  Recently, communications systems that are both energy efficient and reliable
are under investigation. In this paper, we concentrate on an
energy-detection-based transmission scheme where a communication scenario
between a transmitter with one antenna and a receiver with significantly many
antennas is considered. We assume that the receiver initially calculates the
average energy across all antennas, and then decodes the transmitted data by
exploiting the average energy level. Then, we calculate the average symbol
error probability by means of a maximum a-posteriori probability detector at
the receiver. Following that, we provide the optimal decision regions.
Furthermore, we develop an iterative algorithm that reaches the optimal
constellation diagram under a given average transmit power constraint. Through
numerical analysis, we explore the system performance.
