John J. Shynk

Statistical analysis of the single-layer backpropagation algorithm. II. MSE and classification performance

For pt.I see ibid., p.583-91, 1993. The analysis of pt.I is extended to the evaluation of the mean-square error and the probability of correct classification. It is shown that the mean-square error and the corresponding performance surface are such that the single-layer perceptron is prevented from correctly classifying with probability one until the weights converge at infinity. >

Separation of cochannel signals in TDMA mobile radio

We propose a sequential algorithm that separates cochannel time-division multiple-access (TDMA) signals that encounter multipath interference and noise. The receiver employs a multistage architecture where each stage consists of a beamformer and an equalizer that isolates one source, compensates for intersymbol interference (ISI), and demodulates the data. A problem encountered with such bursty sources is that the beamformer/equalizer trained for a particular time slot may not be appropriate for all the data contained in that slot. This occurs because a cochannel source typically overlaps only part of the time slot of interest and may not overlap the training sequence at all. The algorithm presented overcomes this problem by processing the data forward and backward in a sequential noncausal manner. Computer simulations using signals with the IS-54 format are presented to demonstrate the properties of the sequential algorithm.

Statistical analysis of the single-layer backpropagation algorithm. I. mean weight behavior

The single-layer backpropagation algorithm is a gradient-descent method that adjusts the connection weights of a single-layer perceptron to minimize the mean-square error at the output. It is similar to the standard least mean square al- gorithm, except the output of the linear combiner contains a differentiable nonlinearity. In this paper, we present a statis- tical analysis of the mean weight behavior of the single-layer backpropagation algorithm for Gaussian input signals. It is based on a nonlinear system identification model of the desired response which is capable of generating an arbitrary hyper- plane decision boundary. It is demonstrated that, although the weights grow unbounded, the algorithm, on average, quickly learns the correct hyperplane associated with the system iden- tification model.

Stability bounds and steady-state coefficient variance for a second-order adaptive IIR notch filter

In this correspondence, we present a stochastic convergence analysis of a second-order adaptive IIR notch filter. The approach is based on a linearization of the gradient in the vicinity of the optimal solution. Expressions for stability bounds on the algorithm step size and the steady-state coefficient variance are derived. These closed-form analytical results are verified by computer simulations for different signal and noise conditions. >

Separation of cochannel GSM signals using an adaptive array

The Global System for Mobile communications (GSM) is a digital cellular radio network that employs time division multiple access (TDMA). In such a cellular system, frequencies are reused in different regions for spectral efficiency, and thus, the transmissions in a given cell can interfere with those in distant cells. This cochannel interference can be a major impairment to the signal of interest. In this paper, we describe a beamformer and equalizer system that is capable of separating and demodulating several cochannel GSM signals. The signal model includes intersymbol interference (ISI) induced by the Gaussian transmit filter, and the channel model incorporates multipath propagation and additive white Gaussian noise. The GSM synchronization sequences are used to compute the beamformer weights and achieve frame synchronization simultaneously. Decision-feedback equalization is employed to compensate for the transmit filter ISI and to demodulate the data.

A complex adaptive algorithm for IIR filtering

This correspondence generalizes the Gauss-Newton algorithm [1] for adaptive IIR filters to include complex coefficients. The resulting algorithm simultaneously updates the real and imaginary parts of the filter coefficients to minimize the average squared estimation error. It has application in frequency-domain adaptive IIR filtering [2] where the signals and filter coefficients are complex.

Convergence properties of the multistage constant modulus array for correlated sources

A steady-state analysis of the multistage constant modulus (CM) array is presented for the case of correlated source signals. Using a Wiener model for the converged adaptive algorithms, it is demonstrated that because of the cascade structure, signal cross-correlation causes phantom sources to be present. The resulting signal leakage in the adaptive cancellers between stages causes an increase in the minimum mean-square error. A parallel implementation that overcomes this loss in performance is described; it requires an initialization strategy to ensure that each stage captures a different source. Computer simulations are presented to illustrate the convergence properties of the cascade and parallel CM array systems and to verify the theoretical results.

Bandpass adaptive pole-zero filtering

An adaptive pole-zero filter comprised of a bank of bandpass filters is presented. The bandpass filters permit the adaptive filter to be realized in a parallel form of first-order sections. Simple monitoring of the filter poles during adaptation is therefore possible so that stability can be ensured. This paper focuses on bandpass filters which are implemented by a frequency-sampling structure; the use of other types of bandpass filters is briefly discussed. An application in system identification is described and computer simulation results are given.

Misadjustment and tracking analysis of the constant modulus array

The constant modulus (CM) array is a blind adaptive beamformer that can separate cochannel signals. A follow-on adaptive signal canceler may be used to perform direction finding of the source captured by the array. In this paper, we analyze the convergence and tracking properties of the CM array using a least-mean-square approximation. Expressions are derived for the misadjustment of the adaptive algorithms, and a tracking model is developed that accurately predicts the behavior of the system during fades. It is demonstrated that the adaptive canceler contributes more to the overall misadjustment than does the adaptive CM beamformer. Computer simulations are presented to illustrate the transient properties of the system and to verify the analytical results.

A Multistage Hybrid Constant Modulus Array With Constrained Adaptation for Correlated Sources

The multistage constant modulus (CM) array was previously proposed for capturing multiple received signals in a cochannel signal environment. It consists of a cascade of individual CM array stages combined with adaptive signal cancelers that remove the various signals captured across the stages. However, when the received signals are mutually correlated, the signals captured by the CM array stages are not completely canceled, and previous parallel extensions of the system do not guarantee that different signals will be captured across the stages. In this paper, we present a hybrid implementation of the multistage CM array for separating correlated signals where the canceler weights in the cascade structure provide estimates of the direction vectors of the captured signals. These estimates are then used in a parallel implementation of the linearly constrained CM (LCCM) array leading to the hybrid structure. Since the direction vectors are obtained directly from the canceler weights, the hybrid implementation does not require prior knowledge of the array response matrix and is independent of the type of antennas used in the receiver. The effect of a bias in the direction vector estimates for closely-spaced signals is analyzed, and the steady-state performance of the hybrid structure is compared to that of a conventional constrained implementation for correlated sources. Computer simulations for example cochannel scenarios are provided to illustrate various properties of the system. Mean-square-error (MSE) learning curves indicate that the proposed hybrid LCCM algorithm converges faster and has lower MSE than previous implementations