Page 78 - 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

which can be expressed as antenna arrays. Thus, selecting the beam code from a pre‑
ined codebook is frequently considered in THz com‑

a( , ) = [1, ⋯ , 2 sin , ⋯ , 2 ( −1) sin ] , munications.

(5) For a LOS scenario in THz band, the channel is dominated
where is the antenna element index with 0 ≤ ≤ by the LOS component assuming its power is signi icantly
− 1. denotes the number of antennas, is the an‑ larger than that of the other MPCs [8], [6]. In such a

tenna spacing and is the speed of light. In an indoor case, the beamforming problem is ied to inding
2
THz channel, the LOS path gain | ( , )| depends the AoD of the LOS component, and setting the beamfor-

on the spreading loss ( , ) and absorption loss ming vector as the steering vector pointing to the AoD of

( , ), the LOS component. Thus, the codebook is composed

only of steering vectors. In addition, in the LOS
2
| ( , )| = ( , ) ( , ), scenario, the coherence bandwidth is relatively larger

2
due to the dominance of the LOS component, i.e., the LOS
( , ) = ( ) , (6)

2 channel exhibits a latter frequency response than that

( , ) = − ( ) . of the NLOS channel. Thus, neighboring subcarriers can

employ the same beamforming vector.
In (6), stands for the distance between transmit‑ However, in an indoor THz scenario, the LOS propagation
ter and receiver, and ( , ) denotes the frequency‑ might be blocked by the presence of obstacles like mo-

dependent medium absorption coef icient. The NLOS ving persons, furniture, or many diverse objects [6]. In that
components depend additionally on the re lection coef‑ case, the codebook cannot be designed as the composition
icient of the correponding surface. The squared magni‑ of steering vectors anymore but has to be speci ically tai‑
tude of the th NLOS coef icient assuming irst‑order re‑ lored to the NLOS scenario. Also, the NLOS channel may
lection of the re lecting surface is given by be frequency‑selective due to the absence of the LOS
component. Therefore, each subcarrier should be
2
assigned a carefully designed code word.
2
2
| ( , )| = Γ ( , ) ( 2 ( ,1 + ) ) (7) According to the aforementioned difference between the

,2
× − ( ( ,1 + ,2 )) , LOS beamforming and the NLOS beamforming, a pre‑
judgement regarding the propagation scenario has to be
where Γ ( , ) is the product of the Fresnel re lection conducted before beamforming. Since the LOS compo‑

coef icient and the scattering coef icient and can be calcu‑ nent power is nearly 20 dB larger than that of the NLOS
lated as given in [6]. Due to the high re lection loss in the components in the considered typical indoor scenario, the
THz band, the restriction to irst‑order re lection MPCs is channel can be ied by the receive power. For a
justi ied. training block, if the measured receive power is higher
In [22], the authors advocated the extension of a statisti‑ than a threshold , the channel will be ied to a
ℎ
cal channel model to the THz case in order to character‑ LOS channel, and the LOS beamforming procedure will be
ize the re lection behavior of the furniture. As discussed performed in the BA phase. Otherwise, the channel will be
in [8], [24] and [22], modeling the re lection components considered as a NLOS channel and the procedure for the
due to furniture by the ray‑tracing technique is not feasi‑ NLOS beamforming will take place in the following BA
ble due to an extremely high computational load. Thus, phase. The power threshold ℎ depends on the geome‑
we adopt the hybrid channel modeling idea in [22] that try of the propagation scenario, the humidity of the atmo‑
the LOS component and the re lection components due sphere and the material of the lecting objects. Thus, the
to the walls and ceiling are generated by the ray‑tracing power threshold must be designed based on the given
technique and the re lection components due to the fur‑ propagation scenario and no general rule regarding its se‑
niture are generated via the Saleh‑Valenzuela (S‑V) chan‑ lection can be introduced. The adopted power threshold
nel model. We adopt the parameters’ setting of the S‑V choice will be discussed in detail in Section 3. After the
channel model in [22]. The details of this hybrid channel channel assessment, the beamforming vectors for each
modeling can be found in [22]. subcarrier are determined by the corresponding BA
procedure, which will be discussed in detail in Section 4.
2.3 Beamforming framework
3. CODEBOOK DESIGN
From a system level, the beamforming at the transmit‑
ter is required to maximize the sum receive power over In this section, we discuss the hierarchical beam code‑
the transmission band. If H[ ] for all = 1, 2, ⋯ , is book used in hierarchical beam alignment. Hierarchical
known at the transmitter, the optimal beamforming vec‑ codebooks have been already studied in [25]. The hie-
tor can be computed using the approach provided in [10]. rarchical codebook is also the core of the hierarchical
However, in THz communications it is not practical to per‑ beam alignment, which helps to improve the ef iciency in
form an entry‑wise estimation of the channel matrix at searching for the best beam code. In this section, we irst
the transmitter, which has a large scale due to the large introduce the inition of the hierarchical codebooks,
66 © International Telecommunication Union, 2021