# An Energy Efficient Modulation Scheme for Body-Centric Terahertz (THz) Nanonetworks +
## 2 Single-Pulse Variable Duration (SPVD) Modulation  
### Basic Principle  
The basic idea of the proposed scheme, i.e., SPVD, is to transmit a vector of bits by using a waveform that consists of a certain number of silences and a very short pulse (in the order of 100 femtoseconds [PERSON] _et al._ (2016)). More specifically, the bit stream is first separated to \(k\)-th dimensional vectors, where \(k\) is the number of bits per symbol and \(M=2^{k}\) is the modulation order. Then each vector is mapped to a unique waveform, which is implemented by a look-up table through a bijective function. Each waveform consists of a variable number of time slots, i.e., a variable number of silences and only one pulse at the end, which both are of equal duration.  
According to the above description, the signal transmitted by a user can be written as  
\[s_{n}(t)=Ap(t-nt_{s}),\qquad t\leq(n+1)t_{s}, \tag{1}\]  
where \(A\) is the amplitude of the pulse, \(p(t)\) is a 100 femtosecond long pulse, \(n\in\{0,1,...,M-1\}\) is a constant that varies according to the order of the modulation and indicates the number of silences in the waveform, and \(t_{s}\) is the time duration of the time slot.  
Regarding the detection, after the receiver senses the transmitter's preamble signal, it counts the number of silences between the 100 femtosecond long pulse of the previous signal and that of the current signal, and corresponds them to a waveform. As it has already been mentioned, the transmitted pulse for each waveform is always placed at the end of the waveform, which facilitates synchronization, since an erroneous detection of a symbol affects at most two symbols. It is noted that the proposed modulation scheme resembles a PPM, with the main difference being that the duration of each codeword is not constant, but diverges according to the transmitted symbol, in order to reduce the average number of utilized time slots and thus, increase the data rate.  
The advantages of the proposed modulation compared to TS-OOK are due to the nature of the noise in body-centric THz communications. More specifically, the main contribution comes from the _molecular absorption noise_, which is generated from the molecules that re-emit part of the absorbed radiation [7]. As such, this noise is considered to be _self-induced_ affecting only the _pulses_ and not the _silences_[9]. In [6], a model for the power spectral density (PSD) of the noise has been derived, which is based on the Beer-Lambert Law. This model was proved in [10; 11; 12] to fit the in-vivo scenario. According to this model, the molecular absorption becomes negligible when no molecules are irradiated, i.e., when no user is transmitting. In addition, the molecular noise also has a phase component because of the random arrival of reflections at the receiver which are caused by the irradiated molecules in the medium and, thus, can lead to destructive interference with the transmitted pulse [9]. As such, molecular absorption noise cannot be effectively mitigated with the use of an energy detector. Other sources, such as the electronic thermal noise or the noise created by surrounding nanomachines are considered to be negligible, due to their relatively small magnitude. In the modulation scheme proposed in this paper, we manage to send more bits of information, by using more silences and less pulses, thus, effectively minimizing the effect of the molecular absorption noise, which consequently leads to an increase of the signal-to-noise ratio (SNR). In this way, SPVD can achieve a better behavior concerning the error probability compared to TS-OOK, while also consuming less energy to transmit the same number of bits, but as a downside more time is needed to transmit the same number of bits.