Maximum Rate of Unitary-Weight, Single-Symbol Decodable STBCs

TL;DR

This paper establishes an upper bound on the rate of unitary-weight single-symbol decodable space-time block codes, showing it exceeds that of traditional complex orthogonal designs, and explores their properties and optimality conditions.

Contribution

It derives a new upper bound on the rate of unitary-weight SSD codes, surpassing CODs, and investigates their structure, coding gain, and diversity conditions.

Findings

Upper bound on rate: (a/2^{a-1}) for 2^a antennas

All unitary-weight SSD codes share the same coding gain for QAM

Necessary conditions for full diversity and optimal coding gain

Abstract

It is well known that the Space-time Block Codes (STBCs) from Complex orthogonal designs (CODs) are single-symbol decodable/symbol-by-symbol decodable (SSD). The weight matrices of the square CODs are all unitary and obtainable from the unitary matrix representations of Clifford Algebras when the number of transmit antennas $n$ is a power of 2. The rate of the square CODs for $n = 2^a$ has been shown to be $\frac{a+1}{2^a}$ complex symbols per channel use. However, SSD codes having unitary-weight matrices need not be CODs, an example being the Minimum-Decoding-Complexity STBCs from Quasi-Orthogonal Designs. In this paper, an achievable upper bound on the rate of any unitary-weight SSD code is derived to be $\frac{a}{2^{a-1}}$ complex symbols per channel use for $2^a$ antennas, and this upper bound is larger than that of the CODs. By way of code construction, the interrelationship between the weight matrices of unitary-weight SSD codes is studied. Also, the coding gain of all unitary-weight SSD codes is proved to be the same for QAM constellations and conditions that are necessary for unitary-weight SSD codes to achieve full transmit diversity and optimum coding gain are presented.