Page 76 - 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

a large codebook. First, the receiver beam is set to a means clustering for the NLOS THz scenario.
quasi‑omnidirectional beam and the transmitter scans This paper is organized as follows. The system model,
the beam codebook exhaustively for the best transmit channel model and beamforming framework are de‑
beam. Then, the receiver searches for the best beam with scribed in Section 2. In Section 3, the codebook design
quasi‑omnidirectional transmit beam. To further acceler‑ problems in both LOS and NLOS THz propagation are for‑
ate the BA process, we replace the BA step at the receiver mulated. The hierarchical DFT codebook is proven to be
by the frequency‑domain Minimum Mean‑Squared Error a local optimum for the LOS codebook problem and is se‑
(MMSE) equalizer design according to [10] exploiting the lected as the codebook for LOS HBA. A data‑driven code‑
high SNR at the receiver after the transmit BA for chan‑ book design algorithm based on hierarchical k‑means
nel estimation in [11]. Still, the exhaustive search at Tx clustering is proposed for the NLOS HBA. The HBA algo‑
may take up to several seconds with a massive transmit rithm for the SC‑FDMA system operating in both LOS and
antenna array. NLOS scenarios is discussed in Section 4. Numerical re‑
To reduce the duration of the BA process at the Tx, sults are provided in Section 5, followed by conclusions
Multi‑Armed Bandit (MAB) theory has been advocated in Section 6.
in many search strategies for the mmWave BA problem Notation: Bold lowercase letters (e.g., a) and uppercase
[12]. MAB focuses on choosing the best arm with max‑ letters (e.g., A) represent column vectors and matrices,
imal expected gain among multiple actions when each respectively. , represents the ( , )‑th entry of A.
choice’s gain is known after each selection. Based on and a stand for the th entry of a and the th column of

∗

the MAB‑BA problem framework, many variants of MAB A, respectively. (⋅) , (⋅) , (⋅) denote the transpose, con‑

solutions have been adapted to the mmWave commu‑ jugate and Hermitian transpose of a vector or matrix, re‑
nication system. In [13], the authors proposed a cele‑ spectively. All complex‑valued gradients follow the de i‑
brated upper con idence bound beam selection scheme nition according to [18].
in traditional MIMO systems. In [14], the authors in‑
troduced a beam alignment algorithm employing contex‑ 2. SYSTEM MODEL
tual information based on a structured MAB framework.
The algorithm in [15] utilizes latent probability struc‑ 2.1 System model
ture information from the varying transmission environ‑ The block diagram of the SU MIMO SC‑FDMA transmis‑
ments and promises better performance in fast varying sion is shown in Fig. 1.
mmWave channels. Another work proposed a distributed
[m bB@QKMB/B`2+iBQM H #2 K M/ i?2 i` MbKBii2` b+ Mb
BA search method based on adversarial bandit theory, 1 ( ! [#] ) ! [*] N-IDFT + ! [,] CP + !,$ [,]
i?2 #2 K +Q/2#QQF 2t? mbiBp2Hv 7Q` i?2 #2bi i` MbKBi
where Tx and Rx choose their beamforming and combin‑ &['] M-DFT ([#] forming: ⋮ Subcarrier ⋮ ⋮ insertion ⋮
Beam-
ing vector independently of each other [16]. Neverthe‑ ;QQ/ ![#] 1 ( " ! [#] Mapping % ) " ! [*] N-IDFT + " ! [,] CP + " ! ,$ [,]
#2 KX 7i2` i?2 i` MbKBi #2 K Bb /2i2`KBM2/-
aL_ Bb ;m ` Mi22/ i i?2 `2+2Bp2` bB/2X h?mb- i?2
less, these works do not provide a method with a short `2@ insertion
+2Bp2` + M Q#i BM i?2 *aA #v TTHvBM; +? MM2H 2biBK @
training time and accurate beam alignment, especially in Channel
iBQM i2+?MB[m2b ++Q`/BM; iQ (Ry)X KBMBKmK K2 M@
multipath channels. Hence, the authors in [9] proposed a - ! [,]
b[m `2/ 2``Q` UJJa1V bQHmiBQM i _t ++Q`/BM; iQ (RR)
Hierarchical Beam Alignment (HBA) algorithm based on Frequency Demapping . ! [*] N-DFT removal +
CP
+ M #2 /QTi2/ ?2`2X aiBHH- i?2 2t? mbiBp2 b2 `+? i ht
% %
a stochastic MAB scheme, leveraging the inherent corre‑ Detector 0 &['] M-IDFT Domain ⋮ ⋮ - " " [,] ⋮
K v i F2 mT iQ b2p2` H b2+QM/b rBi? K bbBp2 i` MbKBi
Equalizer
CP
Mi2MM `` vX
lation structure among beams. HBA can identify the opti‑ (FDE) /[*] Demapping . " " [*] N-DFT removal +
% %
mal beam accurately with a short exploration time, which ht-
hQ `2/m+2 i?2 /m` iBQM Q7 i?2 " T`Q+2bb i i?2
KmHiB@ `K2/ # M/Bi UJ "V i?2Q`v ? b #22M /pQ+ i2/
ful ills the fast BA requirement in narrowband MIMO LOS 6B;X R Ĝ ai`m+im`2 Q7 al@JAJP a*@6.J i` MbKBbbBQM bvbi2KX
Fig. 1 – Structure of SU‑MIMO SC‑FDMA transmission system.
mmWave communications. However, no speci ic algo‑ (Rk)X ?B2` `+?B+ H +Q/2#QQF miBHBxBM; ?B2` `+?B+ H F@K2 Mb
BM K Mv b2 `+? bi` i2;B2b 7Q` KKq p2 " T`Q#H2K
J " 7Q+mb2b QM +?QQbBM; i?2 #2bi `K rBi? K tBK H
rithm is proposed yet for broadband MIMO THz commu‑ 2t@ Here, the base station and the user
+Hmbi2`BM; 7Q` LGPa h>x b+2M `BQXterminal are equipped
T2+i2/ ; BM KQM; KmHiBTH2 +iBQMb r?2M 2 +? +?QB+2Ƕb
nications. Moreover, if the LOS component of propagation with and antennas, respectively, where is
h?Bb T T2` Bb Q`; MBx2/ b 7QHHQrbX h?2 bvbi2K KQ/2H- set to
; BM Bb FMQrM 7i2` 2 +? b2H2+iBQMX " b2/ QM i?2 J "@

is blocked, the communications quality cannot be guaran‑ be a power of two, e.g., = 4, 8, or 16 .Let [ ],
+? MM2H KQ/2H M/ #2 K7Q`KBM; 7` K2rQ`F `2 /2@ ∈
" T`Q#H2K 7` K2rQ`F- K Mv p `B Mib Q7 J " bQHm@

teed by the aforementioned algorithms. {0, 1, ⋯ , − 1} be the transmit data sequence with
b+`B#2/ BM a2+iBQM kX AM a2+iBQM j- i?2 +Q/2#QQF /2bB;M vari‑
iBQMb ? p2 #22M / Ti2/ iQ i?2 KKq p2 +QKKmMB+ @
T`Q#H2Kb BM #Qi? GPa M/ LGPa h>x T`QT ; iBQM `2
In this paper, we consider the design of HBA algorithm ance corresponding to the symbol vector a for trans‑
2
iBQM bvbi2KX AM (Rj)- i?2 mi?Q`b T`QTQb2/ +2H2#` i2/

7Q`KmH i2/X h?2 ?B2` `+?B+ H .6h +Q/2#QQF Bb T`Qp2M
mTT2` +QM}/2M+2 #QmM/ #2 K b2H2+iBQM b+?2K2 BM i` @
based on [9]. Given a hierarchical codebook, HBA se‑ mission in the SC‑FDMA system. For simplicity, only a sin‑
iQ #2 HQ+ H QTiBKmK 7Q` i?2 GPa +Q/2#QQF T`Q#H2K
AM (R9)- i?2 mi?Q`b
lectsthebeamstomaximizethecumulativereceivepower BMi`Q@ gle block is considered in the following. An ‑point DFT
/BiBQM H JAJP bvbi2KbX
M/ Bb b2H2+i2/ b i?2 +Q/2#QQF 7Q` GPa >" X / i @
/m+2/ #2 K HB;MK2Mi H;Q`Bi?K 2KTHQvBM; +QM
within a certain period in a hierarchical manner utiliz‑i2t@ precoding is applied to symbol block a to transform a to
/`Bp2M +Q/2#QQF /2bB;M H;Q`Bi?K # b2/ QM ?B2` `+?B+ H

im H BM7Q`K iBQM # b2/ QM bi`m+im`2/ J " 7` K2@
ing the hierarchical structure of the codebook. Both the‑ an ×1 vector A = W a in the frequency domain with
F@K2 Mb +Hmbi2`BM; Bb T`QTQb2/ 7Q` i?2 LGPa >" X h?2

rQ`FX h?2 H;Q`Bi?K BM (R8) miBHBx2b H i2Mi T`Q# #BH@

oretical analysis and extensive simulation results demon‑ A = [ [0], [1], ⋯ , [ −1]] . Afterwards, an ×1 dig‑
>" H;Q`Bi?K 7Q` i?2 a*@6.J bvbi2K QT2` iBM; BM
Biv bi`m+im`2 BM7Q`K iBQM 7`QK i?2 p `vBM; i` MbKBbbBQM

#Qi? GPa M/ LGPa b+2M `BQ Bb /Bb+mbb2/ BM a2+iBQM 9X
stratethatHBAcandeterminetheoptimalbeamwithhigh ital precoding vector w[ ] is employed for each frequency
2MpB`QMK2Mi M/ T`QKBb2b #2ii2` T2`7Q`K M+2 BM 7 bi
probability and short latency. Moreover, the hierarchi‑ domain symbol [ ], 0 ≤ ≤ − 1 to form vectors
LmK2`B+ H `2bmHib `2 T`QpB/2/ BM a2+iBQM 8- 7QHHQr2/ #v of
p `vBM; KKq p2 +? MM2HbX MQi?2` rQ`F T`QTQb2/
+QM+HmbBQMb BM a2+iBQM eX
cal codebook design for indoor THz propagation is still size × 1 via
/Bbi`B#mi2/ " b2 `+? K2i?Q/ # b2/ QM /p2`b `B H # M@

/Bi i?2Q`v- r?2`2 ht M/ _t +?QQb2 i?2B` #2 K7Q`KBM;
an open problem. We adopt the hierarchical DFT code‑ LQi iBQM, "QH/ HQr2`+ b2 H2ii2`b U2X;X- V M/ mTT2`+ b2 (1)
̂
A[ ] = w[ ] [ ]
book proposed in [9] to the LOS THz scenario. Further‑ Qi?2` H2ii2`b U2X;X- V `2T`2b2Mi +QHmKM p2+iQ`b M/ K i`B+2b-
M/ +QK#BMBM; p2+iQ` BM/2T2M/2MiHv 7`QK 2 +?
̂
̂
̂
̂
(Re)X L2p2`i?2H2bb- i?2b2 rQ`Fb /Q MQi T`QpB/2 K2i?Q/
more, we propose a data‑driven method according to [17] as shown in Fig. քӴօ 1. Let A = [ [0], [1], ⋯ , [ − 1]]
`2T`2b2Mib i?2 Ԙ ԙ @i? 2Mi`v Q7 X Ԑ
`2bT2+iBp2HvX Ӷ

ֆ

M/ bi M/ 7Q` i?2 Ԛi? 2Mi`v Q7 M/ i?2 Ԛi? +QHmKM
rBi? b?Q`i i` BMBM; iBK2 M/ ++m` i2 #2 K HB;MK2Mi-
to design a hierarchical codebook utilizing hierarchical k‑ denote ֆ the ×1 pre‑coded frequency domain vector cor‑
2bT2+B HHv BM KmHiBT i? +? MM2HbX >2M+2- i?2 mi?Q`b Q7 - `2bT2+iBp2HvX ੁ - ੁ - ੁ թ /2MQi2 i?2 i` MbTQb2-
յ
੟
BM (Rd) T`QTQb2/ ?B2` `+?B+ H #2 K HB;MK2Mi U>" V +QMDm; i2 M/ >2`KBiB M i` MbTQb2 Q7 p2+iQ` Q` K @
H;Q`Bi?K # b2/ QM biQ+? biB+ J " b+?2K2- H2p2` ;@ i`Bt- `2bT2+iBp2HvX ધ ધ Bb i?2 ԁ @MQ`K Q7 i?2 p2+iQ` X
֋
֋
BM; i?2 BM?2`2Mi +Q``2H iBQM bi`m+im`2 KQM; #2 KbX HH +QKTH2t@p Hm2/ ;` /B2Mib 7QHHQr i?2 /2}MBiBQM +@
64 >" + M B/2MiB7v i?2 QTiBK H #2 K ++m` i2Hv rBi? +Q`/BM; iQ (RN)X
© International Telecommunication Union, 2021
b?Q`i 2tTHQ` iBQM iBK2- r?B+? 7mH}HHb i?2 7 bi " `2[mB`2@
K2Mi BM M ``Qr # M/ JAJP GPa KKq p2 +QKKmMB@ kX auah1J JP.1G
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7Q`2K2MiBQM H;Q`Bi?KbX KBbbBQM Bb b?QrM BM 6B;X RX >2`2- i?2 # b2 bi iBQM M/
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֍
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֏
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ϵ
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BKBx2 i?2 +mKmH iBp2 `2+2Bp2 TQr2` rBi?BM +2`i BM T2@ 7Q` i` MbKBbbBQM BM i?2 a*@6.J bvbi2KX 6Q` bBKTHB+@
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b?Q`i H i2M+vX JQ`2Qp2`- i?2 ?B2` `+?B+ H +Q/2#QQF /2@ 7i2`r `/b- M ԃ ੎ /B;Bi H T`2+Q/BM; p2+iQ` r<ᅷ> Bb
֏
bB;M 7Q` BM/QQ` h>x T`QT ; iBQM Bb biBHH M QT2M T`Q#H2KX 2KTHQv2/ 7Q` 2 +? 7`2[m2M+v /QK BM bvK#QH Ӷ<ᅷ> ମ
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֏
(Rd) iQ i?2 GPa h>x b+2M `BQX 6m`i?2`KQ`2- r2 T`Q@
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