Table 1
Analysis of Deviation between the NNB and Chi-Square Distributions for the Case of “0” Transmission (
,
) Using Closed-Form Theoretical Expressions for the Deviation at the Peak Location
and Through Simulation
| | | Theoretical Calculation Using Eqs. (23, 24) | Numerical Calculation Using Eqs. (8, 9) |
---|
Gain |
(theory) |
(actual) |
|
|
|
|
---|
4 | 3 | 3 | 0.0190 | 16.66 | 0.00862 | 7.56 |
11 | 10 | 10 | 0.0018 | 5 | 0.00154 | 4.21 |
50 | 49 | 49 |
| 1.02 |
| 0.99 |
101 | 100 | 100 |
| 0.5 |
| 0.50 |
Table 2
Analysis of Deviation between the NNB and Chi-Square Distributions for the Case of “0” Transmission (
,
) Using Closed-Form Theoretical Expressions for the Deviation at the Peak Location
and through Simulation
| | | Theoretical Calculation Using Eqs (23, 24) | Numerical Calculation Using Eqs. (8, 9) |
---|
Gain |
(theory) |
(actual) |
|
|
|
|
---|
4 | 21 | 21 | 0.0082 | 16.66 | 0.0072 | 14.43 |
11 | 70 | 70 |
|
|
| 4.77 |
50 | 343 | 343 |
| 1.02 |
| 1.01 |
101 | 700 | 700 |
| 0.5 |
| 0.5 |
Table 3
Analysis of Deviation between the NNB and Chi-Square Distributions for the case of “1” Transmission (
,
) Using Closed-Form Theoretical Expressions for the Deviation at the Peak Location
and Numerically
| | | Theoretical Calculation Using Eqs. (28, 29) | Numerical Calculation Using Eqs. (7, 9) |
---|
Gain |
(theory) |
(actual) |
|
|
|
|
---|
3 | 242 | 242 | 0.00161 | 13.53 | 0.00135 | 10.52 |
4 | 323 | 323 |
| 8.37 |
| 7.45 |
11 | 886 | 886 |
| 2.51 |
| 2.41 |
50 | 4026 | 4026 |
| 0.51 |
| 0.51 |
101 | 8131 | 8131 |
| 0.25 |
| 0.25 |
Table 4
Error Analysis for the Case of “1” transmission (
,
) Using Closed-Form Theoretical Expressions for the Deviation at the Peak Location
and Through Simulation
| | | Theoretical Calculation Using Eqs. (28, 29) | Numerical Calculation Using Eqs. (7, 9) |
---|
|
(theory) |
(actual) |
|
|
|
|
---|
3 | 253 | 253 | 0.00162 | 12.83 | 0.001382 | 10.88 |
4 | 340 | 340 |
| 8.59 |
| 7.69 |
11 | 944 | 945 |
| 2.58 |
| 2.50 |
50 | 4313 | 4319 |
| 0.52 |
| 0.53 |
101 | 8718 | 8732 |
| 0.25 |
| 0.26 |
Table 5
Crossover Location (
) of the Semiclassical Distribution for Different Values of Gain with
and the Deviation (
) of the New Threshold Location from the NNB
Gain |
| (
) |
---|
101 | 3306 | 1.22 |
50 | 1632 | 1.14 |
11 | 351 | 0.75 |
4 | 121 | 0.39 |
3 | 88 | 0.29 |
Table 6
Number of Excess Photons Required in the Quantum Model to Achieve the Same BER as the Semiclassical Model for Different Amplifier Gains
Gain | BER (Semiclassical) | BER (Quantum) | Excess Penalty (No. of Photons) | Excess Penalty (in dB) |
---|
3 |
|
| 19 | 0.9254 |
4 |
|
| 13 | 0.6539 |
11 |
|
| 4 | 0.2118 |
50 |
|
| 1 | 0.0539 |
101 |
|
|
| - |