Reduced ML-Decoding Complexity, Full-Rate STBCs for 4 Transmit Antenna Systems

TL;DR

This paper introduces a novel full-rate space-time block code for 4 transmit antennas that reduces ML-decoding complexity while maintaining competitive error performance and higher capacity for fewer receive antennas.

Contribution

The paper presents a new full-rate STBC for 4 transmit antennas with reduced ML-decoding complexity using Clifford Algebra, applicable to any number of receive antennas.

Findings

Offers the lowest ML-decoding complexity among known codes for any $n_r$

Achieves error performance comparable to the perfect code for 4 antennas

Provides higher ergodic capacity when $n_r < 4$

Abstract

For an $n_t$ transmit, $n_r$ receive antenna system ($n_t \times n_r$ system), a {\it{full-rate}} space time block code (STBC) transmits $min(n_t,n_r)$ complex symbols per channel use. In this paper, a scheme to obtain a full-rate STBC for 4 transmit antennas and any $n_r$, with reduced ML-decoding complexity is presented. The weight matrices of the proposed STBC are obtained from the unitary matrix representations of Clifford Algebra. By puncturing the symbols of the STBC, full rate designs can be obtained for $n_r < 4$. For any value of $n_r$, the proposed design offers the least ML-decoding complexity among known codes. The proposed design is comparable in error performance to the well known perfect code for 4 transmit antennas while offering lower ML-decoding complexity. Further, when $n_r < 4$, the proposed design has higher ergodic capacity than the punctured Perfect code. Simulation results which corroborate these claims are presented.