In this section, the performance evaluation of the proposed channel model for the nanocommunications in GWiNoC in THz band is carried out through numerical results and compared against the conventional channel model. In the conventional channel model, only pure air with no MAA (e.g., two-ray channel model in [32]) is considered. In our model (see Figure 1), the medium consists of water vapour and various gas compositions, like carbon dioxide, oxygen, nitrogen, and so forth, parameters of which are obtained from the HITRAN database [30]. Additionally, the power for subbands is allocated as in Proposition 5. The impacts of the transmission medium and various channel environment parameters on the performance of GWiNoC in terms of path loss and channel capacity are evaluated to realise the effectiveness of the proposed channel model over the conventional approach. (In the conventional channel model, only DPL is taken into account, and thus it can be regarded as a special case of our channel model where we consider both the DPL and MAA.)
Let us first investigate the impacts of transmission frequency of GNAs on the channel modeling for GWiNoC. Figures 2 and 3 sequentially plot the total path loss and channel capacity of two considered channel models versus the transmission frequency at
. Two cores and are located within the chip package having the longest side (i.e., ) of 20 mm and the height (i.e., ) of 1 mm. In Figure 2, the distance between and (i.e., ) is set as mm. Each core deploys a GNA having a height of 0.02 mm (i.e., mm). The transmission frequency of the GNA (i.e., ) is assumed to vary in the range from 1 to 3 THz. The system electronic noise temperature (i.e., ) is 296 K and the ambient pressure applied on the chip (i.e.,
) is 1 atm. It can be observed in Figure 2 that the proposed channel model results in a higher total path loss compared to the conventional channel model and a longer distance between the cores causes a considerably increased path loss. Also, the total path loss is not shown to monotonically increase at the THz frequency band due to the fact that the MAA is caused by isotopologues of gases having various absorption coefficients at various frequencies. For example, the MAA causes a considerably higher path loss at 1.21 THz, 1.28 THz, 1.45 THz, and so forth. In fact, such increased path loss is caused by the molecular absorption of isotopologues of various gases since they have different absorption coefficients at different frequencies (detailed molecular spectroscopic data of different molecules can be referred to in [30]).
Figure 2: Total path loss versus frequency.
Figure 3: Channel capacity versus transmission frequency.
Although the total path loss in our proposed model is not much higher than that in the conventional model, it has a significant impact on the channel capacity at the THz band. This indeed can be seen in Figure 3 where the channel capacity achieved in the proposed model is much lower than that of the conventional model. Specifically, at least
bits/s (i.e., 500 Megabits/s) are lost due to the MAA throughout the frequency range from 1 THz to 2 THz. These observations confirm the statements in Remarks 2 and 3 regarding the effectiveness of the proposed channel model with environment-aware property. The proposed channel model can be therefore used to represent the practical scenario of GWiNoC implementation at the THz band where some frequencies (e.g., 1.21 THz, 1.28 THz, and 1.45 THz) causing a significant capacity loss should be avoided in the GNA design.
The impacts of operating temperature of the chip on the channel modeling of the GWiNoC are shown in Figures 4 and 5, where the total path loss and channel capacity of the proposed and the conventional channel models are plotted against the system electronic noise temperature (i.e.,
) with respect to different values of frequency band (i.e., THz, THz, and THz). The size of the chip package, the distance between and
, the height of the GNAs, and the ambient pressure are similarly set as those in Figures 2and 3. It can be observed that the system temperature does not have any effects in the path loss of the conventional channel model, while the total path loss in the proposed channel model is shown to decrease as the temperature increases at all frequency bands. This observation accordingly verifies the statement in Remark 3 on the monotonically decreasing total path loss over the system temperature due to the MAA.
Figure 4: Total path loss versus system electronic noise temperature at different frequencies.
Figure 5: Channel capacity versus system electronic noise temperature.
Regarding the performance of the GWiNoC, it can be observed in Figure 5 that the channel capacity of the proposed model is much lower than that of the conventional model at all temperature range. Specifically, 400 Gigabits/s and 1.1 Tetrabits/s are reduced at frequencies 1.2 THz and 1 THz, respectively, in the proposed model when operating at temperature
K. This again reflects the effects of various gas compositions in the medium causing a considerably reduced channel capacity of up to 26.8% in the nanocommunications within a chip.
Taking into consideration ambient pressure in GWiNoC, Figures 6 and 7 plot the total path loss and channel capacity of various channel models versus the ambient pressure (i.e.,
in kPa) applied on the chip package. (Note that 1 atm = 101.325 kPa.) The GNAs are assumed to operate at frequency THz. Similar to Figure 2, the size of the chip package, the distance between and , the height of the GNAs, and the system electronic noise temperature are set as mm, mm, mm, mm, and
K. It can be seen in Figure 6 that the total path loss in the conventional channel model is independent of the ambient pressure. However, the total path loss in the proposed channel model for practical GWiNoC is shown to exponentially increase as the ambient pressure increases, which confirms the claim of the exponentially increased total path loss over the ambient pressure in Remark 3.
Figure 6: Total path loss versus ambient pressure at different frequencies.
Figure 7: Channel capacity versus ambient pressure.
Furthermore, in Figure 7, the capacity of the proposed channel model is shown to be lower than that of the conventional model over the whole range of pressure, especially a degraded performance of up to 25%, when
THz. This achieved performance is also consistent with the achieved performance in Figures 3 and 5.
Considering the impacts of distance between two cores on the performance of GWiNoC, in Figure 8, the channel capacity of various channel models is plotted as a function of the transmission distance between two cores
and (i.e., ). Both flat and water-filling based approaches are considered for power allocation at subbands. The GNAs are assumed to operate at frequency THz and the distance is assumed to vary in the range
m, while the other simulation parameters are similarly set as in Figure 3. It can be observed that the channel capacity in both the proposed and the conventional channel models decreases as the distance increases, which can be verified from (19) in Theorem 4. Also, in the proposed model, the water-filling based power allocation is shown to provide an improved performance of up to 200 Gigabits/s compared to the flat power allocation, while there is not much difference of the channel capacity of the conventional model using these techniques. Furthermore, the proposed model is shown to achieve a much lower channel capacity compared to the conventional model. For instance, the channel capacity of the proposed model is of up to 31.8% lower than that of the conventional model even when the distance between two cores is only 0.01 mm. This is indeed caused by the introduction of the MAA in the proposed model.
Figure 8: Channel capacity versus distance between two GNAs.
In this paper, we have proposed an efficient channel model for nanocommunications via GNAs in GWiNoC taking into account the practical issues of the propagation medium within the chip package. It has been shown that MAA has a considerable effect on the performance of the practical GWiNoC, especially in THz frequency band. Specifically, the MAA has been shown to cause a very high path loss at certain frequencies (e.g., 1.21 THz, 1.28 THz, and 1.45 THz) rather than monotonically increasing over the whole frequency range as in the conventional pure-air channel model with only DPL. Additionally, the total path loss has been shown to decrease as the system electronic noise temperature increases, while it exponentially increases as the ambient pressure applied on the chip increases. As in the conventional channel model, similar impacts of the distance between two cores on the performance have been verified in the proposed channel model. Furthermore, it has also been shown that the proposed channel model results in a lower channel capacity compared to the conventional channel model, which reflects the practical issues of the nanocommunications in THz band in GWiNoC. Specifically, at least 500 Megabits/s is lower throughout the frequency range from 1 THz to 2 THz, up to 26.8% and 25% of the channel capacity are reduced over the whole range of temperature and ambient pressure, respectively, and also 3.5 Tetrabits/s of up to 31.8% is reduced when the distance between two GNAs is 0.01 mm. For future work, we will investigate a general propagation model with multiple rays. In addition, we will examine the practical issues when deploying the GNAs with different layouts and cross section of chip package.
