fundamental study modular tree transducers abstract a new tree transducer called a modular tree transducer is introduced this device specifies operations on trees and can be considered as a formalization of the concept of nested simultaneous primitive recursion on trees roughly speaking a modular tree transducer is a special left linear and non overlapping term rewriting system of which the set of rules is partitioned into modules each module being equipped with a non negative integer the number of the module then a module with number i may call modules with numbers not less than i three properties are proved 1 modular tree transducers compute exactly the inductively defined class of primitive recursive functions on trees 2 the number of modules in modular tree transducers induces a strict hierarchy on the class of all modular tree transductions and 3 by appropriately restricting the calling structure between modules modular tree transducers characterize the compositions of macro tree transducers where the number of modules and the number of compositions coincide

optimal designs for space time linear precoders and decoders we introduce a new paradigm for the design of transmitter space time coding that we refer to as linear precoding it leads to simple closed form solutions for transmission over frequency selective multiple input multiple output mimo channels which are scalable with respect to the number of antennas size of the coding block and transmit average peak power the scheme operates as a block transmission system in which vectors of symbols are encoded and modulated through a linear mapping operating jointly in the space and time dimension the specific designs target minimization of the symbol mean square error and the approximate maximization of the minimum distance between symbol hypotheses under average and peak power constraints the solutions are shown to convert the mimo channel with memory into a set of parallel flat fading subchannels regardless of the design criterion while appropriate power bits loading on the subchannels is the specific signature of the different designs the proposed designs are compared in terms of various performance measures such as information rate ber and symbol mean square error

noncooperative eigencoding for mimo ad hoc networks a new noncooperative eigencoding algorithm is introduced for multiple input multiple output mimo ad hoc networks the algorithm performs generalized waterfilling with respect to its transmit covariance matrix and the receive node covariance matrix both of which can be estimated locally a cooperative algorithm is also developed as a benchmark in simulations simulation results show that the noncooperative algorithm performance is close to that of the cooperative method and is much better than greedy optimization a game theoretic interpretation of the algorithm is also provided

minimum ber linear transceivers for mimo channels via primal decomposition this paper considers the employment of linear transceivers for communication through multiple input multiple output mimo channels with channel state information csi at both sides of the link the design of linear mimo transceivers has been studied since the 1970s by optimizing simple measures of the quality of the system such as the trace of the mean square error matrix subject to a power constraint recent results showed how to solve the problem in an optimal way for the family of schur concave and schur convex cost functions in particular when the constellations used on the different transmit dimensions are equal the bit error rate ber averaged over these dimensions happens to be a schur convex function and therefore it can be optimally solved in a more general case however when different constellations are used the average ber is not a schur convex function and the optimal design in terms of minimum ber is an open problem this paper solves the minimum ber problem with arbitrary constellations by first reformulating the problem in convex form and then proposing two solutions one is a heuristic and suboptimal solution which performs remarkably well in practice the other one is the optimal solution obtained by decomposing the convex problem into several subproblems controlled by a master problem a technique borrowed from optimization theory for which extremely simple algorithms exist thus the minimum ber problem can be optimally solved in practice with very simple algorithms

macro tree transducers attribute grammars and mso definable tree translations a characterization is given of the class of tree translations definable in monadic second order logic mso in terms of macro tree transducers the first main result is that the mso definable tree translations are exactly those tree translations realized by macro tree transducers mtts with regular look ahead that are single use restricted for this the single use restriction known from attribute grammars is generalized to mtts since mtts are closed under regular look ahead this implies that every mso definable tree translation can be realized by an mtt the second main result is that the class of mso definable tree translations can also be obtained by restricting mtts with regular look ahead to be finite copying i e to require that each input subtree is processed only a bounded number of times the single use restriction is a rather strong static restriction on the rules of an mtt whereas the finite copying restriction is a more liberal dynamic restriction on the derivations of an mtt

progressive linear precoder optimization for mimo packet retransmissions exploiting channel covariance information this work investigates the design of linear precoders for arq packet retransmissions in multi input multi output mimo systems we consider transmitter precoder design based on partial mimo channel information in the form of their covariance feedback our objective is to maximize the ergodic mutual information provided by multiple re transmissions of a packet subject to transmission power constraint we propose a set of near optimal successive linear arq precoders for flat fading mimo channels this progressive linear arq precoder combines the appropriate power loading and the reverse order pairing of singular values in the current retransmission with previous transmissions this reverse order pairing is a special feature unique to our sequential arq preceding approach with demonstrated performance gains

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

generalized linear precoder and decoder design for mimo channels using the weighted mmse criterion we address the problem of designing jointly optimum linear precoder and decoder for a mimo channel possibly with delay spread using a weighted minimum mean squared error mmse criterion subject to a transmit power constraint we show that the optimum linear precoder and decoder diagonalize the mimo channel into eigen subchannels for any set of error weights furthermore we derive the optimum linear precoder and decoder as functions of the error weights and consider specialized designs based on specific choices of error weights we show how to obtain 1 the maximum information rate design 2 qos based design we show how to achieve any set of relative snrs across the subchannels and 3 the unweighted mmse and equal error design for fixed rate systems

asymptotic performance analysis of coded blast architectures with statistical rate and power allocations in this paper we first analyze some mathematical properties of ergodic capacity and outage capacity functions of the layers in bell labs layered space time blast architectures employing successive decoding and interference cancellation we then present statistical rate allocation and power allocation methods that optimize the asymptotic performance of blast architectures since the methods are developed by using ergodic capacity and outage capacity functions of the layers the allocated rates and powers depend only on a given channel statistic finally we prove that the rate allocation yields a better asymptotic performance than the power allocation numerical results show that blast architectures with the rate and power allocation perform better by 4 db and 3 db respectively than a blast architecture with the same rate and power in all layers

optimum linear joint transmit receive processing for mimo channels with qos constraints this paper considers vector communications through multiple input multiple output mimo channels with a set of quality of service qos requirements for the simultaneously established substreams linear transmit receive processing also termed linear precoder at the transmitter and linear equalizer at the receiver is designed to satisfy the qos constraints with minimum transmitted power the exact conditions under which the problem becomes unfeasible are given although the original problem is a complicated nonconvex problem with matrix valued variables with the aid of majorization theory we reformulate it as a simple convex optimization problem with scalar variables we then propose a practical and efficient multilevel water filling algorithm to optimally solve the problem for the general case of different qos requirements the optimal transmit receive processing is shown to diagonalize the channel matrix only after a very specific prerotation of the data symbols for situations in which the resulting transmit power is too large we give the precise way to relax the qos constraints in order to reduce the required power based on a perturbation analysis we also propose a robust design under channel estimation errors that has an important interest for practical systems numerical results from simulations are given to support the mathematical development of the problem

on the inseparability of parallel mimo broadcast channels with linear transceivers parallel multiple input multiple output mimo broadcast channels have been shown to be separable from an information theoretic point of view i e capacity can be achieved with a strategy that performs separate encoding and decoding on each subchannel subject to a power allocation across subchannels in this paper we show that separability does not necessarily hold if the transmit strategy is restricted to linear transceivers the proof will be done by identifying a rate tuple that is achievable in a certain set of channels with joint treatment of the subchannels but lies outside the achievable rate region of separate linear precoding the implications of this result are that any algorithm to optimize transmit strategies in parallel mimo broadcast channels that is based on both linear transceivers and separate encoding on each subchannel does in fact introduce two suboptimalities aandnd not only one

practical algorithms for a family of waterfilling solutions many engineering problems that can be formulated as constrained optimization problems result in solutions given by a waterfilling structure the classical example is the capacity achieving solution for a frequency selective channel for simple waterfilling solutions with a single waterlevel and a single constraint typically a power constraint some algorithms have been proposed in the literature to compute the solutions numerically however some other optimization problems result in significantly more complicated waterfilling solutions that include multiple waterlevels and multiple constraints for such cases it may still be possible to obtain practical algorithms to evaluate the solutions numerically but only after a painstaking inspection of the specific waterfilling structure in addition a unified view of the different types of waterfilling solutions and the corresponding practical algorithms is missing the purpose of this paper is twofold on the one hand it overviews the waterfilling results existing in the literature from a unified viewpoint on the other hand it bridges the gap between a wide family of waterfilling solutions and their efficient implementation in practice to be more precise it provides a practical algorithm to evaluate numerically a general waterfilling solution which includes the currently existing waterfilling solutions and others that may possibly appear in future problems

compression of finite group actions and covariant dimension abstract let g be a finite group and v w an equivariant polynomial map between finite dimensional g modules we say that is faithful if g acts faithfully on v the covariant dimension of g is the minimum of the dimension of v taken over all faithful in hanspeter kraft gerald w schwarz compression of finite group actions and covariant dimension j algebra 313 1 2007 268 291 we investigated covariant dimension and were able to determine it in many cases our techniques largely depended upon finding homogeneous faithful covariants after publication of the paper the junior author of this article pointed out several gaps in our proofs fortunately this inspired us to find better techniques involving multihomogeneous covariants which have enabled us to extend and complete the results simplify the proofs and fill the gaps of our previous work

spatio temporal coding for wireless communication multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels this paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed a compact model is developed for the multiple input multiple output mimo dispersive spatially selective wireless communication channel the multivariate information capacity is analyzed for high signal to noise ratio snr conditions the mimo channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components the number of input antennas or the number of output antennas this desirable result is contrasted with the lower capacity slope of the well studied case with multiple antennas at only one side of the radio link a spatio temporal vector coding stvc communication structure is suggested as a means for achieving mimo channel capacity the complexity of stvc motivates a more practical reduced complexity discrete matrix multitone dmmt space frequency coding approach both of these structures are shown to be asymptotically optimum an adaptive lattice trellis coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the dmmt channel experimental examples that support the theoretical results are presented

a constructive method for abstract algebraic software specification abstract a constructive method for abstract algebraic software specification is presented where the operations are not implicitly specified by equations but by an explicit recursion on the generating operations of an algebra characterizing the underlying data structure the underlying algebra itself may be equationally specified since we cannot assume that all data structures will correspond to free algebras this implies that we distinguish between generating and defined operations and that the underlying algebra has a mechanism of well founded decomposition w r t the generating operations we show that the explicit specification of operations using so called structural recursive schemata offers advantages over purely equational specifications especially concerning the safeness of enrichments the ease of semantics description and the separation between the underlying data structure and the operations defined on it

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

on the duality of mimo transceiver designs with bit allocation bit rate and power are two commonly used optimality criteria for mimo transceiver design in the literature bit rate maximization and power minimization problems are viewed as different problems and solved independently in this paper we derive the duality between these two problems for both the cases with and without integer constraint on bit allocation we will show that if a transceiver is optimal for the power minimizing problem it is also optimal for the rate maximizing problem and the converse is true such a duality has not been stated and proved in the literature to the best of our knowledge the derivation does not involve any existing optimal solution and we can establish duality result even for the rate maximization problem with integer bit constraint which the optimal solution is not known the duality also allows us to develop an algorithm for finding the rate maximizing transceiver with integer bit allocation using the solution of power minimizing system we will also consider some possible generalizations of the problem for example when there is a constraint on the maximal constellation size and when the subchannel bit error rates bers are constrained for each of these cases we will see that the duality between the two problems continued to hold in the simulations we will compute the optimal solutions for these two problems and demonstrate the duality between these two

the generating power of total deterministic tree transducer abstract attributed tree transducers are abstract models used to study properties of attribute grammars one abstraction which occurs when modeling attribute grammars by attributed tree transducers is that arbitrary trees over a ranked alphabet are taken as input instead of derivation trees of a context free grammar in this paper we show that with respect to the generating power this is not an abstraction i e we show that attributed tree transducers and attribute grammars generate the same class of term or tree languages to prove this a number of results concerning the generating power of top down tree transducers are established which are interesting in their own we also show that the classes of output languages of attributed tree transducers form a hierarchy with respect to the number of attributes the latter result is achieved by proving a hierarchy of classes of tree languages generated by context free hypergraph grammars with respect to their rank

multihop nonregenerative mimo relays qos considerations for nonregenerative multihop multiple input multiple output mimo relay communication systems the optimal source precoding matrix and the optimal relay amplifying matrices have been recently established for a broad class of objective functions subjecting to the transmission power constraint at each node however existing works do not consider any quality of service qos constraints which are important in practical communication systems in this paper we derive the optimal source and relay matrices of a multihop mimo relay system that guarantee the predetermined qos criteria be attained with the minimal total transmission power in particular we consider two types of receivers at the destination node the linear minimal mean squared error mmse receiver and the nonlinear decision feedback equalizer dfe based on the mmse criterion we show that for both types of receivers the solution to the original optimization problem can be upper bounded by using a successive geometric programming gp approach and lower bounded by utilizing a dual decomposition technique simulation results show that both bounds are tight and to obtain the same qos the mimo relay system using the nonlinear mmse dfe receiver requires substantially less total transmission power than the linear mmse receiver based system

statistically robust design of linear mimo transceivers the treatment of channel state information csi is critical in the design of mimo systems accurate csi at the transmitter is often not possible or may require high feedback rates herein we consider the robust design of linear mimo transceivers with perfect csi either at the transmitter or at both sides of the link the framework considers the design problem where the imperfect csi consists of the channel mean and covariance matrix or equivalently the channel estimate and the estimation error covariance matrix the robust transceiver design is based on a general cost function of the average mses as well as a design with individual mse based constraints in particular a lower bound of the average mse matrix is explored for the design when only the csi at the transmitter is imperfect under different csi conditions the proposed robust transceivers exhibit a similar structure to the transceiver designs for perfect csi but with a different equivalent channel and or noise covariance matrix

worst case mse precoder design for imperfectly known mimo communications channels this paper considers a worst case precoder design problem for multiple input multiple output mimo wireless communication systems with imperfect channel knowledge at the transmitter when the mimo channel is a full row rank matrix which arises generically when the number n sub t of transmit antennas is greater or equal to the number n sub r of receive antennas and when channel state information is known perfectly at the transmitter the channel can be equalized exactly by employing a precoder equal to the channel pseudo inverse however in actual systems it is necessary to take into account the channel estimation error we consider here a worst case precoder design problem where the goal is to find the precoder minimizing the equalization mean square error for the least favorable channel located in a ball centered about the estimated channel lagrangian optimization is used to convert this min max problem into a min min convex minimization problem over a convex domain which can be solved in closed form the robust precoder and associated least favorable channel have an intuitive interpretation since the least favorable channel zeroes out the weakest subchannels and the robust precoder implements a pseudo inverse only for the remaining subchannels

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

optimal linear precoding strategies for wideband noncooperative systems based on game theory part i nash equilibria in this two part paper we propose a decentralized strategy based on a game theoretic formulation to find out the optimal precoding multiplexing matrices for a multipoint to multipoint communication system composed of a set of wideband links sharing the same physical resources i e time and bandwidth we assume as optimality criterion the achievement of a nash equilibrium and consider two alternative optimization problems 1 the competitive maximization of mutual information on each link given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies and 2 the competitive maximization of the transmission rate using finite order constellations under the same constraints as above plus a constraint on the average error probability in this first part of the paper we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies then we prove that the optimal precoding multiplexing scheme for both games leads to a channel diagonalizing structure so that both matrix valued problems can be recast in a simpler unified vector power control game with no performance penalty thus we study this simpler game and derive sufficient conditions ensuring the uniqueness of the nash equilibrium interestingly although derived under stronger constraints incorporating for example spectral mask constraints our uniqueness conditions have broader validity than previously known conditions finally we assess the goodness of the proposed decentralized strategy by comparing its performance with the performance of a pareto optimal centralized scheme to reach the nash equilibria of the game in part ii we propose alternative distributed algorithms along with their convergence conditions

convex separable problems with linear constraints in signal processing and communications in this work we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints the solution is given in closed form as a function of some lagrange multipliers that can be computed through an iterative procedure in a finite number of steps graphical interpretations are given casting valuable insights into the proposed algorithm and allowing to retain some of the intuition spelled out by the water filling policy it turns out that it is not only general enough to compute the solution to different instances of the problem at hand but also remarkably simple in the way it operates we also show how some power allocation problems in signal processing and communications can be solved with the proposed algorithm

essential dimension of group schemes over a local scheme abstract in this paper we develop the theory of essential dimension of group schemes over an integral base shortly we concentrate over a local base as a consequence of our theory we give a result of invariance of the essential dimension over a field the case of group schemes over a discrete valuation ring is discussed

worst case robust mimo transmission with imperfect channel knowledge in this paper we consider robust transmit strategies against the imperfectness of the channel state information at the transmitter csit for multi input multi output mimo communication systems following a worst case deterministic model the actual channel is assumed to be inside an ellipsoid centered at a nominal channel the objective is to maximize the worst case received signal to noise ratio snr or to minimize the worst case chernoff bound of the error probability thus leading to a maximin problem moreover we also consider the qos problem as a complement of the maximin design which minimizes the transmit power consumption and meanwhile keeps the received snr above a given threshold for any channel realization in the ellipsoid it is shown that for a general class of power constraints both the maximin and qos problems can be equivalently transformed into convex problems or even further into semidefinite programs sdps thus efficiently solvable by the numerical methods the most interesting result is that the optimal transmit directions i e the eigenvectors of the transmit covariance are just the right singular vectors of the nominal channel under some mild conditions this result leads to a channel diagonalizing structure as in the cases of perfect csit and statistical csit with mean or covariance feedback and reduces the complicated matrix valued problem to a scalar power allocation problem then we provide the closed form solution to the resulting power allocation problem

noether s problem and mathbb q generic polynomials for the normalizer of the 8 cycle in s_8 and its subgroups we study noether s problem for various subgroups h of the normalizer ot a group c 8 generated by an 8 cycle in s 8 the symmetric group of degree 8 in three aspects according to the way they act on rational function fields i e q x 0 x 7 q x 1 x 4 and q x y we prove that it has affirmative answers for those h containing c 8 properly and derive a q generic polynomial with four parameters for each h on the other hand it is known in connection to the negative answer to the same problem for c 8 q that there does not exist a q generic polynomial for c 8 this leads us to the question whether and how one can describe for a given field k of characteristic zero the set of c 8 extensions l k one of the main results of this paper gives an answer to this question

mimo transceivers with decision feedback and bit loading theory and optimization this paper considers mimo transceivers with linear precoders and decision feedback equalizers dfes with bit allocation at the transmitter zero forcing zf is assumed considered first is the minimization of transmitted power for a given total bit rate and a specified set of error probabilities for the symbol streams the precoder and dfe matrices are optimized jointly with bit allocation it is shown that the generalized triangular decomposition gtd introduced by jiang li and hager offers an optimal family of solutions the optimal linear transceiver which has a linear equalizer rather than a dfe with optimal bit allocation is a member of this family this shows formally that under optimal bit allocation linear and dfe transceivers achieve the same minimum power the dfe transceiver using the geometric mean decomposition gmd is another member of this optimal family and is such that optimal bit allocation yields identical bits for all symbol streams no bit allocation is necessary when the specified error probabilities are identical for all streams the qr based system used in vblast is yet another member of the optimal family and is particularly well suited when limited feedback is allowed from receiver to transmitter two other optimization problems are then considered a minimization of power for specified set of bit rates and error probabilities the qos problem and b maximization of bit rate for fixed set of error probabilities and power it is shown in both cases that the gtd yields an optimal family of solutions

robust mmse precoding in mimo channels with pre fixed receivers in this paper we design robust precoders under the minimum mean square error mmse criterion for different types of channel state information csi in multiple input multiple output mimo channels we consider low complexity pre fixed receivers that may adapt to the channel but are oblivious to the existence of a precoder at the transmitter in particular three types of csi are taken into account i perfect csi ii statistical csi in the form of mean feedback and iii deterministic imperfect csi assuming that the actual channel is within the neighborhood of a nominal channel which leads to the worst case robust design that is the focus of this paper interestingly it is found that under some mild conditions the optimal transmit directions i e the left singular vectors of the precoder are equal to the right singular vectors of the channel the channel mean and the nominal channel for perfect csi statistical csi and the worst case design respectively consequently the matrix valued problems can be simplified to scalar power allocation problems that either admit closed form solutions or can be efficiently solved by the proposed algorithm

optimal training design for channel estimation in decode and forward relay networks with individual and total power constraints in this paper we study the channel estimation and the optimal training design for relay networks that operate under the decode and forward df strategy with the knowledge of the interference covariance in addition to the total power constraint on all the relays we introduce individual power constraint for each relay which reflects the practical scenario where all relays are separated from one another considering the individual power constraint for the relay networks is the major difference from that in the traditional point to point communication systems where only a total power constraint exists for all colocated antennas two types of channel estimation are involved maximum likelihood ml and minimum mean square error mmse for ml channel estimation the channels are assumed as deterministic and the optimal training results from an efficient multilevel waterfilling type solution that is derived from the majorization theory for mmse channel estimation however the second order statistics of the channels are assumed known and the general optimization problem turns out to be nonconvex we instead consider three special yet reasonable scenarios the problem in the first scenario is convex and could be efficiently solved by state of the art optimization tools closed form waterfilling type solutions are found in the remaining two scenarios of which the first one has an interesting physical interpretation as pouring water into caves

carrier cooperation can reduce the transmit power in parallel mimo broadcast channels with zero forcing even though parallel multiple input multiple output mimo broadcast channels are known to be separable from an information theoretic point of view performing separate encoding and decoding on each of the parallel channels has been shown to be potentially suboptimal in broadcast channels with linear transceivers in this paper we show that suboptimality of such a carrier noncooperative transmission also occurs in broadcast channels with zero forcing and quality of service constraints if time sharing is not allowed the proof is given by constructing a minimal example and identifying a rate tuple that is achievable using carrier cooperative zero forcing with a certain sum power but requires a higher sum power with carrier noncooperative zero forcing this observation is of practical relevance since zero forcing without time sharing is a popular assumption in the design of low complexity optimization algorithms

a robust precoder design based on channel statistics for mimo ofdm systems with insufficient cyclic prefix in this paper we study the precoder design problem for mimo ofdm systems with insufficient cyclic prefix cp using statistical channel state information csi at the transmitter in our previously proposed channel independent precoding scheme an interference nulling based precoding structure is studied which can assist to either cancel interblock interference ibi or separate the subspace occupied by ibi from the subspace used for information symbols in this work we consider a robust precoder design which combines statistical csi at the transmitter and the interference nulling based precoding structure to gain a better performance compared to the channel independent precoding scheme statistical channel state information at the transmitter in the form of covariance matrix of the mimo ofdm channel matrix is utilized to perform the robust precoding the design criterion for the precoder design is to minimize the maximum average mean squared error mse of all the transmitted symbols during one ofdm block interval to achieve this goal the precoder design exhibits a similar procedure to the optimized design framework for mimo transceivers for either perfect or statistical csi with no interference effect but with a distinct equivalent channel since the average mses are set equal using this precoder the ber performance is better than our previously proposed channel independent precoder and the simulation validates this result

filterbank transceivers optimizing information rate in block transmissions over dispersive channels optimal finite impulse response fir transmit and receive filterbanks are derived for block based data transmissions over frequency selective additive gaussian noise agn channels by maximizing mutual information subject to a fixed transmit power constraint both fir and pole zero channels are considered the inherent flexibility of the proposed transceivers is exploited to derive as special cases zero forcing zf and minimum mean square error receive filterbanks the transmit filterbank converts transmission over a frequency selective fading channel affected by additive colored noise into a set of independent flat fading subchannels with uncorrelated noise samples two loading algorithms are also developed to distribute transmit power and number of bits across the usable subchannels while adhering to an upper bound on the bit error rate ber reduction of the signal to noise ratio snr margin required to satisfy the prescribed ber is achieved by coding each subchannel s bit stream the potential of the proposed transceivers is illustrated and compared to discrete multitone dmt with simulated examples

convex primal decomposition for multicarrier linear mimo transceivers the design of linear transceivers for multiple input multiple output mimo communication systems with channel state information is particularly challenging for two main reasons first since several substreams are established through the mimo channel it is not even clear how the quality of the system should be measured second once a cost function has been chosen to measure the quality the optimization of the system according to such criterion is generally difficult due to the nonconvexity of the problem recent results have solved the problem for the wide family of schur concave convex functions resulting in simple closed form solutions when the system is modeled as a single mimo channel however with several mimo channels such as in multi antenna multicarrier systems the solution is generally more involved leading in some cases to the need to employ general purpose interior point methods this problem is specifically addressed in this paper by combining the closed form solutions for single mimo channels with a primal decomposition approach resulting in a simple and efficient method for multiple mimo channels the extension to functions that are not schur concave convex is also briefly considered relating the present work with a recently proposed method to minimize the average bit error rate ber of the system

minimal transmit power in parallel vector broadcast channels with linear precoding we consider the communication over a set of parallel multiple input single output miso broadcast channels with separate linear precoding on each of them in this setup we study the problem of fulfilling per user quality of service constraints expressed in terms of rates using minimal transmit power by means of a dual decomposition approach and a branch and bound algorithm solving the arising nonconvex subproblems we find the so far unknown globally optimal solution for the case of linear precoding with time sharing although prohibitively complex for implementation in a practical system the new power minimization method is highly interesting from a theoretical point of view as it can be used to quantify the performance gap between the outcome of heuristic algorithms and the theoretical limitations of the system with linear transceivers we also extend the approach such that zero forcing constraints can be handled

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

tree transducers with external functions abstract in this paper we investigate the computational power of particular tree transducers viz macro tree transducers and attributed tree transducers the former tree transducers formalize the idea of syntax directed translation with the possibility of handling context the latter tree transducers can serve as a formal model for the reduction semantics of attribute grammars here we generalize these tree transducers by allowing the invocation of external functions during the usual rewriting process the main result of this paper is the characterization of macro tree transducers with external function calls in terms of attributed tree transducers with external function calls furthermore such tree transducers with external function calls induce in an obvious way two operators on the set of all classes of tree functions according to this point of view we define two classes of tree functions inductively in the same way as the class prec of primitive recursive tree functions except that the closure under the scheme of primitive recursion is replaced by the closure under macro tree transducers with external function calls and attributed tree transducers with external function calls respectively as a second result of this paper we prove that these two classes are equal to prec

attributed tree transducers cannot induce all deterministic bottom up tree transformations in this paper we give a deterministic bottom up tree transducer t and show that the tree transformation t induced by it can be induced by no attributed tree transducer

joint transmitter receiver optimization for multi input multi output systems with decision feedback the joint transmit receive optimization problem for multiuser communication systems with decision feedback is investigated it is shown that minimization of the geometric mean squared error defined as the determinant of the error covariance matrix leads to a tractable transmitter optimization problem for general multi input multi output decision feedback systems several computational results are included that highlight system performance for a variety of useful transmission scenarios