Page 173 - ITU Journal Future and evolving technologies – Volume 2 (2021), Issue 2

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 2

( , ) ( ) = min{ , + } + −
, 3 ( ) = ∑ ∑ ℓ , , ( + )

ℎ
,
[4 ( − − )] 2 =1 =0
ℎ

− 2
× exp ( ) , (2) + ( + + )

ℎ
4 ( − − )

ℎ
min{ , + }
= ∑ ∑ ℓ + − ( ) + ( ) (4)
, , ,
=1 =0
where is the diffusion coef icient of information

molecules, is the number of molecules emitted per where is the length of ISI, ℓ , makes a logic decision,
molecular pulse and is the distance between a transmit which is ’1’, when the th nano‑machine uses the th type
nano‑machine and the AP. of molecule to transmit its information within the th chip,
it is ’0’, otherwise. ( ) is the expected concentration of
Due to the free diffusion of molecules, there are possi‑ ,
the th type of molecule at = + , obtained from the
bly three kinds of interference encountered in MTH‑MoSK ℎ
Fick’s law of (2), after molecules of th type was emitted
systems. The irst kind originates from the same type at = 0. Note that,

of molecules emitted repetitively, which generates Inter‑ , (0) corresponds to the peak con‑
centration of the th type of molecule in the current chip,
Symbol Interference (ISI). The second one is the noise re‑ while for > 0, it contributes interference. Finally,
sulted from molecular Brownian motion. Finally, if sev‑ , in
(4) is the Brownian motion noise imposed on the th chip
eral nano‑machines transmit signals depending on the
of the th symbol duration, but relied on the transmission
same type of molecules within one given chip, the signals
of the th type of molecules. It is shown that can be

transmitted by different nano‑machines interfere with ,
approximated as the Gaussian noise with zero mean and
each other. Moreover, because the large delay‑spread
a variance of [14]
of molecular communication channels, the same type of
molecules emitted by different nano‑machines in previ‑
ous chips may also interfere with the signals transmit‑ 1 min{ , + }
2
ted within the current chip. These kinds of interference Δ ( ) = ∑ ∑ ℓ + − , ( ) (5)
,
,
caused by multiple nano‑machines are all classi ied as =1 =0
Multiple‑Access Interference (MAI). Hence, in order to
2
recover the information transmitted by different nano‑ expressed as , ( ) ∼ (0, Δ ( )). In (5), repre‑
,
machines, the design of an ef icient detector in MTH‑ sents the volume of the detection sphere of the receiver.

MoSK DMC systems is critical. Explicitly, the variance of noise is dependent on the trans‑
mitted signals, where signal power results in higher noise
power.
2.2 Received observations
For simplicity, the receiver at the AP is assumed to be con‑
3. EQUAL‑GAIN COMBINING WITH INTER‑
structed by a spherical sensing space with the radius of ,
which is able to ideally measure the concentrations of the FERENCE MITIGATION
different types of molecules presenting in the space. We
assume that is small enough with respect to the com‑ The proposed EGC‑IM scheme is an enhanced single‑user
detection scheme. In comparison with the conventional
municationdistance, so that near‑uniformconcentrations
present in the sensing space. In other words, the sens‑ EGC scheme, EGC‑IM requires a slightly increased com‑
ing space is idealized as a point space. Based on these as‑ putation. However, as the results in Section 4 illustrate,
it has the potential to mitigate the MAI and ISI existing in
sumptions, the received peak concentration within each
2

chip is expected to occur at the time = 6 from the our MTH‑MoSK system and hence, achieves performance

start of each chip [13], which is usually used as the obser‑ improvement when compared with the conventional EGC
scheme.
vation for information detection. Following this conven‑
According to (3), within one symbol duration, we can ob‑
tion, the observation obtained during the th chip of the
tain in total × observations, consisting of the signals
th symbol duration is given by
transmitted by nano‑machines during the current sym‑
bol duration, the interference from previous symbol du‑
( ) = ( = + + ), = 0, 1, … , − 1; rations and background noise. Let us collect the ×
ℎ

,

observations obtained during the th symbol duration to
= 0, 1, … ; = 0, 1, … , − 1 (3) form an observation matrix , whose rows represent

molecular types and columns denote the chips of
the th symbol duration. Furthermore, the ( , )th ele‑
To be more speci ic, when taking account the effect from

Brownian motion noise, the ISI from the desired nano‑ ment of is given by ( ).
,
machine and the MAI generated by other nano‑machines, The principle of the conventional EGC can be found in
the received observation ( ) can be expressed as many references [15]. With the aid of Fig. 2, the principle
,
© International Telecommunication Union, 2021 159