optimization of generalized mean square error in signal processing and communication abstract two matrix optimization problems are analyzed these problems arise in signal processing and communication in the first problem the trace of the mean square error matrix is minimized subject to a power constraint the solution is the training sequence which yields the best estimate of a communication channel the solution is expressed in terms of the eigenvalues and eigenvectors of correlation and covariance matrices describing the communication and an unknown permutation our analysis exhibits the optimal permutation when the power is either very large or very small based on the structure of the optimal permutation in these limiting cases we propose a small class of permutations to focus on when computing the optimal permutation for arbitrary power in numerical experiments with randomly generated matrices the optimal solution is contained in the proposed permutation class with high probability the second problem is connected with the optimization of the sum capacity of a communication channel the second problem which is obtained from the first by replacing the trace operator in the objective function by the determinant minimizes the product of eigenvalues while the first problem minimizes the sum of eigenvalues for small values of the power both problems have the same solution as the power increases the solutions are different since the permutation matrix appearing in the solution of the trace problem is not present in the solution of the determinant problem for large power the ordering of the eigenvectors in the solution of the trace problem is the opposite of the ordering in the determinant problem

generalized christoffel darboux formula for classical skew orthogonal polynomials we show that skew orthogonal functions defined with respect to jacobi weight wa b x 1 x a 1 x b a b 1 including the limiting cases of laguerre wa x xa e x a 1 and gaussian weight satisfy three term recursion relation in the quaternion space from this we derive generalized christoffel darboux gcd formulae for kernel functions arising in the study of the corresponding orthogonal and symplectic ensembles of random 2n 2n matrices using the gcd formulae we calculate the level densities and prove that in the bulk of the spectrum under appropriate scaling the eigenvalue correlations are universal we also provide evidence to show that there exists a mapping between skew orthogonal functions arising in the study of orthogonal and symplectic ensembles of random matrices

asymptotic bep and sep of quadratic diversity combining receivers in correlated ricean fading non gaussian noise and interference in this paper we study the asymptotic behavior of the bit error probability bep and the symbol error probability sep of quadratic diversity combining schemes such as coherent maximum ratio combining mrc differential equal gain combining egc and noncoherent combining nc in correlated ricean fading and non gaussian noise which in our definition also includes interference we provide simple and easy to evaluate asymptotic bep and sep expressions which show that at high signal to noise ratios snrs the performance of the considered combining schemes depends on certain moments of the noise and interference impairing the transmission we derive general rules for calculation of these moments and we provide closed form expressions for the moments of several practically important types of noise such as spatially dependent and spatially independent gaussian mixture noise correlated synchronous and asynchronous co channel interference and correlated gaussian interference from our asymptotic results we conclude that a the asymptotic performance loss of binary frequency shift keying bfsk with nc compared to binary phase shift keying bpsk with mrc is always 6 db independent of the type of noise and the number of diversity branches b the asymptotic performance loss of differential egc compared to mrc is always 3 db for additive white gaussian noise but depends on the number of diversity branches and may be larger or smaller than 3 db for other types of noise and c not only fading correlation but also noise correlation negatively affects the performance of quadratic diversity combiners

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

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

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

on the covering radius of codes the covering radius r of a code is the maximal distance of any vector from the code this work gives a number of new results concerning t n k the minimal covering radius of any binary code of length n and dimension k for example t n 4 and t n 5 are determined exactly and reasonably tight bounds on t n k are obtained for any k when n is large these results are found by using several new constructions for codes with small covering radius one construction the amalgamated direct sum involves a quantity called the norm of a code codes with norm leq 2 r 1 are called normal and may be combined efficiently the paper concludes with a table giving bounds on t n k for n leq 64

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

a novel signaling scheme for blind unique identification of alamouti space time block coded channel in this paper we present a simple signaling scheme to blindly and uniquely identify the alamouti space time block coded channel first under a noise free environment and then under a complex gaussian noise environment in which pth and qth order statistics p and q are coprime of the received signals are available in both cases closed form solutions to determine the channel coefficients are obtained by exploiting specific properties of the alamouti space time block code stbc and the linear diophantine equation theory under gaussian noise when the length of the received data is finite we propose to use the semidefinite relaxation sdr algorithm to approximate maximum likelihood ml detection so that the joint estimation of the channel and symbols can be efficiently implemented simulation results show that while other existing blind methods fail our signaling scheme works well

space time block codes a maximum snr approach in tarokh et al 1999 space time block codes were introduced to obtain coded diversity for a multiple antenna communication system in this work we cast space time codes in an optimal signal to noise ratio snr framework and show that they achieve the maximum snr and in fact they correspond to a generalized maximal ratio combiner the maximum snr framework also helps in calculating the distribution of the snr and in deriving explicit expressions for bit error rates we bring out the connection between the theory of amicable orthogonal designs and space time codes based on this we give a much simpler proof to one of the main theorems on space time codes for complex symbols we present a rate 1 2 code for complex symbols which has a smaller delay than the code already known we also present another rate 3 4 code which is simpler than the one already known in the sense it does not involve additions or multiplications we also point out the connection between generalized real designs and generalized orthogonal designs

super orthogonal space time trellis codes we introduce a new class of space time codes called super orthogonal space time trellis codes these codes combine set partitioning and a super set of orthogonal space time block codes in a systematic way to provide full diversity and improved coding gain over earlier space time trellis code constructions we also study the optimality of our set partitioning and provide coding gain analysis codes operating at different rates up to the highest theoretically possible rate for different number of states can be designed by using our optimal set partitioning super orthogonal space time trellis codes can provide a tradeoff between rate and coding gain simulation results show more than 2 db improvements over the codes presented in the literature while providing a systematic design methodology

orthogonal space time block codes maximum likelihood detection for unknown channels and unstructured interferences space time coding stc schemes for communication systems employing multiple transmit and receive antennas have been attracting increased attention the so called orthogonal space time block codes ostbcs have been of particular interest due to their good performance and low decoding complexity in this paper we take a systematic maximum likelihood ml approach to the decoding of ostbc for unknown propagation channels and unknown noise and interference conditions we derive a low complexity ml decoding algorithm based on cyclic minimization and assisted by a minimum amount of training data furthermore we discuss the design of optimal training sequences and optimal information transfer to an outer decoder numerical examples demonstrate the performance of our algorithm

space time spreading and block coding for correlated fading channels in the presence of interference we consider point to point wireless links with multiple antennas in the presence of interference and exploit channel s spatial correlation and the temporal covariance of the interference to design multiantenna transmitters we develop a space time spreading scheme that maximizes average signal to interference and noise ratio and an optimally power loaded space time beamforming stbf scheme which improves error probability performance in order to increase transmission rates we combine orthogonal space time block coding with stbf optimize power loading across beams and develop low complexity receivers optimal training for least squares error channel estimation and stbf for minimum mean square error channel estimation are also studied our analytical and simulated results corroborate that stbf with optimal power loading can considerably reduce error probability and channel estimation errors

optimizing multiple input single output miso communication systems with general gaussian channels nontrivial covariance and nonzero mean we consider a narrow band point to point communication system with many input transmitters and a single output receiver i e a multiple input single output miso system we assume the receiver has perfect knowledge of the channel but the transmitter only knows the channel distribution we focus on two canonical classes of gaussian channel models a the channel has zero mean with a fixed covariance matrix and b the channel has nonzero mean with covariance matrix proportional to the identity in both cases we are able to derive simple analytic expressions for the ergodic average and the cumulative distribution function c d f of the mutual information for arbitrary input transmission signal covariance with minimal numerical effort we then determine the ergodic and outage capacities and the corresponding capacity achieving input signal covariances interestingly we find that the optimal signal covariances for the ergodic and outage cases have very different behavior in particular under certain conditions the outage capacity optimal covariance is a discontinuous function of the parameters describing the channel such as strength of the correlations or the nonzero mean of the channel

on training optimization for estimation of correlated mimo channels in the presence of multiuser interference in this paper the problem of estimating multiple input multiple output mimo channels in a realistic environment involving correlated channel fading and multiuser interference is considered four estimation schemes are studied including the linear minimum mean squared error lmmse least squares ls and gauss markov gm estimators as well as a novel scheme which is derived here as an alternative to lmmse estimation the mse optimal training sequences for each of them are provided and their requirements for side information feedback are assessed the new scheme is shown to exhibit a performance comparable to or even better than lmmse at a significantly lower feedback and computational cost the analytical comparison of the estimation schemes is supported by numerous simulation results that cover a wide range of antenna configurations relative interference power and channel correlation strengths the results of this paper provide a complete picture for a palette of estimation schemes with their relative performance and costs of training

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

correlation functions cluster functions and spacing distributions for random matrices the usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants from this representation one can deduce formulas for spacing probabilities in terms of fredholm determinants of matrix valued kernels the derivations of the various formulas are somewhat involved in this article we present a direct approach which leads immediately to scalar kernels for the unitary ensembles and matrix kernels for the orthogonal and symplectic ensembles and the representations of the correlation functions cluster functions and spacing distributions in terms of them

on k t subnormal covering codes the concept of a k t subnormal covering code is defined it is discussed how an amalgamated direct sumlike construction can be used to combine such codes the existence of optimal q n m 1 codes c is discussed such that by puncturing the first coordinate of c one obtains a code with q 1 subnorm 2

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

quasi cyclic codes over z sub 4 and some new binary codes previously linear codes over z sub 4 and quasi cyclic qc codes over fields have been shown to yield useful results in coding theory combining these two ideas we study z sub 4 qc codes and obtain new binary codes using the usual gray map among the new codes the lift of the famous golay code to z sub 4 produces a new binary code a 92 2 sup 24 28 code which is the best among all binary codes linear or nonlinear moreover we characterize cyclic codes corresponding to free modules in terms of their generator polynomials

linear codes with covering radius 2 and other new covering codes infinite families of linear binary codes with covering radius r 2 and minimum distance d 3 and d 4 are given using the constructed codes with d 3 r 2 families of covering codes with r 2 are obtained the parameters of many constructed codes with r

on the snr penalty of mpsk with hybrid selection maximal ratio combining over i i d rayleigh fading channels closed form expressions that lower and upper bound the penalty of hybrid selection maximal ratio combining relative to maximal ratio combining mrc for m ary phase shift keying mpsk modulation are proved the bounds offer simple to evaluate explicit expressions and are typically within 0 6 db for hybrid systems with diversity order up to eight that use at least two branches yet are independent of signal to noise ratio snr contrary to conclusions conjectured in a previously published paper it is proved that the snr penalty is not a constant independent of snr it is also shown that previous estimates of the performance losses of selection diversity relative to mrc underestimate or lower bound the losses for mpsk modulation systems and that the true loss can be significantly larger than previously believed an upper bound to this loss is also obtained

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

skew orthogonal polynomials and random matrix ensembles there is considerable interest in understanding the relation between random matrix ensembles and quantum chaotic systems in the context of the universality of energy level correlations in this connection while gaussian ensembles of random matrices have been studied extensively not much is known about ensembles with non gaussian weight functions dyson has shown that the n level correlation functions can be expressed in terms of a kernel function involving orthogonal and skew orthogonal polynomials orthogonal for matrix ensembles with unitary invariance and skew orthogonal for ensembles with orthogonal and symplectic invariances we have obtained the following results 1 skew orthogonal polynomials of both types are derived for the jacobi class of weight functions including the limiting cases of associated laguerre and hermite or gaussian 2 matrix integral representations are given for the general weight functions 3 asymptotic forms of the polynomials are obtained rigorously for the jacobi class and in the form of an ansatz for the general case 4 for the three types of ensembles the asymptotic n level correlation functions with appropriate scaling are shown to be universal being independent of the weight function and location in the spectrum and identical with the well known gaussian results this provides a rigorous justification for the universality of the gaussian ensemble results observed in quantum chaotic systems as expected the level density is not universal

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

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

optimal transmitter eigen beamforming and space time block coding based on channel mean feedback optimal transmitter designs obeying the water filling principle are well documented they are widely applied when the propagation channel is deterministically known and regularly updated at the transmitter because channel state information is impossible to be known perfectly at the transmitter in practical wireless systems we design in this paper an optimal multiantenna transmitter based on the knowledge of mean values of the underlying channels our optimal transmitter design turns out to be an eigen beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the correlation matrix of the estimated channel at the transmitter and with proper power loading across beams the optimality pertains to minimizing an upper bound on the symbol error rate which leads to better performance than maximizing the expected signal to noise ratio snr at the receiver coupled with orthogonal space time block codes two directional eigen beamforming emerges as a more attractive choice than conventional one directional beamforming with uniformly improved performance without rate reduction and without essential increase in complexity with multiple receive antennas and reasonably good feedback quality the two directional eigen beamformer is also capable of achieving the best possible performance in a large range of transmit power to noise ratios without a rate penalty

asymptotic performance of hybrid selection maximal ratio combining over fading channels in this letter we study the asymptotic performance of hybrid selection maximal ratio combining hs mrc and postdetection hs equal gain combining hs egc over generalized fading channels for large average signal to noise ratios asnrs by evaluating the asymptotic moment generating function of the hs mrc output snr at high asnr we derive the diversity and coding gains for hs mrc for a large class of modulation formats and versatile fading conditions including different types of fading channels and nonidentical snr statistics across diversity branches our analytical results reveal that the diversity gains of hs mrc and hs egc are equivalent to that of mrc and the difference in the coding gains for different modulation formats is manifested in terms of a modulation factor defined in this letter some new analytical results about effects of the number of combined branches for hs mrc and noncoherent combining loss of hs egc are also provided

six new binary quasi cyclic codes six new quasi cyclic codes are presented which improve the lower bounds on the minimum distance for a binary code a local exhaustive search is used to find these codes and many other quasi cyclic codes which attain the lower bounds

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

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

chernoff bounds on pairwise error probabilities of space time codes we derive chernoff bounds on pairwise error probabilities of coherent and noncoherent space time signaling schemes first general chernoff bound expressions are derived for a correlated ricean fading channel and correlated additive gaussian noise then we specialize the obtained results to the cases of space time separable noise white noise and uncorrelated fading we derive approximate chernoff bounds for high and low signal to noise ratios snrs and propose optimal signaling schemes we also compute the optimal number of transmitter antennas for noncoherent signaling with unitary mutually orthogonal space time codes

new ternary quasi cyclic codes with better minimum distances one of the most important problems of coding theory is to construct codes with best possible minimum distances in this article using the structure of quasi cyclic qc codes with a bch type bound given by lally and fitzpatrick see wcc 99 workshop on coding and cryptography paris france 1999 we have found 20 new ternary quasi cyclic codes with improved minimum distances

performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha stable process impulsive noise bursts in communication systems are traditionally handled by incorporating in the receiver a limiter which clips the received signal before integration an empirical justification for this procedure is that it generally causes the signal to noise ratio to increase recently very accurate models of impulsive noise were presented based on the theory of symmetric spl alpha stable probability density functions we examine the performance of optimum receivers designed to detect signals embedded in impulsive noise which is modeled as an infinite variance symmetric spl alpha stable process and compare it against the performance of several suboptimum receivers as a measure of receiver performance we compute an asymptotic expression for the probability of error for each receiver and compare it to the probability of error calculated by extensive monte carlo simulation

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

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

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

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

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

new good quasi cyclic ternary and quaternary linear codes let n k d q codes be linear codes of length n dimension k and minimum hamming distance d over gf q the following quasi cyclic codes are constructed in this paper 44 11 20 3 55 11 26 3 66 11 32 3 48 12 21 3 60 12 28 3 56 13 24 3 65 13 29 3 56 14 23 3 60 15 23 3 64 16 25 3 36 9 19 4 90 9 55 4 99 9 61 4 30 10 14 4 50 10 27 4 55 10 30 4 33 11 15 4 44 11 22 4 55 11 29 4 36 12 16 4 48 12 23 4 60 12 31 4 all of these codes have established or exceed the respective lower bounds on the minimum distance given by brouwer

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

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

skew orthogonal polynomials differential systems and random matrix theory we study skew orthogonal polynomials with respect to the weight function exp 2v x with v x 2dk 1 uk k xk u2d 0 d 0 a finite subsequence of such skew orthogonal polynomials arising in the study of orthogonal and symplectic ensembles of random matrices satisfies a system of differential difference deformation equation the vectors formed by such subsequence have the rank equal to the degree of the potential in the quaternion sense these solutions satisfy certain compatibility condition and hence admit a simultaneous fundamental system of solutions

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

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

asymptotical performance of m ary and binary signals over multipath multichannel rayleigh and rician fading this paper presents a general framework for computing the asymptotic error probability i e at high average snrs of m ary and binary signaling schemes over rician and rayleigh fading diversity channels a general theorem theorem 1 relates the asymptotic error rate of multipath and multichannel receivers over awgn isi free channels to the multidimensional integral of the conditional error probability two other theorems are presented for the particular cases where the conditional error probability is a function of the sum of received snrs theorem 2 or received amplitudes theorem 3 theorems 2 and 3 are related for linear coherent systems and closed form expressions are obtained for equal gain combining systems detection structures for typical diversity schemes coherent noncoherent maximal ratio and equal gain combining and quadratic noncoherent combining are considered we analyze the asymptotic error rates of some m ary signaling schemes mpsk mpam with kth order diversity and orthogonal signals with k 1 and with coherent and noncoherent detection binary signaling is also considered in our study

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

blind stbc identification for multiple antenna ofdm systems this paper addresses the problem of space time block code stbc identification for multiple antenna ma orthogonal frequency division multiplexing ofdm systems operating over frequency selective channels for the first time in literature previous investigations published on the topic of stbc identification were restricted to single carrier systems operating over frequency flat channels ofdm systems make this topic more challenging to handle since the identifiers work in frequency selective channels with little or no knowledge of the beginning of the ofdm blocks ofdm parameters and frequency selective channel coefficients we show that by taking advantage of the space time redundancy stbc identification can be performed by exploiting the cross correlation of the signals received from different antennas as a discriminating feature using this feature we develop a binary hypothesis test for decision making the proposed method does not require information about the channel coefficients modulation format noise power or timing of the ofdm and stbc blocks moreover it does not need accurate knowledge of either clock timing information or ofdm parameters including the number of sub carriers and cyclic prefix length extensive simulation experiments have verified the effectiveness of the proposed method

design of multilayer coded modulation for nonergodic block fading channels multilayer coded modulation mlyc in single antenna and multiple antenna wireless fading channels is investigated while the mlyc has been known to achieve ergodic fading channel capacity the problem of interest here is to design practical and efficient mlyc for nonergodic block fading channels we develop a design methodology which maximizes the information rate of mlyc subject to an upper bound on the decoding error probability moreover we show that the mlyc performs closer to channel capacity when the overall diversity order of the channel is higher and proper spatial interleaving is employed the relationship between the mlyc scheme and other transmission techniques such as multilevel coded modulation and bit interleaved coded modulation bicm is also discussed it is shown through simulation examples that in realistic block fading channels the mlyc with practical coded modulation outperforms the bicm without turbo receiver iteration we propose the mlyc as a promising alternative to bicm especially when turbo iterative processing is not desired e g for progressive layered media transmission

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

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

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

on the relation between orthogonal symplectic and unitary matrix ensembles for the unitary ensembles of n n hermitian matrices associated with a weight function w there is a kernel expressible in terms of the polynomials orthogonal with respect to the weight function which plays an important role for the orthogonal and symplectic ensembles of hermitian matrices there are 2 2 matrix kernels usually constructed using skew orthogonal polynomials which play an analogous role these matrix kernels are determined by their upper left hand entries we derive formulas expressing these entries in terms of the scalar kernel for the corresponding unitary ensembles we also show that whenever w w is a rational function the entries are equal to the scalar kernel plus some extra terms whose number equals the order of w w general formulas are obtained for these extra terms we do not use skew orthogonal polynomials in the derivations

performance of bicm sc and bicm ofdm systems with diversity reception in non gaussian noise and interference in this paper we present a general mathematical framework for performance analysis of single carrier sc and orthogonal frequency division multiplexing ofdm systems employing popular bit interleaved coded modulation bicm and multiple receive antennas the proposed analysis is applicable to bicm systems impaired by general types of fading including rayleigh ricean nakagami m nakagami q and weibull fading and general types of noise and interference with finite moments such as additive white gaussian noise awgn additive correlated gaussian noise gaussian mixture noise co channel interference narrowband interference and ultra wideband interference we present an approximate upper bound for the bit error rate ber and an accurate closed form approximation for the asymptotic ber at high signal to noise ratios for viterbi decoding with the standard euclidean distance branch metric for the standard rate 1 2 convolutional code the proposed approximate upper bound and the asymptotic approximation become tight at bers of 10 6 and 10 12 respectively however if the code is punctured to higher rates e g 2 3 or 3 4 the asymptotic approximation also becomes tight at a ber of 10 6 exploiting the asymptotic ber approximation we show that the diversity gain of bicm systems only depends on the free distance of the code the type of fading and the number of receive antennas but not on the type of noise in contrast their coding gain strongly depends on the noise moments our asymptotic analysis shows that as long as the standard euclidean distance branch metric is used for viterbi decoding bicm systems optimized for awgn are also optimum for any other type of noise and interference with finite moments

asymptotic performance of generalized selection combining in generic noise and fading in this letter we investigate the performance of generalized selection combining in channels impaired by generalized fading and generic noise with finite moments in particular we derive accurate high signal to noise ratio approximations for the bit and symbol error rates of linear modulation schemes which offer significant insight into the impact of the number of selected diversity branches the type of fading and the type of noise our analysis is applicable to all practically relevant types of fading including rayleigh rician nakagami q and nakagami m fading all types of noise with finite moments including gaussian noise gaussian mixture noise generalized gaussian noise and co channel interference and non identically distributed fading and noise across the diversity branches our results reveal that while performance always improves with increasing number of selected branches for identically distributed noise this is not necessarily true for non identically distributed noise

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

generalized christoffel darboux formula for skew orthogonal polynomials and random matrix theory we obtain a generalized christoffel darboux gcd formula for skew orthogonal polynomials using this we present an alternative derivation of the level density and two point function for gaussian orthogonal ensembles and gaussian symplectic ensembles of random matrices

distance spectrum analysis of space time trellis coded modulations in quasi static rayleigh fading channels in this correspondence we propose an algorithm for computing the distance spectrum of a space time trellis code achieving maximal diversity gain in quasi static fading channels we further present a state reduction technique for trellis codes that can reduce the complexity of the distance spectrum computation we provide numerical results supporting the empirical evidence that a truncated union bound obtained from the distance spectrum provides an accurate characterization of the relative performance ordering of different space time trellis codes and therefore it offers a tool for better space time trellis code design

new ternary linear codes let n k d q codes be linear codes of length n dimension k and minimum hamming distance d over gf q in this correspondence 18 codes are constructed which improve the known lower bounds on minimum distance

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

on circularity circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors however this concept can be extended in various ways for nonnormal vectors the first purpose of the paper is to introduce and compare some possible definitions of circularity from these definitions it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components therefore the relationships between circularity and stationarity are analyzed in detail finally the theory of linear mean square estimation for complex signals exhibits some connections with circularity and it is shown that without this assumption the estimation theory must be reformulated

unified asymptotic analysis of linearly modulated signals in fading non gaussian noise and interference in this paper we present a unified asymptotic symbol error rate ser analysis of linearly modulated signals impaired by fading and possibly non gaussian noise which in our definition also includes interference the derived asymptotic closed form results are valid for a large class of fading and noise processes our analysis also encompasses diversity reception with equal gain and selection combining and is extended to binary orthogonal modulation we show that for high signal to noise ratios snrs the ser of linearly modulated signals depends on the mellin transform of the probability density function pdf of the noise since the mellin transform can be readily obtained for all commonly encountered noise pdfs the provided ser expressions are easy and fast to evaluate furthermore we show that the diversity gain only depends on the fading statistic and the number of diversity branches whereas the combining gain depends on the modulation format the type of fading the number of diversity branches and the type of noise an exception are systems with a diversity gain of one since their combining gain and asymptotic ser are independent of the type of noise however in general in a log log scale for high snr the ser curves for different types of noise are parallel but not identical and their relative shift depends on the mellin transforms of the noise pdfs

a riemann hilbert problem for skew orthogonal polynomials we find a local d 1 x d 1 riemann hilbert problem characterizing the skew orthogonal polynomials associated to the partition function of orthogonal ensembles of random matrices with a potential function of degree d our riemann hilbert problem is similar to a local dxd riemann hilbert problem found by kuijlaars and mclaughlin characterizing the bi orthogonal polynomials this gives more motivation for finding methods to compute asymptotics of high order riemann hilbert problems and brings us closer to finding full asymptotic expansions of the skew orthogonal polynomials

optimal transmitter eigen beamforming and space time block coding based on channel correlations optimal transmitter designs obeying the water filling principle are well documented and widely applied when the propagation channel is deterministically known and regularly updated at the transmitter because channel state information csi may be costly or impossible to acquire in rapidly varying wireless environments we develop in this paper statistical water filling approaches for stationary random fading channels these approaches require only knowledge of the channel correlations that do not necessitate frequent updates and can be easily acquired applied to a multiple transmit antenna paradigm our optimal transmitter design turns out to be an eigen beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the channel s correlation matrix and with proper power loading across the beams the optimality pertains to minimizing a tight bound on the symbol error rate the resulting loaded eigen beamforming outperforms not only the equal power allocation across all antennas but also the conventional beamformer that transmits the available power along the strongest direction coupled with orthogonal space time block codes two dimensional 2 d eigen beamforming emerges as a more attractive choice than conventional one dimensional 1 d beamforming with uniformly better performance without rate reduction and without complexity increase

some best rate 1 p and rate p 1 p systematic quasi cyclic codes over gf 3 and gf 4 the class of quasi cyclic qc codes has been proven to contain many good codes to date the known qc codes are primarily rate 1 p and p 1 p binary codes constructed from circulant matrices these results are extended to qc codes over gf 3 and gf 4 codes are constructed using integer linear programming and heuristic combinatorial optimization many of these attain the maximum possible minimum distance for any linear code with the same parameters and several improve the maximum known distances the link between power residue pr codes and qc codes is exploited as a means of constructing new qc codes and to initialize the search algorithm previously unknown minimum distances for nonbinary quadratic residue codes are given the minimum distances for the pr codes and the maximum known distances for the qc codes are tabulated

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

a new construction for covering codes a novel method for constructing normal binary nonlinear covering codes is presented the construction improves several upper bounds on k n r the minimum cardinality of a binary code of length n and covering radius r

bulk asymptotics of skew orthogonal polynomials for quartic double well potential and universality in the matrix model we derive bulk asymptotics of skew orthogonal polynomials m 1 4 defined with respect to the weight exp 2nv x v x gx4 4 tx2 2 g 0 and t 0 such that m n cr where cr is the critical value that separates skew orthogonal polynomials with two cuts from those with one cut simultaneously we derive asymptotics for the recursive coefficients of skew orthogonal polynomials the proof is based on obtaining a finite term recursion relation between skew orthogonal polynomials and orthogonal polynomials and using asymptotic results of orthogonal polynomials derived by bleher and its semiclassical asymptotics of orthogonal polynomials riemann hilbert problems and universality in the matrix model ann math 150 185 1999 finally we apply these asymptotic results of skew orthogonal polynomials and their recursion coefficients in the generalized christoffel darboux formula ghosh s generalized christoffel darboux formula for skew orthogona

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

an explicit construction of 2 generator quasi twisted codes quasi twisted qt codes are a generalization of quasi cyclic qc codes based on consta cyclic simplex codes a new explicit construction of a family of 2 generator quasi twisted qt two weight codes is presented it is also shown that many codes in the family meet the griesmer bound and therefore are length optimal new distance optimal binary qc 195 8 96 210 8 104 and 240 8 120 codes and good ternary qc 208 6 135 and 221 6 144 codes are also obtained by the construction

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

combining beamforming and orthogonal space time block coding multiple transmit and receive antennas can be used in wireless systems to achieve high data rate communication efficient space time codes have been developed that utilize a large portion of the available capacity these codes are designed under the assumption that the transmitter has no knowledge about the channel in this work on the other hand we consider the case when the transmitter has partial but not perfect knowledge about the channel and how to improve a predetermined code so that this fact is taken into account a performance criterion is derived for a frequency nonselective fading channel and then utilized to optimize a linear transformation of the predetermined code the resulting optimization problem turns out to be convex and can thus be efficiently solved using standard methods in addition a particularly efficient solution method is developed for the special case of independently fading channel coefficients the proposed transmission scheme combines the benefits of conventional beamforming with those given by orthogonal space time block coding simulation results for a narrow band system with multiple transmit antennas and one or more receive antennas demonstrate significant gains over conventional methods in a scenario with nonperfect channel knowledge

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

asymptotics of skew orthogonal polynomials exact integral expressions of the skew orthogonal polynomials involved in orthogonal 1 and symplectic 4 random matrix ensembles are obtained the even rank skew orthogonal polynomials are average characteristic polynomials of random matrices from there asymptotics of the skew orthogonal polynomials are derived

new quasi twisted quaternary linear codes let n k d sub q codes be linear codes of length n dimension k and minimum hamming distance d over gf q in this article 31 new quaternary q 4 codes are constructed which improve the respective lower bounds on minimum distance in brouwer s tables

constructions for perfect mixed codes and other covering codes a construction for an infinite family of perfect mixed codes with covering radius 2 is presented these are the first known nontrivial perfect mixed codes with covering radius greater than 1 based on mixed codes constructions for binary covering codes that lead to a considerable improvement of upper bounds on the sizes of covering codes are presented these codes and some other codes can be obtained by the blockwise direct sum construction two infinite families of codes are of special interest they are quasi perfect nonlinear union of their disjoint translates covers the space and their density as covering codes is remarkably low

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

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

training signal design for estimation of correlated mimo channels with colored interference in this paper we study the problem of estimating correlated multiple input multiple output mimo channels in the presence of colored interference the linear minimum mean square error mmse channel estimator is derived and the optimal training sequences are designed based on the mse of channel estimation we propose an algorithm to estimate the long term channel statistics needed for the construction of the optimal training sequences we also design an efficient scheme to feed back the required information to the transmitter where we can approximately construct the optimal sequences numerical results show that the optimal training sequences provide substantial performance gain for channel estimation when compared with other training sequences