Ambiguity function

Keywords radar bistatic radar multistatic radar ambiguity function parasitic radar forward scatter Babinet s principle passive coherent location netted radar. 

The ambiguity function represents the output of a matched filter and may be written as... 

Computation of this function results in a three-dimensional plot for which one axis is time delay (or range), the second is Doppler frequency or radial velocity and the third is the output power of the matched filter (usually normalised to unity). The extent of the ambiguity function peak in the Tr and the fd dimensions determines the range and Doppler resolutions respectively. As we are using the directly received signal only we term this self-ambiguity as there is no inclusion of any system geometry dependence on the transmitter and receiver locations. 

Figure 3. The ambiguity function for a BBC radio 4 transmission at 93.5MHz.

Palace with the receiver located at University College London. From the bistatic form of the ambiguity function this can be written as ... 

Here we extend the bistatic case to netted scenarios. The topology selected is the simple case of N transmitters and one common receiver, i.e. we have in effect a series of multiple bistatic geometries with varying baselines. The reason for this choice lies in the fact that it is convenient to reference all calculations to the single receiver, thus obtaining one unified form for the ambiguity function. 

The outcome of this procedure will be the same as in the previous case in terms of the system s parameters (resolution and ambiguity), but not exploited via centralized processing as the ambiguity function seen by each receiver will be individually different. 

The mathematical representation of the ambiguity function for this second method is now different. The matched filtering is performed for each echo and the final output will be a summation of the bistatic ambiguity functions of the various bistatic pairs. The following equation outlines this ... 

Figure 6. Contour plot and cuts along the velocity and range axis of the ambiguity function/bistatic pair dominance case.

The left plot represents the cuts of the bistatic ambiguity function of the first bistatic pair, in the absence of the second transmitter. Adding the emitter, and for this topology where the two weighting factors are comparable, the resolution in range and velocity has improved significantly. Moreover, the ambiguity peaks are suppressed. 

Figure 7. Bistatic and netted cuts of the ambiguity function balanced case.

Tsao, T., Varshent, P., Weiner, D. and Schwarzlander, H. Ambiguity function for a bistatic radar IEEE Trans Aerospace and Electronic Systems, Vol. 33, No. 3, pp 1041-1051, 1997. 

The above equation is very similar to the cross-ambiguity function, but here the time-delay is introduced only in the transmitted signal. This form of the transform is more convenient for digital implementation and will be referred to below as a range-Doppler correlation function. 

Under such transformations = Uo, the ambiguity function of the waveform [Pg.279]

The paper of Parr and Bartolotti is prescient in many ways [1], It defines the shape function and describes its meaning. It notes the previously stated link to Levy s constrained search. It establishes the importance of the shape function in resolving ambiguous functional derivatives in the DFT approach to chemical reactivity—the subdiscipline of DFT that Parr has recently begun to call chemical DFT [6-9]. Indeed, until the recent resurgence of interest in the shape function, the Parr-Bartolotti paper was usually cited because of its elegant and incisive analysis of the electronic chemical potential [10],... 

Ambiguity emerges when different functions are indistinguishable from each other or when objects appear to be something other than what they actually are. Ambiguous functions and structural details create uncertainty in the mind of the observer. Well people usually respond to such uncertainty... 

The signal was sampled via the analyser. The ambiguity function of the signal acquisition can be described by Equations (7) and (8). 

Figure 7. Ambiguity function of IRNSS-IC S-band acquisition...

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