A digital-analogue match filter for piecewise square pulses

Abstract

It is well known that the optimum signal to noise ratio in a radar is obtained when the receiver response is matched to the transmitter pulse shape. A matched receiver has an impulse response, g(t), equal to the negative fold of the transmitter pulse shape, p(t), i .c.: g(t) = p(-t). On the other hand we have that for a given maximum peak and average power the pulse length is shortest when the transmitter pulse has a square or piecewise square shape (sequences of positive and negative pulses. In many cases the square shapes are the easiest, if not the only possible, shapes that can be obtained in a transmitter. Here we use "square" to imply pulses with fairly constant amplitude and relative short transit times. Square-wave receiver input responses can not he Obtained with simple lumped element filters. One needs either taped delay lines or digital techniques. The present note describes a hybrid analog-digital technique to achieve a matched set of piecewise "square" transmitter pulse shapes and receiver input response. The scheme works also for phase (0-180°) coded pulse sequences. The scheme is a natural use for a digital decoder for phase coded pulses. First we shall describe the operation for n single square pulse. The extension to a phase coded sequence is straightforward.