High-precision ranging plays a crucial role in future 6G Integrated Sensing and Communication (ISAC) systems. To improve the ranging performance while maximizing the resource utilization efficiency, future 6G ISAC networks have to reuse data payload signals for both communication and sensing, whose inherent randomness may deteriorate the ranging performance. To address this issue, this paper investigates the power allocation (PA) design for an OFDM-based ISAC system under random signaling, aiming to reduce the ranging sidelobe level of both periodic and aperiodic auto-correlation functions (P-ACF and A-ACF) of the ISAC signal. Towards that end, we first derive the closed-form expressions of the average squared P-ACF and A-ACF, and then propose to minimize the expectation of the integrated sidelobe level (EISL) under arbitrary constellation mapping. We then rigorously prove that the uniform PA scheme achieves the global minimum of the EISL for both P-ACF and A-ACF. As a step further, we show that this scheme also minimizes the P-ACF sidelobe level at every lag. Moreover, we extend our analysis to the P-ACF case with frequency-domain zero-padding, which is a typical approach to improve the ranging resolution. We reveal that there exists a tradeoff between sidelobe level and mainlobe width, and employ the Dinkelbach’s method to seek a globally optimal PA scheme that reduces the EISL. Finally, we validate our theoretical findings through extensive simulation results, confirming the effectiveness of the proposed PA methods in reducing the ranging sidelobe level for random OFDM signals.

Future 6G Integrated Sensing and Communication (ISAC) networks are expected to reuse data payload signals for both communication and sensing. However, the inherent randomness of these signals can degrade ranging accuracy. To address this challenge, this paper studies power allocation (PA) strategies for CP-OFDM-based ISAC systems operating under random signaling, with the goal of reducing the sidelobe levels in the periodic auto-correlation function (P-ACF) of the ISAC signal. Specifically, we first derive closed-form expressions for the average squared P-ACF, and then formulate an optimization problem that minimizes the expected integrated sidelobe level (EISL) under arbitrary constellation mappings. We rigorously prove that, across all constellations, a uniform PA scheme yields the lowest ranging sidelobe levels, both in terms of the EISL and at each individual lag. Additionally, we extend our analysis to scenarios involving frequency-domain zero-padding. In such cases, we show that uniform PA no longer guarantees optimal sidelobe suppression. To address this, we propose a projected gradient descent (PGD) algorithm to find a locally optimal PA scheme that minimizes the EISL. Finally, our theoretical results are substantiated by extensive simulations, which confirm the effectiveness of the proposed PA methods in suppressing the ranging sidelobe levels of random OFDM signals.

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.