For the demand of structural enhancement and backwards compatibility of modern BDS navigation signal which is represented by the pilot channel, BDS has proposed several new constant envelope modulations recently, including QMBOC and ADualQPSK modulations applied to B1 band, TD-AltBOC and ACE-BOC modulations applied to B2 band, DualQPSK modulation applied to B3 band, GCE-BOC modulation that multiplexes arbitrary signals at two different carrier frequencies. All the new modulations were systematically analyzed and a unified analytical expression of constant envelope modulation and multiplexing was summarized on the basis of the GCE-BOC modulation, which can provide an important reference for the comprehensive understanding of the signal design of the BDS global navigation satellite system and the development of new type of constant envelope modulation and multiplexing technology on this basis.