New Sets of Quadriphase Cross Z-Complementary Pairs for Preamble Design in Spatial Modulation

Cross Z-complementary pairs (CZCPs) are a special kind of Z-complementary pairs having zero autocorrelation sums around the in-phase position and end-shift position, also having zero cross-correlation sums around the end-shift position. Recent results have shown that CZCPs are very efficient in designing pilot sequences for spatial modulation enabled multiple-input multiple-output (MIMO) systems. In this paper, we propose systematic constructions of binary and quadriphase CZCPs with new lengths of the form 2M, where even-length binary Z-complementary pairs of length M exists. Interestingly, the proposed binary and quadriphase CZCPs have large CZC ratio (i.e. the ratio of achieved zero correlation zone width over maximum zero correlation zone width). One of the proposed construction can also construct optimal quadriphase CZCPs using quadriphase GCPs.

Introduction

Spatial modulation (SM) optimizes the multiplexing gain of multiple-input multiple-output (MIMO) systems subject to complexity and performance [1]–[2][3][4][5]. SM based MIMO systems use a single radio-frequency (RF) chain. There are two parts of an SM symbol within each time-slot, spatial symbol and constillation symbol. Spatial symbol selects and activates a transmit antenna. Constellation symbol is selected from a conventional phase shift keying (PSK)/quadrature amplitude modulation (QAM) constellation and transmitted from the active transmit antenna. This kind of new transmission scheme of SM allows it to have huge advantages of low energy consumption [6], zero inter-channel interference, and low receiver complexity over conventional MIMO. The “one-RF-chain” principle of SM forbids the transmitter from using simultaneous pilot transmission over all the transmit antennas. Hence, it implies that dense training sequences for traditional MIMO [7]–[8][9] are not applicable in SM enabled MIMO systems.