differential space time modulation over frequency selective channels we present herein a new differential space time frequency dstf modulation scheme for systems that are equipped with an arbitrary number of transmit antennas and operate in frequency selective channels the proposed dstf modulator consists of a concatenating spectral encoder and differential encoder that offer full spatio spectral diversity and significant coding gain a unitary structure is imposed on the differential encoder to admit linear decoupled maximum likelihood ml detection in space and time optimum criteria based on pairwise error probability analysis are developed for spectral encoder design we introduce a class of spectral codes namely linear constellation decimation lcd codes which are nonbinary block codes obtained by decimating a phase shift keying psk constellation with a group of decimation factors that are co prime with the constellation size since lcd codes encode across a minimally necessary set of subchannels for full diversity they incur modest decoding complexity among all full diversity codes numerical results are presented to illustrate the performance of the proposed dstf modulation and coding scheme which compares favorably with several existing differential space time schemes in frequency selective channels

three transmit antenna space time codes based on su 3 fully diverse constellations i e a set of unitary matrices whose pairwise differences are nonsingular are useful in multiantenna communications especially in multiantenna differential modulation since they have good pairwise error properties recently group theoretic ideas especially fixed point free fpf groups have been used to design fully diverse constellations of unitary matrices here we give systematic design methods of space time codes which are appropriate for three transmit antenna differential modulation the structures of the codes are motivated by the special unitary lie group su 3 one of the codes which is called the ab code has a fast maximum likelihood ml decoding algorithm using complex sphere decoding diversity products of the codes can be easily calculated and simulated performance shows that they are better than group based codes especially at high rates and as good as the elaborately designed nongroup code

unitary space time constellations based on quasi orthogonal sequences in this paper we propose a novel class of unitary space time constellations based on quaternary quasi orthogonal sequences qoss minimizing the maximum correlation between the signal matrices the proposed design owing to the underlying algebraic structure of the qoss allows for an efficient decoder structure while offering performance virtually identical to the unitary space time constellation design by hochwald et al

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

obtaining full diversity space frequency codes from space time codes via mapping this paper considers the problem of space frequency code design for frequency selective multiple input multiple output mimo orthogonal frequency division multiplexing ofdm modulation we show that space time codes achieving full diversity in quasistatic flat fading environment can be used to construct space frequency codes that can achieve the maximum diversity available in frequency selective mimo fading channels since the codes are constructed via a simple mapping from space time codes to space frequency codes the abundant classes of existing space time block and trellis codes can be used for full diversity transmission in mimo ofdm systems the proposed mapping provides a tradeoff between the achieved diversity order and the symbol rate moreover we characterize the performance of the space frequency codes obtained via the mapping by finding lower and upper bounds on their coding advantages as functions of the coding advantages of the underlying space time codes this result will allow us to investigate the effects of the delay distribution and the power distribution of the channel impulse responses on the performance of the resulting space frequency codes extensive simulation results are also presented to illustrate and support the theory

tree search multiple symbol differential decoding for unitary space time modulation differential space time modulation dstm using unitary matrix signal constellations is an attractive solution for transmission over multiple input multiple output mimo fading channels without requiring channel state information csi at the receiver to avoid a high error floor for dstm in relatively fast mimo fading channels multiple symbol differential detection msdd has to be applied at the receiver msdd jointly processes blocks of several received matrix symbols and power efficiency improves as the blocksize increases but since the search space of msdd grows exponentially with the blocksize and also with the number of transmit antennas and the data rate the complexity of msdd quickly becomes prohibitive in this paper we investigate the application of tree search algorithms to overcome the complexity limitation of msdd we devise a nested msdd structure consisting of an outer and a number of inner tree search decoders which renders msdd feasible for wide ranges of system parameters decoder designs tailored for diagonal and orthogonal dstm codes are given and a more power efficient variant of msdd so called subset msdd is proposed furthermore we derive a tight symbol error rate approximation for msdd which lends itself to efficient numerical evaluation numerical and simulation results for different dstm constellations and fading channel scenarios show that the new tree search msdd achieves a significantly better performance complexity tradeoff than benchmark decoders

fast multiple antenna differential decoding we present an algorithm based on lattice reduction for the fast decoding of diagonal differential modulation across multiple antenna while the complexity of the maximum likelihood ml algorithm is exponential both in the number of antenna and the rate the complexity of our approximate lattice algorithm is polynomial in the number of antennas and the rate we show that the error performance of our lattice algorithm is very close to the ml algorithm

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

receive antenna selection for unitary space time modulation over semi correlated ricean channels receive antenna selection for unitary space time modulation ustm over semi correlated ricean fading channels is analyzed this work generalizes that of ma and tepedelenlio glu for the independent and identically distributed i i d rayleigh fading case the antenna selection rule is that the receive antennas with the largest signal powers are chosen for single antenna selection we derive the maximum likelihood decoding for the correlated ricean case we also derive the chernoff bound on the pairwise error probability for the high signal to noise ratio snr region and obtain the coding gain and diversity order our results show that even when there are transmitter side correlations and a line of sight component receive antenna selection with ustm preserves the full diversity order if the ustm constellation is of full rank we also give an approximation to the distribution function of a quadratic form of non zero mean complex gaussian variates from nabar et al at the high snr region based on this approximation a closed form expression for the coding gain is also obtained and compared with that of the i i d rayleigh case we also analyze the case of multiple receive antenna selection and derive the coding gain and diversity order we show that ustm constellations which have been proposed for the i i d rayleigh channel can be used with the correlated ricean channel as well

cyclic algebras for noncoherent differential space time coding we investigate cyclic algebras for coding over the differential noncoherent channel cyclic algebras are an algebraic object that became popular for coherent space time coding since it naturally yields linear families of matrices with full diversity coding for the differential noncoherent channel has a similar flavor in the sense that it asks for matrices that achieve full diversity except that these matrices furthermore have to be unitary in this work we give a systematic way to find infinitely many unitary matrices inside cyclic algebras which holds for all dimensions we show how cyclic algebras generalize previous families of unitary matrices obtained using the representation of fixed point free groups as an application of our technique we present families of codes for three and four antennas that achieve high coding gain

existence and construction of noncoherent unitary space time codes we consider transmission using n transmit and reception using m receive antennas in a wireless environment assuming that neither the transmitter nor the receiver knows the channel coefficients for the scenario that the transmission employs noncoherent t spl times n unitary space time codes and for a block fading channel model where the channel is static during t channel uses and varies from t channel uses to the other we establish the bound r spl les min t n n on the diversity advantage rm provided by the code in order to show that the requirement r spl les min t n n cannot be relaxed for any given r n t and r spl les min t n n we then construct unitary t spl times n space time codes of rate r that guarantee diversity advantage rm two constructions are given that are also amenable to simple encoding and noncoherent maximum likelihood ml decoding algorithms

cayley differential unitary space time codes one method for communicating with multiple antennas is to encode the transmitted data differentially using unitary matrices at the transmitter and to decode differentially without knowing the channel coefficients at the receiver since channel knowledge is not required at the receiver differential schemes are ideal for use on wireless links where channel tracking is undesirable or infeasible either because of rapid changes in the channel characteristics or because of limited system resources although this basic principle is well understood it is not known how to generate good performing constellations of unitary matrices for any number of transmit and receive antennas and for any rate this is especially true at high rates where the constellations must be rapidly encoded and decoded we propose a class of cayley codes that works with any number of antennas and has efficient encoding and decoding at any rate the codes are named for their use of the cayley transform which maps the highly nonlinear stiefel manifold of unitary matrices to the linear space of skew hermitian matrices this transformation leads to a simple linear constellation structure in the cayley transform domain and to an information theoretic design criterion based on emulating a cauchy random matrix moreover the resulting cayley codes allow polynomial time near maximum likelihood ml decoding based on either successive nulling canceling or sphere decoding simulations show that the cayley codes allow efficient and effective high rate data transmission in multiantenna communication systems without knowing the channel

asymptotic error probability analysis of quadratic receivers in rayleigh fading channels with applications to a unified analysis of coherent and noncoherent space time receivers a general asymptotic high signal to noise snr error analysis is introduced for quadratic receivers in frequency flat and multipath rayleigh fading channels with multiple transmit and receive antennas asymptotically tight expressions for the pairwise error probabilities are obtained for coherent noncoherent and differentially coherent space time receivers not only is our unified analysis applicable to more general modulation schemes and or channel models than previously considered but it also reveals a hitherto unrecognized eigenvalue structure that is common to all of these problems in addition to providing an easy recipe for computing the asymptotic pairwise error rates we make some conclusions regarding criteria for the design of signal constellations and codes such as a the same design criteria apply for both correlated and independent and identically distributed i i d fading processes and b for noncoherent communications unitary signals are optimal in the sense that they minimize the asymptotic union bound

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

multiple symbol differential detection for mpsk space time block codes decision metric and performance analysis approximately 3 db signal to noise ratio snr loss is always paid with conventional differential space time block codes stbcs compared with coherent stbcs in this paper a multiple symbol differential detection msdd technique is proposed for m ary phase shift keying psk stbcs the new scheme can greatly narrow the 3 db performance gap by extending the observation interval for differential decoding the technique uses maximum likelihood sequence detection instead of traditional symbol by symbol detection and is carried out on the slow flat rayleigh fading channel a generalized decision metric is derived for an observation interval of arbitrary length it is shown that for a moderate number of symbols msdd provides approximately 1 5 db performance improvement over conventional differential detection in addition a closed form pairwise error probability and approximate bit error probability bep are derived for multiple symbol differential binary psk stbc results show that the theoretical bep matches simulation results well the bep is shown to converge asymptotically with the number of symbols in the observation interval to that of the differential scheme with coherent detection

differential space time modulation space time coding and modulation exploit the presence of multiple transmit antennas to improve the performance on multipath radio channels thus far most work on space time coding has assumed that perfect channel estimates are available at the receiver in certain situations however it may be difficult or costly to estimate the channel accurately in which case it is natural to consider the design of modulation techniques that do not require channel estimates at the transmitter or receiver we propose a general approach to differential modulation for multiple transmit antennas based on group codes this approach ran be applied to any number of transmit and receive antennas and any signal constellation we also derive low complexity differential receivers error bounds and modulator design criteria which we use to construct optimal differential modulation schemes for two transmit antennas these schemes can be demodulated with or without channel estimates this permits the receiver to exploit channel estimates when they are available the performance degrades by approximately 3 db when estimates are not available

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

asymptotic analysis of coherent and differential space time codes in non gaussian noise and interference in this paper we provide a unified framework for the asymptotic performance analysis of space time codes stcs in correlated ricean fading and non gaussian noise and interference in particular we derive simple and asymptotically tight expressions for the pairwise error probability pep of coherent and differential stcs which are valid for any type of noise and interference with finite moments and detection with general mahalonobis distance md metrics including euclidean distance ed and noise decorrelating nd metrics these pep expressions can be combined with truncated union bounds to obtain accurate asymptotic approximations for the bit symbol and frame error probabilities of stcs we show that while the diversity gain of an stc is independent of the type of noise and the type of md metric used the coding gain is not and depends on certain moments of the noise and interference we provide closed form expressions for these moments for several practically relevant types of noise and interference we show that for correlated noise significant performance gains can be achieved with the nd metric compared to the ed metric while noise correlations are beneficial at high signal to noise ratios if they can be exploited by the metric they are harmful if this is not the case and the simple ed metric is employed all our analytical findings are confirmed by simulations for various popular stcs and several different types of noise and interference

khatri rao space time codes space time st coding techniques exploit the spatial diversity afforded by multiple transmit and receive antennas to achieve reliable transmission in scattering rich environments st block codes are capable of realizing full diversity and spatial coding gains at relatively low rates st trellis codes can achieve better rate diversity tradeoffs at the cost of high complexity on the other hand v blast supports high rates but has no built in spatial coding and does not work well with fewer receive than transmit antennas we propose a novel linear block coding scheme based on the khatri rao matrix product the proposed scheme offers flexibility for achieving full rate or full diversity or a desired rate diversity tradeoff and it can handle any transmit receive antenna configuration or signal constellation the proposed codes are shown to have numerous desirable properties including guaranteed unique linear decodability built in blind channel identifiability and efficient near maximum likelihood decoding

unitary space time constellation analysis an upper bound for the diversity the diversity product and the diversity sum are two very important parameters for a good performing unitary space time constellation a basic question is what the maximal diversity product or sum is in this correspondence we are going to derive general upper bounds on the diversity sum and the diversity product for unitary constellations of any dimension n and any size m using packing techniques on the compact lie group u n

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

further results on differential space time modulations some novel results on the space time differential modulation schemes described by b m hochwald and w sweldens see ibid vol 48 p 2041 52 2000 and v tarokh and h jafarkhani ieee j select areas commun vol 18 p 1169 74 2000 are derived under the assumption of a quasi static multiple antenna channel first the optimality in the maximum likelihood sense of the one shot detection algorithms of hochwald and sweldens and of tarokh and jafarkhani is proved then the expression of the pairwise error probability for these detectors is derived and as a particular case the bit error rate is computed for the binary phase shift keyed scheme of tarokh and jafarkhani finally a per survivor processing psp detection algorithm for this class of modulations is illustrated numerical results evidence both the superiority of the psp strategy over the one shot space time differential detectors and the accuracy of the above mentioned bit error rate formula

signal design and convolutional coding for noncoherent space time communication on the block rayleigh fading channel we consider the problem of designing signal constellations for the multiple transmit multiple receive antenna rayleigh fading communication channel when neither the transmitter nor the receiver know the fading in particular by employing the asymptotic union bound aub on the probability of error we give a new formulation of the problem of signal design for the noncoherent fading channel since unitary signals are optimal for this channel in the limit of large signal to noise ratios snrs the problem can be posed in terms of packings on the grassmanian manifold a key difference in our approach from that of other authors is that we use a notion of distance on this manifold that is suggested by the union bound as a consequence of our use of this distance measure we obtain signal designs that are guaranteed to achieve the full diversity order of the channel a result that does not hold when the chordal distance is used we introduce a new method of recursively designing signals termed successive updates to approximately optimize this performance measure we then examine the use of our signals with several convolutional codes over the fading channel an upper bound on the bit error probability of the maximum likelihood decoder is presented together with an asymptotic analysis of that bound

bound intersection detection for multiple symbol differential unitary space time modulation this paper considers multiple symbol differential detection msd of differential unitary space time modulation dustm over multiple antenna systems we derive a novel exact maximum likelihood ml detector called the bound intersection detector bid using the extended euclidean algorithm for single symbol detection of diagonal constellations while the ml search complexity is exponential in the number of transmit antennas and the data rate our algorithm particularly in high signal to noise ratio achieves significant computational savings over the naive ml algorithm and the previous detector based on lattice reduction we also develop four bid variants for msd the first two are ml and use branch and bound the third one is suboptimal which first uses bid to generate a candidate subset and then exhaustively searches over the reduced space and the last one generalizes decision feedback differential detection simulation results show that the bid and its msd variants perform nearly ml but do so with significantly reduced complexity

performance and optimized design of space time codes for mimo wireless systems with imperfect channel estimates multiple antennas constitute an effective mean to achieve spatial diversity in emerging bandwidth efficient multiple input multiple output mimo wireless systems until now most contributions in this area are focused on the two limit cases of fully coherent and fully incoherent decoding which in turn occur when perfect channel estimates and no channel estimates are available at the receiver however very accurate channel estimates typically demand long training sequences that reduces spectral efficiency therefore testing capabilities of multiple antenna systems with partially coherent decoding may be appealing for improving power versus bandwidth tradeoff in this contribution we focus on the optimized design and performance evaluations of multiple antenna block coded systems with partially coherent maximum likelihood ml decoding after considering emerging fourth generation wlans 4gwlans as a possible application scenario we present new performance bounds and optimized design criteria together with a new family of robust space time unitary block codes that self match to channel estimation errors we name these codes self matching

an application of the bruhat decomposition to the design of full diversity unitary space time codes a full diversity constellation that is a set of unitary matrices whose differences have nonzero determinant is a design criterion for codes with good performance using differential unitary space time modulation fixed point free groups and the infinite group su 2 have been used to produce full diversity unitary group constellations in this paper we present a new bruhat decomposition design for constructing full diversity unitary space time constellations for any number of antennas they are constructed from cosets of a unitary diagonal subgroup d and our design has a particularly simple structure for the case where the number of transmitter antennas is prime we also consider the extension of these constellation designs for an even number of transmitter antennas by replacing d with a hamiltonian constellation some examples of proposed constellations for two to six transmitter antennas are given simulations show that our proposed constellations perform well in unknown rayleigh fading channel

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

correlation matching approaches for blind ostbc channel estimation in this paper the problem of blind channel estimation under orthogonal space time block coded ostbc transmissions is solved by minimizing some distance measure between the theoretical and estimated correlation matrices of the observations specifically the minimization of the euclidean distance and the kullback leibler divergence leads respectively to the euclidean correlation matching ecm and kullback correlation matching kcm criteria the proposed techniques exploit the knowledge of the source correlation matrix to unambiguously recover the multiple input multiple output mimo channel furthermore due to the orthogonality properties of ostbcs both the ecm and kcm criteria result in closed form solutions in particular the channel estimate is given by the principal eigenvector of a matrix which is obtained from the estimated correlation matrix of the observations modified by the code matrices and a set of weights in the ecm case the weights are fixed and equal to the eigenvalues of the source correlation matrix whereas the kcm weights depend on both the signal to noise ratio snr and the source eigenvalues additionally we show that the proposed approaches are equivalent in the low snr regime whereas in the high snr regime the kcm criterion is asymptotically equivalent to the relaxed blind maximum likelihood ml decoder finally the performance of the proposed criteria is illustrated by means of some numerical examples

systematic design of unitary space time constellations we propose a systematic method for creating constellations of unitary space time signals for multiple antenna communication links unitary space time signals which are orthonormal in time across the antennas have been shown to be well tailored to a rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients the signals can achieve low probability of error by exploiting multiple antenna diversity because the fading coefficients are not known the criterion for creating and evaluating the constellation is nonstandard and differs markedly from the familiar maximum euclidean distance norm our construction begins with the first signal in the constellation an oblong complex valued matrix whose columns are orthonormal and systematically produces the remaining signals by successively rotating this signal in a high dimensional complex space this construction easily produces large constellations of high dimensional signals we demonstrate its efficacy through examples involving one two and three transmitter antennas

space time coding ambiguities in joint adaptive channel estimation and detection this paper studies the error propagation effect that is caused by certain ambiguities in joint data detection channel tracking algorithms for transmission diversity schemes here we use a space time st receiver based on the maximum a posteriori map method that takes into account the channel estimation error assuming the unknown channel to have a given complex multivariate gaussian probability density function pdf i e a ricean channel the decision criterion that is expressed in quadratic form represents either a linear detector or a noncoherent nonlinear detector in extreme cases then the channel pdf for the next iteration is updated by estimates of the second order statistics of the channel coefficients and a very simple decision directed adaptive algorithm is derived for adaptive channel estimation the adaptive algorithm can efficiently track a fast rayleigh fading channel and as a result achieves robust performance however the occurrence of two types of ambiguities initiated in deep fades result in error propagation some remedies called space time ambiguity remedies stars are proposed to prevent error propagation a new time varying space time coding tvst scheme is suggested as a bandwidth efficient method to combat the permutation ambiguity impairment this coding scheme in conjunction with a differential detector can resolve the ambiguity problem

computing the performance of unitary space time group codes from their character table multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment their success however depends on the design of cedes that achieve these promises it is well known that unitary matrices can be used to design differentially modulated space time codes these codes have a particularly efficient description if they form a finite group under matrix multiplication we show how to compute the parameters of such groups crucial for their use as space time codes using only the character table of the group since character tables for many groups are known and tabulated this method could be used to quickly test for a given group which of its irreducible representations can be used to design good unitary space time codes we demonstrate our method by computing the eigenvalues of all the irreducible representations of the special linear group sl sub 2 f sub q over a finite prime field f sub q of odd characteristic and study in detail the performance of a particular eight dimensional representation of sl sub 2 f sub 17

a discrete valued clustering algorithm with applications to biomolecular data this paper presents an algorithm for clustering large n tuple discrete valued data and describes how it is used for analyzing biomolecular data the algorithm consists of a cluster initiation phase and a cluster regrouping phase the former involves the analysis of the nearest neighbour distance configuration using the probability estimate of each sample in the data set it considers only a subset of variables with consigned or transferred interdependency that is these variables reflect many of the data interdependencies among the ensemble the latter involves 1 the selection of relevant attribute values based on their statistical dependence on the initial clusters formed and 2 the inference of the cluster label based on the weight of evidence of the selected attribute values of the samples pertaining to a certain cluster over the others because only a subset of selected attribute values is considered the final clusters can be of any shape and not necessarily globular hence it is not affected by the presence of irrelevant attribute values experimental results on several control data sets as well as a biomolecular data set demonstrate its efficacy for molecular sequence analysis and taxonomy analysis

on the optimum design of unitary cyclic group space time codes in this letter based on the exact pairwise error probability we derive the union bound on the symbol error probability sep of the differential unitary space time dust modulation employing group codes instead of using the rank and determinant or euclidean distance criteria we optimize the cyclic group codes such that the union bound on the sep is minimized for a predetermined scenario taking into account the number of transmit and receive antennas and the operating signal to noise ratio snr our simulation results show that for a wide range of snrs the codes with the minimum union bound for a particular snr outperform the codes designed based on rank and determinant or euclidean distance criteria

iterative decoding of space time differentially coded unitary matrix modulation noncoherent communication over the rayleigh flat fading channel with multiple transmit and receive antennas is investigated codes achieving bit error rate ber lower than 10 sup 4 at bit energy over the noise spectral density ratio e sub b n sub 0 of 0 8 to 2 8 db from the capacity limit were found with coding rates of 0 5 to 2 25 bits per channel use the codes are serial concatenation of a turbo code and a unitary matrix differential modulation code the receiver is based on a high performance joint iterative decoding of the turbo code and the modulation code information theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder

nonintersecting subspaces based on finite alphabets two subspaces of a vector space are here called nonintersecting if they meet only in the zero vector motivated by the design of noncoherent multiple antenna communications systems we consider the following question how many pairwise nonintersecting m sub t dimensional subspaces of an m dimensional vector space v over a field f can be found if the generator matrices for the subspaces may contain only symbols from a given finite alphabet a spl sube f the most important case is when f is the field of complex numbers c then m sub t is the number of antennas if a f gf q it is shown that the number of nonintersecting subspaces is at most q sup m 1 q sup mt 1 and that this bound can be attained if and only if m is divisible by m sub t furthermore these subspaces remain nonintersecting when lifted to the complex field it follows that the finite field case is essentially completely solved in the case when f c only the case m sub t 2 is considered it is shown that if a is a psk configuration consisting of the 2 sup r complex roots of unity the number of nonintersecting planes is at least 2 sup r m 2 and at most 2 sup r m 1 1 the lower bound may in fact be the best that can be achieved

svd iterative decision feedback demodulation and detection of coded space time unitary differential modulation a new suboptimal demodulator based on iterative decision feedback demodulation dfd and a singular value decomposition svd for estimation of unitary matrices is introduced noncoherent communication over the rayleigh flat fading channel with multiple transmit and receive antennas where no channel state information csi is available at the receiver is investigated with four transmit antennas codes achieving bit error rate ber lower than 10 sup 4 at bit energy over the noise spectral density ratio e sub b n sub o of 0 25 db up to 3 5 db with coding rates of 1 6875 to 5 06 bits per channel use were found the performance is compared to the mutual information upper bound of the capacity attaining isotropically random ir unitary transmit matrices the codes achieve ber lower than 10 sup 4 at e sub b n sub o of 3 2 db to 5 8 db from this bound system performance including the iterative dfd algorithm is compared to the one using euclidean distance as a reliability measure for demodulation the dfd system presents a performance gain of up to 1 5 db uncoded systems doing iterative dfd demodulation and idealized pilot sequence assisted modulation psam detection are compared iterative dfd introduces a gain of more than 1 2 db the coded system comprises a serial concatenation of turbo code and a unitary matrix differential modulation code the receiver employs the high performance coupled iterative decoding of the turbo code and the modulation code information theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder

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

svd iterative detection of turbo coded multiantenna unitary differential modulation a new suboptimal demodulator based on a singular value decomposition for estimation of unitary matrices is introduced noncoherent communication over the rayleigh flat fading channel with multiple transmit and receive antennas where no channel state information is available at the receiver is investigated codes achieving bit error rate ber lower than 10 sup 4 at bit energy over the noise spectral density ratio e sub b n sub 0 of 1 6 1 9 db from code restricted capacity limit were found at higher data rates computation of code restricted capacity is impractical therefore the mutual information upper bound of the capacity attaining isotropically random unitary transmit matrices was used the codes achieve ber lower than 10 sup 4 at e sub b n sub 0 of 3 2 6 db from this bound with coding rates of 1 125 5 06 bits per channel use and different modulation decoding complexities the codes comprise a serial concatenation of turbo code and a unitary matrix differential modulation code the receiver employs the high performance coupled iterative decoding of the turbo code and the modulation code information theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder

spectrally efficient noncoherent communication this paper considers noncoherent communication over a frequency nonselective channel in which the time varying channel gain is unknown a priori but is approximately constant over a coherence interval unless the coherence interval is large coherent communication which requires explicit channel estimation and tracking prior to detection incurs training overhead which may be excessive especially for multiple antenna communication in contrast noncoherent detection may be viewed as a generalized likelihood ratio test glrt which jointly estimates the channel and the data and hence does not require separate training the main results in this paper are as follows 1 we develop a signal space criterion for signal and code design for noncoherent communication in terms of the distances of signal points from the decision boundaries 2 the noncoherent metric thus obtained is used to guide the design of signals for noncoherent communication that are based on amplitude phase constellations these are significantly more efficient than conventional differential phase shift keying psk especially at high signal to noise ratio snr also known results on the high snr performance of multiple symbol demodulation of differential psk are easily inferred from the noncoherent metric 3 the glrt interpretation is used to obtain near optimal low complexity implementations of noncoherent block demodulation in particular this gives an implementation of multiple symbol demodulation of differential psk which is of linear complexity in the block length and whose degradation from the exact exponential complexity implementation can be made as small as desired

multiple antenna signaling over fading channels with estimated channel state information performance analysis multiple antenna concepts for wireless communication systems promise high spectral efficiency and low error rates by proper exploitation of the randomness in multipath propagation in this paper we investigate the impact of channel uncertainty caused by channel estimation errors on the error rate performance we consider a training based multiple antenna system that reserves a portion of time to sound the channel training symbols are used to estimate the channel by means of an arbitrary linear filter at the receiver no channel state information csi is assumed at the transmitter we present a new framework to analyze training based multiple antenna systems by introducing an equivalent system model that specifies the channel by the estimated and hence known channel coefficients and an uncorrelated data dependent multiplicative noise we derive the maximum likelihood ml detector and highlight its behavior in the limiting cases of perfect csi and no csi and its relation to several mismatched detectors we deduce new exact expressions and chernoff bounds of the pairwise error probability pep used to assess word error and bit error rate bounds for ml and mismatched detection finally we review the code design guidelines in terms of the deleterious effect of channel uncertainty for coherent and noncoherent signaling schemes and present numerical results

on noncoherent receivers for dstm in spatially correlated fading in this letter we derive a multiple symbol differential detection msdd and a novel msdd based decision feedback differential detection ms dfdd receiver for differential space time modulation transmitted over spatially correlated multiple input multiple output fading channels we show that ms dfdd outperforms previously proposed dfdd schemes that are based on scalar and vector prediction sp dfdd and vp dfdd in addition we prove that at high signal to noise ratio snr vp dfdd is equivalent to sp dfdd and thus fails to properly exploit the spatial fading correlations

closed form blind mimo channel estimation for orthogonal space time block codes in this paper a new computationally simple approach to blind decoding of orthogonal space time block codes ostbcs is proposed using specific properties of ostbcs the authors approach estimates the channel matrix in a closed form and in a fully blind fashion this channel estimate is then used in the maximum likelihood ml receiver to decode the information symbols the proposed estimation technique provides consistent channel estimates and as a result the performance of the authors blind ml receiver approaches that of the coherent ml receiver which exploits the exact channel state information csi simulation results demonstrate the performance improvements achieved by the proposed blind decoding algorithm relative to the popular differential space time modulation scheme

recursive space time trellis codes using differential encoding differential space time modulation dstm has been recently proposed by hughes and hochwald and sweldens when the channel information is not known at the receiver where the demodulation is in fact the same as the coherent demodulation of space time block coding by replacing the channel matrix with the previously received signal matrix on the other hand the dstm also needs a recursive memory of a matrix block at the encoder and therefore provides a trellis structure when the channel information is known at the receiver which is the interest of this paper this recursive structure of the dstm has been adopted lately by schlegel and grant in joint with a conventional binary code and joint iterative decoding demodulation with a superior performance the number of states of the trellis from the recursive structure depends on both the memory size which is fixed in this case and the unitary space time code ustc when a ustc for the dstm forms a group the number of states is the same as the size of the ustc otherwise the number of the states is the size of the semi group generated by the ustc from all the multiplications of the matrices in the ustc it is well known in the conventional convolutional coding cc or the trellis coded modulation tcm the free hamming or euclidean distance or the performance increases when the number of states increases by adding more memory with a properly designed cc or tcm in this paper we systematically study and design the ustc dstm for the recursive space time trellis modulation and show that the diversity product increases when the number of states increases which is not because of the memory size but because of the different ustc designs that generate different sizes of semi groups we propose a new ustc design criterion to ensure that the trellis structure improves the diversity product over the ustc as a block code based on the new criterion we propose a new class of ustc design for an arbitrary number of transmit antennas that has an analytical diversity product formula for two transmit antennas we then follow schlegel and grant s approach for joint encoding and iterative decoding of a binary coded dstm turbo space time coding and numerically show that our new ustc designs for the recursive space time trellis modulation outperforms the group ustc used by schlegel and grant

lattice boltzmann model for nonlinear convection diffusion equations a lattice boltzmann model for convection diffusion equation with nonlinear convection and isotropic diffusion terms is proposed through selecting equilibrium distribution function properly the model can be applied to the common real and complex valued nonlinear evolutionary equations such as the nonlinear schrodinger equation complex ginzburg landau equation burgers fisher equation nonlinear heat conduction equation and sine gordon equation by using a real and complex valued distribution function and relaxation time detailed simulations of these equations are performed and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies

orthogonal space time block codes with sphere packing orthogonal designs have received considerable attention in the development of efficient modulation and coding methods for future multi antenna wireless communication systems due to their special properties in this paper we propose a class of space time block codes constructed by combining orthogonal designs with sphere packing for an arbitrary number of transmit antennas the structure of the orthogonal designs is exploited to guarantee full diversity and sphere packing is used to improve the coding advantage space time block code construction from block orthogonal designs is also considered the full diversity property is ensured by rotating the sphere packing underlying the code and the optimal rotation angle is determined for a class of sphere packing code design examples are provided for two and four transmit antennas and various transmission rates the simulation results show that by jointly designing the symbols in the orthogonal designs the performance of the block codes can be significantly increased

on the complexity of sphere decoding for differential detection multiple symbol differential detection msdd for multiple input multiple output rayleigh fading channels is considered msdd which jointly processes blocks of n received symbols to detect n 1 data symbols allows for power efficient transmission without requiring channel state information at the receiver in previous work the authors showed that computational efficient sphere decoding algorithms can be used to accomplish msdd in this correspondence the computational complexity of this sphere decoding based msdd is analyzed in particular it is proven by means of a lower bound that the complexity of the fincke pohst multiple symbol differential sphere decoder fp msdsd while being very low over wide ranges of n and signal to noise ratios is exponential in n in principle furthermore both exact and simple approximate expressions for the complexity of fp msdsd are derived which allow for quick assessment of ranges of useful window sizes n of fp msdsd and show that the exponential rate of growth of the complexity of fp msdsd is asymptotically equal to that of brute force msdd

precoded and vector ofdm robust to channel spectral nulls and with reduced cyclic prefix length in single transmit antenna systems the performance of orthogonal frequency division multiplexing ofdm systems may be degraded when intersymbol interference isi channels have spectral nulls also when isi channels have many taps the data rate overhead due to the insertion of the cyclic prefix is high we first propose a precoded ofdm system that may improve the performance of the ofdm systems for spectral null channels we also propose size k spl times x1 vector ofdm vofdm systems that reduce the cyclic prefix length by k times compared to the conventional ofdm systems the precoding scheme is simply to insert one or more zeros between each two sets of k consecutive information symbols although it can be generalized to a general form this precoding scheme may be able to remove the spectral nulls of an isi channel without knowing the isi channel when no zero is inserted between each two sets of k consecutive information symbols and only each k consecutive symbols are blocked together we obtain vofdm systems both theoretical performance analysis and simulation results are presented finally we compare the combination of the vofdm systems and the unitary matrix modulation with the conventional ofdm systems and the phase shift keying modulation where both differential noncoherent and coherent modulations and demodulations are considered

unitary space time constellation designs from group codes in this correspondence we propose new unitary space time constellation designs with high diversity products our hamiltonian and product constellations are based on slepian s group codes and can be used for any number of antennas and any data rate our hamiltonian constellations achieve the theoretical upper bound of diversity product when the number of transmitter antennas is even and the cardinality of the signal constellation is less than or equal to 5 many of our hamiltonian and product constellations outperform and have higher diversity products than the best known designs in the literature these include orthogonal designs dicyclic groups cyclic groups parametric codes numerical approaches nongroup designs cayley codes tast codes and some constellations obtained from fixed point free groups

algebraic differential spatial modulation is capable of approaching the performance of its coherent counterpart we show that certain signal constellations invoked for classic differential encoding result in a phenomenon we term as the unbounded differential constellation size udcs various existing differential transmission schemes that suffer from this issue are identified then we propose an enhanced algebraic field extension based differential spatial modulation afe dsm scheme and its enhanced counterpart that strikes a diversity rate tradeoff afe dsm dr both of which overcome the udcs issue without compromising its full transmit diversity advantage furthermore the proposed schemes are extended to incorporate amplitude and phase shift keying apsk in order to exploit all the available degrees of freedom additionally we propose a pair of detection schemes specially designed for apsk aided differential transmission schemes explicitly we conceive the buffered minimum mean squared error b mmse detector and buffered maximum likelihood b ml detector which exploit the knowledge of previously detected symbols in order to further improve the detection performance our simulation results have shown that the proposed detectors are capable of bridging the performance gap between the conventional differential detector cdd and the coherent detector that has full channel state information specifically when employing the proposed apsk aided afe dsm scheme operating at a rate of 2 b per channel use the b mmse and b ml detectors are observed to give about 3 and 3 5 db signal to noise ratio gain with respect to their cdd counterpart at a bit error ratio of 10 5

leveraging coherent space time codes for noncoherent communication via training training codes are introduced for the multiple antenna noncoherent multiple block rayleigh fading channel in which the fading coefficients which are constant over a fixed number of dimensions coherence interval for each block and then change independently to a new realization are known neither at the transmitter nor at the receiver each codeword of a training code consists of a part known to the receiver used to form a minimum mean squared error mmse estimate of the channel and a part that contains codeword s of a space time block or trellis code designed for the coherent channel in which the receiver has perfect knowledge of the channel the channel estimate is used as if it were error free for decoding the information bearing part of the training codeword training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have high rate and to be efficiently decodable conditions for which the estimator detector e d receiver is equivalent to the optimal noncoherent receiver are established a key performance analysis result of this paper is that the training codes when decoded with the e d receiver achieve a diversity order of the error probability that is equal to the diversity order of the underlying coherent code in some cases the performance of training codes can be measured relative to coherent reception via training efficiency which is then optimized over the energy allocation between the training and data phases in the limit of increasing block lengths training codes always achieve the performance of coherent reception the examples of training codes provided in this work have polynomial complexity in rate but an error rate comparable to the best performing unitary designs available even though the latter require exponential decoding complexity

a differential space time modulation scheme for correlated rayleigh fading channels performance analysis and design differential space time modulation dstm is an encoding technique for multiantenna systems that allows the receiver to detect the transmitted signals without the knowledge of the fading channels it can be viewed as an extension of the differential phase shift keying scheme in single antenna systems in this paper we investigate the performance of multiantenna systems employing dstm under spatially correlated rayleigh fading channels we present three expressions for calculating the pairwise error probability pep of the dstm scheme the first expression allows us to numerically calculate the exact pep the remaining two are closed form expressions of the exact pep at asymptotically high signal to noise ratios and the pep upper bound it is found that when the distance matrix is proportional to the identity matrix the error probability is determined by the channel correlation matrix and the initial transmitted code matrix based on the new pep upper bound we derive a criterion for optimizing the initial code matrix for this special case simulation results show that the performance of the differential space time coded systems can be significantly improved by designing the initial transmitted code matrix according to the proposed design criterion

coded unitary space time modulation with iterative decoding error performance and mapping design this paper studies the bit error probability of coded unitary space time modulation with iterative decoding where neither the transmitter nor the receiver knows the channel fading coefficients the tight error bound with respect to the asymptotic performance is first analytically derived for any given unitary constellation and mapping rule design criteria regarding the choice of unitary constellation and mapping are then established furthermore using the unitary constellation obtained from orthogonal design with quadrature phase shift keying qpsk or 4 psk and 8 psk two different mapping rules are proposed the first mapping rule gives the most suitable mapping for systems that do not implement iterative processing which is similar to a gray mapping in coherent channels the second mapping rule yields the best mapping for systems with iterative decoding in particular analytical and simulation results show that with the proposed mappings of the unitary constellations obtained from orthogonal designs the asymptotic error performance of the iterative systems can closely approach a lower bound which is applicable to any unitary constellation and mapping

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

ldpc coded mimo systems with unknown block fading channels soft mimo detector design channel estimation and code optimization this paper considers the design of a practical low density parity check ldpc coded multiple input multiple output mimo system composed of m transmit and n receive antennas operating in a flat fading environment where channel state information csi is assumed to be unavailable both to the transmitter and the receiver a soft iterative receiver structure is developed which consists of three main blocks a soft mimo detector and two ldpc component soft decoders we first propose at the component level several soft input soft output mimo detectors whose performances are much better than the conventional minimal mean square error mmse based detectors in particular one optimal soft mimo detector and two simplified suboptimal detectors are developed that do not require an explicit channel estimate and offer an effective tradeoff between complexity and performance in addition a modified expectation maximization em based mimo detector is developed that completely removes positive feedback between input and output extrinsic information and provides much better performance compared with the direct em based detector that has strong correlations especially in fast fading channels at the structural level the ldpc coded mimo receiver is constructed in an unconventional manner where the soft mimo detector and ldpc variable node decoder form one super soft decoding unit and the ldpc check node decoder forms the other component of the iterative decoding scheme by exploiting the proposed receiver structure tractable extrinsic information transfer functions of the component soft decoders are obtained which further lead to a simple and efficient ldpc code degree profile optimization algorithm with proven global optimality and guaranteed convergence from any initialization finally numerical and simulation results are provided to confirm the advantages of the proposed design approach for the coded mimo system

block differential encoding for rapidly fading channels rapidly fading channels provide doppler induced diversity but are also challenging to estimate to bypass channel estimation we derive two novel block differential bd codecs relying on a basis expansion model for time varying channels our differential designs are easy to implement and can achieve the maximum possible doppler diversity the first design bd i relies on a time frequency duality based on which we convert a time varying channel into multiple frequency selective channels and subsequently into multiple flat fading channels using orthogonal frequency division multiplexing combined with a group partitioning scheme bd i offers flexibility to trade off decoding complexity with performance our second block differential design bd ii improves the bandwidth efficiency of bd i at the price of increased complexity at the receiver which relies on decision feedback decoding simulation results corroborate our theoretical analysis and compare with competing alternatives

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

effects of non identical rayleigh fading on differential unitary space time modulation non identical fading distribution in a multiple input multiple output mimo channel including unequal average channel gains and fade rates often occurs when antennas are not co located in this paper we present an analytical study of the effects of non identical rayleigh fading on the error performance of differential unitary space time modulation dustm the fading processes for different transmit receive antenna pairs are assumed to be independent and time variant we find that the maximum likelihood ml differential detector of dustm over such channels is involved except for differential cyclic group codes the conventional detector is proved to be asymptotically optimal in the limit of high signal to noise ratio snr over static fading channels applying the distribution of quadratic forms of gaussian vectors we then derive closed form expressions for the exact error probabilities of two specific unitary classes namely cyclic group codes and orthogonal codes simple and useful asymptotic bounds on error probabilities are also obtained our analysis leads to the following general findings 1 equal power allocation is asymptotically optimal and 2 non identical channel gain distribution degrades the error performance finally we also introduce a water filling based power allocation to exploit the transmit non identical fading statistics

differential space time modulation with eigen beamforming for correlated mimo fading channels in this paper joint differential space time modulation dstm and eigen beamforming for correlated multiple input multiple output mimo fading channels while dstm does not require knowledge of each channel realization the channel s spatial correlation can be easily estimated without training at the receiver and exploited by the transmitter to enhance the error probability performance a transmission scheme is developed here that combines beamforming with differential multiantenna modulation based on orthogonal space time block coding error probability is analyzed for both spatially correlated and independent rayleigh fading channels based on the error probability analysis power loading coefficients are derived to improve performance the analytical and simulation results presented here corroborate that the proposed scheme can achieve considerable performance gain in correlated channels relative to dstm without beamforming

double differential space time block coding for time selective fading channels most existing space time coding schemes assume time invariant fading channels and offer antenna diversity gains relying on accurate channel estimates at the receiver other single differential space time block coding schemes forego channel estimation but are less effective in rapidly fading environments based on a diagonal unitary matrix group a novel double differential space time block coding approach is derived in this paper for time selective fading channels without estimating the channels at the receiver information symbols are recovered with antenna diversity gains regardless of frequency offsets the resulting transceiver has very low complexity and is applicable to an arbitrary number of transmit and receive antennas approximately optimal space time codes are also designed to minimize bit error rate system performance is evaluated both analytically and with simulations

on decision feedback detection of differential space time modulation in continuous fading we show that linear prediction lp based decision feedback detection dfd for nondiagonal differential space time modulation dstm may suffer from a severe performance degradation in continuously fading channels dstm constellations that incur no degradation in lp dfd are identified as those with a diagonal generator to cater to other constellations we propose a low complexity dfd scheme by inserting decision feedback symbols into the metric of multiple symbol differential detection

noncoherent receivers for differential space time modulation in this paper noncoherent receivers for differential space time modulation dstm are investigated it is shown that the performance of the previously proposed conventional differential detection dd receiver is satisfactory only for very slow flat fading channels however conventional dd suffers from a considerable loss in performance even for moderately fast fading especially if more than one transmit antenna is used in order to overcome this problem two improved noncoherent receivers are considered the first one is the multiple symbol detection msd receiver because of the high computational complexity of msd also a low complexity decision feedback differential detection df dd receiver is derived analytical and simulation results confirm that both receivers perform equally well and can take full advantage of the enhanced diversity provided by multiple transmit antennas even for fast fading

unitary space time group codes diversity sums from character tables diversity sum which is calculated from the frobenius norm of the difference of two distinct elements in a signal constellation is the significant parameter to predict a unitary space time constellation having good performance in low signal to noise ratio snr in this correspondence we propose a method to compute the diversity sum of a unitary group constellation using a character table our proposed analysis is simple requiring only a lookup of the character table we illustrate our method for the finite special linear groups sl 2 and compare codes with high diversity sum against fixed point free groups at low snr we also introduce the notion of a faithful group constellation that is one whose diversity sum is greater than 0 faithful group constellations may be obtained from any nontrivial character of a group we describe the method to do so in this correspondence and illustrate it with the example of the finite projective special linear group psl2

differential unitary space time modulation we present a framework for differential modulation with multiple antennas across a continuously fading channel where neither the transmitter nor the receiver knows the fading coefficients the framework can be seen as a natural extension of standard differential phase shift keying commonly used in single antenna unknown channel systems we show how our differential framework links the unknown channel system with a known channel system and we develop performance design criteria as a special ease we introduce a class of diagonal signals where only one antenna is active at any time and demonstrate how these signals may be used to achieve full transmitter diversity and low probability of error

noncoherent sequence detection of differential space time modulation approximate maximum likelihood noncoherent sequence detection nsd for differential space time modulation dstm in time selective fading channels is proposed the starting point is the optimum multiple symbol differential detection for dstm that is characterized by exponential complexity by truncating the memory of the incremental metric a finite state trellis is obtained so that a viterbi algorithm can be implemented to perform sequence detection compared to existing linear predictive receivers a distinguished feature of nsd is that it can accommodate nondiagonal constellations in continuous fading error analysis demonstrates that significant improvement in performance is achievable over linear prediction receivers by incorporating the reduced state sequence detection techniques performance and complexity tradeoffs can be controlled by the branch memory and trellis size numerical results show that most of the performance gain can be achieved by using an l state trellis where l is the size of the dstm constellation

antenna selection for unitary space time modulation this correspondence studies receive antenna selection as for multiple antenna systems that employ unitary space time st signals where the channel state information csi is known neither at the transmitter nor at the receiver without csi at the receiver we perform as only at the receiver and the selection is based on a maximum norm criterion i e a subset of receive antennas that have the largest received signal power is chosen using a chernoff bound approach we present theoretical performance analysis based on the pairwise error probability pep and quantify the asymptotic performance at high signal to noise ratio snr by giving the diversity and coding gain expressions we prove that with no csi at the receiver the diversity gain with as is preserved for unitary st codes with full spatial diversity the same as the case with known csi as a concrete example for differential unitary st modulation with m 2 transmit antennas and n 2 receive antennas we have devised new excellent performing parametric codes based on the derived pep bound the new codes which are specifically designed for differential as systems outperform known differential codes when as is employed corroborating simulations validate our analysis and code design

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

multisampling decision feedback linear prediction receivers for differential space time modulation over rayleigh fast fading channels novel decision feedback df linear prediction lp receivers which process multiple samples per symbol interval in conjunction with optimal sample combining are proposed for differential space time modulation dstm over rayleigh fast fading channels performance analysis demonstrates that multisampling df lp receivers outperform their symbol rate sampling counterpart in fast fading substantially in addition an asymptotically tight upper bound on the pairwise error probability is derived in view of this bound the design criterion of dstm for fast fading is the same as that for block wise static fading to avoid the estimation of the second order statistics of the channel a polynomial model based df lp receiver is proposed it can approach the performance of the optimum df lp receiver at high signal to noise ratios provided fading is moderate

design of fully diverse multiple antenna codes based on sp 2 fully diverse constellations i e sets of unitary matrices whose pairwise differences are nonsingular are useful in multiple antenna communications especially in multiple antenna differential modulation since they have good pairwise error properties recently group theoretic ideas especially fixed point free fpf groups have been used to design fully diverse constellations of unitary matrices here we construct four transmit antenna constellations appropriate for differential modulation based on the symplectic group sp 2 they can be regarded as extensions of alamouti s celebrated two transmit antenna orthogonal design which can be constructed from the group sp 1 we further show that the structure of sp 2 codes lends itself to efficient maximum likelihood ml decoding via the sphere decoding algorithm finally the performance of sp 2 codes is compared with that of other existing codes including alamouti s orthogonal design a 4 spl times 4 complex orthogonal design cayley differential unitary space time codes and group based codes

bit error probability for orthogonal space time block codes with differential detection explicit closed form expressions of the bit error probabilities are obtained for space time block codes based on generalized orthogonal designs with differential encoding and differential detection using 2 sup b ary phase shift keying mapping the frequency nonselective block wise constant rayleigh fading channel is considered here the results are applicable to any number of transmit and receive antennas where the number of transmit antennas is dictated by the available coding schemes

fano multiple symbol differential detectors for differential unitary space time modulation we present a class of suboptimal multiple symbol differential detectors msdds for differential unitary space time st codes in a time selective rayleigh flat fading channel these noncoherent detectors termed fano st msdds employ the well known fano algorithm as their decoding engines their bit error rate ber performance is excellent as there is no irreducible error floor even at very high fade rates compared with the sphere decoder which is optimal our best detector termed an on demand bi fano st msdd suffers only a 0 3 db degradation in power efficiency however its computational complexity as a function of the signal to noise ratio snr is consistently lower than that of the sphere decoder and does not experience the exponential growth in complexity in the latter when the snr decreases it can thus be concluded that the fano algorithm is a powerful detection strategy for differential st codes in fading channels our main contribution is in making the modifications and improvements to the fano algorithm that enables this realization the innovations include the bi fano edge bi fano and on demand bi fano search strategies as well as a new dynamic threshold adjustment scheme for avoiding unnecessary back and forth node evaluations during backtracking