In the research on FD systems presented in this thesis, it has been been assumed that multiuser access is orthogonal. The other access technique, non-orthogonal frequen- cy multiple access (NOMA) also has attracted much attention, which even demon- strates higher SE than orthogonal multiuser access (OMA) by proper design. Besides, ultra-dense and heterogeneous systems are two key deployments in 5G systems, which provides seamless network coverage and features low money cost and low power con- sumption. However, how to incorporate FD with NOMA, ultra-dense or heterogeneous
systems is still challenging. Hence, the future research topics are summarised in the following.
• The key concept of NOMA is that it allows multiuser occupy the same frequency, time and code. Users’ signals are linearly superimposed and transmitted at the BS. At receiver end, the user with better channel condition decodes the data of another user with worse channel condition, and performs successive interference cancellation to subtract the multiuser interference before detecting its own signal. Recently, in order to further improve the SE performance of NOMA systems, HD cooperative NOMA systems have been proposed, where strong user acts as a HD relay node. As mentioned above, HD relay systems need two orthogonal time slots and inevitably lead to SE loss. As a result, FD cooperative NOMA systems will be addressed in the future.
• FD transmission in ultra-dense small cell or heterogeneous systems has not been investigated. High density of small cell increases the possibility of inter-cell in- terference. The performance of FD transmission may be significantly degraded by noise, self-interference, inter-cell interference and multiuser interference. How to determine the density of small cell, how to organise adjacent small cells for cooperative communications and interference management are challenging and will be investigated thoroughly.
Appendix A
Proof of Theorem 4.1
Hereby the concavity of the EE of FD (PSAC) is proven with respect to the to- tal transmission power Ps (FD (PS) and HD can be seen as special cases). Define
B = {TF D(P SAC)|TF D(P SAC) ∈ (0, ∞)} as the set of the overall throughput, while
A = {Ps|Ps ∈ (0, ∞)} is the corresponding total transmission power. With a specific
mapping function (power allocation method) f : Ps f
−→ TF D(P SAC), the total transmis- sion power and the overall throughput is one-to-one mapped (f : A−→ B ) and higherf transmission power leads to higher throughput. Therefore, if EE ηF D(P SAC) is strictly
quasi-concave with respect to the overall throughput TF D(P SAC), it is also quasi-concave with respect to the total transmission power Ps. The superlevel sets of ηF D(P SAC) is
defined as SΥ = {TF D(P SAC) > 0|ηF D(P SAC) > Υ}. According to [136], ηF D(P SAC) is
strictly quasi-concave with respect to TF D(P SAC) if SΥ is strictly convex for any real
number Υ. If Υ < 0, there is no physical meaning. If Υ ≥ 0, SΥ is equivalent to
SΥ= {TF D(P SAC)> 0|Υ(Ps/ω)PNn=1λ˜n+ Υ(Pc,sta+ PAC) + (Υε − 1)TF D(P SAC)≤ 0}.
It is known that Psis strictly convex with respect to TF D(P SAC)given a sufficiently large
number of subcarriers [2] [53] and with good SIC. The linear part Υ(Pc,sta + PAC) +
(Υε − 1)TF D(P SAC) is convex (not strictly) with respect to throughput TF D(P SAC).
Therefore, the summation Υ(Ps/ω)
PN
n=1λ˜n+ Υ(Pc,sta+ PAC) + (Υε − 1)TF D(P SAC)
is strictly convex with respect to throughput TF D(P SAC). In conclusion, ηF D(P SAC) is strictly quasi-concave with respect to TF D(P SAC), and is strictly quasi-concave with re-
spect to Ps. Under a small maximum transmission power constraint Pmax, ηF D(P SAC)
Appendix B
Derivative Calculation of EE
with respect to the Total
Transmission Power
Hereby we take FD (PSAC) as example to show the derivative calculation of EE with respect to the total transmission power (FD (PS) and HD can be seen as special cases). For the strictly-continuous function ηF D(P SAC) in the region Ps ∈ (0, Pmax], the limit
of the difference quotient when ∆Ps approaches zero, if existing, should represent the
slope of the tangent line to (Ps, ηF D(P SAC)), which is calculated as
∂ηF D(P SAC) ∂Ps |Ps = lim ∆Ps→0 ηF D(P SAC)(Ps+ ∆Ps) − ηF D(P SAC)(Ps) ∆Ps . (B.1)
With a minimal increment ∆Ps that approaches 0, the values of ηF D(P SAC) and
ηF D(P SAC) can be obtained at points Ps+ ∆Ps and Ps, respectively. Substituting the
two terms into (B.1), ∂ηF D(P SAC)/∂Ps can be found. Therefore, calculating ∂P∂ηs can
Appendix C
Energy Efficiency Gain Regions
among FD(PSAC) FD(PS) and
HD
C.1
Energy Efficiency Gain Region between FD (PSAC)
and FD (PS)
The difference between the EEs of FD (PSAC) and FD (PS) is calculated as ηF D(P SAC)− ηF D(P S)= 1 Ps ω PN n=1λ˜n+ εTF D(P S)+ Pc,sta × Ps ω PN n=1λ˜n+ Pc,sta T F D(P SAC) TF D(P S) − 1 − PAC TF D(P S) Ps ω PN n=1˜λn+ εTF D(P SAC)+ Pc,sta+ PAC , (C.1)
where TF D(P SAC) and TF D(P S) represent the throughputs achieved by FD (PSAC)
and FD (PS), respectively. Obviously, the sign of (C.1) is the same as the sign of its numerator.