Average likelihood method for classification of CDMA
Vega Irizarry, Alfredo
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Signal classification or automatic modulation classification is an area of research that has been studied for many years, originally motivated by military applications and in current years motivated by the development of cognitive radios. Its functions may include the surveillance of signals of interest and providing information to blind demodulation systems. The problem of classifying Code Division Multiple Access (CDMA) signals in the presence of Additive White Gaussian Noise (AGWN) is explored using Decision Theory. Prior state-of-the-art has been limited to single channel digital signals such as MPSK and QAM, with few limited attempts to develop a CDMA classifiers. Such classifiers make use of the cyclic correlation spectrum for single user and feature-based neural network approach for multiple user CDMA. Other approaches have focused on blind detection, which could be used for classification in an indirect manner. The discussion is focused on the development of classifiers using the average likelihood function. This approach will ensure that the development is optimal in the sense of minimizing the error in classification when compared with any other types of classification techniques. However, this approach has a challenging problem: it requires averaging over many unknown parameters and can become an intractable problem. This research was successful in reducing some of the complexity of this problem. Starting with the definition of the probability of the code matrix and the development of the likelihood of MPSK signals, it was possible to find an analytical solution for CDMA signals with a small code length. Averaging over matrices with the lowest Total Squared Correlation (TSC) allowed simplifying the equations for higher code lengths. The resulting algorithm was tested using Receiver Operating Characteristic Curves and Accuracy versus Signal-to-Noise Ratio (SNR). The algorithm that classifies CDMA in terms of code length and number of active users was extended to different complex types of CDMA under the assumptions of full-loaded, underloaded, balanced and unbalanced CDMA, for orthogonal or quasi-orthogonal codes, and chip-level synchronization.