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Blind modulation classification (MC) is an intermediate step between signal detection and demodulation, and plays a key role in various civilian and military applications. In this paper, first we provide an overview of decision-theoretic MC approaches. Then we derive the average likelihood ratio (ALR) based classifier for linear and nonlinear modulations, in noisy channels with unknown carrier phase, offset and also in Rayleigh fading channels. Since these ALR-based classifiers are complex to implement, we then develop a quasi hybrid likelihood ratio (QHLR) based classifier, where the unknown parameters are estimated using low-complexity techniques. This QHLR-based classifier is much simpler to implement and is also applicable to any fading distribution, including Rayleigh and Rice. Afterwards, we propose a generic multi-antenna classifier for linear and nonlinear modulations, using an antenna array at the …