A newly developed constant envelope FQPSK modem/radio architecture, which employs a modified double-jump (DJ) filter in the cross-correlated FQPSK system, is proposed for personal communications systems (PCS) and mobile satellite applications, Power efficiency and spectrum efficiency of this system are investigated in a nonlinear amplified (NLA) environment. Bit error rate (BER) performance is evaluated in a noisy Rayleigh fading channel, We demonstrate that with the simplest threshold detectors (binary robust eye diagrams in I and Q channels), this system is 4-7 dB more power efficient than the U.S. digital cellular and Japanese Handyphone standard pi/4-QPSK (50%-100% more spectrally efficient than the recently adopted wireless local area network (LAN) standard GFSK and the European standard GMSK), Results indicate that the proposed DJ filtered FQPSK is a power and spectrally efficient modem/radio technique. By selecting different system parameters, this system can be optimized for a wide range of applications in PCS and mobile satellite communications.