An improved receiver and method estimate one or more parameters, such as amplitude and signal-to-noise ratio, of a received signal, such as an M-QAM or q-ASK signal. The amplitude of an M-QAM signal is estimated based upon known or ascertainable phase information regarding a plurality of transmitted symbols. The amplitude of a q-ASK signal is estimated based upon known or ascertainable magnitude information regarding a plurality of transmitted symbols. In another embodiment, the amplitude of an M-QAM or q-ASK signal is estimated based on statistical knowledge of the amplitude of the transmitted symbols. Other embodiments estimate amplitude, noise power, and signal-to-noise ratio of a received signal utilizing second-order and fourth-order moments of received samples, a maximum likelihood searching process, or a Kurtosis estimation process.