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In this article, the performance of FBG-assisted ICI reduction is compared with that of SG with different OFDM symbol rise times and in presence of CD. Increase in symbol rise times requires the reduced intervals of a SG but the length of FBG remains same. The rise time of 5 ps and presence of delay due to CD, the BER performance of FBG is better than that of SG, especially for transmission distance above 30 km. In the case of middle subcarriers, FBG gives BER < 10 23 for 45 km. In the AO-OFDM system with FBG based passive device, synchronization between the ICIfree region and sampling instant is not needed, which omitting complex tuning circuits and reducing the system cost, and CP is not required due to tolerance to CD increases. 2. N. Cvijetic, OFDM for next generation optical access networks, J Lightwave Technol 30 (2012), 384-398. 3. D. Hillerkuss, et al., 26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing, Nat Photon 5 (2011), 364-371.

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CMAC is one useful learning technique that was developed two decades ago but yet lacks adequate theoretical foundation. Most past studies focused on development of algorithms, improvement of the CMAC structure, and applications. Given a learning problem, very little about the CMAC learning behavior such as the convergence characteristics, effects of hash mapping, effects of memory size, the error bound, etc. can be analyzed or predicted. In this paper, we describe the CMAC technique with mathematical formulation and use the formulation to study the CMAC convergence properties. Both information retrieval and learning rules are described by algebraic equations in matrix form. Convergence characteristics and learning behaviors for the CMAC with and without hash mapping are investigated with the use of these equations and eigenvalues of some derived matrices. The formulation and results provide a foundation for further investigation of this technique.