Impulse response modeling for underwater optical wireless channels

Yiming Li; Mark S. Leeson; Xiaofeng Li

doi:10.1364/AO.57.004815

Applied Optics
Vol. 57,
Issue 17,
pp. 4815-4823
(2018)
•https://doi.org/10.1364/AO.57.004815

Impulse response modeling for underwater optical wireless channels

Yiming Li, Mark S. Leeson, and Xiaofeng Li

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Yiming Li, Mark S. Leeson, and Xiaofeng Li, "Impulse response modeling for underwater optical wireless channels," Appl. Opt. 57, 4815-4823 (2018)

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Abstract

In underwater optical wireless communication (UOWC) channels, impulse response is widely used to describe the temporal dispersion of the received signals. In this paper, we propose a new function to model the impulse response in most realistic cases in UOWC channels. By exploiting the inherent properties of such channels, our newly proposed model is superior to the conventional weighted double gamma functions (WDGF) model in explaining the behavior of the channel. We use Monte Carlo simulation to verify that our newly proposed model has a better accuracy of numerical fitting in most cases. Therefore, this new modeling approach offers a more convenient way to evaluate the performance of different kinds of UOWC channels.

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FOV	$C_{1}$	$C_{2}$	$α$	$β$
$L = 5.47 m$ ( $b L = 10$ ), on-axis, harbor water
20°	$5.244 e - 8$	$5.015 e - 2$	$- 3.681 e - 2$	3.019
40°	$7.937 e - 7$	$2.957 e - 2$	$- 3.595 e - 2$	1.793
180°	$1.390 e - 6$	$2.331 e - 2$	$- 1.966 e - 2$	1.564
$L = 10.93 m$ ( $b L = 20$ ), on-axis, harbor water
20°	$1.677 e - 6$	0.2730	0.6577	3.169
40°	$1.320 e - 5$	0.6657	0.4871	3.216
180°	$9.072 e - 6$	0.4374	0.4798	2.005
$L = 16.40 m$ ( $b L = 30$ ), on-axis, harbor water
20°	$2.168 e - 6$	0.6994	1.569	3.793
40°	$3.207 e - 5$	1.463	1.514	4.211
180°	$2.236 e - 5$	1.818	1.255	3.039
$L = 10.93 m$ ( $b L = 20$ ), off-axis $angle = 10 °$ , harbor water
20°	$9.653 e - 6$	0.3661	3.947	7.765
40°	$1.900 e - 4$	0.8292	2.830	7.129
180°	$2.800 e - 5$	0.4760	3.007	5.183
$L = 45.45 m$ ( $b L = 10$ ), on-axis, coastal water
20°	$4.888 e - 7$	0.4169	$- 3.681 e - 2$	3.019
40°	$5.525 e - 7$	0.2458	$- 3.595 e - 2$	1.793
180°	$5.754 e - 7$	0.1938	$- 1.966 e - 2$	1.564

FOV	$C_{1}$	$C_{2}$	$C_{3}$	$C_{4}$	$α$	$β$
$L = 5.47 m$ ( $b L = 10$ ), on-axis, harbor water
20°	$3.67 e - 5$	57.9	$1.44 e - 5$	17.5	$- 8.32 e - 2$	$3.21 e - 2$
40°	$3.09 e - 5$	64.7	$2.13 e - 5$	15.7	$- 8.68 e - 2$	$3.88 e - 3$
180°	$3.17 e - 5$	63.8	$2.03 e - 5$	13.8	$- 8.50 e - 2$	$3.89 e - 3$
$L = 10.93 m$ ( $b L = 20$ ), on-axis, harbor water
20°	$9.41 e - 7$	8.68	$1.49 e - 7$	2.38	0.556	0.444
40°	$6.06 e - 7$	5.37	$2.23 e - 7$	1.67	0.474	0.461
180°	$5.13 e - 7$	4.51	$2.02 e - 7$	1.07	0.441	0.413
$L = 16.40 m$ ( $b L = 30$ ), on-axis, harbor water
0°	$4.65 e - 9$	2.45	$5.13 e - 10$	0.640	1.12	0.673
40°	$6.44 e - 9$	1.77	$9.84 e - 10$	0.575	1.24	0.890
180°	$4.79 e - 9$	1.30	$1.36 e - 10$	0.432	1.10	0.998
$L = 10.93 m$ ( $b L = 20$ ), off-axis $angle = 10 °$ , harbor water
20°	$4.36 e - 6$	6.83	$9.52 e - 8$	2.35	2.46	1.84
40°	$2.33 e - 6$	4.73	$1.65 e - 7$	2.00	2.24	1.99
180°	$1.84 e - 6$	4.34	$1.69 e - 7$	1.49	2.17	1.82
$L = 45.45 m$ ( $b L = 10$ ), on-axis, coastal water
20°	$1.37 e - 9$	7.00	$4.22 e - 10$	2.13	$- 8.32 e - 2$	$3.21 e - 2$
40°	$1.16 e - 9$	7.82	$6.61 e - 10$	1.92	$- 8.68 e - 2$	$3.88 e - 3$
180°	$1.19 e - 9$	7.70	$6.31 e - 10$	1.69	$- 8.50 e - 2$	$3.89 e - 3$

RMSE			Power Deviation of the Tail
FOV	CEAPF	WDGF	FOV	CEAPF	WDGF
$L = 5.47 m$ ( $b L = 10$ ), on-axis, harbor water
20°	0.18%	0.10%	20°	−13.65%	−28.65%
40°	0.36%	0.11%	40°	30.61%	−42.87%
180°	0.18%	0.11%	180°	15.25%	−54.48%
$L = 10.93 m$ ( $b L = 20$ ), on-axis, harbor water
20°	0.52%	0.95%	20°	15.19%	−87.59%
40°	0.92%	1.01%	40°	17.12%	−63.63%
180°	0.98%	1.15%	180°	34.84%	−55.12%
$L = 16.40 m$ ( $b L = 30$ ), on-axis, harbor water
20°	0.83%	1.34%	20°	−2.30%	−66.04%
40°	0.66%	0.93%	40°	−13.29%	−51.75%
180°	0.83%	1.05%	180°	5.54%	−39.71%
$L = 10.93 m$ ( $b L = 20$ ), off-axis $angle = 10 °$ , harbor water
20°	1.03%	0.52%	20°	−36.62%	−64.70%
40°	0.39%	0.46%	40°	−24.06%	−49.61%
180°	0.30%	0.56%	180°	0.73%	−52.00%
$L = 45.45 m$ ( $b L = 10$ ), on-axis, coastal water
20°	0.18%	0.10%	20°	−13.58%	−27.40%
40°	0.36%	0.11%	40°	23.39%	−41.16%
180°	0.18%	0.11%	180°	8.51%	−51.32%

FOV	$C_{1}$	$C_{2}$	$α$	$β$
$L = 5.47 m$ ( $b L = 10$ ), on-axis, harbor water
20°	$5.244 e - 8$	$5.015 e - 2$	$- 3.681 e - 2$	3.019
40°	$7.937 e - 7$	$2.957 e - 2$	$- 3.595 e - 2$	1.793
180°	$1.390 e - 6$	$2.331 e - 2$	$- 1.966 e - 2$	1.564
$L = 10.93 m$ ( $b L = 20$ ), on-axis, harbor water
20°	$1.677 e - 6$	0.2730	0.6577	3.169
40°	$1.320 e - 5$	0.6657	0.4871	3.216
180°	$9.072 e - 6$	0.4374	0.4798	2.005
$L = 16.40 m$ ( $b L = 30$ ), on-axis, harbor water
20°	$2.168 e - 6$	0.6994	1.569	3.793
40°	$3.207 e - 5$	1.463	1.514	4.211
180°	$2.236 e - 5$	1.818	1.255	3.039
$L = 10.93 m$ ( $b L = 20$ ), off-axis $angle = 10 °$ , harbor water
20°	$9.653 e - 6$	0.3661	3.947	7.765
40°	$1.900 e - 4$	0.8292	2.830	7.129
180°	$2.800 e - 5$	0.4760	3.007	5.183
$L = 45.45 m$ ( $b L = 10$ ), on-axis, coastal water
20°	$4.888 e - 7$	0.4169	$- 3.681 e - 2$	3.019
40°	$5.525 e - 7$	0.2458	$- 3.595 e - 2$	1.793
180°	$5.754 e - 7$	0.1938	$- 1.966 e - 2$	1.564

FOV	$C_{1}$	$C_{2}$	$C_{3}$	$C_{4}$	$α$	$β$
$L = 5.47 m$ ( $b L = 10$ ), on-axis, harbor water
20°	$3.67 e - 5$	57.9	$1.44 e - 5$	17.5	$- 8.32 e - 2$	$3.21 e - 2$
40°	$3.09 e - 5$	64.7	$2.13 e - 5$	15.7	$- 8.68 e - 2$	$3.88 e - 3$
180°	$3.17 e - 5$	63.8	$2.03 e - 5$	13.8	$- 8.50 e - 2$	$3.89 e - 3$
$L = 10.93 m$ ( $b L = 20$ ), on-axis, harbor water
20°	$9.41 e - 7$	8.68	$1.49 e - 7$	2.38	0.556	0.444
40°	$6.06 e - 7$	5.37	$2.23 e - 7$	1.67	0.474	0.461
180°	$5.13 e - 7$	4.51	$2.02 e - 7$	1.07	0.441	0.413
$L = 16.40 m$ ( $b L = 30$ ), on-axis, harbor water
0°	$4.65 e - 9$	2.45	$5.13 e - 10$	0.640	1.12	0.673
40°	$6.44 e - 9$	1.77	$9.84 e - 10$	0.575	1.24	0.890
180°	$4.79 e - 9$	1.30	$1.36 e - 10$	0.432	1.10	0.998
$L = 10.93 m$ ( $b L = 20$ ), off-axis $angle = 10 °$ , harbor water
20°	$4.36 e - 6$	6.83	$9.52 e - 8$	2.35	2.46	1.84
40°	$2.33 e - 6$	4.73	$1.65 e - 7$	2.00	2.24	1.99
180°	$1.84 e - 6$	4.34	$1.69 e - 7$	1.49	2.17	1.82
$L = 45.45 m$ ( $b L = 10$ ), on-axis, coastal water
20°	$1.37 e - 9$	7.00	$4.22 e - 10$	2.13	$- 8.32 e - 2$	$3.21 e - 2$
40°	$1.16 e - 9$	7.82	$6.61 e - 10$	1.92	$- 8.68 e - 2$	$3.88 e - 3$
180°	$1.19 e - 9$	7.70	$6.31 e - 10$	1.69	$- 8.50 e - 2$	$3.89 e - 3$

Abstract

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Tables (3)

Equations (20)

Applied Optics