Page 37 - ITU Journal, Future and evolving technologies - Volume 1 (2020), Issue 1, Inaugural issue

ITU Journal on Future and Evolving Technologies, Volume 1 (2020), Issue 1

Individual constellation UE 1 Individual constellation UE 1
j j
Joint-constellation at the BS Joint-constellation at the BS
1.5j
-1 1 -1 1 1.707j
-j -j
Individual constellation UE 2 Individual constellation UE 2
-1.707 1.707
-1.5 1.5
0.707j
0.5j
-0.5 -1.707j
-1.5j
-0.707 0.707
0.5
-0.5j
-0.707j
Type B Equal Error Protection (EEP)
Fig. 4 – Example of two joint‑constellations, for two UEs and four symbols each. The symbols of UE 1 are shown using different colours and the symbols
of UE 2 are plotted using different markers.

where is the average power of the signal of the ‑th UE, symbol must be properly designed to enable the demodu‑

, denotes the additive white Gaussian noise (AWGN) lation of the transmitted information by all the UEs. Con‑
at ‑th subcarrier, ‑th OFDM symbol and ‑th antenna, sequently, the choice of the individual constellation is cru‑
2
distributed as (0, ); and ℎ , corresponds to the cial to produce a robust joint‑constellation against inter‑
,

channel frequency response between the ‑th UE and the ference and noise effects. The most used constellations
‑th antenna at the ‑th subcarrier and ‑th OFDM sym‑ are the Type B [12] and equal error protection (EEP) [13].
bol, distributed as (0, 1). For simplicity, we assume The constellation of the ‑th UE can be expressed as
here that the channel response is spatially uncorrelated,
while we will use more realistic channel models for per‑ ℳ = {√ exp ( 2 ) ∣ 0 ≤ ≤ − 1} , (8)

formance evaluation. Besides, note that the difference in
among different UEs may be due to the constellation 2

design or to different propagation path loss. In the latter ℳ = {exp ( ( + 2 )) ∣ 0 ≤ ≤ − 1} ,

case, an accurate power control must be implemented to (9)
compensate this difference. for Type B and EEP, respectively, where denotes the

According to [12], , is fed to the differential decoder number of symbols in the constellation. Fig.4 shows
and averaged over the spatial dimension as an illustrative example of these two types of joint‑
constellations, designed for the particular case of UL with
1 ∗ only two UEs, each of them using a 4‑DPSK. In the irst
, = ∑ ( ) , (6)
−1, , case, all UEs have the same 4‑DPSK constellation and
=1
are distinguished with a different amplitude. This pro‑
2 ≤ ≤ , 1 ≤ ≤ , duces the joint‑constellation also shown in the same ig‑
∗
where (•) is the complex conjugate operation and , ure, where we can see that all symbols are equally spaced
denotes the received joint‑symbol at the ‑th subcarrier providing a robustness against possible interference and
and ‑th OFDM symbol. When the number of antennas is noise terms. However, those UEs with a lower amplitude
large enough and making use of the Law of Large Num‑ will obtain a worse performance for the same noise condi‑
bers, , can be approximated as tions as compared to the stronger ones. Indeed, the aver‑
age distance of the symbols of UE = 1 (shown in differ‑
ent colours) is much larger than the distance of UE = 2
→∞
, −−−→ , = ∑ (7) (plotted in different markers). In EEP, both UEs have the
,
=1 same amplitude, and then the same performance. Their
constellations differ in a rotation of 45°. However, this
2 ≤ ≤ , 1 ≤ ≤ ,
option presents several symbols of the joint‑constellation
where , is the joint‑symbol at the ‑th subcarrier and (those placed in the middle) that are too close to each
‑th OFDM symbol. Note that the interference and noise other, degrading the performance.
terms are averaged out thanks to the large number of an‑ The design of optimal individual constellations for multi‑
tennas at the BS, otherwise the performance may be de‑ user NCDS that work well in realistic channel conditions
graded. More details are given in [12] ‑ [17]. is still a very challenging topic, due to the diverse effects
The performance of the overall multi‑user systems de‑ of the channel impairments and interference and the dif‑
pends on the constellation of the joint‑symbol. This joint‑ iculty to analyse them.

© International Telecommunication Union, 2020 17