The multilevel (M-ary) modulation methods utilized thus far encoded information as the parameters of the amplitude, frequency or phase of a sinusoidal carrier. The M-ary ASK, FSK and PSK have been compared to the binary ASK, FSK, and PSK for their bit error rate (BER) performance and bandwidth efficiency. Quadrature amplitude modulation (QAM) encodes information as the amplitude and phase of a sinusoidal carrier and, for the first time, two parameters are used to produce M discernable symbols that are bandwidth efficient and have sufficient BER performance.

A QAM signal modifies the amplitude and shifts the phase angle of the carrier frequency to one of M discrete sets of values during the symbol time T _s for the representation of 2V = log ₂ M binary logic signals for the transmission of information. The QAM in-phase (I) cosine and quadrature (Q) sine carrier signals have a carrier frequency of f _c Hz, and a 0 reference phase angle, as given by the analytical expression in Equation 3.68.

(3.68)

The in-phase A _I ^j and quadrature A _Q ^j carrier amplitudes determine the phase shift and the resulting complex phasor constellation plot for the QAM signal. The constellation plot is usually symmetrical in the four quadrants. The QAM signal, as did the QPSK signal, displays an inherent I-Q decomposition in Equation 3.68.

The input information is straight-binary coded data ( b _{i ,} b _{i +1},..., b _{i +}