Local Bounds based on Log-Concavity Property of the Error Probability in Wireless Communication Systems

In this paper we construct a family of local bounds for the err or probability (EP) of digital wireless communication systems that improve known generic bounds in a given region of the signal-to-noise ratio (SNR). This concept is motivated by the fact that the sy stems often operate in a certain region of interest for the performance and it may be advantageous to ha ve tight bounds within this region instead of bounds valid for all SNRs but far from the exact solution. T he behavior of the EP is important in defining local bounds and the proposed framework is based on t he log-concavity property of the EP which we prove for a wide class of multidimensional modulati on formats in the presence of Gaussian disturbances. This property can have many applications, th us its relevance is beyond the examples of applications made in this paper. Index Terms Andrea Conti and Velio Tralli: ENDIF at University of Ferrar a, Italy and WiLAB at University of Bologna, Italy (e-mail: a.conti@ieee.org, vtralli@ing.unife.it). Dmitry Panchenko: Department of Mathematics, MIT, Cambr idge, MA and Texas A&M University, College Station, TX, USA (e-mail: panchenk@math.tamu.edu). Sergiy Sidenko: Department of Mathematics, MIT, Cambridge, MA, USA (e-mail: sidenko@math.mit.edu). The work of A. Conti and V. Tralli was supported, in part, by Mi nistero dell’Universit̀ a e della Ricerca (MUR), Italy. The work of D. Panchenko was supported, in part, by NSF grant. February 25, 2009 DRAFT