performed, knowledge of the precise Doppler frequency allows ranging without interference from any other targets which are not also moving at exactly the same velocity. This type of ambiguity function is produced by ideal white noise (infinite in duration and infinite in bandwidth). However, this would require infinite power and is not physically realizable. There is no pulse that will produce from the definition of the ambiguity function. Approximations exist, however, and noise-like signals such as binary phase-shift keyed waveforms using maximal-length sequences are the best known performers in this regard. Properties (1) Maximum value (2) Symmetry about the origin (3) Volume invariance (4) Modulation by a linear FM signal (5) Frequency energy spectrum (6) Upper bounds for and lower bounds for exist for the power integrals . These bounds are sharp and are achieved if and only if is a Gaussian function. Square pulse Consider a simple square pulse of duration and amplitude : where is the Heaviside step function. The matched filter output is given by the autocorrelation of the pulse, which is a triangular pulse of height and duration (the zero-Doppler cut). However, if the measured pulse has a frequency offset due to Doppler shift, the matched filter output is distorted into a sinc function. The greater the Doppler shift, the smaller the peak of the resulting sinc, and the more difficult it is to detect the target. In general, the square pulse is not a desirable waveform from a pulse compression standpoint, because the autocorrelation function is too short in amplitude, making it difficult to detect targets in noise, and too wide in time, making it difficult to discern multiple overlapping targets. LFM pulse A commonly used radar or sonar pulse is the linear frequency modulated (LFM) pulse (or "chirp"). It has the advantage of greater bandwidth while keeping the pulse duration short and envelope constant. A constant envelope LFM pulse has an ambiguity function similar to that of the square pulse, except that it is skewed in the delay-Doppler plane. Slight Doppler mismatches for the LFM pulse do not change the general shape of the pulse and reduce the amplitude very little, but they do appear to shift the pulse in time. Thus, an uncompensated Doppler shift changes the target's apparent range; this phenomenon is called range-Doppler coupling. Multistatic ambiguity functions The ambiguity function can be extended to multistatic radars, which comprise multiple non-colocated transmitters