a note on the markov property of stochastic processes described by nonlinear fokker planck equations abstract we study the markov property of processes described by generalized fokker planck equations that are nonlinear with respect to probability densities such as mean field fokker planck equations and fokker planck equations related to generalized thermostatistics we show that their transient solutions describe non markov processes in contrast stationary solutions can describe markov processes as a result nonlinear fokker planck equations can be used to model transient non markov processes that converge to stationary markov processes

on the achievable rate of generalized spatial modulation using multiplexing under a gaussian mixture model spatial modulation sm is a new modulation technique where the information to be sent is encoded using one or more symbols and the subspace over which the symbols are transmitted unfortunately a general capacity analysis that encompasses different forms of sm systems has not been developed in this paper we consider a general form of sm where the number of transmitted data streams is allowed to vary we refer to this form of sm as generalized spatial modulation with multiplexing gsmm a gaussian mixture model gmm is shown to accurately model the transmitted spatially modulated signal using a precoding framework using this transmit model a closed form expression for the achievable rate when operating over rayleigh fading channels is evaluated and tight upper and lower bounds for the achievable rate are proposed the expressions of the achievable rate obtained are flexible enough to accommodate any form of sm where any subspace can be used for the transmission by adjusting the precoding set simulations are presented to show the tightness of the proposed bounds the effect of the system dimensions and a comparison with other prominent capacity results are also demonstrated in simulations

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

a procedure for obtaining general nonlinear fokker planck equations abstract a procedure for deriving general nonlinear fokker planck equations fpes directly from the master equation is presented the nonlinear effects are introduced in the transition probabilities which present a dependence on the probabilities for finding the system in a given state it is shown that the fpes obtained from master equations describing transitions among discrete and continuous sets of states are identical within such a procedure we construct nonlinear fpes that appear to be very general our general fpes recover as particular cases nonlinear fpes investigated previously by many authors introduced on a purely phenomenological basis and they lead to the possibility of more complete and complex diffusive equations

opportunistic group antenna selection in spatial modulation systems this paper proposes an opportunistic spatial modulation osm scheme where the transmit antennas are divided into k geq 1 equal groups and the best antenna from each group is selected to form a k transmit antenna subset for implementing spatial modulation sm thus the activation of one antenna from the subset to transmit one of the m ary modulation symbols achieves a data rate of log 2 k log 2 m bits per channel use notably special cases of osm include conventional sm and pure single transmit antenna selection to characterize and comparatively evaluate osm we first consider phase shift keying modulation and derive a closed form improved union bound of symbol error probability sep with a single antenna receiver explicit expressions for the sep in the high signal to noise ratio regime are also presented extensions to quadrature amplitude modulation analysis and simulations of multiple antenna reception case are also provided simulation results corroborate the analytical results and reveal the interesting interplay between the signal and spatial constellation diagrams for a given number of transmit antennas and targeted data rate asymptotically the sep can be minimized by using only one antenna group and the largest size of signal constellation as this configuration achieves the full diversity order

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

accuracy of the taylor galerkin model for contaminant transport in groundwater the taylor galerkin finite element model tgfem is second order accurate in time however it provides oscillatory results for advection dominated transport the objective of this paper is to develop criteria for the tgfem to provide oscillation free accurate results the accuracy of the tgfem was evaluated by comparing its prediction with the corresponding analytical solution the model was found to provide oscillation free accurate results for peclet number pe as high as 20 and courant number cr 0 10

error performance of generalised space shift keying for indoor visible light communications in this paper the error performance analysis of a low complexity multiple transmitter generalised space shift keying gssk signalling technique for short range indoor visible light communications is presented in an n t transmitter system this signalling technique is capable of achieving a spectral efficiency of n t bits s hz the gssk system has a higher spectral efficiency than the conventional on off keying ook and pulse position modulation ppm techniques the gssk transmitter is much simpler than that of an equivalent regular pulse amplitude modulation pam system with similar spectral efficiency an analytical expression for the symbol error rate ser is presented and verified using simulations the receiver is based on the maximum likelihood criterion and using multiple photodetectors pds in the receiver improves the error performance within the room and the transmitter receiver configuration under consideration with four pds a gain of 6 db is attainable over the single pd system for the case of 2 and 3 bits s hz considering a fixed link range with n t 2 and at a symbol error rate of 10 6 using wide half angle leds with 1 2 60 requires about 12 db less in electrical signal to noise ratio compared with 1 2 30 the beam directivity is however of much lower effect when the room under consideration is equiped with sufficient leds to provide full coverage the gssk technique can also support dimming control by using different pulse widths this however is at a price of reduced spectral efficiency

on the complexity of sphere decoding in digital communications sphere decoding has been suggested by a number of authors as an efficient algorithm to solve various detection problems in digital communications in some cases the algorithm is referred to as an algorithm of polynomial complexity without clearly specifying what assumptions are made about the problem structure another claim is that although worst case complexity is exponential the expected complexity of the algorithm is polynomial herein we study the expected complexity where the problem size is defined to be the number of symbols jointly detected and our main result is that the expected complexity is exponential for fixed signal to noise ratio snr contrary to previous claims the sphere radius which is a parameter of the algorithm must be chosen to ensure a nonvanishing probability of solving the detection problem this causes the exponential complexity since the squared radius must grow linearly with problem size the rate of linear increase is however dependent on the noise variance and thus the rate of the exponential function is strongly dependent on the snr therefore sphere decoding can be efficient for some snr and problems of moderate size even though the number of operations required by the algorithm strictly speaking always grows as an exponential function of the problem size

on channel estimation and detection for multicarrier signals in fast and selective rayleigh fading channels time domain channel estimation and detection techniques are presented for multicarrier signals in a fast and frequency selective rayleigh fading channel as a consequence of the time varying channel the orthogonality between subcarriers is destroyed in conventional frequency domain approaches resulting in interchannel interference which increases an irreducible error floor in proportion to the normalized doppler frequency an important feature of the proposed technique is the ability to exploit the time selective channel as a provider of time diversity this enables us to achieve performance superior to any other structure without increasing bandwidth or incorporating redundancy in order to reduce the complexity of the estimator we apply the theory of optimal low rank approximation to a minimum mean squared error channel estimator and present a theoretical calculation of mean squared error and simulations to confirm that the estimator is robust to changes in channel characteristics

reciprocity relations and generalized classic entropic quantifiers that lack trace form abstract in this effort we show that the legendre reciprocity relations thermodynamics essential formal feature are respected by general classic entropic functionals even if they are not of trace form nature in contrast with shannon s or tsallis cases further with reference to the maximum entropy maxent variational process we encounter important cases relevant to physical applications currently discussed in the research literature in which the associated reciprocity relations exhibit anomalies we show that these anomalies can be cured by carefully discriminating between apparently equivalent entropic forms

finite element analysis of contaminant transport in groundwater in this paper we focus on the development of a finite element model for predicting the contaminant concentration governed by the advective dispersive equation in this study we take into account the first order degradation of the contaminant to realistically model the transport phenomenon in groundwater to solve the resulting unsteady advection diffusion equation with production a finite element model is constructed which employs a quadratic basis function to approximate the contaminant concentration the development of a weighted residuals finite element model involves constructing a biased test function to retain the scheme stability for wide ranges of values of the physical coefficients in the process of constructing the petrov galerkin finite element model for stability reasons it is desirable to obtain an acceptable degree of accuracy the method used to retain stability without loss of accuracy is to approximate the differential equation within the semi discretization framework after discretizing the time derivative term using the euler time stepping scheme the resulting ordinary differential equation which involves only the spatial derivative terms is solved using the nodally exact finite element model for better control of the user s specified time step and mesh size full analysis of the discretization scheme is conducted in this study both modified equation analysis and fourier stability analysis are employed to better understand the proposed semi discretized petrov galerkin finite element model validation of the newly proposed model is accomplished through analysis of the results obtained for several test problems some of them are amenable to analytic solutions the rate of convergence of the employed finite element model then can be obtained

capacity analysis of index modulations over spatial polarization and frequency dimensions determining the capacity of a modulation scheme is a fundamental topic of interest index modulations im such as spatial modulation smod polarized modulation pmod or frequency index modulation fmod are widely studied in the literature however finding a closed form analytical expression for their capacity still remains an open topic in this paper we formulate closed form expressions for the instantaneous capacity of im together with its second and fourth order approximations we show that in average the second approximation error tends to zero for low signal to noise ratio snr and is o left textrm snr right also a detailed analysis of the ergodic capacity over rayleigh rice and nakagami m channel distributions is provided as application of the capacity analysis we leverage the proposed expressions to compute the ergodic capacities of smod for different antenna configuration and correlations pmod for different channel components and conditions and fmod for different frequency separations

joint channel estimation equalization and data detection for ofdm systems in the presence of very high mobility this paper is concerned with the challenging and timely problem of joint channel estimation equalization and data detection for uplink orthogonal frequency division multiplexing ofdm systems in the presence of frequency selective and very rapidly time varying channels the resulting algorithm is based on the space alternating generalized expectation maximization sage technique which is particularly well suited to multicarrier signal formats leading to a receiver structure that also incorporates interchannel interference ici cancelation in order to reduce the computational complexity of the algorithm band limited discrete cosine orthogonal basis functions are employed to represent the rapidly time varying fading channel by the discrete cosine serial expansion coefficients it is shown that depending on the normalized doppler frequency only a small number of expansion coefficients is sufficient to approximate the channel perfectly and there is no need to know the correlation function of the input signal in this way the resulting reduced dimensional channel coefficients are estimated and the data symbols detected iteratively with tractable complexity the proposed sage joint detection algorithm updates the data sequences serially and the channel parameters are updated in parallel leading to a receiver structure that also incorporates ici cancelation computer simulations show that the cosine transformation represents the time varying channel very effectively and the proposed algorithm has excellent symbol error rate and channel estimation performance even with a very small number of channel expansion coefficients employed in the algorithm resulting in substantial reduction of the computational complexity

reduced complexity ml detection and capacity optimized training for spatial modulation systems spatial modulation sm is a recently developed low complexity multiple input multiple output scheme that jointly uses antenna indices and a conventional signal set to convey information it has been shown that the maximum likelihood ml detector of an sm system involves joint detection of the transmit antenna index and of the transmitted symbol hence the ml search complexity grows linearly with the number of transmit antennas and the size of the signal set to circumvent the problem we show that the ml search complexity of an sm system may be rendered independent of the constellation size provided that the signal set employed is a square or a rectangular qam furthermore we derive bounds for the capacity of the sm system and derive the optimal power allocation between the data and the training sequences by maximizing the worst case capacity bound of the sm system operating with imperfect channel state information we show with the aid of our simulation results that the proposed detector is ml optimal despite its lowest complexity amongst the existing detectors furthermore we show that employing the proposed optimal power allocation provides a substantial gain in terms of the sm system s capacity as well as signal to noise ratio compared to its equal power allocation counterpart finally we compare the performance of the sm system to that of the conventional multiple input multiple output mimo system and show that the sm system is capable of outperforming the conventional mimo system by a significant margin when both the systems are employing optimal power splitting

multivariate ornstein uhlenbeck processes with mean field dependent coefficients application to postural sway we study the transient and stationary behavior of many particle systems in terms of multivariate ornstein uhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields mean field approximations of this kind of system are derived in terms of fokker planck equations in such systems multiple stationary solutions as well as bifurcations of stationary solutions may occur in addition strictly monotonically decreasing steady state autocorrelation functions that decay faster than exponential functions are found which are used to describe the erratic motion of the center of pressure during quiet standing

thermodynamics from first principles correlations and nonextensivity the standard formulation of thermostatistics being based on the boltzmann gibbs distribution and logarithmic shannon entropy describes idealized uncorrelated systems with extensive energies and short range interactions in this rapid communication we use the fundamental principles of ergodicity via liouville s theorem the self similarity of correlations and the existence of the thermodynamic limit to derive generalized forms of the equilibrium distribution for long range interacting systems significantly our formalism provides a justification for the well studied nonextensive thermostatistics characterized by the tsallis distribution which it includes as a special case we also give the complementary maximum entropy derivation of the same distributions by constrained maximization of the gibbs shannon entropy the consistency between the ergodic and maximum entropy approaches clarifies the use of the latter in the study of correlations and nonextensive thermodynamics

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

low complexity ml detectors for generalized spatial modulation systems spatial modulation sm combined with spatial multiplexing is a newly developed transmission scheme in multiple input multiple output mimo systems the resultant system referred to as generalized sm gsm can use the maximum likelihood ml detector jointly detecting the antenna subset as index and symbol vector as known the ml detector can achieve optimum performance however its computational complexity can be prohibitively high when the dimension of the gsm system is large in this paper we propose new methods to solve the problem the main idea is to split the detection into two stages one for the as index and the other for the symbol vector for the detection of the as index we develop two methods referred to as gaussian approximation and qr projection once the as index is detected conventional low complexity ml detectors can be applied for the detection of the symbol vector the diversity order for the proposed methods are further analyzed and an enhanced method is also proposed to achieve near optimum performance finally the proposed methods are extended to conduct soft detection of gsm systems simulations show that our methods significantly outperform existing ones while the detection complexity remains similar

nonlinear fokker planck equations and generalized entropies abstract we consider maximum entropy solutions to nonlinear fokker planck equations within general thermostatistical formalisms we show that the family of generalized nonextensive entropies introduced by tsallis is the only one that has an associated family of nonlinear fokker planck equations endowed with time dependent maxent solutions of a generalized gaussian type consequently the natural association that arises between tsallis thermostatistical formalism and special families of nonlinear fokker planck equations is not a universal feature of general thermostatistical formalisms but a particular feature of the tsallis one

stochastic feedback nonlinear families of markov processes and nonlinear fokker planck equations abstract we discuss two fundamental aspects of fokker planck equations that are nonlinear with respect to probability densities first we show that evolution equations of this kind describe processes involving stochastic feedback and interpret stochastic feedback processes in terms of hitchhiker processes and path integral solutions second we demonstrate that nonlinear fokker planck equations can be interpreted as linear fokker planck equations describing nonlinear families of markov diffusion processes we exploit this finding in order to derive complete hierarchies of probability densities from nonlinear fokker planck equations

on a general link between anomalous diffusion and nonextensivity stochastic processes of systems with composable entropy measures are studied the processes are described by fokker planck equations which are nonlinear with respect to their probability densities and whose diffusion coefficients are derived from the entropy measures in questions in nonextensive extensive systems anomalous normal diffusion is found

liouville equation and the q statistical formalism abstract we revisit some aspects of the foundations of the q non extensive thermostatistical formalism which are particularly relevant to its astronomical applications we analyse some important features of escort mean values and escort distributions in connection with the dynamical evolution of ensemble probability distributions associated with the statistical description of general classical dynamical systems furthermore we compare the roles played by escort mean values and escort distributions when studying classical n body systems at the levels of i the liouville equation and ii the vlasov equation

on the performance of spatial modulation optimal constellation breakdown spatial modulation sm is a new transmission technique for multi antenna systems in which the transmit antennas are used to modulate the signal in this paper the symbol error rate ser performance of sm is investigated in sm a signal domain modulation i e amplitude phase modulation and an antenna domain modulation i e space shift keying are combined together to achieve a certain transmission rate while exploiting the properties of two independent modulation domains a key question is the fine balance between the constellation sizes in the two domains when a constant rate is targeted for a fixed rate there are many ways to assign constellation vectors to the spatial and signal domains in this paper we investigate optimal constellation breakdown between space and signal domains the analysis is based on the union bound of the error probability of sm with two typical apm schemes i e phase shift keying psk and square quadrature amplitude modulation s qam it is shown that at any transmission rate there exists an optimal apm dimension in which the ser is minimized furthermore a trade off between the number of transmit antennas and the transmit power is introduced

mutual information analysis on spatial modulation multiple antenna system spatial modulation sm is a recently proposed multiple input multiple output mimo architecture that exploits the space domain for information transmission in this paper sm systems with continuous amplitude phase modulation apm and the corresponding maximum likelihood ml active transmit antenna detector are considered we introduced a method to compute the theoretical transition probability matrix and the mutual information of the ml antenna detector for sm multiple input single output miso system we derive the error probability and the mutual information of the antenna detector in closed form for multiple receive antenna sm system the union bound of error probability and the lower bound of antenna detection mutual information are proposed the analytical results are verified by numerical simulation over rayleigh fading channels we investigate systems with different number of antennas and apm symbol input distributions to evaluate the performance of sm the joint apm and antenna detection mutual information of sm systems is compared to the capacity of vertical bell labs layered space time v blast spatial multiplexing mimo scheme our research gives achievable transmission rates of sm miso mimo systems and can be a guideline for suitable application scenarios

nonlinear fokker planck equations whose stationary solutions make entropy like functionals stationary abstract the present study extends the correspondence principle of martinez et al that establishes a link between nonlinear fokker planck equations nlfpes and the variational principle approach of the theory of canonical ensembles by virtue of the extended correspondence principle we reobtain results of kaniadakis and quarati for bose and fermi systems and find relations similar to those derived by plastino and plastino and recently by borland concerning the entropy of nonextensive thermostatistics introduced in physics by tsallis moreover we propose nlfpes related to the renyi entropy and to the entropy proposed by sharma and mittal the latter comprises tsallis entropy and the renyi entropy

bit error probability for coherent m ary psk systems a simple technique for evaluating the bit error probability of coherent m ary phase shift keying psk with any bit mapping is proposed closed form expressions are given in terms of error functions for half and quadrant plane probabilities in the decision space avoiding the numerical evaluation of complicated integrals that occurs in the direct method bit error probability expressions for m ary psk with gray natural binary and folded binary bit mappings are derived

a unified approach for calculating error rates of linearly modulated signals over generalized fading channels we present a unified analytical framework to determine the exact average symbol error rate ser of linearly modulated signals over generalized fading channels the results are applicable to systems employing coherent demodulation with maximal ratio combining multichannel reception the analyses assume independent fading paths which are not necessarily identically distributed in all cases the proposed approach leads to an expression of the average ser involving a single finite range integral which can be easily computed numerically in addition as special cases ser expressions for single channel reception are obtained these expressions reduce to well known solutions give alternative often simpler expressions for previous results or provide new formulas that are either closed form expressions or simple to compute numerically

spatially modulated orthogonal space time block codes with non vanishing determinants this paper proposes a multiple input multiple output mimo transmission scheme for m ary modulations called spatially modulated orthogonal space time block coding sm ostbc based on the concept of spatial constellation sc codewords introduced by le at el in the proposed scheme transmit codeword matrices are generated by multiplying sc matrices with codewords constructed from orthogonal space time block codes o stbc the maximum spectral efficiency of the proposed scheme is equal to n t 2 log 2 m bpcu where n t is the number of transmit antennas and m is the modulation order the sc matrices provide a means of carrying information bits together with the o stbc codewords and allow the sm ostbc scheme to achieve second order transmit diversity by satisfying the non vanishing determinant property a systematic method to design the sc codewords for an even number of transmit antennas greater than 3 is presented a single stream maximum likelihood ml decoder which requires a low computational complexity thanks to the structure of the sm ostbc codewords and to the orthogonality of the o stbcs and a sphere decoder with further reduced signal processing complexity are developed the bit error rate ber performance of the proposed scheme is studied by using both theoretical union bound analysis and computer simulations finally simulation results are presented in order to compare ber performance energy efficiency and decoding complexity of the proposed scheme with those of several existing mimo transmission schemes

the k best sphere decoding for soft detection of generalized spatial modulation due to the interchannel interference and the varying active antennas in generalized spatial modulation gsm it is challenging to detect the transmitted data effectively while imposing low computational burden to the receiver in this paper we propose a novel algorithm based on the k best sphere decoding for the soft detection of the gsm signal which performs the breadth first tree search in two stages sequentially by exploiting the null space of the gsm channel the inactive antenna searching is carried out antennawise in the first stage in which a recursive algorithm for updating the ql decomposition a decomposition of a matrix into a product of an orthogonal matrix and a lower triangular matrix is proposed to calculate the branch metrics and an effective examination scheme is developed to prune those illegal or repetitive child nodes based on the available ql decomposition structure that has been updated recursively during the first stage the second stage of the proposed detector is then readily concatenated to search for the modulated symbols carried on the active antennas in a one by one manner moreover owing to the soft input soft output nature the proposed detector can be applied in a turbo decoder for a coded gsm system both complexity analysis and simulation results corroborate the superiority of the proposed soft detector for the gsm system

the error probability of the fixed complexity sphere decoder the fixed complexity sphere decoder fsd has been previously proposed for multiple input multiple output mimo detection in order to overcome the two main drawbacks of the sphere decoder sd namely its variable complexity and its sequential structure although the fsd has shown remarkable quasi maximum likelihood ml performance and has resulted in a highly optimized real time implementation no analytical study of its performance existed for an arbitrary mimo system herein the error probability of the fsd is analyzed proving that it achieves the same diversity as the maximum likelihood detector mld independent of the constellation used in addition it can also asymptotically yield ml performance in the high signal to noise ratio snr regime those two results together with its fixed complexity make the fsd a very promising algorithm for uncoded mimo detection

families of fokker planck equations and the associated entropic form for a distinct steady state probability distribution with a known external force field a method of finding entropic form for a given stationary probability distribution and specified potential field is discussed using the steady state fokker planck equation as examples starting with the boltzmann and tsallis distribution and knowing the force field we obtain the boltzmann gibbs and tsallis entropies also the associated entropy for the gamma probability distribution is found which seems to be in the form of the gamma function moreover the related fokker planck equations are given for the boltzmann tsallis and gamma probability distributions

equivalence among different formalisms in the tsallis entropy framework abstract in a recent paper t wada a m scarfone phys lett a 335 2005 351 the authors discussed the equivalence among the various probability distribution functions of a system in equilibrium in the tsallis entropy framework in the present letter we extend these results to a system which is out of equilibrium and evolves to a stationary state according to a nonlinear fokker planck equation nfpe by means of time scale conversion it is shown that there exists a correspondence among the self similar solutions of the nfpes associated with the different tsallis formalisms the time scale conversion is related to the corresponding lyapunov functions of the respective nfpes

transmit antenna selection for multiple input multiple output spatial modulation systems the benefits of transmit antenna selection tas invoked for spatial modulation sm aided multiple input multiple output mimo systems are investigated specifically we commence with a brief review of the existing tas algorithms and focus on the recently proposed euclidean distance based tas ed tas schemes due to their high diversity gain then a pair of novel ed tas algorithms termed as the improved qr decomposition qrd based tas qrd tas and the error vector magnitude based tas evm tas are proposed which exhibit an attractive system performance at low complexity moreover the proposed ed tas algorithms are amalgamated with the low complexity yet efficient power allocation pa technique termed as tas pa for the sake of further improving the system s performance our simulation results show that the proposed tas pa algorithms achieve signal to noise ratio snr gains of up to 9 db over the conventional tas algorithms and up to 6 db over the tas pa algorithm designed for spatial multiplexing systems

threshold accepting a general purpose optimization algorithm appearing superior to simulated annealing abstract a new general purpose algorithm for the solution of combinatorial optimization problems is presented the new threshold accepting method is even simpler structured than the wellknown simulated annealing approach the power of the new algorithm is demonstrated by computational results concerning the traveling salesman problem and the problem of the construction of error correcting codes moreover deterministic versions of the new heuristic turn out to perform nearly equally well consuming only a fraction of the computing time of the stochastic versions as an example the deterministic threshold accepting method yields very near to optimum tours for the famous 442 cities traveling salesman problem of grotschel within 1 to 2 s of cpu time

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

a unified precoding scheme for generalized spatial modulation generalized spatial modulation gsm activates n t out of n t 1 leq n t available transmit antennas and information is conveyed through n t modulated symbols as well as the index of the n t activated antennas gsm strikes an attractive tradeoff between spectrum efficiency and energy efficiency linear precoding that exploits channel state information at the transmitter enhances the system error performance for gsm with n t 1 the traditional sm the existing precoding methods suffer from high computational complexity on the other hand gsm precoding for n t geq 2 is not thoroughly investigated in the open literature in this paper we develop a unified precoding design for gsm systems which universally works for all n t values based on the maximum minimum euclidean distance criterion we find that the precoding design can be formulated as a large scale nonconvex quadratically constrained quadratic program problem then we transform this challenging problem into a sequence of unconstrained subproblems by leveraging augmented lagrangian and dual ascent techniques these subproblems can be solved in an iterative manner efficiently numerical results show that the proposed method can substantially improve the system error performance relative to the gsm without precoding and features extremely fast convergence rate with a very low computational complexity

simplifying performance expressions for noncoherent and differentially coherent modulations over generalized fading multiple channels we further simplify the numerically friendly bit error rate expression presented by simon and alouini see ibid vol 46 p 1625 38 1998 for noncoherent and differentially coherent systems with multichannel reception over additive white gaussian noise and generalized fading channels

a langevin approach for the microscopic dynamics of nonlinear fokker planck equations abstract for stochastic processes defined by nonlinear fokker planck equations a microscopic dynamics is proposed in terms of generalized langevin equations these langevin equations can for example be used to model stochastic processes with mean field interactions and random walks related to the generalized thermostatistics suggested by tsallis

coherent and differential space time shift keying a dispersion matrix approach motivated by the recent concept of spatial modulation sm we propose a novel space time shift keying stsk modulation scheme for multiple input multiple output mimo communication systems where the concept of sm is extended to include both the space and time dimensions in order to provide a general shift keying framework more specifically in the proposed stsk scheme one out of q dispersion matrices is activated during each transmitted block which enables us to strike a flexible diversity and multiplexing tradeoff this is achieved by optimizing both the space time block duration as well as the number of the dispersion matrices in addition to the number of transmit and receive antennas we will demonstrate that the resultant equivalent system model does not impose any inter channel interference ici and hence the employment of single stream maximum likelihood ml detection becomes realistic at a low complexity furthermore we propose a differential stsk dstsk scheme assisted by the cayley unitary transform which does not require any channel state information csi at the receiver here the usual error doubling caused by the differential decoding gives rise to 3 db performance penalty in comparison to coherent stsk cstsk additionally we introduce an enhanced cstsk scheme which avoids the requirement of inter antenna synchronization ias between the rf chains associated with the transmit antenna elements aes by imposing a certain constraint on the dispersion matrix design where each column of the dispersion matrices includes only a single non zero component moreover according to the turbo coding principle the proposed cstsk and dstsk schemes are combined with multiple serially concatenated codes and an iterative bit to symbol soft demapper more specifically the associated stsk parameters are optimized with the aid of extrinsic information transfer exit charts for the sake of achieving a near capacity performance

pre scaling optimization for space shift keying based on semidefinite relaxation the performance of space shift keying ssk is known to be dominated by the minimum euclidean distance med in the received ssk constellation in this paper we propose a method of enhancing the med in the received ssk constellation and improving both the attainable performance and the power efficiency by means of symbol scaling at the transmitter to this aim we formulate a pair of optimization problems one for maximizing the med subject to a specific transmit power constraint and one for minimizing the transmit power subject to a med threshold as these problems are np hard we re formulate their optimization using semidefinite relaxations which results in convex problem formulations that can be efficiently solved using standard approaches moreover we design pre scaling techniques for imperfect channel state information at the transmitter where the existing approaches are inapplicable our results show that the proposed schemes substantially improve the power efficiency of ssk systems with respect to state of the art techniques by offering an improved performance for specific transmit power requirements or equivalently a transmit power reduction for a given med threshold

a mini tutorial on measure valued markov processes and nonlinear martingale problems as a reply to mccauley s comment abstract one goal of this mini tutorial is to provide an introduction into the theory of measure valued markov processes and nonlinear martingales defined by strongly nonlinear fokker planck equations and to discuss the physical relevance of the associated processes another goal is to reply to mccauley s comment on t d frank physica a 331 391 2004 the tutorial addresses in detail two approaches found in physics and mathematics the first approach exploits a mapping between linear and nonlinear fokker planck equations the second approach exploits martingale theory several examples of markov processes and martingales in quantum mechanical nonextensive and self organizing systems defined by nonlinear fokker planck equations are discussed

general exact solution to the problem of the probability density for sums of random variables the exact explicit expression for the probability density p n x for a sum of n random arbitrary correlated summands is obtained the expression is valid for any number n and any distribution of the random summands most attention is paid to application of the developed approach to the case of independent and identically distributed summands the obtained results reproduce all known exact solutions valid for the so called stable distributions of the summands it is also shown that if the distribution is not stable the profile of p n x may be divided into three parts namely a core small x a tail large x and a crossover from the core to the tail moderate x the quantitative description of all three parts as well as that for the entire profile is obtained a number of particular examples are considered in detail

ito versus stratonovich a survey is given of the facts and fancies concerning the nonlinear langevin or ito equation actually it is merely a pre equation which becomes an equation when an interpretation rule is added the rules of ito and stratonovich differ but both are mathematically consistent and therefore equally admissible conventions the reason why they seem to lead to physical differences is that the langevin approach used to arrive at the equation involves a tacit assumption for systems with external noise this assumption can be justified and it is then clear that the stratonovich rule applies systems with internal noise however can only be properly described by a master equation and the ito stratonovich controversy never enters afterward one is free to model the resulting fluctuations either with an ito or a stratonovich scheme but that does not lead to any new information

reduced complexity coherent versus non coherent qam aided space time shift keying a novel reduced complexity near optimal detection algorithm is proposed for enhancing the recent coherently detected space time shift keying cstsk scheme employing arbitrary constellations such as cal l point phase shift keying psk and quadrature amplitude modulation qam the proposed detector relies on a modified matched filter mf concept more specifically we exploit both the constellation diagram of the modulation scheme employed as well as the inter element interference iei free stsk architecture furthermore we generalize the pulse amplitude modulation pam or psk aided differentially encoded stsk dstsk concept and conceive its more bandwidth efficient qam aided counterpart then the proposed reduced complexity cstsk detector is applied to the qam aided dstsk scheme which enables us to carry out low complexity non coherent detection while dispensing with channel estimation it is revealed that the proposed detector is capable of approaching the optimal maximum likelihood ml detector s performance while avoiding the exhaustive ml search interestingly our simulation results also demonstrate that the reduced complexity detector advocated may achieve the same performance as that of the optimal ml detector for the specific stsk scheme s parameters another novelty of this paper is that the star qam stsk scheme tends to outperform its square qam counterpart especially for high number of dispersion matrices furthermore we provided both the theoretical analysis and the simulations in order to support this unexpected fact

dual polarized spatial modulation over correlated fading channels we address multiple input multiple output mimo communication employing spatial modulation sm with dual polarized dp antennas the proposed architecture adds the polarization dimension to the conventional sm mappings and offers performances which are comparable to or under certain conditions even better than those of the uni polarized systems while occupying half as much space we consider the generalized spatially correlated rayleigh and rician fading channel models and present an average bit error probability upper bounding framework for the proposed dp sm mimo system the theoretical error analysis is also extended to the case where the channel coefficients are estimated with gaussian estimation errors this upper bounding method is also used to determine the conditions in which the dual polarized sm is better than equivalent systems with uni polarized antennas theoretical derivations are also validated by extensive simulations both corroborating that sm combined with dual polarization forms an attractive alternative not only for its improved multiplexing gains and space efficiency but also for performance gains over correlated channels

non extensive statistical mechanics and generalized fokker planck equation a non linear generalized fokker planck gfp equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by tsallis in his generalization of statistical mechanics in the case of a constant or linearly varying drift the time dependent solutions of the gfp equation are seen to obey a suitable form of the celebrated h theorem the temporal changes of tsallis entropies are seen to be given in terms of the fisher s information measure particular time dependent solutions of the gfp equation of the maximum tsallis entropy form are obtained

entropy production and nonlinear fokker planck equations the entropy time rate of systems described by nonlinear fokker planck equations which are directly related to generalized entropic forms is analyzed both entropy production associated with irreversible processes and entropy flux from the system to its surroundings are studied some examples of known generalized entropic forms are considered and particularly the flux and production of the boltzmann gibbs entropy obtained from the linear fokker planck equation are recovered as particular cases since nonlinear fokker planck equations are appropriate for the dynamical behavior of several physical phenomena in nature like many within the realm of complex systems the present analysis should be applicable to irreversible processes in a large class of nonlinear systems such as those described by tsallis and kaniadakis entropies

on the cumulative distribution function of quadratic form receivers over generalized fading channels with tone interference in this paper we develop a general and unified framework for estimating the cumulative distribution function cdf of quadratic form receivers the expression of the cdf that we finally achieve takes on the form of a single integral with finite limits and integrand composed of elementary functions which can be readily integrated using standard techniques in particular the specific contribution of this manuscript is twofold i we present a comprehensive framework for the analysis of multi channel reception systems using either non coherent or differentially coherent detectors diversity systems with practical i e noisy channel estimators and transmitted reference tr receiver architectures working in frequency selective fading channels and ii we show that the framework can be efficiently used for performance assessment of wireless systems over generalized fading channels and under mild assumptions over generalized fading channels further impaired by in band multi tone interference

improved methods for calculating vectors of short length in a lattice including a complexity analysis the standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of z in a suitable box however it suffices to consider those x e z which lie in a suitable ellipsoid having a much smaller volume than the box we show in this paper that searching through that ellipsoid is in many cases much more efficient if combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions several randomly constructed numerical examples illustrate the superiority of our new method over the known ones

a unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels we present a unified approach to determine the exact bit error rate ber of noncoherent and differentially coherent modulations with single and multichannel reception over additive white gaussian noise and generalized fading channels the multichannel reception results assume independent fading in the channels and are applicable to systems that employ post detection equal gain combining our approach relies on an alternate form of the marcum q function and leads to expressions of the ber involving a single finite range integral which can be readily evaluated numerically aside from unifying the past results the new approach also allows for a more general solution to the problem in that it includes many situations that in the past defied a simple solution the best example of this occurs for multichannel reception where the fading on each channel need not be identically distributed nor even distributed according to the same family of distributions

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

on the linear discrepancy model and risky shifts in group behavior a nonlinear fokker planck perspective using a nonlinear fokker planck perspective we re formulate the linear discrepancy model proposed by boster and colleagues that describes the emergence of risky shifts during group decision making analytical expressions for the stationary case are derived and risky shifts are obtained by monte carlo simulations striking similarities with the kuramoto model for group synchronization are pointed out

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

a family of evolution equations with nonlinear diffusion verhulst growth and global regulation exact time dependent solutions abstract a family of evolution equations describing a power law nonlinear diffusion process coupled with a local verhulst like growth dynamics and incorporating a global regulation mechanism is considered these equations admit an interpretation in terms of population dynamics and are related to the so called conserved fisher equation exact time dependent solutions exhibiting a maximum nonextensive q entropy shape are obtained

h theorem for a mean field model describing coupled oscillator systems under external forces this article studies the asymptotic behavior of solutions of fokker planck equations describing mean field approximations of weakly coupled oscillator systems subjected to external forces using an h theorem we show that transient probability densities converge to stationary ones furthermore stability criteria are derived for the stationary solutions of these fokker planck equations the obtained results are applied to a model that combines the haken kelso bunz model and the models of weakly coupled oscillators proposed by winfree and kuramoto the stability criteria based on the h theorem agree with those derived in our earlier analyses

nondata aided joint channel estimation and equalization for ofdm systems in very rapidly varying mobile channels this paper is concerned with the challenging and timely problem of joint channel estimation and equalization for orthogonal frequency division multiplexing ofdm systems in the presence of frequency selective and very rapidly time varying channels the resulting algorithm is based on the space alternating generalized expectation maximization maximum a posteriori probability sage map technique which is particularly well suited to multicarrier signal formats the algorithm is implemented in the time domain which enables one to use the gaussian approximation of the transmitted ofdm samples consequently the averaging process of the nonpilot data symbols becomes analytically possible resulting in a feasible and computationally efficient channel estimation algorithm leading to a receiver structure that yields also an equalized output from which the data symbols are detected with excellent symbol error rate ser performance based on this gaussian approximation the exact bayesian cramer rao lower bound crlb as well as the convergence rate of the algorithm are derived analytically to reduce the computational complexity of the algorithm discrete legendre orthogonal basis functions are employed to represent the rapidly time varying fading channel it is shown that depending on the normalized doppler frequency only a small number of expansion coefficients is sufficient to approximate the channel very well and there is no need to know the correlation function of the input signal the computational complexity of the algorithm is shown to be o nl per detected data symbol and per sage map algorithm cycle where is the number of ofdm subcarriers and is the number of multipath components

complete description of a generalized ornstein uhlenbeck process related to the nonextensive gaussian entropy abstract we consider a generalized ornstein uhlenbeck process described by a nonlinear fokker planck equation related to the one parametric nonextensive gaussian entropy which is a special case of the two parametric sharma mittal entropy we derive the entire hierarchy of distribution functions for that process and in doing so derive a complete description of a stochastic process related to a nonextensive entropy measure

a low complexity generalized sphere decoding approach for underdetermined linear communication systems performance and complexity evaluation for underdetermined linear systems original sphere decoding sd algorithms fail due to zero diagonal elements in the upper triangular matrix of the qr or cholesky factorization of the underdetermined matrix to solve this problem this paper presents a low complexity generalized sphere decoding gsd approach by transforming the original underdetermined problem into the full column rank one so that standard sd can be directly applied on the transformed problem since the introduced transformation maintains the dimension of the original problem for all m qam s the proposed gsd approach provides significant reduction in complexity as compared to other gsd schemes especially for m qam with large signaling constellation both performance and expected complexity are analyzed to provide the comprehensive relationships between the performance and complexity of the proposed gsd and its parameters illustrative simulation and analytical results are in good agreement in terms of both the performance and complexity and indicate that with the properly selected design parameters the proposed gsd scheme can approach the optimum maximumlikelihood decoding mld performance with low complexity for underdetermined linear communication systems including underdetermined mimo systems and the proposed expected complexity analysis can be used as reliable complexity estimation for practical implementation of the proposed algorithm and serve as reference for other gsd algorithms

non linear kinetics underlying generalized statistics abstract the purpose of the present effort is threefold firstly it is shown that there exists a principle that we call kinetical interaction principle kip underlying the non linear kinetics in particle systems independently on the picture kramers boltzmann used to describe their time evolution secondly the kip imposes the form of the generalized entropy associated to the system and permits to obtain the particle statistical distribution both as stationary solution of the non linear evolution equation and as the state which maximizes the generalized entropy thirdly the kip allows on one hand to treat all the classical or quantum statistical distributions already known in the literature in a unifying scheme and on the other hand suggests how we can introduce naturally new distributions finally as a working example of the approach to the non linear kinetics here presented a new non extensive statistics is constructed and studied starting from a one parameter deformation of the exponential function holding the relation f x f x 1

generalised sphere decoding for spatial modulation in this paper sphere decoding sd algorithms for spatial modulation sm are developed to reduce the computational complexity of maximum likelihood ml detectors two sds specifically designed for sm are proposed and analysed in terms of bit error ratio ber and computational complexity using monte carlo simulations and mathematical analysis it is shown that by carefully choosing the initial radius the proposed sphere decoder algorithms offer the same ber as ml detection with a significant reduction in the computational complexity a tight closed form expression for the ber performance of sm sd is derived in the paper along with an algorithm for choosing the initial radius which provides near to optimum performance also it is shown that none of the proposed sds are always superior to the others but the best sd to use depends on the target spectral efficiency the computational complexity trade off offered by the proposed solutions is studied via analysis and simulation and is shown to validate our findings finally the performance of sm sds are compared to spatial multiplexing smx applying ml decoder and applying sd it is shown that for the same spectral efficiency sm sd offers up to 84 reduction in complexity compared to smx sd with up to 1 db better ber performance than smx ml decoder

derivation of nonlinear fokker planck equations by means of approximations to the master equation nonlinear fokker planck equations fpes are derived as approximations to the master equation in cases of transitions among both discrete and continuous sets of states the nonlinear effects introduced through the transition probabilities are argued to be relevant for many real phenomena within the class of anomalous diffusion problems the nonlinear fpes obtained appear to be more general than some previously proposed on a purely phenomenological basis ones in spite of this the same kind of solution applies i e it is shown that the time dependent tsallis s probability distribution is a solution of both equations obtained either from discrete or continuous sets of states and that the corresponding stationary solution is in the infinite time limit a stable solution

some general relations in arbitrary thermostatistics abstract the fundamental thermodynamic relation and the connection between the entropy maximum principle and the energy minimum principle are analyzed in arbitrary thermostatistics in the canonical ensemble it is shown that the relation and connection can occur in very general circumstances furthermore the relation is applied in a nonextensive context and the stability of the tsallis thermostatistics is analyzed

exact time dependent solutions of the renyi fokker planck equation and the fokker planck equations related to the entropies proposed by sharma and mittal abstract exact time dependent solutions representing generalized one dimensional ornstein uhlenbeck processes are derived from nonlinear fokker planck equations and the corresponding diffusion processes are studied the corresponding systems are related to the renyi entropy and entropies proposed by sharma and mittal in the former case normal diffusion is found with a diffusion rate depending on the order of the renyi entropy in the latter case we find anomalous diffusion processes

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

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

orthogonal frequency division multiplexing with index modulation in this paper a novel orthogonal frequency division multiplexing ofdm scheme called ofdm with index modulation ofdm im is proposed for operation over frequency selective and rapidly time varying fading channels in this scheme the information is conveyed not only by m ary signal constellations as in classical ofdm but also by the indices of the subcarriers which are activated according to the incoming bit stream different low complexity transceiver structures based on maximum likelihood detection or log likelihood ratio calculation are proposed and a theoretical error performance analysis is provided for the new scheme operating under ideal channel conditions then the proposed scheme is adapted to realistic channel conditions such as imperfect channel state information and very high mobility cases by modifying the receiver structure the approximate pairwise error probability of ofdm im is derived under channel estimation errors for the mobility case several interference unaware aware detection methods are proposed for the new scheme it is shown via computer simulations that the proposed scheme achieves significantly better error performance than classical ofdm due to the information bits carried by the indices of ofdm subcarriers under both ideal and realistic channel conditions

space shift keying ssk mimo with practical channel estimates in this paper we study the performance of space modulation for multiple input multiple output mimo wireless systems with imperfect channel knowledge at the receiver we focus our attention on two transmission technologies which are the building blocks of space modulation i space shift keying ssk modulation and ii time orthogonal signal design tosd ssk modulation which is an improved version of ssk modulation providing transmit diversity we develop a single integral closed form analytical framework to compute the average bit error probability abep of a mismatched detector for both ssk and tosd ssk modulations the framework exploits the theory of quadratic forms in conditional complex gaussian random variables rvs along with the gil pelaez inversion theorem the analytical model is very general and can be used for arbitrary transmit and receive antennas fading distributions fading spatial correlations and training pilots the analytical derivation is substantiated through monte carlo simulations and it is shown over independent and identically distributed i i d rayleigh fading channels that ssk modulation is as robust as single antenna systems to imperfect channel knowledge and that tosd ssk modulation is more robust to channel estimation errors than the alamouti scheme furthermore it is pointed out that only few training pilots are needed to get reliable enough channel estimates for data detection and that transmit and receive diversity of ssk and tosd ssk modulations are preserved even with imperfect channel knowledge