Design of tracking telemetry and command signal based on prolate spheroidal wave functions waveform forming

Enhancing the signal waveform's power efficiency and information transmission efficiency is one of the issues in tracking, telemetry, and command (TT&C) system waveform design. It is found that the basic characteristics such as biorthogonal, optimal time-frequency energy aggregate, and spectral controllable of prolate spheroidal wave functions (PSWFs) make it be a reliable candidate for TT&C signal waveform design. In this paper, PSWF are introduced into TT&C signal waveform design, and a four-dimensional unified spread spectrum TT&C signal waveform design method based on PSWF waveform shaping is proposed. This new idea, by using high-energy aggregation PSWF as waveform shaping functions, can obtain higher power efficiency and information transmission rate, better anti-interference and anti-interception capabilities. It provides a better waveform scheme for the design of TT&C signal waveforms. For instance, the suggested approach can boost the spread spectrum gain by 3.44 dB and the information transmission rate by one when compared to conventional TT&C signals based on rectangular pulse functions under the same system error performance.