Methods of decoding N superimposed coherent optical transmission modes transmitted along a multimode optical fiber are provided where the optical signal detector comprises coherent detection hardware and a digital signal processor. The optical signals are split into N optical detection channels of the coherent detection hardware, which is used to measure the phase and amplitude of the output optical signals as a vector field matrix [ê]1×n. The digital signal processor determines the output principal states [PSout]1×n of the output optical signals from the principal state eigenvectors of an output matrix corresponding to the N propagating optical signals at the receiving portion of the data transmission link and extracts the input optical signals [M]In from the output optical signals using the output principal states [PSout]1×n, the vector field matrix [ê]1×n of the output optical signals, and a time delay τ of each output signal. Optical signal receivers for the execution of the methodology disclosed and contemplated herein are also provided.