Ambiguity Function

The ambiguity function (AF) represents the time response of a filter matched to a given finite energy signal, when the signal is received with a delay ?> and a Doppler shift ?> relative to the nominal values (zeros) expected by the filter. The ambiguity function is defined by the complex envelope of the signal.

The ambiguity function is a major tool for studying and analyzing radar signals. It will be used extensively in the following chapters, where different signals will be described.

The chapter presents four important properties of the ambiguity function and proves them. The properties are:

Maximum at the origin.

Constant volume.

Symmetry with respect to the origin.

Shearing due to Linear-FM

LFM induced shearing is explained. The cuts of the AF along the delay and Doppler axes are described and related to the autocorrelation and spectrum.

The chapter ends with a definition of the periodic ambiguity function (PAF). The PAF is an important tool for analyzing the delay-Doppler response of long periodic signals (including CW), when processed by a correlation receiver with a finite reference signal extended over an integer number of periods. The main properties of the PAF are discussed.

Appendix 3.1 contains a MATLAB code for generating numerical 3-D plots of the AF, of most user defined signals.