Non-Coherent Massive SIMO Systems in ISI Channels: Constellation Design and Performance Analysis

Abstract

A massive single-input multiple-output system with a single transmit antenna and a large number of receive antennas in intersymbol interference channels is considered. Contrast to existing energy detection (ED) based non-coherent receiver where conventional pulse amplitude modulation (PAM) is employed, we propose a constellation design, which minimizes the symbol error rate (SER) with the knowledge of channel statistics. To make a comparison, we derive the SERs of the ED-based receiver with both the proposed constellation and PAM, namely <inline-formula><tex-math notation= LaTeX >$P_{e\\_{\\rm opt}}$</tex-math></inline-formula> and <inline-formula><tex-math notation= LaTeX >$P_{e\\_{\\rm pam}}$</tex-math></inline-formula>. Specifically, asymptotic behaviors of the SER in regimes of a large number of receive antennas and high signal-to-noise ratio are investigated. Analytical results demonstrate that the logarithms of both <inline-formula><tex-math notation= LaTeX >$P_{e\\_{\\rm opt}}$</tex-math></inline-formula> and <inline-formula><tex-math notation= LaTeX >$P_{e\\_{\\rm pam}}$</tex-math></inline-formula> decrease approximately linearly with the number of receive antennas, whereas <inline-formula><tex-math notation= LaTeX >$P_{e\\_{\\rm opt}}$</tex-math></inline-formula> degrades faster. It is also shown that the proposed design is of less cost, because compared with PAM, less antennas are required to achieve the same error rate.