New upper bounds on the Gaussian Q ‐function via Jensen's inequality and integration by parts, and applications in symbol error probability analysis

Using Jensen's inequality and integration by parts, some tight upper bounds are derived on the Gaussian Q ‐function. The tightness of the bounds obtained by Jensen's inequality can be improved by increasing the number of exponential terms, and one of them is invertible. A piece‐wise upper bound is obtained and its application in the analysis of the symbol error probability of various modulation schemes in different channel models is shown.