Page 84 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 7 – Terahertz communications

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 7

In this work, we mainly focus on the beam alignment to be aligned with an optimal beam. Thus, the BA problem
problem for SU‑MIMO transmission. Nevertheless, the is transformed to parallel BA problems, where is the

proposed beam alignment framework can be adjusted to number of sub‑bands. For the th sub‑band, we interpret
the multi‑user case in a straightforward manner due to its receive power as the measured reward , i.e.,

the sub‑band‑wise beam alignment setting. For the multi‑
0 ( )+ −1
user scenario, different users are assigned to different
2
= ∑ ‖r[ ]‖ , (31)
sub‑bands such that the sub‑band‑wise beam alignment 2
= 0 ( )
problem is reformulated to a multi‑user beam alignment
problem. This idea is similar to the frequency division
where r[ ] is the receive signal vector for the th sub‑
multiple access in conventional communication systems.
carrier. Consider the beam codes in the hiearchical DFT
The only change here is the determination of the number
codebook as the arms in an MAB framework. Due to the
of sub‑bands, which should be chosen based on both the
randomness of data and noise, the reward is a random

number of users and the number of transmit antennas.
variable. This indicates that our LOS BA problem can be
4.1.2 NLOS beam alignment classi ied as a stochastic MAB problem. Assuming a sta‑
tionary indoor scenario, we consider the channel as con‑
In the NLOS scenario, the receive signal consists of se- stant during the BA process. For simplicity, the reward
2
is modeled as Gaussian distributed with variance .
veral NLOS MPCs. To utilize the power of the NLOS
The average payoff function [ (w)] for a beam code w
com‑ ponents, the hierarchical k‑means codebook
described in Section 3 is implemented in this scenario. in the hierarchical DFT codebook is equivalent to the
Due to the high frequency selectivity of the considered average receive power (w),

THz NLOS channel, even the frequency response of
[ (w )] = (w ), (32)
two neighbor‑ ing subcarrier may be quite distinct.
Thus, the sub‑band beam alignment as used for the LOS
In the time slot , the transmitter selects a beam code
scenario is not con‑ sidered in the NLOS case. Instead,
w ( ) from the hierarchical DFT codebook W for the

speci ic beams need to be aligned to each subcarrier used th sub‑band. At the receiver, the power (w ( )) of the
in an SC‑FDMA system for a fully optimum performance.
th sub‑band is measured and fed back to the transmit‑
The BA problem for the t h subcarrier is equivalent to
∗ ter. At the end of time slot , the transmitter obtains the
inding the beam code w from the hierarchical k‑means measured rewards of all sub‑bands for this time slot and

codebook with maximal mean receive power for the t h
decides which arm to select for which sub‑band based on
subcarrier. Here, the mean receive power (w ) for pre‑ a speci ic rule for the next time slot + 1.

coding vector w and the t h subcarrier is given by For a stochastic MAB problem, the performance of the al‑

2

(w ) = w H [ ]H[ ]w + . (30) gorithm is evaluated via the expected cumulative regrets

over time slots. Here, the expected cumulative regrets
for the th sub‑band ( ) is de ined as the expected dif‑
Similar to the extension to multi‑user transmission in the
ference between the cumulative reward of the optimal
LOS case, the beam alignment framework for the NLOS
∗
arm w and the cumulative reward of the proposed algo‑
scenario can be adjusted to a multi‑user transmission as
rithm for th sub‑band, given by
well. In the case of multi‑user transmission, different
users are assigned to different subcarriers such that the

subcarrier‑wise beam alignment algorithm is modi ied to ( ) = ∑ ( (w ) − (w ( ))) . (33)
∗
a multi‑user beam alignment algorithm.
=1
4.1.3 HBA problem formulation The objective of the design of the MAB algorithm is to ind
a selection policy that minimizes the sum expected cumu‑
To accelerate the BA process in the large‑scale MIMO case, lative regret ( ) over all sub‑bands, i.e., ( ) =
we reformulate the BA problem to a stochastic MAB prob‑ ∑ ( ).

=1
lem for stationary environments. The transmission sys‑ The BA problem for the NLOS scenario is similar to that
tem is considered as a time slotted system with time for the LOS scenario. Here, the BA problem can be trans‑
slots to search for the optimal beam. At the begining of the formed to parallel BA problem. For the th subcarrier,
2
BA phase, the propagation scenario can be determined we interpret its receive power ‖r[ ]‖ as the measured re‑
2
at the transmitter side based on the feedback of the re‑ ward , and consider the beam codes in the hierarchical

ceive power pro ile. If the propagation environment is an k‑meanscodebookasthearmsinanMABframework. The
LOS scenario, the sub‑band BA discussed in the LOS beam reward is modeled as Gaussian distributed with variance
2
alignment is adopted for the following BA procedure. . The average payoff function [ (w )] for beam code

Otherwise, the subcarrier BA introduced in the NLOS w is equivalent to the average receive power (w ),

beam alignment is utilized.

2

2
If an LOS component can be received, all subcarriers [ (w )] = (w ) = w H [ ] H[ ] w + .

will be divided into sub‑bands and each sub‑band has (34)

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