Efficient power allocation for downlink MIMO-NOMA-based visible light communication systems

Figures & data

Figure 1. The proposed VLC system block diagram.

Figure 2. Geometric model of LOS transmission.

Figure 3. Illustration of a $4\times 4$ MIMO-NOMA based VLC system with K users.

Table 1. Simulation parameters.

Parameter	Symbol	Value
Number of LEDs	i	4
Number of PDs	j	4
System Coverage	R	4 m
Number of User	K	$2-10$ (Variable)
Receiver height	h	0.85 m
Transmitted power	$P_{\mathit{\text{opt}}}$	10 W
Modulation index	$\mu$	0.5
Transmitter semi angle	${\Phi }_{1/2}$	${60}^{°}$
Separation between LED	$d_{\mathit{\text{LED}}}$	1 m
Electronic charge	q	$1.6\times e^{-19}C$
Noise bandwidth factor	$I_2$	0.562
Boltzmann constant	K	$1.38\times e^{-23}$
Absolute temprature	T	300K
Fixed capacitance	$\eta$	$112e^{-12}/1e^{-4}(F/m)$
Open loop voltage gain	G	10
FET transconductance	$g_m$	$30e^{-3}S$
FET channel noise factor	$\gamma$	1.5
Receiver field of view	${\psi }_c$	$72°$
Total bandwidth	Bw	10 MHz
Photodiode responsivity	$\mathfrak{R}$	0.53 A/W
Refractive index	n	1.5
Separation between PD	$d_{\mathit{\text{PD}}}$	4 cm
Gain of optical filter	$T_s(\psi )$	0.9
Physical area of a PD	$A_{\mathit{\text{PD}}}$	1 $c{m}^2$
The power allocation parameter	$\beta$	1

Figure 4. Power allocated for each user of a VLC system with five users.

Table 2. Comparison of power allocation coefficients for five users.

	Power Allocation Coefficient
	LED 1 and LED 3			LED 2 and LED 4
User No	GRPA	NGDPA	Proposed	GRPA	NGDPA	Proposed
1	2.4415$\times e^{-7}$	0.0050	0.0288	0.0023	2.7887$\times e^{-6}$	0.0054
2	4.3278$\times e^{-7}$	0.0201	0.0505	0.0028	2.7907$\times e^{-5}$	0.0102
3	3.4052$\times e^{-6}$	0.0815	0.1140	0.9726	0.9150	0.7737
4	3.2713$\times e^{-4}$	0.2587	0.2619	0.0039	0.0028	0.0369
5	0.9996	0.6345	0.5447	0.0185	0.0822	0.1738

Figure 5. Achievable Sum rate of Proposed NOMA, NGDPA and GRPA vs. r/R ($k=5,6$).

Figure 6. Achievable Sum rate of the proposed NOMA, NGDPA and GRPA vs. r/R ($k=7,8,9,10$).

Table 3. Achievable sumrate comparison of the proposed NOMA scheme with GRPA and NGDPA for 7 and 8 users.

	$S{R}_{\mathit{\text{GRPA}}}$		$S{R}_{\mathit{\text{NGDPA}}}$		$S{R}_{\mathit{\text{PNOMA}}}$
r/R	k = 7	k = 8	k = 7	k = 8	k = 7	k = 8
0.1	268.94	268.94	265.67	265.65	267.17	266.64
0.2	268.93	268.90	261.12	260.72	265.11	263.54
0.3	268.70	267.90	256.69	255.48	263.23	259.97
0.4	265.18	257.68	251.31	249.83	261.10	256.33
0.5	249.74	243.48	246.44	243.28	261.70	253.07
0.6	233.17	229.36	244.18	238.47	263.63	251.90
0.7	215.52	213.52	240.32	232.66	263.38	250.45
0.8	198.26	197.79	232.71	223.17	259.27	246.34
0.9	178.72	171.84	229.57	207.13	257.53	236.53
1	148.30	137.88	223.49	193.36	252.55	228.85

Table 4. Achievable sum rate comparison of proposed NOMA, NGDPA and GRPA (k = 9 and k = 10).

	$S{R}_{\mathit{\text{GRPA}}}$		$S{R}_{\mathit{\text{NGDPA}}}$		$S{R}_{\mathit{\text{PNOMA}}}$
r/R	k = 9	k = 10	k = 9	k = 10	k = 9	k = 10
0.1	268.94	269.33	265.65	265.65	266.33	266.15
0.2	268.84	268.78	260.63	260.62	262.68	262.11
0.3	265.18	261.39	254.57	254.15	258.24	257.08
0.4	252.60	250.64	248.57	247.42	253.27	251.32
0.5	241.07	239.67	241.55	240.22	248.04	245.00
0.6	227.17	226.08	235.30	233.26	244.25	239.68
0.7	212.88	212.83	225.83	222.98	237.47	231.33
0.8	197.66	195.04	216.80	209.02	231.76	219.41
0.9	171.13	173.56	199.85	194.82	219.53	207.89
1	143.34	138.77	181.80	165.44	208.03	182.19

Table 5. Notations and its definition.

Notation	Definition
DC	Direct Current
DD	Direct Detection
FET	Field Effective Transistor
FPA	Fixed Power Allocation
FOV	Field-of-View
GRPA	Gain Ratio Power Allocation
IFFT	Inverse Fast Fourier Transform
IM	Intensity Modulation
LED	Light Emitting Diode
LOS	Line-of-Sight
MA	Multiple Access
MIMO	Multiple-Input-Multiple-Output
NGDPA	Normalized Gain Difference Power Allocation
NLOS	Non-Line-of-Sight
NOMA	Non-Orthogonal Multiple Access
OFDMA	Orthogonal Frequency Division Multiple Access
PD	Photo Detector
QAM	Quadrature Amplitude Modulation
RF	Radio Frequency
SIC	Successive Interference Cancellation
SNR	Signal-to-Noise Ratio
VLC	Visible Light Communication
ZF	Zero Forcing

Figure 7. Achievable Average Sum Rate vs. Number of Users.

Figure 8. Sum rate gain of Proposed NOMA over NGDPA vs. Normalized offset ($k=5,6,$ $\&7$), ($k=8,9,$ $\&10$).

Figure 9. Sum rate gain of Proposed NOMA over GRPA vs. Normalized offset ($k=5,6,$ $\&7$), ($k=8,9,$ $\&10$).