TABLE OF CONTENTS The measurement uncertainties in range and Doppler frequency can be analyzed by the ambiguity function. The function is originally introduced by Woodward [1] from a different perspective; however, the credit is accorded to him. The response function describing the output of a matched filter to a waveform u(t) that is shifted in time delay ? and Doppler frequency f d is
where
| u(t): | The complex envelope of transmitted signal; |
| u*(t- ?): | The complex conjugate of transmitted signal delayed by ? due to target range; |
| f d: | The Doppler shifted carrier frequency; |
| E: | The total energy. |
The above expression is sometimes called the "Time-frequency correlation function" from a mathematician's point of view, or the "uncertainty function" from a physicist's point of view, analogous to Heisenburg's uncertainty principle.
The squared magnitude 
is called the ambiguity function. In our discussion the ambiguity function is 
, and when a need arises to clarify we shall note it with absolute symbol 
.
The ambiguity function has an alternative expression in the frequency domain. The ambiguity function has the following three principal properties:
The property (1) states that the volume under the surface of the ambiguity function in the ?-f d plane is constant, unity. The property (2) states that the function is maximum at the origin and is smaller in magnitude elsewhere. The property (3) states that the function is symmetrical with respect to ? = 0 and f d = 0.
The...
