Selecting smoothing pulses for partial-response digital FM

In recent years, it has been demonstrated that partial-response continuous-phase modulation (sometimes also referred to as partial-response digital FM) is a spectrally efficient constant-envelope digital-modulation method. If maximum-likelihood sequence detection (e.g. the Viterbi detector) is used, these schemes can also be made power efficient. System complexity grows exponentially with the length of the baseband pulse that introduces the memory in the partial-response scheme. The smoothness and the length of this pulse determines the spectral properties. The paper considers binary systems based on short pulses of length ¿¿2 symbol intervals. New spectrum formulas are given for modulation schemes based on pulses with an increasing number of continuous derivatives. It is demonstrated how the spectral mainlobe and the spectral tails are affected by the shape of the pulse. Comparisons are made with binary full-response systems. The tradeoff between error probability and bandwidth is demonstrated.