The authors present a statistical analysis of the steady-state and transient properties 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 hyperplane decision boundary. It is demonstrated that, although the weights grow unbounded, the mean-square error decreases towards zero. These results indicate that the algorithm, on average, quickly learns the correct hyperplane associated with the system identification model. However, the nature of the mean-square error and the corresponding performance surface are such that the perceptron is prevented from correctly classifying with probability one until the weights converge at infinity.>

The LMS canceller structure has been widely used to spatially reject strong interferences from the output of a sonar array. It has generally been assumed that each interference consists of a single plane wave arrival. In some applications, the interference may actually have angular extent which can dramatically influence canceller performance. This paper demonstrates these effects for a bandlimited, spectrally flat interference by means of a computer simulation. Cancellation achieved is determined as a function of source extent, reference hydrophone spacing, and distance between the references and primary. These results are compared to previous results obtained at a single frequency. It is shown that for a well designed canceller, the single frequency results at an effective frequency, fe, predict performance with the broadband interference. This allows a number of design guidelines and closed form approximations developed at a single frequency to be used in the more realistic broadband case.

The performance of a matched filter square-law envelope detector is investigated for a new signal-in-noise model, that of a partially coherent-fading random-phase sine wave in additive zero-mean noise. This model is of interest when analyzing the effects of random amplitude and/or phase channels on narrow-band input signals. The amplitude and the phase of the sine wave are assumed to be independent random processes with known bandwidths. This paper obtains deflection-criteria detection-performance results for the envelope detector as a function of the bandwidths of the amplitude and phase of the signal process, the noise process, the observation time, and the second-moment statistics of the amplitude, phase, and noise processes. The results show quantitatively that the detection performance of the envelope detector is much more sensitive to loss of phase coherence than to loss of amplitude coherence.