Page 36 - 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

non-ideal communication symbols in the time domain, A compromise between these two extremes allows for
which have experienced a nonlinear phase shift due to high bit rates with higher dispersion tolerance when
GVD in the atmosphere, resulting in ISI in the time bandwidth and modulation order are properly balanced.
domain. At this point, AWGN is added to the distorted Note that the remaining combinations of bandwidth and
symbol sequence, which is then demodulated and modulation order fare quite poorly: a high bandwidth link
compared to the original symbol vector to determine the with high order modulation can have a very high capa‑
number of errors. This procedure is repeated until city but suffers severe ISI due to simultaneously high
enough iterations have run to ensure the errors gene‑ dispersion and tight decision boundaries, while a low
rated are true to the stochastic distribution of the noise. band‑width link with low modulation order has greatly
Averaging the error rates observed on each iteration gives reduced data capacity, defeating the purpose of terahertz
the error rate of the link for that particular combination of commu‑ nications. An example of the simulation results
distance, bandwidth, modulation type, and atmospheric that led us to these conclusions is illustrated in Fig. 2,
properties. which shows the bit‑error rate of a 60 Gb/s M‑QAM
communication link for ive different modulation orders
This simulation process has the advantage of abstracting over 0 to 20 km.
away much of the hardware, focusing on the mathemati‑
cal, fundamental interactions between the data‑carrying It is important to note that atmospheric dispersion is a
symbols and the atmospheric channel. Notably, it also cumulative phenomenon, meaning the greater distance a
defines parameters such as received SNR directly prior to signal propagates, the more dispersion accumulates and
demodulation, so that the results are applicable to a affects that signal. It is also important to note that no
broad range of physical systems. For a much more noise is added to the signal in Fig. 2, which allows us to
in‑depth description of the simulation process using a con idently state that any change in error rates observed
slightly different mathematical convention, readers are are due to GVD increasing with distance, and the that
referred to our previous work [26], which is currently differences between the various curves are due to
under consideration for publication at the time of this changes in modulation order (which affects both
writing. bandwidth and symbol spacing on the constellation
diagram). Even in the absence of noise, increasing
dispersion over distance will eventually cause some
3. RESULTS AND DISCUSSION communication symbols to be misinterpreted by the
receiver for all modulation types, resulting in a bit error
A principal result taken from our simulations is that GVD
rate that rises rapidly from insigni icance to some inite
can produce increasing SER in two opposing cases: when
value, often by several orders of magnitude in only a
low bandwidth and high order modulation is employed kilometer or two.
and when high bandwidth and low order modulation
is employed. Moreover, there exists an optimum trade‑ The point at which the error rate jumps from insigni i‑
off between modulation order and bandwidth that mini‑ cance to a inite value is the uncompensated “dispersion
mizes SER due to GVD for a particular desired data rate. In limit” of that link, marked by vertical dashed lines in Fig. 2.
order to clarify this point, we have chosen to conduct our Beyond this limit, the error rate of the link cannot be con‑
simulations such that data rate is held constant, whereas tinuously improved by increasing the SNR, because dis‑
bandwidth and modulation order are variable. Further persion is the dominant source of errors [26]. For the 60
justi ication for this approach is offered later in the discus‑ Gb/s link shown in Fig. 2, BPSK has the lowest dispersion
sion. To elaborate on our results, the following relation‑ limit, meaning it is most severely affected by atmospheric
ships between modulation order and GVD were found: temporal dispersion. 4‑QAM, or QPSK, is next, followed
by 256‑QAM, 16‑QAM, and inally 64‑QAM. In other words,
For a high bandwidth link with low modulation order, the dispersion limit increases with modulation order for
achievable data rate is high, but the link suffers a high most of the modulation orders simulated, meaning there
number of symbol errors because of the large frequency‑ is more robust operation as the bandwidth decreases.
dependent change in refractive index across the band‑
width (high GVD) causes severe ISI, large enough to The results and discussion presented so far may seem
push received symbols across the broadly‑spaced deci‑ obvious and well‑established. It is well‑known that de‑
sion boundaries used in low‑order modulation types. creasing the bandwidth of a wireless link operating in a
frequency‑selective environment will increase the perfor‑
For a low bandwidth link with high order modulation, the mance of the link by ” lattening” the fading pro ile of the
achievable data rate is equally high, but the link still channel, thereby reducing errors, ISI, and the comple-
suffers a high number of symbol errors due to xity of signal processing. The atmosphere is a frequency‑
dispersion. This time, the errors are not because of a selective channel over the huge bandwidths available to
large frequency dependency in the narrow channel, but terahertz communication links, so it may not initially
because decision boundaries are so tightly spaced on the seem surprising that as we decrease the bandwidth we
constellation diagram that even the small amount of GVD also observe an improvement in error rate. However,
exhibited by the channel is enough to push received closer inspection of the data reveal additional and
symbol values across them, again causing ISI. unexpected behaviors that are not readily explained

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