Pilot optimization for time-delay and channel estimation in OFDM systems

Orthogonal frequency division multiplexing (OFDM) communication systems require accurate estimation of timing offset and channel impulse response in order to achieve desirable performance. In this paper, we consider the optimal placement of pilot symbols over the OFDM subcarriers in order to minimize a function of the Cramér-Rao bound on these parameters. Previous work has investigated this problem for channel estimation only, and found that equi-spaced, equi-powered pilots are optimal. We show that when the time-delay must be simultaneously estimated, the optimal pilot distribution is often quite different, with more pilot energy distributed to the edges of the signal bandwidth. Upper and lower bounds for the required number of optimal pilots are also presented for the case where the variance on the time-delay estimate is minimized.