Page 18 - 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

where ( , (ℎ , , ), (ℎ , , )) is the atmospheric where is the Boltzmann’s constant, is the mole-

medium’s transmittance. We employ Line‑By‑Line cular noise temperature obtained as ( , ℎ , , ) =

Radiative Transfer Model (LBLRTM) for obtaining ( , ℎ , , ). Here, is the reference temperature (in
0
0

realistic transmittance values across various atmospheric Kelvin), and is the channel’s emissivity, ( , ℎ , , ) = 1

altitudes [39, 40]. (ℎ , , ) and (ℎ , , ) are the − ( , (ℎ , , ), (ℎ , , )) [14]. Hence, is a

atmospheric temperature (in Kelvin) and water vapor function of transmittance, , which is obtained using
concentration (in %), respectively, for the link between LBLRTM. In the results provided in this paper, for cap‑
the Tx drone hovering at ℎ and Rx drone at ℎ . turing the absorption effect across the THz band

(0.75‑10 THz), US Standard 1976 weather pro ile is set
In regard to the impact of the mobility of the
in LBLRTM [12]. For computing the capacity of THz
communicating drones and the resulting Doppler spread,
drone‑to‑drone links under ideal, no fading channel, the
thanks to the very high operating frequency in the order

of THz, mobile drones observe minimized Doppler effect total channel gain is set as, = . In this paper, we
consider the standard narrowband capacity computation
[15], promising high rate links between communicating
in [14, 45]:
drones. It has been shown in [41, 42] that for a typical
drone relative velocity, = 10 m/s, the maximum 2

| ( ,ℎ , , )|
Doppler shift is negligible. As an example, by considering (ℎ , , ) = ∑ Δ [1 + ( ,ℎ , , ,(Δ )) ] , (8)

2
=1
= 0.75 THz, and = 10 m/s, the maximum Doppler

shift is: . = . / = 25017.31 Hz, which is negligible where total transmit power, , and total antenna gain

in terms of the inter‑carrier interference. Moreover, since (from Tx and Rx antennas), are set to practical values

we are con‑ sidering drone to drone communications, as = 24 dBm (0.25 W) [46] and = 60 dBi [47, 48],

where a swarm (group) of drones move together, can respectively. For power allocation, we consider both the

be less than 10 m/s (up to 0 m/s) and . will be even Water‑Filling (WF) and Equal‑Power (EP) schemes [14].
smaller than the example provided above. Therefore, we In WF allocation, the total transmit power, is optimally

neglect the effect of the Doppler spread in our capacity distributed across the THz band (0.75‑10 THz) compris‑
computations. ing of constant narrowbands, = 1, 2, 3, ..., , each
For beam misalignment fading, we consider the 0.3 GHz wide (i.e., LBLRTM’s spectral resolution), as:
following probability density function for the BM fading
coef icient, , [43]: 1 − 1 , ≥ s.t. ∑ ≤

2 2 = { ∘ ∘ =1 (9)
( ) = −1 , (5) 0 , < ,
2 ∘
0
where = , is the equivalent Tx beam width, where is the optimal power for the constant nar‑
2
denotes the jitter (BM) standard deviation, and is rowband, , is the threshold SNR, is the SNR of . ∘

∘

0

1
1
the fraction of power collected at Rx at no beam misalign‑ is obtained by ∑ =1 ( ∘ − ) = 1 [49].
ment. This BM fading model has been widely employed in In EP allocation, is distributed equally within all

many studies of free space optical systems. For more de‑ across the entire THz band (0.75‑10 THz) [12].
tails of the BM fading model, we refer to our earlier work
[12] and also [43]. For the channel under fading, involvingBM and MP fading,
Finally, for incorporating multipath fading, we consider the channel gain is set as = , and we evaluate

the famous ‑ model as follows [44]: the ergodic capacity by averaging results over 100 real‑
izations, as follows:

( ) = −1 (− ) , (6) | ( ,ℎ , , )|
2
̂
̂ (ℎ , , ) = Δ (∑ [1 + ]) ,
2

Γ( ) =1 ( ,ℎ , , ,(Δ ))
where ( ) is the pdf of the MP fading coef icient, , (10)

is the fading parameter, is the normalized variance of where (. ) denotes the expectation taking over channel
realizations under fading.
the channel envelope under fading, and ̂ is the ‑ root

mean value. The ‑ model is a common model of Next, we present the capacity and ergodic capacity results
several famous fading distributions. For instance, = 2 speci ically for drone scenarios, considering various prac‑
tical settings of Tx and Rx drone altitudes, zenith angles
and = 1 represents Rayleigh fading, etc.
and transmission ranges. Fig. 4(a)‑(c) depict the chan‑
For computing noise power, , we consider a constant nel capacity as the function of transmission range under

narrowband approach [14] across the THz band ideal, i.e., under no fading channel. The capacity results
(0.75‑10 THz), where each narrowband, Δ is 0.3 GHz with no fading (ideal) channel are included in our analy‑
wide, which is the spectral resolution of LBLRTM. sis as the benchmark to compare how much of the capa-
Numerically, city is degraded when realistic beam misalignment fading
( , ℎ , , , Δ ) = ∫ ( , ℎ , , ) , (7) and multipath fading are introduced into the channel, as

Δ provided in the subsequent discussion. Three drone Tx
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