The Design of Orthogonal Prolate Spheroidal Wave Function Pulse Waveform Based on Karhunen-Loeve Transform

The orthogonal pulse design based on Prolate Spheroidal Wave Function (PSWF) is hard for hardware design. By the optimization and integration of the pulse solution and orthogonalizaiton procedure, a novel orthogonal PSWF pulse waveform design based on Karhunen-Loeve transform is proposed. The method represents firstly PSWF into a series of Legendre functions, and the factor matrix for orthogonality is achieved by Karhunen-Loeve transform of the cross correlation matrix. On this basis, an efficient hardware implementation of orthogonal PSWF pulse is put forward. The proposed method builds a mapping between orthogonal PSWF pulse and coefficient vector of Legendre polynomial，and the method can be used to design orthogonal PSWF pulses by changing eigenpolynomial coefficients effectively. Meanwhile, the method has good real-time performance and low hardware complexity and provides a fast and efficient scheme for the engineering realization of orthogonal PSWF pulse.