universal space time coding a universal framework is developed for constructing full rate and full diversity coherent space time codes for systems with arbitrary numbers of transmit and receive antennas the proposed framework combines space time layering concepts with algebraic component codes optimized for single input single output siso channels each component code is assigned to a thread in the space time matrix allowing it thus full access to the channel spatial diversity in the absence of the other threads diophantine approximation theory is then used in order to make the different threads transparent to each other within this framework a special class of signals which uses algebraic number theoretic constellations as component codes is thoroughly investigated the lattice structure of the proposed number theoretic codes along with their minimal delay allow for polynomial complexity maximum likelihood ml decoding using algorithms from lattice theory combining the design framework with the cayley transform allows to construct full diversity differential and noncoherent space time codes the proposed framework subsumes many of the existing codes in the literature extends naturally to time selective and frequency selective channels and allows for more flexibility in the tradeoff between power efficiency bandwidth efficiency and receiver complexity simulation results that demonstrate the significant gains offered by the proposed codes are presented in certain representative scenarios

symbol by symbol map demodulation of cpm and psk signals on rayleigh flat fading channels demodulation using the symbol by symbol maximum a posteriori probability map algorithm is presented the algorithm is derived for the case of continuous phase modulation cpm signals transmitted over rayleigh flat fading channels and a corresponding receiver structure is specified it is shown that the map algorithm requires computing for each trellis branch the sum of the products of the weights of all paths through the trellis which pass through that branch and that this generic computational problem can be solved efficiently by an approach that uses a forward and backward recursion through the trellis simulation results are presented which show both the hard and soft decision performance of the map receiver to be robust even in the presence of fade rates of up to 30 of the symbol rate the application of the receiver concept to phase shift keying psk signals is also discussed and then evaluated via simulation the concept of joint demodulation and decoding using iterative processing techniques is introduced it is shown that the map receiver is well suited for iterative processing applications due to its use of a priori symbol probabilities and its production of optimal soft decisions simulation results for the reception of quaternary psk qpsk show that the bit error rate ber performance of the iterative map receiver can approach that of a receiver operating with perfect knowledge of the fading process

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

error probability analysis of bit interleaved coded modulation this correspondence presents a simple method to accurately compute the error probability of bit interleaved coded modulation bicm thanks to the binary input output symmetric bios nature of the channel the pairwise error probability pep is equal to the tail probability of a sum of random variables with a particular distribution this probability is in turn computed with a saddlepoint approximation its precision is numerically validated for coded transmission over standard gaussian noise and fully interleaved fading channels for both convolutional and turbo like codes

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

the fractional fourier transform and time frequency representations the functional fourier transform frft which is a generalization of the classical fourier transform was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community to which it may however be potentially useful the frft depends on a parameter spl alpha and can be interpreted as a rotation by an angle spl alpha in the time frequency plane an frft with spl alpha spl pi 2 corresponds to the classical fourier transform and an frft with spl alpha 0 corresponds to the identity operator on the other hand the angles of successively performed frfts simply add up as do the angles of successive rotations the frft of a signal can also be interpreted as a decomposition of the signal in terms of chirps the authors briefly introduce the frft and a number of its properties and then present some new results the interpretation as a rotation in the time frequency plane and the frft s relationships with time frequency representations such as the wigner distribution the ambiguity function the short time fourier transform and the spectrogram these relationships have a very simple and natural form and support the frft s interpretation as a rotation operator examples of frfts of some simple signals are given an example of the application of the frft is also given

the contourlet transform an efficient directional multiresolution image representation the limitations of commonly used separable extensions of one dimensional transforms such as the fourier and wavelet transforms in capturing the geometry of image edges are well known in this paper we pursue a true two dimensional transform that can capture the intrinsic geometrical structure that is key in visual information the main challenge in exploring geometry in images comes from the discrete nature of the data thus unlike other approaches such as curvelets that first develop a transform in the continuous domain and then discretize for sampled data our approach starts with a discrete domain construction and then studies its convergence to an expansion in the continuous domain specifically we construct a discrete domain multiresolution and multidirection expansion using nonseparable filter banks in much the same way that wavelets were derived from filter banks this construction results in a flexible multiresolution local and directional image expansion using contour segments and thus it is named the contourlet transform the discrete contourlet transform has a fast iterated filter bank algorithm that requires an order n operations for n pixel images furthermore we establish a precise link between the developed filter bank and the associated continuous domain contourlet expansion via a directional multiresolution analysis framework we show that with parabolic scaling and sufficient directional vanishing moments contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves finally we show some numerical experiments demonstrating the potential of contourlets in several image processing applications

iterative sphere detectors for imperfect channel state information this manuscript presents an iterative detector based on a generalized schnorr euchner enumeration for the case of imperfect channel state information the detector determines the most contributive n 1 2 terms in each of the two log sum exponents the objective function of the tree search is modified to account for a the channel estimation error variance and b the input a priories due to a the decomposition of the objective into the form used in conventional tree search is not possible moreover both a and b invalidate the use of the progressive zigzag order because of this a generalized schnorr euchner enumeration is proposed where explicit sorting is done unlike the conventional tree search the node weights are not computed in an additive way where the weight of a child node is the sum of the weights of the parent and the branch connecting them the advantage of the proposed detectors compared to iterative channel estimation and decoding is that the repetition of the channel estimation and the qr decomposition is not needed also since they are based on the schnorr euchner enumeration they do not require an initial radius estimation and if channel estimation errors are small enough to be ignored the search step becomes division and square root free

continuous stockwell transform coherent states and localization operators there are several methods of interest in signal analysis and image processing the most widely used are the wavelet transform the short time fourier transform the shearlet transform and the stockwell transform putting a filter in the corresponding reproducing formula one gets the well known calderon toeplitz and gabor toeplitz localization operators widely studied in the context of time scale time frequency as well as shearlet analysis using vasilevski s technique of hilbert space decomposition applied for the space of continuous stockwell transforms of l2 functions we get the structural results of the transform space and we study toeplitz operators in this context with many desirable properties of localization operators we find their unitary equivalent images for the case of separable generating symbols and show that the wick symbols for these operators are associated with a well defined calculus also certain algebras generated by these operators are described in detail thus the results

high rate concatenated space time block code m tcm designs in this paper a new technique to design improved high rate space time st codes is proposed based on the concept of concatenated st block code stbc and outer trellis coded modulation m tcm encoder constructions unlike the conventional rate lossy stbc mtcm schemes the proposed designs produce higher rate st codes by expanding the codebook of the inner orthogonal stbc the classic set partitioning concept is adopted to realize the stbc mtcm designs with large coding gains the proposed expanded stbc mtcm designs for the two three and four transmitter cases are illustrated simulation results show the proposed stbc mtcm designs significantly outperform the traditional st tcm schemes furthermore decoding complexity of the proposed scheme is low because signal orthogonality is exploited to ease data decoding

cubature formulas for the surface of the sphere null space arguments are used to derive feasible structures for integration formulas on the surface of the s dimensional sphere structures are obtained for s 3 and s 4 for formulas of degrees 3 to 17 and for general s of degrees 3 to 9 several new formulas in dimension 4 and for arbitrary dimension are constructed

optimal spherical designs and numerical integration on the sphere so called spherical t designs in three dimensional euclidean space r3 are considered it is shown that the maximal possible value of t for designs which are permuted transitively under a finite group of euclidean transformations is 9 this means that we can find a set of 60 points on the surface of the unit sphere in r3 which form an orbit under the icosahedral group such that the average of the function values at the 60 points and the average over the spherical surface are identical for all spherical harmonics of degree less than or equal to t 9 while there is no such orbit for t 10 among all 9 designs which are orbits of the icosahedral group exactly one is optimal with respect to approximation of integrals of harmonics of tenth and eleventh order this set is given in section 2 of this paper it is very well suited for numerically evaluating integrals of continuous functions over the sphere a problem occurring very often in mathematics and science as e g physics astronomy etc

on maximum likelihood detection and the search for the closest lattice point maximum likelihood ml decoding algorithms for gaussian multiple input multiple output mimo linear channels are considered linearity over the field of real numbers facilitates the design of ml decoders using number theoretic tools for searching the closest lattice point these decoders are collectively referred to as sphere decoders in the literature in this paper a fresh look at this class of decoding algorithms is taken in particular two novel algorithms are developed the first algorithm is inspired by the pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the viterbo boutros sphere decoder the connection between the proposed algorithm and the stack sequential decoding algorithm is then established this connection is utilized to construct the second algorithm which can also be viewed as an application of the schnorr euchner strategy to ml decoding aided with a detailed study of preprocessing algorithms a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near ml detection performance this claim is supported by intuitive arguments and simulation results in many relevant scenarios

resolution of the wavefront set using continuous shearlets it is known that the continuous wavelet transform of a distribution f decays rapidly near the points where f is smooth while it decays slowly near the irregular points this property allows the identification of the singular support of f however the continuous wavelet transform is unable to describe the geometry of the set of singularities of f and in particular identify the wavefront set of a distribution in this paper we employ the same framework of affine systems which is at the core of the construction of the wavelet transform to introduce the continuous shearlet transform this is defined by sh f a s t f ast where the analyzing elements ast are dilated and translated copies of a single generating function the dilation matrices form a two parameter matrix group consisting of products of parabolic scaling and shear matrices we show that the elements ast form a system of smooth functions at continuous scales a 0 locations t r 2 and oriented along lines of slope s r in the frequency domain we then prove that the continuous shearlet transform does exactly resolve the wavefront set of a distribution f

a unified framework for tree search decoding rediscovering the sequential decoder we consider receiver design for coded transmission over linear gaussian channels we restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search clps here a tree search framework for solving the clps is adopted in our framework the clps algorithm is decomposed into the preprocessing and tree search stages the role of the preprocessing stage is to expose the tree structure in a form matched to the search stage we argue that the forward and feedback matrix filters of the minimum mean square error decision feedback equalizer mmse dfe are instrumental for solving the joint detection and decoding problem in a single search stage it is further shown that mmse dfe filtering allows for solving underdetermined linear systems and using lattice reduction methods to diminish complexity at the expense of a marginal performance loss for the search stage we present a generic method based on the branch and bound bb algorithm and show that it encompasses all existing sphere decoders as special cases the proposed generic algorithm further allows for an interesting classification of tree search decoders sheds more light on the structural properties of all known sphere decoders and inspires the design of more efficient decoders in particular an efficient decoding algorithm that resembles the well known fano sequential decoder is identified the excellent performance complexity tradeoff achieved by the proposed mmse dfe fano decoder is established via simulation results and analytical arguments in several multiple input multiple output mimo and intersymbol interference isi scenarios

the generalized continuous wavelet transform associated with the fractional fourier transform the main objective of this paper is to study the fractional fourier transform frft and the generalized continuous wavelet transform and some of their basic properties applications of the frft in solving generalized nth order linear nonhomogeneous ordinary differential equations and a generalized wave equation are given the generalized continuous wavelet transform and its inversion formula and the parseval relation are also studied using the fractional fourier transform

the affine uncertainty principle in one and two dimensions abstract in this paper we construct families of wavelets that minimize an uncertainty relation associated with square integrable representations of some canonical groups especially we obtain a new interpretation of the mexican hat function

closest point search in lattices in this semitutorial paper a comprehensive survey of closest point search methods for lattices without a regular structure is presented the existing search strategies are described in a unified framework and differences between them are elucidated an efficient closest point search algorithm based on the schnorr euchner 1995 variation of the pohst 1981 method is implemented given an arbitrary point x spl isin spl ropf sup m and a generator matrix for a lattice spl lambda the algorithm computes the point of spl lambda that is closest to x the algorithm is shown to be substantially faster than other known methods by means of a theoretical comparison with the kannan 1983 1987 algorithm and an experimental comparison with the pohst 1981 algorithm and its variants such as the viterbo boutros see ibid vol 45 p 1639 42 1999 decoder modifications of the algorithm are developed to solve a number of related search problems for lattices such as finding a shortest vector determining the kissing number computing the voronoi 1908 relevant vectors and finding a korkine zolotareff 1873 reduced basis

sphere decoding complexity exponent for decoding full rate codes over the quasi static mimo channel in the setting of quasi static multiple input multiple output channels we consider the high signal to noise ratio snr asymptotic complexity required by the sphere decoding sd algorithm for decoding a large class of full rate linear space time codes with sd complexity having random fluctuations induced by the random channel noise and codeword realizations the introduced sd complexity exponent manages to concisely describe the computational reserves required by the sd algorithm to achieve arbitrarily close to optimal decoding performance bounds and exact expressions for the sd complexity exponent are obtained for the decoding of large families of codes with arbitrary performance characteristics for the particular example of decoding the recently introduced threaded cyclic division algebra based codes the only currently known explicit designs that are uniformly optimal with respect to the diversity multiplexing tradeoff the sd complexity exponent is shown to take a particularly concise form as a non monotonic function of the multiplexing gain to date the sd complexity exponent also describes the minimum known complexity of any decoder that can provably achieve a gap to maximum likelihood performance that vanishes in the high snr limit

eigenfunctions of linear canonical transform the linear canonical transform the lct is a useful tool for optical system analysis and signal processing it is parameterized by a 2 spl times 2 matrix a b c d many operations such as the fourier transform ft fractional fourier transform frft fresnel transform and scaling operations are all the special cases of the lct we discuss the eigenfunctions of the lct the eigenfunctions of the ft frft fresnel transform and scaling operations have been known and we derive the eigenfunctions of the lct based on the eigenfunctions of these operations we find for different cases that the eigenfunctions of the lct also have different forms when a d 2 the eigenfunctions become the chirp multiplication and chirp convolution of self similar functions fractals besides since many optical systems can be represented by the lct we can thus use the eigenfunctions of the lct derived in this paper to discuss the self imaging phenomena in optics we show that there are usually varieties of input functions that can cause the self imaging phenomena for an optical system

soft decision metric generation for qam with channel estimation error the channel code bit log likelihood ratio llr for soft decision decoding is derived for quadrature amplitude modulated signals qam the effect of imperfect channel knowledge on soft decision decoding performance is studied our results indicate this effect increases with channel estimation error and or qam modulation level a metric based on generalized log likelihood ratio gllr is derived for soft decision channel decoding with imperfect channel knowledge numerical results show that the gllr based metric outperforms the conventional minimum distance decoding metric that does not take into account channel estimation error

lattice integration on the 7 sphere abstract recently the 7 sphere s7 has been the subject of increased interest for mathematicians and theoretical physicists in this paper we present integration algorithms of several different orders up to 19 which require no more than a few thousand points in this respect our formulae are highly superior to standard methods e g gaussian integration or the use of spherical t designs

low complexity affine mmse detector for iterative detection decoding mimo ofdm systems iterative turbo processing between detection and decoding shows near capacity performance on a multiple antenna system combining iterative processing with optimum front end detection is particularly challenging because the front end maximum a posteriori map algorithm has a computational complexity that is exponential sub optimum detector such as the soft interference cancellation linear minimum mean square error sic lmmse detector with near front end map performance has been proposed in the literature the asymptotic computational complexity of sic lmmse is o nt 2nr ntnr 3 ntmc2mc per detection decoding cycle where nt is number of transmit antenna nr is number of receive antenna and mc is modulation size a lower complexity detector is the hard interference cancellation lmmse hic lmmse detector hic lmmse has asymptotic complexity of o nt 2nr ntmc2mc but suffers extra performance degradation in this paper two front end detection algorithms are introduced that not only achieve asymptotic computational complexity of o nt 2nr ntnr 2 gamma beta 1 ntmc2mc where gamma beta is a function with discrete output 1 2 3 nt and o ntmc2mc respectively simulation results demonstrate that the proposed low complexity detection algorithms offer exactly same performance as their full complexity counterpart in an iterative receiver while being computational more efficient

achieving a vanishing snr gap to exact lattice decoding at a subexponential complexity this study identifies the first lattice decoding solution that achieves in the general outage limited multiple input multiple output mimo setting and in the high rate and high signal to noise ratio limit both a vanishing gap to the error performance of the exact solution of regularized lattice decoding as well as a computational complexity that is subexponential in the number of codeword bits and in the rate the proposed solution employs lenstra lenstra lovasz based lattice reduction lr aided regularized lattice sphere decoding and proper timeout policies these performance and complexity guarantees hold for most mimo scenarios most fading statistics all channel dimensions and all full rate lattice codes in sharp contrast to the aforementioned very manageable complexity the complexity of other standard preprocessed lattice decoding solutions is revealed here to be extremely high specifically this study has quantified the complexity of regularized lattice sphere decoding and has proved that the computational resources required by this decoder to achieve a good rate reliability performance are exponential in the lattice dimensionality and in the number of codeword bits and it in fact matches in common scenarios the complexity of ml based sphere decoders through this sharp contrast this study was able to for the first time rigorously demonstrate and quantify the pivotal role of lr as a special complexity reducing ingredient

linear canonical stockwell transform abstract the linear canonical transform lct has long been recognized as a competent tool for optics and signal processing however the lct cannot reveal the local lct frequency contents due to its global kernel and as such makes the lct incompetent in situations demanding a joint information of time and linear canonical domain frequency in this paper we propose the linear canonical stockwell transform lcst in order to rectify the limitations of the lct and the stockwell transform st firstly we examine the resolution of the novel transform in the time and lct domains and then derive some of its basic properties such as moyal s formula inversion formula and provide a characterization of the range furthermore we derive a direct relationship between the well known wigner distribution and the proposed lcst in sequel a discrete version of the linear canonical stockwell transform is also presented finally we extend the scope of the proposed work by studying the lcst in the realm of almost periodic functions

localization of the complex spectrum the s transform the s transform which is introduced in the present correspondence is an extension of the ideas of the continuous wavelet transform cwt and is based on a moving and scalable localizing gaussian window it is shown to have some desirable characteristics that are absent in the continuous wavelet transform the s transform is unique in that it provides frequency dependent resolution while maintaining a direct relationship with the fourier spectrum these advantages of the s transform are due to the fact that the modulating sinusoids are fixed with respect to the time axis whereas the localizing scalable gaussian window dilates and translates

bounded power signal spaces for robust control and modeling the nonlinear space of signals allowing wiener s generalized harmonic analysis gha the linear bounded power signal spaces of beurling marcinkiewicz and wiener and a new linear bounded power space are studied from a control and systems theory perspective specifically it is shown that the system power gain is given by the h infty norm of the system transfer function in each of these spaces for a large class of power stable finite and infinite dimensional systems the gha setup is shown to possess several limitations for the purpose of robustness analysis which motivates the use of the other more general nonstationary signal spaces the natural double sided time axis versions of bounded power signal spaces are shown to break the symmetry between hardy space h infty methods and bounded power operators e g the system transfer function being in h infty does not imply that a causal linear time invariant lti system is bounded as an operator on any of the double sided versions of the studied bounded power signal spaces