Continuous Phase Modulation (CPM)

Continuous phase modulation (CPM) is a constant-amplitude modulation scheme that can be considered to be a generalization of continuous phase frequency shift-keying (CPFSK) or minimum shift-keying (MSK). The lack of phase discontinuities reduces high-frequency spectral content, making CPM a highly spectrally efficient scheme.

A form of CPM that can result in significant coding gains is multi-h phase coding, where h stands for the modulation index. This scheme may be viewed as a generalization of CPFSK schemes because different phase changes result from the transmission of the same symbol in two contiguous symbol intervals. A mathematical representation of the signal during the ith interval, iT ≤ t  (i + 1)T, is expressed by the following formula:

where    E_s is the symbol energy

T is the symbol duration

ω_c is the carrier frequency in radians/second

d and ω are the sequences that represent the M-ary information sequence.

d_iω_i(t - iT) and φ are data phase terms that correspond to the phase associated with the current data symbol and the phase accumulation due to the previous data symbol such that

and

where is the angular frequency corresponding to the modulation index used during the ith baud. The different values of h can be used between symbol intervals in a round robin fashion.

Refer to the following resources for more information about the algorithms and methods used in CPM:

• Premji, Al-Nasir and Desmond P. Taylor. "Receiver Structures for Multi-h Signaling Formats." IEEE Transactions on Communications 35,4 (1987).
• Oerder, Martin and Heinrich Mayer. "Digital Filter and Square Timing Recovery." IEEE Transactions on Communications 36, 5 (1988).