Generalized MBI Algorithm for Designing Sequence Set and Mismatched Filter Bank With Ambiguity Function Constraints

A sequence set with ambiguity function (AF) specifications is frequently required in multi-transmit active sensing systems which exploit waveform diversity. This paper formulates a new model to jointly design sequence set and mismatched filter bank with AF requirements, which is a generalization of the auto-AF and cross-AF adopted in the matched filter scheme to attain lower AF sidelobe levels with an increased degree-of-freedom. The aforementioned designs result in nonconvex and nonlinear high-order polynomial (HOP) optimization problems with HOP constraints. Although the maximum block improvement (MBI) method has exhibited the powerful HOP optimization ability to design a short sequence with slow-time AF, it cannot tackle HOP constraints and involves high-complexity tensor operations. To address these issues, we develop a generalized MBI method for the HOP constrained optimization formulations. In addition, the proposed algorithm significantly reduces the computational complexity via designing an equivalent polynomial function for the original multi-linear tensor function. Numerical results demonstrate the excellent performance of our design solutions.