Constant envelope precoding with adaptive receiver constellation in fading channel

Constant envelope (CE) precoding is an appealing transmission technique which enables the use of highly efficient nonlinear radio frequency (RF) power amplifiers (PAs). For CE precoding in a single-user multiple-input single-output (MISO) channel, a desired constellation is feasible at the receiver if and only if it can be scaled to lie in an annulus, whose boundaries are characterized by the instantaneous channel realization. Therefore, if a fixed receiver constellation is used for CE precoding in fading channel, where the annulus is time-varying, there is a non-zero probability of encountering a channel that makes CE precoding infeasible. To tackle this problem, we study the fixed-rate adaptive receiver constellation design for CE precoding to minimize symbol error rate (SER) in a single-user MISO flat-fading channel with an arbitrary number of antennas at the transmitter. Specifically, this paper proposes an efficient algorithm to find the optimal two-ring amplitude-and-phase shift keying (APSK) constellation that is both feasible and of the maximum minimum Euclidean distance (MED), for any given constellation size and instantaneous channel realization. Numerical results show that by using the optimized adaptive receiver constellation, our proposed scheme achieves significantly improved SER performance than CE precoding with fixed receiver constellation. Furthermore, with the PA efficiency gain achieved by CE precoding, our proposed scheme requires less transmitter power consumption to achieve a desired SER level than linear precoding schemes under the less-stringent average per-antenna power constraint (PAPC).