Performance improvement of mode division multiplexing free space optical communication system through various atmospheric conditions with a decision feedback equalizer

Figures & data

Figure 1. DFE block diagram of MDM for FSO.

Table 1. DFE simulation parameters in MDM for the FSO system (Almogahed et al., 2017; Amphawan et al., 2015; Amphawan & Chaudharya, 2015)

Parameters	Values
Data rate	4 x 2.5 Gbps
Transmitted wavelength	850 nm
Power	0 dBm
Link range	40 m − 2 km
Beam divergence	2 murd
Transmitter’s & Receiver’s Apertures	20 cm

Table 2. Attenuation values for different weather conditions (Almogahed et al., 2017; A. Malik & Singh, 2015)

Weather conditions	Attenuation in dB/km
Clear weather	0.155
Medium haze	4.285
Medium rain	9.64
Medium fog	33.961

Figure 2. MMSE-DFE block diagram.

Table 3. BER in clear weather prior to and following the various DFE schemes

Channels	BER before DEF	BER after various DFE schemes
		DFE scheme-1 (FFF = 3 & FBF = 1)	DFE scheme-2 (FFF = 2 & FBF = 3)	DFE scheme-3 (FFF = 4 & FBF = 1)
Channel-1 (HG00)	3.3151 x10^−3	1.1767 x10^−22	8.2448 x10^−18	1.0088 x10^−27
Channel-2 (HG01)	5.3868 x10^−3	3.2149 x10^−19	2.8278 x10^−13	2.3629 x10^−20
Channel-3 (HG02)	2.8700 x10^−3	1.2121 x10^−16	2.2489 x10^−13	2.5611 x10^−21
Channel-4 (HG10)	2.2099 x10^−3	2.3745 x10^−15	8.1798 x10^−17	1.3880 x10^−17

Figure 3. BER comparison for every channel prior to the DFE and after various DFE schemes in clear weather.

Table 4. DFEs taps coefficients from MMSE optimization in the case of four FFF taps and one FBF tap

DFEs	Values for four FFF taps	Values for one FBF tap	Delay
DFE-1	{-2.733686e-001, 9.060727e-001, 7.094516e-001, −3.447143e-001}	{1.630560e-001}	1
DFE-2	{-1.787655e-001, 9.007344e-001, 6.718438e-001, −4.071040e-001}	{1.920320e-001}	1
DFE-3	{-1.911454e-001, 7.669183e-001, 8.449142e-001, −4.048190e-001	{1.953762e-001}	1
DFE-4	{-1.545768e-001, 1.017324e+000, 4.856811e-001, −3.833381e-001}	{1.610685e-001}	1

Figure 4. Eye diagram at transmitter in the case of clear weather.

Table 5. Eye diagram for every channel prior to and following DFE in the case of four FFF taps and one FBF tap

Table 6. BER prior to and following the various DFE schemes in medium haze

Channels	BER before DEF	BER after various DFE schemes
		DFE scheme-1 (FFF = 3 & FBF = 5)	DFE scheme-2 (FFF = 5 & FBF = 2)	DFE scheme-3 (FFF = 3 & FBF = 6)
Channel-1 (HG00)	4.0782 x10^−3	5.8803 x10^−21	5.5072 x10^−12	2.9815 x10^−21
Channel-2 (HG01)	6.5070 x10^−3	2.2136 x10^−17	3.6951 x10^−16	2.4292 x10^−17
Channel-3 (HG02)	3.4644 x10^−3	5.1866 x10^−16	1.2675 x10^−12	4.1816 x10^−16
Channel-4 (HG10)	2.6072 x10^−3	4.3464 x10^−15	1.5174 x10^−15	3.5820 x10^−13

Figure 5. BER comparison for every channel prior to the DFE and after various DFE schemes in medium haze.

Table 7. DFEs taps coefficients from MMSE optimization in the case of 11 FFF taps and three FBF taps

DFEs	Values for three FFF taps	Values for six FBF taps	Delay
DFE-1	{-2.759097e-001, 7.747133e-001, 7.228254e-001}	{3.546009e-001, 6.558281e-002, 2.019477e-003, 1.660587e-003, −4.544905e-003, −9.274059e-003}	1
DFE-2	{-1.956294e-001, 7.697459e-001, 7.255517e-001}	{4.654174e-001, 9.136618e-002, 3.146650e-002, −1.192028e-002, 5.699023e-003, 5.030695e-003}	1
DFE-3	{-2.090714e-001, 7.569076e-001, 7.380806e-001}	{4.408779e-001, 7.618771e-002, 1.010011e-002, 1.535493e-002, 2.403841e-003, 1.337970e-002}	1
DFE-4	{-3.112224e-001, 5.689892e-001, 8.974022e-001}	{3.288464e-001, 6.258148e-002, 1.903789e-002, −1.060165e-003, 1.078281e-002, 1.313643e-002}	1

Figure 6. Eye diagram at transmitter in the case of medium haze.

Table 8. Eye diagram for every channel prior to and following DFE in the case of three FFF taps and six FBF taps

Table 9. BER prior to and following the various dfe schemes in medium rain

Channels	BER before DEF	BER after various DFE schemes
		DFE scheme-1 (FFF = 5 & FBF = 1)	DFE scheme-2 (FFF = 3 & FBF = 7)	DFE scheme-3 (FFF = 7 & FBF = 4)
Channel-1 (HG00)	4.6271 x10^−3	8.4544 x10^−14	5.0652 x10^−18	2.5942 x10^−18
Channel-2 (HG01)	7.2907 x10^−3	1.8922 x10^−13	1.1229 x10^−14	4.2539 x10^−15
Channel-3 (HG02)	3.9095 x10^−3	3.1287 x10^−14	7.3137 x10^−14	7.5053 x10^−12
Channel-4 (HG10)	2.9159 x10^−3	7.0821 x10^−13	3.9172 x10^−13	1.1145 x10^−13

Figure 7. BER comparison for every channel prior to the DFE and after various DFE schemes in medium rain.

Table 10. DFEs taps coefficients from MMSE optimization in the case of seven FFF taps and four FBF taps

DFE	Values for seven FFF taps	Values for four FBF taps	Delay
DFE-1	{3.818063e-002, 2.699810e-002, −7.699857e-002, −1.941425e-001, 3.628574e-001, 7.826640e-001, 4.480981e-001}	{4.909407e-001, 9.289646e-002, 5.719722e-003, −3.139313e-003}	3
DFE-2	{-2.171425e-002, 1.536014e-002, 4.293567e-002, −1.668373e-001, −2.595068e-002, 7.333261e-001, 7.012824e-001}	{4.559886e-001, 8.830721e-002, 3.232389e-002, −1.471778e-002}	3
DFE-3	{1.657212e-001, −2.637346e-001, −4.798893e-002, 2.177919e-001, 7.213914e-001, 6.424294e-001, −1.685412e-001}	{4.160687e-001, 6.118318e-002, 8.074966e-003, 1.805270e-002}	2
DFE-4	{6.238916e-002, −2.979717e-001, 2.208997e-001, 7.802306e-001, 5.065862e-001, 1.572062e-002, 1.082982e-001}	{5.110701e-001, 1.431233e-001, 3.750721e-002, 7.943673e-004}	2

Figure 8. Eye diagram at transmitter in the case of medium rain.

Table 11. Eye diagram for every channel prior to and following DFE in the case of seven FFF taps and four FBF taps

Table 12. BER prior to and following the various DFE schemes in medium fog

Channels	BER before DEF	BER after various DFE schemes
		DFE scheme-1 (FFF = 6 & FBF = 3)	DFE scheme-2 (FFF = 7 & FBF = 2)	DFE scheme-3 (FFF = 5 & FBF = 5)
Channel-1 (HG00)	3.2228 x10^−3	4.9447 x10^−14	1.4230 x10^−29	4.3233 x10^−29
Channel-2 (HG01)	4.1133 x10^−3	2.2225 x10^−13	1.0698 x10^−25	1.6536 x10^−26
Channel-3 (HG02)	2.8009 x10^−3	2.0276 x10^−11	2.2125 x10^−16	3.7008 x10^−21
Channel-4 (HG10)	2.1656 x10^−3	2.3084 x10^−23	1.7204 x10^−22	1.1817 x10^−23

Figure 9. BER comparison for every channel prior to and following various DFE schemes in medium fog.

Table 13. DFEs taps coefficients from MMSE optimization in the case of five FFF taps and five FBF taps

DFE	Values for five FFF taps	Values for five FBF taps	Delay
DFE-1	{1.978969e-002, −2.325259e-001, 3.090010e-001, 8.265375e-001, 4.432056e-001}	{5.021214e-001, 9.473521e-002, 1.056619e-002, −6.056284e-004, −2.924291e-003}	2
DFE-1	{3.995673e-002, −1.369686e-001, −6.094453e-002, 7.413647e-001, 7.121660e-001}	{4.603480e-001, 8.891715e-002, 2.752124e-002, −8.141708e-003, 4.601378e-003}	2
DFE-1	{-1.384077e-001, 8.417046e-001, 7.127215e-001, −1.647734e-001, 3.034922e-001}	{5.823477e-001, 2.202241e-001, 3.500823e-002, 1.820705e-002, 5.799083e-003}	1
DFE-1	{1.190605e-001, −2.458730e-001, −1.158976e-001, 5.966760e-001, 8.421776e-001}	{3.567326e-001, 6.549196e-002, 1.737205e-002, 5.266961e-003, 5.020911e-003}	2

Figure 10. Eye diagram at transmitter in the case of medium fog.

Table 14. The eye diagram for every channel prior to and following DFE in the case of five FFF taps and five FBF taps

Table 15. Comparison performance of the DFE scheme in MDM for FSO system with previous MDM-FSO system

Parameters	MDM-FSO system (Amphawan, Chaudhary, Neo et al., 2015)	DFE scheme in MDM for FSO system
Transmitted power	0 dB	0 dB
Transmitted wavelength	850 nm	850 nm
Mode type	HG	HG
Number of channels	2	4
Data rate	2x2.5 Gbps (Each channel carry 2.5 Gbps)	4x2.5 Gbps (Each channel carry 2.5Gbps)
Distance	400 m-600 m	2 km
Weather condition	Clear	Clear
Simulation tool	OptiSystem	OptSim 5.2

Almogahed, A., Amphawan, A., & Fazea, Y. (2017). Mitigation of atmospheric turbulences using mode division multiplexing based on decision feedback equalizer for free space optics. Journal of Optical Communications, 41(2), 185–193. https://doi.org/10.1515/joc-2017-0169

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