This paper aims to answer a fundamental question in the area of Integrated Sensing and Communications (ISAC): What is the optimal communication-centric ISAC waveform for ranging? Towards that end, we first established a generic framework to analyze the sensing performance of communication-centric ISAC waveforms built upon orthonormal signaling bases and random data symbols. Then, we evaluated their ranging performance by adopting both the periodic and aperiodic auto-correlation functions (P-ACF and A-ACF), and defined the expectation of the integrated sidelobe level (EISL) as a sensing performance metric. On top of that, we proved that among all communication waveforms with cyclic prefix (CP), the orthogonal frequency division multiplexing (OFDM) modulation is the only globally optimal waveform that achieves the lowest ranging sidelobe for quadrature amplitude modulation (QAM) and phase shift keying (PSK) constellations, in terms of both the EISL and the sidelobe level at each individual lag of the P-ACF. As a step forward, we proved that among all communication waveforms without CP, OFDM is a locally optimal waveform for QAM/PSK in the sense that it achieves a local minimum of the EISL of the A-ACF. Finally, we demonstrated by numerical results that under QAM/PSK constellations, there is no other orthogonal communication-centric waveform that achieves a lower ranging sidelobe level than that of the OFDM, in terms of both P-ACF and A-ACF cases.

翻译：本文旨在回答通感一体化领域的一个基本问题：对于测距而言，最优的通信中心化ISAC波形是什么？为此，我们首先建立了一个通用框架，用于分析基于正交信号基和随机数据符号构建的通信中心化ISAC波形的感知性能。接着，我们采用周期和非周期自相关函数来评估其测距性能，并将积分旁瓣电平的期望值定义为感知性能指标。在此基础上，我们证明了在所有采用循环前缀的通信波形中，正交频分复用调制是唯一的全局最优波形，对于正交幅度调制和相移键控星座而言，无论是在积分旁瓣电平期望值还是在周期自相关函数每个单独时延的旁瓣电平方面，均能实现最低的测距旁瓣。进一步地，我们证明了在所有无循环前缀的通信波形中，对于正交幅度调制/相移键控而言，正交频分复用是一种局部最优波形，即它能实现非周期自相关函数积分旁瓣电平期望值的一个局部极小值。最后，我们通过数值结果证明，在正交幅度调制/相移键控星座下，无论是周期自相关函数还是非周期自相关函数情况，都不存在其他正交的通信中心化波形能获得比正交频分复用更低的测距旁瓣电平。