Abstract: ‍ ‍In recent years， the spectrum congestion of the L-band （1164~1610 MHz） has become increasingly serious. Moreover， the available resources of the BeiDou Navigation Satellite System in our country are obviously insufficient. Based on the non-reproducibility of spectrum resources， it is imperative to explore new frequency bands. Because C-band navigation-signal design is not yet mature， and many countries are still investigating C-band navigation-signal systems， it is necessary for our country to conduct a study of C-band navigation signals. Satellite navigation signals at 5010~5030 MHz in the C-band have significant advantages， including less spectral interference and lower ionospheric errors， but the 20 MHz bandwidth has strict requirements for radio frequency compatibility with adjacent service bands such as those of the Radio Astronomy Service and Microwave Landing System. This study first investigated the application of the combined orthogonal frequency division multiplexing-continuous phase modulation （OFDM-CPM） method based on multiple modulation indices （multi-h） for C-band satellite navigation. Then， after analyzing the influences of key parameters on the power spectrum characteristics of a multi-h OFDM-CPM signal， a single-h OFDM-CPM（10） signal with a correlation length （L） of 64 and modulation index （h） of 0.5 and a multi-h OFDM-CPM（10） signal with a correlation length （L） of 64 and h of ［1/16，3/16］ were selected as C-band candidate navigation signals. Finally， basic navigation performance indices were evaluated， including the compatibility， code tracking accuracy， and anti-multipath performance. The study found that OFDM-CPM modulation could take into account both the out-of-band constraints and navigation performance requirements of C-band signals， and OFDM-CPM（10） signals with h=［1/16，3/16］ had the best performance， as shown by the above basic navigation performance indices. In terms of compatibility， it could make up for the slight deficiency of OFDM-CPM（10） signal with h=0.5. However， considering that the multiple modulation index will increase the complexity of the receiver， the multi-h OFDM-CPM signal is a better choice than the single-h OFDM-CPM signal for C-band navigation only when the receiver adopts a low-complexity detection algorithm.