Page 86 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 7 – Terahertz communications
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ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 7
Attribute update Table 1 – SC‑FDMA system setting
In this step, the attributes of all nodes in the search tree Parameter Numerical Value
T +1 are updated based on the feedback of the measured DFT size 1200
reward in the current time slot. For LOS BA, is the DFT size 2048
measured receive power of one sub‑band, while is the Cyclic pre ix length 512
measured receive power of one subcarrier in the NLOS Transmission band 0.1 − 0.1281 THz
case. The details of the attribute update are shown in Al‑ Number of transmit antennas 64
gorithm 2 from line 12 to line 22. The update of ‑values Number of receive antennas 2
consists of the following steps.
At irst, the number of times ℎ, ( ) that node (ℎ, ) has Antenna gain , , = 20 dBi
been visited until time slot is updated as Signal constellation 4QAM
narrow its searching coverage in the highest layer. The
ℎ, ( ) = ℎ, ( − 1) + 1, ∀(ℎ, ) ∈ . (37) algorithm will be terminated, if no new node has been se‑
lected and the selection result no longer changes, i.e.,
Node (ℎ, ) must have been visited one time when it is
selected as the new node for the search tree. (ℎ, ) will T +1 = T . (41)
be visited one more time when one of its descendants is
added to the search tree T . The average measured re‑ Then, the currently selected beam w( ,
ward ℎ, of (ℎ, ) is updated by ) is the de‑
rived beam for the correponding sub‑band and subcarrier
( ℎ, ( ) − 1) ℎ, ( − 1) + in LOS and NLOS cases, respectively. According to [9], the
ℎ, ( ) = ( ) , ∀(ℎ, ) ∈ . computational complexity of the HBA is quadratic in the
2
ℎ,
(38) number of processed time slots, ( ).
The empirical average reward ℎ, ( ) of node (ℎ, ) in
time slot is de ined as 4.3 Complexity analysis
2
ℎ
( ) + √ 2 log + , if ( ) > 0 At time slot , for one subcarrier or sub‑band, the deci‑
ℎ, ( ) = { ℎ, ℎ, ( ) 1 ℎ, sion tree contains nodes as the tree is extended by one
+∞, otherwise node in each time slot. The attributes of all nodes in a de‑
(39) cision tree should be updated in each time slot, and hence
2
where√ 2 log representsthecon idencemarginrelated the run time in time slot is linear in , i.e., ( ). As
ℎ, ( )
the algorithm is executed for time slots, the total com‑
to the uncertainty of rewards, related to random data
and noise. With increasing ℎ, ( ), the uncertainty of putational complexity of the proposed HBA algorithm is
2
the reward of (ℎ, ) becomes lower, since there are more quadratic in , i.e., ( ) [9].
available observations. The idence margin is
5. NUMERICAL RESULTS
designed based on Bayesian principle and derived in
[26]. Here, 0 < < 1 and > 0 are parameters of the
1
ℎ In the following, we investigate a THz SC‑FDMA system,
algorithm, and speci ies the maximum variation of whose parameter settings are provided in Table 1.
1
the average reward function within beam coverage
The transmission scenario is the indoor scenario consi-
(w(ℎ, )) [26], which depend on the codebook structure.
dered in [6]. The transmitter is ixed at the center of the
The datails re‑ garding and selection can be found in
room ceiling and the location of the receiver with ixed
[26] and [9]. If and is chosen based on the bounded
diameter prin‑ ciple and well‑shaped region principle height ℎ = 1.5 m is uniformly distributed within the in‑
door environment. The results are averaged over 500
from [9], HBA will converge to the optimal beam code
channel realizations. The proposed algorithm is com‑
with high probability. In the initial phase of the HBA, no pared to the following benchmarks:
information regarding the rewards is available. Hence,
Optimal SC‑FDMA beamforming: In this beamforming
ℎ, ( ) is initialized by in inity. With abundant observed
rewards within (ℎ, ) available, we can tighten the scheme, the CSI is considered as known at both the re‑
upperbound of mean rewards step by step. ceiver and the transmitter. Thus, an MMSE frequency do‑
main equalizer according to [10] can be designed. This
Finally, the estimated maximum mean reward (ℎ, ) in
algorithm aims to minimize the MSE after equalization,
beam coverage (ℎ, ) is determined as [26]
which can be formulated as a convex optimization prob‑
⎧ min{ ℎ, ( ), lem. The optimal solution is derived in [10], and its per‑
{ max { ( ), ( )}}, formance can be regarded as a performance upper bound
ℎ+1,2 −1
ℎ, ( ) = ⎨ if ( ) > 0 ℎ+1,2 (40) for our proposed scheme.
{ ℎ,
⎩ +∞, otherwise Random beamforming: In random beamforming, the
beamforming vector for each subcarrier or sub‑band is a
When the HBA algorithm has obtained a suf icient num‑ random complex vector with constant ‑norm and ran‑
2
ber of observed rewards within the searching tree, it will dom phase pro ile. An MMSE equalizer is employed at the
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