MLSD for Hexagonal Multicarrier Transmission With Time–Frequency Localized Pulses

Due to the well-separated lattice structure, the excellent time-frequency (T-F) concentration of the modulation pulses, and the under spread property of the mobile radio channels, the pulse cross-correlation matrix (PCCM) at the receiver in a properly designed hexagonal multicarrier transmission scheme essentially takes on a band-limited and sparse structure. By neglecting the almost-zero-valued entries in the PCCM and rearranging the data vector with the aid of the pilot symbols, we propose a parallel maximum-likelihood sequence detection (MLSD), which decomposes the original large-sized MLSD into several small-sized MLSDs that independently operate. With the parallel MLSD via the dynamic programming algorithm, the global maximization of the log likelihood is guaranteed. The signal-to-noise ratio (SNR) loss due to such idealization of the PCCM is analytically evaluated. It is shown that, when the signaling efficiency, i.e., a quantity characterizing the density of symbols in the T-F plane, is not so large, the performance degradation is negligible, compared with that caused by the background noise in practical environment. Simulation results are presented to confirm the effectiveness of the proposed parallel MLSD scheme.