This paper derives probability density functions (PDFs) to describe the behavior of data demodulated with imperfect channel estimation. The PDFs apply to cases of flat Rayleigh-fading, multiple-diversity reception Rayleigh-fading, and flat Ricean-fading. These PDFs can be used to determine analytically both the symbol error rate and bit error rate for multi-amplitude constellations with in-phase and quadrature components, thus avoiding the need for extensive computer simulation