Aerospace and Electronic Systems Magazine February 2018 - 12

Cyber-Secure Multiuser Superposition Covert Avionics System

Figure 9.

Capacity region comparison with different channel conditions.

put is achieved. OMA curves are obtained by varying the bandwidth allocation factor β from 0 to 1. Comparing the dotted curves
(green, magenta, and cyan) with the fixed power allocation (θ =
0.2, 0.5, or 0.8), it is observed that when θ = β, OMA can achieve
the best capacity region AD (solid red line) for Users 1 and 2.
However, the capacity region of NOMA, which is represented by
the blue solid curve 
AB, is much wider than that of OMA. For
example, when R2,NOMA = 2 bps, R1,NOMA in NOMA with θ > 0.5
can be 0.54 bps, which is greater than 0.36 bps in OMA, because
the throughput for User 2 is bandwidth limited rather than power
limited. The superposition coding with User 1 allows User 2 to use
the full bandwidth. Besides, User 2 only imparts a small amount
of interference to User 1 due to its smaller allocated transmission

power and a lower channel gain p2|h1|2. The blue-dotted curve CD
illustrates the capacity region if removing the constraint of θ ≥ 0.5.
It is observed that if θ < 0.5, the capacity region of NOMA is less
than that of OMA, because when θ < 0.5, the decoding order has
been changed. User 1 having a poorer channel condition has to
perform interference cancellation, and it also imports a relatively
higher interference, p1|h2|2 to User 2.
In Figure 9, we compared the capacity regions of noise-modulated NOMA and noise-modulated OMA with different channel
conditions. When Γ1 = Γ2, the channels are symmetric, and the user
data rate pair on the blue solid line segment coincides with that
on the blue dash line segment. This means that in the symmetric
channel, the capacity region of NOMA and OMA are identical;
however, in the asymmetric channel, NOMA outperforms OMA.
Moreover, with a large disparity between the channel conditions,
Γ1 and Γ2, NOMA is able to achieve a better performance gain
over OMA. For example, when Γ1 = 0 dB and Γ2 = 20 dB, R2 for
12

NOMA is approximately twofold higher in data rate transmission
than that for NOMA, when R1 = 0.6 bps. Therefore, it is beneficial
to implement multiuser superposition transmission (i.e., NOMA)
in environments when channel conditions are remarkably different
for various users. Such situations exist when there are different
platforms in the airspace, such as commercial aircraft, private airplanes, and unmanned air vehicles.
Furthermore, a system-level simulation was created to demonstrate the performance improvement brought by NOMA. Specifically, the simulation is based on a multiuser multiple input and
multiple output (MU-MIMO) system with 100 users, which represents communications at an airfield. At each time slot, small-scale
fading is generated on the basis of the Rayleigh fading channel
model [27]. A brute-force search algorithm is used to find the best
two users, i.e., total throughput (2) for N = 2, to apply superposition transmission over a frequency bandwidth of 180 kHz. Due to
space availability, more details of the static problem formulation
for the communication design can be found in our previous work
[23].
Figure 10 compares the performance with different power allocation factor θ. It is observed that as θ decreases, users have a relatively higher average data rate. This is because a small θ reflects
a relatively large power disparity within the superposed signal
components at receiver terminals. Thereby, NOMA can improve
the system throughput considerably. Our observation is consistent
with the finding in [28]. In contrast, as θ increases, the received
power disparity is not distinct. Thus NOMA no longer contributes
notable performance gains. When θ = 1, the system evolves into
a pure Multi-User Miulti-Input Multi-Output (MU-MIMO) system without NOMA operation, and most of the users have a lower

IEEE A&E SYSTEMS MAGAZINE

FEBRUARY 2018

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine February 2018