optimum sequence multisets for synchronous code division multiple access channels it is shown that the sum capacity of the symbol synchronous code division multiple access channel with equal average input energy constraints is maximized precisely by those spreading sequence multisets that meet welch s lower bound on total squared correlation it is further shown that the symmetric capacity of the channel determined by these same sequence multisets is equal to the sum capacity

the combinatorial structure of generalized eigenspaces from nonnegative matrices to general matrices abstract the perron frobenius spectral theory of nonnegative matrices motivated an intensive study of the relationship between graph theoretic properties and spectral properties of matrices while for about seventy years research focused on nonnegative matrices in the past fifteen years the study has been extended to general matrices over an arbitrary field one of the major original problems in this context is determining the relations between the matrix analytic height characteristic of a matrix and the graph theoretic level characteristic in this article the history of this problem is reviewed from its introduction for nonnegative matrices through its complete solution for nonnegative matrices to the solution of the generalized version of the problem for general matrices

experiments with some low order finite element schemes for the navier stokes equations abstract it is shown how a consistent finite element approximation to the navier stokes equations can be constructed on a general grid using an arrangement equivalent to the mac stencil it is known that the standard galerkin construction does not give a consistent result unless at least quadratic velocities are used in this type of element however the use of either a finite difference approximation to the pressure gradient term or a galerkin scheme equivalent to a vorticity method appears to give a consistent scheme both alternatives are tested and the vorticity method is shown to be superior

cdma codeword optimization interference avoidance and convergence via class warfare interference avoidance has been shown to reduce total square correlation tsc for given ensembles of user signature waveforms codewords in a synchronous code division multiple access cdma system in all experiments we have conducted sequential application of interference avoidance produces an optimal codeword set when starting from randomly chosen initial codewords here we provide the first formal proof of convergence to optimal codeword ensembles for greedy interference avoidance algorithms augmented by a technique called class warfare whereby users which reside in more heavily loaded areas of the signal space purposely interfere with attack the reception of users in less crowded areas coordination of deliberate interference by a complete class of aggrieved user is also sometimes necessary such attacks and subsequent codeword adjustment by attacked users are shown to strictly decrease tsc along the way we also show using linear algebra and a variant of stochastic ordering equivalence between minimization of tsc and maximization of sum capacity

matrix roots of eventually positive matrices abstract eventually positive matrices are real matrices whose powers become and remain strictly positive as such eventually positive matrices are a fortiori matrix roots of positive matrices which motivates us to study the matrix roots of primitive matrices using classical matrix function theory and perron frobenius theory we characterize classify and describe in terms of the real jordan canonical form the p th roots of eventually positive matrices

bandwidth constrained signature waveforms and walsh signal space receivers for synchronous cdma systems synchronous cdma systems whose transmission bandwidth is quantified through the fractional out of band energy fobe constraint are considered either a conventional matched filter mf receiver or a minimum mean square error mmse receiver is employed for users data detection the total squared correlation tsc and the total mean square error tmse are proposed as the performance parameters for the mf and mmse receivers respectively these parameters need to be minimized in order to maximize the signal to interference ratios sirs at the receivers outputs for a given fobe bandwidth constraint the sets of signature waveforms that minimize either tsc or tmse are obtained from the prolate spheroidal wave functions pswfs furthermore if the number of users is the size of a hadamard matrix then optimal signature waveforms can be obtained to maximize the individual sir for every user due to the complicated nature of the pswfs simplified mf and mmse receivers based on the walsh signal space are developed

optimal sequences and sum capacity of synchronous cdma systems the sum capacity of a multiuser synchronous cdma system is completely characterized in the general case of asymmetric user power constraints this solves the open problem posed by rupf and massey see ibid vol 40 p 1261 6 1994 which had solved the equal power constraint case we identify the signature sequences with real components that achieve sum capacity and indicate a simple recursive algorithm to construct them

inverses of m type matrices created with irreducible eventually nonnegative matrices abstract an m matrix is a matrix that can be expressed as i p where p is entry wise nonnegative and p it is well known that the inverse of a nonsingular irreducible m matrix is positive in this paper matrices of the form i p where p is an irreducible eventually nonnegative matrix and p are studied it is shown that if index 0 p 1 then there exists a positive number such that if p then the inverse of i p is positive

maximizing the spectral efficiency of coded cdma under successive decoding we investigate the spectral efficiency achievable by random synchronous code division multiple access cdma with quaternary phase shift keying qpsk modulation and binary error control codes in the large system limit where the number of users the spreading factor and the code block length go to infinity for given codes we maximize spectral efficiency assuming a minimum mean square error mmse successive stripping decoder for the cases of equal rate and equal power users in both cases the maximization of spectral efficiency can be formulated as a linear program and admits a simple closed form solution that can be readily interpreted in terms of power and rate control we provide examples of the proposed optimization methods based on off the shelf low density parity check ldpc codes and we investigate by simulation the performance of practical systems with finite code block length

on complex power nonnegative matrices abstract power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power we exploit the possibility of deriving a perron frobenius like theory for these matrices obtaining three main results and drawing several consequences we study in particular the relationships with the set of matrices having eventually nonnegative powers the inverse of m type matrices and the set of matrices whose columns rows sum up to one

matrix roots of imprimitive irreducible nonnegative matrices abstract using matrix function theory perron frobenius theory combinatorial matrix theory and elementary number theory we characterize classify and describe in terms of the jordan canonical form the matrix p th roots of imprimitive irreducible nonnegative matrices preliminary results concerning the matrix roots of reducible matrices are provided as well

minimum total squared correlation quaternary signature sets new bounds and optimal designs we derive new bounds on the total squared correlation tsc of quaternary quadriphase signature sequence sets for all lengths l and set sizes k then for all k l we design minimum tsc optimal sets that meet the new bounds with equality direct numerical comparison with the tsc value of the recently obtained optimal binary sets shows under what k l realizations gains are materialized by moving from the binary to the quaternary code division multiplexing alphabet on the other hand comparison with the welch tsc value for real complex field sets shows that arguably not much is to be gained by raising the alphabet size above four for any k l the sum capacity as well as the maximum squared correlation and total asymptotic efficiency of minimum tsc quaternary sets is also evaluated in closed form and contrasted against the sum capacity of minimum tsc optimal binary and real complex sets

eventually nonnegative matrices are similar to seminonnegative matrices in this paper it is shown that the necessary and sufficient conditions on the jordan form of a seminonnegative matrix identified by zaslavsky and mcdonald are in fact necessary and sufficient conditions on the jordan form of every eventually nonnegative matrix thus every eventually nonnegative matrix is similar to a seminonnegative matrix in linear algebra appl 372 2003 253 they show that several of the combinatorial properties of reducible nonnegative matrices carry over to reducible seminonnegative matrices in this paper it is shown that a property on the index of cyclicity of an irreducible nonnegative matrix carries over to the seminonnegative matrices

finite step algorithms for constructing optimal cdma signature sequences a description of optimal sequences for direct spread code division multiple access ds cdma is a byproduct of recent characterizations of the sum capacity this paper restates the sequence design problem as an inverse singular value problem and shows that the problem can be solved with finite step algorithms from matrix theory it proposes a new one sided algorithm that is numerically stable and faster than previous methods

nonnegative and eventually positive matrices abstract we characterize those eventually positive matrices a such that the sum of a and every nonnegative matrix remains eventually positive for n 3 we show that for every eventually positive matrix a m n r there exists an eventually positive matrix b such that a b is not eventually positive

rms bandwidth constrained signature waveforms that maximize the total capacity of pam synchronous cdma channels optimum time limited signal sets of equal and unequal energies are obtained under root mean square rms bandwidth constraints the total capacity and the total asymptotic efficiency of the pam synchronous gaussian cdma psg cdma channel are considered as the optimality criteria the latter measure is monotonic with the determinant of the correlation matrix r and the former is monotonic with det i spl sigma sup 2 r where spl sigma sup 2 represents the noise level average as well as maximum rms bandwidth constraints are considered in the equal energy case and the energy weighted rms bandwidth constraint is considered for unequal energy signals for the equal energy problem signal sets are found that simultaneously optimize the total asymptotic efficiency under both average and maximum rms bandwidth constraints for the total capacity measure such simultaneously optimal signal sets are also obtained albeit under the restriction that the number of signals n be a hadamard matrix dimension when the hadamard dimension is in particular a power of two we obtain optimum signal sets that are shown to yield equal optimum multiuser detector asymptotic efficiencies for all users of an uncoded psg cdma channel unequal energy signal sets are also found under an energy weighted rms bandwidth constraint for both optimality criteria

on the jordan form of an irreducible matrix with eventually nonnegative powers abstract in terms of the concept of a frobenius collection of elementary jordan blocks which we introduce we characterize the collection of elementary jordan blocks that appear in the jordan form of an irreducible m cyclic eventually nonnegative matrix whose m th power is permutationally similar to a direct sum of m eventually positive matrices

bandwidth constrained signature waveforms for maximizing the network capacity of synchronous cdma systems synchronous code division multiple access systems where each receiver is a minimum mean squared error receiver and each user has the same received power signaling rate and required signal to interference ratio are considered based on the results viswanath anantharam and tse see ieee trans inform theory vol 45 p 1968 83 1999 the optimal signature waveforms under both fractional out of band energy and root mean square bandwidth constraints that maximize the network capacity are determined comparison to various suboptimal signature waveforms including the ones constructed from rectangular pulses is also made to quantify the gain achieved by the optimal signature waveforms

towards a perron frobenius theory for eventually positive operators abstract this article is a contribution to the spectral theory of so called eventually positive operators i e operators t which may not be positive but whose powers t n become positive for large enough n while the spectral theory of such operators is well understood in finite dimensions the infinite dimensional case has received much less attention in the literature we show that several sensible notions of eventual positivity can be defined in the infinite dimensional setting and in contrast to the finite dimensional case those notions do not in general coincide we then prove a variety of typical perron frobenius type results we show that the spectral radius of an eventually positive operator is contained in the spectrum we give sufficient conditions for the spectral radius to be an eigenvalue admitting a positive eigenvector and we show that the peripheral spectrum of an eventually positive operator is a cyclic set under quite general assumptions all our results are formulated for operators on banach lattices and many of them do not impose any compactness assumptions on the operator

a characterization of jordan canonical forms which are similar to eventually nonnegative matrices with the properties of nonnegative matrices abstract in this paper we give necessary and sufficient conditions for a matrix in jordan canonical form to be similar to an eventually nonnegative matrix whose irreducible diagonal blocks satisfy the conditions identified by zaslavsky and tam and whose subdiagonal blocks with respect to its frobenius normal form are nonnegative these matrices are referred to as seminonnegative matrices and we show that they exhibit many of the same combinatorial spectral properties as nonnegative matrices this paper extends the work on jordan forms of irreducible eventually nonnegative matrices to the reducible case

jordan chains of h cyclic matrices abstract arising from the classification of the matrix roots of a nonnegative imprimitive irreducible matrix we present results concerning the jordan chains of an h cyclic matrix we also present ancillary results applicable to nonnegative imprimitive irreducible matrices and demonstrate these results via examples

on the ergodic capacity as a function of the correlation properties in systems with multiple transmit antennas without csi at the transmitter in this letter the impact of correlation of the transmit antennas of a multiple input single output miso system with no channel state information csi at the transmitter and perfect csi at the receiver is analyzed we show that the ergodic capacity for the single user miso system is schur concave with respect to the vector with eigenvalues of the channel covariance matrix i e the more correlation that exists between the transmit antennas the less is the achievable capacity furthermore the capacity loss for fully correlated transmit antennas in comparison with the uncorrelated case is derived the results for the ergodic capacity are compared with the impact of correlation on the outage probability the relationship between correlation properties and outage probability is more complicated than the relationship between the correlation properties and the ergodic capacity it is shown that the outage probability is schur convex in the high signal to noise ratio snr regime and schur concave in the low snr regime

asynchronous cdma systems with random spreading part i fundamental limits spectral efficiency for asynchronous code division multiple access cdma with random spreading is calculated in the large system limit allowing for arbitrary chip waveforms and frequency flat fading signal to interference and noise ratios sinrs for suboptimal receivers such as the linear minimum mean square error mmse detectors are derived the approach is general and optionally allows even for statistics obtained by undersampling the received signal all performance measures are given as a function of the chip waveform and the delay distribution of the users in the large system limit it turns out that synchronizing users on a chip level impairs performance for all chip waveforms with bandwidth greater than the nyquist bandwidth e g positive roll off factors for example with the pulse shaping demanded in the umts standard user synchronization reduces spectral efficiency up to 12 at 10 db normalized signal to noise ratio the benefits of asynchronism stem from the finding that the excess bandwidth of chip waveforms actually spans additional dimensions in signal space if and only if the users are desynchronized at chip level the analysis of linear mmse detectors shows that the limiting interference effects can be decoupled both in the user domain and in the frequency domain such that the concept of effective interference spectral density arises this generalizes and refines tse and hanly s concept of effective interference in part ii the analysis is extended to any linear detector that admits a representation as multistage detector and guidelines for the design of low complexity multistage detectors with universal weights are provided

the influence of the marked reduced graph of a nonnegative matrix on the jordan form and on related properties a survey abstract for a nonnegative matrix p we discuss the relation of its marked reduced graph to that part of the jordan form that is associated with the perron frobenius root to the nonnegativity of the eigenvectors and generalized eigenvectors to the nonnegativity of solutions of linear equations and to the asymptotic growth of powers of the matrix results are often stated in terms of m matrices and standard results on irreducible matrices are assumed we give examples to illustrate the theorems surveyed

multiuser constrained water pouring for continuous time overloaded gaussian multiple access channels in this paper signature waveforms and signal powers are jointly optimized for multiuser communications over strictly bandlimited continuous time overloaded channels corrupted by additive white gaussian noise awgn the total signal power is minimized subject to general asymmetric signal to interference plus noise ratio sinr constraints at the output of linear minimum mean squared error lmmse receivers using vectorized fourier transform vft technique the optimal solutions as well as a necessary and sufficient condition for the existence of a feasible solution are derived in the frequency domain it turns out that every optimal solution performs the same as the optimal frequency division multiple access fdma system a geometric procedure called multiuser constrained water pouring is developed to construct every possible optimal solution of which profiles of signal power and equivalent bandwidth are respectively the same as those of signal power and physical bandwidth of the optimal fdma system it is shown that orthogonal signature waveforms are assigned to oversized users and continuous time equivalents of generalized welch bound equality cte gwbe sequences are assigned to non oversized users

on quasi orthogonal signatures for cdma systems sum capacity optimal signatures in synchronous code division multiple access cdma systems are functions of the codebook length as well as the number of active users a new signature set must be assigned every time the number of active users changes this correspondence considers signature sets that are less sensitive to changes in the number of active users equiangular signature sequences are proven to solve a certain max min signal to interference plus noise problem which results from their interference invariance unions of orthonormal bases have subsets that come close to satisfying the welch bound bounds on the maximum number of bases with minimum maximum correlation are derived and a new construction algorithm is provided connections are made between these signature design problems grassmannian line packing frame theory and algebraic geometry

power minimization for cdma under colored noise rate constrained power minimization pmin over a code division multiple access cdma channel with correlated noise is studied pmin is shown to be an instance of a separable convex optimization problem subject to linear ascending constraints pmin is further reduced to a dual problem of sumrate maximization rmax the results highlight the underlying unity between pmin rmax and a problem closely related to pmin but with linear receiver constraints subsequently conceptually simple sequence design algorithms are proposed to explicitly identify an assignment of sequences and powers that solve pmin the algorithms yield an upper bound of 2n 1 on the number of distinct sequences where n is the processing gain the sequences generated using the proposed algorithms are in general real valued if a rate splitting and multi dimensional cdma approach is allowed the upper bound reduces to n distinct sequences in which case the sequences can form an orthogonal set and be binary plusmn1 valued

multirate zero forcing tx rx design for mimo channel under ber constraints this paper is concerned with communicating parallel independent streams of data possibly of different rates through a multiple input multiple output channel each data stream is required to satisfy a bit error rate ber constraint this scenario arises in multimedia communications we find the linear zero forcing transmitter receiver tx rx matrix pair that requires the minimum transmitter power to achieve the ber constraints it is well known that the tx rx pair can be chosen to partition the matrix channel into scalar subchannels corresponding to singular values and different data streams can be transmitted through different subchannels this design is suboptimum in general the optimum design has the following structure the set of input data streams is partitioned into groups called signal groups the set of subchannels is conformably partitioned into subchannel groups each signal group is collectively transmitted through its assigned subchannel group with each signal subchannel group pair is associated a unitary matrix that mixes the signals at the transmitter and unmixes them at the receiver we derive a simple algorithm to determine the optimum signal and subchannel groups we then use a known algorithm from majorization theory to determine the unitary matrices using these we completely specify the optimum tx rx pair

analysis of some mixed finite element methods related to reduced integration we prove error estimates for the following two mixed finite element methods related to reduced integration a method for stokes problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress the main idea of the proof in the case of stokes problem is to combine a weak babuska brezzi type stability estimate for the pressure with a superapproximability property for the velocities a similar technique is used in the case of the plate problem

high snr performance analysis of blind minimum output energy receivers for large ds cdma systems high signal to noise ratio snr properties of the minimum output energy moe receiver and the capon channel estimation technique are analyzed in the case of large direct sequence code division multiple access ds cdma systems it is shown that if the noise power tends to zero and the system load is less than one then the signal to interference plus noise ratio sinr of the moe receiver tends to infinity and the capon channel estimate converges to a scaled version of the channel vector of the user of interest for the case when the system load is larger than one an asymptotic sinr expression is obtained furthermore expressions for the efficiency and asymptotic efficiency of the moe receiver are derived simple approximations of and upper lower bounds on these expressions are found and the effects of the system physical parameters on the performance of the moe receiver are discussed