrices whose column sequences satisfy a correlation constraint the design algorithm recursively builds a collection of 2t 1 mutually orthogonal mo complementary set matrices starting from a companion pair of sequences we relate correlation properties of column sequences to that of the companion pair and illustrate how to select an appropriate companion pair to ensure that a given column correlation constraint is satisfied for t 0 companion pair properties directly determine matrix column correlation properties the proposed companion pair based design can construct binary complementary sets with either a minimum out of phase autocorrelation magnitude or a minimum sum of out of phase autocorrelation magnitude for column sequences of length at least up to 28 for t ges 1 reducing correlation merits of the companion pair may lead to improved column correlation properties exhaustive search for companion pairs satisfying a column correlation constraint is infeasible for medium length and long sequences we instead search for two shorter length sequences by minimizing a cost function in terms of their autocorrelation and cross correlation merits in addition by exploiting the well known welch bound sufficient conditions for the existence of companion pairs which satisfy a set of column correlation constraints are given

a framework for the construction ofgolay sequences in 1999 davis and jedwab gave an explicit algebraic normal form for m 2 2h m 1 ordered golay pairs of length 2mmiddot over z2h involving m 2 2h m 1 golay sequences in 2005 li and chu unexpectedly found an additional 1024 length 16 quaternary golay sequences fiedler and jedwab showed in 2006 that these new golay sequences exist because of a crossover of the aperiodic autocorrelation function of certain quaternary length eight sequences belonging to golay pairs and that they spawn further new quaternary golay sequences and pairs of length 2m for m 4 under budisin s 1990 iterative construction the total number of golay sequences and pairs spawned in this way is counted and their algebraic normal form is given explicitly a framework of constructions is derived in which turyn s 1974 product construction together with several variations plays a key role all previously known golay sequences and pairs of length 2m over z2h can be obtained directly in explicit algebraic normal form from this framework furthermore additional quaternary golay sequences and pairs of length 2m are produced that cannot be obtained from any other known construction the framework generalizes readily to lengths that are not a power of 2 and to alphabets other than z2h

kronecker products unitary matrices and signal processing applications discrete unitary transforms are extensively used in many signal processing applications and in the development of fast algorithms kronecker products have proved quite useful in this semitutorial paper we briefly review properties of kronecker products and direct sums of matrices which provide a compact notation in treating patterned matrices a generalized matrix product which inherits some useful algebraic properties from the standard kronecker product and allows a large class of discrete unitary transforms to be generated from a single recursion formula is then introduced the notation is intimately related to sparse matrix factorizations and examples are included illustrating the utility of the new notation in signal processing applications finally some novel characteristics of hadamard transforms and polyadic permutations are derived in the framework of kronecker products

on the autocorrelation properties of truncated maximum length sequences and their effect on the power spectrum truncated maximum length binary sequences are studied in this paper the impact of truncation on their autocorrelation properties and power spectral density is investigated several new analytical results are given and validated through simulation the first and second order statistics of the periodic autocorrelation function and the spectral peak amplitudes over the ensemble of all possible starting seeds are analyzed explicit bounds are found for the mean square of the periodic autocorrelation function an analytical technique for evaluating the maximum spectral peak values is derived as a case study high data rate space links using lfsr randomizers are considered truncation may induce high peaks in the spectrum requiring suitable margins to comply with power flux density constraints the new results allow to analytically estimate the margin providing useful information for the link design

generalized signal richness preservation problem and vandermonde form preserving matrices in this paper a theoretical problem arising in digital communications namely the generalized signal richness preservation problem is addressed and studied in order to solve the problem a special class of square matrices namely the vandermonde form preserving vfp matrices is introduced and found to be highly relevant to the problem several properties of vfp matrices are studied in detail the necessary and sufficient conditions of the problem have been found and a systematic proof is also presented

n shift cross orthogonal sequences n shift cross orthogonal sequences and a complete complementary code derived from them are defined and discussed a general method for generating this code is also discussed a synchronous multiple user spread spectrum multiple system is proposed that uses n shift cross orthogonal sequences

efficient architectures for the generation and correlation of binary css derived from different kernel lengths complementary sets of sequences css are used as basic building blocks for the development of generalized orthogonal go sequences in the design of practical sequences are desirable both optimal correlation properties and an efficient implementation of their corresponding correlators i e with a reduced number of operations per input sample traditionally the efficient algorithms for the generation correlation of k binary css have been constrained to those of lengths l kn where k 2 and n is a non negative integer this constraint implies that many binary css of known lengths cannot be generated and correlated efficiently thus limiting their practical application this paper proposes novel efficient architectures for the generation and correlation of k binary css of length l k 2 2n 10m 26p with n m and p non negative integers the proposal allows the efficient generation and correlation of binary css of many more lengths than previous efficient architectures can handle therefore the use of the proposed architectures allows selecting with more flexibility the processing gain needed for each particular application

modular architecture for efficient generation and correlation of complementary set of sequences golay sequences and complementary sets of sequences have been long studied for their application in multisensor and communication systems the feasibility of these systems strongly depends on the design of an efficient generator and correlator with the aim of reducing the computational load and hardware complexity recursive algorithms which allow efficient architectures are available in the case of complementary pairs of sequences and complementary sets of four sequences this work presents a generalization of these algorithms with the purpose of obtaining complementary sets of m sequences with length l the number of sequences m being a power of two m 2m and the length l a power of m l 2mn with m nisin n 0 this fact allows an ideal kroumlnecker delta function of weight mmiddotl in the addition of the autocorrelation functions of the m sequences of the set furthermore the generation of m different mutually orthogonal sets can be obtained this fact makes their application suitable in simultaneous multiemission systems with the proposed algorithm an effective reduction in the number of operations necessary to implement the correlator can be obtained if it is compared with the straightforward implementation also a regular structure is provided that allows implementation of the generator and or the correlator for complementary sets of m sequences based on the structure for complementary sets of m 2 sequences the sequence length can also be easily extended to any multiple of m finally the generation and correlation of m different mutually orthogonal complementary sets of m sequences can be immediately derived

a note concerning quantum integrability heuristic arguments are presented supporting the conjecture that almost all quantum hamiltonians are integrable in the sense that there exist n n number of freedoms mutually commuting observables which in analogy with the classical action variables can be chosen to be the number operators this follows from perturbational considerations the series may converge for almost all perturbations that preserve the discreteness of the spectra because a quantum small denominator almost always uniformly satisfies the condition of sufficient irrationality the radius of convergence vanishes if h cross 0 the classical limit as h cross to 0 of the quantum integrals of motion generically does not exist

nonsingular almost strictly sign regular matrices abstract the class of nonsingular almost strictly totally positive matrices has been characterized m gasca j m pena characterizations and decompositions of almost strictly positive matrices siam j matrix anal appl 28 2006 1 8 in this paper we discuss the class of almost strictly sign regular matrices that includes almost strictly totally positive matrices a characterization is provided for these matrices in terms of their nontrivial minors using consecutive rows and consecutive columns in particular we present a characterization of certain almost strictly sign regular matrices in terms of a very reduced number of boundary almost trivial minors

general factorization of conjugate symmetric hadamard transforms complex valued conjugate symmetric hadamard transforms bbc csht are variants of complex hadamard transforms and found applications in signal processing in addition their real valued transform counterparts bbr cshts perform comparably with hadamard transforms hts despite their lower computational complexity closed form factorizations of bbc cshts and bbr cshts have recently been proposed to make calculations more efficient however there is still room to find effective and general factorizations this paper presents a simple closed form complete factorization of bbc cshts based on that of bbr cshts the proposed factorization can be applied to both bbc and bbr cshts with one factorization and it provides several benefits 1 it can save total implementation costs for both bbc cshts and bbr cshts 2 the generalized bbr csht factorization significantly reduces its computational cost 3 memory saved local orientation detection of images can be achieved 4 a fast direction aware transform can be attained 5 it clarifies that bbc and bbr cshts are closely related to common block transforms such as the discrete fourier transform dft bindct and ht and 6 it achieves a new integer complex valued transform which can approximate the dft better than the original bbc csht the image orientation estimation and performance in image coding of our bbr cshts were evaluated through examples of practical applications based on the proposed factorization

computational design of sequences with good correlation properties in this paper we introduce a computational framework based on an iterative twisted approximation itrox and a set of associated algorithms for various sequence design problems the proposed computational framework can be used to obtain sequences or complementary sets of sequences possessing good periodic or aperiodic correlation properties and in an extended form to construct zero or low correlation zone sequences furthermore as constrained e g finite alphabets are of interest in many applications we introduce a modified version of our general framework that can be useful in these cases several applications of itrox are studied and numerical examples focusing on the construction of real valued and binary sequences are provided to illustrate the performance of itrox for each application

a matricial description of neville elimination with applications to total positivity abstract the neville elimination process used by the authors in some previous papers in connection with totally positive matrices is studied in detail in the case of nonsingular matrices a wide class of matrices is found where neville elimination has a lower computational cost than gauss elimination finally some new characterizations are obtained for strictly totally positive and nonsingular totally positive matrices in terms of their neville elimination and that of their inverses

a new construction framework for polyphase complete complementary codes with various lengths complete complementary codes ccc with equal sequence lengths have found numerous applications in wireless communications owing to their ideal correlation properties in modern multi user multi rate communication systems cccs with various sequence lengths for different complementary codes are desirable in this paper we propose a new construction of polyphase ccc with various lengths by using unimodular paraunitary pu matrices our key idea is to decompose a large square pu matrix into direct sum of matrices with smaller sizes which is equivalent to block diagonalization of matrices in order to construct ccc with various lengths we show that our proposed constructions not only generalize several previously known methods but also lead us to new cccs with both equal and various lengths