Effect of Antenna Correlation

6.4 Simulation Results and Discussion

6.4.3 Effect of Antenna Correlation

Figs. 6.9-6.11 showPCversus SNR in the case of classifying BPSK, OQPSK andQ1 using the feature vectoru^M over an AF- relay fading channel for different antenna correlation values.

It is observed thatPC decreases with an increase in the antenna correlation value. For instance, with an SNR value of 12 dB, N = 2000 and NC = 4, the classifier with u^M as feature vector TH-2361_126102009

6. Automatic Modulation Classification over a Correlated MIMO Amplify and Forward (AF)-Relay Fading Channel

5 10 15 20

0.4 0.5 0.6 0.7 0.8 0.9 1

SNR (dB)

P C

NC=2 NC=4 NC=10

Figure 6.7: PC versus SNR in the case of classifying QPSK, ^π₄-QPSK, 8-PSK and 16-QAM using the feature vectorv^MwithN=2000 and|ρR|=|ρT|=0

10 12 14 16 18 20 22 24 26 28 30

SNR(dB) 0.65

0.7 0.75 0.8 0.85 0.9 0.95 1

P C N

C=2 NC=4 NC=10

Figure 6.8: P_C versus SNR in the case of classifying BPSK, OQPSK, QPSK, ^π₄-QPSK, 8-PSK and 16-QAM using the RA-AMC technique withN=2000 and|ρR|=|ρT|=0

6.4 Simulation Results and Discussion

Table 6.2: P_C with an SNR value of 12 dB, N = 2000 and|ρR| = |ρT| = 0 in the case of classifying QPSK, ^π₄-QPSK, 8-PSK and 16-QAM using the feature vectorv^Mfor different values ofNC

NC PC

2 0.7732

4 0.9018

10 0.9732

Table 6.3: PC with an SNR value of 12 dB, N = 2000 and|ρR| = |ρT| = 0 in the case of classifying BPSK, OQPSK, QPSK,^π₄-QPSK, 8-PSK and 16-QAM using the RA-AMC technique for different values ofN_C

NC PC

2 0.7850

4 0.8620

10 0.9125

attains PC = 0.9702 for |ρR| = |ρT| = 0.5, while at the same SNR, N and NC, it attains PC = 0.9546 for|ρR| = |ρT| = 0.7. Table 6.4 shows PC attained by the classifier withu^M as feature vector with an SNR value of 12 dB, N = 2000 and NC = 4 for different antenna correlation values. The decrease inPC with an increase in the antenna correlation value is attributed to the reduced diversity gain as a correlated low rank channel model yields only receiver array gain.

Figs. 6.12-6.14 showPC versus SNR in the case of classifying QPSK, ^π₄-QPSK, 8-PSK and 16-QAM using the feature vector v^M over an AF- relay fading channel for different antenna correlation values. There is a decrease in PC with an increase in the antenna correlation value.

For instance, with an SNR value of 12 dB, N = 2000 and NC = 10, the classifier withv^M as feature vector attains PC = 0.9034 for |ρR| = |ρT| = 0.5, while at the same SNR, N and NC, it attains PC = 0.7881 for |ρR| = |ρT| = 0.7. Table 6.5 shows PC attained by the classifier withv^M as feature vector with an SNR value of 12 dB, N = 2000 andNC = 10 for different antenna correlation values. The decrease inPc with an increase in the antenna correlation value is contributed by the noise amplification at the equalizer output.

Figs. 6.15-6.17 show PC versus SNR in the case of classifying BPSK, OQPSK, QPSK,

π

4-QPSK, 8-PSK and 16-QAM using the RA-AMC technique (two-step classification) over an AF- relay fading channel for different antenna correlation values. There is a decrease in PC

with an increase in the antenna correlation value. For instance, with an SNR value of 12 dB, TH-2361_126102009

6. Automatic Modulation Classification over a Correlated MIMO Amplify and Forward (AF)-Relay Fading Channel

N = 2000 and NC = 10, the RA-AMC technique attains PC = 0.9125 for|ρR| = |ρT| = 0.5, while at the same SNR,N andNC, it attainsPC = 0.8225 for|ρR|= |ρT|=0.7. Table 6.6 shows PC attained by the RA-AMC technique with an SNR value of 12 dB, N = 2000 andNC = 10 in the case of classifying BPSK, OQPSK, QPSK, ^π₄-QPSK, 8-PSK and 16-QAM for different antenna correlation values. The decrease in PC with an increase in the antenna correlation is because of the reduced diversity gain and the noise amplification at the equalizer output.

One can also note from Figs. 6.9-6.17 that PC improves as SNR increases. For example, one can note from Fig. 6.16 that for N = 2000, NC = 4 and |ρR| = |ρT| = 0.7, RA-AMC attainsPC = 0.7853 at an SNR value of 12 dB while for the same value of N, NC and antenna correlation, the RA-AMC technique attainsPC = 0.9037 at an SNR value of 16 dB. Table 6.7 shows thePCattained by the RA-AMC technique at different SNR values forN =2000,NC =4 and|ρR|=|ρT|= 0.7. It is clear from Table 6.7 thatPC improves as SNR increases.

5 10 15 20

0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

SNR (dB)

P C

|ρT| =| ρ

R| = 0

|ρT| =| ρ

R| = 0.5

|ρT| =| ρ

R| = 0.7

Figure 6.9: PC versus SNR in the case of classifying BPSK, OQPSK and Q₁ using the feature vector u^MwithN=500 andN_C =4

6.4 Simulation Results and Discussion

5 10 15 20

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

SNR (dB)

P C |ρ

T| =| ρ

R| = 0

|ρT| =| ρ

R| = 0.3

|ρT| =| ρ

R| = 0.5

Figure 6.10: PC versus SNR in the case of classifying BPSK, OQPSK andQ₁using the feature vector u^MwithN=2000 andNC =4

5 10 15 20

0.7 0.75 0.8 0.85 0.9 0.95 1

SNR (dB)

P C |ρ

T| =| ρ

R| = 0

|ρT| =| ρ

R| = 0.5

|ρT| =| ρ

R| = 0.7

Figure 6.11: P_C versus SNR in the case of classifying BPSK, OQPSK andQ₁using the feature vector u^MwithN=4000 andN_C =4

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5 10 15 20

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

SNR (dB)

P C

|ρT| =| ρ

R| = 0

|ρT| =| ρ

R| = 0.5

|ρT| =| ρ

R| = 0.7

Figure 6.12: PC versus SNR in the case of classifying QPSK, OQPSK, ^π₄-QPSK and 8-PSK using the feature vectorv^MwithN=500 andNC =10

5 10 15 20

0.4 0.5 0.6 0.7 0.8 0.9 1

SNR (dB)

P C

|ρT| =| ρ

R| = 0

|ρT| =| ρ

R| = 0.5

|ρT| =| ρ

R| = 0.7

Figure 6.13: P_C versus SNR in the case of classifying QPSK, OQPSK, ^π₄-QPSK and 8-PSK using the feature vectorv^MwithN=2000 andN_C =10

6.4 Simulation Results and Discussion

5 10 15 20

0.4 0.5 0.6 0.7 0.8 0.9 1

SNR (dB)

P C

|ρT| =| ρ

R| = 0

|ρT| =| ρ

R| = 0.5

|ρT| =| ρ

R| = 0.7

Figure 6.14: PC versus SNR in the case of classifying QPSK, OQPSK, ^π₄-QPSK and 8-PSK using the feature vectorv^M withN =4000 andNC =10

12 14 16 18 20 22 24 26 28 30

SNR (dB) 0.7

0.75 0.8 0.85 0.9 0.95 1

P C

| _T| =| _R| = 0

| _T| =| _R| = 0.5

| _T| =| _R| = 0.7

Figure 6.15: P_C versus SNR in the case of classifying BPSK, OQPSK, QPSK, ^π₄-QPSK, 8-PSK and 16-QAM using the RA-AMC technique withN=2000 andN_C =2

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6. Automatic Modulation Classification over a Correlated MIMO Amplify and Forward (AF)-Relay Fading Channel

10 12 14 16 18 20 22 24 26 28 30

SNR (dB) 0.65

0.7 0.75 0.8 0.85 0.9 0.95 1

P C

| T| =|

R| = 0

| _T| =| _R| = 0.5

| _T| =| _R| = 0.7

Figure 6.16: PC versus SNR in the case of classifying BPSK, OQPSK, QPSK, ^π₄-QPSK, 8-PSK and 16-QAM using the RA-AMC technique withN=2000 andNC=4

8 10 12 14 16 18 20 22 24 26 28 30

SNR (dB) 0.55

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

P C

| T| =|

R| = 0

| T| =|

R| = 0.5

| T| =|

R| = 0.7

Figure 6.17: P_C versus SNR in the case of classifying BPSK, OQPSK, QPSK, ^π₄-QPSK, 8-PSK and 16-QAM using the RA-AMC technique withN=2000 andN_C=10

6.4 Simulation Results and Discussion

Table 6.4: PC with an SNR value of 12 dB, N = 2000 andNC = 4 in the case of classifying BPSK, OQPSK andQ₁using the feature vectoru^M for different antenna correlation values|ρ|=|ρR|=|ρT|

|ρ| PC

0 0.9787

0.5 0.9702

0.7 0.9546

Table 6.5: P_C with an SNR value of 12 dB, N = 2000 and N_C = 10 in the case of classifying QPSK,^π₄-QPSK, 8-PSK and 16-QAM using the feature vectorv^Mfor different antenna correlation values

|ρ|=|ρR|=|ρT|

|ρ| PC

0 0.9708

0.5 0.9034

0.7 0.7881

Table 6.6: P_C with an SNR value of 12 dB,N = 2000 andN_C = 10 in the case of classifying BPSK, OQPSK, QPSK, ^π₄-QPSK, 8-PSK and 16-QAM using the RA-AMC technique for different antenna correlation values|ρ|=|ρR|=|ρT|

|ρ| PC

0 0.9640

0.5 0.9125

0.7 0.8225

Table 6.7: PC atN = 2000,NC = 4 and|ρR| = |ρT| = 0.7 in the case of classifying BPSK, OQPSK, QPSK, ^π₄-QPSK, 8-PSK and 16-QAM using the RA-AMC technique for different SNR values

SNR (dB) PC

12 0.7853

14 0.8475

16 0.9037

18 0.9320

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