A Geometric Derivation of Forney's Upper Bound

Vol. 54, No. 6, July-August 1975 Printed in U.S.A. A Geometric Derivation of Forney's Upper Bound By J. E. MAZO (Manuscript received January 17, 1975) Effective analyses of performance for detection schemes that optimally decode digital data in the presence of inter symbol interference have been slow in coming. Recently, however, Forney has given an upper bound on the bit error probability for maximum-likelihood sequence estimation. Starting from a standard geometrical framework, we give a much simplified derivation of this upper bound. Our derivation places the validity of this important bound more in evidence in that the concepts of whitened matched filter and error event are not introduced. Let ay, j = 1 , 2 , · · ·, N, be independent, equilikely binary random variables taking values =fcl. Data transmission usually involves estimating the a, from a pulse sequence of the form ZaMt-jT), -- °°