Large intelligent surfaces (LIS) present a promising new technology for enhancing the performance of wireless communication systems. Realizing the gains of LIS requires accurate channel knowledge, and in practice the channel estimation overhead can be large due to the passive nature of LIS. Here, we study the achievable rate of a LIS-assisted single-input single-output communication system, accounting for the pilot overhead of a least-squares channel estimator. We demonstrate that there exists an optimal $K^{*}$, which maximizes achievable rate by balancing the power gains offered by LIS and the channel estimation overhead. We present analytical approximations for $K^{*}$, based on maximizing an analytical upper bound on average achievable rate that we derive, and study the dependencies of $K^*$ on statistical channel and system parameters.
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