Kiran, T and Rajan, Sundar B (2005) STBCSchemes with Nonvanishing Determinant for Certain Number of Transmit Antennas. In: IEEE Transactions on Information Theory, 51 (8). pp. 29842992.

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Abstract
A spacetime blockcode scheme (STBCscheme) is a family of STBCs {{C(SNR)}}, indexed by the signaltonoise ratio (SNR)such that the rate of each STBC scales with SNR. An STBCscheme is said to have a nonvanishing determinant if the coding gain of every STBC in the scheme is lowerbounded by a fixed nonzero value. The nonvanishing determinant property is important from the perspective of the diversity multiplexinggain (DMG) tradeoff: a concept that characterizes the maximum diversity gain achievable by any STBCscheme transmitting at a particular rate. This correspondence presents a systematic technique for constructing STBCschemes with nonvanishing determinant, based on cyclic division algebras. Prior constructions of STBCschemes from cyclic division algebra have either used transcendental elements, in which case the scheme may have vanishing determinant, or is available with nonvanishing determinant only for two, three, four, and six transmit antennas. In this correspondence, we construct STBCschemes with nonvanishing determinant for the number of transmit antennas of the form $2^k$, $3 . 2^k$, $2 . 3^k$, and $q^k(q  1)/2$, where q is any prime of the form $4_s + 3$. For cyclic division algebra based STBCschemes, in a recentwork by Elia et al., the nonvanishing determinant property has been shown to be sufficient for achieving DMG tradeoff. In particular, it has been shown that the class of STBCschemes constructed in this correspondence achieve the optimal DMG tradeoff. Moreover, the results presented in this correspondence have been used for constructing optimal STBCschemes for arbitrary number of transmit antennas, by Elia et al..
Item Type:  Journal Article 

Publication:  IEEE Transactions on Information Theory 
Publisher:  IEEE 
Additional Information:  ©2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. 
Keywords:  cyclic division algebra;diversitymultiplexing gain (DMG) tradeoff;multipleinput multipleoutput (MIMO) channel;nonvanishing determinant;number field;spacetime block code (STBC);STBCscheme 
Department/Centre:  Division of Electrical Sciences > Electrical Communication Engineering 
Date Deposited:  24 Aug 2005 
Last Modified:  19 Sep 2010 04:19 
URI:  http://eprints.iisc.ac.in/id/eprint/3555 
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