Simplified derivation of the modified Chernoff upper bound

Modified forms of the Chernoff bound were first presented in 1982, offering improvements on the Chernoff bound for systems corrupted by additive interference and independent zero-mean Gaussian noise. Both upper and lower bounds were developed, with the upper bound generally being significantly tighter than the Chernoff bound. However, despite this it has not been as widely adopted in practice as one might expect given its accuracy and inherent simplicity. It is conjectured that this is due, at least in part, to the relatively obtuse, nonintuitive character of the derivation, involving analytic continuation and contour integration in the complex plane. A new, direct derivation is presented that enables the essential underlying simplicity and ease of application to be readily appreciated. To highlight this simplicity details are provided of example applications, as well as a prescriptive demonstration of the formulation of the MCB from first principles. As validation of the use of this technique comparisons are made of the performance and complexity of the MCB with other commonly used error rate calculation techniques.