Modulation classification is an intermediate step between signal detection and demodulation, and plays a key role in various civilian and military applications. In this correspondence, higher-order cyclic cumulants (CCs) are explored to discriminate linear digital modulations in flat fading channels. Single-and multi-antenna CC-based classifiers are investigated. These benefit from the robustness of the CC-based features to unknown phase and timing offset. Furthermore, the latter provides significant performance improvement due to spatial diversity used to combat the fading effect. Classifier performances are investigated under a variety of channel conditions. In addition, analytical closed-form expressions for the cyclic cumulant polyspectra of linearly digitally modulated signals affected by fading, carrier frequency and timing offsets, and additive Gaussian noise are derived, along with a condition for the oversampling factor to avoid aliasing in the cycle and spectral frequency domains. Part of this work was published in a preliminary form and presented at the IEEE Military Communication Conference (MILCOM) 2003 and 2005, USA, under the titles "Higher-order cyclic cumulants for high order modulation classification," and "Selection combining for modulation recognition in fading channels," respectively. O. A. Dobre (B)