theoretical analysis and performance of ofdm signals in nonlinear awgn channels orthogonal frequency division multiplexing ofdm baseband signals may be modeled by complex gaussian processes with rayleigh envelope distribution and uniform phase distribution if the number of carriers is sufficiently large the output correlation function of instantaneous nonlinear amplifiers and the signal to distortion ratio can be derived and expressed in an easy way as a consequence the output spectrum and the bit error rate ber performance of ofdm systems in nonlinear additive white gaussian noise channels are predictable both for uncompensated amplitude modulation amplitude modulation am am and amplitude modulation pulse modulation am pm distortions and for ideal predistortion the aim of this work is to obtain the analytical expressions for the output correlation function of a nonlinear device and for the ber performance the results in closed form solutions are derived for am am and am pm curves approximated by bessel series expansion and for the ideal predistortion case

existence and qualitative properties of travelling waves for an epidemiological model with mutations in this article we are interested in a non monotone system of logistic reaction diffusion equations this system of equations models an epidemics where two types of pathogens are competing and a mutation can change one type into the other with a certain rate we show the existence of minimal speed travelling waves that are usually non monotonic we then provide a description of the shape of those constructed travelling waves and relate them to some fisher kpp fronts with non minimal speed

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

maximum likelihood detection of nonlinearly distorted multicarrier symbols by iterative decoding this paper proposes a new method for decoding multicarrier symbols with severe nonlinear distortion the first part evaluates mutual information expressions for practical nonlinear models and shows the performance bounds for commonly used receiver structures then we derive the maximum likelihood ml sequence estimator which unfortunately has an exponential complexity due to the nonlinear distortion this extremely large complexity can be reduced with a simple algorithm that iteratively estimates the nonlinear distortion thereby reducing the exponential ml to the standard ml without nonlinear distortion the proposed method can be used to reduce the peak to average power ratio of multicarrier signals by clipping the transmit sequence it can also be used to correct any nonlinear distortion present in transmitter receiver amplifiers that are operating close to saturation

orthogonal designs with maximal rates orthogonal designs have been used as space time block codes for wireless communications with multiple transmit antennas which can achieve full transmit diversity and have a very simple decoupled maximum likelihood decoding algorithm the rate of an orthogonal design is defined as the ratio of the number of transmitted information symbols in a block of channel uses to the length of the given block which reflects the bandwidth efficiency of the employed space time block code constructed from the orthogonal design this paper focuses on the analysis and synthesis of orthogonal designs with the maximum possible rates which may be real or complex and square or rectangular matrices we first provide several representations of orthogonal designs and their characterizations in terms of hurwitz radon matrix equations next we observe that the real orthogonal designs square or rectangular and the complex square orthogonal designs with maximal rates have been well understood from the existing results in the mathematics literature which can be dated back to 1890s however unfortunately it is not the case for the complex rectangular orthogonal designs with rates as high as possible we then construct a class of complex orthogonal designs for any number of transmit antennas the proposed complex orthogonal designs for the number of transmit antennas n 2m 1 and 2m have the same rate m 1 and 2m where m is any natural number finally we demonstrate that for n 2m 1 and 2m with any given natural number m the value m 1 and 2m is the maximum possible rate that the complex orthogonal designs square or rectangular with n transmit antennas can achieve

performance analysis of deliberately clipped ofdm signals we analyze the performance of the clipped orthogonal frequency division multiplexing ofdm system in terms of peak power reduction capability and degradation of channel capacity the clipping is performed on the baseband ofdm signals with and without oversampling followed by the ideal low pass filter first the effect of the envelope clipping on the peak to average power ratio papr and the instantaneous power of the band limited ofdm signal is studied we then discuss the channel capacity of the oversampled and clipped ofdm signals over the additive white gaussian noise and ideally interleaved rayleigh fading channels the capacity is calculated based on the assumption that the distortion terms caused by the clipping are gaussian it is shown that the snr penalty due to the clipping can be considerably alleviated by using optimal coding and reducing the information data rate the results are justified by the simulation results using near optimal turbo codes

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

cloaking due to anomalous localized resonance in plasmonic structures of confocal ellipses if a core of dielectric material is coated by a plasmonic structure of negative dielectric material with nonzero loss parameter then anomalous localized resonance may occur as the loss parameter tends to zero and the source outside the structure can be cloaked in this paper we consider cloaking by anomalous localized resonance calr on structures where the core and the shell are confocal ellipses for such structures we compute the critical elliptic radii such that for any source inside it calr takes place and for any source outside it calr does not take place the method of this paper uses the spectral analysis of the neumann poincare type operator associated with two interfaces the boundaries of the core and the shell which was developed in h ammari g ciraolo h kang h lee and g w milton arch ration mech anal 208 2013 pp 667 692

closed form designs of complex orthogonal space time block codes of rates k 1 2k for 2k 1 or 2k transmit antennas in this correspondence we present systematic and closed form constructions of complex orthogonal space time block codes from complex orthogonal designs of rates k 1 2k for 2k 1 or 2k transmit antennas for any positive integer k

the existence of periodic travelling waves for singularly perturbed predator prey equations via the conley index this paper is concerned with the existence of periodic travelling wave solutions of reactiondiffusion equations which arise as models of predator prey interactions in mathematical ecology the relevant equations are somewhat similar to the fitz hugh nagumo equations and our results apply to this latter system as well in studying the fitz hugh nagumo equations conley 3 i initiated a new topological approach to this problem his method depends on the construction of an isolating neighborhood cf section 2a about a singular periodic solution associated with such a neighborhood is a topological invariant the conley index which when nontrivial implies the existence of a smooth solution near the singular one the new aspects of the present discussion are in the method used to construct the isolating neighborhood in ifi4 and in the computation of the index with regard to the isolating neighborhood our construction is global in that a parameter taken to be small in conley s equations is now allowed to assume large values in order to compute the index we continue our equations to those studied by conley actually we go one step further and continue conley s equations to the van der pol equations crossed with a pair of linear equations admitting a repelling critical point the index for this latter system is easily computed and turns out to be non trivial it follows from the invariance of the index under continuation 21 that the desired

single symbol maximum likelihood decodable linear stbcs space time block codes stbcs from orthogonal designs ods and coordinate interleaved orthogonal designs ciod have been attracting wider attention due to their amenability for fast single symbol maximum likelihood ml decoding and full rate with full rank over quasi static fading channels however these codes are instances of single symbol decodable codes and it is natural to ask if there exist codes other than stbcs form ods and ciods that allow single symbol decoding in this paper the above question is answered in the affirmative by characterizing all linear stbcs that allow single symbol ml decoding not necessarily full diversity over quasi static fading channels calling them single symbol decodable designs sdd the class sdd includes ods and ciods as proper subclasses further among the sdd a class of those that offer full diversity called full rank sdd fsdd are characterized and classified we then concentrate on square designs and derive the maximal rate for square fsdds using a constructional proof it follows that 1 except for n 2 square complex ods are not maximal rate and 2 a rate one square fsdd exist only for two and four transmit antennas for nonsquare designs generalized coordinate interleaved orthogonal designs a superset of ciods are presented and analyzed finally for rapid fading channels an equivalent matrix channel representation is developed which allows the results of quasi static fading channels to be applied to rapid fading channels using this representation we show that for rapid fading channels the rate of single symbol decodable stbcs are independent of the number of transmit antennas and inversely proportional to the block length of the code significantly the ciod for two transmit antennas is the only stbc that is single symbol decodable over both quasi static and rapid fading channels

a theoretical characterization of nonlinear distortion effects in ofdm systems this paper presents a theoretical characterization of nonlinear distortion effects in orthogonal frequency division multiplexing ofdm transmission systems in the theoretical framework developed it is shown that the effects on the decision variables of the in band distortion introduced by a bandpass memoryless nonlinearity can be described by means of a complex gain and an additive gaussian term with zero mean and suitable variance analytical expressions for gain and variance are given the conditions which allow this description are emphasized and discussed as a consequence a completely analytical procedure to evaluate error probability is also obtained and illustrated using ofdm discrete multitone modulation dmt systems with rectangular pulse shaping for the soft envelope limiter nonlinearity a closed form is derived a comparison with simulation results is carried out to verify the accuracy of this method

improved quasi orthogonal codes through constellation rotation in this letter we show that the performance of recently proposed quasi orthogonal space time codes can be improved by phase shifting the constellations of the symbols constituting the code the optimal rotation of the symbols increases the minimum distance of the corresponding space time codewords leading to substantially improved performance

on the nonexistence of rate one generalized complex orthogonal designs orthogonal space time block coding proposed recently by alamouti 1998 and tarokh et al 1999 is a promising scheme for information transmission over rayleigh fading channels using multiple transmit antennas due to its favorable characteristics of having full transmit diversity and a decoupled maximum likelihood ml decoding algorithm tarokh et al extended the theory of classical orthogonal designs to the theory of generalized real or complex linear processing orthogonal designs and then applied the theory of generalized orthogonal designs to construct space time block codes stbc with the maximum possible diversity order while having a simple decoding algorithm for any given number of transmit and receive antennas it has been known that the stbc constructed in this way can achieve the maximum possible rate of one for every number of transmit antennas using any arbitrary real constellation and for two transmit antennas using any arbitrary complex constellation contrary to this in this correspondence we prove that there does not exist rate one stbc from generalized complex linear processing orthogonal designs for more than two transmit antennas using any arbitrary complex constellation

capacity approaching space time codes for systems employing four transmitter antennas the design of space time codes that are capable of approaching the capacity of multiple input single output miso antenna systems is a challenging problem yet one of high practical importance while a remarkably simple scheme of alamouti 1998 is capable of attaining the channel capacity in the case of two transmitter and one receiver antennas 2 1 no such schemes are known for the case of more than two transmitter antennas we propose a family of space time codes that are especially designed for the case of four transmitter antennas and that are shown to allow the attainment of a significant fraction of the open loop shannon capacity of the 4 1 channel

single symbol ml decoding for orthogonal and quasi orthogonal stbc in clipped mimo ofdm systems using a clipping noise model with gaussian approximation an efficient way to reduce the peak to average power ratio papr in ofdm systems is clipping after the clipping in an mimo ofdm system the additive noise may not be white in this paper we develop fast single symbol ml decoding algorithms for orthogonal space time block codes ostbc and linearly transformed quasi orthogonal space time block codes qostbc in clipped mimo ofdm systems by using a clipping noise model with gaussian approximation by using the statistics of the clipping distortions our newly developed fast ml decoding algorithms improve the performance for clipped mimo ofdm systems with ostbc and qostbc while the decoding complexities are not increased simulation results are presented to illustrate the improvement

upper bounds of rates of complex orthogonal space time block codes we derive some upper bounds of the rates of generalized complex orthogonal space time block codes we first present some new properties of complex orthogonal designs and then show that the rates of complex orthogonal space time block codes for more than two transmit antennas are upper bounded by 3 4 we show that the rates of generalized complex orthogonal space time block codes for more than two transmit antennas are upper bounded by 4 5 where the norms of column vectors may not be necessarily the same we also present another upper bound under a certain condition for a generalized complex orthogonal design its variables are not restricted to any alphabet sets but are on the whole complex plane a generalized complex orthogonal design with variables over some alphabet sets on the complex plane is also considered we obtain a condition on the alphabet sets such that a generalized complex orthogonal design with variables over these alphabet sets is also a conventional generalized complex orthogonal design and therefore the above upper bounds on its rate also hold we show that commonly used quadrature amplitude modulation qam constellations of sizes above 4 satisfy this condition

signal constellations for quasi orthogonal space time block codes with full diversity space time block codes stbcs from orthogonal designs proposed by alamouti and tarokh jafarkhani calderbank have attracted considerable attention lately due to their fast maximum likelihood ml decoding and full diversity however the maximum symbol transmission rate of an stbc from complex orthogonal designs for complex signals is only 3 4 for three and four transmit antennas and it is difficult to construct complex orthogonal designs with rate higher than 1 2 for more than four transmit antennas recently jafarkhani tirkkonen boariu hottinen and papadias foschini proposed stbcs from quasi orthogonal designs where the orthogonality is relaxed to provide higher symbol transmission rates with the quasi orthogonal structure the quasi orthogonal stbcs still have a fast ml decoding but do not have the full diversity the performance of these codes is better than that of the codes from orthogonal designs at low signal to noise ratio snr but worse at high snr this is due to the fact that the slope of the performance curve depends on the diversity it is desired to have the quasi orthogonal stbcs with full diversity to ensure good performance at high snr in this paper we achieve this goal by properly choosing the signal constellations specifically we propose that half of the symbols in a quasi orthogonal design are chosen from a signal constellation set a and the other half of them are chosen from a rotated constellation e sup j spl phi a the resulting stbcs can guarantee both full diversity and fast ml decoding moreover we obtain the optimum selections of the rotation angles spl phi for some commonly used signal constellations simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high snrs

propagation in a kinetic reaction transport equation travelling waves and accelerating fronts in this paper we study the existence and stability of travelling wave solutions of a kinetic reaction transport equation the model describes particles moving according to a velocity jump process and proliferating thanks to a reaction term of monostable type the boundedness of the velocity set appears to be a necessary and sufficient condition for the existence of positive travelling waves the minimal speed of propagation of waves is obtained from an explicit dispersion relation we construct the waves using a technique of sub and supersolutions and prove their weak stability in a weighted l2 space in case of an unbounded velocity set we prove a superlinear spreading it appears that the rate of spreading depends on the decay at infinity of the velocity distribution in the case of a gaussian distribution we prove that the front spreads as t3 2

on optimal quasi orthogonal space time block codes with minimum decoding complexity orthogonal space time block codes ostbc from orthogonal designs have both advantages of complex symbol wise maximum likelihood ml decoding and full diversity however their symbol rates are upper bounded by 3 4 for more than two antennas for complex symbols to increase the symbol rates they have been generalized to quasi orthogonal space time block codes qostbc in the literature but the diversity order is reduced by half and the complex symbol wise ml decoding is significantly increased to complex symbol pair wise pair of complex symbols ml decoding the qostbc has been modified by rotating half of the complex symbols for achieving the full diversity while maintaining the complex symbol pair wise ml decoding the optimal rotation angles for any signal constellation of any finite symbols located on both square lattices and equal literal triangular lattices have been found by su xia where the optimality means the optimal diversity product or product distance qostbc has also been modified by yuen guan tjhung by rotating information symbols in another way such that it has full diversity and in the meantime it has real symbol pair wise ml decoding the same complexity as complex symbol wise decoding and the optimal rotation angle for square and rectangular qam constellations has been found in this paper we systematically study general linear transformations of information symbols for qostbc to have both full diversity and real symbol pair wise ml decoding we present the optimal transformation matrices among all possible linear transformations not necessarily symbol rotations of information symbols for qostbc with real symbol pair wise ml decoding such that the optimal diversity product is achieved for both general square qam and general rectangular qam signal constellations furthermore our newly proposed optimal linear transformations for qostbc also work for general qam constellations in the sense that qostbc have full diversity with good diversity product property and real symbol pair wise ml decoding interestingly the optimal diversity products for square qam constellations from the optimal linear transformations of information symbols found in this paper coincide with the ones presented by yuen guan tjhung by using their optimal rotations however the optimal diversity products for nonsquare rectangular qam constellations from the optimal linear transformations of information symbols found in this paper are better than the ones presented by yuen guan tjhung by using their optimal rotations in this paper we also present the optimal transformations for the co ordinate interleaved orthogonal designs ciod proposed by khan rajan for rectangular qam constellations