Page 35 - 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

Fig. 1 – Bit error rate versus SNR “waterfall” plots for an M‑QAM communication system, with M = 2, 4, 16, 64, and 256. Higher‑order modulations
have closer symbol spacing under equivalent power requirements, resulting in a higher SNR required for equivalent error performance to a lower order
modulation, assuming the absence of group velocity dispersion.

2. METHODOLOGY gether these terms determine the complex index of refrac‑
tion of the atmosphere. This complex index is obtained by
In order to quantitatively measure the impact of ISI
a combination of Molecular Response Theory (MRT) [23]
caused by atmospheric GVD, bit error rate simulations and continuum effects [24, 25], in which the broadened
were performed using a channel model founded upon an absorption lines of all the H O and O molecular reso‑
2
2
accurate understanding of atmospheric molecular reso‑ nances from 0 to 5 THz are found by MRT , summed, then
nances. It is from this atmospheric model that all the added to the continuum absorption. This has been shown
effects accounted for in this work were derived. Speci i‑ to accurately model atmospheric behavior over the sub‑
cally, the channel considered in this study was a Linear terahertz bands, and accounts for the contribution of all
Time‑Invariant (LTI) channel with Additive White Gaus‑ relevant molecular resonances up to 5 THz.
sian Noise (AWGN) and no obstruction, multipath pro-
pagation, or Doppler effects. However, the transfer In addition to the atmospheric effects, pulse shaping il‑
function of the atmosphere itself was modeled as variable ters also shape the transmitted waveform, limit the band‑
over frequency in both absorption and refractive index, width of the signal, and reduce ISI. In our simulations,
which gives rise to the behavior observed in our results. a raised cosine ilter ( ) with a roll‑off factor of 1 was

Even though our assumption of an L TI AWGN channel is used, and incorporated into the channel model by
much simpler than the environments usually applying it directly to the atmospheric transfer function
encountered by wireless link designers at terahertz in frequency domain, yielding a channel transfer function
frequencies, the fact that our results arise from the ( ) = ( ) × ( ). The impulse response of the

properties of the atmosphere rather than complex and complex channel transfer function can then be derived as
−1
ic channel effects make them applicable ℎ ( ) = ℱ [ ( )], where ℱ −1 indicates the inverse

to a wide range of channels, including those signi icantly Fourier transform.
more complex that that presented here [22].
Once the impulse response of the channel is known, a
The atmospheric transfer function is described most data vector containing complex valued communication
generally as ( ) = ( ) exp[− ( )], where ( ) symbols is generated. The symbols in the data stream

and ( ) are the frequency‑dependent attenuation and occur with equal distribution, but the data stream is not
phase shift imparted by the atmosphere, respectively, completely random. Rather, it is generated such that
√
and = −1. This non‑unity transfer function arises combinations of symbols are also equally distributed, so
from the interaction of various atmospheric gas species every possible permutation of symbols occurs an equal
with terahertz‑frequency radiation. Most notable among number of times for a speci ied . This is necessary
these are water vapor and diatomic oxygen, which exhibit because the severity of ISI experienced by a
strong rotational and vibrational resonances within and communication symbol depends on the value and order
above the terahertz bands. While the amplitude (absorp‑ of the neighboring symbols, not on the value of the
tion) term of ( ) is most often discussed, the phase symbol itself. This data stream is convolved with the

term ( ) is equally important to propagation, and to‑ channel impulse response, resulting in a sequence of

© International Telecommunication Union, 2021 23