Analysis of bandwidth efficiency and modulation parameter for chirp-rate modulation

A code transmission method of chirp-rate modulation is proposed based on partial overlap of the pulse-width. Accordingly the improving coefficient of bandwidth efficiency is derived, and the analytic expression of improving maximum is obtained using the demodulation method in the fractional Fourier domain. Next, the chirp-rate modulation parameter is analyzed from the orthogonality of modulated signals and the error about discrete sampling position. It is found that not only the cross-correlation function but also the error of sampling position run to zero as the time-bandwidth product of modulated signal increases. Even if the time-bandwidth product is not large enough, the appropriate modulation parameter can be accepted for maintaining the orthogonality or reducing this error. Finally, the simulations are made to prove the above-mentioned theories.