Design of OFDM sequences for joint communications and positioning based on the asymptotic expected CRB

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. Previously, A capacity maximizing design by taking into account the effects of channel and time-delay estimation for finite number of subcarriers and channel taps has been investigated. Increasing the number of subcarriers and channel taps make the matrix inversions in the non-asymptotic bounds close to singular or badly conditioned. Furthermore, computational complexity of such a system designed by non-asymptotic bounds grows significantly. In this paper, a method based on the asymptotic expected Cramér-Rao bound of joint time-delay and channel coefficients by increasing the number of subcarriers and channel taps has been proposed. The method reduces the complexity of the design considerably. Specifically, by increasing the number of channel taps the number of operations to compute matrix inversions is significantly reduced by asymptotic bounds. Numerical results show that as the number of subcarriers increases, the asymptotic bounds converge to the non-asymptotic bounds. 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.