Implementations of cyclic cross-ambiguity functions in FPGAs for large scale signals

Abstract

This work presents theoretical formulations and algorithm development techniques for implementing the cross-ambiguity function on field programmable gate arrays (FPGA). Signal algebra operator techniques are utilized to formulate the cross-ambiguity function as a composition of cyclic mappings over finite dimensional Hilbert spaces. These formulations of linear operator compositions are proven to be essential to effect large scale FPGA implementations. Results are presented for Virtex 5 implementations of cross-ambiguity function operations using high order numeric sequences of up to 16384 samples in length. These results are being used in the development of a modeling framework for the study of MIMO radar waveform diversity design.