Auto-Tuning PID Distributed Power Control for Next-Generation Passive Optical Networks

Layhon R. R. dos Santos; Fábio R. Durand; Alessandro Goedtel; Taufik Abrão

doi:10.1364/JOCN.10.00D110

Journal of Optical Communications and Networking
Vol. 10,
Issue 10,
pp. D110-D125
(2018)
•https://doi.org/10.1364/JOCN.10.00D110

Auto-Tuning PID Distributed Power Control for Next-Generation Passive Optical Networks

Layhon R. R. dos Santos, Fábio R. Durand, Alessandro Goedtel, and Taufik Abrão

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Layhon R. R. dos Santos, Fábio R. Durand, Alessandro Goedtel, and Taufik Abrão, "Auto-Tuning PID Distributed Power Control for Next-Generation Passive Optical Networks," J. Opt. Commun. Netw. 10, D110-D125 (2018)

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Abstract

This work proposes an adaptive auto-tuning distributed power control strategy aided by proportional-integral-derivative (PID) and by Adaline artificial neural network (AANN) approaches. The power control mechanism is realized for the upstream of next-generation passive optical networks (NG-PON), primarily deployed in the context of optical code division multiplexing access passive networks. The primary results demonstrate the ability of control and adaptive auto-tuning of the proposed AANN-based DPCA, considering realistic error estimates in the optical channel. For the sake of comparison, an adaptive auto-tuning procedure through the Tyreus–Lyuben method is included, indicating superior Euclidean norm of the NMSE performance combined with the lower complexity of the proposed NN-based DPCA method.

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Stp.1	Gain candidates
	a) $w_{i}$ (initial) = gain candidates
Stp.2	compute Eq. (16)
Stp.3	evaluate Eq. (22) for $E_{q m_{i}}$
Stp.4	for each epoch:
	a) compute Eq. (16) times $g (\cdot)$ , Fig. 2
	b) gains adjustment¹
Stp.5	operate the equations:
	a) (22) for $E_{q m_{i}}$
	b) (11) for $‖ NMSE ‖$
	c) (14) for $\bar{ITSE}$
Stp.6	epoch: $e p = e p + 1$ ;
Stp.7	operate Eq. (23) for $a_{E q m_{i}}$ computation:
	if $a_{E q m_{i}} > λ$
	return to Stp.3
	else
	a) return to $w_{i}$ ;
	exit
Note 1	For ${DPCA - PID - AANN}_{DR}$ : Eq. (21);
	For ${DPCA - PID - AANN}_{RLS}$ : Eqs. (25)–(27);

Stp.1	calculates initial $k_{p}$
Stp.2	compute Eqs. (30), (31), and (32)
Stp.3	if ( $M e_{1} > M e_{2}$ )
	a) $k_{p} = k_{p} + 10^{- 4}$
	b) compute Eqs. (30), (31), and (32)
	c) if ( $M e_{1} < M e_{2}$ )
	c1) $k_{p} = k_{p} - 10^{- 4}$
	c2) $k_{c r} = k_{p}$ ;
	c3) exit;
	d) else
	d1) return to Stp.3;
Stp.4	if ( $M e_{1} < M e_{2}$ )
	a) $k_{p} = k_{p} - 10^{- 4}$
	b) compute Eqs. (30), (31), and (32)
	c) if ( $M e_{1} > M e_{2}$ )
	c1) $k_{p} = k_{p} + 10^{- 4}$
	c2) $k_{c r} = k_{p}$ ;
	c3) exit;
	d) else
	d1) return to Stp.4

Variable	Adopted Value
Minimum Tx power	$P_{\min} = - 100 dBm$
Maximum Tx power	$P_{\max} = 20 dBm$
Fiber loss coefficient	$α_{f} = 0.2 dB / km$
Link length	$d_{i j} \in [42; 90] km$
Planck constant	$h = 6.63 \cdot 10^{- 34} J / Hz$
Light frequency	$f = 193.1 THz$
Optical bandwidth	$B_{o} = 100 GHz$
Spontaneous emission factor	$n_{sp} = 2$
Erbium-doped fiber amplifier gain	$G_{amp} = 20 dB$
Code length	$N = 64$
Individual bit rate	$R_{i} = 40 Gbps$
Chip rate	$R_{c} = 320 Gchips$
AWG loss	$L_{AWG} = 16 dB$
Bragg Loss	$L_{Bragg} = 6.7 dB$
Target SNIR	$γ^{*} = 20 dB$
# Iterations in the control algorithm	250
Uncertainty in optical channel estimations	$ε \in [0; 30] %$

Realiz.	$ε$ [%]	$P_{c r}$	$k_{c r}$	$k_{p}$	$k_{i}$	$k_{d}$
$T_{1}, T_{2}$	0	1	1.0393	0.4724	0.1074	0.1500
$T_{3}, T_{4}$	10	1	1.0200	0.4636	0.1054	0.1472
$T_{5}, T_{6}$	20	1	1.0200	0.4636	0.1054	0.1472
$T_{7}, T_{8}$	30	1	1.0200	0.4636	0.1054	0.1472

Realiz.	$ε_{%}$	$i_{s}$	$σ_{s}$	$σ_{s}^{2}$	$i_{a}$	$σ_{a}$	$σ_{a}^{2}$
$T_{1}, T_{2}$	0	193	26.4977	702.1280	193	26.4977	702.1280
$T_{3}, T_{4}$	10	203	27.2811	744.2571	203	27.2811	744.2571
$T_{5}, T_{6}$	20	200	31.1549	970.6290	200	31.1549	970.6290
$T_{7}, T_{8}$	30	196	27.6642	765.3054	196	27.6642	765.3054

Realiz.	$ε_{%}$	${‖ NMSE ‖}_{2}$	NMSE[250]	$\bar{ITSE}$
$T_{1}$	0	3.3714	$1.4538 E - 10$	$4.4766 E - 2$
$T_{2}$	10	3.3848	$1.6635 E - 10$	$4.5357 E - 2$
$T_{3}$	20	3.3692	$1.7118 E - 10$	$4.8421 E - 2$
$T_{4}$	30	3.3750	$1.8750 E - 10$	$4.8191 E - 2$

Variable	Adopted Value
Learning rate	$η = 25$
Target precision	$λ = 10^{- 4}$
Initial values of PID gains	$k_{p} = k_{i} = k_{d} = 0$

Realiz.	$ε_{%}$	Epoch	$E (k_{p})$	$E (k_{i})$	$E (k_{d})$
$T_{1 DR}$	0	7	−0.0522	0.4395	−0.0179
$T_{1 RLS}$	0	5	−0.2483	1.0672	−0.1391
$T_{2 DR}$	0	7	−0.0584	0.4624	−0.0209
$T_{2 RLS}$	0	5	−0.2488	1.0684	−0.1396
$T_{3 DR}$	10	7	−0.0528	0.4322	−0.0197
$T_{3 RLS}$	10	5	−0.2471	1.0643	−0.1375
$T_{4 DR}$	10	7	−0.0427	0.3709	−0.0122
$T_{4 RLS}$	10	5	−0.2463	1.0626	−0.1373
$T_{5 DR}$	20	7	−0.0656	0.5033	−0.0220
$T_{5 RLS}$	20	6	−0.2496	1.0756	−0.1418
$T_{6 DR}$	20	7	−0.0651	0.5292	−0.0233
$T_{6 RLS}$	20	5	−0.2476	1.0695	−0.1398
$T_{7 DR}$	30	7	−0.0526	0.4443	−0.0205
$T_{7 RLS}$	30	5	−0.2435	1.0653	−0.1376
$T_{8 DR}$	30	7	−0.0446	0.4095	−0.0140
$T_{8 RLS}$	30	5	−0.2461	1.0721	−0.1396

Realiz.	$ε_{%}$	${MO}_{%}$	$i_{MO}$	$σ_{MO}$	$σ_{MO}^{2}$
$T_{1 RLS}$	0	0.2509	5	$9.2743 e E - 4$	$8.6013 E - 7$
$T_{2 RLS}$	0	0.2682	5	$9.0373 E - 4$	$8.1674 E - 7$
$T_{3 RLS}$	10	0.2140	7	$1.3919 E - 6$	$1.9374 E - 6$
$T_{4 RLS}$	10	0.0016	6	$1.5680 E - 6$	$2.4586 E - 6$
$T_{5 RLS}$	20	0.3951	6	$3.3939 E - 6$	$1.1519 E - 6$
$T_{6 RLS}$	20	1.3980	4	$4.4066 E - 3$	$1.9418 E - 6$
$T_{7 RLS}$	30	0.6608	5	$4.1472 E - 3$	$1.7199 E - 5$
$T_{8 RLS}$	30	0.6347	6	$4.1841 E - 3$	$1.7507 E - 5$

Iterations	Attainable SINR, $γ_{A}$ [dB] with Probability
	$\Pr (γ \leq γ_{A}) = 0.5$
$ρ$	PID-TL	${PID - AANN}_{DR}$	${PID - AANN}_{RLS}$
5	11.75	15.88	19.57
10	14.45	17.91	19.94
15	16.12	18.86	19.96
30	17.98	19.69	20.00
200	19.93	20.00	20.00

Iterations	Attainable SINR, $γ_{A}$ [dB] with Probability
	$\Pr (γ \leq γ_{A}) = 1$
$ρ$	PID-TL	${PID - AANN}_{DR}$	${PID - AANN}_{RLS}$
5	11.75	19.98	19.99
10	14.45	19.99	20.00
15	16.12	20.00	20.00
30	17.98	20.00	20.00
200	19.93	20.00	20.00

Realiz.	$ε_{%}$	$i_{s}$	$σ_{s}$	$σ_{s}^{2}$	$i_{a}$	$σ_{a}$	$σ_{a}^{2}$
$T_{1 DR}$	0	60	4.9867	24.8669	60	4.9867	24.8669
$T_{1 RLS}$	0	4	1.2297	1.5121	11	2.2424	5.0282
$T_{2 DR}$	0	60	6.9789	48.7056	60	6.9789	48.7056
$T_{2 RLS}$	0	4	$8.8388 eE - 1$	$7.8125 E - 1$	11	1.9815	3.9264
$T_{3 DR}$	10	70	7.3916	54.6361	70	7.3916	54.6361
$T_{3 RLS}$	10	6	2.3692	5.6129	16	4.3671	19.0716
$T_{4 DR}$	10	67	6.9442	48.2218	67	6.9442	48.2218
$T_{4 RLS}$	10	5	1.9383	3.7571	14	3.5717	12.7571
$T_{5 DR}$	20	58	7.3834	54.5151	58	7.3834	54.5151
$T_{5 RLS}$	20	5	1.6580	2.7490	19	4.3329	18.7742
$T_{6 DR}$	20	47	7.0867	50.2218	47	7.0867	50.2218
$T_{6 RLS}$	20	4	0.0000	0.0000	19	4.8083	23.1200
$T_{7 DR}$	30	72	11.7045	136.9960	72	11.7045	136.9960
$T_{7 RLS}$	30	5	1.3198	1.7419	20	5.9126	34.9587
$T_{8 DR}$	30	67	8.9627	80.3296	67	8.9627	80.3296
$T_{8 RLS}$	30	5	1.6052	2.5766	19	5.3938	29.0927

Realiz.	$ε_{%}$	${‖ NMSE ‖}_{2}$	NMSE[250]	$\bar{ITSE}$	$\bar{E_{q m}}$
$T_{1 DR}$	0	1.4314	$2.4114 E - 15$	$1.7405 E - 3$	$7.6848 E - 4$
$T_{1 RLS}$	0	1.0930	$6.8879 E - 16$	$6.0690 E - 4$	$5.1952 E - 4$
$T_{2 DR}$	0	1.4038	$7.1482 E - 16$	$1.7515 E - 3$	$8.0544 E - 4$
$T_{2 RLS}$	0	1.0930	$8.2469 E - 16$	$6.6883 E - 4$	$5.7252 E - 4$
$T_{3 DR}$	10	1.4362	$6.2759 E - 3$	$1.7464 E - 3$	$7.5589 E - 4$
$T_{3 RLS}$	10	1.0976	$6.2759 E - 3$	$6.2571 - 3$	$5.3367 E - 4$
$T_{4 DR}$	10	1.5370	$3.4673 E - 3$	$1.7333 E - 3$	$6.5342 E - 4$
$T_{4 RLS}$	10	1.0939	$3.4673 E - 3$	$4.6319 - 4$	$3.9704 E - 4$
$T_{5 DR}$	20	1.3867	$9.0574 E - 3$	$1.7202 E - 3$	$8.5615 E - 4$
$T_{5 RLS}$	20	1.1021	$9.0574 E - 3$	$7.2054 E - 4$	$6.1678 E - 4$
$T_{6 DR}$	20	1.3526	$7.6670 E - 3$	$1.8208 E - 3$	$9.2730 E - 4$
$T_{6 RLS}$	20	1.0890	$7.6670 E - 3$	$7.5455 - 4$	$6.5621 E - 4$
$T_{7 DR}$	30	1.4462	$1.4694 E - 2$	$1.8002 E - 3$	$7.9123 E - 4$
$T_{7 RLS}$	30	1.1152	$1.4694 E - 2$	$6.4230 E - 4$	$5.5090 E - 4$
$T_{8 DR}$	30	1.4915	$9.6036 E - 3$	$1.8002 E - 3$	$7.2987 E - 4$
$T_{8 RLS}$	30	1.1033	$9.6036 E - 3$	$5.3740 E - 4$	$4.5693 E - 4$

Realiz.	$ε_{%}$	$i_{s}$	$σ_{s}$	$σ_{s}^{2}$	$i_{a}$	$σ_{a}$	$σ_{a}^{2}$
$T_{1 DR}$	0	60	4.9867	24.8669	60	4.9867	24.8669
$T_{1 RLS}$	0	4	1.2297	1.5121	11	2.2424	5.0282
$T_{2 DR}$	0	60	6.9789	48.7056	60	6.9789	48.7056
$T_{2 RLS}$	0	4	$8.8388 eE - 1$	$7.8125 E - 1$	11	1.9815	3.9264
$T_{3 DR}$	10	70	7.3916	54.6361	70	7.3916	54.6361
$T_{3 RLS}$	10	6	2.3692	5.6129	16	4.3671	19.0716
$T_{4 DR}$	10	67	6.9442	48.2218	67	6.9442	48.2218
$T_{4 RLS}$	10	5	1.9383	3.7571	14	3.5717	12.7571
$T_{5 DR}$	20	58	7.3834	54.5151	58	7.3834	54.5151
$T_{5 RLS}$	20	5	1.6580	2.7490	19	4.3329	18.7742
$T_{6 DR}$	20	47	7.0867	50.2218	47	7.0867	50.2218
$T_{6 RLS}$	20	4	0.0000	0.0000	19	4.8083	23.1200
$T_{7 DR}$	30	72	11.7045	136.9960	72	11.7045	136.9960
$T_{7 RLS}$	30	5	1.3198	1.7419	20	5.9126	34.9587
$T_{8 DR}$	30	67	8.9627	80.3296	67	8.9627	80.3296
$T_{8 RLS}$	30	5	1.6052	2.5766	19	5.3938	29.0927

Realiz.	$ε_{%}$	${‖ NMSE ‖}_{2}$	NMSE[250]	$\bar{ITSE}$	$\bar{E_{q m}}$
$T_{1 DR}$	0	1.4314	$2.4114 E - 15$	$1.7405 E - 3$	$7.6848 E - 4$
$T_{1 RLS}$	0	1.0930	$6.8879 E - 16$	$6.0690 E - 4$	$5.1952 E - 4$
$T_{2 DR}$	0	1.4038	$7.1482 E - 16$	$1.7515 E - 3$	$8.0544 E - 4$
$T_{2 RLS}$	0	1.0930	$8.2469 E - 16$	$6.6883 E - 4$	$5.7252 E - 4$
$T_{3 DR}$	10	1.4362	$6.2759 E - 3$	$1.7464 E - 3$	$7.5589 E - 4$
$T_{3 RLS}$	10	1.0976	$6.2759 E - 3$	$6.2571 - 3$	$5.3367 E - 4$
$T_{4 DR}$	10	1.5370	$3.4673 E - 3$	$1.7333 E - 3$	$6.5342 E - 4$
$T_{4 RLS}$	10	1.0939	$3.4673 E - 3$	$4.6319 - 4$	$3.9704 E - 4$
$T_{5 DR}$	20	1.3867	$9.0574 E - 3$	$1.7202 E - 3$	$8.5615 E - 4$
$T_{5 RLS}$	20	1.1021	$9.0574 E - 3$	$7.2054 E - 4$	$6.1678 E - 4$
$T_{6 DR}$	20	1.3526	$7.6670 E - 3$	$1.8208 E - 3$	$9.2730 E - 4$
$T_{6 RLS}$	20	1.0890	$7.6670 E - 3$	$7.5455 - 4$	$6.5621 E - 4$
$T_{7 DR}$	30	1.4462	$1.4694 E - 2$	$1.8002 E - 3$	$7.9123 E - 4$
$T_{7 RLS}$	30	1.1152	$1.4694 E - 2$	$6.4230 E - 4$	$5.5090 E - 4$
$T_{8 DR}$	30	1.4915	$9.6036 E - 3$	$1.8002 E - 3$	$7.2987 E - 4$
$T_{8 RLS}$	30	1.1033	$9.6036 E - 3$	$5.3740 E - 4$	$4.5693 E - 4$

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Journal of Optical Communications and Networking