Feature based order recognition of continuous-phase FSK using principal component analysis

Principal component analysis (PCA) is a technique that performs a linear transformation on the input space to align directions of maximum variation with the directions of the axises. In this paper, we study the feasibility of principal component analysis based order recognition of continuous phase FSK. The approximate entropy (ApEn) of the received signal, ApEn of the phase of the received signal, and ApEn of the instantaneous frequency of the received signal are used as a set of distinguishing features. The work aims in devising an unsupervised learning algorithm under noisy, carrier frequency offset and fast fading channel conditions. The instantaneous frequency is shaped by using root raised cosine pulses. Performance of principal component based method is compared to stacked autoencoder (SAE) based approach which is more computationally complex technique that can model relatively complicated relationships and non-linearities. For fair comparison both the PCA and SAE based methods use approximate entropy features. The benefit of employing PCA is that after PCA transformations the computation cost can really be decreased a lot. Also in both methods, no a priori information is required about carrier phase, symbol rate and carrier amplitude. The PCA based method shows higher accuracy than the SAE method.