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1. Introduction
Nowadays, wireless communication is playing a very important role in our daily life. The growing demands on wireless multimedia services and products lead to increasing needs for radio spectrum and data rates. Thereby, the research on modulations with high bandwidth efficiency is on focus [1]. In order to satisfy the higher and higher demand for communication systems, an extended binary phase shift keying (EBPSK) system with very high spectra efficiency is introduced in [2]. A special impacting filter (SIF) which can produce high impact at the phase jumping point, narrow in bandwidth, and great improvement in SNR, was applied at the demodulator [3]. Therefore, a simple amplitude detector followed would perform the demodulation of EBPSK signals [4]. However, the conventional threshold decision may not be best to achieve the optimum performance, and the SIF used in EBPSK demodulator brings more difficulty in obtaining posterior probability for low-density parity check (LDPC) codes decoding. A simple and general bit metric generation method is proposed by Hyun and Yoon [5] for the soft information to initial channel decoding. We modify the scheme to suit our system and the method is referred to as MHY in this paper. Meanwhile, nonlinear detectors are specifically designed to get the optimum performance of a blind multiuser detector [6, 7] and nonlinear channel equalization [8–10] and providing accurate posterior probability estimates (PPEs) for LDPC decoding [11, 12]. All results have shown that a nonlinear demodulator performs similar to an optimum receiver. One of the goals of this paper is the analysis of nonlinear demodulation with the channel decoder. We make use of the fact that the demodulator performance should not only be measured by low BER, but also in its ability to provide accurate PPEs that can be exploited by a soft-input channel decoder to achieve capacity. In this paper, we will introduce a nonlinear demodulation technique called the support vector machine (SVM) classifier [13]. The design approach is completely novel, where we select only a few samples of the SIF output for SVM training and testing at intermediate frequency (IF)...