This paper introduces a novel noncoherent linear channel equalization structure for time dispersive channels subjected to non negligible carrier frequency offsets for double differential phase shift keying (DDPSK) modulation. An optimization criterion for the adjustment of the coefficients of this equalization structure, termed cross-differential minimum mean square error (CDMMSE), is also proposed. In contrast to a previous work in the literature where the equalizer coefficients needed to be iteratively calculated without assurance of global convergence, the proposed CDMMSE criterion accepts a closed form solution. It will be shown that this solution coincides with that of the optimum coherent linear minimum mean square error (MMSE) equalizer when the transmitted symbols possess constant modulus. Simulation results are presented that corroborate the predicted performance of the proposed approach