the wssus pulse design problem in multicarrier transmission optimal link adaption to the scattering function of wide sense stationary uncorrelated scattering wssus mobile communication channels is still an unsolved problem despite its importance for next generation system design in multicarrier transmission such link adaption is performed by pulse shaping i e by properly adjusting the transmit and receive filters for example pulse shaped offset quadrature amplitude modulation oqam systems have recently been shown to have superior performance over standard cyclic prefix orthogonal frequency division multiplexing ofdm while operating at higher spectral efficiency in this paper we establish a general mathematical framework for joint transmitter and receiver pulse shape optimization for so called weyl heisenberg or gabor signaling with respect to the scattering function of the wssus channel in our framework the pulse shape optimization problem is translated to an optimization problem over trace class operators which in turn is related to fidelity optimization in quantum information processing by convexity relaxation the problem is shown to be equivalent to a convex constraint quasi convex maximization problem thereby revealing the nonconvex nature of the overall wssus pulse design problem we present several iterative algorithms for optimization providing applicable results even for large scale problem constellations we show that with transmitter side knowledge of the channel statistics a gain of 3 6 db in signal to interference and noise ratio sinr can be expected

sequential sequence estimation for channels with intersymbol interference of finite or infinite length a sequential sequence estimator for channels with finite or infinite intersymbol interference isi is proposed it consists of a whitened matched filter followed by a sequential algorithm a key component of a sequential estimator is a suitable metric that accounts for the unequal search depth this metric is derived for the isi channel computer simulations for three different channels show that the sequential sequence estimator has considerably less computational complexity than a maximum likelihood sequence estimator using the viterbi algorithm mlse va while still maintaining the optimum estimation performance of the mlse va a performance not achievable with any reduced state viterbi algorithm

difference metric viterbi decoding of multilevel class iv partial response signals the paper describes the decoding of unconstrained l ary signals l spl ges 2 transmitted over a noisy partial response channel with transfer function 1 d sup 2 signals received at even and odd sampling times are independently decoded in a pipeline fashion after stating the known results for full state maximum likelihood sequence decoding a 2 state decoding algorithm is introduced in which the difference between the metrics of the retained two most likely states is iteratively computed an analysis of its error event probability shows that two types of error events are most likely regular free distance events and induced free distance events the latter cause only a rather small degradation of error performance compared to full state decoding in addition the symbol error probability for modulo l encoded user symbols and decoding with finite decoding delay is computed the 2 state decoder can be realized for arbitrary values of l with low hardware complexity

a family of distributed space time trellis codes with asynchronous cooperative diversity in current cooperative communication schemes to achieve cooperative diversity synchronization between terminals is usually assumed which may not be practical since each terminal has its own local oscillator in this paper based on the stack construction proposed by hammons and el gamal we first construct a family of space time trellis codes for bpsk modulation scheme that is characterized to possess the full cooperative diversity order without the synchronization assumption we then generalize this family of the space time trellis codes from bpsk to higher order qam and psk modulation schemes based on the unified construction proposed by lu and kumar some diversity product properties of space time trellis codes are studied and simplified decoding methods are discussed simulation results are given to illustrate the performance of the newly proposed codes

suboptimum multiuser receivers for convolutionally coded asynchronous ds cdma systems motivated by the high complexity of the optimal sequence estimator for convolutionally coded asynchronous code division multiple access cdma systems developed by giallorenzi and wilson see ibid vol 44 no 8 p 997 1996 and the potentially poor performance of the conventional receiver due to multiuser interference and the near far problem we examine relatively simple multiuser receivers which perform nearly as well as the optimal receiver the multiuser receivers discussed are of two types the first set of approaches are partitioned approaches that treat the multiuser interference equalization problem and the decoding problem separately the second set of approaches are integrated approaches that perform both the equalization and decoding operations together we study linear decision feedback and trellis tree based approaches in each category the asymptotic efficiency of this receiver relative to an uncoded coherent binary phase shift keying bpsk receiver termed asymptotic multiuser coding gain or amcg is used as a performance criterion throughout also computer simulations are used whenever the computation of the amcg is not feasible it is shown that a number of the approaches which are introduced achieve a high performance level with a moderate complexity

temporally asymmetric learning supports sequence processing in multi winner self organizing maps we examine the extent to which modified kohonen self organizing maps soms can learn unique representations of temporal sequences while still supporting map formation two biologically inspired extensions are made to traditional soms selection of multiple simultaneous rather than single winners and the use of local intramap connections that are trained according to a temporally asymmetric hebbian learning rule the extended som is then trained with variable length temporal sequences that are composed of phoneme feature vectors with each sequence corresponding to the phonetic transcription of a noun the model transforms each input sequence into a spatial representation final activation pattern on the map training improves this transformation by for example increasing the uniqueness of the spatial representations of distinct sequences while still retaining map formation based on input patterns the closeness of the spatial representations of two sequences is found to correlate significantly with the sequences similarity the extended model presented here raises the possibility that soms may ultimately prove useful as visualization tools for temporal sequences and as preprocessors for sequence pattern recognition systems

block decision feedback equalization a natural generalization of the conventional decision feedback equalizer dfe based on block processing and maximum a posteriori decisions is presented this block dfe is indexed by two parameters depending on the block length p and the number of decisions q

pseudobinary and pseudoquaternary detection processes for linearly distorted multilevel qam signals the paper describes two new detection processes suitable for qam signals that have 16 or more levels possible data symbol values and that have been subjected to linear distortion causing severe intersymbol interference in the received signal the detectors are developments of the pseudobinary systems previously described and are designed to operate in the presence of severe intersymbol interference results of computer simulation tests are presented comparing the tolerances to additive white gaussian noise of various arrangements of each detector with those of more conventional detectors the tests have been carried out on a model of a 19 200 bit s synchronous serial data transmission system operating with a 64 level qam signal that is transmitted in turn over two different telephone circuits

delayed decision feedback sequence estimation the authors delayed decision feedback sequence estimation ddfse for uncoded pam signals is considered estimates on the performance of the algorithm are given and simulation results are provided for several examples a more general form of ddfse applicable to coded modulation systems is also presented as an example detection of trellis coded qpsk quadrature phase shift keyed signals over intersymbol interference channels is discussed

trellis coded constant envelope modulations with linear receivers we present two multilevel constant envelope continuous phase modulation cpm schemes with four dimensional 4 d trellis coding the receiver is composed of a simple quadrature demodulator followed by a symbol rate sampler and a viterbi decoder matched to the code trellis the first modulation is a quaternary cpm scheme whose phase transitions over a symbol interval are those of spl pi 4 shift quaternary phase shift keying qpsk the demodulator filter is optimized so as to minimize the combined effect of intersymbol interference isi and noise at the decision instants we use wei s 1987 16 state 4 d trellis code and redefine the set partitioning tree so as to maintain the same minimum distance between parallel transitions as in quadrature amplitude modulation qam signal sets the resulting modulation outperforms minimum shift keying msk by as much as 3 5 db in addition to reducing the 30 db signal bandwidth by 20 next we introduce an octonary 8 level cpm scheme whose phase transitions are those of spl pi 8 shift 8psk the same trellis code and receive filter optimization are also applied to this modulation which is shown to achieve better error rate performance than msk while saving some 60 of the transmitted signal bandwidth

iterative map equalization and decoding in wireless mobile coded ofdm orthogonal frequency division multiplexing ofdm system suffers extra performance degradation in fast fading channels due to intercarrier interference ici combining frequency domain equalization and bit interleaved coded modulation bicm the iterative receiver is able to harvest both temporal and frequency diversity realizing that ici channels are intrinsically isi channels this paper proposes a soft in soft out siso maximum a posteriori map equalizer by extending ungerboeck s maximum likelihood sequence estimator mlse formulation to ici channels the siso map equalizer employs bcjr algorithm and computes the bit log likelihood ratios llr for the entire received sequence by efficiently constructing a trellis that takes into account of the ici channel structure a reduced state rs formulation of the siso map equalizer which provides good performance complexity tradeoff is also described utilizing the fact that ici energy is clustered in adjacent subcarriers frequency domain equalization is made localized this paper further proposes two computational efficient linear minimum mean square error lmmse based equalization methods recursive q tap sic lmmse equalizer and recursive sliding window sw sic lmmse equalizer respectively simulations results demonstrate that the iterative siso rs map equalizer achieves the performance of no ici with normalized doppler frequency fdts up to 20 46 in realistic mobile wimax environment

blind equalization of iir channels using hidden markov models and extended least squares in this paper we present a blind equalization algorithm for noisy iir channels when the channel input is a finite state markov chain the algorithm yields estimates of the iir channel coefficients channel noise variance transition probabilities and state of the markov chain unlike the optimal maximum likelihood estimator which is computationally infeasible since the computing cost increases exponentially with data length our algorithm is computationally inexpensive our algorithm is based on combining a recursive hidden markov model hmm estimator with a relaxed spr strictly positive real extended least squares els scheme in simulation studies we show that the algorithm yields satisfactory estimates even in low snr we also compare the performance of our scheme with a truncated fir scheme and the constant modulus algorithm cma which is currently a popular algorithm in blind equalization

cochannel interference suppression through time space diversity wireless systems are subject to a time varying and unknown a priori combination of cochannel interference fading and gaussian noise it is well known that multiple antennas can provide diversity in space that allows system tradeoffs between interference suppression and mitigation of fading this paper describes how to achieve these same tradeoffs through diversity in time provided by channel coding the mathematical description of time diversity is identical to that of space diversity and what emerges is a unified framework for signal processing decoding algorithms are provided for repetition codes rate 1 n convolutional codes first order reed muller codes and a new class of linear combination codes that provide cochannel interference suppression in all cases it is possible to trade performance for complexity by choosing between joint estimation and a novel low complexity linear canceler structure that treats interference as noise this means that a single code can be used in a variety of system environments just by changing the processing in the receiver

bayesian techniques for known channel deconvolution this paper introduces a new family of deconvolution filters for digital communications subject to severe intersymbol interference these fixed lag smoothing filters for known channel demodulation are called bayesian filters bayesian filters are derived using a new approach to suboptimal recursive minimum mean square error estimation for non gaussian processes the family of bayesian filters interpolates between the optimum fixed lag linear filter i e the kalman filter and the optimum fixed lag symbol by symbol demodulator in both performance and complexity the complexity of the bayesian filter is exponential in a parameter typically chosen smaller than the channel length and the filter lag hence the bayesian filter decouples the channel length and the filter lag from the exponential complexity in these parameters found in many other high performance demodulation algorithms simulations characterize the performance and compare the bayesian filter to both optimal and reduced complexity demodulation algorithms

adaptive noncoherent dfe for mdpsk signals transmitted over isi channels a novel noncoherent decision feedback equalization ndfe scheme for m ary differential phase shift keying signals transmitted over intersymbol interference channels is presented a suboptimum version with lower computational complexity and a noncoherent linear equalizer nle are derived from the original ndfe scheme furthermore the relation of the novel nle to a previously proposed nle is investigated in contrast to known ndfe schemes the novel scheme can approach the performance of coherent minimum mean squared error decision feedback equalization for adaptation of the feedforward and feedback filters efficient novel modified least mean square and recursive least squares algorithms are presented finally it is shown that the proposed adaptive ndfe scheme is robust against frequency offset

the zeros of random polynomials further results and applications we consider the density of the zeros of random polynomials with nonzero mean correlated gaussian coefficients we show that for most communication problems the original result by hammersley 1956 can be expressed in a simpler form in order to illustrate the usefulness of the presented theory two applications are considered first the zeros of frequency selective ricean fading channels are investigated second the zeros of the transfer function corresponding to channel impulse response estimates obtained by a least squares approach are calculated for both applications implications for equalizer design are discussed

nonlinear techniques for the joint estimation of cochannel signals cochannel interference occurs when two or more signals overlap in frequency and are present concurrently unlike in spread spectrum multiple access systems where the different users necessarily share the same channel cochannel interference is a severe hindrance to frequency and time division multiple access communications and is typically minimized by interference rejection suppression techniques rather than using interference suppression we are interested in the joint estimation of the information bearing narrow band cochannel signals novel joint estimators are proposed that employ a single input demodulator with oversampling to compensate for timing uncertainties assuming finite impulse response channel characteristics maximum likelihood ml and maximum a posteriori map criteria are used to derive cochannel detectors of varying complexities and degrees of performance in particular a suboptimal two stage joint map symbol detector jmapsd is introduced that has a lower complexity than the single stage estimators while accruing only a marginal loss in error rate performance at high signal to interference ratios assuming only reliable estimates of the primary and secondary signal powers a blind adaptive jmapsd algorithm for a priori unknown channels is also derived the performance of these nonlinear joint estimation algorithms is studied through example computer simulations for two cochannel sources

multiple symbol differential detection with diversity reception in this letter we first consider the maximum likelihood sequence estimator for multiple symbol differential detection msdd over the slow fading diversity channel since this optimum decision metric results in a complex receiver implementation whose average bit error probability bep performance is difficult if not impossible to obtain analytically we then focus our attention on evaluating the average bep for msdd with diversity reception in the form of postdetection equal gain combining egc giving emphasis to its ability to bridge the gap between egc of conventional differentially detected m psk and maximal ratio combining of coherently detected m psk with differential encoding

constante de bers en genre 2 we introduce a new tool the contiguity graph which enables us to determine the bers s constant in genus two

noncoherent sequence detection new noncoherent sequence detection algorithms for combined demodulation and decoding of coded linear modulations transmitted over additive white gaussian noise channels possibly affected by intersymbol interference are presented optimal sequence detection in the presence of a random rotation of the signal phase assumed to be constant during the entire transmission requires a receiver complexity exponentially increasing with the duration of the transmission based on proper approximations simple suboptimal detection schemes based on the viterbi algorithm are presented whose performance approaches that of coherent detection in a companion paper by colavolpe and raheli see ibid vol 47 no 9 p 1303 7 1999 noncoherent sequence detection is extended to continuous phase modulations in the proposed schemes the tradeoff between complexity and performance is simply controlled by a parameter referred to as implicit phase memory and the number of states of a trellis diagram besides being realizable these schemes have the convenient feature of allowing us to remove the constant phase assumption and encompass time varying phase models the proposed schemes compare favorably with other solutions previously proposed in the technical literature

non binary and precoded faster than nyquist signaling faster than nyquist ftn signaling is an important method of narrowband coding the concept is extended here to non binary signal constellations these are much more bandwidth efficient than binary ones a powerful method of finding the minimum distance for binary and non binary ftn is presented preceding ftn transmissions with short linear filters proves to be an effective way to gain distance a shannon limit to bit error rate is derived that applies for ftn tests of an m algorithm receiver are performed and compared to this limit

estimation of co channel signals with linear complexity to increase wireless system capacity using co channel signals and multiple receiver antennas we develop the partitioned viterbi algorithm pva the pva estimation complexity increases linearly with each additional co channel signal rather than exponentially as it does with joint maximum likelihood sequence estimation mlse the estimation problem involves multiple signals simultaneously transmitted and observed through slow fading frequency selective channels although transmission is assumed to be in bursts according to a time division multiple access scheme more than one signal can occupy the same time and frequency slot these signals are referred to as co channel signals separation and estimation of the symbol bursts is accomplished by exploiting channel differences pva estimation consists of a set of viterbi detectors one per signal that operate in parallel with cross coupling to allow approximate interference cancellation by means of tentative decisions the forward filter of a decision feedback equalizer dfe is used to prefilter received signals prior to pva estimation prefiltering delays the energy of interfering signals so that tentative decisions become reliable enough to use simulation results show pva performance remains near optimal with respect to the performance of joint mlse

reduced complexity sequence estimation using state partitioning a reduced state sequence estimator rsse for linear dispersive channels is described the technique is based on partitioning the set of all channel states in a way that defines a trellis with fewer states the new technique generalizes trellises that were previously obtained by duel hallen and heegard 1989 and eyouboglu and qureshi 1988 while the approach followed by duel hallen results in powers of two state trellises the new technique generates trellises with an arbitrary number of states using the state partitioning approach one could also generalize the trellises obtained by eyouboglu therefore the approach described in this paper provides a better performance complexity tradeoff

bound intersection detection for multiple symbol differential unitary space time modulation this paper considers multiple symbol differential detection msd of differential unitary space time modulation dustm over multiple antenna systems we derive a novel exact maximum likelihood ml detector called the bound intersection detector bid using the extended euclidean algorithm for single symbol detection of diagonal constellations while the ml search complexity is exponential in the number of transmit antennas and the data rate our algorithm particularly in high signal to noise ratio achieves significant computational savings over the naive ml algorithm and the previous detector based on lattice reduction we also develop four bid variants for msd the first two are ml and use branch and bound the third one is suboptimal which first uses bid to generate a candidate subset and then exhaustively searches over the reduced space and the last one generalizes decision feedback differential detection simulation results show that the bid and its msd variants perform nearly ml but do so with significantly reduced complexity

viterbi decoding of differentially encoded psk signals transmitted over rayleigh frequency flat fading channels maximum likelihood bit detection of differentially encoded m psk signals on rayleigh fading channels is investigated it is shown that the solution to this problem can be related to previous results vitetta and taylor 1994 and leads to the implementation of a receiver structure based on the viterbi algorithm and employing per survivor processing the error rate performance of this receiver is evaluated by means of computer simulations for both trellis coded and uncoded systems

maximum likelihood sequence estimation from the lattice viewpoint considers the problem of data detection in multilevel lattice type modulation systems in the presence of intersymbol interference and additive white gaussian noise the conventional maximum likelihood sequence estimator using the viterbi algorithm has a time complexity of o m sup spl nu 1 operations per symbol and a space complexity of o spl delta m sup spl nu storage elements where m is the size of input alphabet spl nu is the length of channel memory and spl delta is the truncation depth by revising the truncation scheme and viewing the channel as a linear transform the authors identify the problem of maximum likelihood sequence estimation with that of finding the nearest lattice point from this lattice viewpoint the lattice sequence estimator for pam systems is developed which has the following desired properties 1 its expected time complexity grows as spl delta sup 2 as snr spl rarr spl infin 2 its space complexity grow as spl delta and 3 its error performance is effectively optimal for sufficiently large m a tight upper bound on the symbol error probability of the new estimator is derived and is confirmed by the simulation results of an example channel it turns out that the estimator is effectively optimal for m spl ges 4 and the loss in signal to noise ratio is less than 0 5 db even for m 2 finally limitations of the proposed estimator are also discussed

reduced complexity delayed decision algorithm for context based image processing systems it is well known that the performance of context based image processing systems can be improved by allowing the processor e g an encoder or a denoiser a delay of several samples before making a processing decision often however for such systems traditional delayed decision algorithms can become computationally prohibitive due to the growth in the size of the space of possible solutions in this paper we propose a reduced complexity one pass delayed decision algorithm that systematically reduces the size of the search space while also preserving its structure in particular we apply the proposed algorithm to two examples of adaptive context based image processing systems an image coding system that employs a context based entropy coder and a spatially adaptive image denoising system for these two types of widely used systems we show that the proposed delayed decision search algorithm outperforms instantaneous decision algorithms with only a small increase in complexity we also show that the performance of the proposed algorithm is better than that of other higher complexity delayed decision algorithms

sequential decoding of convolutional codes in channels with intersymbol interference sequential sequence estimation for communications channels with convolutionally coded input sequences and intersymbol interference isi is proposed the receiver consists of a whitened matched filter wmf and a vector sequential decoder the metric of the vector sequential algorithm sa is derived analytical results for error probability and computational complexity of the sequential decoder are presented the error probability is found to be dominated by the minimum euclidean distance between the possible output sequences and the computational distribution is pareto typical of a sequential decoder the computational cut off code rate r sub comp and its lower bound r sub comp are also derived numerical simulation results of the error probability and the computational complexity are presented comparing with the viterbi algorithm va reveals that the sa essentially has the same error performance as that of the va while its average computational complexity is one to two orders of magnitude less than that of the va

coset codes for partial response channels or coset codes with spectral nulls known coset codes are adapted for use on partial response channels or to generate signals with spectral nulls by using coset precoding and running digital sum feedback any desired tradeoff can be achieved between the power and spectra of the relevant sequences up to the optimum tradeoff possible a fundamental theorem specifying this optimum tradeoff is given a maximum likelihood sequence estimation mlse decoder for the original code may be used for the adapted code and such a decoder then attains the minimum squared distance of the original code these methods sometimes generate codes with greater minimum squared distance than that of the original code this distance can be attained by augmented decoders although such decoders inherently require long decoding delays and may be subjected to quasi catastrophic error propagation the authors conclude that at least for sequences supporting large numbers of bits per symbol coset codes can be adapted to achieve effectively the same performance and complexity on partial response channels or for sequences with spectral nulls as they do in the ordinary memoryless case

the structure and design of realizable decision feedback equalizers for iir channels with colored noise a simple algorithm for optimizing decision feedback equalizers dfes by minimizing the mean square error mse is presented a complex baseband channel and correct past decisions are assumed the dispersive channel may have infinite impulse response and the noise may be colored consideration is given to optimal realizable stable and finite lag smoothing forward and feedback filters in discrete time they are parameterized as recursive filters in the special case of transmission channels with finite impulse response and autoregressive noise the minimum mse can be attained with transversal feedback and forward filters in general the forward part should include a noise whitening filter the inverse noise model the finite realizations of the filters are calculated using a polynomial equation approach to the linear quadratic optimization problem the equalizer is optimized essentially by solving a system of linear equations ax b where a contains transfer function coefficients from the channel and noise model no calculation of correlations is required with this method a simple expression for the minimal mse is presented the dfe is compared to mse optimal linear recursive equalizers expressions for the equalizer in the limiting case of infinite smoothing lags are also discussed

joint signal detection and parameter estimation in multiuser communications the problem of simultaneously detecting the information bits and estimating signal amplitudes and phases in a k user asynchronous direct sequence spread spectrum multiple access communication system is addressed the joint maximum likelihood ml estimator has a computational complexity that is exponential in the total number of bits transmitted and thus does not represent a practical solution to the problem an estimator that combines a suboptimum tree search algorithm with a recursive least squares estimator of complex signal amplitude is considered the complexity of this estimator is o k sup 2 computations per decoded bit and its performance is very close to that of the joint ml receiver this receiver has the advantage that the transmitted signal powers and phases are extracted from the received signal in an adaptive fashion without using a test sequence

the viterbi algorithm for sparse channels this paper presents a reduced complexity viterbi algorithm for use as sequence estimator for linear intersymbol interference channels with coarsely located coefficients in particular the complexity does not depend on the channel impulse response length but only on the number of nonzero coefficients no approximations are used in the algorithm we consider a multipath environment producing time spreads

receivers with widely linear processing for frequency selective channels we propose several equalization schemes based on widely linear processing wlp the received signal and its complex conjugate are separately filtered and the results are linearly combined it is shown that wlp yields a gain in performance if the noiseless received signal can be interpreted as the convolution of a real valued data sequence and an equivalent complex valued intersymbol interference channel impulse response such a model applies to e g amplitude shift keying offset quadrature amplitude modulation and binary minimum shift keying type modulation we consider receivers without and with decision feedback finite impulse response filters are derived for these structures which are optimum with respect to the zero forcing and minimum mean squared error mmse criteria respectively in the mmse case adaptive algorithms for filter adjustment are given infinite filter orders are investigated in order to obtain analytical performance results furthermore suboptimum trellis based detection with widely linear preprocessing is briefly discussed it is demonstrated analytically and by numerical examples that widely linear schemes may outperform conventional schemes significantly depending on the considered application

signal codes convolutional lattice codes the coded modulation scheme proposed in this paper has a simple construction an integer sequence representing the information is convolved with a fixed continuous valued finite impulse response fir filter to generate the codeword a lattice point due to power constraints the code construction includes a shaping mechanism inspired by precoding techniques such as the tomlinson harashima filter we naturally term these codes convolutional lattice codes or alternatively signal codes due to the signal processing interpretation of the code construction surprisingly properly chosen short fir filters can generate good codes with large minimal distance decoding can be done efficiently by sequential decoding or for better performance by bidirectional sequential decoding error analysis and simulation results indicate that for the additive white gaussian noise awgn channel convolutional lattice codes with computationally reasonable decoders can achieve low error rate close to the channel capacity

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

a geometric parametrization for the virtual euler characteristics of the moduli spaces of real and complex algebraic curves we determine an expression 9 1x for the virtual euler characteristics of the moduli spaces of s pointed real y 1 2 and complex y 1 algebraic curves in particular for the space of real curves of genus g with a fixed point free involution we find that the euler characteristic is 2 s 1 1 29 1 g s 2 bg g where bg is the gth bernoulli number this complements the result of harer and zagier that the euler characteristic of the moduli space of complex algebraic curves is 1 s g s 2 bg g 1 g 1 the proof uses strebel differentials to triangulate the moduli spaces and some recent techniques for map enumeration to counit cells the approach involves a parameter y that permits specialization of the formula to the real and complex cases this suggests that 4 y itself may describe the euler characteristics of some related moduli spaces although we do not yet know what these spaces might be

a soft output hybrid algorithm for ml map sequence estimation the classical viterbi algorithm ml sequence estimation can be computed using a forward backward structure similar to that of the classical hidden markov model forward backward algorithm map state estimation this similarity is exploited to develop a hybrid algorithm which provides a mathematical connection between ml sequence estimation and map state estimation

computing the minimum phase filter using the ql factorization we investigate the ql factorization of a time invariant convolutive filtering matrix and show that this factorization not only provides the finite length equivalent to the minimum phase filter but also gives the associated all pass filter the convergence properties are analyzed and we derive the exact convergence rate and an upper bound for a simple single input single output system with filter length finally this upper bound is used to derive an approximation of the convergence rate for systems of arbitrary length implementation wise the method has the advantage of being numerically stable and straight forward to extend to the multiple input multiple output case furthermore due to the existence of fast ql factorization methods it is possible to compute the filters efficiently

sequence detection in nonlinear channels a convenient alternative to analog predistortion a new maximum likelihood sequence detection receiver for spectrally efficient linear modulations on bandlimited bandpass nonlinear channels is proposed the receiver is based on oversampling the received signal corrupted by noise and nonlinear distortion contrary to other solutions in the literature in the proposed technique there is no need for a bank of matched filters and the receiver front end reduces to a single lowpass filter for a given peak power level a performance gain can be achieved over more traditional approaches to transmission on nonlinear channels such as those based on predistortion if a moderate spectral expansion is allowed to analyze the receiver performance the concept of distance spectrum is employed since the minimum distance alone cannot account for a reliable performance evaluation both analysis and simulation are carried out for realistic narrowband nonlinear channels possibly employing reduced state sequence detection appreciable gain margins are confirmed to be possible in these realistic cases

harmonic maps from degenerating riemann surfaces we study harmonic maps from degenerating riemann surfaces with uniformly bounded energy and show the so called generalized energy identity we find conditions that are both necessary and sufficient for the compactness in w 1 2 and c 0 modulo bubbles of sequences of such maps

multistep detector for linear isi channels incorporating degrees of belief in past estimates this paper formulates the channel equalization problem in the framework of constrained maximum likelihood estimation this allows us to highlight key issues including the need to summarize past data and to apply a finite alphabet constraint over a sliding optimization window the approach adopted here leads to embellishments of the usual nonadaptive decision feedback equalizer and its multistep extensions it includes a provision for degrees of belief in past estimates which addresses the problem of error propagation

breadth first maximum likelihood sequence detection geometry sa b c is an algorithm penetrating a tree or trellis breadth first it performs maximum likelihood sequence detection mlsd under that structural constraint and also under the complexity constraints determined by the parameters b and c first c is the number of partitions into which the states are distributed and b denotes the number of paths in each partition recursively selecting paths which are closest to the received signal in the euclidean distance hamming distance sense guarantees constrained mlsd for the additive white gaussian binary symmetric channel the previously presented vector euclidean distance ved is an important tool for analyzing sa b c over the additive white gaussian noise awgn channel a geometric interpretation of the signals involved clarifies the basic properties of this ved and other relevant general results invariance monotonicity these results also form a basis for the construction of an algorithm for the efficient and fast calculation of minimum veds of interest for large signal to noise ratio snr detection performance this in turn reveals the necessary complexity requirements to meet specified performance requirements for concrete trellis coded systems here the simple example of convolutionally coded rate 1 2 with gray coded quaternary phase shift keying over the awgn channel is considered when c 1 and choosing b spl sim spl radic s s being the number of states in the code trellis gives the same asymptotic detection performance large snr as unconstrained mlsd e g implemented using the viterbi algorithm

on the nonexistence of completely transitive codes completely transitive codes were introduced by p sole 1990 as a special case of binary linear completely regular codes the existence of such codes is closely related to the existence of certain permutation groups the nonexistence of highly transitive permutation groups allows us to prove the nonexistence of completely transitive codes with error correcting capability greater than 4

a new framework for soft decision equalization in frequency selective mimo channels we introduce a novel framework for soft input soft output siso equalization in frequency selective multipleinput multiple output mimo channels based on the well known belief propagation bp algorithm as in the bp equalizer we model the multipath channels using factor graphs fgs where the transmitted and received signals are represented by the function and variable nodes respectively the edges connecting the function and variable nodes illustrate the dependencies of the multipath channel and soft decisions are developed by exchanging information on these edges iteratively we incorporate powerful techniques such as groupwise iterative multiuser detection imud probabilistic data association pda and sphere decoding sd in order to reduce the computational complexity of bp equalizer with relatively small degradation in performance the computational complexity of this new reduced complexity bp rcbp equalizer grows linearly with block size and memory length of the channel the proposed framework has a flexible structure that allows for parallel as well as serial detection we will illustrate through simulations that the rcbp equalizer can even handle overloaded scenarios where the channel matrix is rank deficient and it can achieve excellent performance by applying iterative equalization using the low density parity check codes ldpc

joint optimization of fir prefilter and channel estimate for sequence estimation we provide simple analytical results for the coefficients of a finite impulse response fir prefilter and the effective channel impulse response ir for use in cellular communication systems we show that using a fir filter with both causal and anticausal filter taps it is possible to find the jointly optimized impulse response such that the signal to noise ratio is maximized in the least squares sense we show via computer simulation for 8 ary phase shift keying in enhanced data rates for global evolution edge that the joint optimization of the prefilter and ir produces results similar to the minimum mean square error decision feedback equalizer prefilter in thermal noise but yields gain in colored noise

non negative matrix factorization with sparseness constraints non negative matrix factorization nmf is a recently developed technique for finding parts based linear representations of non negative data although it has successfully been applied in several applications it does not always result in parts based representations in this paper we show how explicitly incorporating the notion of sparseness improves the found decompositions additionally we provide complete matlab code both for standard nmf and for our extension our hope is that this will further the application of these methods to solving novel data analysis problems

decision feedback sequence estimation for continuous phase modulation on a linear multipath channel an approach to reduced complexity detection of partial response continuous phase modulation cpm on a linear multipath channel is presented the method referred to as decision feedback sequence estimation dfse is based on a conventional viterbi algorithm va using a reduced state trellis combined with decision feedback df by varying the number of states in the va the receiver structure can be changed gradually from a df receiver to the optimal maximum likelihood sequence estimator mlse in this way different tradeoffs between performance and complexity can be obtained results on the receiver performance based on minimum distance calculations and bit error rate simulations are given for gaussian minimum shift keying modulation on typical mobile radio channels it is shown that for channels with a long memory a significant complexity reduction can be achieved at the cost of a moderate degradation in performance

a model for learning topographically organized parts based representations of objects in visual cortex topographic nonnegative matrix factorization object representation in the inferior temporal cortex it an area of visual cortex critical for object recognition in the primate exhibits two prominent properties 1 objects are represented by the combined activity of columnar clusters of neurons with each cluster representing component features or parts of objects and 2 closely related features are continuously represented along the tangential direction of individual columnar clusters here we propose a learning model that reflects these properties of parts based representation and topographic organization in a unified framework this model is based on a nonnegative matrix factorization nmf basis decomposition method nmf alone provides a parts based representation where nonnegative inputs are approximated by additive combinations of nonnegative basis functions our proposed model of topographic nmf tnmf incorporates neighborhood connections between nmf basis functions arranged on a topographic map and attains the topographic property without losing the parts based property of the nmf the tnmf represents an input by multiple activity peaks to describe diverse information whereas conventional topographic models such as the self organizing map som represent an input by a single activity peak in a topographic map we demonstrate the parts based and topographic properties of the tnmf by constructing a hierarchical model for object recognition where the tnmf is at the top tier for learning high level object features the tnmf showed better generalization performance over nmf for a data set of continuous view change of an image and more robustly preserving the continuity of the view change in its object representation comparison of the outputs of our model with actual neural responses recorded in the it indicates that the tnmf reconstructs the neuronal responses better than the som giving plausibility to the parts based learning of the model

on the friedlander nadirashvili invariants of surfaces let m be a closed smooth manifold in 1999 friedlander and nadirashvili introduced a new differential invariant i 1 m using the first normalized nonzero eigenvalue of the lalpace beltrami operator delta g of a riemannian metric g they defined it taking the supremum of this quantity over all riemannian metrics in each conformal class and then taking the infimum over all conformal classes by analogy we use k th eigenvalues of delta g to define the invariants i k m indexed by positive integers k in the present paper the values of these invariants on surfaces are investigated we show that i k m i k mathbb s 2 unless m is a non orientable surface of even genus for orientable surfaces and k 1 this was earlier shown by petrides in fact friedlander and nadirashvili suggested that i 1 m i 1 mathbb s 2 for any surface m different from mathbb rp 2 we show that surprisingly enough this is not true for non orientable surfaces of even genus for such surfaces one has i k m i k mathbb s 2 we also discuss the connection between the friedlander nadirashvili invariants and the theory of cobordisms and conjecture that i k m is a cobordism invariant

near optimum soft decision equalization for frequency selective mimo channels in this paper we develop soft decision equalization sde techniques for frequency selective multiple input multiple output mimo channels in the quest for low complexity equalizers with error performance competitive to that of maximum likelihood ml sequence detection we demonstrate that decision feedback equalization dfe based on soft decisions expressed via the posterior probabilities associated with feedback symbols is able to outperform hard decision dfe with a low computational cost that is polynomial in the number of symbols to be recovered and linear in the signal constellation size building on the probabilistic data association pda multiuser detector we present two new mimo equalization solutions to handle the distinctive channel memory the first sde algorithm adopts a zero padded transmission structure to convert the challenging sequence detection problem into a block by block least square formulation it introduces key enhancement to the original pda to enable applications in rank deficient channels and for higher level modulations the second sde algorithm takes advantage of the toeplitz channel matrix structure embodied in an equalization problem it processes the data samples through a series of overlapping sliding windows to reduce complexity and at the same time performs implicit noise tracking to maintain near optimum performance with their low complexity simple implementations and impressive near optimum performance offered by iterative soft decision processing the proposed sde methods are attractive candidates to deliver efficient reception solutions to practical high capacity mimo systems simulation comparisons of our sde methods with minimum mean square error mmse based mimo dfe and sphere decoded quasi ml detection are presented

the viterbi algorithm and markov noise memory this work designs sequence detectors for channels with intersymbol interference isi and correlated and or signal dependent noise we describe three major contributions i first by modeling the noise as a finite order markov process we derive the optimal maximum likelihood sequence detector mlsd and the optimal maximum a posteriori map sequence detector extending to the correlated noise case the viterbi algorithm we show that when the signal dependent noise is conditionally gauss markov the branch metrics in the mlsd are computed from the conditional second order noise statistics we evaluate the branch metrics using a bank of finite impulse response fir filters ii second we characterize the error performance of the mlsd and map sequence detector the error analysis of these detectors is complicated by the correlation asymmetry of the channel noise we derive upper and lower bounds and computationally efficient approximations to these bounds based on the banded structure of the inverses of gauss markov covariance matrices an experimental study shows the tightness of these bounds iii finally we derive several classes of suboptimal sequence detectors and demonstrate how these and others available in the literature relate to the mlsd we compare their error rate performance and their relative computational complexity and show how the structure of the mlsd and the performance evaluation guide us in choosing a best compromise between several types of suboptimal sequence detectors

prefiltered space time m bcjr equalizer for frequency selective channels this paper addresses the problem of soft equalization for space time coded transmissions over frequency selective fading channels the structure of the space time code is embedded in the channel impulse response for efficient joint equalization and decoding the proposed equalization decoding approach uses a prefilter to concentrate the effective channel power in a small number of taps followed by a reduced complexity maximum a posteriori probability map equalizer decoder to produce soft decisions the prefilter introduces residual intersymbol interference which degrades the performance of map when applied to the trellis of the shortened channel however the shape of the overall shortened channel impulse response allows the m algorithm to approximate the prefiltered map performance with a small number of states based on this general framework we investigate several enhancements such as using different prefilters for the forward and backward recursions concatenating two trellis steps during decoding and temporal oversampling the performance is evaluated through simulations over the edge typical urban channel

novel reduced state bcjr algorithms bcjr algorithm is an exact and efficient algorithm to compute the marginal posterior distributions of state variables and pairs of consecutive state variables of a trellis structure due to its overwhelming complexity reduced complexity variations such as the m bcjr algorithm have been developed in this paper we propose improvements upon the conventional m bcjr algorithm based on modified active state selection criteria we propose selecting the active states based on estimates of the fixed lag smoothed distributions of the state variables we also present gaussian approximation techniques for the low complexity estimation of these fixed lag smoothed distributions the improved performance over the m bcjr algorithm is shown via computer simulations

optimal and suboptimal symbol by symbol demodulation of continuous phase modulated signals in applications requiring soft decision metrics e g systems with interleaved coded modulation symbol by symbol detection is preferred to sequence detection this paper develops the optimum soft output algorithm osa for the demodulation of continuous phase modulated cpm signals since this optimum detector is computationally complex a class of suboptimum symbol by symbol detectors called the reduced state soft output algorithm rs soa is developed by varying certain parameters the rs soa offers an effective tradeoff between performance and complexity as measured by arithmetic operation count and the number of integrators required additionally some simple complexity reduction schemes can be used in conjunction with the osa and the rs soa the properties of the osa and the rs soa and the various complexity reduction schemes are explored in an extensive simulation study

expectation propagation as turbo equalizer in isi channels in probabilistic equalization of channels with inter symbol interference the bcjr algorithm and its approximations become intractable for high order modulations even for moderate channel dispersions in this paper we introduce a novel soft equalizer to approximate the symbol a posteriori probabilities app where the expectation propagation ep algorithm is used to provide an accurate estimation this new soft equalizer is presented as a block solution denoted as block ep bep where the structure of the matrices involved is exploited to reduce the complexity order to mathcal o l n 2 i e linear in the length of the channel l and quadratic in the frame length n the solution is presented in complex valued formulation within a turbo equalization scheme this algorithm can be cast as a linear minimum mean squared error lmmse turbo equalization with double feedback architecture where constellations being discrete is a restriction exploited by the ep that provides a first refinement of the app in the experiments included the bep exhibits a robust performance regardless of the channel response with gains in the range 1 5 5 db compared with the lmmse equalization

a reduced complexity online state sequence and parameter estimator for superimposed convolutional coded signals this paper develops a reduced complexity online state sequence and parameter estimator for superimposed convolutional coded signals joint state sequence and parameter estimation is achieved by iteratively estimating the state sequence via a variable reduced complexity viterbi algorithm vrcva and the model parameters via a recursive expectation maximization em approach the vrcva is developed from a fixed reduced complexity viterbi algorithm frcva the frcva is a special case of the delayed decision feedback sequence estimation ddfse algorithm the performance of online versions of the frcva vrcva and the standard viterbi algorithm va are compared when they are used to estimate the state sequence as part of the reduced complexity online state sequence and parameter estimator

an efficient low complexity technique for mlse equalizers for linear and nonlinear channels in this paper a novel sequence equalizer which belongs to the family of cluster based sequence equalizers is presented the proposed algorithm achieves the maximum likelihood solution to the equalization problem in a fraction of computational load compared with the classic maximum likelihood sequence estimation mlse equalizers the new method does not require the estimation of the channel impulse response instead it utilizes the estimates of the cluster centers formed by the received observations furthermore a new cluster center estimation scheme which exploits the intrinsic dependencies among the cluster centers is proposed the new center estimation method exhibits enhanced performance with respect to convergence speed compared with an lms based channel estimator moreover this gain in performance is obtained at substantially lower computational load the method is also extended in order to cope with nonlinear channels the performance of the new equalizer is tested with several simulation examples using both the quadrature phase shift keying qpsk and the 16 quadrature amplitude modulated qam signaling schemes for linear and nonlinear communication channels

on the application of factor graphs and the sum product algorithm to isi channels in this paper based on the application of the sum product sp algorithm to factor graphs fgs representing the joint a posteriori probability app of the transmitted symbols we propose new iterative soft input soft output siso detection schemes for intersymbol interference isi channels we have verified by computer simulations that the sp algorithm converges to a good approximation of the exact marginal apps of the transmitted symbols if the fg has girth at least 6 for isi channels whose corresponding fg has girth 4 the application of a stretching technique allows us to obtain an equivalent girth 6 graph for sparse isi channels the proposed algorithms have advantages in terms of complexity over optimal detection schemes based on the bahl cocke jelinek raviv bcjr algorithm they also allow a parallel implementation of the receiver and the possibility of a more efficient complexity reduction the application to joint detection and decoding of low density parity check ldpc codes is also considered and results are shown for some partial response magnetic channels also in these cases we show that the proposed algorithms have a limited performance loss with respect to that can be obtained when the optimal serial bcjr algorithm is used for detection therefore for their parallel implementation they represent a favorable alternative to the modified parallel bcjr algorithm proposed in the literature for the application to magnetic channels

mmse decision feedback equalizers and coding i equalization results the minimum mean squared error decision feedback equalizer mmse dfe has properties that suggest that it is a canonical equalization structure for systems that combine equalization with coded modulation the structure and performance of the mmse dfe are succinctly derived using linear estimation theoretic principles in this first part of this two part paper the front end of the mmse dfe called the mean square whitened matched filter ms wmf is preferable in some ways to a matched filter or a whitened matched filter as a canonical receiver front end in a coded system the feedback filter of the mmse dfe may be implemented in the transmitter using precoding the mmse dfe can perform significantly better than a zero forcing decision feedback equalizer particularly at moderate to low snr s and on severe isi channels the mmse dfe is biased the optimum unbiased mmse dfe is the mmse dfe with the bias removed removing bias improves error probability but reduces the snr to snr sub mmse dfe u snr sub mmse dfe 1 it is shown that this snr relationship is a particular case of a very general result and that snr sub mmse dfe u gives a more realistic estimate of snr the results are extended to partial response equalization and to equalization with correlated inputs in an appendix

mlse and soft output equalization for trellis coded continuous phase modulation this paper presents two equalizer structures for trellis coded continuous phase modulation tc cpm on multipath fading intersymbol interference isi channels an equivalent discrete time dt model is developed by combining the tapped delay line tdl model of the frequency selective channel and by oversampling at the receiver the noninterleaved fractionally spaced maximum likelihood sequence estimation mlse equalizer performs continuous phase modulation cpm demodulation trellis coded modulation tcm decoding and channel equalization by exploiting the finite state nature of the isi corrupted tc cpm signal both simulation and analytical results show diversity like improvement when performing joint mlse decoding and equalization for the interleaved soft output equalizer the soft symbol metric is delivered to the tcm decoder by using a forward and backward recursion algorithm three variants of the soft output equalizer are examined we conclude that the backward recursion is essential to partial response cpm schemes and with moderate complexity the soft output equalizer can have a substantial advantage over a noninterleaved mlse equalizer

decision feedback differential detection in impulse radio ultra wideband systems in this paper we present decision feedback differential detection df dd schemes for autocorrelation based detection in impulse radio ultra wideband ir uwb systems a signaling scheme regarded as a promising candidate in particular for low complexity wireless sensor networks to this end we first discuss ideal noncoherent sequence estimation and approximations thereof based on block wise multiple symbol differential detection msdd and the viterbi algorithm va from the perspective of tree search trellis decoding exploiting relations well known from tree search decoding we are able to derive the novel decision feedback differential detection df dd schemes a comprehensive comparison with respect to performance and complexity of the presented schemes in a typical ir uwb scenario reveals along with novel insights in techniques for complexity reduction of the sphere decoder applied for msdd that sorted df dd achieves close to optimum performance at very low and in particular constant receiver complexity

vector coding for partial response channels a linear technique for combining equalization and coset codes on partial response channels with additive white gaussian noise is developed the technique vector coding uses a set of transmit filters or vectors to partition the channel into an independent set of parallel intersymbol interference isi free channels for any given finite or infinite block length the optimal transmit vectors for such channel partitioning are shown to be the eigenvectors of the channel covariance matrix for the specified block length and the gains of the individual channels are the eigenvalues an optimal bit allocation and energy distribution are derived for the set of parallel channels under an accurate extension of the continuous approximation for power in optimal multidimensional signal sets for constellations with unequal signal spacing in different dimensions examples are presented that demonstrate performance advantages with respect to zero forcing decision feedback methods that use the same coset code on the same partial response channel only resampling the channel at an optimal rate and assuming no errors in the feedback path will bring the performance of the decision feedback methods up to the level of the vector coded system

learning sparse representations by non negative matrix factorization and sequential cone programming we exploit the biconvex nature of the euclidean non negative matrix factorization nmf optimization problem to derive optimization schemes based on sequential quadratic and second order cone programming we show that for ordinary nmf our approach performs as well as existing state of the art algorithms while for sparsity constrained nmf as recently proposed by p o hoyer in jmlr 5 2004 it outperforms previous methods in addition we show how to extend nmf learning within the same optimization framework in order to make use of class membership information in supervised learning problems

realizable minimum mean squared error channel shorteners we present an analysis of realizable i e causal stable and of finite degree minimum mean squared error mmse channel shorteners for multiple input multiple output mimo systems driven by spatially and temporally white signals and subject to a constant output power constraint this is of interest since this design has recently been shown to result in near optimal rate performance in multitone transceivers and the performance of conventional finite impulse response fir shorteners is upper bounded by that of realizable schemes the mmse shortener is shown to consist of a prewhitening filter followed by an fir postfilter of order equal to the sum of the overall delay and the target shortening length it is shown that this design results in output decorrelation and that the shortener output enjoying the smallest mmse sees a target impulse response without zeros inside the unit disk the asymptotic behavior of the shortened system is explored and performance bounds are provided in terms of the channel frequency response and the noise power spectral density

noncoherent sequence detection of differential space time modulation approximate maximum likelihood noncoherent sequence detection nsd for differential space time modulation dstm in time selective fading channels is proposed the starting point is the optimum multiple symbol differential detection for dstm that is characterized by exponential complexity by truncating the memory of the incremental metric a finite state trellis is obtained so that a viterbi algorithm can be implemented to perform sequence detection compared to existing linear predictive receivers a distinguished feature of nsd is that it can accommodate nondiagonal constellations in continuous fading error analysis demonstrates that significant improvement in performance is achievable over linear prediction receivers by incorporating the reduced state sequence detection techniques performance and complexity tradeoffs can be controlled by the branch memory and trellis size numerical results show that most of the performance gain can be achieved by using an l state trellis where l is the size of the dstm constellation

an efficient dfe a ml suboptimum receiver for data transmission over dispersive channels using two dimensional signal constellations the dfe ml receiver is presented for data transmission systems using qam modulation a substantial improvement in performance results as compared to other one or two stage receiver structures at relatively low computational complexity

breadth first maximum likelihood sequence detection basics the problem of performing breadth first maximum likelihood sequence detection mlsd under given structural and complexity constraints is solved and results in a family of optimal detectors given a trellis with s states these are partitioned into c classes where b paths into each class are selected recursively in each symbol interval the derived result is to retain only those paths which are closest to the received signal in the euclidean hamming distance sense each member in the sa b c family of sequence detectors sa denotes search algorithm performs complexity constrained mlsd for the additive white gaussian noise awgn bsc channel the unconstrained solution is the viterbi algorithm va analysis tools are developed for each member of the sa b c class and the asymptotic snr probability of losing the correct path is associated with a new euclidean distance measure for the awgn case the vector euclidean distance ved the traditional euclidean distance is a scalar special case of this termed the scalar euclidean distance sed the generality of this ved is pointed out some general complexity reductions exemplify those associated with the va approach

topographic independent component analysis in ordinary independent component analysis the components are assumed to be completely independent and they do not necessarily have any meaningful order relationships in practice however the estimated independent components are often not at all independent we propose that this residual dependence structure could be used to define a topographic order for the components in particular a distance between two components could be defined using their higher order correlations and this distance could be used to create a topographic representation thus we obtain a linear decomposition into approximately independent components where the dependence of two components is approximated by the proximity of the components in the topographic representation

range of the first two eigenvalues of the laplacian for each planar domain d of unit area the first two dirichlet eigenvalues of on d determine a point 1 d 2 d in the 1 2 plane as d varies over all such domains this point varies over a set r which we determine its boundary consists of two semi infinite straight lines and a curve connecting their endpoints this curve is found numerially we also show how to minimize the n th eigenvalue when the minimizing domain is diconnected for n 3 we show that the minimizing domain is connected and that 3 is a local minimum for d a circular disc

reduced state sequence estimation with set partitioning and decision feedback a reduced state sequence estimator for linear intersymbol interference channels is described the estimator uses a conventional viterbi algorithm with decision feedback to search a reduced state subset trellis that is constructed using set partitioning principles the complexity of maximum likelihood sequence estimation mlse due to the length of the channel memory and the size of the signal set is systematically reduced an error probability analysis shows that a good performance complexity tradeoff can be obtained in particular the results indicate that the required complexity to achieve the performance of mlse is independent of the size of the signal set for large enough signal sets simulation results are provided for two partial response systems a simple technique for quadrature partial response signaling qprs is described that eliminates the quasicatastrophic nature of the ml trellis

expectation maximization algorithms for map estimation of jump markov linear systems in a jump markov linear system the state matrix observation matrix and the noise covariance matrices evolve according to the realization of a finite state markov chain given a realization of the observation process the aim is to estimate the state of the markov chain assuming known model parameters computing conditional mean estimates is infeasible as it involves a cost that grows exponentially with the number of observations we present three expectation maximization em algorithms for state estimation to compute maximum a posteriori map state sequence estimates which are also known as bayesian maximum likelihood state sequence estimates mlses the first em algorithm yields the map estimate for the entire sequence of the finite state markov chain the second em algorithm yields the map estimate of the continuous state of the jump linear system the third em algorithm computes the joint map estimate of the finite and continuous states the three em algorithms optimally combine a hidden markov model hmm estimator and a kalman smoother ks in three different ways to compute the desired map state sequence estimates unlike the conditional mean state estimates which require computational cost exponential in the data length the proposed iterative schemes are linear in the data length

reduced complexity detection and phase synchronization of cpm signals based on an extension of laurent 1986 decomposition of continuous phase modulation cpm signals into a sum of linearly modulated components we derive a class of reduced complexity maximum likelihood ml coherent detection and closed loop phase synchronization schemes the complexity of the resulting detection schemes expressed in terms of the number of matched filters and states of a viterbi algorithm is significantly reduced with respect to that of optimal coherent receivers with negligible performance loss this result extends a known one valid for the binary case to multilevel cpm the proposed synchronization schemes do not require an increased number of matched filters and are perfectly suitable to be used in conjunction with these receivers based on the phase locked loop pll equivalent linear model a method for optimizing the parameters of digital second order pll s is presented numerical examples based on theoretical analysis and computer simulation are provided for two specific formats in the cpm class tamed frequency modulation tfm and a quaternary raised cosine rc modulation

frequency hopped spread spectrum transmission with band efficient modulations and simplified noncoherent sequence estimation frequency hopped spread spectrum transmission using band efficient modulations that are phase continuous during each hop is presented a range of system parameters is considered including signaling spectrum reception system complexity and performance in the presence of noise and jamming the particular cases where the hopped modulation is minimum shift keying msk duobinary minimum shift keying dmsk or tamed fm tfm are studied in detail results are presented for various modulation indexes rectangular and raised cosine pulse shapings and a range of hop interval lengths sequence estimation on a hop by hop basis is considered the noncoherent likelihood sequence receiver must keep all possible paths and so the computation and complexity becomes large for system transmitting many bits per hop therefore a simplified noncoherent viterbi like sequence estimation algorithm with reduced complexity is introduced system performance has been evaluated in gaussian noise partial band jamming and multiple tone jamming using bounds and a system simulation the compact nature of the hopped spectrum when a number of bits are transmitted per hop offers greater spectrum utilization and the prospect of improved performance in the presence of multiple tone jamming or interference

on line estimation of hidden markov model parameters based on the kullback leibler information measure sequential or online hidden markov model hmm signal processing schemes are derived and their performance is illustrated by simulation the online algorithms are sequential expectation maximization em schemes and are derived by using stochastic approximations to maximize the kullback leibler information measure the schemes can be implemented either as filters or fixed lag or sawtooth lag smoothers they yield estimates of the hmm parameters including transition probabilities markov state levels and noise variance in contrast to the offline em algorithm baum welch scheme which uses the fixed interval forward backward scheme the online schemes have significantly reduced memory requirements and improved convergence and they can estimate hmm parameters that vary slowly with time or undergo infrequent jump changes similar techniques are used to derive online schemes for extracting finite state markov chains imbedded in a mixture of white gaussian noise wgn and deterministic signals of known functional form with unknown parameters