Tighter Bounds on the Gaussian $Q$ Function and Its Application in Nakagami- ${m}$ Fading Channel

In this letter, using the Trapezoidal rule of numerical integration, we propose simpler and tighter approximations for the Gaussian Q function. These can be efficiently applied to compute the integrals in symbol error probability (SEP) expressions of various digital modulation schemes over additive white Gaussian noise as well as fading channels. Using the proposed approximations, we present a closed-form solution to these integrals for Nakagami-m fading channel, which are valid for the entire range of fading parameter (m). To further validate the closed-form solution of these integrals, the SEP of 16-HQAM signal is also analyzed and compared with existing approximations.