Probability of Error for complementary signals as function of ?N. The following worksheet specifies a 10-sample binary data signal s1 in B4:B13. A random transmitted bit Dt is computed in B1. The transmitted signal sTi (in C4:C13) = si if Dt=1 and =-si if Dt=0. The Gaussian noise sequence Ni SD ?N is specified in F1. The detected signal Xi is computed in E4:E13. The matched processor component siXi is computed in F4:F13, and the matched processor output V is computed in F15. The detected bit Dr is computed in D1.

Question

The probability of error is estimated by computing the ratio of errors to transmitted data in I5 as

the noise ?N varies from 0 to 14?? in steps of ?? specified in I1. The total number of data bits to

be transmitted nT is specified in I2. The number of transmissions accomplished in shown in I3

and the number of errors in I4. Three VBA Macros are present:

? ResetCS resets the counts in I3 and I4.

? XmitCS increments the number of transmissions and, if an error occurs, increments the

error count.

? AutoCS computes the P[error] for nT transmissions as ?N varies and displays the results in

H8:I15.

a. What is the formula that computes Dt

in B1?

b. What is the formula that computes the transmitted signal sT2 in C6?

c. What is the formula that computes the noise component N2 in D6?

d. What is the formula that computes the detected signal X2 in E6?

e. What is the formula that computes the processor component s2X2 in F6?

f. What is the formula that computes the processor output V in F15?

g. What is the formula that computes Dr

in D1?

h. What is the formula that computes P[error] in I6 that produces 0 for #mits = 0?

i. Compose ResetCS.

j. Compose XmitCS.

k. Compose AutoCS.

Answer 1

Solution



Sub ResetCS()

Range("I3").Value = 0

Range("I4").Value = 0

End Sub

Sub XmitCS()

Range("I3").Value = Range("I3").Value + 1

If Range("B1").Value <> Range("D1").Value Then ' error

Range("I4").Value = Range("I4").Value + 1

End If

End Sub

Sub AutoCS()

Dim Row As Integer

Row = 8

Range("H8:I15").Clear

Range("F1").Value = 0

Do While Row < 16

ResetCS

Do While Range("I3").Value < Range("I2").Value

XmitCS

Loop

Range("H" & Row).Value = Range("F1").Value

Range("I" & Row).Value = Range("I5").Value

Range("F1").Value = Range("F1").Value + Range("I1").Value

Row = Row + 1

Loop

End Sub