Constant Envelope Precoding with Adaptive Receiver Constellation in MISO Fading Channel

TL;DR

This paper proposes an adaptive receiver constellation design for constant envelope precoding in MISO fading channels, significantly improving error rates by optimizing constellation parameters based on channel conditions.

Contribution

It introduces an efficient algorithm for designing optimal adaptive APSK constellations with two rings, enhancing CE precoding performance in fading channels.

Findings

Optimized adaptive constellations reduce SER compared to fixed ones.

The proposed variable-rate scheme improves transmission robustness.

Numerical results confirm the effectiveness of the adaptive design.

Abstract

Constant envelope (CE) precoding is an appealing transmission technique which enables the realization of high power amplifier (PA) efficiency. 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 a fading channel, where the annulus is time-varying, there is in general a non-zero probability of encountering a channel that makes CE precoding infeasible, thereby causing a high probability of error. To tackle this problem, this paper studies the adaptive receiver constellation design for CE precoding in a single-user MISO flat-fading channel with an arbitrary number of antennas at the transmitter. We first investigate the fixed-rate adaptive receiver constellation design to minimize the symbol error rate (SER). Specifically, an efficient algorithm is proposed to find the optimal amplitude-and-phase shift keying (APSK) constellation with two rings 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 fixed-rate adaptive receiver constellation, our proposed scheme achieves significantly improved SER performance over CE precoding with a fixed receiver constellation. Furthermore, based on the family of optimal fixed-rate adaptive two-ring APSK constellation sets, a variable-rate CE transmission scheme is proposed and numerically examined.