University of California, Electrical Engineering Department, Los Angeles, CA 90024, USA U.S.A.
Abstract:
Fixed point properties of the binomial function are developed. It is shown that for any 1 < L < N, TLNhas a unique fixed point p? in (0, 1), and that for large N, the fixed point is L/N. This has application to signal detection schemes commonly used in communication systems. When detecting the presence or absence of a signal with an initial false alarm probability pFAand an initial detection probability pD, then TLN(pFA) < pFAand TLN(pD) > pDif, and only if, pFA < p? < pD. When this condition is satisfied, as N → ∞, TLN(pFA) → 0 and TLN(pD → 1.
