On the Pilot-Data Power Trade Off in Single Input Multiple Output Systems

We consider a single cell single input multiple output (SIMO) system employing orthogonal frequency division multiplexing (OFDM). In such systems, setting the pilot-to-data power ratio (PDPR) has a large impact on the spectral and energy efficiency. In this paper we provide a closed form solution for the mean square error (MSE) of the received data as a function of the PDPR assuming Gaussian channels and minimum mean square error (MMSE) equalization. In numerical experiments we find that the MSE is a convex function of the PDPR and study the optimal PDPR as the number of antennas at the base station (BS) grows large. We find that the optimal PDPR heavily depends on the number of antennas and the path loss between the mobile station and the BS. Specifically, as the number of antennas grows large, a larger portion of the total power budget needs to be allocated for pilot signals, especially for low path loss users.