We present the theoretical analysis and the numerical simulations of a polarization-independent coherent receiver for binary intensity-modulated (IM) signals. The receiver is designed for access networks or data centers and is DSP-free. It is based on a 3 × 3 symmetric coupler with phase-diversity detection. To achieve polarization independence, the receiver conveniently exploits the third input of the 3 × 3 coupler, which was previously left unused. We first introduce the scheme of the receiver and derive the analytical expressions for the final output signal, which is produced by analog processing. We then confirm the approach by numerical simulations. These are used to assess the practical potential and indicate the possible limitations. We finally discuss the role of the key parameters that must be considered in upgrading to higher bit rates and the extension to other modulation formats.