On the impact of antenna correlation on the pilot-data balance in multiple antenna systems

We consider the uplink of a single cell single input multiple output (SIMO) system, in which the mobile stations use intra-cell orthogonal pilots to facilitate uplink channel estimation. In such systems, the problem of transmission power balancing between pilot and data is known to have a large impact on the mean square error (MSE) for the received signal and, consequently, on the achievable uplink data rate. In this paper, we derive a closed form expression of the MSE for the received signal as a function of the pilot and data power levels under a per-user sum pilot-data power constraint. As a major contribution, our model is developed for arbitrary channel covariance matrices and it enables us to study the impact of the number of antennas and antenna correlation structures, including the popular 3GPP spatial channel model. Numerical results suggest that the effect of the antenna spacing is limited, but the angle of arrival and angular spread have a strong and articulated impact on the MSE performance. Moreover, as the number of antennas at the base station grows large, we show that a higher percentage of the power budget should be allocated to pilot signals than with a lower number of antennas.