spatio temporal covariance and cross covariance functions of the great circle distance on a sphere abstractin this article we propose stationary covariance functions for processes that evolve temporally over a sphere as well as cross covariance functions for multivariate random fields defined over a sphere for such processes the great circle distance is the natural metric that should be used to describe spatial dependence given the mathematical difficulties for the construction of covariance functions for processes defined over spheres cross time approximations of the state of nature have been proposed in the literature by using the euclidean based on map projections and the chordal distances we present several methods of construction based on the great circle distance and provide closed form expressions for both spatio temporal and multivariate cases a simulation study assesses the discrepancy between the great circle distance chordal distance and euclidean distance based on a map projection both in terms of estimation and prediction in a space time and a bivariate spatial setting where t

hermite birkhoff interpolation on scattered data on the sphere and other manifolds abstract the hermite birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered each proposed interpolant is expressed as a linear combination of basis functions the combination coefficients being incomplete taylor expansions of the interpolated function at the interpolation points the basis functions depend on the geodesic distance are orthonormal with respect to the point evaluation functionals and have all derivatives equal zero up to a certain order at the interpolation points a remarkable feature of such interpolants which belong to the class of partition of unity methods is that their construction does not require solving linear systems numerical tests are given to show the interpolation performance

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

on space time code design with a conditional pic group decoding space time code designs based on a partial interference cancellation pic group decoding have been recently proposed the pic group decoding complexity depends on the group size and is between the lowest linear receiver complexity and the highest ml decoding complexity the symbol rate for a space time code achieving full diversity with the pic group decoding is also between those for the linear receivers and the ml decoding in this paper we propose a new decoding called conditional pic group decoding that is between the pic group decoding and the ml decoding with the proposed new decoding we obtain a new design criterion for space time codes to achieve full diversity which is also between the one with the pic group decoding and the one with the ml decoding we then present some designs that satisfy the new criterion and in the meantime have higher symbol rates than that for the pic group decoding

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

fast decodable asymmetric space time codes from division algebras multiple input double output mido codes are important in the near future wireless communications where the portable end user device is physically small and will typically contain at most two receive antennas especially tempting is the 4 2 channel due to its immediate applicability in the digital video broadcasting dvb such channels optimally employ rate two space time st codes consisting of 4 4 matrices unfortunately such codes are in general very complex to decode hence setting forth a call for constructions with reduced complexity recently some reduced complexity constructions have been proposed but they have mainly been based on different ad hoc methods and have resulted in isolated examples rather than in a more general class of codes in this paper it will be shown that a family of division algebra based mido codes will always result in at least 37 5 worst case complexity reduction while maintaining full diversity and for the first time the nonvanishing determinant nvd property the reduction follows from the fact that similarly to the alamouti code the codes will be subsets of matrix rings of the hamiltonian quaternions hence allowing simplified decoding at the moment such reductions are among the best known for rate two mido codes 5 6 several explicit constructions are presented and shown to have excellent performance through computer simulations simulations

shift full rank matrices and applications in space time trellis codes for relay networks with asynchronous cooperative diversity to achieve full cooperative diversity in a relay network most of the existing space time coding schemes require the synchronization between terminals a family of space time trellis codes that achieve full cooperative diversity order without the assumption of synchronization has been recently proposed the family is based on the stack construction by hammons and el gamal and its generalizations by lu and kumar it has been shown that the construction of such a family is equivalent to the construction of binary matrices that have full row rank no matter how their rows are shifted where a row corresponds to a terminal or transmit antenna and its length corresponds to the memory size of the trellis code on that terminal we call such matrices as shift full rank sfr matrices a family of sfr matrices has been also constructed but the memory sizes of the corresponding space time trellis codes the number of columns of sfr matrices grow exponentially in terms of the number of terminals the number of rows of sfr matrices which may cause a high decoding complexity when the number of terminals is not small in this paper we systematically study and construct sfr matrices of any sizes for any number of terminals furthermore we construct shortest square sfr ssfr matrices that correspond to space time trellis codes with the smallest memory sizes and asynchronous full cooperative diversity we also present some simulation results to illustrate the performances of the space time trellis codes associated with sfr matrices in asynchronous cooperative communications

generalized silver codes for an nt transmit nr receive antenna system nt nr system a full rate space time block code stbc transmits at least nmin min nt nr complex symbols per channel use the well known golden code is an example of a full rate full diversity stbc for two transmit antennas its ml decoding complexity is of the order of m2 5 for square m qam the silver code for two transmit antennas has all the desirable properties of the golden code except its coding gain but offers lower ml decoding complexity of the order of m2 importantly the slight loss in coding gain is negligible compared to the advantage it offers in terms of lowering the ml decoding complexity for higher number of transmit antennas the best known codes are the perfect codes which are full rate full diversity information lossless codes for nr nt but have a high ml decoding complexity of the order of mntnmin for nr nt the punctured perfect codes are considered in this paper a scheme to obtain full rate stbcs for 2a transmit antennas and any nr with reduced ml decoding complexity of the order of mnt nmin 3 4 0 5 is presented the codes constructed are also information lossless for nr nt like the perfect codes and allow higher mutual information than the comparable punctured perfect codes for nr nt these codes are referred to as the generalized silver codes since they enjoy the same desirable properties as the comparable perfect codes except possibly the coding gain with lower ml decoding complexity analogous to the silver code and the golden code for two transmit antennas simulation results of the symbol error rates for four and eight transmit antennas show that the generalized silver codes match the punctured perfect codes in error performance while offering lower ml decoding complexity

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

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

error estimates for scattered data interpolation on spheres we study sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the n sphere the interpolation knots are scattered our approach partly follows the general theory of golomb and weinberger and related estimates these error estimates are then based on series expansions of smooth functions in terms of spherical harmonics the markov inequality for spherical harmonics is essential to our analysis and is used in order to find lower bounds for certain sampling operators on spaces of spherical harmonics

on the sphere decoding complexity of high rate multigroup decodable stbcs in asymmetric mimo systems a space time block code stbc is said to be multigroup decodable if the information symbols encoded by it can be partitioned into two or more groups such that each group of symbols can be maximum likelihood ml decoded independently of the other symbol groups in this paper we show that the upper triangular matrix r encountered during the sphere decoding of a linear dispersion stbc can be rank deficient even when the rate of the code is less than the minimum of the number of transmit and receive antennas we then show that all known families of high rate rate greater than 1 multigroup decodable codes have rank deficient r matrix even when the rate is less than the number of transmit and receive antennas and this rank deficiency problem arises only in asymmetric mimo systems when the number of receive antennas is strictly less than the number of transmit antennas unlike the codes with full rank r matrix the complexity of the sphere decoding based ml decoder for stbcs with rank deficient r matrix is polynomial in the constellation size and hence is high we derive the ml sphere decoding complexity of most of the known high rate multigroup decodable codes and show that for each code the complexity is a decreasing function of the number of receive antennas

full diversity high rate space time block codes from division algebras we present some general techniques for constructing full rank minimal delay rate at least one space time block codes stbcs over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras field extensions as well as using noncommutative division algebras of the rational field spl qopf embedded in matrix rings the first half of the paper deals with constructions using field extensions of spl qopf working with cyclotomic field extensions we construct several families of stbcs over a wide range of signal sets that are of full rank minimal delay and rate at least one appropriate for any number of transmit antennas we study the coding gain and capacity of these codes using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas we also present a method of constructing stbcs using noncyclotomic field extensions in the later half of the paper we discuss two ways of embedding noncommutative division algebras into matrices left regular representation and representation over maximal cyclic subfields the 4 spl times 4 real orthogonal design is obtained by the left regular representation of quaternions alamouti s 1998 code is just a special case of the construction using representation over maximal cyclic subfields and we observe certain algebraic uniqueness characteristics of it also we discuss a general principle for constructing cyclic division algebras using the nth root of a transcendental element and study the capacity of the stbcs obtained from this construction another family of cyclic division algebras discovered by brauer 1933 is discussed and several examples of stbcs derived from each of these constructions are presented

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

distributed differential space time coding for wireless relay networks distributed space time coding is a cooperative transmission scheme for wireless relay networks with this scheme antennas of the distributive relays work as transmit antennas of the sender and generate a space time code at the receiver it achieves the maximum diversity although the scheme needs no channel information at relays it does require full channel information both the channels from the transmitter to relays and the channels from relays to the receiver at the receiver in this paper we propose a differential transmission scheme which requires channel information at neither relays nor the receiver for wireless relay networks as distributed space time coding can be seen as the counterpart of space time coding in the network setting this scheme is the counterpart of differential space time coding compared to coherent distributed space time coding the differential scheme is 3db worse in addition we show that alamouti square real orthogonal and sp 2 codes can be used differentially in networks with corresponding numbers of relays we also propose distributed differential space time codes that work for networks with any number of relays using circulant matrices

on the sphere decoding algorithm i expected complexity the problem of finding the least squares solution to a system of linear equations where the unknown vector is comprised of integers but the matrix coefficient and given vector are comprised of real numbers arises in many applications communications cryptography gps to name a few the problem is equivalent to finding the closest lattice point to a given point and is known to be np hard in communications applications however the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known therefore in this paper rather than dwell on the worst case complexity of the integer least squares problem we study its expected complexity averaged over the noise and over the lattice for the sphere decoding algorithm of fincke and pohst we find a closed form expression for the expected complexity both for the infinite and finite lattice it is demonstrated in the second part of this paper that for a wide range of signal to noise ratios snrs and numbers of antennas the expected complexity is polynomial in fact often roughly cubic since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial this suggests that maximum likelihood decoding which was hitherto thought to be computationally intractable can in fact be implemented in real time a result with many practical implications

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

effect of mmse channel estimation on ber performance of orthogonal space time block codes in rayleigh fading channels we present a simple closed form expression for the ber of orthogonal space time block codes ostbcs with mmse channel estimation assuming pam and qam constellations and flat rayleigh block fading the ber expression is exact for a certain class of ostbcs and provides a very accurate approximation for other ostbcs

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

an enhanced dmt optimality criterion for stbc schemes for asymmetric mimo systems for any nt transmit nr receive antenna nt nr multiple input multiple output mimo system in a quasi static rayleigh fading environment it was shown by elia that linear space time block code schemes lstbc schemes that have the nonvanishing determinant nvd property are diversity multiplexing gain tradeoff dmt optimal for arbitrary values of nr if they have a code rate of nt complex dimensions per channel use however for asymmetric mimo systems where with the exception of a few lstbc schemes it is unknown whether general lstbc schemes with nvd and a code rate of nr complex dimensions per channel use are dmt optimal in this paper an enhanced sufficient criterion for any stbc scheme to be dmt optimal is obtained and using this criterion it is established that any lstbc scheme with nvd and a code rate of min nt nr complex dimensions per channel use is dmt optimal this result settles the dmt optimality of several well known low ml decoding complexity lstbc schemes for certain asymmetric mimo systems

a meshless interpolation algorithm using a cell based searching procedure in this paper we propose a fast algorithm for bivariate interpolation of large scattered data sets it is based on the partition of unity method for constructing a global interpolant by blending radial basis functions as local approximants and using locally supported weight functions the partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cell based searching procedure more precisely we construct a cell structure which partitions the domain and strictly depends on the dimension of the subdomains thus providing a meaningful improvement in the searching process compared to the nearest neighbour searching techniques presented in allasia et al 2011 and cavoretto and de rossi 2010 2012 in fact this efficient algorithm and in particular the new searching procedure enable us a fast computation also in several applications where the amount of data to be interpolated is often very large up to many thousands or even millions of points analysis of computational complexity shows the high efficiency of the proposed interpolation algorithm this is also supported by numerical experiments

a trivariate interpolation algorithm using a cube partition searching procedure in this paper we propose a fast algorithm for trivariate interpolation which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported weight functions the partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cube partition searching procedure more precisely we construct a cube structure which partitions the domain and strictly depends on the size of its subdomains so that the new searching procedure and accordingly the resulting algorithm enable us to efficiently deal with a large number of nodes complexity analysis and numerical experiments show high efficiency and accuracy of the proposed interpolation algorithm

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

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

two designs of space time block codes achieving full diversity with partial interference cancellation group decoding a partial interference cancellation pic group decoding based space time block code stbc design criterion was recently proposed by guo and xia where the decoding complexity and the code rate traeoff is dealt when the full diversity is achieved in this paper two designs of stbc are proposed for any number of transmit antennas that can obtain full diversity when a pic group decoding with a particular grouping scheme is applied at receiver with the pic group decoding and an appropriate grouping scheme for the decoding the proposed stbc are shown to obtain the same diversity gain as the ml decoding but have a low decoding complexity the first proposed stbc is designed with multiple diagonal layers and it can obtain the full diversity for two layer design with the pic group decoding and the rate is up to 2 symbols per channel use with pic sic group decoding the first proposed stbc can obtain full diversity for any number of layers and the rate can be full the second proposed stbc can obtain full diversity and a rate up to 9 4 with the pic group decoding some code design examples are given and simulation results show that the newly proposed stbc can well address the rate performance complexity tradeoff of the mimo systems

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

a quasi orthogonal space time block code it has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space time block code is not possible for more than two antennas previous attempts have been concentrated in generalizing orthogonal designs which provide space time block codes with full diversity and a high transmission rate we design rate one codes which are quasi orthogonal and provide partial diversity the decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols

euclidean and space time block codes relationship optimality performance analysis revisited an equivalent model for a multiple input multiple output communication system with space time block codes stbcs is proposed based on a revealed connection between stbcs and euclidean codes examples of distance spectra signal constellations and signal coordinate diagrams of euclidean codes equivalent to simplest orthogonal stbcs are given a new asymptotic upper bound for the symbol error rate ser of stbcs based on the distance spectra of the equivalent euclidean codes is derived and new general design criteria for signal constellations of the optimal code are proposed some bounds relating distance properties dimensionality and cardinality of stbcs with constituent signals of equal energy are given and new signal constellations with cardinalities of 8 and 16 for alamouti s code are designed a general methodology for performance analysis of stbcs is revisited as an example of the application of this methodology an exact evaluation of the ser of an orthogonal stbc is given namely a new expression for the ser of alamouti s code with binary phase shift keying signals is derived

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

new algebraic constructions of rotated z sup n lattice constellations for the rayleigh fading channel in this correspondence we present various families of full diversity rotated z sup n lattice constellations based on algebraic number theory constructions we are able to give closed form expressions of their minimum product distance using the corresponding algebraic properties

on the relation of ostbc and code rate one qstbc average rate ber and coding gain recently the statistical properties of the equivalent channel representation of a multiple input multiple output mimo system employing code rate one quasi orthogonal space time block codes qstbc which are constructed by using orthogonal space time block codes ostbc as building elements was characterized based on these characterizations we analyze the average rate or mean mutual information the bit error rate performance and the coding gain achieved with qstbc for any number of receive and nt 2n n ges 2 transmit antennas first we study constellation rotation using a systematic approach in order to maximize the coding gain and to achieve full diversity qstbc moreover we present an upper bound on the coding gain we derive a lower and upper bound on the ber performance for qstbc furthermore we analyze the average rate achievable with qstbc in case of an uninformed transmitter and also the case in which the transmitter knows the mean channel matrix whereas the receiver has perfect csi along with the analysis we compare all the results of these performance measures with the results achieved with ostbc revealing important connections between ostbc and qstbc for example the coding gain of a qstbc is upper bounded by the coding gain of the underlying ostbc also the ber of a qstbc for nt transmit and nr receive antennas is tightly lower bounded by the ber of a full diversity providing intersymbol interference free system in addition to that we show that gains in terms of average rate by using a qstbc and thus with higher nt instead of the underlying ostbc are only attainable if the available channel state information at the transmitter csit is utilized finally we illustrate our theoretical results using numerical simulations

radial basis functions for the multivariate interpolation of large scattered data sets an efficient method for the multivariate interpolation of very large scattered data sets is presented it is based on the local use of radial basis functions and represents a further improvement of the well known shepard s method although the latter is simple and well suited for multivariate interpolation it does not share the good reproduction quality of other methods widely used for bivariate interpolation on the other band radial basis functions which have proven to be highly useful for multivariate scattered data interpolation have a severe drawback they are unable to interpolate large sets in an efficient and numerically stable way and maintain a good level of reproduction quality at the same time both problems have been circumvented using radial basis functions to evaluate the nodal function of the modified shepard s method this approach exploits the flexibility of the method and improves its reproduction quality the proposed algorithm has been implemented and numerical results confirm its efficiency

on fast decodable space time block codes we focus on full rate fast decodable space time block codes stbcs for 2 times 2 and 4times2 multiple input multiple output mimo transmission we first derive conditions and design criteria for reduced complexity maximum likelihood ml decodable 2times2 stbcs and we apply them to two families of codes that were recently discovered next we derive a novel reduced complexity 4times2 stbc and show that it outperforms all previously known codes with certain constellations

full diversity non coherent alamouti based toeplitz space time block codes recently the liu zhang wong s toeplitz space time block code and the shang xia s alamouti code based overlapped space time block code have been developed to enable coherent full diversity with the linear receivers for a wireless communication system having multiple transmitter antennas and a single receiver antenna in this paper such a noncoherent system is considered in which channel state information is unavailable at both the transmitter and receiver using the alamouti coding scheme and the toeplitz matrix structure a novel noncoherent nonunitary space time block code which is called an alamouti based toeplitz space time block code is proposed by the fundamentals of galois theory and algebraic number theory two important properties on the two alamouti codes generated from a pair of coprime phase shift keying psk constellations i e the uniqueness of factorization itself and the shift invariant uniqueness of factorization are first revealed and rigorously proved then it is further shown that it is these two kinds of unique factorizations that enable the unique blind identification of both the channel coefficients and the transmitted signals by only processing two block received signals as well as noncoherent full diversity with a generalized likelihood ratio test glrt receiver in addition a full diversity unitary code design is also proposed by simply applying the qr decomposition to the full diversity nonunitary alamouti based toeplitz space time block code computer simulations demonstrate that the nonunitary and unitary codes presented in this paper outperform the differential codes and the signal to noise ratio snr efficient training scheme based on the coherent orthogonal space time block codes in the current literature

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

quaternion orthogonal designs from complex companion designs abstract the success of applying generalized complex orthogonal designs as space time block codes recently motivated the definition of quaternion orthogonal designs as potential building blocks for space time polarization block codes this paper offers techniques for constructing quaternion orthogonal designs via combinations of specially chosen complex orthogonal designs one technique is used to build quaternion orthogonal designs on complex variables for any even number of columns a second related technique is applied to maximum rate complex orthogonal designs to generate an infinite family of quaternion orthogonal designs on complex variables such that the resulting designs have no zero entries this second technique is also used to generate an infinite family of quaternion orthogonal designs defined over quaternion variables that display a regular redundancy the proposed constructions are theoretically important because they provide the first known direct techniques for building infinite families of orthogonal designs over quaternion variables for any number of columns

maximum likelihood detection of orthogonal space time block coded ofdm in unknown block fading channels for orthogonal space time block coded orthogonal frequency division multiplexing ostbc ofdm systems many of the existing blind detection and channel estimation methods rely on the assumption that the channel is static for many ostbc ofdm blocks this paper considers the blind semiblind maximum likelihood ml detection problem of ostbc ofdm with a single ostbc ofdm block only the merit of such an investigation is the ability to accommodate channels with shorter coherence time we examine both the implementation and identifiability issues with a focus on bpsk or qpsk constellations in the implementation we propose reduced complexity detection schemes using subchannel grouping in the identifiability analysis we show that the proposed schemes can ensure a probability one identifiability condition using very few number of pilots for example the proposed semiblind detection scheme only requires a single pilot code for unique data identification while the conventional pilot based channel estimation method requires l pilots where l denotes the channel length our simulation results demonstrate that the proposed schemes can provide performance close to that of their nonblind counterparts

fast decodable mido codes with large coding gain in this paper a new method is proposed to obtain full diversity rate 2 rate of two complex symbols per channel use space time block codes stbcs that are full rate for multiple input double output mido systems using this method rate 2 stbcs for 4 2 6 2 8 2 and 12 2 systems are constructed and these stbcs are fast ml decodable have large coding gains and stbc schemes consisting of these stbcs have a non vanishing determinant nvd so that they are dmt optimal for their respective mido systems it is also shown that the srinath rajan code for the 4 2 system which has the lowest ml decoding complexity among known rate 2 stbcs for the 4 2 mido system with a large coding gain for 4 16 qam has the same algebraic structure as the stbc constructed in this paper for the 4 2 system this also settles in positive a previous conjecture that the stbc scheme that is based on the srinath rajan code has the nvd property and hence is dmt optimal for the 4 2 system

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

fast and stable rational rbf based partition of unity interpolation abstract we perform a local computation via the partition of unity pu method of rational radial basis function rbf interpolants we investigate the well posedness of the problem and we provide error bounds the resulting scheme efficiently implemented by means of the deflation accelerated conjugate gradient dacg enables us to deal with huge data sets and thanks to the use of variably scaled kernels vsks it turns out to be stable for functions with steep gradients or discontinuities which are truly common in applications the results show that the new proposed method outperforms the classical and rescaled pu schemes

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

fast and accurate interpolation of large scattered data sets on the sphere in this paper a new efficient algorithm for spherical interpolation of large scattered data sets is presented the solution method is local and involves a modified spherical shepard s interpolant which uses zonal basis functions as local approximants the associated algorithm is implemented and optimized by applying a nearest neighbour searching procedure on the sphere specifically this technique is mainly based on the partition of the sphere in a suitable number of spherical zones the construction of spherical caps as local neighbourhoods for each node and finally the employment of a spherical zone searching procedure computational cost and storage requirements of the spherical algorithm are analyzed moreover several numerical results show the good accuracy of the method and the high efficiency of the proposed algorithm

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

information lossless space time block codes from crossed product algebras it is known that the alamouti code is the only complex orthogonal design cod which achieves capacity and that too for the case of two transmit and one receive antenna only damen proposed a design for two transmit antennas which achieves capacity for any number of receive antennas calling the resulting space time block code stbc when used with a signal set an information lossless stbc in this paper using crossed product central simple algebras we construct stbcs for arbitrary number of transmit antennas over an a priori specified signal set alamouti code and quasi orthogonal designs are the simplest special cases of our constructions we obtain a condition under which these stbcs from crossed product algebras are information lossless we give some classes of crossed product algebras from which the stbcs obtained are information lossless and also of full rank we present some simulation results for two three and four transmit antennas to show that our stbcs perform better than some of the best known stbcs and also that these stbcs are approximately 1 db away from the capacity of the channel with quadrature amplitude modulation qam symbols as input

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

mesh free semi lagrangian methods for transport on a sphere using radial basis functions abstract we present three new semi lagrangian methods based on radial basis function rbf interpolation for numerically simulating transport on a sphere the methods are mesh free and are formulated entirely in cartesian coordinates thus avoiding any irregular clustering of nodes at artificial boundaries on the sphere and naturally bypassing any apparent artificial singularities associated with surface based coordinate systems for problems involving tracer transport in a given velocity field the semi lagrangian framework allows these new methods to avoid the use of any stabilization terms such as hyperviscosity during time integration thus reducing the number of parameters that have to be tuned the three new methods are based on interpolation using 1 global rbfs 2 local rbf stencils and 3 rbf partition of unity for the latter two of these methods we find that it is crucial to include some low degree spherical harmonics in the interpolants standard test cases consisting of solid body rotation and deformational flow are used to compare and contrast the methods in terms of their accuracy efficiency conservation properties and dissipation dispersion errors for global rbfs spectral spatial convergence is observed for smooth solutions on quasi uniform nodes while high order accuracy is observed for the local rbf stencil and partition of unity approaches

scattered and track data interpolation using an efficient strip searching procedure abstract a new local algorithm for bivariate interpolation of large sets of scattered and track data is presented the method which changes partially depending on the kind of data is based on the partition of the interpolation domain in a suitable number of parallel strips and starting from these on the construction for any data point of a square neighbourhood containing a convenient number of data points then the well known modified shepard s formula for surface interpolation is applied with some effective improvements the proposed algorithm is very fast owing to the optimal nearest neighbour searching and achieves good accuracy computational cost and storage requirements are analyzed moreover the efficiency and reliability of the algorithm are shown by several numerical tests also performed by renka s algorithm for a comparison

stbc schemes with nonvanishing determinant for certain number of transmit antennas a space time block code scheme stbc scheme is a family of stbcs c snr indexed by the signal to noise ratio snr such that the rate of each stbc scales with snr an stbc scheme is said to have a nonvanishing determinant if the coding gain of every stbc in the scheme is lower bounded by a fixed nonzero value the nonvanishing determinant property is important from the perspective of the diversity multiplexing gain dm g tradeoff a concept that characterizes the maximum diversity gain achievable by any stbc scheme transmitting at a particular rate this correspondence presents a systematic technique for constructing stbc schemes with nonvanishing determinant based on cyclic division algebras prior constructions of stbc schemes from cyclic division algebra have either used transcendental elements in which case the scheme may have vanishing determinant or is available with nonvanishing determinant only for two three four and six transmit antennas in this correspondence we construct stbc schemes with nonvanishing determinant for the number of transmit antennas of the form 2 sup k 3 spl middot 2 sup k 2 spl middot 3 sup k and q sup k q 1 2 where q is any prime of the form 4s 3 for cyclic division algebra based stbc schemes in a recent work by elia et al the nonvanishing determinant property has been shown to be sufficient for achieving dm g tradeoff in particular it has been shown that the class of stbc schemes constructed in this correspondence achieve the optimal dm g tradeoff moreover the results presented in this correspondence have been used for constructing optimal stbc schemes for arbitrary number of transmit antennas by elia et al

generalized distributive law for ml decoding of space time block codes the problem of designing good space time block codes stbcs with low maximum likelihood ml decoding complexity has gathered much attention in the literature all the known low ml decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast decodable conditionally multigroup decodable structure of a code we refer to this well known technique of decoding stbcs as conditional ml cml decoding in this paper we introduce a new framework to construct ml decoders for stbcs based on the generalized distributive law gdl and the factor graph based sum product algorithm we say that an stbc is fast gdl decodable if the order of gdl decoding complexity of the code with respect to the constellation size m is strictly less than m where is the number of independent symbols in the stbc we give sufficient conditions for an stbc to admit fast gdl decoding and show that both multigroup and conditionally multigroup decodable codes are fast gdl decodable for any stbc whether fast gdl decodable or not we show that the gdl decoding complexity is strictly less than the cml decoding complexity for instance for any stbc obtained from cyclic division algebras which is not multigroup or conditionally multigroup decodable the gdl decoder provides about 12 times reduction in complexity compared to the cml decoder similarly for the golden code which is conditionally multigroup decodable the gdl decoder is only half as complex as the cml decoder

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

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

examples of infinite covolume subgroups of rm psl 2 mathbb r r with big limit sets we provide examples of finitely generated infinite covolume subgroups of rm psl 2 mathbb r r with a big limit set e g that contains an open subset of the geometric boundary they are given by the so called semi arithmetic fuchsian groups admitting modular embeddings

perfect space time block codes in this paper we introduce the notion of perfect space time block codes stbcs these codes have full rate full diversity nonvanishing constant minimum determinant for increasing spectral efficiency uniform average transmitted energy per antenna and good shaping we present algebraic constructions of perfect stbcs for 2 3 4 and 6 antennas

energy efficient full diversity collaborative unitary space time block code designs via unique factorization of signals in this paper a novel concept called a uniquely factorable constellation pair ufcp is proposed for the systematic design of a noncoherent full diversity collaborative unitary space time block code by normalizing two alamouti codes for a wireless communication system having two transmitter antennas and a single receiver antenna it is proved that such a unitary ufcp code assures the unique identification of both channel coefficients and transmitted signals in a noise free case as well as full diversity for the noncoherent maximum likelihood receiver in a noise case to further improve error performance an optimal unitary ufcp code is designed by appropriately and uniquely factorizing a pair of energy efficient cross quadrature amplitude modulation qam constellations to maximize the coding gain subject to a transmission bit rate constraint after a deep investigation of the fractional coding gain function a technical approach developed in this paper to maximizing the coding gain is to carefully design an energy scale to compress the first three largest energy points in the corner of the qam constellations in the denominator of the objective as well as carefully design a constellation triple forming two ufcps with one collaborating with the other two so as to make the accumulated minimum euclidean distance along the two transmitter antennas in the numerator of the objective as large as possible and at the same time to avoid as many corner points of the qam constellations with the largest energy as possible to achieve the minimum of the numerator in other words the optimal coding gain is attained by intelligent constellations collaboration and efficient energy compression computer simulations demonstrate that error performance of the optimal unitary ufcp code presented in this paper outperforms those of the differential code and the signal to noise ratio efficient training code

low ml decoding complexity stbcs via codes over the klein group in this paper we give a new framework for constructing low ml decoding complexity space time block codes stbcs using codes over the klein group k almost all known low ml decoding complexity stbcs can be obtained via this approach new full diversity stbcs with low ml decoding complexity and cubic shaping property are constructed via codes over k for number of transmit antennas n 2m m 1 and rates r 1 complex symbols per channel use when r n the new stbcs are information lossless as well the new class of stbcs have the least known ml decoding complexity among all the codes available in the literature for a large set of n r pairs

strictly positive definite functions on spheres in euclidean spaces in this paper we study strictly positive definite functions on the unit sphere of the m dimensional euclidean space such functions can be used for solving a scattered data interpolation problem on spheres since positive definite functions on the sphere were already characterized by schoenberg some fifty years ago the issue here is to determine what kind of positive definite functions are actually strictly positive definite the study of this problem was initiated recently by xu and cheney proc amer math soc 116 1992 977 981 where certain sufficient conditions were derived a new approach which is based on a critical connection between this problem and that of multivariate polynomial interpolation on spheres is presented here the relevant interpolation problem is subsequently analyzed by three different complementary methods the first is based on the de boor ron general least solution for the multivariate polynomial interpolation problem the second which is suitable only for m 2 is based on the connection between bivariate harmonic polynomials and univariate analytic polynomials and reduces the problem to the structure of the integer zeros of bounded univariate exponentials finally the last method invokes the realization of harmonic polynomials as the polynomial kernel of the laplacian thereby exploiting some basic relations between homogeneous ideals and their polynomial kernels

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

multigroup ml decodable collocated and distributed space time block codes in this paper collocated and distributed space time block codes dstbcs which admit multigroup maximum likelihood ml decoding are studied first the collocated case is considered and the problem of constructing space time block codes stbcs which optimally tradeoff rate and ml decoding complexity is posed recently sufficient conditions for multigroup ml decodability have been provided in the literature and codes meeting these sufficient conditions were called clifford unitary weight cuw stbcs an algebraic framework based on extended clifford algebras ecas is proposed to study cuw stbcs and using this framework the optimal tradeoff between rate and ml decoding complexity of cuw stbcs is obtained for few specific cases code constructions meeting this tradeoff optimally are also provided the paper then focuses on multigroup ml decodable dstbcs for application in synchronous wireless relay networks and three constructions of four group ml decodable dstbcs are provided finally the orthogonal frequency division multiplexing ofdm based alamouti space time coded scheme proposed by li xia for a 2 relay asynchronous relay network is extended to a more general transmission scheme that can achieve full asynchronous cooperative diversity for arbitrary number of relays it is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node four group decodable dstbcs applicable in the proposed ofdm based transmission scheme are also given

spherical spline interpolation basic theory and computational aspects abstract the purpose of the paper is to adapt to the spherical case the basic theory and the computational method known from surface spline interpolation in euclidean spaces spline functions are defined on the sphere the solution process is made simple and efficient for numerical computation in addition the convergence of the solution obtained by spherical spline interpolation is developed using estimates for legendre polynomials

a novel construction of multi group decodable space time block codes complex orthogonal design cod codes are known to have the lowest detection complexity among space time block codes stbcs however the rate of square cod codes decreases exponentially with the number of transmit antennas the quasi orthogonal design qod codes emerged to provide a compromise between rate and complexity as they offer higher rates compared to cod codes at the expense of an increase of decoding complexity through partially relaxing the orthogonality conditions the qod codes were then generalized with the so called g symbol and g group decodable stbcs where the number of orthogonal groups of symbols is no longer restricted to two as in the qod case however the adopted approach for the construction of such codes is based on sufficient but not necessary conditions which may limit the achievable rates for any number of orthogonal groups in this paper we limit ourselves to the case of unitary weight uw g group decodable stbcs for 2a transmit antennas where the weight matrices are required to be single thread matrices with non zero entries 1 j and address the problem of finding the highest achievable rate for any number of orthogonal groups this special type of weight matrices guarantees full symbol wise diversity and subsumes a wide range of existing codes in the literature we show that in this case an exhaustive search can be applied to find the maximum achievable rates for uw g group decodable stbcs with g 1 for this purpose we extend our previously proposed approach for constructing uw 2 group decodable stbcs based on necessary and sufficient conditions to the case of uw g group decodable stbcs in a recursive manner

explicit space time codes achieving the diversity multiplexing gain tradeoff a recent result of zheng and tse states that over a quasi static channel there exists a fundamental tradeoff referred to as the diversity multiplexing gain d mg tradeoff between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space time st code this tradeoff is precisely known in the case of independent and identically distributed i i d rayleigh fading for tgesnt nr 1 where t is the number of time slots over which coding takes place and nt nr are the number of transmit and receive antennas respectively for t nt case we present two general techniques for building d mg optimal rectangular st codes from their square counterparts a byproduct of our results establishes that the d mg tradeoff for all tgesnt is the same as that previously known to hold for tgesnt n r 1

a new family of unitary space time codes with a fast parallel sphere decoder algorithm in this paper we propose a new design criterion and a new class of unitary signal constellations for differential space time modulation for multiple antenna systems over rayleigh flat fading channels with unknown fading coefficients extensive simulations show that the new codes have significantly better performance than existing codes we have compared the performance of our codes with differential detection schemes using orthogonal design cayley differential codes fixed point free group codes and product of groups and for the same bit error rate our codes allow smaller signal to noise ratio snr by as much as 10 db the design of the new codes is accomplished in a systematic way through the optimization of a performance index that closely describes the bit error rate as a function of the snr the new performance index is computationally simple and we have derived analytical expressions for its gradient with respect to constellation parameters decoding of the proposed constellations is reduced to a set of one dimensional closest point problems that we solve using parallel sphere decoder algorithms this decoding strategy can also improve efficiency of existing codes

a linear fractional semidefinite relaxation approach to maximum likelihood detection of higher order qam ostbc in unknown channels this paper considers the blind maximum likelihood ml detection problem for orthogonal space time block codes ostbcs in multiple input multiple output flat fading channels while the blind ml detection problem for general space time codes is difficult to solve it has been shown that for ostbcs with constant modulus constellations the blind ml detection problem can be formulated as a discrete quadratic program and then handled by a powerful convex approximation technique known as semidefinite relaxation sdr in this paper we turn our attention to the case of higher order qam ostbcs due to the nonconstant modulus nature of higher order qam signals the blind ml detection problem turns out to be a discrete rayleigh quotient maximization problem and as a result the current sdr technique is no longer directly applicable we propose a linear fractional sdr lfsdr approach to this problem this approach first relaxes the higher order qam blind ml detection problem into a quasi convex problem followed by a simple solution approximation procedure in general quasi convex problems are computationally more complex to solve than convex problems but we show that an optimum solution of our quasi convex problem can be efficiently obtained by solving a convex semidefinite program the approximation accuracy of the proposed approach relative to other possible relaxation approaches is also studied simulation results are presented to demonstrate that the proposed lfsdr based blind ml detector outperforms some existing suboptimal detectors and can yield promising performance even with a small to moderate number of code blocks

a geometric characterization of arithmetic fuchsian groups the trace set of a fuchsian group encodes the set of lengths of closed geodesics in the surface h luo and sarnak showed that the trace set of a cofinite arithmetic fuchsian group satisfies the bounded clustering property sarnak then conjectured that the b c property actually characterizes arithmetic fuchsian groups schmutz stated the even stronger conjecture that a cofinite fuchsian group is arithmetic if its trace set has linear growth he proposed a proof of this conjecture in the case when the group contains at least one parabolic element but unfortunately this proof contains a gap in the present paper we point out this gap and we prove sarnak s conjecture under the assumption that the fuchsian group contains parabolic elements

space time block coded spatial modulation a novel multiple input multiple output mimo transmission scheme called space time block coded spatial modulation stbc sm is proposed it combines spatial modulation sm and space time block coding stbc to take advantage of the benefits of both while avoiding their drawbacks in the stbc sm scheme the transmitted information symbols are expanded not only to the space and time domains but also to the spatial antenna domain which corresponds to the on off status of the transmit antennas available at the space domain and therefore both core stbc and antenna indices carry information a general technique is presented for the design of the stbc sm scheme for any number of transmit antennas besides the high spectral efficiency advantage provided by the antenna domain the proposed scheme is also optimized by deriving its diversity and coding gains to exploit the diversity advantage of stbc a low complexity maximum likelihood ml decoder is given for the new scheme which profits from the orthogonality of the core stbc the performance advantages of the stbc sm over simple sm and over v blast are shown by simulation results for various spectral efficiencies and are supported by the derivation of a closed form expression for the union bound on the bit error probability

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

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

approximately universal codes over slow fading channels performance of reliable communication over a coherent slow fading multiple input multiple output mimo channel at high signal to noise ratio snr is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains this paper studies the problem of designing codes that optimally tradeoff the diversity and multiplexing gains the main contribution is a precise characterization of codes that are universally tradeoff optimal i e they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel this characterization is referred to as approximate universality the approximation is in the connection between error probability and outage capacity with diversity and multiplexing gains respectively the characterization of approximate universality is then used to construct new coding schemes as well as to show optimality of several schemes proposed in the space time coding literature

a symbol by symbol channel estimation receiver for space time block coded systems and its performance analysis on the nonselective rayleigh fading channel we present a symbol by symbol channel estimation receiver for an orthogonal space time block coded system and derive its analytical performance on a slow nonselective rayleigh fading channel exact closed form expressions for its bit error probability bep performance for m ary phase shift keying modulations are obtained which enable us to theoretically predict the actual performance achievable under practical conditions with channel estimation error our bep expressions show explicitly the dependence of bep on the mean square error of the channel estimates which in turn depend on the channel fading model and the channel estimator used tight upper bounds are presented that show more clearly the dependence of the bep on various system parameters simulation results using various fading models are obtained to demonstrate the validity of the analysis

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

full diversity blind space time block codes in this paper the systematic design of a space time block code is considered for a wireless communication system with multiple transmitter receiver antennas and flat fading in which channel state information is completely unknown from the viewpoint of blind signal processing a necessary and sufficient condition is given for the unique identification of the multi input multi output flat fading channel and transmitted signal then some novel unique factorizations for a pair of coprime p ary and q ary phase shift keying psk constellations are established with this and currently available coherent space time block code designs a method is developed to systematically construct full diversity blind nonunitary space time block codes as well as unitary codes by just performing the qr decomposition of the nonunitary codes it is proved that under a noise free environment the code design proposed in this paper can guarantee that the transmitted signals and the channel coefficients are uniquely identified and that under a complex gaussian noise environment in which pth order and q th order statistics p and q are co prime of the received signals are available the channel coefficients can be still uniquely identified in addition a closed form solution to determine the channel coefficients is obtained