Page 66 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 3 – Internet of Bio-Nano Things for health applications

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 3

Further, Table 4 compares the various modulation Gaussian distributed signals is given by
schemes in terms of their ISI mitigation capability and
( )
the types of molecules required. In traditional OOK, no µ j1 + µ j0 2 P(b j = 1)
λ j = 0.5 σ ln , (9)
ISI mitigation is possible while the MoSK modulation µ j1 − µ j0 P(b j = 0)
suppresses the ISI moderately. The types of the molecule
2
where σ is the AWGN variance. Further, for Poisson dis‑
required in MoSK increase with the modulation order
tributed signals, the detection threshold in jth bit‑interval
n. The MTSK [45] modulation also mitigates the ISI but
[133] can also be obtained by substituting PDF/PMF
the types of the molecule required are larger than MoSK.
equations in LRT expression (shown in Fig. 17) as
Further, OSK [63] has a good ISI mitigation capability
and the types of molecules required are only 2. D‑MoSK ( )
[121] is a ied version of MoSK modulation that ln P(b j =1)
P(b j =0) + µ j1 − µ j0
needs fewer types of the molecule than MoSK for a λ j = . (10)
given modulation order. Also, MSSK and QMSSK [107] ln(µ j1 ) − ln(µ j0 )
modulations use antenna separation to suppress the ISI
In (9) and (10), the quantities µ j1 and µ j0 denote the mean
and the ILI, and the types of the molecule required are
less than most of the modulation schemes. of received signals corresponding to the transmission of
bit‑1 and bit‑0, respectively. The probabilities P(b j = 1)
and P(b j = 0) represent the a priori probabilities for bit‑
2.4 Challenges in detection and possible 1 and bit‑0, respectively. For the case when the noise and
solutions ISI are present, as shown in Fig. 14, sampling at t peak can
2.4.1 Noise and ISI in diffusive MC channel cause incorrect detection. The received signal including
ISI (for OOK at transmitter) is given as
The major challenge in detection arises due to noise
∞
and ISI experienced in the diffusing MC channel even for ∑
y(t) = b j N rx (r, t − jT b ) + n(r, t), (11)
the static scenario where the distance between transmit‑
j=0
ter and receiver is constant. The number of received
molecules N rx (r, t) at time t and at a distance r from a
where b j ∈ {0, 1} is transmitted bit in jth bit‑interval, T b
point transmitter is given by [133] is the bit duration and n(r, t) is the signal dependent noise
whose variance is given as [39]
N tx V rx −r /4Dt
2
N rx (r, t) = e , (6)
(4πDt) 3/2 2 3
σ [n(r, t)] = N rx (r, t), (12)
4πr 3
where N tx represents the number of transmitted rx
molecules, V rx is the volume of the receiver, D is the where r rx is the radius of the receiver.
diffusion coef icient of a signaling molecule. Since the
distance r between the communicating nano‑machines is Fig. 14 shows the received signal perturbed by the noise
constant, the time at which N rx (r, t) is maximum, can be and ISI for the transmitted bit sequence [1 1 0 1 0]. In
obtained by differentiating (6) with respect to t and set it the 3rd and 5th bit‑intervals the transmitted bit was 0,
equal to zero, as but the maximum signal in those bit‑intervals is above the
r 2 threshold that lead to incorrect decoding if we employ an
t peak = . (7) asynchronous peak detector. In the MC channel, the noise
6D
can be iltered out, as shown in [34] and maximum like‑
Also, the peak amplitude can be obtained by substituting lihood sequence‑based detection can be used at the re‑
(7) in (6)
ceiver to enhance the system performance under ISI. Also,
( ) 3/2 MMSE equalizer and DFE can be considered for ISI mit‑
3 N tx
[N rx (r, t)] max = . (8) igation [40, 45]. It is worth noting that these equalizers
2πe r 3
are less complex than the maximum likelihood sequence‑
It can be observed from (8) that the peak amplitude is in‑ based detection. Moreover, the detection in the presence
8
dependent of the diffusion coef icient D; however, varies of time varying diffusion coef icient can also be done by
inversely as the third power of distance r. For the case using a channel estimator proposed in [40].
when r and D are constant, and the noise and ISI are ab‑
sent, as shown in Fig. 13, then detection at the receiver 2.4.2 Unknown channel model
can be easily performed by sampling at a ixed peak time If the channel model is not known at the receiver then
t peak and comparing N rx (r, t peak ) against a threshold. non‑coherent detection schemes such as [52] can be em‑

The threshold can be obtained by applying MAP‑based ployed, which relies on the local geometry of the received
rule [80] to the PDF of the received signals, as shown signal and the energy difference between received signals
in Fig. 17. According to the MAP‑based rule, the opti‑ 8 A time‑varying diffusion coef icient can exist in multilayered channels
mal threshold required for detection in jth bit‑interval for such as alveolar‑blood barrier [134].

54 © International Telecommunication Union, 2021