Symbol Synchronization for Optical Intrabody Nanocommunication Using Noncoherent Detection

Abstract

Optical intrabody wireless nanosensor networks (OiWNSNs) enable groundbreaking biomedical applications via optical nanocommunication within biological tissues. Synchronization is critical for accurate data recovery in these energy- and size-constrained nanonetworks. In this study, we investigate timing synchronization in a highly dispersive and noisy intravascular optical channel, particularly under an on–off keying preamble comprising Gaussian optical pulses. We proposed a synchronization scheme based on the repetitive transmission of a preamble and noncoherent detection using continuous-time moving average filters with multiple integrator windows. The simulation results reveal that increasing the communication distance degrades the synchronization performance. To counter this degradation, we can increase the number of preamble repetitions, which markedly improves the system reliability and timing accuracy due to the averaging gain, although the performance saturates due to the dispersion floor inherent in the blood channel. Moreover, we found that low-resolution nanoreceivers with fewer integrators outperform high-resolution designs in dispersive environments, as they mitigate the energy-splitting problem due to pulse broadening. This tradeoff between temporal resolution and robustness highlights the importance of channel-aware receiver design. Overall, this study provides key insights into the physical layer design of OiWNSNs and offers practical guidelines for achieving robust synchronization under realistic biological conditions.

1. Introduction

Advances in nanotechnology have paved the way for developing of intrabody wireless nanosensor networks (iWNSNs)—a subsystem of the internet of bio-nano things [1,2]—which hold transformative potential for applications such as real-time disease diagnosis, targeted drug delivery [3,4,5], neural interfacing [6], and continuous health monitoring [7,8,9]. Particularly, iWNSNs comprise ultra-small, biocompatible devices—nanosensors and nanomachines—capable of performing tasks such as sensing, communication, storage, processing, and localized actuation in biological environments [10]. Unlike traditional medical devices, iWNSNs operate at scales of nanometers to micrometers, allowing unprecedented access to cellular and molecular processes. In other words, iWNSNs can help monitor health or control body functions at a microscopic level—even inside cells. For instance, nanosensors in the bloodstream can detect diseases early, monitor health continuously, and even help in fixing problems at a cellular level. A single nanosensor has a very limited view of its environment. However, a swarm of nanosensors communicating over short distances can work together to perform sophisticated diagnostic tasks. Imagine a scenario in which nanosenors are searching for early-stage cancer cells. One sensor might detect a faint chemical signal and then communicate its finding to its neighbors a few micrometers away. By sharing information, the swarm can collectively confirm the finding, map the boundary of a tumorous region, or pinpoint the disease source with much higher accuracy than any single device could. This allows unprecedented access to cellular and molecular processes for real-time disease diagnosis.

For the nanosensors to work, they need to communicate among themselves; one way to do this is by sending signals using electromagnetic (EM) waves. Therefore, the nanocommunication in iWNSNs plays a pivotal role in enabling several functionalities by allowing nanosensors to exchange information with each other and with external macroscale devices. However, designing a reliable and safe intrabody nanocommunication system poses considerable challenges due to the complex and lossy propagation environment inside biological tissues and the strict constraints on biocompatibility and power consumption. The current state of the art in iWNSN EM communication focuses primarily on two EM spectrum bands: the terahertz (THz) band (0.1–10 THz) [11,12,13,14] and the optical frequency band (infrared: 30–400 THz and visible: 400–750 THz) [15,16,17,18]. In particular, the THz band has attracted considerable attention due to its balance between wavelength and tissue penetration depth. THz waves can propagate over millimeter-scale distances in biological media with relatively lower path loss compared with optical waves [11,15]. The propagation characteristics of THz waves—moderate tissue penetration and wide bandwidth—enable high data rates, making them suitable for deep-tissue communication. Recent advances in nanoelectronics, especially with graphene-based materials, have led to the design of compact and low-power THz transceivers using plasmonic nanoantennas [19]. However, a major limitation of THz nanocommunication is the strong absorption of THz radiation by water molecules, which can result in tissue heating and photothermal damage if not carefully managed [9]. Therefore, recent studies emphasize the importance of power control and thermal safety to maintain biocompatibility while achieving data rates up to 100 kbit/s [15,20]. Meanwhile, the optical frequency band offers advantages in terms of biocompatibility, as it induces lower photothermal effects in biological tissues. Optical signals interact favorably with biological structures; for example, red blood cells (RBCs) can act as natural microlenses that enhance signal focusing and propagation [17,18]. Moreover, advances in nanophotonics, including plasmonic nanolasers [21,22], biophotonic waveguides [23], and nanophotonic detectors [24] have enabled the development of compact, energy-efficient optical transceivers for applications such as subcutaneous implants and wearable nanophotonic devices [16]. In this study, we focus on the optical frequency band as a preferable communication band due to its biocompatibility, hereinafter referred to as optical iWNSNs (OiWNSNs).

Regarding communication techniques, recent research has introduced on–off keying (OOK) modulation schemes, such as Gaussian pulse train OOK (GPT-OOK) and raised-cosine pulse OOK (RCP-OOK) [15], which use ultrashort optical pulses to reduce the EM exposure time, thereby limiting heat generation while maintaining reliable data transmission. In addition, the dynamic nature of intrabody channels, influenced by cell movements, necessitates robust modulation schemes to ensure a low bit error rate (BER) (≤${10}^{-2})$ [15,16]. However, the effectiveness of these techniques hinges on the precise synchronization between nanodevices to ensure accurate data transmission and reception. Most existing work has focused on physical-layer communication techniques—modulation schemes, channel modeling, and biocompatibility—while often assuming ideal or implicit synchronization. However, in practical deployments, achieving reliable symbol-level synchronization is essential to ensure accurate data decoding at the receiver and network coordination. In addition, given the use of pulse-based modulations in which data are encoded in the presence or absence of ultrashort pulses, synchronization in OiWNSNs becomes critical.

Traditional synchronization techniques [25,26] are impractical for nanoscale devices due to their complexity, energy demands, and hardware limitations. For instance, previous studies have typically been conducted in free-space or low-scattering dielectric environments, focusing on maximizing the signal-to-noise ratio (SNR) and minimizing the timing jitter, using relatively high-energy pulses, and operating without strict biocompatibility constraints on the power density or duty cycle. In this study, we establish synchronization principles in a highly dispersive, highly scattering intravascular optical channel, operating in the visible/near-infrared (NIR) band where hemoglobin (Hb) absorption is pronounced, with strict per-pulse energy limits and cooling intervals to meet photothermal safety thresholds. Although THz intrabody communication [12] also faces biocompatibility concerns, the physical sources of the problems differ, primarily due to strong water absorption. The proposed optical scheme is uniquely designed to navigate the specific absorption peaks of Hb and leverage the relative transparency windows in the visible/NIR spectrum, making our biocompatibility constraints and solutions distinct. Overall, OiWNSNs rely on simple, asynchronous ultrashort pulse-based transmission. Moreover, in biological environments, nanosensors may lack precise clocks and must operate under stringent power and biocompatibility limits.

In this study, we propose a preamble-based noncoherent low-power synchronization scheme for OiWNSNs using an energy detection receiver. This scheme relies on a known sequence of pulses (preamble) sent at the start of each transmission, enabling the nanoreceiver (NRx) to estimate the timing through energy accumulation rather than complex processing. The proposed scheme is tailored to ultralow-power operation, short-range communication, and in vivo biocompatibility. By leveraging the simplicity of intensity detection and a robust preamble design, the proposed scheme enables reliable symbol-level synchronization with minimal energy overhead, making it suitable for practical intrabody nanonetworks. Notably, as asynchronous pulse-based communication methods, such as GPT-OOK and RCP-OOK, avoid the need for tight synchronization by encoding data in the presence or absence of a pulse, the proposed synchronization scheme is suitable for this environment. Further, the receiver uses a noncoherent energy detection technique to locate the timing of incoming symbols based on a predefined optical preamble. This avoids the need for complex demodulation or local oscillators, making it suitable for ultralow-power operation. Meanwhile, the preamble is designed to operate at low optical intensity and short duration, ensuring minimal photothermal effect on tissues.

The remainder of this article is organized as follows. Section 2 describes the system model, including the preamble design structure. Section 3 describes the intravascular optical channel model considering the effects of RBCs and other cellular structures. Section 4 introduces the optical NRx model. Next, Section 5 describes the proposed synchronization scheme and explains the biocompatibility and energy issues. Section 6 presents the simulation results with various simulation parameters. Finally, Section 7 concludes this study.

2. System Model

We consider a communication scenario of active nanomachines in blood vessels [15,16]. These nanomachines, equipped with biosensors, nanotransceivers, and nanoantennas, operate in the bloodstream, performing tasks and communicating with each other or an external receiver. Particularly, we consider a point-to-point optical communication link between a nanotransmitter (NTx) and NRx (cf., Figure 1). The NTx emits a sequence of intensity-modulated optical pulses, operating in the visible spectrum, where biological tissues are partially transparent and the photothermal effects are minimal. The link is assumed to be short-ranged (sub-centimeter scale), quasi-static, and severely impacted by channel effects.

As shown, various cell types influence how light propagates through the bloodstream in distinct manners. Human blood primarily comprises RBCs, white blood cells, and platelets. Among these, RBCs are the most numerous—making up approximately 45% of the blood volume—and the largest, with an average diameter of approximately 7 μm. Owing to their abundance and size, RBCs play a pivotal role in determining the optical properties of blood. RBCs are suspended in the blood plasma, which constitutes approximately 55% of total blood volume and primarily comprises water (approximately 92%). Therefore, we consider RBCs immersed in plasma in this study.

Preamble Signal

The preamble comprises a sequence of $N_p$ optical pulses transmitted at fixed intervals to facilitate symbol-level synchronization (as shown in Figure 2). In other words, the preamble signal comprises $N_p$ equally spaced intensity bursts [27]. The preamble’s basic unit is an optical subpulse, denoted $w\left(t\right)$, and is defined as the first-derivative Gaussian pulse:

$$w\left(t\right)=-{\displaystyle \frac{A(t-\mu )}{\sqrt{2\pi }{\sigma }_{\mathrm{std}}^3}}exp\left(-{\displaystyle \frac{{(t-\mu )}^2}{2{\sigma }_{\mathrm{std}}^2}}\right),$$

(1)

where $\mu$ denotes the temporal pulse center, A denotes the normalization constant to adjust the pulse energy, ${\sigma }_{\mathrm{std}}$ denotes the standard deviation of the pulse controlling its width, given as ${\sigma }_{\mathrm{std}}=T_w/\left(2\sqrt{2ln\left(2\right)}\right)$, where $T_w$ can be interpreted as the approximate pulse duration. The normalization constant, A, is chosen to ensure that the subpulse energy, $E_w$, is given by

$${\int }_{-\infty }^{\infty }{w}^2\left(t\right)dt=E_w\Rightarrow A=\sqrt{4\sqrt{\pi }{\sigma }_{\mathrm{std}}^3{E}_w},$$

(2)

where $E_w$ is typically constrained to picojoule levels to align with the nanosensor power budgets. In line with the current literature [15,16], we assume a Gaussian pulse shape suitable for noncoherent energy detection where the exact waveform is less critical than its energy.

The subpulse energy density spectrum, $S_w$, is given by

$$S_w\left(f\right)=A^2{\left(2\pi f\right)}^{2}exp\left(-4{\pi }^2{\sigma }_{\mathrm{std}}^2{f}^2\right),$$

(3)

where f denotes the frequency. Each pulse unit $p_i\left(t\right)$ comprises $N_{p_i}$ subpulses, where $N_{p_i}\in \{0,1,\dots ,N_p\}$, and $N_p=\lfloor T_p/T_w\rfloor$ denote the maximum number of subpulses within a pulse duration $T_p$. Therefore, the preamble pulse is defined as follows:

$$p_i\left(t\right)=\sum _{k=0}^{N_{p_i}-1}w(t-k{T}_w),$$

(4)

with energy $E_{p_i}=N_{p_i}{E}_w$. The signaling part of the preamble, $s\left(t\right)$, is defined as follows:

$$\begin{array}{cc}\hfill s\left(t\right)& =\sum _{i=1}^{N_p}{p}_i\left(t-i{T}_p\right)\hfill \\ \hfill & =\sum _{i=1}^{N_p}\sum _{k=0}^{N_{p_i}-1}{w}_l\left(t-k{T}_w-i{T}_p\right)t\in [0,T_s],\hfill \end{array}$$

(5)

where $T_s=N_p{T}_p$ denotes the duration of the signaling part. The entire preamble $x\left(t\right)$ includes the signaling part followed by a cooling interval and is defined as follows:

$$x\left(t\right)=\left\{\begin{array}{cc}s\left(t\right),\hfill & 0\le t<T_s\hfill \\ 0,\hfill & T_s\le t<T_b\hfill \end{array}\right.,$$

(6)

where $T_b=2T_s$. To enhance the synchronization reliability, the preamble signal is transmitted N times. Accordingly, the total transmitted signal is given by

$$x_{\mathrm{total}}\left(t\right)=\sum _{n=0}^{N-1}x(t-n{T}_b).$$

(7)

Figure 3 depicts the preamble subpulse in the time and frequency domains. The primary spectral components of the subpulse lie within the optical range. The spectrum peaks at a frequency of approximately 400 $\mathrm{T}$$\mathrm{Hz}$, corresponding to the visible/NIR optical frequency band. Recent advances in nanotechnology have experimentally demonstrated optical nanoantennas using advanced fabrication techniques [28,29]. Nanolens structures can be employed to finely control light propagation at the nanoscale [30]. Devices with footprints of a few micrometers, such as microring lasers, have been developed and are capable of generating output power in the microwatt range [31,32]. These lasers support high-speed modulation schemes. For instance, plasmonic Mach–Zehnder modulators and tunable plasmonic cavities both operate efficiently at the nanoscale [21,33,34]. In addition, ref. [35] showed that Yagi–Uda nanoantennas can achieve unidirectional optical radiation with a front-to-back ratio of >10 dB and directivity ∼6 dBi. This could reduce the energy dispersion in tissues and increase communication reliability. Bowtie antennas have demonstrated electric field enhancement factors exceeding ${10}^3$ at the antenna gap center. Gap dimensions as small as $10\mathrm{nm}$ lead to optical field localization within volumes less than ${\left(20\mathrm{nm}\right)}^3$, enabling the highly sensitive detection or emission of sub-picojoule optical pulses, which aligns well with the energy constraints in the proposed OiWNSN model [35].

3. Intrabody Optical Channel Model

Although the topic of light–tissue interaction has been widely researched from a biomedical perspective [36,37,38], there are very few intrabody optical channel models that comprehensively account for all propagation effects that light waves undergo while traveling through, for instance, a blood vessel [15,16,17]. In this study, we adopted a blood vessel channel from previous studies [16,17], which is modeled as a medium containing blood plasma and RBCs (cf. Figure 1). As shown in Figure 1, RBCs are biconcave discs roughly 6–8 μm in diameter and approximately 2.5 μm thick. As aforementioned, in blood, RBCs vastly outnumber other cells (there are approximately 4000 times more RBCs than white blood cells) and hence dominate optical propagation effects due to their large size and refractive index contrast with plasma [39]. In this study, we model an RBC as an optically homogeneous sphere with a volume equal to that of the actual discocyte. This simplification allows the use of the Mie theory to compute scattering [40]. Moreover, although it is not geometrically accurate, this spherical approximation is widely accepted in optical simulations because it allows for closed-form solutions and simplifies simulation [41,42]. Further, for simplicity, we assume that all RBCs share a single effective radius.

Mathematically, plasma is modeled as a lossy medium. Its optical behavior is modeled like that of water, as the plasma is mostly water. This is based on complex permittivity, which captures both the energy storage and loss mechanisms from light waves. As shown in Figure 4, RBCs are modeled as spheres with three layers: the core (Hb), cytoplasm (intracellular fluid, mainly water), and membrane (the outer lipid layer). We begin with the frequency domain propagation characteristics of the optical waves. For simplicity, we consider line-of-sight (LoS) communication. Although light can have several effects when interacting with a medium, including reflection, absorption, diffraction, and scattering, for light–tissue interaction, where the particle size is considerably higher than the wavelength, the diffraction effect is negligible [16]. Similarly, the reflection does not play a pivotal role in the channel response, particularly in the LoS communication; thus, we ignore its effect [16]. For instance, for a typical visible-light wavelength of 450 $\mathrm{n}$$\mathrm{m}$ and at the fat–cytoplasm interface, only 0.2% of the light intensity from the LoS path is reflected. This is very small, indicating that 99.8% of the light continues forward [16].

3.1. Total Path Loss

The major path loss in a turbid medium is due to the spreading loss $A_{\mathrm{spr}}\left(·\right)$, molecular absorption loss $A_{\mathrm{abs}}\left(·\right)$, and scattering loss $A_{\mathrm{sca}}\left(·\right)$. In this study, we consider a directional light source and an isotropic antenna. The total path loss, $A\left(·\right)$, can be expressed as follows:

$$A(f,l)=A_{\mathrm{spr}}(f,l)A_{\mathrm{abs}}(f,l)A_{\mathrm{sca}}(f,l),$$

(8)

where l denotes the path length. The spreading loss, $A_{\mathrm{spr}}(f,l)$, also known as geometric attenuation, occurs due to the divergence of a wavefront as it travels away from the source. In conventional free-space optical models, the EM wave propagation is accompanied by a geometric spreading loss, which scales with distance and frequency. However, in our scenario, light propagation is confined within a microscopic biological medium, specifically through RBCs, cytoplasm, and surrounding plasma, over distances on the order of 10–20 μm. Owing to the highly scattering and absorptive nature of the tissue environment and the fact that light does not freely diverge in a spherical wavefront, geometric spreading loss does not play a pivotal role. Instead, the dominant mechanisms of energy attenuation are molecular absorption (primarily by Hb) and Mie-type scattering due to cellular structures. In addition, the extremely short propagation distances are within the near-field or Fresnel regime of optical propagation, where spherical divergence is negligible. Further, biological structures, such as RBCs and vessel boundaries, act as scattering-based optical waveguides that suppress geometric spreading. Thus, absorption and scattering dominate the path loss in this regime. Consequently, spreading loss is considered negligible and is excluded from our total attenuation model.

Notably, the proposed channel model, based on the Beer–Lambert law, is a well-established simplification of the more general radiative transfer equation. This simplification specifically models the attenuation of the ballistic (unscattered) light component traveling along the LoS path. For a symbol synchronization task over ultrashort distances, the arrival of the first and least-dispersed part of the optical pulse is the most critical information for accurate timing estimation. Although multiply-scattered (diffuse) photons also contribute to the received energy, they arrive with a temporal delay and spread, which are less useful for achieving precise synchronization. Therefore, focusing on the LoS component attenuation is a standard and appropriate methodology for this specific application.

3.1.1. Scattering Loss

When light encounters a particle, it may not pass straight through; instead, it can be scattered, meaning it is deflected in various directions. The attenuation caused by the scattering along the LoS path can be modeled using the inverse Beer–Lambert law [43], expressed as follows:

$$A_{\mathrm{sca}}(f,l)=e^{{\sum }_j{\mu }_{\mathrm{sca}}^j\left(f\right)l},$$

(9)

where the summation accounts for the scattering contributions from all scattering species. In general, the scattering coefficient for the j-th species is calculated as

$${\mu }_{\mathrm{sca}}^j\left(f\right)=N_{\mathrm{sca}}^j{\sigma }_{\mathrm{sca}}^j\left(f\right),$$

(10)

where $N_{\mathrm{sca}}^j$ denotes the number density of the j-th scattering species in the blood plasma.

Scattering can be modeled based on the particle size relative to the light wavelength, which is usually expressed as a nondimensional size parameter, $\psi$, given by [37]

$$\psi =\kappa r=\left({\displaystyle \frac{2\pi n_b}{\lambda }}\right)r,$$

(11)

where $\kappa$ denotes the wavenumber, $\lambda$ denotes the wavelength of the incident radiation in a vacuum, r denotes the radius of the spherical particle, and $n_b$ denotes the refractive index of the background medium, i.e., blood plasma. At visible frequencies, particle size is comparable to the light wavelength; thus, Mie scattering is dominant [36,37]. In addition, Mie scattering is characterized by strong forward scattering, consistent with the behavior of RBCs acting as optical lenses in blood plasma [16,44]. Therefore, the proposed model correctly captures this essential feature. Notably, the scattering of light by a spherical particle of any size can be modeled exactly by the Mie theory. For a spherical particle j, the scattering cross-section, which quantifies the effective area that intercepts and scatters light, is expressed as follows [37]:

$${\sigma }_{\mathrm{sca}}^j\left(f\right)={\displaystyle \frac{\lambda }{\kappa n_b}}\sum _{n=1}^{\infty }\left(2n+1\right)\left(|a_n{|}^2+{\left|b_n\right|}^2\right),$$

(12)

where $a_n$ and $b_n$ are the complex Mie coefficients for the sphere, corresponding to the electric and magnetic multipole modes of order n, respectively. These coefficients were determined by applying boundary conditions at the sphere surface. In addition, they depend on the size parameter $\psi$ and relative refractive index m, where $m=n_{\mathrm{RBC}}/n_{\mathrm{plasma}}$. For RBCs, $n_{\mathrm{RBC}}\approx 1.4$ and $n_{\mathrm{plasma}}\approx 1.33$ at a wavelength of 600 $\mathrm{n}$$\mathrm{m}$, resulting in $m\approx 1.05$ [45]. Although their full expressions are complex, the first Mie coefficient $a_1$ is given using the Riccati–Bessel functions ${\psi }_n$ and ${\xi }_n$) as [36,37,38]

$$a_1={\displaystyle \frac{m{\psi }_1\left(m\psi \right){\xi }_1^{\prime }\left(\psi \right)-{\xi }_1\left(\psi \right){\psi }_1^{\prime }\left(m\psi \right)}{m{\psi }_1\left(m\psi \right){\psi }_1^{\prime }\left(\psi \right)-{\psi }_1\left(\psi \right){\psi }_1^{\prime }\left(m\psi \right)}},$$

(13)

and similarly for higher orders $a_n$ and for $b_n$, which have a similar form with m and $1/m$ swapped in one term. Here, ${\psi }_n$ and ${\xi }_n$ are related to spherical Bessel and Hankel functions of the first kind, respectively, and the primes denote differentiation with respect to the argument. The size parameter, $\psi$, essentially dictates how many terms in the series are significant. For an RBC in plasma at a wavelength of $\lambda \approx 0.6$ μm, $\psi$ is in the order of 20–30, indicating that several terms contribute significantly.

Figure 5 depicts the scattering results of a single RBC inside a blood vessel. In Figure 5a, we observe that Hb is a dominant scatterer inside the RBC, whereas scattering from the membrane and cytoplasm is comparatively negligible. In Figure 5b, we observe that the scattering-induced path loss increases from 400 THz, peaks around 550 THz and then gradually decreases toward 750 THz. In our model, Hb is considered a large spherical scatterer using the Mie theory, where the Hb-rich region of the RBC cytoplasm is approximated as a homogeneous and isotropic Mie particle, rather than modeling individual Hb molecules. This behavior is indicative of a Mie resonance effect, which leads to nonmonotonic scattering characteristics. Specifically, at certain frequencies (corresponding to particular wavelengths), the particle becomes strongly resonant with the incident EM wave, resulting in a peak in the scattering. Notably, Mie scattering introduces more complex interactions. The scattering efficiency, $Q_{\mathrm{sca}}\left(f\right)$, given by ${\sigma }_{\mathrm{sca}}\left(f\right)/\pi r^2$, depends on the size parameter and is governed by the oscillatory Mie coefficients $a_n$ and $b_n$, which are nonlinear functions of frequency. As the frequency increases, the scattering initially increases due to the growing size parameter. Then, interference between the multipole terms leads to resonant peaks and dips. Finally, $Q_{\mathrm{sca}}$ decreases at very high frequencies. This results in the nonmonotonic behavior observed in both the scattering coefficient and path loss curve. In other words, for particles much larger than the wavelength, Mie scattering exhibits oscillatory patterns due to the constructive and destructive interference of the scattered fields.

3.1.2. Absorption Loss

The absorption loss accounts for the light beam attenuation due to molecular absorption and is defined as follows:

$$A_{\mathrm{abs}}(f,l)=e^{{\sum }_j{\mu }_{\mathrm{abs}}^j\left(f\right)l},$$

(14)

where ${\mu }_{\mathrm{abs}}^j\left(f\right)$ denotes the absorption coefficient of the j-th species. In a medium containing several particles with number density $N_{\mathrm{abs}}^j$, the absorption coefficient can be considered as the total cross-sectional area for absorption per unit volume [38,46]:

$${\mu }_{\mathrm{abs}}^j\left(f\right)=N_{\mathrm{abs}}^j{\sigma }_{\mathrm{abs}}^j\left(f\right),$$

(15)

where ${\sigma }_{\mathrm{abs}}^j\left(f\right)$ denotes the absorption cross-section, given by ${\sigma }_{\mathrm{abs}}^j\left(f\right)=Q_{\mathrm{abs}}^j\left(f\right){\sigma }_{\mathrm{g}}^j$, and ${\sigma }_{\mathrm{g}}^j$ denotes the geometric cross-sectional area, and $Q_{\mathrm{abs}}^j\left(f\right)$ denotes the absorption efficiency of the jth absorbing particle. Absorption by different particles is considered to be independent. In our scenario, the optical absorption in a blood vessel primarily originates from Hb. The absorption coefficients can be directly computed from the literature [47,48,49].

Figure 6 depicts the molecular absorption results for a single RBC inside a blood vessel. In particular, Figure 6a shows the absorption coefficients of Hb, cell membrane, and plasma—the primary ingredients of an RBC— as a function of the optical frequency. Hb exhibits extremely high absorption, exhibiting low-amplitude absorption peaks at 520 and $553\mathrm{THz}$, with values on the order of a few ${10}^2{\mathrm{cm}}^{-1}$ in those regions. The cell membrane mainly comprises lipids (fats), which are nearly flat or slightly increasing over the frequency range of interest. The plasma absorption coefficient remains very small and exhibits a decreasing trend with increasing frequency. In a typical visible-light blood spectrum expressed in frequency, lipid absorption manifests as only a slight baseline offset. This behavior is because water absorbs more strongly at lower frequencies (longer wavelengths), due to the onset of vibrational overtone absorption mechanisms. Figure 6b shows the absorption-induced path loss. As expected, the path loss increases monotonically with optical path length. Remarkably, the frequency-dependent trend exhibits two prominent absorption features. Specifically, a strong peak around 700 THz (corresponding to 430 nm) is observed, attributable to the Soret band of Hb. This band results from the electronic transitions in the heme group and represents the highest absorption in the visible range [37]. A set of smaller peaks around 520–550 THz (corresponding to 540–580 nm) can also be seen, corresponding to the $\alpha$ and $\beta$ bands of Hb. These absorption features arise from the vibronic transitions. Particularly, the Soret band dominates in the blue region, whereas the green–yellow region (500–600 THz) exhibits moderate absorption. Beyond 750 THz and below 400 THz, absorption decreases markedly and is mostly governed by the water and lipid components. This validates that the proposed optical absorption model for RBCs realistically captures the dominant spectral features and their impact on light attenuation across varying distances.

3.2. Channel Impulse Response

In the time domain, the channel model can be expressed simply as the inverse Fourier transform of the path loss:

$$h(t,l)={\mathcal{F}}^{-1}\left[\left({\displaystyle \frac{1}{\sqrt{A_{\mathrm{abs}}(f,l)A_{\mathrm{sca}}(f,l)}}}\right)exp\left(-j\varphi (f,l)\right)\right],$$

(16)

with

$$\varphi (f,l)=2\pi f{\displaystyle \frac{l}{c_{\mathrm{blood}}}},$$

(17)

where $c_{\mathrm{blood}}=c/n_{\mathrm{plasma}}$ for the EM waves traveling inside a blood vessel. We assume a linear phase term, where $c_{\mathrm{blood}}$ is the speed of light in the propagation medium.

Figure 7 depicts the channel model. Figure 7a illustrates the frequency response corresponding to different signal propagation distances. The non-flat, frequency-selective nature of $H(f,l)$ indicates the need for careful selection of the transmission frequency to avoid spectral regions with strong absorption. As expected, the channel gain decreases with increasing path length because of the enhanced molecular absorption and scattering losses. In addition, notable dips in the frequency response occur in specific bands, namely, around the $\alpha$, $\beta$, and Soret bands. The deepest attenuation is observed in the Soret band due to the strong absorption by Hb. This frequency range corresponds to the blue and violet spectrum region, where light is strongly absorbed by Hb molecules. In this resonance region, where the absorption cross-section of the Hb peaks, the channel gain decreases markedly. The secondary peaks at the $\alpha$ and $\beta$ bands lead to moderate attenuation, resulting in smaller but clear dips. Overall, frequencies below 500 THz (longer wavelengths in the red–infrared range) exhibit relatively lower attenuation, suggesting that they are a more suitable window for reliable intrabody nanocommunication.

Figure 7b shows the channel time response corresponding to the same three propagation path lengths. As expected, the impulse response peak attenuates and shifts to the right as the propagation length increases. This propagation delay corresponds directly to the prolonged time taken by the optical pulse to travel through a longer segment of the medium. In addition, the impulse response exhibits temporal spreading due to chromatic dispersion. That is, the impulse width broadens with increasing distance due to the cumulative dispersive and absorptive effects of the medium. Further, small oscillations or ringing can be observed immediately before and after the main pulse. This effect is a direct consequence of the characteristics of channel filtering. The frequency response acts as a band-pass filter, allowing frequencies in the optical window to pass while severely attenuating the frequencies in the Soret band region. An ideal impulse has a perfectly flat spectrum. When this flat spectrum is multiplied by a frequency response with sharp features or band edges, it causes ringing in the time domain, a phenomenon related to the Gibbs effect [50].

4. Receiver Model

The preamble signal propagates through the intrabody optical channel with additive noise. The received signal $r\left(t\right)$ is given by

$$r\left(t\right)=x_{\mathrm{total}}\left(t\right)\ast h\left(t\right)+n\left(t\right),$$

(18)

where * denotes convolution, and $n\left(t\right)$ denotes additive white Gaussian noise (AWGN) due to thermal and photonic effects. The dominant noise sources in our scenario are typically thermal noise from the transimpedance amplifier (TIA), which is accurately modeled as AWGN, and shot noise, which can be approximated as Gaussian when the number of detected photons is sufficiently high. Figure 8 depicts the block diagram of the NRx. First, the photodiode converts optical pulses into current. Second, the TIA converts the detector’s current output to voltage. The band-pass filter limits the signal bandwidth to the expected optical modulation band, reducing the out-of-band noise. Next, the square-law device implements energy detection, which is generally part of the photonic detection process or can be implemented as a separate quadratic amplifier. The integrator integrates the squared signal over each preamble symbol’s time duration, thereby smoothing short-term fluctuations and capturing symbol energy. The Max detector/comparator then compares the energy in each integrator to determine the maximum energy integrator. Finally, the decision device uses the maximum energy integrator’s starting time to align symbol and timing and achieve symbol-level synchronization.

Nanophotodetectors, such as PIN diodes, avalanche photodiodes, single-photon avalanche diodes (SPADs), or superconducting nanowire single-photon detectors, naturally implement square law detection by converting the incident optical intensity into current or voltage outputs proportional to the square of the EM field, thereby fitting seamlessly into an energy detector NRx [51,52]. Their small footprint, fast response, and compatibility with integrated circuits make them ideal for OiWNSNs requiring symbol-level synchronization and ultralow-power operation. In particular, CMOS-compatible SPAD arrays [53] can achieve timing resolutions (jitter) in the range of tens of picoseconds. This high-speed capability is more than sufficient for detecting the femtosecond-to-picosecond-scale optical pulses used in the proposed synchronization scheme. Recent advances in SPAD fabrication have demonstrated fast response times and count rates exceeding 100 Mcps per pixel [54,55]. These advances support the feasibility of the proposed architecture, particularly for synchronization tasks that rely on statistical photon accumulation rather than high-resolution waveform digitization.

CMOS-compatible photodiodes, SPAD arrays, or nanowire sensors can be monolithically integrated on-chip, thereby meeting the ultracompact and ultralow-power requirements of nanomachines. Their fast response times (picoseconds–nanoseconds) align perfectly with the picosecond-to-nanosecond pulses used in GPT-OOK modulation or synchronization. Miniature photodetectors integrated on-chip using various technologies have also been reported in the literature [56,57]. These components are critical for implementing noncoherent energy detection architectures. Moreover, the rapid progress in silicon photonics has enabled the development of photonic integrated circuits (PICs) that operate using light instead of electrical signals. These PICs leverage mature silicon fabrication techniques to enable scalable and cost-effective manufacturing [58]. Using this platform, arrays of nanoantennas and nanotransceivers can be integrated to enhance the communication capabilities and range of nanosensor nodes [59,60]. Despite these advances, as shown in the channel model, the extremely short wavelengths of optical signals continue to pose challenges for propagation, particularly within biological environments.

5. Proposed Synchronization Scheme

In traditional wireless communication, including OOK, a common approach for noncoherent synchronization is to transmit a known preamble sequence at the start of a frame or packet [25,26,61]. In an optical in vivo nanosensor link, a preamble is highly practical. It provides a data-aided strategy to achieve synchronization quickly at the start of each communication session, which is crucial given the low SNR and considerable channel noise expected inside the body. Resource-constrained nanodevices benefit from the low complexity of this strategy—the synchronization task is reduced to detecting a known bit sequence, a process suitable for simple correlators or integrators. In addition, the preamble sequence should be designed for robustness and biocompatibility. Instead of using a long continuous ON burst (which could cause tissue heating), the preamble could comprise a pattern of short optical pulses spaced by gaps, making it easily distinguishable but not exceeding the safe optical exposure limits. For instance, ref. [15] demonstrated that splitting an OOK symbol into multiple short pulses with cooling intervals (a GPT-OOK scheme) keeps the tissue temperature below safety thresholds because each subpulse causes only a small temperature increase, and the gaps allow heat dissipation. This scheme maintains the advantages of a preamble for synchronization while ensuring that optical signaling remains within the biocompatible limits. Our preamble design serves the same purpose.

At the NRx, it can integrate the photodetector current over the expected symbol duration during the preamble and slide this window until a clear energy peak is observed. This peak indicates alignment. This approach inherently averages out fast noise spikes and gathers the total energy of a scattered optical pulse, thereby making synchronization detection more reliable. It also obviates the need for a tight phase lock; a moderate timing offset will simply reduce the peak slightly rather than causing a miss, provided the main pulse lobe is captured [62]. Once the timing is acquired, the same energy-detection NRx can demodulate the OOK data symbols by comparing the integrated energy in each symbol slot to a threshold (essentially a noncoherent detection). The scheme avoids continuous synchronization signals for energy efficiency. The NTx can remain silent when it has no data, and the NRx’s front end can be extremely low-power. Synchronization is only performed when needed (on a data burst), which saves energy compared with maintaining a running clock lock. In addition, if the NTx and NRx have fairly stable clocks (likely at short range and constant temperature inside the body), the system could even reuse synchronization over multiple packets. The synchronization pulses should be of sufficiently low power and short duration to stay within medical safety limits (ANSI Z136.1–2022) [63,64,65]. As in our preamble design, spreading each “ON” period into a series of short pulses (with the total energy split among them) can drastically reduce the peak thermal effects. Notably, our design parameters were chosen to be consistent with the biocompatible constraints established and validated in [15,16].

5.1. Synchronization Process

The synchronization process is a form of maximum-likelihood estimation based on energy collection. The receiver divides the preamble duration frame into K overlapping search windows, with each window corresponding to one parallel integrator [27]. Each integrator computes the squared received signal energy over a specific time window as follows [27]:

$$z_{k,n}={\int }_{t_{s,k}+n{T}_b}^{t_{s,k}+n{T}_b+T_s}{r}^2\left(t\right)dt,$$

(19)

where $t_{s,k}$ denotes the starting point of the kth integrator for the nth preamble repetition and is given by [27]

$$t_{s,k}=t_s+(k-1){\displaystyle \frac{T_b}{N_{\mathrm{int}}}}.$$

(20)

For N repetitions, the total integrator output is given by [27]

$$Z_k=\sum _{n=0}^{N-1}{z}_{k,n},k=1,2,\dots ,N_{\mathrm{int}}.$$

(21)

The estimated synchronization point is then determined by selecting the integrator with the maximum energy output as follows [27]:

$${\widehat{t}}_{\mathrm{sync}}=t_s+(j-1){\displaystyle \frac{T_b}{N_{\mathrm{int}}}},$$

(22)

where

$$j=arg\underset{k}{max}\left(Z_k\right).$$

(23)

The synchronization process is shown in Figure 9. To ensure robust detection even under dispersive channel conditions, we optimized the energy loading across the pulse units in the preamble. The energy allocation was constrained such that the preamble delivers the most energy to the first integrator (cf. Figure 9). This optimization was performed using constrained minimization, with a circulant weight matrix modeling energy spillover among adjacent windows [27].

5.2. Energy Detection

In the proposed noncoherent synchronization scheme, the start time of the received preamble is unknown and may occur at any offset within a symbol duration, i.e., $\tau \in [0,T_b]$. The receiver employs $N_{\mathrm{int}}$ parallel integrators, each covering a sub-interval of duration $T_b/N_{\mathrm{int}}$, allowing for a parallel search over the synchronization uncertainty window. Assuming that the true synchronization point aligns with the first integrator, synchronization is deemed correct if its energy output $Z_1$ is greater than those of all other integrators. That is,

$$Z_1>Z_2,Z_3,\dots ,Z_{N_{\mathrm{int}}}.$$

(24)

Each integrator accumulates energy over a window of length $T_s$, and the energy collected by the k-th integrator is given by (21). When only noise is present, each integrator output $Z_k$ follows a central chi-squared distribution as follows:

$$Z_k\sim {\chi }_{2B{T}_s}^2,$$

(25)

where B denotes the optical pulse bandwidth. If a preamble plus noise is present in the integration window, $Z_k$ follows a noncentral chi-squared distribution as follows:

$$Z_k\sim {\chi }_{2B{T}_s}^2\left(\iota \right),\iota ={\displaystyle \frac{2E_k}{N_0}},$$

(26)

where $E_k$ denotes the signal energy captured in the k-th integration window, and $N_0$ denotes the one-sided power spectral density of the noise. For a preamble with N repetitions, the degrees of freedom scale accordingly as

$$\nu =2B{T}_{s}N.$$

(27)

The exact probability that the first integrator yields the maximum energy is difficult to compute analytically due to inter-integrator dependencies. However, this statistical distinction between the central and noncentral chi-squared distributions allows the synchronization algorithm to detect the correct alignment by identifying the integrator with the maximum accumulated energy. The synchronization time accuracy is bounded by [27]

$$t_{\mathrm{sync}}-{\displaystyle \frac{T_b}{2N_{\mathrm{int}}}}<{\widehat{t}}_{\mathrm{sync}}<t_{\mathrm{sync}}+{\displaystyle \frac{T_b}{2N_{\mathrm{int}}}},$$

(28)

where $t_{\mathrm{sync}}$ denotes the optimal synchronization point. Thus, the synchronization time accuracy depends on the number of integrators. We define the correct synchronization time, $t_{\mathrm{sync}}$, as the delay leading to the maximum preamble signal energy collection for the transmitted symbol. In other words, the correct synchronization point is the delay that maximizes the preamble signal energy collection.

6. Simulation Results

This section details the simulation parameters and presents and analyzes the synchronization performance results under realistic intrabody channel conditions. As aforementioned, the simulation framework was designed to model an intrabody optical communication link through a blood vessel. The foundational signal was a first-derivative Gaussian optical pulse with a width of 2.5 fs.

Table 1. Default simulation parameters.

Parameter	Value
Pulse units per symbol, $N_s$	12
Number of integrators, $N_{\mathrm{int}}$	12
Preamble repetitions, N	10
Monte Carlo runs	10,000
Propagation distances, l	10, 15, 20 μm
Number of subpulses, $N_{p_i}$	3

summarizes the preamble structure and synchronization parameters. The channel impulse responses for the three distances were precomputed based on the biophotonic model incorporating the absorption and scattering effects, before then being loaded into the simulation. The probability of correct synchronization, $P_{\mathrm{sync}}$, is the primary metric for evaluating the system reliability. It is defined as the probability that the NRx correctly identifies the integrator corresponding to the true signal arrival time. In addition, we computed the average normalized mean squared error, ${\mathrm{NMSE}}_{\mathrm{avg}}$, which measures the average squared error between the estimated synchronization time and the true time, providing insight into the timing estimation accuracy.

6.1. Performance According to Communication Distances

Figure 10 depicts $P_{\mathrm{sync}}$ and ${\mathrm{NMSE}}_{\mathrm{avg}}$ as a function of SNR. Figure 10a shows the $P_{\mathrm{sync}}$ for three different communication distances inside the blood vessel. For all three distances, $P_{\mathrm{sync}}$ increases with SNR. At low SNR values, the signal is weak compared with the noise. The NRx’s energy detector struggles to distinguish the true signal peak from random noise fluctuations, leading to frequent errors and a low synchronization probability. At high SNR values, the signal is much stronger than the noise. The energy peak from the preamble becomes distinct and easily detectable, resulting in a high probability of correct synchronization (with $P_{\mathrm{sync}}$ approaching its maximum). Another notable observation is the performance gap between different propagation distances. The 10 μm link achieves reliable synchronization at a much lower SNR than the other distances, demonstrating its superiority. Meanwhile, the 20 μm link exhibits the worst performance, requiring a markedly higher SNR to achieve the same level of synchronization reliability. This behavior arises from two fundamental physical mechanisms. First, as light travels longer distances, more of its energy is lost due to absorption by Hb and scattering by RBCs. Consequently, the received signal at the detector is physically weaker. Second, the longer propagation path also causes increased temporal pulse broadening (dispersion). The dispersed pulse spreads out over time, reducing its peak energy. Even if the total energy remains the same, a lower peak energy makes it harder to distinguish the pulse from the noise, thus degrading the synchronization performance.

Figure 10b depicts the ${\mathrm{NMSE}}_{\mathrm{avg}}$ for the same three values of l. As aforementioned, the ${\mathrm{NMSE}}_{\mathrm{avg}}$ measures the timing estimation accuracy. A lower ${\mathrm{NMSE}}_{\mathrm{avg}}$ value means that the NRx’s estimate of the signal’s arrival time is highly accurate. In the figure, three distinct regions of behavior can be identified. First, an error floor is observed in the high-SNR region ($\mathrm{SNR}>0\mathrm{dB}$). The NMSE is very low and relatively flat in this region; as expected, a higher SNR leads to improved timing accuracy. In the high-SNR region, the signal power markedly exceeds the noise power. The NRx almost always identifies the correct integrator corresponding to the signal’s true arrival time. However, a small residual error remains due to the local timing jitter. Here, the noise slightly distorts the received pulse shape, causing the estimated energy peak to shift by a small amount within the correct integration window. This residual jitter sets the best-case achievable timing accuracy of the system. Interestingly, the 10 μm link shows a slightly higher error floor than the 15 μm and 20 μm links. This counterintuitive result occurs because the less dispersed 10 μm pulse is temporally sharper. A very sharp peak is more sensitive to noise-induced fluctuations in its exact maximum position than a broader, flatter peak, leading to a slightly larger timing variance even at high SNR.

Second, in the low-SNR region ($\mathrm{SNR}<-15\mathrm{dB}$), a random guessing plateau is observed. The ${\mathrm{NMSE}}_{\mathrm{avg}}$ is high and plateaus at a constant value (approximately $0.36$–$0.38$). The signal is completely overwhelmed by noise. The NRx energy detector cannot reliably identify the true signal arrival window because noise peaks dominate the detection process. Consequently, the NRx effectively makes a random guess among the $N_{\mathrm{int}}$ integrator windows, each with equal probability. Thus, the timing error follows a uniform distribution across the entire search range, and the high, flat ${\mathrm{NMSE}}_{\mathrm{avg}}$ value corresponds to the expected mean squared error of this random guessing scenario.

Finally, an ${\mathrm{NMSE}}_{\mathrm{avg}}$ “hump” is observed in the mid-SNR region (approximately between $\mathrm{SNR}=-15\mathrm{dB}$ and $\mathrm{SNR}=0\mathrm{dB}$). This is the most critical feature of the ${\mathrm{NMSE}}_{\mathrm{avg}}$, which occurs due to the threshold effect. As the SNR increases from low values, the NMSE initially increases—worsening before it improves—creating a distinct hump or peak in the error. This represents the transition between the random guessing region (at low SNR) and the reliable lock region (at high SNR). As the signal begins to emerge from the noise, it is not yet strong enough for the NRx to always select the correct integrator window. However, it becomes sufficiently strong to influence the decision process. The NRx stops making purely random guesses across the $N_{int}$ integrator windows and starts making large, systematic timing errors, often confusing the main energy peak with its neighboring shoulders or energy spillover into adjacent integrators. These near-miss errors are critical; the squared error for being off by one slot is large, and during this threshold region, these specific large errors occur more frequently than either correct detections or purely random, widely distributed errors at low SNR. The average of these frequent, large squared errors causes the ${\mathrm{NMSE}}_{\mathrm{avg}}$ to temporarily rise above the level seen in the random guessing plateau, creating the hump. As the SNR increases further, the main signal peak becomes clearly distinguishable. Large errors cease, and the system rapidly transitions into a reliable tracking regime, leading the ${\mathrm{NMSE}}_{\mathrm{avg}}$ to a marked decrease toward its floor. The location of this hump indicates the minimum SNR required for the system to begin reliable synchronization.

This can also be understood by directly linking it to the channel impulse response (Figure 7b). As discussed in Section 3.2, the sharp frequency notches in the channel create ringing in the time-domain impulse response. This is a Gibbs-like effect. The result is that a received pulse is not a clean, single peak; it is a main peak accompanied by smaller, oscillating energy shoulders (or side lobes). As the signal begins to emerge from the noise, the main peak is not yet strong enough to be detected unambiguously. However, the energy in the ringing shoulders is now strong enough that, when combined with noise, it can be mistaken for the main peak. This causes the receiver to frequently make a specific type of large error: locking onto the integrator immediately adjacent to the correct one (a near-miss). These frequent near-miss errors, although only off by one time slot, contribute substantially to the squared error calculation. In this transition region, the rate of these specific large errors is higher than both the rates of correct detections and purely random errors. This temporary dominance of frequent, large errors is what causes the average NMSE to increase, creating the characteristic hump before the system finally transitions to a reliable lock at high SNRs.

6.2. Performance According to Number of Integrators

Figure 11a shows the $P_{\mathrm{sync}}$ versus SNR for a fixed communication distance of $10$ μm. The three different curves represent the three NRx designs, each with a different number of integrators ($N_{\mathrm{int}}$). The key result, which might seem counterintuitive at first, is that using fewer integrators (lower resolution) yields better performance. This occurs because the intravascular communication channel is dispersive. When the smeared-out energy pulse arrives, its entire width fits comfortably inside one single, wider integrator. The NRx sees one integrator with a lot of energy and the others with very little. The choice is clear and easy, leading to a high probability of success. Meanwhile, when $N_{\mathrm{int}}$ is 24, the smeared-out received energy pulse is now wider than a single subintegration window. As a result, the pulse’s energy is split across several adjacent subintegrators. It becomes very difficult for the NRx to make a decision. Moreover, a small amount of noise can easily cause an error. Overall, making the NRx too precise (using too many integrators) is counterproductive. It becomes overly sensitive to the pulse spreading caused by the channel, leading to ambiguity and frequent errors. A low-resolution NRx is more robust because its wide integration windows are better at capturing the total energy of dispersed signals.

Figure 11b shows the average NMSE of the timing estimate. The lowest-resolution NRx has the highest accuracy, whereas the highest-resolution NRx has the lowest accuracy. This is a direct consequence of the $P_{\mathrm{sync}}$ results. The NMSE is the average of the squared timing error over all the Monte Carlo runs. This average includes both the small errors from successful runs and the large errors from failed runs. When $N_{\mathrm{int}}=24$, the $P_{\mathrm{sync}}$ plot indicates that the system is unreliable. It fails to synchronize correctly approximately 46% of the time. When it fails, the timing error is very large. Therefore, the NMSE calculation averages the small errors from the 54% of successful runs with the massive errors from the 46% of unsuccessful runs. Because the failures are so frequent, these massive errors dominate the average, resulting in a very high NMSE. The system’s theoretical precision is overshadowed by its frequent catastrophic mistakes. Meanwhile, when $N_{\mathrm{int}}=6$, the $P_{\mathrm{sync}}$ plot indicates that the system is reliable. It succeeds approximately 88% of the time at a high SNR. When it fails, the error is large, but the failures are infrequent. Therefore, the NMSE calculation mostly averages the small timing jitter from the 88% successful runs. Because the system is so reliable, the average error remains low.

6.3. Performance According to Number of Preamble Repetitions

Figure 12a depicts $P_{\mathrm{sync}}$ versus SNR for a fixed communication distance of $l=10$ μm while varying the preamble repetition factor, N. As N increases, the performance curve shifts to the left, indicating substantial performance improvement. For instance, $N=15$ demonstrates the best performance, achieving any given $P_{\mathrm{sync}}$ at the lowest SNR, whereas $N=5$ demonstrates the worst performance, requiring the highest SNR to achieve the same reliability. This behavior is a direct result of the averaging process at the NRx. The preamble signal is the same for each N repetitions. When the NRx averages these repetitions, the signal components constructively add up. AWGN is random and uncorrelated from one repetition to the next. When averaged, the noise tends to cancel itself out. This process effectively increases the SNR of the signal that the NRx uses to make its final decision.

Another crucial observation is that all three curves appear to saturate at the same maximum $P_{\mathrm{sync}}$ value. This indicates an error floor (Figure 12b) in the system that is not due to noise. This floor is induced by the fundamental physical limitations of the channel and NRx designs. As discussed, the intravascular blood channel is dispersive, smearing the pulse out in time. The NRx uses a finite number of integrators ($N_{\mathrm{int}}$). If the dispersed pulse is sufficiently wide to consistently spill a large amount of energy into adjacent integrator windows, the NRx will make errors even in the complete absence of noise. Overall, increasing N is extremely effective in mitigating random noise. However, it cannot solve the systemic problem of energy splitting due to channel dispersion. Therefore, although a higher N helps reach the system’s maximum possible performance at a lower SNR, it cannot raise that maximum performance ceiling. This ceiling is dictated by the channel dispersion and NRx’s resolution ($N_{\mathrm{int}}$). This leads directly to the practical engineering tradeoff—using a higher N yields better performance, but at the cost of increased acquisition time and higher NRx complexity, which are critical constraints for in vivo nanonetworks.

Figure 12b depicts the average NMSE for the same set of simulation parameters. Increasing N unambiguously improves the timing accuracy, lowering the NMSE across the entire operational SNR range. Again, this improvement stems directly from the processing gain provided by averaging over N repetitions. In addition, as N increases, the entire curve—including the hump—shifts to the left. As aforementioned, the hump represents the critical SNR region where the NRx transitions from random guessing to making frequent near-miss errors. Because a higher N provides an SNR boost, the system reaches this critical transition point at a lower SNR input. For instance, the $N=15$-based system, with its pronounced processing gain, starts to reliably lock onto the signal at a much lower input power level than the $N=5$-based system; thus, its threshold region is shifted to the left.

7. Conclusions

This study addressed the critical challenge of timing synchronization in iWNSNs operating over a highly dispersive intravascular optical channel. In particular, we proposed and evaluated a lightweight synchronization scheme based on repetitive preambles and energy detection with a finite number of integrators. Through detailed simulations, we demonstrated that distance substantially affects the synchronization performance. In addition, we demonstrated that increasing the preamble repetition factor improves the synchronization reliability and accuracy by leveraging the averaging gain. However, the performance saturates due to a fundamental dispersion floor, independent of noise, caused by pulse broadening in the biological medium. Notably, the findings of this study reveal that lower-resolution NRxs with fewer integrators outperform their high-resolution counterparts in dispersive channels. This counterintuitive result is attributed to the energy-splitting effect, where the narrow integrator windows fragment the dispersed pulse energy, increasing the synchronization errors. Meanwhile, wider integrators collect energy more reliably, yielding better performance. These insights highlight a critical tradeoff between temporal resolution and robustness, emphasizing the need for channel-aware NRx design in nanoscale biomedical systems. Overall, this work advances the understanding of synchronization in in vivo nanocommunications and offers practical design guidelines for future implementations of OiWNSNs.