on optimal multilayer cyclotomic space time code designs high rate and large diversity product or coding advantage or coding gain or determinant distance or minimum product distance are two of the most important criteria often used for good space time code designs in recent linear lattice based space time code designs more attention is paid to the high rate criterion but less to the large diversity product criterion in this paper we consider these two criteria together for multilayer cyclotomic space time code designs in a previous paper we recently proposed a systematic cyclotomic diagonal space time code design over a general cyclotomic number ring that has infinitely many designs for a fixed number of transmit antennas where diagonal codes correspond to single layer codes in this paper in this paper we first propose a general multilayer cyclotomic space time codes we present a general optimality theorem for these infinitely many cyclotomic diagonal or single layer space time codes over general cyclotomic number rings for a general number of transmit antennas we then present optimal multilayer full rate cyclotomic space time code designs for two and three transmit antennas we also present an optimal two layer cyclotomic space time code design for three and four transmit antennas the optimality here is in the sense that for a fixed mean transmission signal power its diversity product is maximized or equivalently for a fixed diversity product its mean transmission signal power is minimized it should be emphasized that all the optimal multilayer cyclotomic space time codes presented in this paper have the nonvanishing determinant property

uniqueness for an inverse problem for a nonlinear parabolic system with an integral term by one point dirichlet data abstract we consider an inverse problem arising in laser induced thermotherapy a minimally invasive method for cancer treatment in which cancer tissues is destroyed by coagulation for the dosage planning quantitatively reliable numerical simulation are indispensable to this end the identification of the thermal growth kinetics of the coagulated zone is of crucial importance mathematically this problem is a nonlinear and nonlocal parabolic inverse heat source problem we show in this paper that the temperature dependent thermal growth parameter can be identified uniquely from a one point measurement

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

kalman filtering in triplet markov chains let x xn nisinin be a hidden process y yn nisinin an observed process and r rn nisinin some additional process we assume that t x r y is a so called triplet vector markov chain tmc we first show that the linear tmc model encompasses and generalizes among other models the classical state space systems with colored process and or measurement noise s we next propose restoration kalman like filters for arbitrary linear gaussian lg tmc

on transceiver signal linearization and the decoding delay of maximum rate complex orthogonal space time block codes complex orthogonal designs cods have been successfully implemented in wireless systems as complex orthogonal space time block codes costbcs certain properties of the underlying cods affect the performance of the codes in addition to the main properties of a cod s rate and decoding delay a third consideration is whether the cod can achieve transceiver signal linearization a property that facilitates practical implementation by for example significantly simplifying the receiver structure for iterative decoding it has been shown that a cod can achieve this transceiver signal linearization if the nonzero entries in any given row of the matrix are either all conjugated or all nonconjugated this paper determines the conditions under which maximum rate cods can achieve this desirable property for an odd number of transmit antennas it is shown that maximum rate cods that achieve the lower bound on decoding delay can also achieve transceiver signal linearization in contrast for an even number of transmit antennas maximum rate cods that achieve the lower bound on delay cannot achieve this linearization in this latter case linearization is possible only if the cod achieves at least twice the lower bound on delay this work highlights the tradeoffs among these three important properties

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

unbiased fir filtering of discrete time polynomial state space models we address an unbiased finite impulse response fir filter for discrete time state space models with polynomial representation of the states the unique l degree polynomial fir filter gain and the estimate variance are found for a general case the noise power gain ng is derived for white gaussian noises in the model and in the measurement the filter does not involve any knowledge about noise in the algorithm it is unstable at short horizons 2 les n les l and inefficient ng exceeds unity in the narrow range l 1 the estimate noise becomes negligible and the filter thus optimal in the sense of zero bias and zero noise having such properties the proposed unbiased fir filter fits well slowly changing with time models an example is given for a two state system

high rate single symbol ml decodable precoded dstbcs for cooperative networks distributed orthogonal space time block codes dostbcs achieving full diversity order and single symbol maximum likelihood ml decodability have been introduced recently by yi and kim for cooperative networks and an upper bound on the maximal rate of such codes along with code constructions has been presented in this paper a new class of single symbol ml decodable precoded distributed space time block codes ssd pdstbcs called semiorthogonal ssd pdstbcs semi ssd pdstbcs is introduced wherein the source performs linear precoding of information symbols appropriately before transmitting it to all the relays it is shown that dostbcs are a special case of semi ssd pdstbcs a special class of semi ssd pdstbcs having diagonal covariance matrix at the destination is studied and an upper bound on the maximal rate of such codes is derived the bounds obtained are approximately twice larger than that of the dostbcs a systematic construction of semi ssd pdstbcs is presented when the number of relays k ges 4 the constructed codes are shown to achieve the upper bound on the rate when k is of the form 0 or 3 modulo 4 for the rest of the values of k the constructed codes are shown to have rates higher than that of dostbcs it is shown that semi ssd pdstbcs cannot be constructed with any form of linear processing at the relays when the source does not perform linear precoding of the information symbols

linear optimal unbiased filter for time variant systems without apriori information on initial conditions in this technical note an optimal unbiased filter ouf is derived for time variant systems to relax the initial condition assumption in kalman filter kf by minimizing the mean square errors subject to the unbiasedness condition a solution is derived in a batch computation form first to facilitate the on line application a recursive realization is further developed the effect of removing the initial condition assumption on the estimation performance is analysed and we show that the proposed algorithm converges to the kf asymptotically two state harmonic model and four state moving target tracking model are employed to demonstrate that the ouf can improve transient estimation performance significantly and can be used in place of the kf when the apriori information about the initial state values is not available

fast kalman like optimal unbiased fir filtering with applications in this paper an optimal unbiased finite impulse response oufir filter is proposed as a linking solution between the unbiased fir ufir filter and the kalman filter kf we first derive the batch oufir estimator to minimize the mean square error mse subject to the unbiasedness constraint and then find its fast iterative form it is shown that the oufir filter is full horizon fh and that its estimate converges to the kf estimate by increasing the horizon length n as a special feature we note that the fh oufir filter operates almost as fast as the kf several other critical properties of the oufir filter are illustrated based on simulations and practical applications similar to the ufir filter and contrary to the kf the oufir filter is highly insensitive to the initial conditions it has much better robustness than kf against temporary model uncertainties finally the oufir filter allows for ignoring system noise which is typically not well known to the engineer

on the minimum decoding delay of balanced complex orthogonal designs a complex orthogonal design cod with parameter p n k is a combinatorial design used in space time block codes stbcs for stbcs n is the number of antennas k p is the rate and p is the decoding delay a class of rate 1 2 cods called balanced complex orthogonal designs bcods has been proposed by adams et al who constructed bcods with rate k p 1 2 and decoding delay p 2 m for n 2m furthermore they proved that the constructions have optimal decoding delay when m is congruent to 1 2 or 3 modulo 4 they conjectured that for the case m 0 mod 4 2 m is also a lower bound on p in this paper we prove this conjecture

square matrix embeddable space time block codes for complex signal constellations space time block codes for providing transmit diversity in wireless communication systems are considered based on the principles of linearity and unitarity a complete classification of linear codes is given in the case when the symbol constellations are complex and the code is based on a square matrix or restriction of such by deleting columns antennas maximal rate delay optimal codes are constructed within this category the maximal rates allowed by linearity and unitarity fall off exponentially with the number of transmit antennas

brief paper state estimation in the presence of bounded disturbances this contribution proposes a robust recursive algorithm for the state estimation of linear models with unknown but bounded disturbances corrupting both the state and measurement vectors a novel approach based on state bounding techniques is presented the proposed algorithm can be decomposed into two steps time updating and observation updating that uses a switching estimation kalman like gain matrix particular emphasis will be given to the design of a weighting factor that ensures the stability of the estimation error

bayesian state estimation on finite horizons the case of linear state space model abstract the finite impulse response fir filter and infinite impulse response filter including the kalman filter kf are generally considered as two different types of state estimation methods in this paper the sequential bayesian philosophy is extended to a filter design using a fixed amount of most recent measurements with the aim of exploiting the fir structure and unifying some basic fir filters with the kf specifically the conditional mean and covariance of the posterior probability density functions are first derived to show the fir counterpart of the kf to remove the dependence on initial states the corresponding likelihood is further maximized and realized iteratively it shows that the maximum likelihood modification unifies the existing unbiased fir filters by tuning a weighting matrix moreover it converges to the kalman estimate with the increase of horizon length and can thus be considered as a link between the fir filtering and the kf several important properties including stability and robustness against errors of noise statistics are illustrated finally a moving target tracking example and an experiment with a three degrees of freedom helicopter system are introduced to demonstrate effectiveness

on the dimension of spaces of linear transformations satisfying rank conditions abstract let l c n c m be the space from c n to c m let l k n m be the maximal dimension of a linear subspace v of l c n c m such that every nonzero map in v has rank k in this paper we develop some techniques for estimating l from above

novel constructions of improved square complex orthogonal designs for eight transmit antennas constructions of square maximum rate complex orthogonal space time block codes co stbcs are well known however codes constructed via the known methods include numerous zeros which impede their practical implementation by modifying the williamson and wallis whiteman arrays to apply to complex matrices we propose two methods of construction of square order 4n co stbcs from square order n codes which satisfy certain properties applying the proposed methods we construct square maximum rate order 8 co stbcs with no zeros such that the transmitted symbols are equally dispersed through transmit antennas those codes referred to as the improved square co stbcs have the advantages that the power is equally transmitted via each transmit antenna during every symbol time slot and that a lower peak to average power ratio papr is required to achieve the same bit error rates as the conventional co stbcs with zeros

representation theory for high rate multiple antenna code design multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment but the practical success of using multiple antennas depends crucially on our ability to design high rate space time constellations with low encoding and decoding complexity it has been shown that full transmitter diversity where the constellation is a set of unitary matrices whose differences have nonzero determinant is a desirable property for good performance we use the powerful theory of fixed point free groups and their representations to design high rate constellations with full diversity furthermore we thereby classify all full diversity constellations that form a group for all rates and numbers of transmitter antennas the group structure makes the constellations especially suitable for differential modulation and low complexity decoding algorithms the classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd we therefore also consider extensions of the constellation designs to nongroups we conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels

the minimum decoding delay of maximum rate complex orthogonal space time block codes the growing demand for efficient wireless transmissions over fading channels motivated the development of space time block codes space time block codes built from generalized complex orthogonal designs are particularly attractive because the orthogonality permits a simple decoupled maximum likelihood decoding algorithm while achieving full transmit diversity the two main research problems for these complex orthogonal space time block codes costbcs have been to determine for any number of antennas the maximum rate and the minimum decoding delay for a maximum rate code the maximum rate for costbcs was determined by liang in 2003 this paper addresses the second fundamental problem by providing a tight lower bound on the decoding delay for maximum rate codes it is shown that for a maximum rate costbc for 2m 1 or 2m antennas a tight lower bound on decoding delay is r m 1 2m this lower bound on decoding delay is achievable when the number of antennas is congruent to 0 1 or 3 modulo 4 this paper also derives a tight lower bound on the number of variables required to construct a maximum rate costbc for any given number of antennas furthermore it is shown that if a maximum rate costbc has a decoding delay of r where r r les 2r then r 2r this is used to provide evidence that when the number of antennas is congruent to 2 modulo 4 the best achievable decoding delay is 2 m 1 2m

square root receding horizon information filters for nonlinear dynamic system models new nonlinear filtering algorithms are designed based on a receding horizon strategy i e a finite impulse response fir structure and square root information filtering to achieve high accuracy and good performance in empirical error covariance tests the new nonlinear receding horizon filters reduce approximation errors in nonlinear filtering by considering a set of recent observations with non informative initial conditions by applying information filtering we are able to manage the non informative initial conditions and thus propose the square root version of the algorithm as a means of retaining the positive definiteness of the error covariance based on the proposed strategy we then implement known nonlinear filtering frameworks simulation results confirm that the new nonlinear receding horizon filters outperform existing nonlinear filters in well known nonlinear examples

analysis and optimization of diagonally layered lattice schemes for mimo fading channels embodiments of the diagonal bell laboratories layered space time d blast architecture for multiple input multiple output mimo communication are developed wherein information symbol vectors are encoded using codewords from a lattice code called a diagonally layered lattice dll code which are formatted onto the diagonals of a space time frame decoding is done using a sphere decoder for each diagonal based on soft statistics obtained after zero forcing zf or minimum mean square error mmse filtering and decision feedback these operations give rise to an effective parallel channel model with channel gains with nonidentical statistics and additive noise which is gaussian in the zf filtering case and non gaussian in the mmse filtering case the so called full modulation diversity fmd property is nevertheless shown to yield the maximum achievable diversity orders over the mimo channel for both the zf and the mmse filtering based decoders respectively for any arbitrary fading distribution in the case of the independent identically distributed i i d rayleigh fading mimo channel with k transmit and n receive antennas with ngesk these diversity orders are nk k k 1 2 and nk for zf and mmse filtering based decoding respectively the error probability analysis also yields a design criterion for optimizing transmit power allocations several lattice design methods are proposed for the effective parallel channel models two methods are proposed to achieve high coding gain in the rayleigh fading mimo channel a third method is proposed that minimizes the exact symbol error probability sep and can be tailored for any given fading distribution a novel soft decision feedback decoder is also proposed based on the list sphere decoder to mitigate error propagation due to hard decision feedback the salient feature of the proposed dll schemes is that they have nearly full rate and full or high diversity order and yet a much lower decoding complexity than other existing full rate full diversity space time block codes stbcs the frame error probability fep performance of the optimized dll schemes for moderate to high spectral efficiencies and a wide range of signal to noise ratios snrs can be quite close to the performance of the best performing but more complex to decode stbcs moreover the proposed dll schemes significantly outperform other existing mimo systems of comparable decoding complexity

unitary space time modulation for multiple antenna communications in rayleigh flat fading motivated by information theoretic considerations we propose a signaling scheme unitary space time modulation for multiple antenna communication links this modulation is ideally suited for rayleigh fast fading environments since it does not require the receiver to know or learn the propagation coefficients unitary space time modulation uses constellations of t spl times m space time signals spl phi sub i l 1 l where t represents the coherence interval during which the fading is approximately constant and m t is the number of transmitter antennas the columns of each spl phi sub i are orthonormal when the receiver does not know the propagation coefficients which between pairs of transmitter and receiver antennas are modeled as statistically independent this modulation performs very well either when the signal to noise ratio snr is high or when t spl gt m we design some multiple antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding we demonstrate that two antennas have a 6 db diversity gain over one antenna at 15 db snr

full diversity codes for miso systems equipped with linear or ml detectors in this paper a general criterion for space time block codes stbc to achieve full diversity with a linear receiver is proposed for a wireless communication system having multiple transmitter and single receiver antennas multiple input single output miso particularly the stbc with toeplitz structure satisfies this criterion and therefore enables full diversity further examination of this toeplitz stbc reveals the following important properties 1 the symbol transmission rate can be made to approach unity 2 applying the toeplitz code to any signalling scheme having nonzero distance between the nearest constellation points results in a nonvanishing determinant in addition if quadratic amplitude modulation qam is used as the signalling scheme then for independent miso flat fading channels the toeplitz codes is proved to approach the optimal diversity versus multiplexing tradeoff with a zero forcing zf receiver when the number of channel uses is large this is so far the first nonorthogonal stbc shown to achieve the optimal tradeoff for such a receiver on the other hand when maximum likelihood ml detection is employed in a miso system the toeplitz stbc achieves the maximum coding gain for independent channels when the channel fading coefficients are correlated the inherent transmission matrix in the toeplitz stbc can be designed to minimize the average worst case pairwise error probability

orthogonal designs with maximal rates orthogonal designs have been used as space time block codes for wireless communications with multiple transmit antennas which can achieve full transmit diversity and have a very simple decoupled maximum likelihood decoding algorithm the rate of an orthogonal design is defined as the ratio of the number of transmitted information symbols in a block of channel uses to the length of the given block which reflects the bandwidth efficiency of the employed space time block code constructed from the orthogonal design this paper focuses on the analysis and synthesis of orthogonal designs with the maximum possible rates which may be real or complex and square or rectangular matrices we first provide several representations of orthogonal designs and their characterizations in terms of hurwitz radon matrix equations next we observe that the real orthogonal designs square or rectangular and the complex square orthogonal designs with maximal rates have been well understood from the existing results in the mathematics literature which can be dated back to 1890s however unfortunately it is not the case for the complex rectangular orthogonal designs with rates as high as possible we then construct a class of complex orthogonal designs for any number of transmit antennas the proposed complex orthogonal designs for the number of transmit antennas n 2m 1 and 2m have the same rate m 1 and 2m where m is any natural number finally we demonstrate that for n 2m 1 and 2m with any given natural number m the value m 1 and 2m is the maximum possible rate that the complex orthogonal designs square or rectangular with n transmit antennas can achieve

blind ml detection of orthogonal space time block codes identifiability and code construction the blind maximum likelihood ml detection of a general space time block code stbc is considered a challenging implementation problem recent work has revealed that for the orthogonal stbcs ostbcs their special code structures can be exploited to formulate highly effective blind ml based algorithms attracted by this realization merit this paper investigates the blind ml identifiability of ostbcs with an emphasis on the binary psk bpsk and quaternary psk qpsk constellations we find a class of ostbcs called the nonrotatable ostbcs that can be uniquely identified up to a sign uiuts almost surely under a few mild assumptions for example for an independently distributed rayleigh channel with any number of receiver antennas a nonrotatable ostbc can be uiuts with probability 1 while this identifiability looks appealing already we further examine a subclass of nonrotatable ostbcs called the nonintersecting subspace nis ostbcs we prove that nis ostbcs are uiuts for any nonzero channel however nis ostbcs are not available in the existing literature to fill this gap we devise a code construction procedure that can convert any bpsk or qpsk ostbc to an nis ostbc

novel classes of minimal delay and low papr rate 1 over 2 complex orthogonal designs complex orthogonal designs cods of rate 1 2 have been considered recently for use in analog transmissions and as an alternative to maximum rate cods due to the savings in decoding delay as the number of antennas increases while algorithms have been developed to show that an upper bound on the minimum decoding delay for rate 1 2 cods with n 2m 1 or n 2m columns is n 2m 1 or n 2m depending on the parity of n modulo 8 it remains open to determine the exact minimum delay this paper shows that this bound n is also a lower bound on minimum decoding delay for a major class of rate 1 2 cods named balanced complex orthogonal designs bcods and that this is the exact minimum decoding delay for most bcods these rate 1 2 codes are conjugation separated and thus permit a linearized description of the transceiver signal bcods also display other combinatorial properties that are expected to be useful in implementation such as having no linear processing an elegant construction is provided for a class of rate 1 2 cods that have no zero entries effectively no irrational coefficients no linear processing and have each variable appearing exactly twice per column the resulting codes meet the aforementioned bound on decoding delay in most cases this class of cods will be useful in practice due to their low peak to average power ratio papr and other desirable properties

single symbol ml decodable distributed stbcs for cooperative networks in this correspondence the distributed orthogonal space time block codes dostbcs which achieve the single symbol maximum likelihood ml decodability and full diversity order are first considered however systematic construction of the dostbcs is very hard since the noise covariance matrix is not diagonal in general thus some special dostbcs which have diagonal noise covariance matrices at the destination terminal are investigated these codes are referred to as the row monomial dostbcs an upper bound of the data rate of the row monomial dostbc is derived and it is approximately twice higher than that of the repetition based cooperative strategy furthermore systematic construction methods of the row monomial dostbcs achieving the upper bound of the data rate are developed when the number of relays and or the number of information bearing symbols are even

optimal memory for discrete time fir filters in state space in this correspondence we propose an efficient estimator of optimal memory averaging interval for discrete time finite impulse response fir filters in state space its crucial property is that only real measurements and the filter output are involved with no reference and noise statistics testing by the two state polynomial model has shown a very good correspondence with predicted values even in the worst case of the harmonic model the estimator demonstrates practical applicability

an iterative kalman like algorithm ignoring noise and initial conditions we address a p shift finite impulse response fir unbiased estimator ue for linear discrete time varying filtering p 0 p step prediction p 0 and p lag smoothing p 0 in state space with no requirements for initial conditions and zero mean noise a solution is found in a batch form and represented in a computationally efficient iterative kalman like one it is shown that the kalman like fir ue is able to outperform the kalman filter if the noise covariances and initial conditions are not known exactly noise is not white and both the system and measurement noise components need to be filtered out otherwise the errors are similar extensive numerical studies of the fir ue are provided in gaussian and non gaussian environments with outliers and temporary uncertainties

the final case of the decoding delay problem for maximum rate complex orthogonal designs complex orthogonal space time block codes costbcs based on generalized complex orthogonal designs cods have been successfully implemented in wireless systems with multiple transmit antennas and single or multiple receive antennas it has been shown that for a maximum rate cod with 2m 1 or 2m columns a lower bound on decoding delay is m 1 2m and this delay is achievable when the number of columns is congruent to 0 1 or 3 modulo 4 in this paper the final case is addressed and it is shown that when the number of columns is congruent to 2 modulo 4 the lower bound on decoding delay cannot be achieved in this case the shortest decoding delay a maximum rate cod can achieve is twice the lower bound new techniques for analyzing cods are introduced with connections to binary vector spaces

on the design of minimum ber linear space time block codes for mimo systems equipped with mmse receivers in this paper we consider the design of a full rate linear space time block code for coherent multiple input multiple output mimo communication systems under a quasi static rayleigh flat fading environment our design targets specifically at the use of a linear minimum mean square error mmse receiver that minimizes the asymptotic average bit error rate ber when the transmitted signal is selected from a 4 qam constellation this optimization problem is solved in two main stages 1 a lower bound on the ber is first minimized and 2 how this minimized lower bound can be achieved is then shown by exploiting a rigorous convex optimization technique without any assumption on the code we prove that individual unitary and trace orthogonal structures are the necessary and sufficient conditions to assure the minimum asymptotic average ber with an mmse detector an algorithm is provided for an efficient generation of our codes and simulation results confirm that our optimally designed codes are indeed superior in performance compared to some other commonly used codes

fast kalman like filtering for large dimensional linear and gaussian state space models this article considers the filtering problem for linear and gaussian state space models with large dimensions a setup in which the optimal kalman filter kf might not be applicable owing to the excessive cost of manipulating huge covariance matrices among the most popular alternatives that enable cheaper and reasonable computation is the ensemble kf enkf a monte carlo based approximation in this article we consider a class of a posteriori distributions with diagonal covariance matrices and propose fast approximate deterministic based algorithms based on the variational bayesian vb approach more specifically we derive two iterative kf like algorithms that differ in the way they operate between two successive filtering estimates one involves a smoothing estimate and the other involves a prediction estimate despite its iterative nature the prediction based algorithm provides a computational cost that is on the one hand independent of the number of iterations in the limit of very large state dimensions and on the other hand always much smaller than the cost of the enkf the cost of the smoothing based algorithm depends on the number of iterations that may in some situations make this algorithm slower than the enkf the performances of the proposed filters are studied and compared to those of the kf and enkf through a numerical example

two generalized complex orthogonal space time block codes of rates 7 11 and 3 5 for 5 and 6 transmit antennas space time block codes from orthogonal designs have two advantages namely fast maximum likelihood ml decoding and full diversity rate 1 real pulse amplitude modulation pam space time codes real orthogonal designs for multiple transmit antennas have been constructed from the real hurwitz radon families which also provides the rate 1 2 complex quadrature amplitude modulation qam space time codes complex orthogonal designs for any number of transmit antennas rate 3 4 complex orthogonal designs space time codes for three and four transmit antennas have existed in the literature but no high rate 1 2 complex orthogonal designs for other numbers of transmit antennas exist we present rate 7 11 and rate 3 5 generalized complex orthogonal designs for five and six transmit antennas respectively

complex orthogonal designs with forbidden 2 times 2 submatrices complex orthogonal designs cods are used to construct space time block codes cod oz with parameter p n k is a p n matrix where nonzero entries are filled zi by zi i 1 2 k or such that ozhoz z1 2 z2 2 zk 2 in n define oz a first type cod if and only if oz does not contain submatrix zj 0 0 zj or zj 0 0 zj it is already known that all cods with maximal rate i e maximal k p are of the first type in this paper we will determine all achievable parameters p n k of first type cod as well as all their possible structures the existence of parameters is proved by explicit form constructions new cods with parameters p n k n w 1 n w 1 n n w for 0 w n are constructed which demonstrate the possibility of sacrificing code rate to reduce decoding delay it is worth mentioning that all maximal rate minimal delay cods are contained in our constructions and their uniqueness under equivalence operation is proved

closed form designs of complex orthogonal space time block codes of rates k 1 2k for 2k 1 or 2k transmit antennas in this correspondence we present systematic and closed form constructions of complex orthogonal space time block codes from complex orthogonal designs of rates k 1 2k for 2k 1 or 2k transmit antennas for any positive integer k

minimum variance distortionless response estimators for linear discrete state space models for linear discrete state space models under certain conditions the linear least mean squares filter estimate has a convenient recursive predictor corrector format aka the kalman filter the purpose of this paper is to show that the linear minimum variance distortionless response mvdr filter shares exactly the same recursion except for the initialization which is based on a weighted least squares estimator if the mvdr filter is suboptimal in mean squared error sense it is an infinite impulse response distortionless filter a deconvolver which does not depend on the prior knowledge first and second order statistics on the initial state in other words the mvdr filter can be pre computed and its behaviour can be assessed in advance independently of the prior knowledge on the initial state

diversity analysis and design of space time multiblock codes for mimo systems equipped with linear mmse receivers this paper addresses the problem of designing optimum full symbol rate linear space time block codes stbc for a multi input multi output mimo communication system with m transmitter and n m receiver antennas and a linear minimum mean square error mmse receiver by analyzing the detection error probability expression for the optimized stbc it is shown that for qam signaling the maximum diversity gain for such a system is n m 1 the minimum probability of error stbc design is then extended to systems in which the transmission spans l independent realizations from a block fading channel model and a multiblock linear mmse receiver is employed necessary and sufficient conditions for the optimality of the code are obtained and a systematic design method for generating codes that satisfy these conditions is presented the detection error probability and diversity gain of this optimized linear multiblock transceiver are analyzed it is proved that the error probability decreases with l and it is shown numerically that the diversity gain increases with l thus if the corresponding latency can be accommodated for sufficiently large l an optimally designed multiblock system with a linear receiver can exploit the temporal diversity provided by the block fading channel and achieve higher diversity gain than that of any single block system of the same symbol rate with a maximum likelihood ml receiver the optimized multiblock linear system achieves this diversity at a substantially lower computational cost in fact the structure of the optimal codes can be exploited to significantly reduce the cost of the multiblock linear receiver

single symbol maximum likelihood decodable linear stbcs space time block codes stbcs from orthogonal designs ods and coordinate interleaved orthogonal designs ciod have been attracting wider attention due to their amenability for fast single symbol maximum likelihood ml decoding and full rate with full rank over quasi static fading channels however these codes are instances of single symbol decodable codes and it is natural to ask if there exist codes other than stbcs form ods and ciods that allow single symbol decoding in this paper the above question is answered in the affirmative by characterizing all linear stbcs that allow single symbol ml decoding not necessarily full diversity over quasi static fading channels calling them single symbol decodable designs sdd the class sdd includes ods and ciods as proper subclasses further among the sdd a class of those that offer full diversity called full rank sdd fsdd are characterized and classified we then concentrate on square designs and derive the maximal rate for square fsdds using a constructional proof it follows that 1 except for n 2 square complex ods are not maximal rate and 2 a rate one square fsdd exist only for two and four transmit antennas for nonsquare designs generalized coordinate interleaved orthogonal designs a superset of ciods are presented and analyzed finally for rapid fading channels an equivalent matrix channel representation is developed which allows the results of quasi static fading channels to be applied to rapid fading channels using this representation we show that for rapid fading channels the rate of single symbol decodable stbcs are independent of the number of transmit antennas and inversely proportional to the block length of the code significantly the ciod for two transmit antennas is the only stbc that is single symbol decodable over both quasi static and rapid fading channels

rate one space time block codes with full diversity orthogonal space time block codes provide full diversity and maximum likelihood ml decoding for orthogonal codes can be realized on a symbol by symbol basis it has been shown that rate one complex orthogonal codes do not exist for systems with more than two transmit antennas for a general system with n transmit and m receive antennas it is very desirable to design rate one complex codes with full diversity in this letter we provide a systematic method of designing rate one codes real or complex for a general multiple input multiple output system full diversity of these codes is then achieved by constellation rotation a generalized reduced complexity decoding method for rate one codes is also provided

intrinsically bayesian robust kalman filter an innovation process approach in many contemporary engineering problems model uncertainty is inherent because accurate system identification is virtually impossible owing to system complexity or lack of data on account of availability time or cost the situation can be treated by assuming that the true model belongs to an uncertainty class of models in this context an intrinsically bayesian robust ibr filter is one that is optimal relative to the cost function in the classical sense and the prior distribution over the uncertainty class in the bayesian sense ibr filters have previously been found for both wiener and granulometric morphological filtering in this paper we derive the ibr kalman filter that performs optimally relative to an uncertainty class of state space models introducing the notion of bayesian innovation process and the bayesian orthogonality principle we show how the problem of designing an ibr kalman filter can be reduced to a recursive system similar to the classical kalman recursive equations except with effective counterparts such as the effective kalman gain matrix after deriving the recursive ibr kalman equations for discrete time we use the limiting method to obtain the ibr kalman bucy equations for continuous time finally we demonstrate the utility of the proposed framework for two real world problems sensor networks and gene regulatory network inference

stable determination of a semilinear term in a parabolic equation in 5 the flrst and third authors establish holder type stability estimates for the inverse problem consisting in the determination of a semilinear term of a parabolic equation from a single boundary measurement when the domain is a rectangle in the present paper we extend the results in 5 for a general smooth domain

quasi deadbeat minimax filters for deterministic state space models in this note a quasi deadbeat property is introduced and a quasi deadbeat minimax filter dmf is proposed as a new class of filters for deterministic discrete time state space models constraints such as linearity quasi deadbeat property and independence of the initial state information will be required in advance in addition to a new performance index of the worst case gain between the disturbance and the current estimation error the proposed dmf is obtained by directly minimizing the new performance index with above constraints finite impulse response fir and infinite impulse response iir structures are suggested with emphasis on the fir structure the proposed dmf is represented first in a standard batch form and then in an iterative form it is shown that the dmf with fir and iir structures for deterministic systems are similar in form to the existing receding horizon unbiased fir filter rhuff and the kalman filter respectively for stochastic systems

unicity in an inverse problem for an unknown reaction term in a reaction diffusion equation in this paper we consider an inverse problem in which we seek to deter mine an unknown source or reaction term in a reaction diffusion equation from overspecified data measured on the boundary of the spatial region where the equation applies the analysis is based on the observation that the overspecified data depends monotonically on the unknown source term in the equation here we use this monotonicity to establish a type of unicity result for the inverse problem the attractiveness of the monotonicity methods illustrated here lies in their versatility surveying the rapidly expanding literature devoted to the topic of inverse problems one finds a considerable variety of ad hoc approaches methods which apply to a general class of problems seem to be few monotonicity methods however apply to a variety of inverse problems involving partial differential equations of parabolic or elliptic type this paper is organized as follows in section 1 we formulate the direct initial boundary value problem ibvp and state assumptions on the data and a priori assumptions on the unknown source term several properties of the solution to the direct problem are derived in section 2 the principal monotonicity estimates are established and in section 3 these are applied to the inverse problem to prove a type of unicity result for the solution to the inverse problem in particular it is a corollary of theorem 3 2 that in the class of analytic source terms the solution of the inverse problem is unique the problem of identifying an unknown source term in a heat equation 155

brief a receding horizon unbiased fir filter for discrete time state space models this paper concerns with a new linear finite impulse response fir filter called the receding horizon unbiased fir rhuf filter for the state estimation in discrete time state space models to obtain the rhuf filter linearity unbiasedness and fir structure will be required beforehand in addition to a performance criteria of minimum variance the rhuf filter is obtained by directly solving an optimization problem with the unbiasedness constraint the rhuf filter has time invariance and deadbeat properties the rhuf filter is represented in both a batch form and an iterative form it is shown that the rhuf filter is equivalent to the existing receding horizon kalman fir rhkf filter whose optimality is not clear to understand the former is more systematic and logical while the latter is heuristic due to handling of infinite covariance of the initial state information

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

unified forms for kalman and finite impulse response filtering and smoothing the kalman filter and smoother are optimal state estimators under certain conditions the kalman filter is typically presented in a predictor corrector format but the kalman smoother has never been derived in that format we derive the kalman smoother in a predictor corrector format thus providing a unified form for the kalman filter and smoother we also discuss unbiased finite impulse response ufir filters and smoothers which can provide a suboptimal but robust alternative to kalman estimators we derive two unified forms for ufir filters and smoothers and we derive lower and upper bounds for their estimation error covariances

minimum variance unbiased fir filter for discrete time variant systems this paper is concerned with the minimum variance unbiased mvu finite impulse response fir filtering problem for linear system described by discrete time variant state space models an mvu fir filter is derived by minimizing the variance from the unbiased fir ufir filter the relationship between the filter gains of mvu fir ufir and optimal fir ofir filters is derived analytically and the mean square errors mses of different fir filters are compared to provide an insight into the estimation performance simulations provided verify that errors in the mvu fir filter are in between the ufir and ofir filters it is also shown that the mvu fir filter can offer optimal estimates without a prior knowledge of the initial state and exhibits better robustness against temporary modeling uncertainties than the kalman filter

a counterexample for the open problem on the minimal delays of orthogonal designs with maximal rates x liang systematically investigated orthogonal designs with maximal rates gave the maximal rates of complex orthogonal designs and a concrete construction procedure for complex orthogonal designs with the maximal rates he also posed an open problem on the minimal decoding delays of complex orthogonal designs with maximal rates and proved that the problem is correct for less than or equal to six transmit antennas in this correspondence we give a counterexample for the open problem for n 8 and prove that the minimal delay for complex orthogonal designs with eight columns is 56 hence we give a negative answer for the open problem

semiorthogonal space time block codes in this paper a new class of full diversity rate one space time block codes stbcs called semiorthogonal algebraic space time block codes sast codes is proposed sast codes are delay optimal when the number of transmit antennas is even the sast codeword matrix has a generalized alamouti structure where the transmitted symbols are replaced by circulant matrices and the commutativity of circulant matrices simplifies the detection of transmit symbols sast codes with maximal coding gain are constructed by using rate one linear threaded algebraic space time ltast codes compared with ltsat codes sast codes not only reduce the complexity of maximum likelihood detection but also provide remarkable performance gain they also outperform other stbc with rate one or less sast codes also perform well with suboptimal detectors such as the vertical bell laboratories layered space time v blast nulling and cancellation receiver finally sast codes attain nearly 100 of the shannon capacity of open loop multiple input single output miso channels

on the nonexistence of rate one generalized complex orthogonal designs orthogonal space time block coding proposed recently by alamouti 1998 and tarokh et al 1999 is a promising scheme for information transmission over rayleigh fading channels using multiple transmit antennas due to its favorable characteristics of having full transmit diversity and a decoupled maximum likelihood ml decoding algorithm tarokh et al extended the theory of classical orthogonal designs to the theory of generalized real or complex linear processing orthogonal designs and then applied the theory of generalized orthogonal designs to construct space time block codes stbc with the maximum possible diversity order while having a simple decoding algorithm for any given number of transmit and receive antennas it has been known that the stbc constructed in this way can achieve the maximum possible rate of one for every number of transmit antennas using any arbitrary real constellation and for two transmit antennas using any arbitrary complex constellation contrary to this in this correspondence we prove that there does not exist rate one stbc from generalized complex linear processing orthogonal designs for more than two transmit antennas using any arbitrary complex constellation

on channel orthogonalization using space time block coding with partial feedback orthogonal space time block codes ostbcs yield full diversity gain even while requiring only a linear receiver such full rate rate one orthogonal designs are available for complex symbol constellations only for n 2 transmit antennas in this paper we propose a new family of full rate space time block codes stbcs using a single parameter feedback for communication over rayleigh fading channels for n 3 4 transmit antennas and m receive antennas the proposed rate one codes achieve full diversity and the performance is similar to maximum receiver ratio combining the decoding complexity of these codes are only linear even while performing maximum likelihood decoding the partial channel information is a real phase parameter that is a function of all the channel gains and has a simple closed form expression for n 3 4 this feedback information enables us to derive channel orthogonal designs starting from quasi orthogonal stbcs the feedback complexity is significantly lower than conventional closed loop transmit beamforming we compare the proposed codes with the open loop ostbcs and also with the closed loop equal gain transmission egt scheme which uses equal power loading on all antennas simulated error rate performances indicate that the proposed channel orthogonalized stbcs significantly outperform the open loop orthogonal designs for the same spectral efficiency moreover even with significantly lower feedback and computational complexity the proposed scheme outperforms the egt technique for m n

linear optimal fir estimation of discrete time invariant state space models this paper addresses a general p shift linear optimal finite impulse response fir estimator intended for solving universally the problems of filtering p 0 smoothing p 0 of discrete time invariant models in state space an optimal solution is found in the batch form with the initial mean square state function self determined by solving the discrete algebraic riccati equation an unbiased solution represented both in the batch and recursive forms does not involve any knowledge about noise and initial state the mean square errors in both the optimal and unbiased estimates are found via the noise power gain npg and a recursive algorithm for fast computation of the npg is supplied applications are given for fir filtering with fixed receding and full averaging horizons

modeling and estimation of multiresolution stochastic processes an overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing a natural framework for developing such a theory is the study of stochastic processes indexed by nodes on lattices or trees in which different depths in the tree or lattice correspond to different spatial scales in representing a signal or image in particular it is shown how the wavelet transform directly suggests such a modeling paradigm this perspective then leads directly to the investigation of several classes of dynamic models and related notions of multiscale stationarity in which scale plays the role of a time like variable the investigation of models on homogeneous trees is emphasized the framework examined here allows for consideration in a very natural way of the fusion of data from sensors with differing resolutions also thanks to the fact that wavelet transforms do an excellent job of compressing large classes of covariance kernels it is seen that these modeling paradigms appear to have promise in a far broader context than one might expect

single symbol ml decoding for orthogonal and quasi orthogonal stbc in clipped mimo ofdm systems using a clipping noise model with gaussian approximation an efficient way to reduce the peak to average power ratio papr in ofdm systems is clipping after the clipping in an mimo ofdm system the additive noise may not be white in this paper we develop fast single symbol ml decoding algorithms for orthogonal space time block codes ostbc and linearly transformed quasi orthogonal space time block codes qostbc in clipped mimo ofdm systems by using a clipping noise model with gaussian approximation by using the statistics of the clipping distortions our newly developed fast ml decoding algorithms improve the performance for clipped mimo ofdm systems with ostbc and qostbc while the decoding complexities are not increased simulation results are presented to illustrate the improvement

lower bounds on the minimal delay of complex orthogonal designs with maximal rates the maximal rates and the minimal delays are basic problems of space time block codes from complex orthogonal designs liang systematically solved the problem on the maximal rates of complex orthogonal designs and posed an open problem on the minimal delays recently the authors gave the negative answer for the open problem in this letter we give lower bounds on the minimal delays

improved cubature kalman filter for gnss ins based on transformation of posterior sigma points error tightly coupled gnss ins has been widely approved as a promising substitute for standalone gnss in urban areas navigation however due to the frequent gnss signal outages the filter used in gnss ins should be insensitive to the less informative observations in this paper a novel sigma points update method is proposed to enhance the robustness of cubature kalman filter ckf under the circumstance of unavailable observations first the problems of existing sampling based filters are analyzed then by transforming the posterior sigma points error matrix from prediction phase of filtering to the posterior domain of update the updated sigma points are expected to capture the covariance more precisely than traditional sigma points finally an improved ckf ickf is developed by embedding these points into the bayesian estimation framework and the upper bounds of error covariance matrices are analyzed theoretically signal outages with different durations are simulated and results demonstrate that ickf outperforms state of the art methods

upper bounds of rates of complex orthogonal space time block codes we derive some upper bounds of the rates of generalized complex orthogonal space time block codes we first present some new properties of complex orthogonal designs and then show that the rates of complex orthogonal space time block codes for more than two transmit antennas are upper bounded by 3 4 we show that the rates of generalized complex orthogonal space time block codes for more than two transmit antennas are upper bounded by 4 5 where the norms of column vectors may not be necessarily the same we also present another upper bound under a certain condition for a generalized complex orthogonal design its variables are not restricted to any alphabet sets but are on the whole complex plane a generalized complex orthogonal design with variables over some alphabet sets on the complex plane is also considered we obtain a condition on the alphabet sets such that a generalized complex orthogonal design with variables over these alphabet sets is also a conventional generalized complex orthogonal design and therefore the above upper bounds on its rate also hold we show that commonly used quadrature amplitude modulation qam constellations of sizes above 4 satisfy this condition

four group decodable space time block codes two new rate one full diversity space time block codes stbcs are proposed they are characterized by the lowest decoding complexity among the known rate one stbc arising due to the complete separability of the transmitted symbols into four groups for maximum likelihood detection the first and the second codes are delay optimal if the number of transmit antennas is a power of 2 and even respectively the exact pairwise error probability is derived to allow for the performance optimization of the two codes compared with existing low decoding complexity stbc the two new codes offer several advantages such as higher code rate lower encoding decoding delay and complexity lower peak to average power ratio and better performance

suboptimal fir filtering of nonlinear models in additive white gaussian noise the first and second order extended finite impulse response efir1 and efir2 respectively filters are addressed for suboptimal estimation of nonlinear discrete time state space models with additive white gaussian noise it is shown that unlike the extended kalman filter ekf and efir2 filter the efir1 one does not require noise statistics and initial errors only within a narrow region around actual noise covariances efir filters fall a bit short of ekf and they demonstrate better performance otherwise it is shown that the optimal averaging interval for efir filters can be determined via measurement without a reference model in a learning cycle we also notice that the second order approximation can improve the local performance but it can also deteriorate it we thus have no recommendations about its use at least for tracking considered as an example of applications

signal constellations for quasi orthogonal space time block codes with full diversity space time block codes stbcs from orthogonal designs proposed by alamouti and tarokh jafarkhani calderbank have attracted considerable attention lately due to their fast maximum likelihood ml decoding and full diversity however the maximum symbol transmission rate of an stbc from complex orthogonal designs for complex signals is only 3 4 for three and four transmit antennas and it is difficult to construct complex orthogonal designs with rate higher than 1 2 for more than four transmit antennas recently jafarkhani tirkkonen boariu hottinen and papadias foschini proposed stbcs from quasi orthogonal designs where the orthogonality is relaxed to provide higher symbol transmission rates with the quasi orthogonal structure the quasi orthogonal stbcs still have a fast ml decoding but do not have the full diversity the performance of these codes is better than that of the codes from orthogonal designs at low signal to noise ratio snr but worse at high snr this is due to the fact that the slope of the performance curve depends on the diversity it is desired to have the quasi orthogonal stbcs with full diversity to ensure good performance at high snr in this paper we achieve this goal by properly choosing the signal constellations specifically we propose that half of the symbols in a quasi orthogonal design are chosen from a signal constellation set a and the other half of them are chosen from a rotated constellation e sup j spl phi a the resulting stbcs can guarantee both full diversity and fast ml decoding moreover we obtain the optimum selections of the rotation angles spl phi for some commonly used signal constellations simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high snrs

a receding horizon kalman fir filter for discrete time invariant systems a receding horizon kalman fir filter is presented that combines the kalman filter and the receding horizon strategy when the horizon initial state is assumed to be unknown the suggested filter is a fir filter form which has many good inherent properties it can always be defined irrespective of singularity problems caused by unknown information about the horizon initial state the suggested filter can be represented in either an iterative form or a standard fir form it is also shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat property irrespective of any horizon initial condition the validity of the suggested filter is illustrated by numerical examples

on full diversity space time block codes with partial interference cancellation group decoding in this paper we propose a partial interference cancellation pic group decoding strategy scheme for linear dispersive space time block codes stbc and a design criterion for the codes to achieve full diversity when the pic group decoding is used at the receiver a pic group decoding decodes the symbols embedded in an stbc by dividing them into several groups and decoding each group separately after a linear pic operation is implemented it can be viewed as an intermediate decoding between the maximum likelihood ml receiver that decodes all the embedded symbols together i e all the embedded symbols are in a single group and the zero forcing zf receiver that decodes all the embedded symbols separately and independently i e each group has and only has one embedded symbol after the zf operation is implemented the pic group decoding provides a framework to adjust the complexity performance tradeoff by choosing the sizes of the information symbol groups our proposed design criterion group independence for the pic group decoding to achieve full diversity is an intermediate condition between the loosest ml full rank criterion of codewords and the strongest zf linear independence condition of the column vectors in the equivalent channel matrix we also propose asymptotic optimal ao group decoding algorithm which is an intermediate decoding between the mmse decoding algorithm and the ml decoding algorithm the design criterion for the pic group decoding can be applied to the ao group decoding algorithm because of its asymptotic optimality it is well known that the symbol rate for a full rank linear stbc can be full i e nt for nt transmit antennas it has been recently shown that its rate is upper bounded by 1 if a code achieves full diversity with a linear receiver the intermediate criterion proposed in this paper provides the possibility for codes of rates between nt and 1 that achieve full diversity with the pic group decoding this therefore provides a complexity performance rate tradeoff some design examples are given

generalized psk in space time coding a wireless communication system using multiple antennas promises reliable transmission under rayleigh flat fading assumptions design criteria and practical schemes have been presented for both coherent and noncoherent communication channels in this paper we generalize one dimensional 1 d phase shift keying psk signals and introduce space time constellations from generalized psk gpsk signals based on the complex and real orthogonal designs the resulting space time constellations reallocate the energy for each transmitting antenna and feature good diversity products consequently their performances are better than some of the existing comparable codes moreover since the maximum likelihood ml decoding of our proposed codes can be decomposed to 1 d psk signal demodulation the ml decoding of our codes can be implemented in a very efficient way

a construction technique for generalized complex orthogonal designs and applications to wireless communications abstract we introduce a construction technique for generalized complex linear processing orthogonal designs which are p n matrices x satisfying x h x fi where f is a complex quadratic form i is the identity matrix and x has complex entries these matrices generalize the familiar notions of orthogonal designs and generalized complex orthogonal designs we explain the application of these matrices to space time block coding for multiple antenna wireless communications in particular we discuss the practical strengths of the space time block codes constructed via our proposed technique

on optimal quasi orthogonal space time block codes with minimum decoding complexity orthogonal space time block codes ostbc from orthogonal designs have both advantages of complex symbol wise maximum likelihood ml decoding and full diversity however their symbol rates are upper bounded by 3 4 for more than two antennas for complex symbols to increase the symbol rates they have been generalized to quasi orthogonal space time block codes qostbc in the literature but the diversity order is reduced by half and the complex symbol wise ml decoding is significantly increased to complex symbol pair wise pair of complex symbols ml decoding the qostbc has been modified by rotating half of the complex symbols for achieving the full diversity while maintaining the complex symbol pair wise ml decoding the optimal rotation angles for any signal constellation of any finite symbols located on both square lattices and equal literal triangular lattices have been found by su xia where the optimality means the optimal diversity product or product distance qostbc has also been modified by yuen guan tjhung by rotating information symbols in another way such that it has full diversity and in the meantime it has real symbol pair wise ml decoding the same complexity as complex symbol wise decoding and the optimal rotation angle for square and rectangular qam constellations has been found in this paper we systematically study general linear transformations of information symbols for qostbc to have both full diversity and real symbol pair wise ml decoding we present the optimal transformation matrices among all possible linear transformations not necessarily symbol rotations of information symbols for qostbc with real symbol pair wise ml decoding such that the optimal diversity product is achieved for both general square qam and general rectangular qam signal constellations furthermore our newly proposed optimal linear transformations for qostbc also work for general qam constellations in the sense that qostbc have full diversity with good diversity product property and real symbol pair wise ml decoding interestingly the optimal diversity products for square qam constellations from the optimal linear transformations of information symbols found in this paper coincide with the ones presented by yuen guan tjhung by using their optimal rotations however the optimal diversity products for nonsquare rectangular qam constellations from the optimal linear transformations of information symbols found in this paper are better than the ones presented by yuen guan tjhung by using their optimal rotations in this paper we also present the optimal transformations for the co ordinate interleaved orthogonal designs ciod proposed by khan rajan for rectangular qam constellations

methods for sparse signal recovery using kalman filtering with embedded pseudo measurement norms and quasi norms we present two simple methods for recovering sparse signals from a series of noisy observations the theory of compressed sensing cs requires solving a convex constrained minimization problem we propose solving this optimization problem by two algorithms that rely on a kalman filter kf endowed with a pseudo measurement pm equation compared to a recently introduced kf cs method which involves the implementation of an auxiliary cs optimization algorithm e g the dantzig selector our method can be straightforwardly implemented in a stand alone manner as it is exclusively based on the well known kf formulation in our first algorithm the pm equation constrains the l 1 norm of the estimated state in this case the augmented measurement equation becomes linear so a regular kf can be used in our second algorithm we replace the l 1 norm by a quasi norm lp 0 p 1 this modification considerably improves the accuracy of the resulting kf algorithm however these improved results require an extended kf ekf for properly computing the state statistics a numerical study demonstrates the viability of the new methods

communication on the grassmann manifold a geometric approach to the noncoherent multiple antenna channel we study the capacity of multiple antenna fading channels we focus on the scenario where the fading coefficients vary quickly thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver we use a noncoherent block fading model proposed by marzetta and hochwald see ibid vol 45 p 139 57 1999 the model does not assume any channel side information at the receiver or at the transmitter but assumes that the coefficients remain constant for a coherence interval of length t symbol periods we compute the asymptotic capacity of this channel at high signal to noise ratio snr in terms of the coherence time t the number of transmit antennas m and the number of receive antennas n while the capacity gain of the coherent multiple antenna channel is min m n bits per second per hertz for every 3 db increase in snr the corresponding gain for the noncoherent channel turns out to be m 1 m t bits per second per hertz where m min m n t 2 the capacity expression has a geometric interpretation as sphere packing in the grassmann manifold

the theory of quaternion orthogonal designs over the past several years there has been a renewed interest in complex orthogonal designs for their application in space time block coding motivated by the success of this application this paper generalizes the definition of complex orthogonal designs by introducing orthogonal designs over the quaternion domain this paper builds a theory of these novel quaternion orthogonal designs offers examples and provides several construction techniques these theoretical results along with the results of preliminary simulations lay the foundation for developing applications of these designs as orthogonal space time polarization block codes