19. Error correction using three FDMA orthogonal signals.

Question

The following worksheet specifies three 10-sample FDMA orthogonal data signals: sA sub “1” in B5:B14, sB sub “1” in C5:C14 and sC sub “1” in D5:D14. Random transmitted bit D sub “T” is computed in C1. The transmitted signal sAT sub “i” (in E5:E14) = sA sub “i” if D sub “i”=1 and =-sA sub “i” if D sub “t”=0. The transmitted signal sBT sub “i” (in F5:F14) = sB sub “i” if D sub “t”=1 and =-sB sub “i” if D sub “t”=0. The transmitted signal sCTi (in G5:G14) = sC sub “i” if D sub “i”=1 and =-sB sub “i” if D sub “t”=0. The Gaussian noise sequence N sub “i” SD ? sub “N” is specified in I1. The detected signal X sub “i” is computed as the sum of the three signals and noise in I5:I14. The matched processor component sA sub “i”X sub “i” is computed in J5:J14 and VA is computed in J16. The matched processor component sB sub “i”X sub “i” is computed in K5:K14 and VB is computed in K16. The matched processor component sC sub “i”X sub “i” is computed in L5:L14 and VC is computed in L16. The detected bit DA sub “r” is computed in B2 from VA, DB sub “r” is computed in D2 from VB, and DCr is computed in F2 from VC. The received data bit Dr in E2 is computed using error correction applied to DA sub “r”, DB sub “r” and DC sub “r”

The probability of error is estimated by computing the ratio of errors to transmitted data in O5 as the noise ? sub “N” varies from 0 in steps of ?? = (E sub “s”/2) with exponent of 1/2 using E sub “s” computed in I2. The total number of data bits to be transmitted nT is specified in O2. The number of transmissions accomplished in shown in O3 – with 1 bit per three-signal transmission - and the number of errors in O4. Three VBA Macros are present:

• ResetEC resets the counts in O3 and O4.

• XmitEC increments the number of transmissions by one for each signal transmission and, if an error occurs (D sub “r” ? D sub “t”) increments the error count.

• AutoEC computes the P[error] for n sub “T” transmissions as ? sub “N” varies and displays the results in N8:O16.



a. What is the formula in C1?

b. What is the formula in E10?

c. What is the formula in F10?

d. What is the formula in G10?

e. What is the formula in H10?

f. What is the formula in I10?

g. What is the formula in K10?

h. What is the formula in K16?

i. What is the formula in B2?

j. What is the formula in D2?

k. What is the formula in F2?

l. What is the formula in E1?

m. What is the formula in 01?

n. What is the formula in O5?

o. Compose ResetEC.

p. Compose XmitEC.

q. Compose AutoEC.

Answer 1

Sub ResetEC()

Range("O3").Value = 0

Range("O4").Value = 0

End Sub



Sub XmitEC()

Range("O3").Value = Range("O3").Value + 1 ' 1 data bit xmitted

If Range("C1").Value <> Range("E1").Value Then ' error

Range("O4").Value = Range("O4").Value + 1

End If

End Sub



Sub AutoEC()

Dim Row As Integer

Row = 8

Range("N8:O16").Clear

Range("I1").Value = 0

Do While Row < 17

ResetEC

Do While Range("O3").Value < Range("O2").Value

XmitEC

Loop

Range("N" & Row).Value = Range("I1").Value

Range("O" & Row).Value = Range("O5").Value

Range("I1").Value = Range("I1").Value + Range("O1").Value

Row = Row + 1

Loop

End Sub