Alamouti space-time block code (STBC) combined with a simple heterodyne coherent receiver enables phase diverse coherent detection without any optical polarization tracking. While such a system consisting of only a 3-dB coupler and a single balanced photodiode has been recently demonstrated using orthogonal frequency-division multiplexed (OFDM) signals, herein we report the first application to single-carrier systems. Applicability of such technique for single-carrier systems is not straightforward since specialized digital signal processing (DSP) algorithms are required for data recovery. In this paper, we address the implementing issues and DSP algorithms applicable for single-carrier (SC) Alamouti STBC based simplified heterodyne receivers. Polarization-insensitive operation of the proposed scheme and its performance are verified by means of simulation for a 12-Gbits/s quadrature phase-shift keying (QPSK) transmission system.