  Assume the communication between a source and a destination is supported by a
large reflecting surface (LRS), which consists of an array of reflector
elements with adjustable reflection phases. By knowing the phase shifts induced
by the composite propagation channels through the LRS, the phases of the
reflectors can be configured such that the signals combine coherently at the
destination, which improves the communication performance. However, perfect
phase estimation or high-precision configuration of the reflection phases is
unfeasible. In this paper, we study the transmission through an LRS with phase
errors that have a generic distribution. We show that the LRS-based composite
channel is equivalent to a point-to-point Nakagami fading channel. This
equivalent representation allows for theoretical analysis of the performance
and can help the system designer study the interplay between performance, the
distribution of phase errors, and the number of reflectors. Numerical
evaluation of the error probability for a limited number of reflectors confirms
the theoretical prediction and shows that the performance is remarkably robust
against the phase errors.
