In this problem we explore the approximations to the probability of an error, Pe, for the pair of antipodal signals shown in Figure in the presence of additive white Gaussian noise of power spectral density N0/2. The exact formula for Pe is Pe = ½ erfc (√Eb/N0). (This formula is derived in Section 6.3)
(a) Using the two upper bounds for the complementary error function given in Note 3, derive the corresponding approximations to P.
(b) Compare the approximations derived in part (a) for Pe to the exact formula for Eb/N0 = 9. For the exact calculation of Pe, you may use Table on the error function.