Improving the Ranging Performance of Random ISAC Signals Through Pulse Shaping Design

In this paper, we propose a novel pulse shaping design for single-carrier integrated sensing and communication (ISAC) transmission. Due to the communication information embedded in the ISAC signal, the resulting auto-correlation function (ACF) is determined by both the information-conveying random symbol sequence and the signaling pulse, where the former leads to random fluctuations in the sidelobes of the ACF, impairing the range estimation performance. To overcome this challenge, we first analyze the statistical characteristics of the random ACF under the symbol-wise pulse shaping (SWPS) regime. As a step further, we formulate an optimization problem to design ISAC pulse shaping filters, which minimizes the average integrated sidelobe level ratio (ISLR) while meeting the Nyquist criterion, subject to power and bandwidth constraints. We then show that the problem can be recast as a convex quadratic program by expressing it in the frequency domain, which can be readily solved through standard tools. Numerical results demonstrate that the proposed pulse shaping design achieves substantial ranging sidelobe reduction compared to the celebrated root-raised cosine (RRC) pulse shaping, given that the communication throughput is unchanged.