Cross Ambiguity Function Computation Using Over-Sampled DFT Filter Banks

Abstract:- This paper will demonstrate a new method to compute the Cross Ambiguity Function (CAF) using over-sampled Perfect Reconstruction Discrete Fourier Transform (DFT) filter Banks, and compare it to previous work with maximally decimated DFT Filter Banks [1]. As was shown in our previous work, the DFT Filter Bank can be used to efficiently filter the signal into sub-bands, compute the CAF in each sub-band, and then reconstruct the CAFs coherently. This method has the advantage that Narrow Band (NB) interference can be removed prior to the reconstruction. If the prototype filter satisfies specific conditions, the CAF can be reconstructed coherently, thereby improving the Time Difference of Arrival (TDOA) estimate while maintaining the Frequency Difference of Arrival (FDOA) estimate. Maximally decimated Filter Banks are most efficient from a computational viewpoint, but the choice of the prototype filter is limited to a very simple filter with poor (13 dB) side-lobes. The over-sampled DFT filter bank is somewhat more computationally complex, but filters can be designed with better side-lobe properties, so that interference can be removed more efficiently. The prototype filter for the over-sampled filter bank can be designed with lower side-lobes, which removes more of the interferer and less of the signal of interest. The design constraints for the prototype filter for the over-sampled filter bank are the same as that of the cosine modulated filter bank