In this study, we analyze the Cramér-Rao lower bound (CRLB) and Ziv-Zakai lower bound (ZZLB) to evaluate the time delay estimation performance of various pilot signal designs in a cyclic prefix orthogonal frequency division multiplexing (CP-OFDM) system. Unlike previous studies that focused on additive white Gaussian noise (AWGN) channels, we specifically consider the CP-OFDM system where the delay is uniformly distributed within a given range. We aim to extend the understanding of how different waveform designs influence the bound on delay estimation accuracy. Our analysis shows that within the CP-OFDM system framework, the ZZLB of the delay estimate is only dependent on the power allocation across sub carriers, regardless of their phase. This holds true when the pilot symbol detection uncertainty is within the CP duration, and the CP is removed at the receiver prior to delay estimation. This observation simplifies the pilot signal design process. Through simulations, we examine Dirac rectangular and triangular power allocation profiles, and observe trends consistent with single-carrier waveforms using the same profiles. However, with minimal delay variation and a small number of allocated sub carriers, optimally allocating pilot power to edge sub carriers yields no transition region between profiles.