continuous phase modulation part i full response signaling the continuous phase modulation cpm signaling scheme has gained interest in recent years because of its attractive spectral properties data symbol pulse shaping has previously been studied with regard to spectra for binary data and modulation index 0 5 in this paper these results have been extended to the m ary case where the pulse shaping is over a one symbol interval the so called full response systems results are given for modulation indexes of practical interest concerning both performance and spectrum comparisons are made with minimum shift keying msk and systems have been found which are significantly better in e b n 0 for a large signal to noise ratio snr without expanded bandwidth schemes with the same bit error probability as msk but with considerably smaller bandwidth have also been found significant improvement in both power and bandwidth are obtained by increasing the number of levels m from 2 to 4

an upper bound on the bit error probability of combined convolutional coding and continuous phase modulation the bit error probability properties of signals consisting of convolutional coding combined with partial response multilevel continuous phase modulation cpm are studied it is assumed that the channel is an additive white gaussian noise channel and that the receiver performs coherent maximum likelihood sequence detection by means of the viterbi algorithm an upper bound on the bit error probability is derived using the average generating function technique and evaluated numerically for a number of coded multilevel full response cpm schemes simulation results are also presented it is concluded that the free euclidean distance is the best one parameter description of the error probability for the considered class of signals for high signal to noise ratios however the upper bound results show that the free distance alone yields pessimistic bit error probability behavior for some interesting cases

minimum euclidean distance for combinations of short rate 1 2 convolutional codes and cpfsk modulation continuous phase frequency shift keying cpfsk is a constant amplitude modulation method with good spectral sidelobe properties good error probability properties can be obtained with coherent maximum likelihood detection in this paper we study the euclidean distance properties of signals formed by a conventional rate 1 2 convolutional encoder followed by a binary or 4 level cpfsk modulator the minimum euclidean distance is calculated for these signal sets as a function of the modulation index and the observation interval length the optimum detector is discussed for rational modulation index values the best obtainable codes are found for the case of short rate 1 2 codes with binary or 4 level cpfsk modulation lists of the best codes are given among the results are that the noncatastrophic rate 1 2 convolutional codes with optimum free hamming distance do not in general give the best euclidean distance with cpfsk

reduced complexity near capacity joint channel estimation and three stage turbo detection for coherent space time shift keying we propose a low complexity joint channel estimation ce and three stage iterative demapping decoding scheme for near capacity coherent space time shift keying cstsk based multiple input multiple output mimo systems in the proposed scheme only a minimum number of space time shift keying training blocks are employed for generating an initial least square channel estimate which is then used for initial data detection as usual the detected soft information is first exchanged a number of times within the inner turbo loop between the unity rate code urc decoder and the cstsk soft demapper and the information gleaned from the inner urc decoder is then iteratively exchanged with the outer decoder in the outer turbo loop our ce scheme is embedded into the outer turbo loop which exploits the a posteriori information produced by the cstsk soft demapper to select a sufficient number of high quality decisions only for ce since the ce is embedded into the iterative three stage demapping decoding process no additional iterative loop is required for exchanging information between the decision directed channel estimator and the three stage turbo detector hence the computational complexity of the proposed joint ce and three stage turbo detection remains similar to that of the three stage turbo detection decoding scheme with the given channel estimate moreover our proposed low complexity semi blind scheme is capable of approaching the optimal maximum likelihood turbo detection performance attained with the aid of perfect channel state information with the same low number of turbo iterations as the latter as confirmed by our extensive simulation results

linear dispersion codes for mimo systems based on frame theory multiple input multiple output mimo wireless communication systems provide high capacity due to the plurality of modes available in the channel existing signaling techniques for mimo systems have focused primarily on multiplexing for high data rate or diversity for high link reliability in this paper we present a new linear dispersion code design for mimo rayleigh fading channels the proposed design bridges the gap between multiplexing and diversity and yields codes that typically perform well both in terms of ergodic capacity as well as error probability this is important because as we show designs performing well from an ergodic capacity point of view do not necessarily perform well from an error probability point of view various techniques are presented for finding codes with good error probability performance monte carlo simulations illustrate performance of some example code designs in terms of ergodic capacity codeword error probability and bit error probability

design of serially concatenated systems depending on the block length based on extrinsic information transfer exit charts the convergence behavior of iterative decoding is studied for a number of serially concatenated systems such as a serially concatenated code coded data transmission over an intersymbol interference channel bit interleaved coded modulation or trellis coded modulation efficient optimization algorithms based on simplified exit chart construction are devised to find irregular codes improving the convergence of iterative decoding one optimization criterion is to find concatenated systems exhibiting thresholds of successful decoding convergence which are close to information theoretic limits however these thresholds are approached only for very long block lengths to overcome this problem the decoding convergence after a fixed finite number of iterations is optimized which yields systems performing very well for short block lengths too as an example optimal system configurations for communication over an additive white gaussian noise channel are presented

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

use of the viterbi algorithm to compute error events of trellis phase coding in order of increasing distance the use of the viterbi algorithm to evaluate the minimum distance parameters of trellis phase codes is extended to evaluate distances and paths of error events other than the free distance event distances and paths are found for error events sequentially in order of increasing distance starting with the free distance event memory requirements increase slowly with the number of error events required the time taken to find the next error event increases slowly with the number of error events already found results of sample calculations and computation times are included

extrinsic information transfer functions model and erasure channel properties extrinsic information transfer exit charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems a model is introduced that applies to decoding problems including the iterative decoding of parallel concatenated turbo codes serially concatenated codes low density parity check ldpc codes and repeat accumulate ra codes exit functions are defined using the model and several properties of such functions are proved for erasure channels one property expresses the area under an exit function in terms of a conditional entropy a useful consequence of this result is that the design of capacity approaching codes reduces to a curve fitting problem for all the aforementioned codes a second property relates the exit function of a code to its helleseth klove levenshtein information functions and thereby to the support weights of its subcodes the relation is via a refinement of information functions called split information functions and via a refinement of support weights called split support weights split information functions are used to prove a third property that relates the exit function of a linear code to the exit function of its dual

power bandwidth performance of smoothed phase modulation codes constant envelope phase varying sinusoids of the form sqrt 2e t cos omega c t phi t are studied in which the phase function phi t follows some coded pattern in response to data power and bandwidth performance are studied for such patterns the patterns depend on a phase shaping function a modulation index h and a sequence of m ary underlying changes in phase which are chosen at random a cutoff rate like parameter r 0 is computed which guarantees existence of codes at all rates r bits t interval whose error performance varies as exp n r 0 r where n is the code word length in t intervals plots of r 0 are given as a function of interval energy e the shaping function h and m extensive spectral calculations give the spectra of these phased sinusoids and their performance is plotted in the power bandwidth plane the results give strong evidence that phase codes can approximate any power bandwidth combination consistent with shannon s gaussian channel capacity and that linear channels are not required for narrow band transmission

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

optimization of trellis coded tfm via matched codes a matched code is a convolutional code chosen in such a way that when combined with modulation with memory the resulting receiver for the coded modulation has the smallest possible number of states in the paper the matched coding technique is applied to coded tamed frequency modulation tfm schemes and a formal procedure is developed to find the best combination of a code and a modulation the optimization criterion is the maximum free euclidean distance for a given code rate and a given number of states in the viterbi receiver used for the coded modulation a search for the best codes was carried out for code rates 1 2 and 2 3 and for receivers with up to 256 and 64 states respectively good coding gains more than 7 db for rate 1 2 were achieved some of the best codes were catastrophic yet the coded modulation was not the codes obtained using the matched coding approach were in many cases better than those obtained using traditional optimization techniques

nonlinear continuous phase frequency shift keying a novel signal space coded cpm continuous phase modulated signaling technique called nonlinear cpfsk continuous phase frequency shift keying signaling which guarantees the maximum constraint length allowed by the number of states is introduced nonlinear cpfsk signals use a suitably selected state transition matrix during all signaling intervals the selected state transition matrix is realized by changing the modulation index of the signals hence the modulation index used during any interval depends on the transmitted symbol as well as on the state of the system binary nonlinear cpfsk signaling schemes are constructed and analyzed numerical results indicate that nonlinear cpfsk signals can achieve attractive minimum distances compared with other existing cpm signaling formats

joint source and channel coding using punctured ring convolutional coded cpm in this paper a novel trellis source encoding scheme based on punctured ring convolutional codes is presented joint source and channel coding jscc using trellis coded continuous phase modulation cpm with punctured convolutional codes over rings is investigated the channels considered are the additive white gaussian noise awgn channel and the rayleigh fading channel optimal soft decoding for the proposed jscc scheme is studied the soft decoder is based on the a posteriori probability app algorithm for trellis coded cpm with punctured ring convolutional codes it is shown that these systems with soft decoding outperform the same systems with hard decoding especially when the systems operate at low to medium signal to noise ratio snr furthermore adaptive jscc approaches based on the proposed source coding scheme are investigated compared with jscc schemes with fixed source coding rates the proposed adaptive approaches can achieve much better performance in the high snr region the novelties of this work are the development of a trellis source encoding method based on punctured ring convolutional codes the use of a soft decoder the app algorithm for the combined systems and the adaptive approaches to the jscc problem

nonlinear multi h phase codes for cpfsk signaling two novel trellis coding techniques called nonlinear multi h signaling and nonlinear asymmetrical multi h signaling which achieve higher constraint length than ordinary multi h signals are introduced with cpfsk signals in contrast to ordinary multi h signaling where the modulation index is changed at the end of every symbol interval nonlinear multi h signals are constructed by changing the modulation index based on the previous symbol and the current symbol interval a class of nonlinear asymmetrical multi h signals which change the modulation index based on the current symbol too is then constructed by extending nonlinear multi h signals and combining them with asymmetrical multi h signals binary full response nonlinear multi h and nonlinear asymmetrical multi h cpfsk signals are constructed and analyzed minimum euclidean distances and spectral properties of these signals are calculated at different phase states and various selected modulation index patterns numerical results indicate that nonlinear multi h and nonlinear asymmetrical multi h signals achieve significantly higher distance than other existing multi h formats reported in the literature

combined coded multi h cpfsk signaling a continuous phase frequency shift keying cpfsk signaling technique is suggested that combines convolutional encoding and multi h signaling in contrast to regular multi h signaling this technique changes the modulation index in a preselected pattern in order to maximize the minimum euclidean distance a rate 1 2 convolutional encoder along with a 2 h quaternary cpfsk modulator which uses two fixed modulation indexes is considered minimum euclidean distances are calculated corresponding to the best encoder mapper combinations for different modulation index patterns at attractive pairs of modulation indexes numerical results obtained for encoder memory lengths of one and two are used to illustrate that the minimum euclidean distance of coded cpfsk signals can be significantly increased by combining with multi h signaling modulation index patterns which perform significantly better than regular multi h signals are determined an error event analysis over the additive white gaussian noise channel is carried out to investigate the actual error rate performance and to verify the theoretical results

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

on joint source and channel coding using trellis coded cpm analytical bounds on the channel distortion joint source and channel coding jscc using trellis coded quantization tcq in conjunction with trellis coded continuous phase modulation cpm is studied the channel is assumed to be the additive white gaussian noise awgn channel analytical bounds on the channel distortion for the investigated systems with maximum likelihood sequence detection mlsd are developed the bounds are based on the transfer function technique which was modified and generalized to include continuous amplitude discrete time signals for a memoryless uniform source the constructed bounds for the investigated systems are shown to be asymptotically tight for increasing channel signal to noise ratio snr values for a memoryless nonuniform source the constructed bounds are not as tight as the one for the uniform source however it still can be used as an indication to how the system performs it is concluded that the minimum euclidean distance of the system alone is not enough to evaluate the performance of the considered systems the number of error events having minimum euclidean distance and the total distortion caused by those error events also affect the asymptotic performance this work provides an analysis tool for the investigated systems the analysis method is very general it may be applied to any trellis based jscc schemes

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

on the blind equalization of continuous phase modulated signals using the constant modulus criterion the use of the constant modulus cm criterion to achieve blind equalization of continuous phase modulated cpm signals is investigated in this paper solutions to the cm criterion are characterized it is shown that blind equalization using the cm criterion may be unsuccessful in the sense that the output of the equalizer does not necessarily coincides with a delayed and rotated version of the input signal an indeterminacy indeed remains and this residual indeterminacy is characterized as an application of our results a blind equalization criterion that allows us to eliminate the latter indeterminacy is proposed simulation results sustain theoretical claims and illustrate the attractive performance of the proposed criterion

spatial modulation and space time shift keying optimal performance at a reduced detection complexity in this paper we propose a comprehensive reduced complexity detector both for hard decision aided as well as for the soft decision assisted spatial modulation sm space time shift keying stsk more explicitly the detection of the sm scheme which activates a single one out of m antennas to transmit a single lpsk qam symbol may be carried out by detecting the antenna activation index m and the lpsk qam symbol st separately so that the detection complexity may be reduced from the order of o m l to the lower bound of o m log2 l however the qam aided stsk hard detection proposed in 1 results in a performance loss furthermore the max log map algorithm proposed for soft stsk detection in 2 only takes into account the maximum a posteriori probabilities which also imposed a performance degradation therefore in this paper we propose a novel solution for hard decision aided sm stsk detection which retains its optimal performance despite its reduced detection complexity when either lpsk or lqam is employed furthermore we propose the reduced complexity approx log map algorithm conceived for the soft decision aided sm stsk detector in order to replace the suboptimal max log map algorithm

signal detection in antenna hopping space division multiple access systems with space shift keying modulation to take the advantages of the m ary space shift keying mssk modulation invented recently a mssk fast antenna hopping space division multiple access mssk fah sdma scheme is proposed and studied in this paper in addition to supporting multiple access the fah is introduced also to achieve transmit diversity by sending every mssk symbol over several time slots under the control of a fah pattern address associated with the mssk fah sdma a range of linear and nonlinear detection schemes are studied specifically the linear detection schemes considered include the matched filtering single user detector mf sud zero forcing multiuser detector zf mud and minimum mean square error mmse mud while the nonlinear detection schemes addressed include the maximum likelihood ml mud and the receiver multiuser diversity aided multi stage mmse rmd ms mmse mud the single user pairwise error probability su pep and bit error rate ber union bound of the single user mssk fah sdma systems employing ml detection are analyzed in detail based on the su pep the minimum transmit diversity order of the mssk fah sdma systems is specified for the mssk fah sdma systems with linear detection we study two types of mssk demodulation schemes which are referred to as the intrauser detections iuds named as the maximum likelihood ml iud and direct d iud for the mssk fah sdma systems employing the rmd ms mmse mud two types of reliability measurement rm schemes are proposed which are the maximum a posteriori map rm and ratio test rt rm finally the ber performance of the mssk fah sdma systems with various combinations of the proposed techniques is studied when assuming that the channels from any transmit antennas to any receive antennas experience independent and identically distributed i i d rayleigh fading

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

the hawking penrose singularity theorem for c 1 1 lorentzian metrics we show that the hawking penrose singularity theorem and the generalisation of this theorem due to galloway and senovilla continue to hold for lorentzian metrics that are of c 1 1 regularity we formulate appropriate weak versions of the strong energy condition and genericity condition for c 1 1 metrics and of c 0 trapped submanifolds by regularisation we show that under these weak conditions causal geodesics necessarily become non maximising this requires a detailed analysis of the matrix riccati equation for the approximating metrics which may be of independent interest

a new approximation to the symbol error probability for coded modulation schemes with maximum likelihood sequence detection the power efficiency of coded modulation schemes in additive white gaussian noise depends on the signal space distribution of their most common error events symbol error probability calculation allowing for the pairwise interaction of these error events is discussed two optimality criteria are considered for detectors the first minimizes the probability of symbol error for each symbol decision this is called the symbol to symbol detector the second which is superior is the maximum likelihood sequence detector mlsd a lower bound for the symbol to symbol detector and an approximation to the mlsd symbol error probability are described the theoretical performance difference between these two detectors is given the results are more accurate than minimum squared euclidean distance predictions especially at low and intermediate signal to noise ratios the mlsd symbol error probability approximation is obtained for considerably less cost than computer simulation and gives more insight into the signal space structure of the scheme being analyzed numerical results are presented for a continuous phase modulation cpm example

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

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

singularity theorems for c 1 lorentzian metrics continuing recent efforts in extending the classical singularity theorems of general relativity to low regularity metrics we give a complete proof of both the hawking and the penrose singularity theorem for c 1 lorentzian metrics a regularity where one still has existence but not uniqueness for solutions of the geodesic equation the proofs make use of careful estimates of the curvature of approximating smooth metrics and certain stability properties of long existence times for causal geodesics on the way we also prove that for globally hyperbolic spacetimes with a c 1 metric causal geodesic completeness is c 1 fine stable this improves a similar older stability result of beem and ehrlich where they also used the c 1 fine topology to measure closeness but still required smoothness of all metrics lastly we include a brief appendix where we use some of the same techniques in the riemannian case to give a proof of the classical myers theorem for c 1 metrics

nonlinear psk and combined nonlinear psk fsk modulation two classes of constant envelope signals called nonlinear psk and combined nonlinear psk fsk are introduced nonlinear psk signals select a constant phase angle during each interval depending on the state of the signal and the transmitted symbol combined nonlinear psk fsk signals select a linear phase variation during each interval and a discrete phase variation at the end of each interval depending on the current state and the transmitted symbol both classes of signals achieve the highest constraint length allowed by the number of states the numerical results presented at preselected numbers of states show that these signals produce significantly high minimum distances distances higher than those found in the literature at the same number of states are reported the spectra of nonlinear psk signals are almost identical to the spectrum of bpsk signals while those of combined nonlinear psk fsk signals are continuous but similar to that of bpsk signals

symbol error probability bounds for coherently viterbi detected continuous phase modulated signals recently the minimum euclidean distance and bandwidth properties of continuous phase modulated cpm signals have been considered it has also been shown that for rational modulation indexes a state description of these signals is possible and that the viterbi algorithm va can be used for demodulation in this paper the performance analysis of cpm systems is extended to obtain bounds on the symbol error probability when the va is used the calculation of these bounds is based on the transfer function technique which has been generalized from numerical comparisons of the upper and lower bounds it is concluded that the minimum euclidean distance is a good performance measure for a broad class of cpm signals even when the symbol error probability is as large as 10 2

minimum euclidean distance and power spectrum for a class of smoothed phase modulation codes with constant envelope a class of smoothed phase modulation codes is analyzed in terms of power spectral density and error probability for large signal to noise ratios the signals have constant envelope and the information carrying phase function is of multi h partial response continuous phase type a cyclic variation of modulation index from symbol time interval to symbol time interval is introduced coherent transmission and an additive white gaussian channel are assumed both power and bandwidth efficient signals are to be found in the above class comparisons are made between fixed h and multi h systems both for the binary and multilevel cases tradeoff is performed between bandwidth and error probability performance for large signal to noise ratios it is concluded that quaternary and octal systems always seem preferable increasing the number of modulation indexes from one in the fixed h case to two in the simplest multi h case gives performance advantages at the expense of increased system complexity

generalized precoder design formulation and iterative algorithm for spatial modulation in mimo systems with csit in this paper we propose two generalized precoder designs to enhance the bit error rates for the general category of spatial modulation sm in multiple input multiple output mimo systems with channel state information at the transmitter csit we investigate typical sm mimo systems and propose two optimization formulations for designing precoders our design rationale for the first formulation is to maximize the minimum euclidean distance among codewords for the second formulation it is to minimize the total signal power for the lower bounded euclidean distances among codewords since both formulations are non convex and their optimal solutions are generally intractable we propose an algorithm that acquires effective solutions by iteratively solving the alternative convex problem linearized and approximated from the original non convex problem discussions on complexity analysis performance comparisons design challenges and robustness in imperfect csit are then provided by generalizing the design formulations the proposed precoder designs can be extended to generalized sm which completes the investigation for virtually all sm type systems simulation results show that the proposed designs improve the performance of sm gsm mimo systems and outperform existing precoding methods with a potentially higher complexity cost

simulated symbol error probability for a matched filter differential detector with variable delay for continuous phase modulation a matched filter differential detector for continuous phase modulation is proposed and simulated error probability for this detector is presented the detector consists of a conventional differential detector operating with a delay a bank of matched filters and a viterbi processor to perform sequence decision the author shows that quaternary schemes outperform binary schemes when the schemes are compared in a power bandwidth tradeoff schemes that lose about 3 4 db compared to coherently detected minimum shift keying msk at 10 sup 3 on a gaussian channel but with a bandwidth of about 0 6 times the msk bandwidth are presented

on the geometry of metric measure spaces ii we introduce a curvature dimension condition cd k n for metric measure spaces it is more restrictive than the curvature bound underline text curv left m text d m right k introduced in sturm k t 2006 on the geometry of metric measure spaces i acta math 196 65 131 which is recovered as the borderline case cd k the additional real parameter n plays the role of a generalized upper bound for the dimension for riemannian manifolds cd k n is equivalent to text ric m left xi xi right k left xi right 2 and dim m n the curvature dimension condition cd k n is stable under convergence for any triple of real numbers k n l the family of normalized metric measure spaces m d m with cd k n and diameter l is compact condition cd k n implies sharp version of the brunn minkowski inequality of the bishop gromov volume comparison theorem and of the bonnet myers theorem moreover it implies the doubling property and local scale invariant poincare inequalities on balls in particular it allows to construct canonical dirichlet forms with gaussian upper and lower bounds for the corresponding heat kernels

nonlinear multipulse block coding of cpfsk signals a nonlinear multipulse block coding technique is proposed to improve cpfsk signaling formats the coding technique is developed to prevent merging events with lower distances by separating the respective paths in the time domain coded schemes are constructed with constant h 2 h and trellis coded cpfsk signals the spectral variations and the performance bandwidth tradeoffs of the proposed coded signals are found and compared to those without coding it is concluded from the numerical results that the proposed coding technique can significantly improve the performance bandwidth tradeoff of many cpfsk signaling formats particularly at lower bandwidths

woven coded cpfsk with hierarchical code structure we introduce hierarchical woven coded continuous phase frequency shift keying hierarchical wccpfsk as the serial concatenation of different outer convolutional codes and inner cpfsk we compare it to wccpfsk with identical outer convolutional codes with the proposed code combinations hierarchical wccpfsk achieves superior decoding capability simulations show that it performs better at medium snrs

serially concatenated continuous phase modulation with convolutional codes over rings in this paper we investigate serially concatenated continuous phase modulation sccpm with convolutional codes cc over rings the transmitted signals are disturbed by additive white gaussian noise the properties for systems with both infinite and finite block lengths are investigated for an infinite length system we check the convergence threshold using the extrinsic information transfer chart for a finite length system we use union bound techniques to estimate the error floors in the union bound analysis we consider both the order and the position of nonzero permuted symbols a simple method for determining a cpm error event through the sum of the input symbol sequence is shown thus we can determine if the output symbol sequence of an error event in the ring cc can form an error event in cpm two properties concerning the interleaver gain ig are investigated a recursive search algorithm for the maximal ig is shown compared with previous sccpm with a binary cc the proposed system shows an improvement concerning the convergence threshold or error floors

ricci curvature for metric measure spaces via optimal transport we dene a notion of a measured length space x having nonnegative n ricci curvature for n 2 1 1 or having1 ricci curvature bounded below byk fork2 r the denitions are in terms of the displacement convexity of certain functions on the associated wasserstein metric space p2 x of probability measures we show that these properties are preserved under measured gromov hausdor limits we give geometric and analytic consequences this paper has dual goals one goal is to extend results about optimal transport from the setting of smooth riemannian manifolds to the setting of length spaces a second goal is to use optimal transport to give a notion for a measured length space to have ricci curvature bounded below we refer to 11 and 44 for background material on length spaces and optimal transport respectively further bibliographic notes on optimal transport are in appendix f in the present introduction we motivate the questions that we address and we state the main results to start on the geometric side there are various reasons to try to extend notions of curvature from smooth riemannian manifolds to more general spaces a fairly general setting is that of length spaces meaning metric spaces x d in which the distance between two points equals the inmum of the lengths of curves joining the points in the rest of this introduction we assume that x is a compact length space alexandrov gave a good notion of a length space having curvature bounded below by k with k a real number in terms of the geodesic triangles in x in the case of a riemannian manifold m with the induced length structure one recovers the riemannian notion of having sectional curvature bounded below by k length spaces with alexandrov curvature bounded below by k behave nicely with respect to the gromovhausdor topology on compact metric spaces modulo isometries they form

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