Suboptimal Maximum Likelihood Research Articles

Performance Study of Suboptimum Maximum-Likelihood Receivers for FFH/MFSK Systems With Multitone Jamming Over Fading Channels

We derive two suboptimum maximum-likelihood (ML) receivers for fast frequency-hopped M-ary frequency-shift-keying (FSK) spread-spectrum (SS) communication systems. These two receiver structures attempt to countermeasure the effects of the worst case multitone jamming (MTJ) and additive white Gaussian noise over Rayleigh- and Rician-fading channels, respectively. In addition, analytical bit-error-rate (BER) expressions for the two proposed suboptimum structures are derived and validated by simulation results. Performance comparisons among various receivers show that the proposed suboptimum receivers significantly outperform the other existing receivers over fading channels. The optimum diversity level of the suboptimum ML receiver for the Rayleigh-fading case is found to be higher than that of the Rician-fading case. In addition, the proposed suboptimum ML receivers with optimum diversity levels can effectively remove the effect of MTJ, even under very low signal-to-jamming ratio conditions.

Performance Analysis of Soft-Output Post-Processing Detection for Data-Dependent Media Noise Channels

A soft-output data-detection scheme optimized for data-dependent media-noise recording channels is investigated that uses signal-dependent correlation-sensitive (SDCS) metric computation for post-processing decoding. This media-noise soft-output (MNS) decoding scheme achieves suboptimal maximum-likelihood (ML) sequence detection in a nonstationary media-noise channel, while still using traditional Viterbi detection. Because it drastically reduces SDCS metric computation by focusing on correcting only the dominant error events in the ML detector, it is less complex than other suboptimal detection schemes. Moreover, the MNS decoding scheme provides parity-check-code decoding with more reliable soft-output information. Simulation showed that MNS decoding in conjunction with a conventional ME/sup 2/PRML system, provides an excellent tradeoff between data-detection performance and computation complexity for a jitter-noise dominant high-density recording channel.

Joint maximum-likelihood parameter estimation for burst DS spread-spectrum transmission

We first derive the joint optimal maximum-likelihood (ML) estimator of the carrier phase, both Doppler shift and Doppler rate, and the spreading code delay for a short burst direct sequence/spread spectrum (DS/SS) transmission in the absence of the data modulation. The typical burst duration is three data bit periods (60 ms). The performance of the joint estimator is analytically derived separately for high and low carrier-to-noise ratio (CNR) values. A suboptimal ML estimator based on the method of averaged periodogram is proposed for the data modulation present case, allowing the joint estimation of the data bit values. Then the above parameters are assumed correctly estimated and a segmentation approach is adopted, deriving the optimal joint ML estimator for the bit synchronization epoch and data. Simulations show the joint estimators perform reliable down to a CNR of approximately 30 dB/spl middot/Hz.

Signal processing in satellite-borne radar altimeter

A new Suboptimal Maximum Likelihood Estimation (SMLE) algorithm based on full-deramp model and its implementation in satellite-borne radar altimeter are presented, with emphasis on the influence of both the return fluctuation and the receiver noise on height and slope estimation precision. Some conclusions are obtained and varified by computer simulation.

Simulations of satellite-borne altimeter tracking system with transponder in calibration test

Abstract This article describes a simulation of the satellite-borne altimeter tracking system and its calibration. This calibration simulation uses a point target such as a land-based transponder to check the measurement accuracy of the altimeter. It introduces the Advanced Altimeter Tracker (AAT) which is used in this simulation and analyses two tracking algorithms: Offset Centre Of Gravity (OCOG) and Sub-optimal Maximum Likelihood Estimator (SMLE) in detail. The response of the AAT to the transponder pulse is also given. After a set of simulations of the AAT with the input composite signal of transponder pulse and ocean echoes the effect of the noise and ocean echoes on the transponder-based calibration is given. This result is also suitable for other radar point target calibration case.

Suboptimum Maximum Likelihood Estimation of Structural Parameters from Multiple-Excitation Vibration Data

In this paper an effective stochastic and multiple-excitation single-response approach to structural dynamics identification is introduced. The proposed approach accounts for many previously unaccounted for aspects of the problem, as it is based on: A proper, special-form, scalar ARMAX-type representation of the structural and noise dynamics; a new Suboptimum Maximum Likelihood (SML) discrete estimation algorithm (Fassois and Lee, 1990); systematic and efficient modeling strategy and model validation procedures; as well as accurate modal parameter extraction that is compatible with the employed model structure and excitation signal forms. In addition to its comprehensiveness, the proposed approach overcomes the well-known limitations of deterministic time-domain methods in dealing with noise-corrupted data records, while also circumventing some of the major difficulties of existing stochastic schemes by featuring guaranteed algorithmic stability, elimination of wrong convergence problems, very modest computational complexity, and minimal operator intervention. The effectiveness of the approach is verified through numerical simulations with noise-corrupted vibration data, and structural systems characterized by well-separated and closely-spaced vibrational modes. Comparisons with the classical Frequency Domain Method (FDM) are also made, and the approach’s advantages over deterministic methods are demonstrated through comparisons with the Eigensystem Realization Algorithm (ERA). Experimental results, where the proposed approach is used for the modal analysis of a flexible beam from laboratory data, are also presented.

Suboptimum Maximum Likelihood Identification of ARMAX Processes

A Suboptimum Maximum Likelihood (SML) method for ARMAX process identification from input-output observations is proposed. The proposed method is based on a quadratic approximation of the asymptotic negative log-likelihood function about an estimated point in the Moving Average parameter subspace, as well as an asymptotic ARX representation and fundamental properties of linear stochastic systems. The proposed method is shown to overcome the main drawbacks of the standard Maximum Likelihood and other alternative approaches by offering a low computational load and effectively circumventing the local extrema/wrong convergence problems and the need for initial guess parameter values. In addition, the consistency of the method is established, its extension to the multiple-input case presented, and, in contrast to most alternative approaches, its stability is mathematically guaranteed. The effectiveness of the proposed method is finally demonstrated through numerical simulations and comparisons with the Maximum Likelihood approach.

A Fast Rational Model Approach to Parametric Spectral Estimation—Part I: The Algorithm

A novel, fast rational model (ARMA) approach to parametric spectral estimation, based on correlation-type and guaranteed-stability versions of the Suboptimum Maximum Likelihood scheme that utilizes a quadratic approximation of the negative log-likelihood about an initial estimate in the MA parameter subspace, inverse function estimates, and fundamental ARMA process properties, is introduced. The proposed approach is exclusively based on linear operations, uses the autocovariance function as a “sufficient statistic,” and overcomes the main drawbacks/limitations of alternative approaches by offering high accuracy, minimal computational and memory storage requirements, no need for a priori information, mathematically guaranteed stability (and therefore the capability of estimating all types of spectra, including those characterized by sharp valleys), and complete elimination of the local extrema problem by yielding a unique estimate that is shown to asymptotically converge to the true spectrum. The paper is divided into two parts: The basic form of the proposed approach is derived in the first part, whereas in the second (Fassois, 1990), its consistency is proven, two guaranteed-stability versions developed, and its performance evaluated via numerical simulations and comparisons with standard techniques.

Viterbi detection with simultaneous suboptimal maximum likelihood carrier phase estimation

The authors consider maximum-likelihood (ML) detection of convolutionally coded data over the AWGN channel with unknown carrier phase. A receiver is developed for simultaneous ML data decoding and suboptimal ML carrier-phase estimation. The receiver is readily implementable and, for a circular signal constellation, it is totally linear. Computer simulations using two different models of the time-varying carrier phase indicate that the receiver provides good bit error probability performance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Estimation of Time Varying Delays in Linear Stochastic Systems

A class of estimators is presented for the estimation of unknown time varying delays in a linear discrete time stochastic system. The proposed suboptimum maximum likelihood (SML) techniques are shown to be realized by parallel Kalman Filtering (PKF) coupled with a suboptimum Viterbi Algorithm (SVA). The SVA estimates the delay sequence and the Kalman Filter bank generates all the components needed by the SVA. The analysis and simulations show that the sub-optimum estimators closely approximate the optimum maximum likelihood estimator while possessing significant computational advantages. The relation between performance of the algorithm and the output distinguishableity is derived.

Suboptimal Maximum Likelihood Timing Estimator for a PCM Regenerative Repeater

This paper introduces a modified likelihood function and then provides the suboptimal maximum likelihood (SML) timing estimator which is applicable to PCM regenerative repeaters because of its structural simplicity. Since the SML timing estimator tracks a difference waveform balancing point, as opposed to its conventional maximum likelihood (ML) counterpart, which tracks a derivative waveform zero-crossing point, its performance is rather immune against channel phase distortion. Analyses and experiments are also presented to validate the SML timing estimator for timing extraction from a band-limited PAM signal.

Estimation of parameters in lossless layered media systems

In this paper we develop a procedure for estimating the parameters (reflection coefficients and travel times) of lossless layered media systems. The estimation criterion is maximum likelihood. It is shown that maximum-likelihood estimates of the parameters of a layer may be obtained by first determining the maximum-likelihood estimate of the upgoing waveform (one of the states) in that layer, and then estimating the parameters from the estimated upgoing waveform as if the estimated waveform is the output of the layer under consideration. A maximum-likelihood state estimator is developed. It is shown that the state waveforms are composed of overlapping wavelets, and estimation of the parameters of a layer is essentially equivalent to estimation of the amplitude and time-delay of the first wavelet in the upgoing waveform of the layer under consideration. A suboptimal maximum-likelihood parameter estimator is developed. It consists of two filters connected in series: a matched filter to treat noise; and a transversal equalizing-filter to correct for wavelet overlapping effects. Numerical results which illustrate the performance of this maximum-likelihood procedure for different noise levels are presented.

Maximum likelihood identification of time varying and random system parameters†

Abstract In many investigations of system identification, severe restrictions on the system are necessary in order to obtain the estimation/identification alogrithms; i.e., the system and observation model parameters (Φ, H, T) and the plant and observation noise moments are constrained to be time-invariant. In many cases of interest, however, the system parameters and/or plant and measurement noise moments are not constant, but time varying and perhaps even random parameters. The method of suboptimal maximum likelihood identification is extended such that the adaptive gains can be computed based on estimates of the random parameters or possibly by implementation of an augmented extended Kalman filter. This method leads to a nonlinear two-point boundary value problem which is resolved by the method of invariant embedding such as to lead to sequential identification algorithms. Examples demonstrate the efficiency of the proposed algorithms