Simplified bounds for the complementary error function; application to the performance evaluation of signal-processing systems

Any signal-processing scheme requires evaluation of the performance. Very often in such applications the complementary error function (the Gaussian Q-function) occurs. In this paper, we present new upper and lower bounds for this function in the form of one exponential function only. We give examples of applying the derived bounds for the performance evaluation relating to a few recently proposed signal processing schemes. We show that using the suggested estimates results in simple closed-form expressions for the error probability in the considered schemes and provides rather accurate approximations of the exact decisions obtained numerically. Application areas for the proposed approximations are also discussed.