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

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

weighted quadrature rules with weight function x pe 1x on 0 abstract in this paper we introduce an analytical class of weighted quadrature rules whose weight function is as w x p x p e 1 x on 0 the formulas given in this work generally obey the following form 0 x p e 1 x f x d x i 1 n w i f x i r n f in which x i are the zeros of polynomials orthogonal with respect to the introduced weight function w i are the corresponding coefficients and r n f is the related error it should be pointed out that the above formula is valid only for the finite values of n in other words the condition p 2 max n 1 is essential in order to be applicable the above quadrature rule some analytical examples are finally given and compared

turing instability for a ratio dependent predator prey model with diffusion abstract ratio dependent predator prey models have been increasingly favored by field ecologists where predator prey interactions have to be taken into account the process of predation search in this paper we study the conditions of the existence and stability properties of the equilibrium solutions in a reaction diffusion model in which predator mortality is neither a constant nor an unbounded function but it is increasing with the predator abundance we show that analytically at a certain critical value a diffusion driven turing type instability occurs i e the stationary solution stays stable with respect to the kinetic system the system without diffusion we also show that the stationary solution becomes unstable with respect to the system with diffusion and that turing bifurcation takes place a spatially non homogenous non constant solution structure or pattern arises a numerical scheme that preserve the positivity of the numerical solutions and the boundedness of prey solution will be presented numerical examples are also included

stability and hopf bifurcation in a delayed competition system abstract in this paper hopf bifurcation for two species lotka volterra competition systems with delay dependence is investigated by choosing the delay as a bifurcation parameter we prove that the system is stable over a range of the delay and beyond that it is unstable in the limit cycle form i e there are periodic solutions bifurcating out from the positive equilibrium our results show that a stable competition system can be destabilized by the introduction of a maturation delay parameter further an explicit algorithm for determining the direction of the hopf bifurcation and the stability of the bifurcating periodic solutions is derived by using the theory of normal forms and center manifolds and numerical simulations supporting the theoretical analysis are also given

group detection for synchronous gaussian code division multiple access channels the concept of group detection is introduced to address the design of suboptimum multiuser detectors for code division multiple access cdma channels a group detection scheme consists of a bank of p group detectors one each for detecting the information symbols of users in each group of a p group partition of the k simultaneously transmitting users in a parallel group detection scheme these group detectors operate independently whereas in a sequential scheme each group detector uses the decisions of the previous group detectors to successively cancel the interference from those users group detectors based on the generalized likelihood ratio test glrt are obtained for the synchronous gaussian cdma channel the complexity of these detectors is exponential in the group size whereas that of the optimum detector is exponential in k since the partition of users is a design parameter group sizes can be chosen to satisfy a wide range of complexity constraints a key performance result is that the glrt group detectors are optimally group near far resistant furthermore upper and lower bounds on the asymptotic efficiency of the sequential group detectors are derived these bounds reveal that the sequential group detectors can under certain conditions perform as well as glrt group detectors of much larger group sizes group detection provides a unifying approach to multiuser detection when the users are partitioned into k single user groups the glrt a modified form of glrt and the sequential group detectors reduce to previously proposed suboptimal detectors namely the decorrelator the two stage detector and the decorrelating decision feedback detector respectively for the other nontrivial partitions the group detectors are new and have a performance that is commensurate with their complexity

derivatives of a finite class of orthogonal polynomials defined on the positive real line related to f distribution among the six classes of classical orthogonal polynomials three of them are infinite namely jacobi hermite and laguerre and the remaining three are finite and characterized by masjed jamei 2002 5 in this work we consider derivatives of one such finite class of orthogonal polynomials that are orthogonal with respect to the weight function which is related to the probability density function of the f distribution for this derivative class besides orthogonality we find various other related properties such as the normal form and the self adjoint form the corresponding gaussian quadrature formulae are also given examples are provided to support the advantages of considering this derivative class of the finite class of orthogonal polynomials

multiuser detection for overloaded cdma systems multiuser detection for overloaded code division multiple access cdma systems in which the number of users is larger than the dimension of the signal space is of particular interest when bandwidth is at a premium in this paper certain fundamental questions are answered regarding the asymptotic forms and performance of suboptimum multiuser detectors for cases where the desired and or interfering signal subspaces are of reduced rank and or have a nontrivial intersection in the process two new suboptimum detectors are proposed that are especially well suited to overloaded systems namely the group pseudo decorrelator and the group minimum mean squared error mmse detector the former is seen to be the correct extension of the group decorrelator in the sense that it is the limiting form in the low noise regime of the group mmse detector pseudo decorrelation is also used as a feedforward filter in a new decision feedback scheme for the particular case of real valued modulation it is shown that the proposals of the so called improved linear also known as linear conjugate or widely linear detectors were more simply derived earlier using the idea of minimal sufficiency which we also apply to the new detectors of this paper

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

derivatives of a finite class of orthogonal polynomials related to inverse gamma distribution abstract in this work we consider derivatives of a finite class of orthogonal polynomials with respect to weight function which is related to the probability density function of the inverse gamma distribution over the positive real line general properties for this derivative class such as orthogonality rodrigues formula recurrence relation generating function and various other related properties such as self adjoint form and normal form are indicated the corresponding gaussian quadrature formulae are introduced with examples these examples are provided to support the advantages of considering the derivatives class of the finite class of orthogonal polynomials related to inverse gamma distribution the orthogonality property related to the fourier transform of the derivative class under discussion is also given

stacked ostbc error performance and rate analysis it is well known that the alamouti scheme is the only space time code from orthogonal designs achieving the capacity of a multiple input multiple output mimo wireless communication system with nt 2 transmit antennas and nr 1 receive antenna in this paper we propose the n times stacked alamouti scheme for nt 2n transmit antennas and show that this scheme achieves the capacity in the case of nr 1 receive antenna this result may regarded as an extension of the alamouti case for the more general case of more than one receive antenna we show that if the number of transmit antennas is higher than the number of receive antennas we achieve a high portion of the capacity with this scheme further we show that the mimo capacity is at most twice the rate achieved with the proposed scheme for all signal to noise ratio snr we derive lower and upper bounds for the rate achieved with this scheme and compare it with upper and lower bounds for the capacity in addition to the capacity analysis based on the assumption of a coherent channel we analyze the error rate performance of the stacked orthogonal space time block code ostbc with the optimal maximum likelihood ml detector and with the suboptimal lattice reduction lr aided zero forcing detector we compare the error rate performance of the stacked ostbc with spatial multiplexing sm and full diversity achieving schemes finally we illustrate the theoretical results by numerical simulations

a fast recursive algorithm for g stbc this paper proposes a fast recursive algorithm for group wise space time block code g stbc which takes full advantage of the alamouti structure in the equivalent channel matrix to reduce the computational complexity with respect to the existing efficient algorithms for g stbc the proposed algorithm achieves better performance and usually requires less computational complexity

decision feedback multiuser detection a systematic approach a systematic approach to decision feedback multiuser detection is introduced for the joint detection of symbols of k simultaneously transmitting users of a synchronous correlated waveform multiple access cwma channel with gaussian noise a new performance criterion called symmetric energy is defined which is a low noise indicator of the joint error rate that at least one user is detected erroneously even the best linear detectors can perform poorly in terms of symmetric energy compared to the maximum likelihood detector a general class of decision feedback detectors dfds is defined with o k implementational complexity per user the symmetric energy of arbitrary dfd and bounds on their asymptotic effective energy aee performance are obtained along with an exact bit error rate and aee analysis for the decorrelating dfd the optimum dfd that maximizes symmetric energy is obtained each one of the k optimum decorrelating and conventional dfds that correspond to the k orders in which the users can be detected are shown to outperform the linear optimum decorrelating and conventional detectors respectively in terms of symmetric energy moreover algorithms are obtained for determining the choice of order of detection for the three dfds which guarantee that they uniformly user wise outperform their linear counterparts in addition to optimality in symmetric energy it is also shown that under certain conditions the optimum dfd achieves the aee performance of the exponentially complex maximum likelihood detector for all users simultaneously none of the results of this paper make the perfect feedback assumption the implications of our work on power control for multiuser detection are also discussed

secure steganographic communication algorithm based on self organizing patterns a secure steganographic communication algorithm based on patterns evolving in a beddington de angelis type predator prey model with self and cross diffusion is proposed in this paper small perturbations of initial states of the system around the state of equilibrium result in the evolution of self organizing patterns small differences between initial perturbations result in slight differences also in the evolving patterns it is shown that the generation of interpretable target patterns cannot be considered as a secure mean of communication because contours of the secret image can be retrieved from the cover image using statistical techniques if only it represents small perturbations of the initial states of the system an alternative approach when the cover image represents the self organizing pattern that has evolved from initial states perturbed using the dot skeleton representation of the secret image can be considered as a safe visual communication technique protecting both the secret image and communicating parties

performance analysis of zf and mmse equalizers for mimo systems an in depth study of the high snr regime this paper presents an in depth analysis of the zero forcing zf and minimum mean squared error mmse equalizers applied to wireless multiinput multioutput mimo systems with no fewer receive than transmit antennas in spite of much prior work on this subject we reveal several new and surprising analytical results in terms of output signal to noise ratio snr uncoded error and outage probabilities diversity multiplexing d m gain tradeoff and coding gain contrary to the common perception that zf and mmse are asymptotically equivalent at high snr we show that the output snr of the mmse equalizer conditioned on the channel realization is mmse zf ssrsnr where zf is the output snr of the zf equalizer and that the gap ssrsnr is statistically independent of zf and is a nondecreasing function of input snr furthermore as ssr snr ura ssrsnr converges with probability one to a scaled f random variable it is also shown that at the output of the mmse equalizer the interference to noise ratio inr is tightly upper bounded by ssrsnr zf using the decomposition of the output snr of mmse we can approximate its uncoded error as well as outage probabilities through a numerical integral which accurately reflects the respective snr gains of the mmse equalizer relative to its zf counterpart the e outage capacities of the two equalizers however coincide in the asymptotically high snr regime we also provide the solution to a long standing open problem applying optimal detection ordering does not improve the d m tradeoff of the vertical bell labs layered space time v blast architecture it is shown that optimal ordering yields a snr gain of 10log10n db in the zf v blast architecture where n is the number of transmit antennas whereas for the mmse v blast architecture the snr gain due to ordered detection is even better and significantly so

an analysis of the mimo sdma channel with space time orthogonal and quasi orthogonal user transmissions and efficient successive cancellation decoders we consider space time transceiver architectures for space division multiple access sdma fading channels with simultaneous transmissions from multiple users each user has up to four transmit antennas and employs a space time orthogonal or a quasi orthogonal design as an inner code at the multiple antenna receiver efficient successive group interference cancellation strategies based on zero forcing or minimum mean square error mmse filtering are employed in some fixed or channel dependent order these strategies are efficient in the sense that they exploit the special structure of the inner codes to yield much higher diversity orders than would be otherwise possible while at the same time preserving what we call the decoupling property of the constituent inner codes which enables the use of low complexity outer encoders decoders for each user motivated by the special structure of the effective channel matrix induced by the inner codes we obtain several new distribution results on the qr and eigenvalue decompositions of certain structured random matrices these results are the key to a comprehensive performance analysis of the proposed multiuser transceiver architectures including the characterization of diversity multiplexing tradeoff dmt curves and exact per user bit error rates bers without making simplifying assumptions about error propagation

turing instability and pattern induced by cross diffusion in a predator prey system with allee effect to have spatial patterns form small allee effect admits relatively large range of predator mortality rate found cross diffusion is the key mechanism of spatial pattern formation obtained amplitude equations suggest both supercritical and subcritical bifurcation may occur weak allee effect admits supercritical bifurcation while strong one allows subcritical bifurcation in this paper we first propose a mathematical model for a spatial predator prey system with allee effect and then by using the proposed model we investigate the turing instability and the phenomena of pattern formation we show how cross diffusion destabilizes the spatially uniform steady state the method of multiple time scales is employed to derive the amplitude equations which is the cubic stuart landau equation in the supercritical case and the quintic in the subcritical case based on the amplitude equations we obtain the asymptotic solutions of the model close to the onset of instability

stability of steady state solutions to a prey predator system with cross diffusion abstract this paper is concerned with a cross diffusion system arising in a prey predator population model the main purpose is to discuss the stability analysis for coexistence steady state solutions obtained by kuto and yamada j differential equations to appear we will give some criteria on the stability of these coexistence steady states furthermore we show that the hopf bifurcation phenomenon occurs on the steady state solution branch under some conditions

existence of spatial patterns in a predator prey model with self and cross diffusion in this work we investigate the spatiotemporal dynamics of reaction diffusion equations subject to cross diffusion in the frame of a two dimensional ratio dependent predator prey model the conditions for diffusion driven instability are obtained and the turing space in the parameters space is achieved moreover the criteria for local and global asymptotic stability of the unique positive homogeneous steady state without diffusion are discussed numerical simulations are carried out in order to validate the feasibility of the obtained analytical findings different types of spatial patterns through diffusion driven instability of the proposed model are portrayed and analysed lastly the paper finishes with an external discussion of biological relevance of the analysis regarding cross diffusion and pattern issues

3 2 type criteria for global attractivity of lotka volterra competition system without instantaneous negative feedbacks this paper deals with a two species lotka volterra competition model with discrete delays but without instantaneous negative feedbacks motivated by wright s 3 2 global attractivity result for the delayed scalar logistic equation we establish some new 3 type criteria for global attractivity of the positive equilibrium of the system these criteria provide convenient and better than some existing estimates for the diagonal delays

cross diffusion induced turing instability for a competition model with saturation effect abstract competitive behavior like predation widely exists in the world which has influences on the dynamics of ecosystems though a good knowledge for the patten formation and selection of predator prey models with diffusion is known in the literature little is known for that of a diffused competition model as a result a competition model with saturation effect and self and cross diffusion is proposed and analyzed in this paper firstly by making use of nullcline analysis we derive the condition of existence and stability of positive equilibrium and prove global stability then using the linear stability analysis the turing bifurcation critical value and the condition of the occurrence of turing pattern are obtained when control parameter is selected finally we deduce the amplitude equations around the turing bifurcation point by using the standard multiple scale analysis meanwhile a series of numerical simulations are given to expand our theoretical analysis this work shows that cross diffusion plays a key role in the formation of spatial patterns for competitive model with saturation effect

analysis of decision feedback detection for mimo rayleigh fading channels and the optimization of power and rate allocations for an uncoded k transmit n receive antenna coherent narrow band communication system employing a decorrelating decision feedback detector d dfd the exact average over channel realizations joint error probability jep as well as the average per symbol error probabilities seps are derived without making any simplifying assumptions on error propagation it is proved that the diversity orders of the jep and the sep of every symbol is limited by error propagation to n k 1 based on our exact error probability analysis however we suggest an optimization of jep over nonnegative quadrature amplitude modulation qam constellation sizes rates and average powers across transmitters which yield significant improvements over the usual equal power and equal rate assignment in fact the jep of such an optimized design has the much improved diversity order of n which is also the diversity order obtained through the optimum maximum likelihood ml detector moreover it is seen that these simple optimized designs can achieve a significant fraction of the spl epsi outage capacity even without outer codes it is also known but only through simulations that when the symbols are detected in certain channel realization dependent orders it is possible to improve substantially over fixed order detection in the case of the equal rate and equal power assignment we provide an analysis for a recently proposed channel dependent ordering rule and show that it does not provide an improvement of the diversity order of the jep beyond n k 1 another ordering rule that was proposed earlier to maximize the worst case post detection signal to noise ratio snr under the perfect feedback assumption is shown to be optimal under a more compelling criterion that does not involve that simplifying assumption while efficiently computable this ordering rule is seen to perform almost as well as the optimal channel dependent ordering rule that minimizes the conditional jep and hence the jep nevertheless a multiple input multiple output mimo system with an optimized rate and power allocation and a fixed order of detection is not only less complex but also has a significantly lower jep than that of the equal power equal rate system where transmitters are detected in a channel dependent order optimal or otherwise

delay induced turing instability in reaction diffusion equations time delays have been commonly used in modeling biological systems and can significantly change the dynamics of these systems quite a few works have been focused on analyzing the effect of small delays on the pattern formation of biological systems in this paper we investigate the effect of any delay on the formation of turing patterns of reaction diffusion equations first for a delay system in a general form we propose a technique calculating the critical value of the time delay above which a turing instability occurs then we apply the technique to a predator prey model and study the pattern formation of the model due to the delay for the model in question we find that when the time delay is small it has a uniform steady state or irregular patterns which are not of turing type however in the presence of a large delay we find spiral patterns of turing type for such a model we also find that the critical delay is a decreasing function of the ratio of carrying capacity to half saturation of the prey density