Low-Complex Synchronization Method for Intra-Body Links in the Terahertz Band
Jorge Torres Gómez, Senior Member, IEEE, Jennifer Simonjan, Member, IEEE, and Falko Dressler, Fellow, IEEE
Abstract—Precision medicine applications supported by nanotechnologies enforce designing a communication interface between in-body nanosensors and external gateways. Such a communication interface will enable both a data and a control channel between nanodevices operating within the human body and external control units. In this direction, recent literature focuses on deriving analytic channel models for intra-body links through the human tissues, including the analysis of achievable communication capacities in the terahertz band. A yet missing component, however, is a synchronization module to implement communication schemes in the intra-body link. Such synchronization module will ultimately bound the communication performance regarding the perceived signal to noise ratio (SNR) and bit error rate (BER), for instance. This paper contributes to the state of the art in two directions: (a) evaluating the bounds on the communication performance with the Cramer-Rao lower bound (CRLB) for the synchronization symbol timing offset (STO) and (b) designing a low-complex mechanism to synchronize communication. This analysis considers a communication link between external gateways located on the skin and nanosensor devices flowing in the human vessels. Using envelope and slope detectors, we devise a low-complex solution that relies on the received signal strength (RSS) metric to trigger data emissions. The method estimates the peak of the received RSS metric to ignite communication in the most favorable location, i.e., when the nanosensor is located at the shortest distance in the communication range with external gateways. Our findings illustrate the feasibility of such a low-complex synchronization method. Performance −5 illustrates a BER less than 1×10 for those nanosensors traveling close to the upper vessel wall. Index Terms—Intra-body terahertz communication, Synchro-
1!!\times!10^{-5}
Index Terms—Intra-body terahertz communication, Synchronization, Localization, In-body nanosensors
I. INTRODUCTION
DVANCES in nanotechnologies progressively bridge the Aboundaries between the human body and the digital world. Battery-free electronics smoothly integrate with the skin as unnoticeable patches [1], integrating processing units running artificial intelligence (AI) modules, sensors [2], and radio frequency (RF) interfaces [3]. Inside the human body, nanotechnologies also allow radiating information from sensors to the outside through plasmonic antennas in the THz band [4]. Measurements with human-phantoms demonstrate the communication capabilities through the human tissues [5]. Such promising technologies advocate the paradigm of cellconnected-to-internet, where specific body regions are monitored and treated from remote locations, with impactful Jorge Torres Gómez and Falko Dressler are with the School for Electrical
applications in precision medicine [6]. Making use of gateway systems, very powerful communication and control applications become possible [7], [8]. The THz band is becoming a promising means to convey
The THz band is becoming a promising means to convey information exchange in the nanoscale for precision medicine applications; see [9] for instance. Illustrative designs of RF components affords miniaturization in the µm size using graphene antennas [10], [11]. Numerous research advances the use of THz band communication, enabling communication among nanosensors in the human body and with external devices for monitoring and controlling applications [12]. Specifically, for intra-body links (inside to outside the
devices for monitoring and controlling applications [12]. Specifically, for intra-body links (inside to outside the body), recent studies on models render the propagation of THz waveforms, allowing us to evaluate the communication performance. These models compute the path loss when rays undergo through the tissue and define the noise produced by the surrounding molecules in the link [13]. Research also commends low-complex modulation schemes [14] like on-off keying (OOK) [4] and pulse position modulation (PPM) [15] to convey information between the nanonodes. However, fulfilling the communication exchange in realistic
However, fulfilling the communication exchange in realistic scenarios requires implementing a synchronization scheme between emitter and receiver nodes [12], [16]. In the THz band, research reports timing acquisition algorithms detecting the average [17] and power levels [18] of received pulses, as well as using the maximum likelihood (ML) criterion with a training sequence [19]. Also, in the spectral domain, the phase of the incoming symbols is estimated using the Fourier transform as in [19]. Although these examples illustrate the feasibility of recovering the symbol timing in the THz band, these solutions are not applied to the particular case of intrabody channels. This requires a more thorough analysis and implementation when the communication happens through the human tissues. Aiming to frame a communication interface in the THz
To implement such a synchronization mechanism, based Jennifer Simonjan is with Technology Innovation Institute, Masdar City, on the spatial location of the nanosensor, we perform the periodic emission of pulses at the gateway and evaluate
Jorge Torres Gómez and Falko Dressler are with the School for Electrical Engineering and Computer Science, TU Berlin, Berlin, Germany, email: {torresgomez, dressler}@ccs-labs.org. Jennifer Simonjan is with Technology Innovation Institute, Masdar City,
Jennifer Simonjan is with Technology Innovation Institute, Masdar City, Abu Dhabi, UAE, e-mail: Jennifer.Simonjan@tii.ae. Manuscript received October XX, 2023; revised YYYY XX, 2023.
Manuscript received October XX, 2023; revised YYYY XX, 2023.
the backscattered received signal strength (RSS) from the nanosensor. The method, running at the more powerful gateway device, conceives a peak detector to evaluate the RSS’s peak as an indicator of the shortest communication distance with the nanosensor. The RSS peak detection is used as a synchronization signal to trigger the data emission from nanosensors to the gateway. Following the above, our key contributions can be summa-
Fig. 1. Conceptual representation of nanosensors flowing through the HCS and a gateway attached to the hand of the person to collect the sensor data.
nanosensors to the gateway. Following the above, our key contributions can be summarized as follows: • We design a low-complex synchronization method to trigger the communication in the intra-body link. We provide an analytic model describing the randomness
• We provide an analytic model describing the randomness of the RSS peak detection in the intra-body link. We evaluate the Cramer-Rao lower bound (CRLB) metric
• We evaluate the Cramer-Rao lower bound (CRLB) metric to evaluate the minimum variance of the RSS peak detection. We evaluate the performance for the proposed method
• We evaluate the performance for the proposed method with the symbol timing offset (STO) and the impact on the achievable BER. Our findings illustrate the feasibility of devising a synchroniza-
II. STATE OF THE ART
Our findings illustrate the feasibility of devising a synchronization signal that triggers communication when the nanosensor travels near the vessel’s upper wall. Elaborating on these contributions, the rest of the paper
travels near the vessel’s upper wall. Elaborating on these contributions, the rest of the paper is structured as follows. We discuss the state of the art in Section II. Details on the system model introducing the mobility of nanosensors and the communication channel model are given in Section III. In Section IV, we provide insights on the core idea to devise a synchronization signal with the RSS’s peak and evaluate the minimum variance of such an estimation with the CRLB formulation. We detail the proposed low-complex mechanism in Section V with the corresponding block diagram and design parameters. Section VI illustrates the performance of the proposed design with the STO and the BER metrics. Finally, we summarize open research directions in Section VII and conclude the work in Section VIII
works on synchronization of emissions with the position of the nanosensor. In this section, we therefore discuss relevant works focusing on developing clock recovery methods. Furthermore, we included comprehensive surveys on THz channel modeling and synchronization for further reading. Gupta et al. [17] proposed a synchronization scheme for
Gupta et al. [17] proposed a synchronization scheme for pulse-based THz-band communications, which aims at jointly determining the symbol start time and the observation window length. This is achieved by successively narrowing down the integration window to the true location of the pulse. Furthermore, the authors investigated the symbol error rate, the synchronization preamble length and the maximum number of bits to be transmitted before requiring re-synchronization analytically. Han et al. [19] proposed two timing acquisition algorithms
Han et al. [19] proposed two timing acquisition algorithms for pulse-based communications in the THz band. A low sampling rate (LSR) and maximum-likelihood (ML) algorithm are proposed for timing acquisition. They investigate the LSR algorithm by considering the antenna gain, the distance, the number of frames per symbol and the pulse width. However, the proposed LSR works only well if the SNR is significantly high. The ML approach instead adopts a two-step acquisition procedure to derive the timing acquisition solutions based on the ML criterion and works better in low SNR scenarios. Overall, the authors provide promising angles to efficiently and reliably solve the timing acquisition problem for pulsebased THz band wireless systems. Furthermore, this work provides a comprehensive overview of existing synchronization approaches. A link-layer synchronization and medium access control
A link-layer synchronization and medium access control (MAC) protocol for very-high-speed wireless communication networks in the THz band has been presented by Xia et al. [21]. The proposed protocol relies on a receiver-initiated handshake as well as a sliding window flow control mechanism to guarantee synchronization between transmitter and receiver, maximize the channel utilization and minimize the packet discard probability. A novel receiver architecture for pulse-based electromagnetic
discard probability. A novel receiver architecture for pulse-based electromagnetic nanonetworks in the Terahertz band has been proposed by Cid- Fuentes et al. [18]. The proposed architecture is based on a Continuous-time Moving Average (CTMA) symbol detection scheme and bases its symbol decision on the received signal power maximum peak after the CTMA, which is implemented with a single low-pass filter. Furthermore, there are some recent interesting and com-
with a single low-pass filter. Furthermore, there are some recent interesting and comprehensive surveys discussing THz technologies, channel models, modulation schemes, topologies, synchronization and localization techniques, which we would like to refer the reader to. For example, Saeed et al. [22] presented a study of the THz band for body-centric networks, by surveying works on THz device technologies, channel and noise modeling, modulation schemes, and networking topologies. Another relevant survey has been published by Lemic et al.
Chen et al. [23] presented an extensive overview of existing THz systems and localization surveys. Even if the study focuses on macro-scale setups rather than on the in-body scenario, it includes important discussions about THz channels and points to further surveys and works dealing with localization. Finally, Akyildiz et al. [16] reviewed the recent advancements and highlighted the open research directions of THz communications thoroughly, discussing also synchronization and localization specifics of the THz band. In these reported works, a synchronization module for
In these reported works, a synchronization module for intra-body links is still missing. To design such a module, we rely on our prior work [20], which studies the intrabody communication channel between nanosensors in the bloodstream and gateways attached to the skin using the THz spectrum. In [20], we focused on developing a communication scheme that considers the waveform to be travelling through three layers of skin, tissue, and blood. The main conclusion of this work was that optimal communication happens when the nanosensor is below the gateway. This requires the development of a module to synchronize emissions with the nanosensor’s location. Contributing to that direction, this work now focuses on developing and analyzing the performance of a low-complex mechanism to ignite communications between nanosensors and the gateway.
III. SYSTEM MODEL
III. SYSTEM MODEL As for the system model, we consider the intra-body communication link between nanosensors traveling through the human vessels and an external gateway located on the skin’s surface. This system is sketched in Fig. 2, illustrating the local communication scenario between the nanosensor and the gateway. The reference coordinates are centered horizontally with the gateway location and in the ordinate with the upper vessel wall, where the lv-coordinate defines the vessel stream. The nanosensor passively moves straight from left to right along the vessel stream, driven by the blood flow and at a constant speed vlv, which defines the nanosensor position along 1 the x-axis as x = vlvt. Besides, we implicitly assume that advection dominates
(1)
l_{v}
l_{v}
The nanosensor and the gateway communicate along three layers through the blood vessels, the fat tissue, and the skin. Communication occurs in the THz band 0.1 to 10 THz [13]. We perform emissions at the center frequency of fc= 0.14 THz, with the communication bandwidth BW = 40 MHz, and with isotropic antennas. We assume that the communication distance is at most dmax= 1.5 mm 3 to avoid that much attenuation level [26]. Further details on
d_{\mathrm{m a x}}=1.5
v_{l_{v}}
x=v_{l,},.
vbegin{}{v_{l_{v}};\gg;\frac{D}{L_{\mathrm{c o m m}}}}\end{array}
\left(l_{v}\right)
Fig. 2. System model for the communication system between the nanosensor and the gateway.
these physiological parameters are given in Table I and the corresponding references [27]–[29]. As a result, the communication range [−Lcomm(lv), Lcomm(lv)] in the direction of mobility, see Fig. 2, will be determined by
(2)
\left[-L_{\mathrm{c o m m}}(l_{v}),,L_{\mathrm{c o m m}}(l_{v})\right]
L_{\mathrm{c o m m}}\big(l_{v}\big)=\sqrt{d_{\mathrm{m a x}}^{2}-(L_{v}+L_{t}+l_{v})^{2}},
P_{\mathrm{T x}}
which is dependent on the nanosensor’s vessel stream lv. The received signal at the gateway is modeled with the
\frac\1{2}
v The received signal at the gateway is modeled with the channel path loss and including the impact of additive white gaussian noise (AWGN) as4 r
r(t)=\sqrt{\frac{P_{\mathrm{A t t}}}{2}P_{\mathrm{T x}}}s(t)+w(t)
P_{\mathrm{A t t}}
where s(t) is the emitted sequence, PAttis the power attenuation introduced by the channel in one direction only, and PTx 1 is the transmission’s power. We include the factor as we 2 consider the backscatter signal, i.e., the signal travels from the gateway to the nanosensor and is backscattered to the gateway by the nanosensor. Consequently, the received signal will be a Gaussian variable following the distribution r P!
\mathrm{a s}^{4}
r(t)\sim\mathcal{N}\left(\sqrt{\frac{P_{\operatorname{A t t}}}{2}P_{\operatorname{T x}}}s(t),\sigma^{2}\right),
t=0
We assume the noise level produced by the human tissue (molecular absorption noise) is negligible compared to the noise produced by the receptor circuit. To illustrate this concern, the noise produced by the human tissue will be less than the amount kBTmolBW, where kBis the Boltzmann −4πfc(Lv+Lt+Ls)k/c constant, Tmol= T0(1 − e), T0 = 310 K
is the reference temperature, k = 0.0072 is the extinction coefficient, and BW is the communication bandwidth. Evaluating
ficient, and BW is the communication bandwidth. Evaluating the minimum bandwidth (BW), as two times the sampling
the minimum bandwidth (BW), as two times the sampling 2 time, yields BW = = 40 MHz, as for T Ts value listed in Table I. To illustrate, with this formulation the power of the molecular absorption noise results in ∼−140 dB. On the other hand, the noise level in the receptor circuit is evaluated with the noise equivalent power metric, which 1/2 is reported as 1 nW/Hz
the minimum bandwidth (BW), as two times the sampling = 40 MHz, as for Tswe follow the value listed in Table I. To illustrate, with this formulation the power of the molecular absorption noise results in ∼−140 dB. On the other hand, the noise level in the receptor circuit is evaluated with the noise equivalent power metric, which 1/2 at 0.04 and 0.14 THz [30]. As-
1Implicitly, here we assume that t = 0 corresponds to the nanosensor’s position just below the gateway. 2The nanosensor’s diffusion coefficients will be directly related its size and
\textsf{t}k_{B}T_{\mathrm{m o l}}\mathrm{B}
2The nanosensor’s diffusion coefficients will be directly related its size and shape, see examples in [24, Fig. 4.5 pag. 57] 3Distances less than 2 mm happen between on the wrist between the skin
\sigma^{2}
4Following our previous work in [20] we assume transmissions are performed along the channel coherence time, thereby avoiding the impact of mobility with the Doppler effect.
3Distances less than 2 mm happen between on the wrist between the skin surface and the capillaries, for instance.
the resulting noise level by the circuit is evaluated √ 1/2 as 1 nW/Hz × BW, yielding ∼−62 dB. This value is comparatively larger than the noise level in the human tissue (∼−140 dB), allowing us to disregard the molecular absorption noise. In Eq. (3), the attenuation power in the human tissues follows
\ 1\mathrm{n W/H z}^{\bar{\ }/2}\times\sqrt{\mathrm{B W}}
(\sim-140,\mathrm{d B})
In Eq. (3), the attenuation power in the human tissues follows the predefined equations in [26, Eq. (2)], accounting for the spreading and molecular absorption losses, as
\begin{aligned}{P_{\operatorname{A t t}}=e^{-\mu_{v}d_{v}}\times\left(\frac{\lambda_{v}}{4\pi d_{v}}\right)^{2}\times}&{{}e^{-\mu_{t}d_{t}}\times\left(\frac{\lambda_{t}}{4\pi d_{t}}\right)^{2}}\ {\times}&{{}e^{-\mu_{s}d_{s}}\times\left(\frac{\lambda_{s}}{4\pi d_{s}}\right)^{2},}\ \end{aligned}
(4)
including the attenuation in the three layers (vessel, tissue, and skin), where µv, µt, µsare the molecular absorption coefficients, and λv, λt, and λsare the effective wavelengths 5 of the vessel, tissue, and skin, respectively. The variables dv, dt, and dsaccount for the communication distance between the nanosensor and the gateway in the vessel, tissue, and skin, respectively, see their representation in Fig. 2. These communication distances can be evaluated with the
\mu_{v},\ \mu_{t},\ \mu_{s}
\lambda_{v},,\lambda_{t}
\lambda_{s}
d_{v}
d_{t}.
d_{s}
These communication distances can be evaluated with the time-varying position of the nanosensor along the x-axis as given by x = vlvt. Using the cosine function for the incidence angle of the communication signal ray (φ in Fig. 2), straightforward calculations evaluate dv, dt, and dsas l L L
x,=,v_{l_{v}}t
(\varphi)
d_{v},,d_{t}
d_{s}
\begin{aligned}{d_{v}=\frac{l_{v}}{\operatorname{c o s}\varphi},\quad d_{t}=\frac{L_{t}}{\operatorname{c o s}\varphi},:\mathtt{a n d}:::d_{s}=\frac{L_{s}}{\operatorname{c o s}\varphi},}\ {\operatorname{w i t h}\quad\operatorname{c o s}\varphi=\sqrt{1-\bigg(\frac{v_{l_{v}}t}{l_{v}+L_{t}+L_{s}}\bigg)^{2}},}\ \end{aligned}
(5)
which is ultimately parametrized with time (t) and the vessel
stream (lv). The term vlvevaluates the speed with the vessel
stream, which follows a parabolic profile as in [24, Eq. (4.9)
pag. 54]
4vm 2
v = (L l − l), (6)
(l_{v})
v_{l_{v}}
(6)
v_{l_{v}}=\frac{4v_{m}}{L_{v}^{2}}(L_{v}l_{v}-l_{v}^{2}),
IV. IDENTIFICATION OF OPTIMAL POSITION FOR COMMUNICATION As we discussed in our previous work in [20], the optimum
where vmdenotes the maximum speed as in the vessel center. Finally, considering all the above expressions in Equations (5) and (6), we remark that the path loss in Eq. (4) will ultimately be a time varying function and dependent on the vessel stream the nanosensor travels with the variable lv.
l_{v}
v_{m}
Fig. 3. Resulting BER and total of emission blocks, see [20].
time. In this plot, the nanosensor always emits the first block just below the gateway, and the remaining ones at shifted nanosensor’s positions, as driven by the blood flow. Less transmission bandwidth implies emitting more than one block, which implies a degraded BER. On the other hand, increased transmission bandwidth will
(left(l_{v}\right)
On the other hand, increased transmission bandwidth will increase the impact of noise and eventually degrade the BER. Consequently, the optimum communication performance is “spatially located” where the communication distance is minimum, i.e., at φ = 0 in Fig. 2. Besides, this optimal transmission strategy occurs with less possible transmission bandwidth that allows emissions to be performed within a single communication block. Following this rationale, a strategy to optimize the commu-
\varphi,=,0
(7)
Following this rationale, a strategy to optimize the communication performance is to estimate the distance between the traveling nanosensor and the gateway. Then, synchronously ignite the data emission when this distance is the minimum along the nanosensor’s path. The literature reports two primary metrics to estimate the distance with the received signal: the RSS and the time of flight (ToF). To conceive the less complex scheme, we analyze the RSS metric and let for future work the ToF and the combination of both. With the RSS metric, the minimum distance can be detected with the maximum power of the received signal evaluated as
l_{v}
P_{\operatorname{R x}}=\frac{1}{2}P_{\operatorname{A t t}}(t;l_{v})P_{\operatorname{T x}}.
As expected, all the peaks occur at x = 0 where the gateway is located, see Fig. 4a). However, depending on the nanosensor’s vessel stream, the peak is observed earlier or later with time, see Fig. 4b). The peak appears earliest when lvapproaches the vessel center, where the blood speed is the fastest, and it delays with the decreasing distance to the vessel edges, where the blood speed approaches zero. Specifically, the time instant
5The molecular absorption coefficients and the effective wavelengths are evaluated as indicated in [26, Eq. (3)] and using the parameters in Table I in the same reference. Besides, although not directly stated here, PAttin Eq. (4) is also frequency dependent with the effective wavelength parameters.
for the RSS’ peaks can be readily evaluated as
t_{\mathrm{p e a k}}=\frac{L_{\mathrm{c o m m}}(l_{v})}{v_{l_{v}}},
(8)
as the nanosensor displaces with constant speed along the vessel stream with Lcomm(lv) as given in Eq. (1). Estimating the peak location with tpeakin Eq. (8) will readily provide the synchronization signal needed to ignite the optimum communication performance. However, estimating the peak location will inherently en-
However, estimating the peak location will inherently encompass an error, which is lower bounded by the variance produced by the noise component. The location and amplitude of the RSS’s peak will be a random variable that depends on the random vessel stream the nanosensor travels and the noise that is part of the communication channel. The parameter lvis a random variable of arbitrary distribution, and the amplitude of the received signal is also impacted with the AWGN random noise w(t) as in Eq. (2). In the next Sections, we derive such a variance with the CRLB metric and illustrate the boundaries on the communication performance for reported electronic noise-powers.
l_{v}
w(t)
A. Minimum STO to estimate the RSS peak location
We evaluate the minimum error for the RSS peak detection with the STO metric. The STO refers to the time difference between the detected symbol and the actual arrival time instants [32]. This metric evaluates the accuracy of synchronizers and ascertains communication metrics like the signal to noise ratio (SNR) and the BER. As the RSS peak’s location is a random variable, the STO
ratio (SNR) and the BER. As the RSS peak’s location is a random variable, the STO will be lower bounded with half of the standard deviation of tpeak, yielding
(9)
| Parameter | Variable | Value | Reference |
|---|---|---|---|
| Pulse shape | Rectangular pulse | ||
| Pulse duration | T | 1μs | |
| Pulse period | Tp | 1ms | |
| Receiver's sensitivity | 0.1nW/Hz$^{1/2}$ | [30] | |
| Center Frequency | fc | 0.14THz | [30] |
| Sampling time | Ts | 50ns | |
| Blood speed in the veins | v | 0.03m/s | [31] |
| Skin thickness | Lskin | 76μm | [27] |
| Tissue thickness | Ltissue | 1mm | [28] |
| Vessel thickness | LVessel | 200μm | [29] |
t_{\mathrm{p e a k}}
TABLE I SIMULATION PARAMETERS
f_{c}
0.1,\mathrm{{n W}/z^{1/2}}
To evaluate var(tˆpeak) in Eq. (9), we resort to the CRLB metric, as it assesses the lower bound for unbiased estimators [33, Chap. 3]. As tpeakdepends on the vessel stream
\mathrm{S T O} {\mathrm*{m i n}}=\frac{1}{2}\sqrt{\mathrm{v a r}(\hat{t}{\mathrm{p e a k}})},
\ _{s}
v
L_{\mathrm{s k i n}}
76,\upmu\mathrm{m}
\begin{array}{r l}&{\boxed l{\ l_{v}=6\ {\mathcal{V}}{L_{v}}\quad l_{v}=12\ {\mathcal{V}}{{L} {v}}\quad l l l{v}=12\ {\mathcal{V}}{L{} {v}}\quad l l{v}=19%{\mathcal{V}}{L{L} {v}}}\ &{\box l{{\longrightarrow}}{{l}{v}}=8.1{\mathcal{V}}{{L} {v}}\quad\ l l{v}=14\ {\mathcal{V}}{{6} {v}}\mathrm{-----R}c e c i v e r\ \ s{s e n s i t i v i t y}}\ &{\longmapsto l{v}=10%{l_{v}}\quad l_{v}=17%{L\mathcal{V}}{{L}_{v}}}\end{array}
200,\upmu\mathrm{m}
(a) Received power with the x-coordinate
t_{\mathrm{p e a k}}
(10)
Fig. 4. Received power at the gateway with the nanosensor’s position along the x-direction and with time.
\textstyle{\big(\sqrt{\frac{P_{\mathrm{A t t}}}{2}}P_{\mathrm{T x}}}nonumber\,
parameter lv(see Eq. (8)), we formulate the CRLB for tpeak in terms of the CRLB for lvas [33, Eq. (3.16) pag. 37]
\begin{array}{l}{{\sf{n e t e r}}l_{v}\ (\mathrm{s e e E q.(3)},\ \mathrm{w e f o r m u l a t e t h e C R L B f r}}\ {{\sf{m s o f f t t e}}\ \mathrm{C R E B. f o r}\ l_{v}\ \mathrm{a s}[33\ ,\ q.\ (3.16)\ \mathrm{p a g. 37}}\ {{\sf{v a r}}(\hat{t} {\mathrm{p e a k}})\geq\mathrm{C R L B}{t_{\mathrm{p e a k}}}}\end{array}
allowing us to focus on evaluating the lower bound for the
lvparameter estimation instead. In this equation, the partial
derivative is solved directly by derivating Eq. (8) after replacing
its numerator with Eq. (1) and its denominator with Eq. (6).
The term CRLBlin Eq. (10) refers to evaluating the
The term CRLBlvin Eq. (10) refers to evaluating the
minimum variance to estimate the vessel stream lvbased on the
received amplitude. Its calculation becomes straightforward due
to the dependence of the amplitude sequence with the vessel
stream, as follows from Equations (4), (5) and (7). To evaluate q
PAtt
this term, the amplitude of the received signal ( PTxin
2
Eq. (2)) is conveniently isolated when sampling r(t) with the
6
emitted pulse period (Tp), and assuming the pulse’s amplitude
(T_{p}),^{6}
6Without restraining the theoretical calculations for the minimum variance
of the peak location, we assume such an ideal sampling process with the pulse
period.
\
- *
as one. Sampling Eq. (2) with Tp, the resulting sequence will
follow the received amplitude level as follows
T_{p}
r[n]=A[n;l_{v}]+w[n],
(11)
where
A[n;l_{v}]=\sqrt{\frac{P_{\mathrm{A t t}}(n T_{p};l_{v})}{2}P_{\mathrm{T x}}}.
(12)
Eq. (11) yields a constant A[n; lv] embedded in a white
Gaussian noise variable w[n], as w[n] is the sampling of
the white Gaussian variable w(t) in Eq. (3). Finally, due to
Gaussian distribution for A[n; lv], we use [33, Eq. (3.14) pag.
36] to evaluate the CRLBlvterm as follows
A[n;l_{v}]
w[n]
w[n]
A[n;l_{v}]
\operatorname{C R L B} {l{\tau}}
\operatorname{C R L B} {l{v}}=\frac{\sigma^{2}}{\sum_{n=0}^{N_{l_{v}}}\left(\frac{\partial A[n;l_{v}]}{\partial l_{v}}\right)^{2}},
where Nlvdenotes the total of samples in the time window
where the received amplitude is above the receptors’ sensitivity
level. As illustrated in Fig. 4 b), this time window will depend
on the vessel stream lvas it decreases with lvapproaching the
vessel center.
Following this development, we provide a straightforward
N_{l_{v}}
l_{v}
l_{v}
Following this development, we provide a straightforward
calculation path for the STOmin. After calculating the partial
derivative in Eq. (10), and evaluating the CRLBlvwith Eq. (13),
we can readily compute the right term in Eq. (10). The next
Section illustrates its calculation with the parameters provided
in Table I.
\mathrm{S T O_{m i n}}
\mathrm{C R L B} {l{\nu}}
B. Evaluating the CRLB and the resulting SNR
B. Evaluating the CRLB and the resulting SNR
To illustrate, Fig. 5 depicts the evaluation of Eq. (9) with
7
the vessel stream. This plot is derived using the communication and vessels parameters listed in Table I, as well as
electric parameters in the human body from [26, Table I].
We evaluate the noise power as explained in Section III
yielding σ2 = −− 62 dB. According to this plot, the STOmin
results in the order of the ms. Such an STO amount can be
only produced when the nanosensor travels quite close to the
vessel walls (in this plot depicted in the range 6 to 10 % of the
vessel thickness); rapidly increasing to the units of seconds for
larger lv’s.
As a result of the non-zero STO in this range, the commu-
As Fig. 6 depicts, the received power becomes comparable to
the noise level when the vessel stream becomes larger than 7 %,
as a result of SNR ≈ 0. The impact of the STO rapidly
increases the gap with the ideal receiver.
These theoretical results indicate the need to conceive a
7%
\mathrm{S T O_{m i l}}
\mathrm{S N R}\ \approx\ 0
\operatorname{S N R} {\operatorname{d}}=\frac{P{\operatorname{R x}}(t_{\operatorname{p e a k}}+\operatorname{S T O};l_{v})}{\sigma^{2}},
{{{l_{v}}}S}
\sigma^{2}=--62,\mathrm{d B}
Fig. 5. Minimum STO with the vessel stream lv when the noise power
(13)is σ2 = −62 dB.
l_{v}
Fig. 6. Perceived SNR with the vessel stream lv when the noise power
is σ2= −62 dB.
Section introduces a low-complex synchronization scheme to
illustrate a method that can be implemented in practice. Based
on this proposal, we later evaluate its limits on the achievable
communication distance with the BER, as introduced in the
Results Section.
V. SYNCHRONIZATION METHOD
\sigma^{2}=-62,.
We realize the synchronization method at the gateway
due to its more extensive computational capabilities than the
nanosensor. The gateway emits a pulse train sequence that
travels into the tissue and measures the RSS metric for the
bounced signal. The synchronization signal will be generated
at the gateway with the detection of the RSS’s peak.
Fig. 7 depicts the synchronization scheme implemented at
\sigma^{2}=-62,\
7The code to evaluate the CRLB is publicly accessible at https://github.com/
jorge-torresgomez/Terahertz_C_Matlab_codes
8In this scheme, we omitted to represent the upconversion and downconversion steps. Implicitly, we assume both operations are compensating to each
others.
\
- *
- *
Fig. 7. Reference coordinate system for a nanosensor flowing through a blood vessel and communicating to a gateway outside the body.
The gateway detects the incoming sequence with a matched
filter to maximize the detection performance [34]. The matched
filter is implemented with a finite impulse response (FIR) filter,
where the coefficients are the samples of the emitted rectangular
pulse after normalizing it with the square root of its average
power. Then, the gateway recovers the envelope at the output
of the matched filter block exhibiting a peak close to tbelow,
Fig. 8.
as sketches Fig. 7 d). Finally, a peak detector module will
locate the envelope’s peak with the zero crossing time of the
slope, as represented in Fig. 7 e). The gateway will produce
magnitude, introducing the least amplitude distortion on the
the synchronization signal by detecting the zero crossing of
recovered envelope; see [36, Appendix B.1].
the differentiator’s output.
magnitude, introducing the least amplitude distortion on the
recovered envelope; see [36, Appendix B.1].
We implement a 12th-order Butterworth filter in the discrete
Fig. 8. Synchronization scheme.
We implement a 12th-order Butterworth filter in the discrete
domain with the 3 dB cutoff frequency at half the pulse train
1
periodicity (fc=), with Tp= 1 ms according to the
2Tp
9
parameters in Table I. Fig. 9 depicts the filter’s magnitude
and group delay response. As expected, the magnitude results
flat in the bandpass, and the non-zero group delay introduces
a time shift in the peak amplitude of less than 5 ms. This time
shift will introduce additional STO due to the digital signal
processing (DSP) operation.
(f_{c},=,{\textstyle{\frac{1}{2T_{p}}}})
\ {\mathrm{I}}^{\ 9}
9See details on Butterworth filter design in [36, Sec. 7.1 pag. 442]
\
- *
- *
(a) Magnitude response for the Butterworth filter
(b) Group delay for the Butterworth filter
We implement the peak detector, evaluating the slope at
the output of the Envelope detector block and comparing it to
zero. This low complex mechanism is depicted with the two
blocks in Fig. 8. We implement a differentiator with a delay
and a subtractor blocks to follow the slope of the envelope.
The differentiator’s output is compared to zero to produce
the synchronization signal with the nanosensor’s position. To
reduce the variability at the output, the differentiator employs
a delay block equivalent to 20 pulse periods, which in turn
introduces an additional processing delay of 20 × Tp= 20 ms.
In total, the DSP chain in Fig. 8 introduces a minimum STO
of 25 ms.
Fig. 10 illustrate the functioning of the synchronization
B. Peak Detector Scheme
20\times T_{p}=20,\mathrm{m s}.
Fig. 10. Recovered synchronization signal.
C. Complexity of the Proposed Synchronization Scheme
The proposed scheme for the synchronizer is comprised
mainly of three blocks: the matched filter, the envelope detector,
and the peak detector, as depicted in Fig. 8. We evaluate
complexity regarding the multipliers and adders needed for
each individual block as summarized in Table II. We count the
multipliers with the total of coefficients not equal to zero or
one. For instance, all the matched filter coefficients are equal to
one (as the reference signal is a rectangular pulse of amplitude
one, see Fig. 7 a)), thereby its implementation only consists
of adders. Furthermore, we used the pulse duration T and
sampling time Tsas given in Table I to compute the matched
filter total of coefficients, as indicated in Table II.
We remark that the complexity of the proposed scheme
increases linearly with the symbol time and similarly with the
sampling frequency. As follows from the “Matched Filter” entry
in Table II, the total of adders increases linearly with T and
with the sampling frequency (fs), as Ts=. The hardware
f1s
implementation for this scheme will require 23 adders and 19
multipliers in total. We also notice that the Butterworth filter is
the most complex block to conceive, which can be reduced by
implementing a more efficient filter like the elliptic one [36]
or decreasing the filter order, we discuss further remarks on
this in Section VII.
\begin{array}{r}{T_{s}=\frac{1}{f_{s}}}\ {\cdots=\frac{1}{f_{s}}}\end{array}
TABLE II
COMPLEXITY OF THE PROPOSED SYNCHRONIZATION SCHEME.
| Block | Non-zero coefficients | | Adders | Multipliers |
| --- | --- | --- | --- | --- |
| Matched Filter | $\frac{T}{T_{s}}=5$ | | 4 | 0 |
| Square block | | | | 1 |
| Butterworth Filter | 18 | | 18 | 18 |
| Differentiator | 2 | | 1 | 0 |
| Total | | | 23 | 19 |
\
- *
- *
Fig. 11. Symbol timing offset curves when detecting the peak with the zero
interception, and the minimum STO when the noise power is σ2= −86.5 dB.
\sigma^{2}=-86.5,\mathrm{d B}.
VI. RESULTS
We evaluate results for the proposed synchronization method
illustrating the resulting STO metric and its impact on the BER.
We simulate emissions through the channel model introduced
in Section III using the reference coordinates in Fig. 2. As
for the communication and physiological parameters of the
human tissues, we use the values summarized in Table I and
in [26, Table I]. Besides, we also evaluate the CRLB as the
benchmark for the STO metric.
Fig. 11 illustrates the STO metric with the vessel stream
benchmark for the STO metric.
Fig. 11 illustrates the STO metric with the vessel stream
the nanosensor travels, where lv∈ (0, Lvessel). We also plot
the minimum STO using the CRLB formulation, as given in
Section IV-A. For this evaluation, we use the noise level at
the input of the peak detector block; see Fig. 8. The resulting
noise level is approximately −86.5 dB due to the lowpass filter
operation, as implemented by the envelope detector block; see
Fig. 9.
The STO for the peak detector is in the order of the ms as
\sigma^{2}=-86.5,\mathrm{d B}
Fig. 9.
The STO for the peak detector is in the order of the ms as
the case for the minimum STO. Its declining behavior obeys
the increased sharpness of the amplitude level with lv(see
Fig. 4 b)), which produces a more abrupt intersection with zero
for the slope. Although the STO for the proposed scheme is 5
to 10 times larger than the optimum solution, its impact on
the communication performance is quite satisfactory regarding
the achievable BER. As depicted in Fig. 12, the BER is less
−5
than 1×10 units and the SNR larger than 13 dB. These results
are attainable by the nanosensors traveling at less than 8 % of
the vessel thickness from the vessel wall.
To compute the BER, we assume the simple communication
:mathrm B B E Q\left(\sqrt{\mathrm{S N R}_{\mathrm{d}}}\right),
l_{v},\in,(0,,L_{\mathrm{v e s s e l}})
where we evaluate the noise power as σ2 = −86.5 dB.
The resulting STO for the proposed method is produced by
the delay introduced in the processing chain, mainly by two
1!\times!10^{-5}
Fig. 12. Comparative BER curves versus SNR for the ideal receiver and the
synchronization scheme with zero-crossing detector when the noise power is
σ2= −86.5 dB.
{dot\sigma}^{2}=-86.5,\mathrm{d B}
8,%
blocks. On the one hand, by the lowpass filter, and on the other
hand, the delay introduced by the differentiator scheme; see
Fig. 8. Overcoming this delay, the STO can be further reduced
when anticipating the RSS’s peak. That can be accomplished
when comparing the estimated envelope with a positive value
instead of zero.
To illustrate the room for performance improvements, Fig. 11
l_{v}
instead of zero.
To illustrate the room for performance improvements, Fig. 11
depicts the resulting STO when increasing the threshold to a
−17
positive value; 3×10 in this case. This threshold value was
manually adjusted after visualizing the computed slope (see
Fig. 10). Although this positive threshold value is not optimal,
it still reduces the STO along the vessel stream compared to
the case where the threshold is zero. A real system application
will require an adaptive or learning mechanism to anticipate the
RSS peak with the vessel stream lv; in this way compensating
for the processing-chain delays.
In contrast to the CRLB formulation, both mechanisms
VII. FURTHER RESEARCH DIRECTIONS
for the processing-chain delays.
In contrast to the CRLB formulation, both mechanisms
sketch a declining behavior for the STO in the range 6.8 to 8 %
with lv, as depicted in Fig. 11. This behavior obeys the
increased sharpness with lvfor the RSS amplitude, as illustrated in Fig. 4 b). The narrower the peak, the more abrupt
the transition with zero, thereby, a more accurate estimate
of the symbol arrival. Although this is the case with the
proposed method, more accurate solutions will exhibit the
same increasing behavior of the CRLB with lv.
Finally, we also illustrate results in Fig. 13 for the BER
3{\times}1\bar{0}^{-17}
During this research, we also identified several open research
directions. Aiming to advance the receiver’s design further, we
elaborate on the following items
Designing the synchronization scheme with the optimal
• Designing the synchronization scheme with the optimal
complexity: According to the discussion in Section V-C,
l_{v}.
10Using this formulation, we implicitly assume there is an ideal clock
recovery mechanism; performance degradation is only produced due to
transmissions occurring at shifted positions from below the gateway location.
\
- *
- *
Fig. 13. Comparative BER curves versus SNR for the ideal receiver and the
synchronization scheme when using a positive threshold.
the lowpass filter in the Envelope Detector block (see
Fig. 8) results in the most complex block to implement
due to the number of multipliers and adders needed. This
complexity can be reduced at the expense of increased
variability for the filter’s output signal, which eventually
will increase the STO when detecting the envelope’s peak.
However, the envelope’s variability can be reduced by
increasing the buffer size for the differentiator block,
although it will also increase the STO. For a given STO,
it is still pending to minimize the complexity, looking
at the balance between the lowpass filter’s order and the
differentiator block’s buffer size.
• Reducing further the STO adapting the threshold value:
• Reducing further the STO adapting the threshold value:
Aiming to reduce the STO, the received RSS’s peak
can be anticipated with a positive threshold value; see
the discussion in Section VI. This value will depend
on the vessel stream the nanosensor is traveling in,
which is generally unknown. However, this threshold can
be adjusted heuristically by implementing an adaptive
mechanism with the slope of the received RSS sequence.
For instance, as the slope increases, the threshold can
increase to anticipate the RSS’s peak, and it can stop
increasing with the this slope approaching zero. This way,
the estimated RSS’s peak can be closer to the actual one.
• Implementing RADAR signal processing solutions to
further reduce the STO: Another direction to reduce the
frequency-modulated pulses in [37, Sec. 4.6].
• More realistic models: The antenna beam pattern will
also impact the perceived power and the synchronization
performance. This work assumes an isotropic antenna;
however, in practice, the gateway and nanosensor antennas
implement a radiation pattern with a given communication
19.5
direction. With the nanosensor’s mobility in the blood
vessels, the antennas will not always be oriented to each19
other, thereby preventing a direct communication link
18.5
with the gateway. A model accounting for the impact of
antennas orientation in the synchronization performance
will account for more realistic results. Furthermore, with
smaller nanosensor sizes, it will also vary its radial
position when traveling in the blood; see simulation
results in [38]. In such a case, diffusion might dominate
advection, causing the received signal strength variability.
Such variability will also impact the detection for the
RSS’s peak, thereby the synchronization performance. A
model for the impact of nanosensor’s radial mobility in
the synchronization performance is missing.
• Synchronization of a cluster of nanosensors with the
the synchronization performance is missing.
• Synchronization of a cluster of nanosensors with the
gateway: When considering a cluster of nanosensors,
some of them will travel closer to the gateway, enabling
communication, and some others will be limited. In
this regard, there is a need to account for models that
evaluate the amount of nanosensors that might travel in
the communication range of the gateway. It is necessary to
model their distribution across the vessel’s cross-sectional
area and devise communication schemes between the
nanosensors at the farthest distance and those closer
to the gateway. Recent studies can be used to include
realistic transport models for the traveling nanosensors in
the capillaries. As indicated in [38], the radial transport
in the capillary flow highly depends on the nanosensor
size, which will ultimately determine their communication
capabilities with the gateway.
peak
Going well beyond the state of the art, we introduced
can be anticipated with a positive threshold value; see
a low-complex synchronization method enabling terahertz
the discussion in Section VI. This value will depend
communications via intra-body links. The proposed scheme
in,
becomes relevant for interfaces between external gateways and
which is generally unknown. However, this threshold can
nanosensors operating in the human body. In addition to the
be adjusted heuristically by implementing an adaptive
conceptual design, we analyzed the communication performechanism with the slope of the received RSS sequence.
mance’s theoretical bounds. Using a Cramer-Rao lower bound
For instance, as the slope increases, the threshold can
formulation, the minimum achievable symbol timing offset
increase to anticipate the RSS’s peak, and it can stop
(STO) is in the order of the ms when nanosensors travel in the
increasing with the this slope approaching zero. This way,
proximity of the vessel walls and for typical noise power values
the estimated RSS’s peak can be closer to the actual one.
in the terahertz band. Our findings illustrate the feasibility of
to
such a low-complex synchronization method achieving a BER
further reduce the STO: Another direction to reduce the−5
less than 1×10 for those nanosensors traveling close to the
STO is looking at RADAR-based solutions like pulse
upper vessel wall. Next research direction is to integrate this
compression techniques. These signal-processing methods
synchronization method with a realistic communication scheme,
narrow the envelope of the received signal after detection,
where a clock synchronization method needs to be implemented.
thereby improving the peak location with time. Instead of
In addition, this paper also summarized challenging research
emitting a sequence of pulses, as illustrated in Fig. 7 b), a
directions to advance the receiver’s design further and introduce
frequency-modulated pulse can be emitted to later decode
more realistic scenarios.
it with reduced time-variability; see, for instance, linear
The reported research was supported by the project NaBo-
Com, funded by the German Research Foundation (DFG) under
grant DR 639/21-2 as well as by the project IoBNT, funded
1!\times!10^{-5} by the Federal Ministry of Education and Research (BMBF,
Germany) under grant 16KIS1986K.
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Jorge Torres Gómez received the B.Sc., M.Sc., and Ph.D. degrees from the Technological Uni- versity of Havana, CUJAE, Cuba, in 2008, 2010, and 2015, respectively. He is currently with the Telecommunication Networks Group, Department of Telecommunication Systems, Technical University of Berlin. He holds a position as head of educational activities at the IEEE Germany Section, supporting teaching activities and chairing conference events in education. Since 2008, he has been with the School of Telecommunications and Electronics, CUJAE University, where he was a Lecturer from 2008 to 2018. He has been with the Department of Signal Theory and Communications, Carlos III University of Madrid, Leganés Campus, Madrid, Spain, as a guest lecturer, and with the Department of Digital Signal Processing and Circuit Technology, Chemnitz University of Technology as a postdoc. His research interests include molecular communications, nanonetworks, the age of information, and digital signal processing.
Jennifer Simonjan received her Ph.D. degree in In- formation and Communication Engineering from the University of Klagenfurt, Austria in 2019. After her Ph.D, she gathered experience working as a post doc at the Georgia Institute of Technology in Atlanta, US and as a researcher in Austria. Currently, she works as a lead researcher in the Autonomous Robotics Re- search Center at the Technology Innovation Institute in Abu Dhabi, UAE. Her research interest comprise self-organization and communication in nanoscale and macroscale sensor networks as well as robotic networks.
Falko Dressler is full professor and Chair for Data Communications and Networking at the School of Electrical Engineering and Computer Science, TU Berlin. He received his M.Sc. and Ph.D. degrees from the Dept. of Computer Science, University of Erlangen in 1998 and 2003, respectively. Dr. Dressler has been associate editor-in-chief for IEEE Trans. on Mobile Computing and Elsevier Computer Communications as well as an editor for journals such as IEEE/ACM Trans. on Networking, IEEE Trans. on Network Science and Engineering, Elsevier Ad Hoc Networks, and Elsevier Nano Communication Networks. He has been chairing conferences such as IEEE INFOCOM, ACM MobiSys, ACM MobiHoc, IEEE VNC, IEEE GLOBECOM. He authored the textbooks Self- Organization in Sensor and Actor Networks published by Wiley & Sons and Vehicular Networking published by Cambridge University Press. He has been an IEEE Distinguished Lecturer as well as an ACM Distinguished Speaker. Dr. Dressler is an IEEE Fellow as well as an ACM Distinguished Member. He is a member of the German National Academy of Science and Engineering (acatech). He has been serving on the IEEE COMSOC Conference Council and the ACM SIGMOBILE Executive Committee. His research objectives include adaptive wireless networking (sub-6GHz, mmWave, visible light, molecular communication) and wireless-based sensing with applications in ad hoc and sensor networks, the Internet of Things, and Cyber-Physical Systems.
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