carrier phase and frequency estimation bounds for transmissions with embedded reference symbols the true crame spl acute r rao lower bound crlb for the joint estimation of carrier phase and frequency is derived for transmission bursts with interleaved reference and phase shift keying quadrature amplitude modulated data symbols results are presented for the special cases of midamble and preamble and postamble pilot symbol insertion the derivation reveals that the crlb is a function of the location of the reference symbols in the burst the number of reference symbols the number of data symbols the signal to noise ratio and the data modulation scheme by distributing the reference symbols symmetrically about the center of the burst and analyzing relative to the middle of the signal vector the joint frequency and phase estimation can be decoupled and the optimal phase estimation is achieved in the decoupled case the phase crlb is independent of the location of reference symbols in the burst in a symmetrical burst the use of a preamble and postamble is found to provide a lower frequency estimation crlb than that with a midamble it appears that the frequency crlb is reduced as the reference symbols are symmetrically distributed closer to the ends of the burst

pilot symbol assisted and code aided phase error estimation for high order qam transmission in this paper we present a novel phase error estimation scheme for low density parity check ldpc coded high order quadrature amplitude modulation qam transmission systems and we provide a theoretical analysis of its performance the scheme uses known pilot symbols which are assumed to be placed at equally spaced positions and phase errors occurred at these pilot symbol positions are first estimated they are then interpolated over the other positions by using a wiener filter wf and estimation accuracy is next refined by using an ldpc code aided phase locked loop pll we present an efficient implementation of this two stage pilot symbol assisted and code aided psa ca scheme and evaluate its performance by means of power spectrum analysis we determine the mean square error at each step of the psa ca scheme and we find an optimal value of the noise equivalent loop bandwidth of the pll under the assumption that local oscillator phase noise can be modeled as a single pole single zero model we show through simulations that the psa ca scheme has a very high phase noise tolerance comparable to that of state of the art phase estimation schemes and provides a computationally efficient alternative

low complexity frequency estimation using multiple disjoint pilot blocks in burst mode communications two low complexity data aided frequency estimators suitable for use in burst mode communications are described and analyzed the estimators are based on pilot symbols organized into disjoint blocks embedded in the burst the first estimator is a generalization of the phase increment frequency estimation technique and the second estimator is a generalization of the autocorrelation frequency estimation technique the generalizations are needed to account for the spacings between the pilot blocks it is shown that the frequency estimators exhibit good accuracy while maintaining useful operating ranges

a geometric treatment of implicit differential algebraic equations abstract a differential geometric approach for proving the existence and uniqueness of implicit differential algebraic equations is presented it provides for a significant improvement of an earlier theory developed by the authors as well as for a completely intrinsic definition of the index of such problems the differential algebraic equation is transformed into an explicit ordinary differential equation by a reduction process that can be abstractly defined for specific submanifolds of tangent bundles here called reducible submanifolds local existence and uniqueness results for differential algebraic equations then follow directly from the final stage of this reduction by means of an application of the standard theory of ordinary differential equations

on the computation of impasse points of quasi linear differential algebraic equations abstract we present computational algorithms for the calculation of impasse points and higher order singularities in quasilinear differential algebraic equations our method combines a reduction step transforming the dae into a singular ode with an augmentation procedure inspired by numerical bifurcation theory singularities are characterized by the vanishing of a scalar quantity that may be monitored along any trajectory two numerical examples with physical relevance are given

phase noise in mimo systems bayesian cramer rao bounds and soft input estimation this paper addresses the problem of estimating time varying phase noise caused by imperfect oscillators in multiple input multiple output mimo systems the estimation problem is parameterized in detail and based on an equivalent signal model its dimensionality is reduced to minimize the overhead associated with phase noise estimation new exact and closed form expressions for the bayesian cramer rao lower bounds bcrlbs and soft input maximum a posteriori map estimators for online i e filtering and offline i e smoothing estimation of phase noise over the length of a frame are derived simulations demonstrate that the proposed map estimators mean square error mse performances are very close to the derived bcrlbs at moderate to high signal to noise ratios to reduce the overhead and complexity associated with tracking the phase noise processes over the length of a frame a novel soft input extended kalman filter ekf and extended kalman smoother eks that use soft statistics of the transmitted symbols given the current observations are proposed numerical results indicate that by employing the proposed phase tracking approach the bit error rate performance of a mimo system affected by phase noise can be significantly improved in addition simulation results indicate that the proposed phase noise estimation scheme allows for application of higher order modulations and larger numbers of antennas in mimo systems that employ imperfect oscillators

the modified cramer rao bound in vector parameter estimation in this paper we extend the scalar modified cramer rao bound mcrb to the estimation of a vector of nonrandom parameters in the presence of nuisance parameters the resulting bound is denoted with the acronym mcrvb where v stands for vector as with the scalar bound the mcrvb is generally looser than the conventional crvb but the two bounds are shown to coincide in some situations of practical interest the mcrvb is applied to the joint estimation of carrier frequency phase and symbol epoch of a linearly modulated waveform corrupted by correlated impulsive noise encompassing white gaussian noise as a particular case wherein data symbols and noise power are regarded as nuisance parameters in this situation calculation of the conventional crvb is infeasible while application of the mcrvb leads to simple useful expressions with moderate analytical effort when specialized to the case of white gaussian noise the mcrvb yields results already available in the literature in fragmentary form and simplified contexts

adaptive iterative detectors for phase uncertain channels via variational bounding the problem of iterative detection decoding of data symbols transmitted over an additive white gaussian noise awgn channel in the presence of phase uncertainty is addressed in this paper by modelling the phase uncertainty either as an unknown deterministic variable process or random variable process with a known a priori probability density function a number of non bayesian and bayesian detection algorithms with various amount of suboptimality have been proposed in the literature to solve the problem in this paper a new set of suboptimal iterative detection algorithms is obtained by utilizing the variational bounding technique especially applying the generic variational bayesian vb framework efficient iterative joint estimation and detection decoding schemes are derived for the constant phase model as well as for the dynamic phase model in addition the relation of the vb based approach to the optimal noncoherent receiver as well as to the classical approach via the expectation maximization em algorithm is provided performance of the proposed detectors in the presence of a strong dynamic phase noise is compared to the performance of the existing detectors furthermore an incremental scheduling of the vb or em algorithm is shown to reduce the overall complexity of the receiver

block processing soft input soft output demodulator for coded psk using dct based phase noise estimation this paper considers the detection of coded phaseshift keying signals subjected to additive white gaussian noise and oscillator phase noise we propose a detector that partitions the received frame into smaller blocks and models the unknown phasor variations over each block as a truncated discrete cosine transform dct expansion detection and decoding are iteratively performed between a soft input soft output siso demodulator a siso demapper and a siso decoder based on the sum product algorithm and the factor graph framework whereas the expectation maximization algorithm is used in the demodulator for the dct coefficients estimation the resulting demodulator is shown to have an excellent performance complexity tradeoff and to be well suited for parallel processing on multiple cores

solvability of general differential algebraic equations in the last few years there has been considerable research on differential algebraic equations daes f t x x 0 where f x is identically singular most of this effort has focused on computing a solution that is assumed to exist that is the dae is assumed solvable more recently there have been existence results developed using differential geometry for complex higher index systems these characterizations can be hard to verify in practice in this paper the computational verification of solvability is investigated this first requires developing an alternative set of sufficient conditions for solvability which are more amenable to computation verification of these conditions using readily available numerical and symbolic software is then discussed an example from robotics where classical graph theoretical approaches give an incorrect answer is worked to illustrate the usefulness of the sufficient condition and the computational approach

numerical solution of hybrid systems of differential algebraic equations abstract we present a mathematical framework for general over and under determined hybrid switched systems of differential algebraic equations hdaes we give a systematic formulation of hdaes and discuss existence and uniqueness of solutions the treatment of the switch points and how to perform consistent initialization at switch points we show how numerical solution methods for daes can be adapted for hdaes and present a numerical results for these methods for the real world example of simulating an automatic gearbox

on the true and the modified cramer rao bounds for the estimation of a scalar parameter in the presence of nuisance parameters we consider the cramer rao bound crb for the estimation of a scalar parameter in the presence of nuisance parameters whereas this true crb is hard to evaluate in general we present a simple analytical expression for its high snr asymptote i e the asymptotic crb acrb we show that this acrb is related to the crb for the joint estimation of the scalar parameter and the nuisance parameters previously a modified crb mcrb for the estimation of a scalar parameter in the presence of nuisance parameters has been derived this mcrb is also simple to evaluate and is related to the crb for the estimation of the scalar parameter assuming that the value of the nuisance parameters is a priori known we show that the mcrb can be quite loose at high snr when the scalar parameter is coupled with the nuisance parameters in the case of synchronization parameter estimation we find that the acrb equals the mcrb whether or not some of the nuisance parameters are a priori known

the modified cramer rao bound and its application to synchronization problems we introduce the modified cramer rao bound crb which like the true crb is a lower bound to the error variance of any parameter estimator the modified crb proves useful when in addition to the parameter to be estimated the observed data also depend on other unwanted parameters the relationship between the modified and true crb is established and applications are discussed regarding the estimation of carrier frequency offset carrier phase and timing epoch in linearly modulated signals modified crbs for phase and timing estimation have been already discussed in previous works where it is shown that several practical carrier phase and clock recovery circuits do attain such bounds frequency discrimination instead is not so well represented in the literature and a significant contribution of this paper is the calculation of the modified crb for frequency estimation this bound is compared with the performance of some frequency detectors and it is concluded that further work is needed in search of more efficient frequency discrimination methods

adaptive control of a constrained robot ensuring zero tracking and zero force errors a constrained robot is a mathematical model that describes the interaction between a robot and the environment as the robot moves along a prescribed trajectory the main difficulty in the control of constrained robots is to ensure zero error for the constraint force in addition to accurate trajectory tracking this study extends the result of slotine and li 1991 to design a simple adaptive controller for constrained robots the proposed controller achieves both control objectives in the presence of dynamic parameter uncertainty the overall system is proven to be globally stable in the lyapunov sense simulation results are provided to demonstrate the performance of the proposed method

pilot aided carrier recovery in the presence of phase noise the paper deals with carrier recovery based on pilot symbols in single carrier systems the system model considered in the paper includes the channel additive white noise and the phase noise that affects the local oscillators used for up down conversion wiener s method is used to determine the optimal filter in estimation of phase noise assuming that a sequence of equally spaced pilot symbols is available our analysis allows to capture the cyclostationary performance of the estimate a phenomenon that is not considered in the previous literature in the paper closed form formulas for the transfer function of the optimal filter and for the mean square phase error are derived for the case where the phase noise is modelled as random phase walk for this case a suboptimal filter is proposed numerical results are presented to substantiate the analysis

force motion control of constrained robots using sliding mode a sliding mode control algorithm is presented for trajectory tracking of an end effector on a constrained surface with specified constraint forces by using the theory of variable structure systems the development of the algorithm is based on a new formulation of the dynamic model and the expansion of sliding surfaces to include the constraint force error the proposed sliding controller is explicit which ensures the occurrence of the sliding mode on the intersection of the surfaces a detailed numerical example is presented to illustrate the method

optimum pilot sequences for data aided synchronization we compute the pilot sequences that minimize the cramer rao bound crb for carrier phase offset carrier frequency offset and symbol timing offset estimation if we require the pilot sequence to be drawn from a discrete set of constellation points then the alternating sequence is the crb minimizing sequence if we relax the constellation constraint and apply a total energy constraint we obtain three different sequences that minimize the crb for each of the synchronization parameters we show that the maximum likelihood ml estimator achieves the crb for any of the sequences presented we also explore the impact of using the pilot symbols in a preamble with unknown data symbols immediately following the interference caused by the unknown data symbols reduces the performance of the ml estimator beyond an snr threshold

joint estimation of channel and oscillator phase noise in mimo systems oscillator phase noise limits the performance of high speed communication systems since it results in time varying channels and rotation of the signal constellation from symbol to symbol in this paper joint estimation of channel gains and wiener phase noise in multi input multi output mimo systems is analyzed the signal model for the estimation problem is outlined in detail and new expressions for the cramer rao lower bounds crlbs for the multi parameter estimation problem are derived a data aided least squares ls estimator for jointly obtaining the channel gains and phase noise parameters is derived next a decision directed weighted least squares wls estimator is proposed where pilots and estimated data symbols are employed to track the time varying phase noise parameters over a frame in order to reduce the overhead and delay associated with the estimation process a new decision directed extended kalman filter ekf is proposed for tracking the mimo phase noise throughout a frame numerical results show that the proposed ls wls and ekf estimators performances are close to the crlb finally simulation results demonstrate that by employing the proposed channel and time varying phase noise estimators the bit error rate performance of a mimo system can be significantly improved

on impasse points of quasilinear differential algebraic equations abstract this paper presents a mathematical characterization of the impasse points of quasilinear dae s a x g x where then a x is a nxn matrix having constant but not full r n in the domain of interest we show that a reduction procedure permits to reduce the dae to a quasilinear ode al xi xi g1 xi rr and that impasse points correspond to special singularities of the reduced ode impasse points of higher index dae s can also be defined the only difference is that the above reduction procedure takes more than one step

the hopf bifurcation theorem for quasilinear differential algebraic equations we prove a generalization of the hopf bifurcation theorem for quasilinear differential equations daes i e equations of the form a g where the matrix a has constant but not full rank and hence the system cannot be made into an explicit ode the paper includes an appendix by j ernsthausen addressing the numerical calculation of the hopf points in the dae setting

pilot symbol assisted phase noise compensation with forward backward wiener smoothing filters we present a novel wiener smoothing filter procedure for pilot symbol assisted estimation of oscillator phase noise the procedure consists of forward and backward first order infinite impulse response filtering the pilot symbols and combining the filter outputs to generate an estimate of the phase noise we analyze the mean square error performance of this pilot symbol assisted forward backward wiener smoothing filter fbwsf procedure and show its optimality under the assumption that the phase noise is modeled as a first order autoregressive moving average process we then apply the fbwsf as a code aided phase noise compensation technique in an iterative receiver framework the iterative receiver presented here first estimates phase noise roughly by using the pilot symbol assisted fbwsf then it refines the estimates with the code aided version of fbwsf the resulting receiver achieves excellent error performance at a feasible level of computational complexity

time dependent linear daes with discontinuous inputs existence and uniqueness results are proved for initial value problems associated with linear time varying differential algebraic equations the right hand sides are chosen in a space of distributions allowing for solutions exhibiting discontinuities as well as impulses this approach also provides a satisfactory answer to the problem of inconsistent initial conditions of crucial importance for physical applications furthermore our theoretical results yield an efficient numerical procedure for the calculation of the jump and impulse of a solution at a point of discontinuity numerical examples are given

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

discontinuous solutions of semilinear differential algebraic equations ii p consistency abstract part 1 of this paper presented a theory of distribution solutions of semilinear differential algebraic equations dae s in particular it was shown that uniqueness of solutions of initial value problems breaks down completely in the class of discontinuous solutions here a mathematical procedure is introduced for selecting physically acceptable solutions which satisfy some new consistency condition relative to admissible perturbations of the original dae several nonlinear circuit examples are given to support the theory an

discontinuous solutions of semilinear differential algebraic equations i distribution solutions abstract there is strong physical evidence that a full treatment of differential algebraic equations should be incorporate solutions with jump discontinuities it is shown here that for semilinear problems the setting of distributions allows for the development of a theory where indeed such discontinuities may occur this approach also settles the problem of inconsistent initial conditions in a very simple way on the other hand new issues arise as not only uniqueness but even countability of the number of solutions of initial value problems may now be lost a physically motivated but purely mathematical selection procedure to overcome this difficulty is discussed in part 2 of this paper an

bayesian and hybrid cramer rao bounds for the carrier recovery under dynamic phase uncertain channels in this paper we study bayesian and hybrid cramer rao bounds bcrb and hcrb for the code aided ca the data aided da and the non data aided nda dynamical phase estimation of qam modulated signals we address the bounds derivation for both the offline scenario for which the whole observation frame is used and the online which only takes into account the current and the previous observations for the ca scenario we show that the computation of the bayesian information matrix bim and of the hybrid information matrix him is np hard we then resort to the belief propagation bp algorithm or to the bahl cocke jelinek raviv bcjr algorithm to obtain some approximate values moreover in order to avoid the calculus of the inverse of the bim and of the him we present some closed form expressions for the various crbs which greatly reduces the computation complexity finally some simulations allow us to compare the possible improvements enabled by the offline and the ca scenarios

phase and frequency estimation for psk packets bounds and algorithms new cramer rao lower bounds crbs are derived for the estimation of phase offset and frequency offset from a block of random bpsk or qpsk symbols at low signal to noise snr ratios these bounds are compared to existing bounds which apply to the unmodulated carrier or to known psk symbols and to the performance of some estimation algorithms

cramer rao lower bounds for qam phase and frequency estimation in this paper we present the true cramer rao lower bounds crlbs for the estimation of phase offset for common quadrature amplitude modulation qam psk and pam signals in awgn channels it is shown that the same analysis also applies to the qam fsk and pam crlbs for frequency offset estimation the ratio of the modulated to the unmodulated crlbs is derived for all qam psk and pam signals and calculated for specific cases of interest this is useful to determine the limiting performance of synchronization circuits for coherent receivers without the need to simulate particular algorithms the hounds are compared to the existing true crlbs for an unmodulated carrier wave cw bpsk and qpsk we investigated new and existing qam phase estimation algorithms in order to verify the new phase crlb this showed that new minimum distance estimator performs close to the qam bound and provides a large improvement over the power law estimator at moderate to high signal to noise ratios

combined adaptive and variable structure control for constrained robots abstract this paper addresses the problem of controller design for constrained robots a control algorithm described as a combination of the direct adaptive and the variable structure method is presented for the trajectory tracking of an end effector on a constrained surface with specified constraint forces this scheme has certain advantages both with respect to computational efficiency and with respect to design with respect to computational efficiency the calculation of the regressor is avoided with respect to design since the number of parameter update laws required in the adaptation is independent of the number of links of the robot the difficulty of tuning numerous adaptation gains is avoided

implicit differential equations near a singular point abstract this paper presents general and precise results on existence and number of solutions to implicitly defined ordinary differential equations in the vicinity of a singular point where the equation is not equivalent to an explicit one unlike in most if not in all other studies devoted to this problem in the literature it is not assumed that either rank drop occurs on an entire neighborhood of the singular point or that the equation is a scalar one attention is confined to the simplest but most frequently encountered kind of singular points it is shown that such standard singular points split into two complementary classes those from which exactly two distinct solutions emanate and those at which exactly two distinct solutions terminate whether a point of the latter class is eventually encountered is unaffected by slight modifications of the nonsingular initial condition and further evolution of the system governed by the singular ode then requires using a suitable jump condition according to appropriate physical criteria points of the former class are also shown to play a more subtle but equally important role in the dynamics the phenomena described here are relevant in various problems from the sciences such as phase transitions or plasticity they should also be relevant in some aspects of the classical domain of application of differential algebraic equations singular perturbations of ode s

carrier phase and frequency estimation for pilot symbol assisted transmission bounds and algorithms in this paper we consider the cramer rao lower bound crb for the joint estimation of the carrier phase and the frequency offset from a noisy linearly modulated burst signal containing random data symbols dss as well as known pilot symbols pss we point out that the crb depends on the location of the pss in the burst the number of pss the number of dss the signal to noise ratio snr and the data modulation scheme distributing the pss symmetrically about the center of the burst and estimating the carrier phase in the center of the burst interval decouples the frequency and phase estimation making the crb for phase estimation independent of the specific location of the pss at low and moderate snr the crbs for both phase and frequency estimation decrease as the fraction of the pss in the burst increases in addition the crb for frequency estimation decreases as the pss are separated with more dss numerical evaluation of the crb indicates that the carrier phase and frequency of a hybrid burst i e containing pss and dss can be estimated more accurately when exploiting both the presence of the dss and the a priori knowledge about the pss instead of using only the knowledge about the pss and ignoring the dss or considering all the received symbols pss and dss as unknown and ignoring the knowledge about the pss comparison of the crb with the performance of existing carrier synchronizers shows that the iterative soft decision directed sdd estimator with data aided da initialization performs very closely to the crb and provides a large improvement over the classical non data aided nda estimator at lower snr