Abstract:
Optimizing the diversity product of two-antenna diagonal space time
codes can be phrased as finding, for a given integer L, the maximum
over all positive integers u less than L of the minimum over all positive
integers x less than L of the expression |sin(pi*x/L)*sin(pi*x*u/L)|. We
establish a relationship between this optimization problem and the
elementary theory of continued fractions. In particular, we show that
the u that maximizes the diversity product must have the property that
u/L cannot be ``approximated too well'' by fractions a/b with b less
than L.
Inspired by the well-known fact that quotients of Fibonacci numbers
have such a property, we study the case where L is a Fibonacci number
and derive bounds for the best diversity product.
Status:
Submitted to IEEE Trans. Info. Theory, October 2000.
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