Approaching the Shannon Limit by Means of Optimal FTN Signals with Increased Size of PAM Signal Constellation

Application of Faster than Nyquist (FTN) signals allows achieving high spectral and energy characteristics of the communication system. Further approaching the Shannon limit that determines the channel throughput is related to increasing the size of the signal constellation. However, an increase in the size of the signal constellation results in sharp growth of energy losses for FTN signals. To reduce these energy losses optimal FTN pulses obtained as a result of solving the optimization problem with the constraint on signal constellation size M may be used. In this work, optimal pulse shapes for pulse-amplitude modulation (PAM) with M=4, 16, 64, 256 were found. It was shown that applying optimal FTN signals with PAM allows reducing energy losses by 4 dB regarding the FTN signals based on root-raised-cosine pulses for coherent symbol-by-symbol detection algorithm. In terms of approaching the Shannon limit, the closest results are provided by determining the bandwidth containing 99% of signal energy.