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Receiver structures for the direct detection of binary and multilevel digital optical modulation schemes employing the modulation of the state of polarization of light, or polarization shift keying (POLSK), are proposed and accurately analyzed, in the presence of optical amplifier ASE noise and electrical receiver noise. A comprehensive set of results shows that the performance of the binary system is approximately 3 dB better than IM/DD (on peak optical power), and stays so for a wide range of optical filter bandwidths. As a somewhat unexpected result, the multilevel schemes show a lower sensitivity to the use of a wide optical filter than the binary one. As a consequence, transmitting 3 b/symbol on a cubic constellation on the Poincare sphere brings about virtually no penalty, whereas transmitting 2 b/symbol has a better performance than binary transmission, for even relatively low values of the optical filter bandwidth …