Phase Shift Keyed (PSK) and Frequency Shift Keyed (FSK) modems are the core of many satellite and man-pack radio communication systems. Modulation limited to phase only assures us a constant envelope modulated signal. Constant modulation envelope permits operation of the output power amplifier near the edge of saturation, a region that has the highest efficiency. High power amplifier efficiency improves battery life in radios. Continuous Phase Modulation (CPM) maintains constant amplitude and exhibits reasonable spectral confinement. CPM is a distinct type of modulation as it is a nonlinear process with memory while most other modulations schemes are linear and are memoryless. Continuous Phase Modulation, Vestigial Sideband Modulation (VSB) and Gaussian Minimum Shift Keying (GMSK) notably used in the Global System for Mobile Communication (GSM) are all similar class of modulation as they exhibit a constant envelope. The similarity of these systems to Offset Quadrature Phase Shift Keying (OQPSK) is so striking that almost all designs revert back to OQPSK to perform demodulation even though they are Phase Modulated. System performance is reduced when OQPSK, a linear time invariant receiver, is used to process CPM, a non-linear system with memory. We note that the maximum likelihood implementation of the CPM receiver requires individual, complex weight, matched filters for each phase profile in the CPM signal set while the OQPSK receiver requires a single quadrature matched filter. We design the modulation and demodulation structure for the phase demodulation of CPM signals. We address one of the biggest concerns of CPM demodulated process, the challenge of estimating and removing significant Doppler offsets. We develop synchronization loops for Doppler carrier frequency recovery, carrier phase recovery, and symbol timing recovery that operate with traditional preamble sequences as well as random data signal sequences.