5.19 In this problem we explore the approximations to the probability of an error, P, for the pair of antipodal signals shown in Figure P5.19 in the presence of additive white Gaussian noise of power spectral density No/2. The exact formula for P, is E erfc No (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, to the exact formula for E/No - 9. For the exact calculation of P, you may use Table A6.6 on the error function. -VE, VE FIGURE P5.19
5.19 In this problem we explore the approximations to the probability of an error, P, for the pair of antipodal signals shown in Figure P5.19 in the presence of additive white Gaussian noise of power spectral density No/2. The exact formula for P, is E erfc No (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, to the exact formula for E/No - 9. For the exact calculation of P, you may use Table A6.6 on the error function. -VE, VE FIGURE P5.19
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Transcribed Image Text:5.19 In this problem we explore the approximations to the probability of an error, P, for the
pair of antipodal signals shown in Figure P5.19 in the presence of additive white Gaussian
noise of power spectral density No/2. The exact formula for P, is
Et
P. = erfe
No
(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. to the exact formula for
E/No = 9. For the exact calculation of P. you may use Table A6.6 on the error
function.
-VES
VES
FIGURE P5.19
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