Signal region characterization and exact phase recovery for constant envelope precoding in single-user large-scale MISO channels

This paper considers constant envelope (CE) precoding in single-user MISO downlink systems. CE precoding is a transmission scheme recently proposed for very large antenna arrays, in which the use of highly power-efficient RF amplifiers is a requirement. There are two important issues in CE precoding, namely the characterization of the region of all possible noise-free receive signals, and the recovery of the phases of the transmitting signal. An existing result by Mohammed and Larsson showed that the noise-free receive signal region can be geometrically interpreted as a region between two circles centered at the origin of the complex plane. However, this result did not prove the expression of the radius of the inner circle. We provide a new analysis approach to characterize the noise-free receive signal region. Our result shows that the radius of the inner circle has a simple closed-form expression, there by completing the result by Mohammed and Larsson. In addition, we propose an algorithm that can recover the phases of the transmitting signal exactly with a complexity linear in the number of antennas. Simulation results show that the proposed method can be significantly faster than an existing phase recovery algorithm.