Probability of Error for complementary signals as function of ? sub “N”

Question

The following worksheet specifies a 10-sample binary data signal s sub "1" in B4:B13. A random transmitted bit D sub "t" is computed in B1. The transmitted signal sT sub "i" (in C4:C13) = s sub "i" if Dt=1 and =-s sub "i" if D sub "t" =0. The Gaussian noise sequence N sub "i" SD on the first image is specified in F1. The detected signal X sub "i" is computed in E4:E13. The matched processor component s sub "i" X sub "i" is computed in F4:F13, and the matched processor output V is computed in F15. The detected bit D sub "r" is computed in D1.

The probability of error is estimated by computing the ratio of errors to transmitted data in I5 as the noise ? sub "N" varies from 0 to 14?? in steps of ?? specified in I1. The total number of data bits to be transmitted n sub "T" 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.



What will be an ideal response?

Answer 1

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