This paper studies the Cramér-Rao bound (CRB) for burst-mode transmission synchronization of Single-Sideband Frequency Shift Keying (SSB-FSK). Based on the CRB computations of burst-mode CPM, for conventional double sided schemes, it was shown that it is possible to obtain an optimum training sequence that minimizes the CRBs simultaneously for the joint estimation of symbol timing, frequency offset, and carrier phase. However, due to the SSB-FSK non-antipodal alphabet, it is impossible to use the same optimum sequence to minimize the CRBs for all parameters simultaneously. Meanwhile, in this paper, we propose a new general training sequence that can minimize the sum of all CRBs for any binary SSB-FSK. The derived results can be helpful for data-aided (DA) synchronization of SSB-FSK modulation.

This study revokes the performance of continuous phase modulation (CPM) able to generate a single-sideband (SSB) spectrum directly. This signal is analyzed in terms of modulation indices, pulse lengths, and pulse widths, all of which affect error probability, bandwidth, SSB property, and receiver complexity. The error probability performance is based on an approximation of the minimum Euclidean distance. A numerical power spectral density calculation for this particular SSB modulation in terms of the modulation index is presented. Reasonable tradeoffs in designing modulation schemes have been proposed using multi-objective optimization to ensure sizable improvements in bit error rate (BER), spectral efficiencies, and complexity without losing the property of being a SSB signal. Performance comparisons are made with known CPM schemes, e.g., Gaussian Minimum Shift Keying (GMSK) and Raised Cosine based CPM (RC).