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Parameters of Terahertz Channel with Nanonetwork

By Vandana Sharma, on July 16, 2017

Power Allocation and Channel Capacity

In this section an investigation of the Terahertz channel by using the developed model is done. Terahertz band is a single transmission window almost 10 THz wide. Terahertz channel is highly frequency selective and in addition the molecular absorption noise is non-white based on proposed channel. The capacity can be obtained by dividing the total Band width into many narrow sub-bands and summary the individual capacities. The ith sub band is centered around frequency fi where i =1, 2,3,4,5,6 and it has width ∆f. If the sub band width is small enough, the channel appears as frequency nonselective and the noise power spectral density can be considered locally flat. The resulting capacity in bits/sec.

Where d=total path length, S=Transmitted signal p.sd, A=Channel path loss, N=noise p.s.d.

From this, the optimal transmission frequency and its associated band width for a given transmission distance can be determined. Within a nanonetwork, it is unlikely to consider single hop transmission distances above several tens of millimeters. This opens a wide range of opportunities for communications from femtosecond long pulse based communication systems to multiple access methods based on frequency division techniques. For short range macroscale communications i.e. upto a few meters, the channel conditions define a set of transmission windows upto several tens of gigahertz wide each. Current research on terahertz communication is mainly aimed to exploit the first available window below 350 GHz.

Numerical Results

Various parameters like path loss, noise and channel capacity etc. have been analyzed in this section.

1. Path Loss

It is dependent on the EM wave frequency, the transmission distance d and the composition of the medium that is being considered in order to illustrate the interrelations between these variables.

In order to exemplify and understand the different properties of the Terahertz Band from the communication viewpoint, the proposed channel model is evaluated for different medium compositions, in terms of total path loss, molecular absorption noise and channel capacity. In this analysis, the contributions to molecular absorption from oxygen, carbon dioxide, methane, nitrogen dioxide, ozone, nitrous oxide, carbon monoxide, and water vapor are considered.

Their average concentration in a dry atmosphere is used unless the contrary stated is shown in dB as a function of both the frequency (x-axis) and the distance (y-axis) for different concentrations of water vapor molecules. In a homogeneous channel, this is directly proportional to the molecular cross- section and the total path length d. The main features of the Terahertz Band from the communication perspective are summarized in the following lines. From this, the optimal transmission frequency and its associated bandwidth for a given transmission distance can be determined. Within a nanonetwork, it is unlikely to consider single hop transmission distances above several tens of millimeters. Within this range, the available bandwidth is almost the entire band, from a few hundreds of gigahertz to almost ten Terahertz, even for high concentrations of water vapor molecules, which is the major factor affecting the channel path loss. This opens a wide range of opportunities for communications, from femtosecond long pulse-based communication systems to multiple access methods based on frequency division techniques. For short-range macroscale communications, i.e., up to a few meters, the channel conditions define a set of transmission windows up to several tens of gigahertz wide each. Current research on Terahertz communication is mainly aimed to exploit the first available window below 350GHz.The development of graphene-based devices implicitly working in this domain can potentially enable the (simultaneous) use of all them in a cognitive fashion.

In figure below, the total path loss in dB as a function of the frequency and the distance for two different concentrations of water vapor molecules & Molecular absorption noise temperature 𝑇 in Kelvin as a function of the frequency and the distance for two different concentrations of water vapor molecules are shown.

Figure: Total Path Loss in dB and Molecular Absorption Noise Temperature 𝑇 in Kelvin[Kanai Yosuke, Jeffrey B. Neaton, Jeffrey C. Grossman, 2010,”Theory and simulation of Nanostructured Materials for Photovoltaic Applications”, Computing in Science and Engineering]

2. Noise

The total noise power, P_n given by, in a Terahertz communication system depends on the electronic noise temperature at the receiver, T_SYS, and the molecular absorption noise temperature created by the channel, T_mol, the electronic noise temperature of the system is expectedly low due to the electron transport properties of graphene. In the following, taking into account that the computation of the molecular absorption noise power would require the dentition of the usable bandwidth 𝐵, the molecular absorption noise temperature is calculated instead. The molecular absorption noise temperature, T_mol, is shown in Fig as a function of the frequency (x-axis) and the distance (y-axis) for different concentrations of water vapor molecules.

In the very short range, the absence of highly absorbent molecules in the medium results in very low noise temperatures. The presence of water vapor molecules is again the main factor affecting the properties of the Terahertz channel. For the short range, the wise selection of center frequency and bandwidth can diminish the effect of the noise on the system performance.

3. Channel Capacity

The capacity, C, of the Terahertz channel is determined by the channel path loss, A, the noise p.s.d., N and the p.s.d. of the transmitted EM wave. In an intent to keep our numerical results realistic, and in light of the state of the art in molecular-electronics, the total signal energy is kept constant and equal to 500 pJ independently of the specific power spectral distribution. This number is chosen in light of the state of the art in novel energy harvesting systems for nano-devices, such as piezoelectric nano-generators. These mechanisms are able to harvest energy from ambient vibrations, which is then stored in a nano-battery or a nano-ultra-capacitor. These mechanisms have been successfully used to power a laser diode and a PH nanosensor. The maximum amount of energy harvested by these mechanisms depends on several factors, such as the nano-battery size of the frequency of the harvested vibration, but values in the orders of hundreds of nJ have been illustrated. Because of this, we consider that the chosen energy is a reasonable value. a uniform distribution of the power within the entire Terahertz Band, Sflat, the p.s.d. corresponding to the first time derivative of a 100 fs long Gaussian pulse, S(1) p, and the p.s.d for the case in which a transmission window at 350 GHz, Swin, is usedIn this case, uniformly distributing the power across the entire band tends to the optimal p.s.d .On the contrary, by utilizing a single transmission window even if 51 GHz wide, the capacity in this case would be up to two orders of magnitude below the optimal p.s.d. When the transmission distance is increased, the effect of the molecular absorption is intensified, and uniformly distributing the power along the band is no longer a capacity efficient option. From these results, we also high- light that the exchange of femtosecond-long pulses is a good compromise between achievable information capacity in the Terahertz Band and nano-transceiver architecture complexity.