Jitendra K. Tugnait

Identification and deconvolution of multichannel linear non-Gaussian processes using higher order statistics and inverse filter criteria

This paper is concerned with the problem of estimation and deconvolution of the matrix impulse response function of a multiple-input multiple-output (MIMO) system given only the measurements of the vector output of the system. The system is assumed to be driven by a temporally i.i.d. and spatially independent non-Gaussian vector sequence (which is not observed). An iterative, inverse filter criteria-based approach is developed using the third-order or the fourth-order normalized cumulants of the inverse filtered data at zero lag. Stationary points of the proposed cost functions are investigated. The approach is input iterative, i.e., the input sequences are extracted and removed one by one. The matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs. Identifiability conditions are analyzed. The strong consistency of the proposed approach is also briefly discussed. Computer simulation examples are presented to illustrate the proposed approaches.

Identification of linear stochastic systems via second- and fourth-order cumulant matching

The identification problem for time-invariant single-input single-output linear stochastic systems driven by non-Gaussian white noise is considered. The system is not restricted to be minimum phase, and it is allowed to contain all-pass components. A least-squares criterion that involves matching the second- and the fourth-order cumulant functions of the noisy observations is proposed. Knowledge of the probability distribution of the driving noise is not required. An order determination criterion that is a modification of the Akaike information criterion is also proposed. Strong consistency of the proposed estimator is proved under certain sufficient conditions. Simulation results are presented to illustrate the method.

On channel estimation using superimposed training and first-order statistics

Channel estimation for single-input multiple-output (SIMO) time-invariant channels is considered using only the first-order statistics of the data. A periodic (nonrandom) training sequence is added (superimposed) at a low power to the information sequence at the transmitter before modulation and transmission. Recently superimposed training has been used for channel estimation assuming no mean-value uncertainty at the receiver and using periodically inserted pilot symbols. We propose a different method that allows more general training sequences and explicitly exploits the underlying cyclostationary nature of the periodic training sequences. We also allow mean-value uncertainty at the receiver. Illustrative computer simulation examples are presented.

Single-user channel estimation and equalization

There has been much interest in blind (self-recovering) channel estimation and blind equalization where no training sequences are available or used. In multipoint networks, whenever a link from the server to one of the tributary stations is interrupted, it is clearly not feasible (or desirable) for the server to start sending a training sequence to re-establish a particular link. In digital communications over fading/multipath channels, a restart is required following a temporary path interruption due to severe fading. During on-line transmission impairment monitoring, the training sequences are obviously not supplied by the transmitter. Consequently, the importance of blind channel compensation research is also strongly supported by practical needs. We present a comprehensive summary of research development on single-user channel estimation and equalization, focusing on both training-based and blind approaches. Our emphasis is on linear time-invariant channels.

Brief Tracking of multiple maneuvering targets in clutter using IMM/JPDA filtering and fixed-lag smoothing

We consider the problem of tracking multiple maneuvering targets in clutter using switching multiple target motion models. A suboptimal filtering algorithm is developed by applying the basic interacting multiple model (IMM) approach and the joint probabilistic data association (JPDA) technique to a Markovian switching system. A suboptimal fixed-lag smoothing algorithm is developed by applying the IMM and the JPDA approaches to a state-augmented system. The algorithms are illustrated via a simulation example involving tracking of two highly maneuvering targets.

Identification of non-minimum phase linear stochastic systems

Abstract The identification of time-invariant, non-minimum phase, stochastic systems driven by non-Gaussian white noise is considered, given only (the noisy observations of the system output. A two-step procedure is proposed. In the first step a spectrally equivalent system is estimated using a standard technique that exploits only the second order statistics of the measurements. In the second step a partial set of 4th order cumulants of the measurements is exploited to resolve the location of the system zeros. Knowledge of the probability distribution of the driving noise is not required. Strong consistency of the proposed estimator is proved under certain sufficient conditions. Simulation results are also presented in support of the theory.

On blind identifiability of multipath channels using fractional sampling and second-order cyclostationary statistics

The problem of blind identifiability of digital communication multipath channels using fractionally spaced samples is considered. Fractionally sampled data are cyclostationary rather than stationary. The problem is cast into a mathematical framework of parameter estimation for a vector stationary process with single input (information sequence) and multiple outputs, by using a time-series representation of a cyclostationary process. A necessary and sufficient condition for channel identifiability from the correlation function of the vector stationary process is derived. This result provides an alternative but equivalent statement of an existing result. Using this result, it is shown that certain class of multipath channels cannot be identified from the second-order statistics irrespective of how the sampling rate is chosen. >

On superimposed training for channel estimation: performance analysis, training power allocation, and frame synchronization

Channel estimation for single-input multiple-output (SIMO) time-invariant channels using superimposed training has been recently considered by several authors. A periodic (nonrandom) training sequence is arithmetically added (superimposed) at a low power to the information sequence at the transmitter before modulation and transmission. In particular, in , the channel is estimated using only the first-order statistics of the data under a fixed power allocation to training and under the assumption that the superimposed training sequence at the receiver is time-synchronized with its transmitted counterpart (frame synchronization). In this paper, we remove these restrictions. We first present a performance analysis of the approach of to obtain a closed-form expression for the channel estimation variance. We then address the issue of superimposed training power allocation for complex Gaussian random (Rayleigh) channels. Using the developed channel estimation variance expression, we cast the power allocation problem as one of optimizing a signal-to-noise ratio for equalizer design. Finally, we propose a novel approach for frame synchronization. All the results are illustrated via simulation examples involving frequency-selective Rayleigh fading. Simulation comparisons with an existing approach to frame synchronization is also provided.

Brief paper: A detection-estimation scheme for state estimation in switching environments

A combined detection-estimation scheme is proposed for state estimation in linear systems with random Markovian noise statistics. The optimal MMSE estimator requires exponentially increasing memory and computations with time. The proposed approach is an attempt to circumvent this problem. Simulation results are presented which show the advantages of the proposed scheme over some of the existing suboptimal approaches.

Blind identifiability of FIR-MIMO systems with colored input using second order statistics

We show that a finite impulse response and multi-input-multi-output (FIR-MIMO) system with colored input is blindly identifiable up to a permutation and scaling using the second order statistics (SOS) of the systems output if (a) the system function is irreducible, and (b) the input signals are uncorrelated from each other and have distinct power spectra. Condition (a) is weaker than several conditions reported previously. It suggests a further potential of developing more robust blind algorithms.