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Under certain assumptions, simple analytical expressions can be derived for the expected value of bilinear and multilinear time-frequency representations of any quadrature-amplitude modulated communication signal (QAM). The symbol sequence should be i.i.d. and the modulation constellation should have independent and identically distributed real and imaginary parts. Initially, a characterization of QAM modulation schemes using second-order and higher-order moments and spectra-based time-frequency distributions is given. Then this characterization is exploited to derive QAM signal detection schemes. These schemes are tested in low SNR and against narrowband interference.