on the kz reduction the korkine zolotareff kz reduction is one of the often used reduction strategies for lattice decoding in this paper we first investigate some important properties of kz reduced matrices specifically we present a linear upper bound on the hermit constant which is around 7 8 times of the existing sharpest linear upper bound and an upper bound on the kz constant which is polynomially smaller than the existing sharpest one we also propose upper bounds on the lengths of the columns of kz reduced matrices and an upper bound on the orthogonality defect of kz reduced matrices which are even polynomially and exponentially smaller than those of boosted kz reduced matrices respectively then we derive upper bounds on the magnitudes of the entries of any solution of a shortest vector problem svp when its basis matrix is lll reduced these upper bounds are useful for analyzing the complexity and understanding numerical stability of the basis expansion in a kz reduction algorithm finally we propose a new kz reduction algorithm by modifying the commonly used schnorr euchner search strategy for solving svps and the basis expansion method proposed by zhang et al simulation results show that the new kz reduction algorithm is much faster and more numerically reliable than the kz reduction algorithm proposed by zhang et al especially when the basis matrix is ill conditioned

on optimal multilayer cyclotomic space time code designs high rate and large diversity product or coding advantage or coding gain or determinant distance or minimum product distance are two of the most important criteria often used for good space time code designs in recent linear lattice based space time code designs more attention is paid to the high rate criterion but less to the large diversity product criterion in this paper we consider these two criteria together for multilayer cyclotomic space time code designs in a previous paper we recently proposed a systematic cyclotomic diagonal space time code design over a general cyclotomic number ring that has infinitely many designs for a fixed number of transmit antennas where diagonal codes correspond to single layer codes in this paper in this paper we first propose a general multilayer cyclotomic space time codes we present a general optimality theorem for these infinitely many cyclotomic diagonal or single layer space time codes over general cyclotomic number rings for a general number of transmit antennas we then present optimal multilayer full rate cyclotomic space time code designs for two and three transmit antennas we also present an optimal two layer cyclotomic space time code design for three and four transmit antennas the optimality here is in the sense that for a fixed mean transmission signal power its diversity product is maximized or equivalently for a fixed diversity product its mean transmission signal power is minimized it should be emphasized that all the optimal multilayer cyclotomic space time codes presented in this paper have the nonvanishing determinant property

faster recursions in sphere decoding most of the calculations in standard sphere decoders are redundant in the sense that they either calculate quantities that are never used or calculate some quantities more than once a new method which is applicable to lattices as well as finite constellations is proposed to avoid these redundant calculations while still returning the same result pseudocode is given to facilitate immediate implementation simulations show that the speed gain with the proposed method increases linearly with the lattice dimension at dimension 60 the new algorithms avoid about 75 of all floating point operations

sparse grid quadrature nonlinear filtering in this paper a novel nonlinear filter named sparse grid quadrature filter sgqf is proposed the filter utilizes weighted sparse grid quadrature points to approximate the multi dimensional integrals in the nonlinear bayesian estimation algorithm the locations and weights of the univariate quadrature points with a range of accuracy levels are determined by the moment matching method then the univariate quadrature point sets are extended to form a multi dimensional grid using the sparse grid theory compared with the conventional point based methods the estimation accuracy level of the sgqf can be flexibly controlled and the number of sparse grid quadrature points for the sgqf is a polynomial of the dimension of the system which alleviates the curse of dimensionality for high dimensional problems the unscented kalman filter ukf is proven to be a subset of the sgqf at the level 2 accuracy the performance of this filter is demonstrated by an orbit estimation problem the simulation results show that the sgqf achieves higher accuracy than the extended kalman filter ekf the ukf and the cubature kalman filter ckf in addition the sgqf is computationally much more efficient than the multi dimensional gauss hermite quadrature filter ghqf with the same performance

the cardinality balanced multi target multi bernoulli filter and its implementations it is shown analytically that the multitarget multibernoulli member recursion proposed by mahler has a significant bias in the number of targets to reduce the cardinality bias a novel multibernoulli approximation to the multi target bayes recursion is derived under the same assumptions as the member recursion the proposed recursion is unbiased in addition a sequential monte carlo smc implementation for generic models and a gaussian mixture gm implementation for linear gaussian models are proposed the latter is also extended to accommodate mildly nonlinear models by linearization and the unscented transform

a multiple detection probability hypothesis density filter most conventional target tracking algorithms assume that one target can generate at most one detection per scan however in many practical target tracking applications one target may generate multiple detections in one scan because of multipath propagation or high sensor resolution or some other reason if the multiple detections from the same target can be effectively utilized the performance of the multitarget tracking system can be improved however the challenge is that the uncertainty in the number of targets and the measurement set to target association will increase the complexity of tracking algorithms to solve this problem the random finite set rfs modeling and the random finite set statistics fisst are used in this paper without any extra approximation beyond those made in the standard probability hypothesis density phd filter a general multi detection phd md phd update formulation is derived it is also established in this paper that with certain reasonable assumptions the proposed md phd recursion can function as a generalized extended target phd or multisensor phd filter furthermore a gaussian mixture gm implementation of the proposed md phd formulation called the md gm phd filter is presented the proposed md gm phd filter is demonstrated on a simulated over the horizon radar othr scenario

a newborn track detection and state estimation algorithm using bernoulli random finite sets in multi target tracking mtt problems there are many important issues that affect performance including statistical filtering measurement target association and estimating the number of targets while newborn target detection and state estimation should also be considered as important factors in mtt only a few studies have addressed these topics in this paper a novel newborn track detection and state estimation method is proposed using the concept of bernoulli random finite sets the posterior finite set statistical probability density function fisst pdf of a newborn target is analytically derived and a tractable implementation scheme is proposed using importance sampling finally the validity of the proposed method is demonstrated via integration with a gaussian mixture probability hypothesis density gm phd filter and subsequent application to mtt problems

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

soft input soft output single tree search sphere decoding soft input soft output siso detection algorithms form the basis for iterative decoding the computational complexity of siso detection often poses significant challenges for practical receiver implementations in particular in the context of multiple input multiple output mimo wireless communication systems in this paper we present a low complexity siso sphere decoding algorithm based on the single tree search paradigm proposed originally for soft output mimo detection in studer soft output sphere decoding algorithms and vlsi implementation ieee j sel areas commun vol 26 no 2 pp 290 300 feb 2008 the new algorithm incorporates clipping of the extrinsic log likelihood ratios llrs into the tree search which results in significant complexity savings and allows to cover a large performance complexity tradeoff region by adjusting a single parameter furthermore we propose a new method for correcting approximate llrs resulting from sub optimal detectors which often significantly improves detection performance at low additional computational complexity

perturbation analysis of the qr factor r in the context of lll lattice basis reduction in 1982 arjen lenstra hendrik lenstra jr and laszlo lovasz introduced an efficiently computable notion of reduction of basis of a euclidean lattice that is now commonly referred to as lll reduction the precise definition involves the r factor of the qr factorisation of the basis matrix a natural mean of speeding up the lll reduction algorithm is to use a floating point approximation to the r factor in the present article we investigate the accuracy of the factor r of the qr factorisation of an lll reduced basis our main contribution is the first fully rigorous perturbation analysis of the r factor of lll reduced matrices under column wise perturbations our results should be very useful to devise lll type algorithms relying on floating point approximations

integrability of the boundary sine gordon model we construct a boundary lagrangian for the supersymmetric sine gordon model which preserves b type supersymmetry and integrability to all orders in the bulk coupling constant g the supersymmetry constraint is expressed in terms of matrix factorizations

fundamental properties and performance of conventional bearings only target motion analysis this paper considers the problem of estimating the position and velocity of an object from noise corrupted bearing measurements obtained by a single moving observation platform the process is inherently nonlinear and exhibits unusual observability properties that are geometry dependent a maximum likelihood estimate mle of the target motion analysis solution is developed and its performance analyzed a comparison is drawn between the mle and two previously reported methods a nonlinear modified instrumental variable estimate miv and the pseudo linear estimate ple both the miv and ple are shown to derive from approximations to the nonlinear measurement equation and therefore share some common properties with the mle the limits on performance that can be expected from processing bearing data are detailed specifically for long range to baseline geometries approximate expressions for the cramer rao bound are derived extension of the results to the practical filters approximately predicts numerically observed behavior for less restrictive geometries bounds are presented incorporation of a target speed constraint on the mle results in a transition to a lower dimensional problem as noise level and range increases monte carlo experimental results are presented and the improvements realized by the mle techniques are evident

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

derivation of the phd and cphd filters based on direct kullback leibler divergence minimization in this paper we provide novel derivations of the probability hypothesis density phd and cardinalised phd cphd filters without using probability generating functionals or functional derivatives we show that both the phd and cphd filters fit in the context of assumed density filtering and implicitly perform kullback leibler divergence kld minimizations after the prediction and update steps we perform the kld minimizations directly on the multitarget prediction and posterior densities

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

sphere constrained ml detection for frequency selective channels the maximum likelihood ml sequence detection problem for channels with memory is investigated the viterbi algorithm va provides an exact solution its computational complexity is linear in the length of the transmitted sequence but exponential in the channel memory length on the other hand the sphere decoding sd algorithm also solves the ml detection problem exactly and has expected complexity which is a low degree polynomial often cubic in the length of the transmitted sequence over a wide range of signal to noise ratios we combine the sphere constrained search strategy of sd with the dynamic programming principles of the va the resulting algorithm has the worst case complexity determined by the va but often significantly lower expected complexity

minkowski s convex body theorem and integer programming the paper presents an algorithm for solving integer programming problems whose running time depends on the number n of variables as non this is done by reducing an n variable problem to 2n5i 2 problems in n i variables for some i greater than zero chosen by the algorithm the factor of on5 2 per variable improves the best previously known factor which is exponential in n minkowski s convex body theorem and other results from geometry of numbers play a crucial role in the algorithm several related algorithms for lattice problems are presented the complexity of these problems with respect to polynomial time reducibilities is studied

reduced and fixed complexity variants of the lll algorithm for communications the lenstra lenstra lovasz lll algorithm is a popular lattice reduction algorithm in communications in this paper variants of the lll algorithm with either reduced or fixed complexity are proposed and analyzed specifically the use of effective lll reduction for lattice decoding is presented where size reduction is only performed for pairs of consecutive basis vectors its average complexity measured by the number of floating point operations and averaged over i i d standard normal lattice bases is shown to be o n 3 log n where n is the lattice dimension this average complexity is an order lower than previously thought to address the issue of variable complexity of the lll algorithm two fixed complexity approximations are proposed one is fixed complexity effective lll for which the first vector of the basis is proven to be bounded in length the other is fixed complexity lll with deep insertion which is shown to be closely related to the well known v blast algorithm such fixed complexity structures are much desirable in hardware implementation since they allow straightforward constant throughput implementation

on full diversity space time block codes with partial interference cancellation group decoding in this paper we propose a partial interference cancellation pic group decoding strategy scheme for linear dispersive space time block codes stbc and a design criterion for the codes to achieve full diversity when the pic group decoding is used at the receiver a pic group decoding decodes the symbols embedded in an stbc by dividing them into several groups and decoding each group separately after a linear pic operation is implemented it can be viewed as an intermediate decoding between the maximum likelihood ml receiver that decodes all the embedded symbols together i e all the embedded symbols are in a single group and the zero forcing zf receiver that decodes all the embedded symbols separately and independently i e each group has and only has one embedded symbol after the zf operation is implemented the pic group decoding provides a framework to adjust the complexity performance tradeoff by choosing the sizes of the information symbol groups our proposed design criterion group independence for the pic group decoding to achieve full diversity is an intermediate condition between the loosest ml full rank criterion of codewords and the strongest zf linear independence condition of the column vectors in the equivalent channel matrix we also propose asymptotic optimal ao group decoding algorithm which is an intermediate decoding between the mmse decoding algorithm and the ml decoding algorithm the design criterion for the pic group decoding can be applied to the ao group decoding algorithm because of its asymptotic optimality it is well known that the symbol rate for a full rank linear stbc can be full i e nt for nt transmit antennas it has been recently shown that its rate is upper bounded by 1 if a code achieves full diversity with a linear receiver the intermediate criterion proposed in this paper provides the possibility for codes of rates between nt and 1 that achieve full diversity with the pic group decoding this therefore provides a complexity performance rate tradeoff some design examples are given

maximum likelihood sequence estimators a geometric view communication issues are described in terms of macro operations between the data and the observation spaces the problem of recovering the data is related to the inversion of an operator the channel mapping for this reason results available in linear algebra and functional analysis are applicable traditional concepts in communications are identified with these operations an approach to the maximum likelihood sequence estimator based on a sufficient statistic derived from these concepts is proposed intersymbol interference is removed by linear equalization and a viterbi like dynamic programming algorithm takes into account the correlated noise in the metric evaluation the performance of suboptimal receivers obtained by means of metric simplification is analyzed

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

quasi maximum likelihood detector based on geometrical diversification greedy intensification this letter proposes a quasi optimum maximum likelihood detection technique based on geometrical diversification and greedy intensification gdgi the presented detector scheme is shown to achieve almost optimal performance for all signal to noise ratio snr values and a cubic computation complexity in the problem dimension it possesses a regular structure well suited for hardware implementation simulation results show that for a system with a high dimension of n 60 the loss is approximately 0 35 db at ber 10 5 compared to an optimal decoding

the gaussian mixture probability hypothesis density filter a new recursive algorithm is proposed for jointly estimating the time varying number of targets and their states from a sequence of observation sets in the presence of data association uncertainty detection uncertainty noise and false alarms the approach involves modelling the respective collections of targets and measurements as random finite sets and applying the probability hypothesis density phd recursion to propagate the posterior intensity which is a first order statistic of the random finite set of targets in time at present there is no closed form solution to the phd recursion this paper shows that under linear gaussian assumptions on the target dynamics and birth process the posterior intensity at any time step is a gaussian mixture more importantly closed form recursions for propagating the means covariances and weights of the constituent gaussian components of the posterior intensity are derived the proposed algorithm combines these recursions with a strategy for managing the number of gaussian components to increase efficiency this algorithm is extended to accommodate mildly nonlinear target dynamics using approximation strategies from the extended and unscented kalman filters

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

the spline probability hypothesis density filter the probability hypothesis density phd filter is a multitarget tracker that can alleviate the computational intractability of the optimal multitarget bayes filter the phd filter recursively estimates the number of targets and their phd from a set of observations and works well in scenarios with false alarms and missed detections two distinct phd filter implementations are available in the literature the sequential monte carlo probability hypothesis density smc phd and the gaussian mixture probability hypothesis density gm phd filters while particle based phd implementations may suffer from degeneracy gm based methods may not be suitable for highly nonlinear non gaussian systems this paper proposes a b spline based spline probability hypothesis density sphd filter which has the capability to better approximate any arbitrary probability density function the resulting algorithm can handle linear non linear gaussian and non gaussian models the sphd filter can provide continuous estimates of the probability density function of the system state and it is immune to the degeneracy problem the sphd filter can maintain highly accurate tracks by taking advantage of dynamic knot movement but at the expense of higher computational complexity which makes it suitable for tracking a few high value targets under difficult conditions the sphd filter derivations and simulations are provided in this paper

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