# STBCs with Optimal Diversity-Multiplexing Tradeoff for 2, 3 and 4 Transmit Antennas

Shashidhar, V. and Rajan, Sundar B and Kumar, Vijay P (2004) STBCs with Optimal Diversity-Multiplexing Tradeoff for 2, 3 and 4 Transmit Antennas. In: International Symposium on Information Theory, 2004. ISIT 2004, 27 June-2 July, Chicago, p. 125.

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We show that the codes from division algebras [1] achieve the optimal diversity-multiplexing tradeo. for $n$ transmit and $n$ receive antennas for $n=2,3,4$ by simulation. Also, we present a lower bound for the tradeoff curve which shows that codes from division algebras for arbitrary number of transmit and receive antennas achieve points corresponding to zero diversity gain and zero multiplexing gain. Let $S$ be the signal set over which we want to construct fullrank STBCs. Then, let $m$ be an integer such that $x^n- w_m$ is irreducible over $F= Q(S,w_m)$, where $Q$ is the field of rational numbers and $w_m = e^{^j2\pi/m}$. The extension field obtained from this irreducible polynomial is $K=F(w_{mn})$.