J. J. Spilker, Jr.
Philco Western Development Laboratories
Palo Alto, California
This work was supported by the Philco WDL Independent Development Program. This paper, submitted after the Symposium, represents a more detailed presentation of some of the issues raised in the discussion sessions at the Symposium and hence, constitutes a worthwhile addition to the Proceedings.
INTRODUCTION
One of the most important objectives in processing a stream of data is to determine and detect the presence of any invariant or quasi-invariant “features” in that data stream. These features are often initially unknown and must be “learned” from the observations. One of the simplest features of this form is a finite length signal which occurs repetitively, but not necessarily periodically with time, and has a waveshape that remains invariant or varies only slowly with time.
In this discussion, we assume that the data stream has been pre-processed, perhaps by a detector or discriminator, so as to exhibit this type of repetitive (but unknown) waveshape or signal structure. The observed signal, however, is perturbed by additive noise or other disturbances. It is desired to separate the quasi-invariance of the data from the truly random environment. The repetitive waveform may represent, for example, the transmission of an unknown sonar or radar, a pulse-position modulated noise-like waveform, or a repeated code word.
The problem of concern is to estimate the signal waveshape and to determine the time of each signal occurrence. We limit this discussion to the situation where only a single repetitive waveform is present and the signal sample values are binary. The observed waveform is assumed to be received at low signal-to-noise ratio so that a single observation of the signal (even if one knew precisely the arrival time) is not sufficient to provide a good estimate of the signal waveshape. The occurrence time of each signal is assumed to be random.
THE ADAPTIVE DETECTION MACHINE
The purpose of this note is to describe very briefly a machine[2] which has been implemented to recover the noise-perturbed binary waveform. A simplified block diagram of the machine is shown in [Figure 1]. The experimental machine has been designed to operate on signals of 10³ samples duration.
Each analog input sample enters the machine at left and may either contain a signal sample plus noise or noise alone. In order to permit digital operation in the machine, the samples are quantized in a symmetrical three-level quantizer. The samples are then converted to vector form, e.g., the previous 10³ samples form the vector components. A new input vector, Y⁽ⁱ⁾, is formed at each sample instant.