Page 174 - ITU Journal Future and evolving technologies – Volume 2 (2021), Issue 2

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

no ISI and one maximum element of each row is removed.
Then, we can know that all the interfering elements in
, Samples , Equal gain , max{ , } ෠
Erasure rows 0, 1, 2, 4 and 6 will be removed. At the same time, the
matrix combining
maximum of Row 5 is removed, which will reduce the out‑
= 5, =[4,3,7,6,2,5] put of inal combining, as shown below. However, Row 5
,
= 3, =[2,4,6,3,1,7]
7 still has 5 elements containing the desired signal and the
7 TH address 6
6 matrix 5 symbol of nano‑machine 1 can be detected free from in‑
5
4
4 terference.
3
3
2 Let the detection matrix of nano‑machine after the IM
2
1
1 operations be expressed as ′
0 , with its elements as
0 0 1 2 3 4 5
̄
0 1 2 3 4 5 ( ) ( ). Then, based on ′ , EGC is implemented to
( , ) ,
form decision variables as
Fig. 2 – Schematic block diagram showing the EGC‑IM assisted detec‑
tion. −1
( )
̄
( ) = ∑ ( ) ( ), =0, 1, … , − 1;
of EGC‑IM can be described as follows. Let us assume that ( , )
=0
there are = 2 nano‑machines and their MTH addresses (7)
are = [4, 3, 7, 6, 2, 5] and = [2, 4, 6, 3, 1, 7], respec‑ =1, 2, … ,
1 1 1
2 2 2
tively; The symbols sent by these two nano‑machines are for each of = 0, 1, …. The last step of the EGC‑IM as‑
( ) = 5 and ( ) = 3. Then, the observation ma‑ sisted detection is to select the largest of the deci‑
1
2
trix has the form shown in Fig. 2, where the square sion variables { ( ) ( ), ( ) ( ), … , ( )

and circle elements are respectively activated by the irst 0 1 −1 ( )} provided
by (7), whose index for represents the detected ‑ary
and second nano‑machines. From previous description
we can know that these marked elements consist of sig‑ symbol transmitted by the desired nano‑machine . This
nal, interference and noise, while the other empty ele‑ is expressed as
ments contain only noise and interference. ̂ ( )
( ) = arg max{ ( )}, = 1, 2, … , (8)
Having obtained the observation matrix , next, we can

invoke the MTH address code of the desired nano‑

machine (to be detected) to de‑hop the observation ma‑ where ( ) ∈ { ( ), ( ), … , ( ) ( )}.
( )
( )
( )
trix , generating the detection matrix , for nano‑ 0 1 −1

Note that, as mentioned above, the erasure operation can
machine . To be more speci ic, the de‑hopping operation
mitigate MAI/ISI, while also reduce the output value of the
shifts the ( , )th element ( ) in to the new location
,

( ⊖ ( ), ) in , , which can be described as desired decision variable, yielding a trade‑off between the

value of and the achievable performance. Hence, for a

( ) ( ) = ( ), = 0, 1, … , − 1; given Signal‑to‑Noise (SNR), a given number of nano‑
( ⊖ ( ), ) ,
=0, 1, … , − 1; = 1, 2, … , (6) machines and a given number of chips per symbol dura‑
tion, there exists an optimum value for , which results in
Speci icall y for the example shown in Fig. 2, after applying the best performance, as to be demonstrated in Section 4.
the MTH address = (4, 3, 7, 6, 2, 5) of the irst nano‑
1
machine to de‑hop , the detection matrix 1, is ob‑

tained, as shown in Fig. 2. Explicitly, all the elements acti‑ 4. PERFORMANCE RESULT
vated by the irst nano‑machine are shifted to the 5th row, In this section, the error performance of the MTH‑MoSK
whose index explains that the ‑ary symbol transmitted DMC systems with EGC‑IM is demonstrated and com‑
by the irst nano‑machine is ( ) = 5. By contrast, the pared with that of the MTH‑MoSK DMC systems with the
1
elements activated by the second nano‑machine scatter conventional EGC. In following igur es, SNR is the ratio be‑
randomly in different rows. tween the power of one pulse of molecules released for
It can be reasoned that the elements activated by the transmitting one bit information and noise power, given by
interfering nano‑machines should be expected to have
higher energy than the elements containing only inter‑ 2 ( ) (9)
ference plus noise. Hence, in the EGC‑IM assisted detec‑ SNR = ( ) / = ( )
tion, we may make use of this property to mitigate MAI.
Speci icall y, to detect a nano‑machine’s information, we where ( ) is the peak concentration and is the volume
irst identify the ( < ) largest elements in each row of the receiver detection space.
of , and substitute them with zeros. Following the From (9) we can know that SNR is linearly proportional to
above analysis, this operation will most probably remove the number of molecules emitted per pulse, as ( ) is a
the elements activated by the interfering nano‑machines, linear function of , as shown in (2). However, using SNR
or the elements experiencing high interference due to ISI instead of directly the number of molecules has the ad‑
and MAI. This can be understood with the aid of the exam‑ vantage that it can take the volume of detection space (or
ple shown in Fig. 2. For principle, we assume that there is the capability of receiver) into account. This is because
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