Langford B. White

Robust extended Kalman filtering

Linearization errors inherent in the specification of an extended Kalman filter (EKF) can severely degrade its performance. This correspondence presents a new approach to the robust design of a discrete-time EKF by application of the robust linear design methods based on the H/sub /spl infin// norm minimization criterion. The results of simulations are presented to demonstrate an advantage for signal demodulation and nonlinear equalization applications.

Cross spectral analysis of nonstationary processes

Consideration is given to the generalization of stationary cross spectral analysis methods to a class of nonstationary processes, specifically, the class of semistationary finite energy processes possessing sample functions that are of finite energy almost surely. A new quantity called the time-frequency coherence (TFC) is defined, and it is demonstrated that its properties are analogous to those possessed by the stationary coherence function. The problem of estimating the TFC by using elements of L. Cohens (1966) class of joint time-frequency representations is investigated. It is shown that the only admissible estimators are those based on the class of time-frequency smoothed periodograms. Thus, the familiar procedure of segmentation and (smoothed) short-time Fourier analysis cannot be improved upon (within the framework considered) by the use of the higher-resolution nonparametric time-frequency methods. Procedures for selection of the appropriate estimators and a possible application are suggested. >

Lumpable hidden Markov models-model reduction and reduced complexity filtering

This paper is concerned with filtering of hidden Markov processes (HMP) which possess (or approximately possess) the property of lumpability. This property is a generalization of the property of lumpability of a Markov chain which has been previously addressed by others. In essence, the property of lumpability means that there is a partition of the (atomic) states of the Markov chain into aggregated sets which act in a similar manner as far as the state dynamics and observation statistics are concerned. We prove necessary and sufficient conditions on the HMP for exact lumpability to hold. For a particular class of hidden Markov models (HMM), namely finite output alphabet models, conditions for lumpability of all HMP representable by a specified HMM are given. The corresponding optimal filter algorithms for the aggregated states are then derived. The paper also describes an approach to efficient suboptimal filtering for HMP which are approximately lumpable. By this we mean that the HMM generating the process may be approximated by a lumpable HMM. This approach involves directly finding a lumped HMM which approximates the original HMM well, in a matrix norm sense. An alternative approach for model reduction based on approximating a given HMM by an exactly lumpable HMM is also derived. This method is based on the alternating convex projections algorithm. Some simulation examples are presented which illustrate the performance of the suboptimal filtering algorithms.

Cooperative resource allocation games in shared networks: symmetric and asymmetric fair bargaining models

The high cost associated with the rollout of 3G services encourages operators to share network infrastructure. Network sharing poses a new challenge in devising fair and Pareto optimal resource allocation strategies to distribute system resources among users and operators in the network. Cooperative game theory provides a framework for formulating such strategies. In this paper, we propose two models (i.e. symmetric and asymmetric) for cooperative resource bargaining among the users and mobile virtual network operators (MVNOs) of each operator in shared networks based on the concept of preference functions. The bargaining solutions proposed vary according to a parameter beta that considers the tradeoff between ones gain and the losses of others. The well-known Nash and Raiffa- Kalai-Smorodinsky solutions are special instances of the solutions proposed. The symmetric model assumes that all players have equal bargaining powers while in the asymmetric case, players are allowed to submit bids to the network operator to influence the final bargaining outcome. Due to the diversity of demand patterns, temporary resource exchange among operators can provide benefits in terms of better communication quality to their users. To avoid selfish behaviour of the operators, we propose a resource sharing model that allocates extra resources based on the past allocations and contributions of each operator.

Signal design for MIMO diversity systems

This paper addresses the problem of waveform design for general diversity systems. The paper firstly introduces a general model for such systems, and then considers linear and nonlinear cases. Examples of each case are given n the linear case, the MIMO communications design problem; in the nonlinear case, the MIMO radar waveform design problem. In the latter case, a simulation example is provided which illustrates the potential benefits, which might be obtained. Finally, the paper concludes with a brief discussion of the MIMO radar tracking problem.

On estimating the instantaneous frequency of a Gaussian random signal by use of the Wigner-Ville distribution

The form of the one-dimensional probability distribution function for the Wigner-Ville, or evolutive spectrum, and the instantaneous frequency of a Gaussian random process is derived by use of an orthogonal decomposition of the process covariance matrix. No narrowband assumptions are made. Natural estimators for the evolution spectrum and the instantaneous frequency are defined, and the form of the distribution functions is derived. The properties of these estimators are examined with particular reference to the effects of windowing operations used in the calculation. The usefulness of the results is indicated, and examples are presented. >

Transition kernels for bilinear time-frequency distributions

The author proposes a sequence of time-frequency signal representations which offer a continuous transition from time smoothed pseudo-Wigner-Ville distributions (PWVD) to a specified class of positive representations. This allows the selection of a representation which offers the desired tradeoff between the inherent localization properties of the PWVD and the lack of interference terms present in the class of positive representations, a cause of some criticism of the method. The sequence converges uniformly to the specified positive distribution. >

Time-frequency analysis and pattern recognition using singular value decomposition of the Wigner-Ville distribution

Time-Frequency analysis based on the Wigner-Ville Distribution (WVD) is shown to be optimal for a class of signals where the variation of instantaneous frequency is the dominant characteristic. Spectral resolution and instantaneous frequency tracking is substantially improved by using a Modified WVD (MWVD) based on an Autoregressive spectral estimator. Enhanced signal-to-noise ratio may be achieved by using 2D windowing in the Time-Frequency domain. The WVD provides a tool for deriving descriptors of signals which highlight their FM characteristics. These descriptors may be used for pattern recognition and data clustering using the methods presented in this paper.

Optimum Receiver Design for Broadband Doppler Compensation in Multipath/Doppler Channels With Rational Orthogonal Wavelet Signaling

In this paper, we address the issue of signal transmission and Doppler compensation in multipath/Doppler channels. Based on a wavelet-based broadband Doppler compensation structure, this paper presents the design and performance characterization of optimum receivers for this class of communication systems. The wavelet-based Doppler compensation structure takes account of the coexistence of multiple Doppler scales in a multipath/Doppler channel and captures the information carried by multiple scaled replicas of the transmitted signal rather than an estimation of an average Doppler as in conventional Doppler compensation schemes. The transmitted signal is recovered by the perfect reconstruction (PR) wavelet analysis filter bank (FB). We demonstrate that with rational orthogonal wavelet signaling, the proposed communication structure corresponds to a Lth-order diversity system, where L is the number of dominant transmission paths. Two receiver designs for pulse amplitude modulation (PAM) signal transmission are presented. Both receiver designs are optimal under the maximum-likelihood (ML) criterion for diversity combination and symbol detection. Good performance is achieved for both receivers in combating the Doppler effect and intersymbol interference (ISI) caused by multipath while mitigating the channel noise. In particular, the second receiver design overcomes symbol timing sensitivities present in the first design at reasonable cost to performance.

An iterative method for exact maximum likelihood estimation of the parameters of a harmonic series

A procedure is described for determining the exact maximum-likelihood (ML) estimates of the parameters of a harmonic series (i.e. the fundamental frequency, and the amplitude and phase of each harmonic). Existing ML methods are only approximate in the sense that terms present due to mixing between the harmonics are ignored; these terms asymptotically reduce to zero as the sample size increases to infinity. It is argued that these terms can be significant for short signal lengths. The application of the expectation-maximization algorithm results in an iterative procedure that converges to a stationary point on the true parameter likelihood surface. If global convergence results, this point yields the exact ML estimates. Simulation studies illustrate the advantages of the method when short data lengths are used. >