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We investigate novel transmission schemes over multimode fiber with multiple output detectors, providing more efficient utilization of the available spatial-temporal degrees of freedom of the system by combining coherent phase shift keying transmission with direct detection. We evaluate the statistics of the electrical charge generated by each detector, and its dependence on factors such as detector type, dimension and offset position. In the frequency-selective case, we reveal that temporal degrees of freedom resulting from nonoverlapping time pulses modify the decision variable statistics. We apply the ensuing model to propose a novel phase-modulated single input multiple output (SIMO) multimode fiber transmission system employing multiple detectors and multiple input multiple output (MIMO) space-time postdetection signal processing in order to mitigate the ISI stemming from intermodal dispersion.