tomlinson harashima precoding in mimo systems a unified approach to transceiver optimization based on multiplicative schur convexity this paper deals with the design of a multicarrier multiple input multiple output system which performs nonlinear tomlinson harashima precoding at the transmitter and linear equalization at the receiver the goal is the joint optimization of the processing matrices at both ends of the wireless link assuming a constraint on the overall transmit power we consider different design criteria which require the maximization minimization of objective functions that depend on the mean square errors over the individual data streams a unified framework for the solution of a great number of optimization problems is developed based on the concept of multiplicative schur convexity we show that many widely used design criteria can be easily accommodated in our framework our analysis is centered on two theorems which in the case of cooperative processing among the different subcarriers provide closed form solutions to a number of optimization problems on the other hand when an independent processing is assumed at each subcarrier closed form solutions may not exist nonetheless exploiting the results of the two theorems we show that for a variety of cost functions the optimization problem can be efficiently solved theoretical analysis and computer simulations are used to assess the performance of the proposed schemes and make comparisons with linear transceiver architectures it turns out that nonlinear precoding provides better results than linear prefiltering when the cost function is multiplicatively schur convex in contrast when the cost function is multiplicatively schur concave the nonlinear scheme is equivalent to the linear one

the heteroscedastic graded response model with a skewed latent trait testing statistical and substantive hypotheses related to skewed item category functions the graded response model grm samejima estimation of ability using a response pattern of graded scores psychometric monograph no 17 richmond va the psychometric society 1969 can be derived by assuming a linear regression of a continuous variable z on the trait to underlie the ordinal item scores takane de leeuw in psychometrika 52 393 408 1987 traditionally a normal distribution is specified for z implying homoscedastic error variances and a normally distributed in this paper we present the heteroscedastic grm with skewed latent trait which extends the traditional grm by incorporation of heteroscedastic error variances and a skew normal latent trait an appealing property of the extended grm is that it includes the traditional grm as a special case this enables specific tests on the normality assumption of z we show how violations of normality in z can lead to asymmetrical category response functions the ability to test this normality assumption is beneficial from both a statistical and substantive perspective in a simulation study we show the viability of the model and investigate the specificity of the effects we apply the model to a dataset on affect and a dataset on alexithymia

limited and full information estimation and goodness of fit testing in 2n contingency tables high dimensional contingency tables tend to be sparse and standard goodness of fit statistics such as x2 cannot be used without pooling categories as an improvement on arbitrary pooling for goodness of fit of large 2n contingency tables we propose classes of quadratic form statistics based on the residuals of margins or multivariate moments up to order r these classes of test statistics are asymptotically chi squared distributed under the null hypothesis further the marginal residuals are useful for diagnosing lack of fit of parametric models we show that when r is small r 2 3 the proposed statistics have better small sample properties and are asymptotically more powerful than x2 for some useful multivariate binary models related to these test statistics is a class of limited information estimators based on low dimensional margins we show that these estimators have high efficiency for one commonly used latent trait model for binary data

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

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

distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution summary a fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry and to generate a whole set of non symmetric densities the approach is sufficiently general to encompass some recent proposals in the literature variously related to the skew normal distribution the special case of skew elliptical densities is examined in detail establishing connections with existing similar work the final part of the paper specializes further to a form of multivariate skew t density likelihood inference for this distribution is examined and it is illustrated with numerical examples

asymptotic robustness study of the polychoric correlation estimation asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied the asymptotic normality of the pseudo maximum likelihood estimator is derived using the two step estimation procedure the t distribution assumption and the skew normal distribution assumption are used as alternatives to the normal distribution assumption in a numerical study the numerical results show that the underlying normal distribution can be substantially biased even though skewness and kurtosis are not large the skew normal assumption generally produces a lower bias than the normal assumption thus it is worth using a non normal distributional assumption if the normal assumption is dubious

on the spectral and combinatorial structure of 2d positive systems abstract the dynamics of a 2d positive system depends on the pair of nonnegative square matrices that provide the updating of its local states in this paper several spectral properties such as finite memory separability and property l which depend on the characteristic polynomial of the pair are investigated under the nonnegativity constraint and in connection with the combinatorial structure of the matrices some aspects of the perron frobenius theory are extended to the 2d case in particular conditions are provided guaranteeing the existence of a common maximal eigenvector for two nonnegative matrices with irreducible sum finally some results on 2d positive realizations are presented

space time codes for high data rate wireless communication performance criteria in the presence of channel estimation errors mobility and multiple paths space time coding is a bandwidth and power efficient method of communication over fading channels that realizes the benefits of multiple transmit antennas specific codes have been constructed using design criteria derived for quasi static flat rayleigh or rician fading where channel state information is available at the receiver it is evident that the practicality of space time codes will be greatly enhanced if the derived design criteria remain valid in the absence of perfect channel state information it is even more desirable that the design criteria not be unduly sensitive to frequency selectivity and to the doppler spread this paper presents a theoretical study of these issues beginning with the effect of channel estimation error here it is assumed that a channel estimator extracts fade coefficients at the receiver and for constellations with constant energy it is proved that in the absence of ideal channel state information the design criteria for space time codes is still valid the analysis also demonstrates that standard channel estimation techniques can be used in conjunction with space time codes provided that the number of transmit antennas is small we also derive the maximum likelihood detection metric in the presence of channel estimation errors next the effect of multiple paths on the performance of space time codes is studied for a slowly changing rayleigh channel it is proved that the presence of multiple paths does not decrease the diversity order guaranteed by the design criteria used to construct the space time codes similar results hold for rapid fading channels with or without multiple paths the conclusion is that the diversity order promised by space time coding is achieved under a variety of mobility conditions and environmental effects

simulating multivariate nonnormal distributions a method for generating multivariate nonnormal distributions with specified intercorrelations and marginal means variances skews and kurtoses is proposed as an example the method is applied to the generation of simulated scores on three psychological tests administered to a single group of individuals

understanding the quintile portfolio the heuristic 1 n i e equally weighted portfolio and heuristic quintile portfolio are both popular simple strategies in financial investment in the 1 n portfolio a fraction of 1 n of the wealth is allocated to each of the n available assets in the quintile portfolio first the assets are sorted according to some characteristics e g expected returns and then the strategy equally longs the top 20 i e top quintile and perhaps shorts the bottom 20 i e bottom quintile although they have been criticized for their lack of mathematical justification when proposed by practitioners they have shown great advantage over more sophisticated portfolios in terms of stable performance and easy deployment in this paper we reinterpret the 1 n and quintile portfolios as solutions to a mathematically sound robust portfolio optimization under different levels of robustness level in the stocks characteristics a variance adjusted robustness uncertainty set is also proposed leading to the inverse volatility portfolios whose nonzero weights are inversely proportional to their standard deviation

linear decoupled and quasi decoupled space time codes space time transmit diversity results in coupling of transmitted symbols across different antennas which increases the complexity of maximum likelihood decoding symbol coupling can be completely or partially avoided if the space time code stc satisfies specific decoupling conditions examples of such codes are orthogonal space time block codes and quasi orthogonal codes in this letter we study decoupling conditions for a linear full diversity stc quasi decoupled codes are proposed as a partially decoupled full diversity stc of any rate for any number of transmit antennas with minimum decoding delay by optimizing the coding gain of quasi decoupled codes it is shown that quasi orthogonal codes have competitive performance with respect to the alamouti code and the more recent threaded algebraic space time tast codes and abba codes a general full diversity decoupling condition is considered and the general solution to this case which also encompasses previously known orthogonal stcs is derived

on the general ber expression of one and two dimensional amplitude modulations quadrature amplitude modulation qam is an attractive technique to achieve high rate transmission without increasing the bandwidth a great deal of attention has been devoted to the study of bit error rate ber performance of qam and approximate expressions for the bit error probability of qam have been developed in many places in the literature however the exact and general ber expression of qam with an arbitrary constellation size has not been derived yet we provide an exact and general closed form expression of the ber for one dimensional and two dimensional amplitude modulations i e pam and qam under an additive white gaussian noise awgn channel when gray code bit mapping is employed the provided ber expressions offer a convenient way to evaluate the performance of pam and qam systems for various cases of practical interest moreover simple approximations can be found from our expressions which are the same as the well known approximations if only the dominant terms are considered

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

linear precoder optimization for mimo systems with joint power constraints this paper considers linear precoder optimization problems for multiple input multiple output mimo systems in addition to the conventionally used sum power constraint maximum eigenvalue constraint on the precoding matrix is also considered so as to account for power limitations imposed on each antenna by the linearity of its own power amplifier in practical implementations a framework employing directional derivative is developed to obtain optimal precoder designs for different criteria including maximizing the information rate and minimizing the sum of mean square error mse it turns out that power allocations in such situations are piecewise linear in sum power space the piecewise linear property allows us to generate the entire path of solution through finding out a finite number of breakpoints a homotopy type algorithm is then proposed to obtain the solution for an arbitrary sum power constraint the number of breakpoints to be determined in our exact piecewise linear solution is in fact only about two times of the number of transmit antennas so that our method is super fast and outperforms existing approximate solutions in the literature in both effectiveness and efficiency simulated experiments are performed to verify our theoretical analysis

trace orthonormal full diversity cyclotomic space time codes in this paper we consider the design of full diversity space time codes for a coherent multiple input multiple output mimo communication system starting from both the information theoretic and detection error viewpoints we first establish that a desirable property for general linear dispersion ld codes is to have an interunitary as well as an intraunitary structure a structure we call trace orthonormality by imposing the trace orthonormal structure on an ld code and applying cyclotomic number theory we establish for an arbitrary number of transmitter and receiver antennas a systematic and simple method to jointly design a unitary cyclotomic matrix the diophantine number and the corresponding constellation for an ld code as a result this enables us to construct full diversity rectangular cyclotomic ld codes with any symbol transmission rate less than or equal to the number of transmitter antennas in addition for the case when the number of transmitter antennas is greater than the number of receiver antennas by taking advantage of the delay we also arrive at the design of a special trace orthonormal full diversity cyclotomic space time block code which for the number of transmitter antenna being equal to 2m can be proved to minimize the worst case pairwise error probability of a maximum likelihood ml detector for a q ary quadrature amplitude modulation qam signal constellation and therefore achieves optimal coding gain computer simulations show that these codes have bit error performance advantages over currently available codes

fourth order statistics for blind classification of spatial multiplexing and alamouti space time block code signals blind signal classification a major task of intelligent receivers has important civilian and military applications this problem becomes more challenging in multi antenna scenarios due to the diverse transmission schemes that can be employed e g spatial multiplexing sm and space time block codes stbcs this paper presents a class of novel algorithms for blind classification of sm and alamouti stbc al stbc transmissions unlike the prior art we show that signal classification can be performed using a single receive antenna by taking advantage of the space time redundancy the first proposed algorithm relies on the fourth order moment as a discriminating feature and employs the likelihood ratio test for achieving maximum average probability of correct classification this requires knowledge of the channel coefficients modulation type and noise power to avoid this drawback three algorithms have been further developed their common idea is that the discrete fourier transform of the fourth order lag product exhibits peaks at certain frequencies for the al stbc signals but not for the sm signals and thus provides the basis of a useful discriminating feature for signal classification the effectiveness of these algorithms has been demonstrated in extensive simulation experiments where a nakagami m fading channel and the presence of timing and frequency offsets are assumed

on mimo beamforming systems using quantized feedback we propose the hadamard matrix as a codebook for multiple input multiple output mimo beamforming systems and show that a quantized equal gain transmission qegt scheme using the hadamard codebook has the same symbol error probability performance as a receiver selection diversity combining scheme operating in independent generalized rayleigh fading channels we show that a mimo beamforming system using quantized feedback over rician fading channels can be analyzed by considering a corresponding receiver selection combining scheme operating in single input multiple output simo systems over correlated generalized rician fading channels also we propose a greedy cophasing scheme for mimo beamforming systems using quantized feedback the greedy cophasing scheme provides 3 2 db power gain over an orthogonal space time block code when the number of transmit antennas is four the number of receive antennas is one and the number of feedback bits is three

the multivariate skew normal distribution summary the paper extends earlier work on the so called skew normal distribution a family of distributions including the normal but with an extra parameter to regulate skewness the present work introduces a multivariate parametric family such that the marginal densities are scalar skew normal and studies its properties with special emphasis on the bivariate case

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

jointly minimum ber transmitter and receiver fir mimo filters for binary signal vectors a theory is developed for jointly minimizing the bit error rate ber between the desired and decoded signals with respect to the coefficients of transmitter and receiver finite impulse response fir multiple input multiple output mimo filters the original signal is assumed to be a vector time series with equally likely memoryless bernoulli vector components the channel model constitutes of a known fir mimo transfer function and gaussian additive noise independent of the original signal the channel input signal is assumed to be power constrained based on the formulas obtained an iterative numerical optimization algorithm is proposed when compared with other design methods available in the literature the proposed method yields better results due to the generality of the model considered and the joint optimization of the transmitter receiver pair

unknown input observers for 2d state space models in this paper dead beat unknown input observers uios for two dimensional 2d state space models are investigated dead beat uios are observers which produce an exact estimate of the original system state trajectory after a finite number of evolution steps independently of the system and observer initial conditions and of the unknown disturbances that affect the system functioning necessary and sufficient conditions for the existence of dead beat uios are provided as well as a parameterization of all dead beat uio transfer matrices comparisons with luenberger type uios are also carried out and the extension of the paper results to the case of asymptotic uios with a given rate of convergence and to roesser models are finally discussed

the geometric mean decomposition given a complex matrix h we consider the decomposition h qrp where q and p have orthonormal columns and r is a real upper triangular matrix with diagonal elements equal to the geometric mean of the positive singular values of h this decomposition which we call the geometric mean decomposition has application to signal processing and to the design of telecommunication networks the unitary matrices correspond to information lossless filters applied to transmitted and received signals that minimize the maximum error rate of the network another application is to the construction of test matrices with specified singular values

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

multiuser detection of alamouti signals in a mimo multiple access channel where users employ space time block codes stbc interference cancellation can be used to suppress co channel interference and recover the desired signal of each user at the receiver leveraging the special properties of alamouti matrices we first show that spatial multiplexing of alamouti signals retains the space time diversity gain of alamouti signaling using our proposed low complexity alamouti blast mmse a blast algorithm next in contrast to traditional transmit diversity that focuses on stbc construction at the transmitter this paper looks at transmit diversity from the perspective of the receiver in other words the receiver gets to choose the stbciquests which are favourable to the channel assuming a fixed blast receive algorithm in a multiusermac setting we first present a systematic methodology to exploit different decomposition structure in alamouti matrices each with different tradeoff between performance and decoding complexity using possibly different mimo receive algorithms we then demonstrate that the notion of angles the inner product of two quaternionic vectors between multiuser channels determines the performance of mimo receive algorithms as an application of the general theory we transform the decoding problem for several types of quasi orthogonal stbc qostbc into multiuser detection of virtual alamouti users building upon our a blast algorithm we propose new algorithms for decoding single user and multiuser qostbc in particular we show that bit error probability is a function of the quaternionic angle between virtual users for a single user or multiple users this angle varies with the type of qostbc and leads to a new form of adaptive modulation called code diversity where feedback instructs the transmitter how to choose from a plurality of codes

on the computation of the capacity region of the discrete mac the computation of the channel capacity of discrete memoryless channels is a convex problem that can be efficiently solved using the arimoto blahut ab iterative algorithm however the extension of this algorithm to the computation of capacity regions of multiterminal networks is not straightforward since it gives rise to non convex problems in this context the ab algorithm has only been successfully extended to the calculation of the sum capacity of the discrete memoryless multiple access channel dmac thus the computation of the whole capacity region still requires the use of computationally demanding search methods in this paper we first give an alternative reformulation of the capacity region of the dmac which condenses all the non convexities of the problem into a single rank one constraint then we propose efficient methods to compute outer and inner bounds on the capacity region of the two user dmac by solving a relaxed version of the problem and projecting its solution onto the original feasible set targeting numerical results we first take a randomization approach focusing on analytical results we study projection via minimum divergence which amounts to the marginalization of the relaxed solution in this case we derive sufficient conditions and necessary and sufficient conditions for the bounds to be tight furthermore we are able to show that the class of channels for which the marginalization bounds match exactly the capacity region includes all the two user binary input deterministic dmacs as well as other non deterministic channels in general however both methods are able to compute very tight bounds as shown for various examples

diversity multiplexing tradeoff and outage performance for rician mimo channels in this paper we analyze the diversity multiplexing tradeoff dmt originally introduced by zheng and tse and outage performance for rician multiple input multiple output mimo channels the dmt characteristics of rayleigh and rician channels are shown to be identical in a high signal to noise ratio snr regime the log log plot of outage probability versus snr curve for a rician channel is a shifted version of that for the corresponding rayleigh channel the snr gap between the outage curves of the rayleigh and rician channels is derived the dmt and outage performance are also analyzed for rician multiple input single output miso single input multiple output simo channels over a finite snr regime a closed form expression for the outage probability is derived and the finite snr dmt characteristic is analyzed it is observed that the maximum diversity gain can be achieved at some finite snr the maximum gain tends to increase linearly with the rician factor the finite snr diversity gain is shown to be a linear function of the finite snr multiplexing gain the consistency between the dmts for finite and infinite snrs is also shown

generally explicit space time codes with nonvanishing determinants for arbitrary numbers of transmit antennas nonvanishing determinants have emerged as an attractive criterion enabling a space time code achieve the optimal diversity multiplexing gains tradeoff it seems that cyclic division algebras play the most crucial role in designing a space time code with nonvanishing determinants in this paper we explicitly construct space time codes for arbitrary numbers of transmit antennas that achieve nonvanishing determinants and the optimal diversity multiplexing gains tradeoff over z i unlike previous methods usually arising a field compositum for two or more fields our scheme which only requires one simple extension constitutes a much more efficient and feasible advancement whether in theory or practice

mimo antenna subset selection with space time coding this paper treats multiple input multiple output mimo antenna subset selection employing space time coding we consider two cases differentiated based on the type of channel knowledge used in the selection process we address both the selection algorithms and the performance analysis we first consider the case when the antenna subsets are selected based on exact channel knowledge eck our results assume the transmission of orthogonal space time block codes with emphasis on the alamouti see ieee j select areas commun vol 16 p 1451 68 oct 1998 code next we treat the case of antenna subset selection when statistical channel knowledge sck is employed by the selection algorithm this analysis is applicable to general space time coding schemes when eck is available we show that the selection algorithm chooses the antenna set that maximizes the channel frobenius norm leading to both coding and diversity gain when sck is available the selection algorithm chooses the antenna set that maximizes the determinant of the covariance of the vectorized channel leading mostly to a coding gain in case of eck based selection we provide analytical expressions for average snr and outage probability improvement for the case when sck based selection is used we derive expressions for coding gain we also present extensive simulation studies validating our results

equal diagonal qr decomposition and its application to precoder design for successive cancellation detection in multiple input multiple output mimo multiuser detection theory the qr decomposition of the channel matrix h can be used to form the back cancellation detector in this paper we propose an optimal qr decomposition which we call the equal diagonal qr decomposition or briefly the qrs decomposition we apply the decomposition to precoded successive cancellation detection where we assume that both the transmitter and the receiver have perfect channel knowledge we show that for any channel matrix h there exists a unitary precoder matrix s such that hs qr where the nonzero diagonal entries of the upper triangular matrix r in the qr decomposition of hs are all equal to each other the precoder and the resulting successive cancellation detector have the following properties a the minimum euclidean distance between two signal points at the channel output is equal to the minimum euclidean distance between two constellation points at the precoder input up to a multiplicative factor that equals the diagonal entry in the r factor b the superchannel hs naturally exhibits an optimally ordered column permutation i e the optimal detection order for the vertical bell labs layered space time v blast detector is the natural order c the precoder s minimizes the block error probability of the qr successive cancellation detector d a lower and an upper bound for the free distance at the channel output is expressible in terms of the diagonal entries of the r factor in the qr decomposition of a channel matrix e the precoder s maximizes the lower bound of the channel s free distance subject to a power constraint f for the optimal precoder s the performance of the qr detector is asymptotically at large signal to noise ratios snrs equivalent to that of the maximum likelihood detector mld that uses the same precoder further we consider two multiplexing schemes time division multiple access tdma and orthogonal frequency division multiplexing ofdm we d

integer forcing linear receivers linear receivers are often used to reduce the implementation complexity of multiple antenna systems in a traditional linear receiver architecture the receive antennas are used to separate out the codewords sent by each transmit antenna which can then be decoded individually although easy to implement this approach can be highly suboptimal when the channel matrix is near singular this paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer valued entries rather than attempting to recover transmitted codewords directly the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix the codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords provided that the effective channel is full rank these integer combinations can then be digitally solved for the original codewords this paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter s which corresponds either to a multiuser uplink scenario or to single user v blast encoding in this setting the proposed integer forcing linear receiver significantly outperforms conventional linear architectures such as the zero forcing and linear minimum mean squared error receiver in the high signal to noise ratio regime the proposed receiver attains the optimal diversity multiplexing tradeoff for the standard multiple input multiple output mimo channel with no coding across transmit antennas it is further shown that in an extended mimo model with interference the integer forcing linear receiver achieves the optimal generalized degrees of freedom

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

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

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

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

scrip successive convex optimization methods for risk parity portfolio design the traditional markowitz portfolio optimization proposed in the 1950s has not been embraced by practitioners despite its theoretical elegance recently an alternative risk parity portfolio design has been receiving significant attention from both the theoretical and practical sides due to its advantage in diversification of ex ante risk contributions among assets such risk contributions can be deemed good predictors for the ex post loss contributions especially when there exist huge losses most of the existing specific problem formulations on risk parity portfolios are highly nonconvex and are solved via standard off the shelf numerical optimization methods e g sequential quadratic programming and interior point methods however for nonconvex risk parity formulations such standard numerical approaches may be highly inefficient and may not provide satisfactory solutions in this paper we first propose a general risk parity portfolio problem formulation that can fit most of the existing specific risk parity formulations and then propose a family of simple and efficient successive convex optimization methods for the general formulation the numerical results show that our proposed methods significantly outperform the existing ones

iterative rate distortion optimization of h 264 with constant bit rate constraint in this paper we apply the primal dual decomposition and subgradient projection methods to solve the rate distortion optimization problem with the constant bit rate constraint the primal decomposition method enables spatial or temporal prediction dependency within a group of picture gop to be processed in the master primal problem as a result we can apply the dual decomposition to minimize independently the lagrangian cost of all the mbs using the reference software model of h 264 furthermore the optimal lagrange multiplier is iteratively derived from the solution of the dual problem as an example we derive the optimal bit allocation condition with the consideration of temporal prediction dependency among the pictures experimental results show that the proposed method achieves better performance than the reference software model of h 264 with rate control

distributed optimal beamformers for cognitive radios robust to channel uncertainties through spatial multiplexing and diversity multi input multi output mimo cognitive radio cr networks can markedly increase transmission rates and reliability while controlling the interference inflicted to peer nodes and primary users pus via beamforming the present paper optimizes the design of transmit and receive beamformers for ad hoc cr networks when cr to cr channels are known but cr to pu channels cannot be estimated accurately capitalizing on a norm bounded channel uncertainty model the optimal beamforming design is formulated to minimize the overall mean square error mse from all data streams while enforcing protection of the pu system when the cr to pu channels are uncertain even though the resultant optimization problem is non convex algorithms with provable convergence to stationary points are developed by resorting to block coordinate ascent iterations along with suitable convex approximation techniques enticingly the novel schemes also lend themselves naturally to distributed implementations numerical tests are reported to corroborate the analytical findings

a note on the state space realization of 2d fir transfer functions abstract some properties of minimal state space realizations of 2d fir transfer functions are investigated it is shown that hidden modes are allowed in minimal realization and consequently there exist internally unstable minimal realizations of fir transfer functions

statistical inference based on pseudo maximum likelihood estimators in elliptical populations in this article we develop statistical inference based on the maximum likelihood method in elliptical populations with an unknown density function the method assuming the multivariate normal distribution using the sample mean and the sample covariance matrix is basically correct even for elliptical populations under a certain kurtosis adjustment but is not statistically efficient especially when the kurtosis of the population distribution has higher than moderate values on the other hand several methods of statistical inference assuming a particular family e g multivariate t distribution of elliptical distributions have been recommended as a robust procedure against outliers or distributions with heavy tails such inference also will be important to maintain a high efficiency of statistical inference in elliptical populations in practice however it is very difficult to choose an appropriate family of elliptical distributions and one may misspecify the family furthermore extra parameters

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

an efficient detector for combined space time coding and layered processing group layered space time architecture glst combines space time block coding and layered space time processing where the transmit stream is partitioned into different groups and in each group space time block coding is applied in the traditional receiver of glst group detection is applied first to suppress the interference from other groups and then decoding is performed for the desired group in this letter a novel detector is proposed in which the entire groups are decoded first and then group detection is performed next theoretical analysis will demonstrate that the new detector can achieve a significant capacity gain compared with the traditional one simulation results will further show that the proposed detector can obtain at least 4 db gain at a frame error rate of 10 sup 2 for instance

a short note on the estimation of the asymptotic covariance matrix for polychoric correlations by using a taylor expansion of the equations that define the two step estimator for polychoric correlations the asymptotic covariance matrix for the estimated correlations can be derived in a simple and straightforward way

goodman and kruskal s gamma coefficient for ordinalized bivariate normal distributions we consider a bivariate normal distribution with linear correlation formula see text whose random components are discretized according to two assigned sets of thresholds on the resulting bivariate ordinal random variable one can compute goodman and kruskal s gamma coefficient formula see text which is a common measure of ordinal association given the known analytical monotonic relationship between pearson s formula see text and kendall s rank correlation formula see text for the bivariate normal distribution and since in the continuous case kendall s formula see text coincides with goodman and kruskal s formula see text the change of this association measure before and after discretization is worth studying we consider several experimental settings obtained by varying the two sets of thresholds or equivalently the marginal distributions of the final ordinal variables this study confirming previous findings shows how the gamma coefficient is always larger in absolute value than kendall s rank correlation this discrepancy lessens when the number of categories increases or given the same number of categories when using equally probable categories based on these results a proposal is suggested to build a bivariate ordinal variable with assigned margins and goodman and kruskal s formula see text by ordinalizing a bivariate normal distribution illustrative examples employing artificial and real data are provided

directed graphs 2d state models and characteristic polynomials of irreducible matrix pairs abstract the definition and main properties of a 2d digraph namely a directed graph with two kinds of arcs are introduced under the assumption of strong connectedness the analysis of its paths and cycles is performed based on an integer matrix whose rows represent the compositions of all circuits and on the corresponding row module natural constraints on the composition of the paths connecting each pair of vertices lead to the definition of a 2d strongly connected digraph for a 2d digraph of this kind the set of vertices can be partitioned into disjoint 2d imprimitivity classes whose number and composition are strictly related to the structure of the row module irreducible matrix pairs i e pairs endowed with a 2d strongly connected digraph are subsequently discussed equivalent descriptions of irreducibility naturally extending those available for a single irreducible matrix are obtained these refer to the free evolution of the 2d state models described by the pairs and to their characteristic polynomials finally primitivity is viewed as a special case of irreducibility and completely characterized in terms of 2d digraphs characteristic polynomials and 2d system dynamics

interpolation based transmit beamforming for mimo ofdm with limited feedback transmit beamforming and receive combining are simple methods for exploiting spatial diversity in multiple input multiple output orthogonal frequency division multiplexing mimo ofdm system optimal beamforming requires channel state information in the form of the beamforming vectors for each ofdm subcarrier this paper proposes a limited feedback architecture that combines beamforming vector quantization and smart vector interpolation in the proposed system the receiver sends a fraction of information about the optimal beamforming vectors to the transmitter and the transmitter computes the beamforming vectors for all subcarriers through interpolation a new spherical interpolator is developed that exploits parameters for phase rotation to satisfy the phase invariance and unit norm properties of the transmitted beamforming vectors the beamforming vectors and phase parameters are quantized at the receiver and the quantized information is provided to the transmitter the proposed quantization system provides only a moderate increase in complexity versus over comparable approaches numerical simulations show that the proposed scheme performs better than existing diversity techniques with the same feedback data rate

limited information goodness of fit testing in multidimensional contingency tables we introduce a family of goodness of fit statistics for testing composite null hypotheses in multidimensional contingency tables these statistics are quadratic forms in marginal residuals up to order r they are asymptotically chi square under the null hypothesis when parameters are estimated using any asymptotically normal consistent estimator for a widely used item response model when r is small and multidimensional tables are sparse the proposed statistics have accurate empirical type i errors unlike pearson s x2 for this model in nonsparse situations the proposed statistics are also more powerful than x2 in addition the proposed statistics are asymptotically chi square when applied to subtables and can be used for a piecewise goodness of fit assessment to determine the source of misfit in poorly fitting models

reduced feedback mimo ofdm precoding and antenna selection transmitter precoding for multiple input multiple output orthogonal frequency division multiplexing mimo ofdm is an effective way of leveraging the diversity gains afforded by a multiple transmit multiple receive antenna system in a frequency selective environment in the limited feedback scenario optimal precoder representation for narrowband mimo systems using moderately sized codebooks designed on the grassmann manifold has been shown to perform remarkably well in mimo ofdm systems precoder matrices have to be designed for all subcarriers and the amount of feedback can get prohibitively large this is especially true for next generation wireless local area networks and wireless metropolitan area networks which have a large number of subcarriers in this paper we present techniques to reduce this feedback requirement and the performance of these algorithms is numerically shown to provide improvement over existing schemes

tomlinson harashima precoding for multiuser mimo systems with quantized csi feedback and user scheduling this paper studies the sum rate performance of a low complexity quantized csi based tomlinson harashima th precoding scheme for downlink multiuser mimo transmission employing greedy user selection the asymptotic distribution of the output signal to interference plus noise ratio of each selected user and the asymptotic sum rate as the number of users k grows large are derived by using extreme value theory for fixed finite signal to noise ratios and a finite number of transmit antennas n t we prove that as k grows large the proposed approach can achieve the optimal sum rate scaling of the mimo broadcast channel we also prove that if we ignore the precoding loss the average sum rate of this approach converges to the average sum capacity of the mimo broadcast channel our results provide insights into the effect of multiuser interference caused by quantized csi on the multiuser diversity gain

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

item response theory with estimation of the latent population distribution using spline based densities the purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines a spline based density estimation system provides a flexible alternative to existing procedures that use a normal distribution or a different functional form for the population distribution a simulation study shows that the new procedure is feasible in practice and that when the latent distribution is not well approximated as normal two parameter logistic 2pl item parameter estimates and expected a posteriori scores eaps can be improved over what they would be with the normal model an example with real data compares the new method and the extant empirical histogram approach

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

space time frequency shift keying frequency shift keying fsk is a popular modulation scheme in power limited communication links this paper introduces space time fsk st fsk which does not require any channel state information at the transmitter and the receiver as in conventional noncoherent fsk st fsk can be viewed as a special unitary st modulation design however st fsk has a number of advantages over existing unitary st modulation designs st fsk is easier to design and enjoys lower decoding complexity furthermore st fsk guarantees full diversity finally st fsk can be adopted in the digital as well as in the analog domain and merges very naturally with frequency hopping multiple access as expected all these advantages come at the cost of a decrease in spectral efficiency

optimal linear precoding strategies for wideband non cooperative systems based on game theory part ii algorithms in this two part paper we address the problem of finding the optimal precoding multiplexing scheme for a set of noncooperative links sharing the same physical resources e g time and bandwidth we consider two alternative optimization problems p l the maximization of mutual information on each link given constraints on the transmit power and spectral mask and p 2 the maximization of the transmission rate on each link using finite order constellations under the same constraints as in p l plus a constraint on the maximum average error probability on each link aiming at finding decentralized strategies we adopted as optimality criterion the achievement of a nash equilibrium and thus we formulated both problems p l and p 2 as strategic noncooperative matrix valued games in part i of this two part paper after deriving the optimal structure of the linear transceivers for both games we provided a unified set of sufficient conditions that guarantee the uniqueness of the nash equilibrium in this part ii of the paper we focus on the achievement of the equilibrium and propose alternative distributed iterative algorithms that solve both games specifically the new proposed algorithms are the following 1 the sequential and simultaneous iterative waterfilling based algorithms incorporating spectral mask constraints and 2 the sequential and simultaneous gradient projection based algorithms establishing an interesting link with variational inequality problems our main contribution is to provide sufficient conditions for the global convergence of all the proposed algorithms which although derived under stronger constraints incorporating for example spectral mask constraints have a broader validity than the convergence conditions known in the current literature for the sequential iterative waterfilling algorithm

asymptotic information lossless designs and the diversity multiplexing tradeoff it is known that neither the alamouti nor the v blast scheme achieves the zheng tse diversity multiplexing tradeoff dmt of the multiple input multiple output mimo channel with respect to the dmt curve the alamouti scheme achieves the point corresponding to maximum diversity gain only whereas v blast meets only the point corresponding to maximum multiplexing gain it is also known that d blast achieves the optimal dmt for n transmit and n receive antennas but only under the assumption that the leading and trailing zeros are ignored when these zeros are taken into account d blast achieves the point corresponding to zero multiplexing gain but not the point corresponding to zero diversity gain the first scheme to achieve the dmt is the coding scheme of yao and wornell for the case of two transmit and two receive antennas in this paper we introduce the notion of an asymptotic information lossless aill design and obtain a necessary and sufficient condition under which a design is aill analogous to the result that full rank designs achieve the point corresponding to the zero multiplexing gain of the optimal dmt curve we show aill to be a necessary and sufficient condition for a design to achieve the point on the dmt curve corresponding to zero diversity gain we also derive a lower bound on the tradeoff achieved by designs from field extensions and show that the tradeoff is very close to the optimal tradeoff in the case of a single receive antenna a lower bound to the tradeoff achieved by designs from division algebras is presented which indicates that these designs achieve both extreme points corresponding to zero diversity and zero multiplexing gain of the optimal dmt curve finally we present simulations results for n transmit and n receive antennas for n 2 3 4 which suggest that designs from division algebras are likely to have the property of being dmt achieving

limited information estimation and testing of discretized multivariate normal structural models discretized multivariate normal structural models are often estimated using multistage estimation procedures the asymptotic properties of parameter estimates standard errors and tests of structural restrictions on thresholds and polychoric correlations are well known it was not clear how to assess the overall discrepancy between the contingency table and the model for these estimators it is shown that the overall discrepancy can be decomposed into a distributional discrepancy and a structural discrepancy a test of the overall model specification is proposed as well as a test of the distributional specification i e discretized multivariate normality also the small sample performance of overall distributional and structural tests as well as of parameter estimates and standard errors is investigated under conditions of correct model specification and also under mild structural and or distributional misspecification it is found that relatively small samples are needed for parameter estimates standard errors and structural tests larger samples are needed for the distributional and overall tests furthermore parameter estimates standard errors and structural tests are surprisingly robust to distributional misspecification

matrix pairs in two dimensional systems an approach based on trace series and hankel matrices two dimensional system dynamics depends on matrix pairs that represent the shift operators along coordinate axes the structure of a matrix pair is analysed according to its characteristic polynomial and to the traces of suitable matrices in the algebra generated by the elements of the pair necessary and sufficient conditions for properties l and p are provided by resorting to hankel matrix theory finite memory and separable systems as well as two dimensional systems whose characteristic polynomials exhibit one dimensional structures are finally characterized in terms of spectral properties and traces

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

multistage iterative decoding with complexity reduction for concatenated space time codes space time encoders exploiting concatenated coding structures are efficient in attaining the high rates available to large dimensional multiple transmitter multiple receiver wireless systems under fading conditions while also providing maximal diversity benefits we present a multistage iterative decoding structure that takes full advantage of the concatenated nature of the transmission path treating the modulator and channel stages as an additional encoder in serial concatenation this iterative decoder architecture allows an encoder employing decoupled coding and modulation to reach the performance of coded modulation systems it also admits reduced complexity decoding with a computational load that is nonexponential in the number of antennas or the transmission bit rate and makes practical decoding for large transmitter arrays possible the performance curves for these methods follow the shape of the fano bound with only a modest power penalty

on the estimation of polychoric correlations and their asymptotic covariance matrix a general theory for parametric inference in contingency tables is outlined estimation of polychoric correlations is seen as a special case of this theory the asymptotic covariance matrix of the estimated polychoric correlations is derived for the case when the thresholds are estimated from the univariate marginals and the polychoric correlations are estimated from the bivariate marginals for given thresholds computational aspects are also discussed

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

robust training sequence design for correlated mimo channel estimation we study how to design a worst case robust training sequence for multiple input multiple output mimo channel estimation we consider mean squared error of channel estimates as the figure of merit which is a function of second order statistics of the mimo channel i e channel covariance matrix in order to optimize training sequences under a total power constraint in practical applications the channel covariance matrix is not known perfectly thus the main aspect of our design is to improve robustness of the training sequences against possible uncertainties in the available channel covariance matrix using a deterministic uncertainty model we formulate a robust training sequence design as a minimax optimization problem where we take such imperfections into account we investigate the robust design problem assuming the general case of an arbitrarily correlated mimo channel and a non empty compact convex uncertainty set we prove that such a problem admits a globally optimal solution by exploiting the convex concave structure of the objective function and propose numerical algorithms to address the robust training design problem we proceed the analysis by considering multiple input single output miso channels and kronecker structured mimo channels along with unitarily invariant uncertainty sets for these scenarios we show that the problem is diagonalized by the eigenvectors of the nominal covariance matrices so that the robust design is significantly simplified from a complex matrix variable problem to a real vector variable power allocation problem for the miso channel we provide closed form solutions for the robust training sequences with the uncertainty sets defined by the spectral norm and nuclear norm

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