Aerospace and Electronic Systems Magazine February 2018 - 11
Xu et al.
Figure 8.
Capacity region comparison between noise-modulated NOMA and noise-modulated OMA.
To better demonstrate the improvement of the noise-modulated
multiuser superposition transmission mechanism, the same scenarios are used, as illustrated in Figure 5. At the platform terminal
2
2
h
h
receiver, we have 1 < 2 , and User 2 will first detect the sigN 0,1 N 0,2
nal of User 1 because p1 > p2. Then, it subtracts the signal of User
1 from the received aggregated signal and decodes its own signal.
User 1 will decode its signal directly without performing interference cancellation. Therefore, on the basis of Shannon's equation
[26], the unit achievable user data rate in terms of bits per second
per hertz can be represented as
2
2
p1 h1
θ P h1
=
+
log
1
R1, NOMA = log 2 1 +
2
2
2
(3)
p2 h1 + N 0,1
(1 − θ ) P h1 + N 0,1
θ Γ1
⇔ log 2 1 +
,
θ
−
Γ
+
(1
)
1
1
p h 2
(1 − θ ) P h
2
R2, NOMA = log 2 1 + 2 2 = log 2 1 +
N 0,2
N 0,2
⇔ log 2 (1 + (1 − θ )Γ 2 )
where Γ1 =
P h1
2
and Γ 2 =
P h2
2
p h 2
R1,OMA = β log 2 1 + 1 1
β N 0,1
θ Γ1
⇔ β log 2 1 +
,
β
(4)
2
. is denoted as the signal-to-
(5)
2
p2 h2
(1 − θ )Γ 2
⇔ (1 − β )log 2 1 +
R2,OMA = (1 − β )log 2 1 +
. (6)
(1 − β ) N 0,2
1− β
Assume the bandwidth is 1 Hz, and the asymmetric channels are
Γ1 = 0 dB and Γ2 = 10 dB, respectively. Figure 8 compares the
capacity regions between noise-modulated NOMA and noisemodulated OMA. Point A is located at 0,log 2 1 + Γ1 when all
the transmit power and bandwidth is assigned to User 1, which
is achieved by both NOMA and OMA. Point B is located at
Γ1
Γ
+
log 2 1 + 2 ,log 2 1 +
where θ = 0.5 . Point C is lo
2
2
+
Γ
1
(
N 0,1
N 0,2
noise ratio (SNR) loss caused by noise modulation. Without loss
of generality, SNR is set to 0.5 dB for both NOMA and OMA. It
FEBRUARY 2018
is shown that users' data rates are closely related to the power allocation factor θ.
In contrast, for OMA (e.g., OFDMA), the bandwidth allocation
coefficient β varies in the range of 0 to 1. The power allocation coefficient θ is set to 0.2, 0.5, 0.8, or θ = β. For each θ and β pair, we
can calculate the data rates and plot them in Figure 8. It is observed
that OMA can achieve the best capacity region when θ = β. The
data rate of user k, is given by
)
Γ1
Γ 2
cated at log 2 1 +
where θ = 0.5-. Point
,log 2 1 +
2
2
+
Γ
1
D is located at log 2 1 + Γ 2 ,0 , where all the transmit power and
bandwidth is assigned to User 2, and the maximum total through-
IEEE A&E SYSTEMS MAGAZINE
(
)
11
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