Optimal OFDM pilot sequences for time-delay and channel estimation based on the expected CRB for a large number of subcarriers

A key aspect to design an OFDM system for combined positioning and high-data-rate communications is to find optimal data and pilot power allocations. Previous work has investigated the capacity maximizing design taking into account the effects of channel and time-delay estimation for finite number of subcarriers and channel taps. In this paper, we propose a method based on the asymptotic expected Cramér-Rao bound of joint time-delay and channel coefficients that reduces the complexity of the bounds by increasing the number of subcarriers or channel taps for data and pilot power allocations design. Specifically, for long channels a general form of matrix inversion, which is computationally complex, is converted to only the inversion at strong eigenvalues or pilots. Numerical results show that as the number of subcarriers increases, the non-asymptotic bounds converge to the asymptotic bounds at a fast speed. Moreover, even for a finite number of subcarriers or channel taps the difference between joint data and pilot power allocations is negligible compared to the non-asymptotic expected Cramér-Rao bounds.