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arXiv · 1101.2516

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

Sanjay Karmakar·K. Pavan Srinath·B. Sundar Rajan
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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.

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Sanjay Karmakar, K. Pavan Srinath, B. Sundar Rajan. 2011-01-13. Maximum Rate of Unitary-Weight, Single-Symbol Decodable STBCs. https://doi.org/10.1109/tit.2011.2170106

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