Lower boundary capacity estimations of frequency-selective communication channels with PAM-n-signals achievable using resolution time theory

The issue of ensuring high specific capacity of promising wire telecommunication systems is one of the key problems of the last decade. At the same time, despite the existing spectrally efficient modulation methods that are used in existing communication systems, the majority of leading researchers associate further solution of this issue with the transition to the mode of information transmission at a rate "Faster-than-Nyquist" rate (FTN), in which the information receiving about the channel symbol occurs with pronounced intersymbol interference. In turn, this causes difficulties in the practical implementation of the receiver when using optimal signal processing algorithms with nonpolynomial computational complexity, and in the case of suboptimal demodulation methods implementing various types of channel equalization, due to conceptual limitations cannot provide a wide coverage of speeds in this mode. In this regard, the study of an alternative approach to processing signals with multi-position PAM-n-signals on the output of baseband frequency-selective channels (FSC) is relevant. The object of this paper is the study of the possibilities offered by the theory of resolution time for baseband FSC of the, in which information is transmitted using the PAM-n-signal, in the FTN mode. A modified mathematical model of FSC is presented, thanks to which analytical expressions are obtained for estimating the specific capacity in terms of the low bound capacity estimation introduced by Sh. Shamai, expressions for estimating the BER, including the case under the action of destabilizing factors on the symbol synchronization system. Auxiliary capacity estimations and rules for calculating the conditions for achieving them are introduced, convenient for engineering analysis. By means of numerical simulating for the most typical conditions inherent in wired FSC, which are modeled in this work by Chebyshev filters with ripple level of 3 dB and Butterworth filters, it is shown that in the FSN mode with a S/N ratio of no more than 40 dB and instability of the symbol synchronization system operation of 2.5% of the channel symbol duration with a bit error probability of 10–12, it is possible to expect a specific capacity of 5.7–8 bits/Hz*s. It is shown that these results are achieved by using hybrid forms of partial pulses. Recommendations for choosing a partial pulse shape are presented, their main properties are studied from the point of view of their engineering application.