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Continuous phase modulation (CPM) is a power and bandwidth efficient modulation scheme used in cellular, personal, and satellite communications among other applications. If the modulation index of the CPM waveform used by the transmitter is unavailable at the receiver, serious performance degradation may occur. This paper investigates the problem of modulation index estimation for partial response continuous phase modulation schemes. Specifically, we propose two novel estimators for the CPM signal observed in an additive white Gaussian noise channel. A non-data aided method of moments (MoM) estimator based upon the fourth-order cumulants and a data-aided best linear unbiased estimator (BLUE) based upon an approximate linear phase model of the received CPM signal have been proposed. Modified Cramer-Rao lower bound is derived for the partial response CPM schemes to assess the …