In this problem we explore the approximations to the probability of an error, P_e, 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 P_e is P_e = ? erfc (?E_b/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 P_e to the exact formula for E_b/N₀ = 9. For the exact calculation of P_e, you may use Table on the error function.

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