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A novel digital signal processing (DSP) scheme for quadrature duobinary (QDB) spectrum shaped polarization multiplexed quadrature phase shift keying (PM-QPSK) based on multi-modulus blind equalizations (MMBE) is proposed and demonstrated with both simulation and experimental results. The key algorithms for this novel digital signal processing scheme include the cascaded multi-modulus algorithm (CMMA) for blind polarization de-multiplexing, multi-modulus QPSK partitioning frequency offset estimation (FOE) and two stage carrier phase recovery (CPR) with maximum likelihood phase estimation. The final signal is detected by maximum-likelihood sequence detection (MLSD) for data BER measurement. It shows that CMMA have better frequency response performance compared with CMA for noise compression. The performances of FOE and CPR are also investigated with different spectrum shaping bandwidth, group size and laser linewidth. Finally, the feasibility of the proposed digital signal processing scheme is demonstrated by the experiment of 112 Gb/s QDB spectrum shaped PM-QPSK signal with a 25 GHz bandwidth waveshaper for Nyquist WDM channels.