Modulation classification via hierarchical agglomerative cluster analysis

Automatic recognition of digital modulation schemes (identification of the symbol constellation) is increasingly important in both overt and covert operations. Previous approaches have exploited specific characteristics of the signaling schemes in order to distinguish between members of a limited set of constellation types. When the signal-to-noise ratio (SNR) is high, the received symbol sequence (i.e., after carrier, timing, and baseband recovery) forms natural clusters in the I-Q plane; hence, the clusters can be easily detected. This is the basis of pattern (template) matching schemes. However, the situation is not so nice when SNR is low, or in the presence of carrier and phase offsets and inter-symbol interference. We propose to use a hierarchical agglomerative cluster analysis algorithm (HACA) which, for a specified number of clusters, will yield the virtual constellation which best describes the data. The number of clusters can be estimated from plots of the cluster separation distance. By proper choice of the dissimilarity measure used in HACA, problems due to frequency offset and phase jitter can be handled. We note that a specific advantage of HACA is that it can be used to detect an unknown constellation. Pattern matching schemes can also be used to decide between different constellations with the same number of symbols and the virtual constellation estimated by HACA. Preliminary classification can be accomplished by using elementary higher-order statistics (HOS). Simulation results illustrating the performance of the proposed algorithms are included.