Fundamental limits on multiple PRF radar performance

The product of the unambiguous range and doppler bandwidth of a multiple PRF radar is equal to:
R_{\max} \cdot BW_{\max} = \frac{c}{2} \frac{lcm of PRF's}{gcd of PRF's}
While this number can be increased without limit by suitable choices of the PRF's, the probability of error in resolution of ambiguity will in general increase with it, although not monotonically. In the paper new results are derived which quantify the relationship between the PRF values and the robustness of the resolution of ambiguity in the presence of measurement error. The maximum likelihood ambiguity resolution algorithm for the case of gaussian measurement errors is shown to be equivalent to mapping the time and frequency measurement vectors to the nearest points in two lattices, the product of whose densities is equal to a constant times the product of unambiguous ranges given above.