A miniaturized and low-energy subcutaneous optical telemetry module for neurotechnology

Objective. This study presents a proof-of-concept optical telemetry module that leverages a single light-emitting diode (LED) to transmit data at a high bit rate while consuming low power and occupying a small area. Our experiments showed that we could achieve 108 Mbit s−1 and 54 Mbit s−1 back telemetry data rates for tissue thicknesses of 3 mm and 8 mm, respectively. Approach. The proposed module is designed to be powered by near-field coupling and achieve bidirectional communication by low-speed downlink from near-field communication. It aims to minimize the size of the implant while providing reliable transmission that meets the requirements of high-speed wireless communication from a multi-electrode array neurotechnology implant outside the body. Results. The power consumption of the module is 1.57 mW, including the power consumption of related circuits, resulting in an efficiency of 14.5 pJ bit−1, at a tissue thickness of 3 mm and a data rate of 108 Mbit. The use of an optical lens, combined with tissue scattering effect and optimized emission angle, makes the module robust to misalignments of up to ±5 mm and ±15° between the implantable and external units. The LED in the implantable unit is only 0.98 × 0.98 × 0.6 mm3, and the testing module is composed of discrete components and laboratory instruments. Significance. This work aims to show how it is possible to strike a balance between a small, reliable, and high-bit-rate data uplink between a neural implant and its proximal, wirelessly connected external unit. This optical telemetry module has the potential to be integrated into a significantly miniaturized system through an application-specific integrated circuit and can support up to 1000 channels of neural recordings, each sampled at 9 kSps with a 12-bit readout resolution.


Introduction
Uncovering the neurophysiology mechanism with the electrophysiology approaches has pushed the development of neuro signal sensor implants with higher spatial and temporal resolution [1]. With the advancement of integrated circuits and materials, the state-of-the-art neuro signal sensor implants for animal research have 768 electrodes in a 750 × 720 µm 2 area and can record 10 240 sites from two probes [2]. The sensors for human clinical studies now include two 96-channels in less than 36 mm 2 [3]. Some independent company, such as Neuralink, is developing systems has more than 1000 channels for human [4]. The demand for a better understanding of neural activities and improving the performance of decoding neural signals have pushed the analog-to-digital converter (ADC) sampling rate to over 30 kHz for each recording channel with 10-16-bit resolution [5]. With those high-performance neural signal sensors, more and more brain-computer interfaces (BCIs) have achieved promising results, such as accurately controlling a robotic arm, moving a computer cursor, and typing at a speed close to handwriting [6][7][8][9].
BCI devices or neural signal recording systems comprise signal collecting, processing, and executing units. However, limitations in power and size have prevented the development of stand-alone devices with the desired human functions. These systems are currently divided into internal and external units. The internal unit, which is an implant or a set of implants located near the sensing or stimulation site, should be miniaturized to minimize invasiveness. It contains only electrodes, lead wires, electronic hermetic housing, and signal acquisition circuits. On the other hand, the external unit functions as a power source, accommodating components that exceed the volume or power constraints of the implant or serving as a relay to transmit neural activities to another processing unit. An interface between the internal and external units is required to deliver data and energy. In some advanced BCIs, the standard setup (mainly research-driven) uses wire as the internal and external interface [9,10]. The reason is that the highperformance multichannel neural signal sensors have pushed the data streaming requirement to tens of megabits per second for raw data. The wired solutions provide the simplest way to meet the design requirements of high data rate, small size, adequate power supply, and safety concerns. Still, the wired system significantly limited the clinical applications and the diversity and duration of research experiments. The wired systems also increase the risk of device failure and tissue infection.
Currently, we can see a high degree of engineering efforts to achieve wireless transcutaneous systems to transfer high-rate data [11][12][13]. The medium that can establish the transcutaneous data and energy transfer includes ultrasound, magnetic field, electric field, electromagnetic field, and optical links.
Ultrasound channels offer one of the deepest penetrations into soft tissue, making them an attractive option for deep neural implants. The transducer for the acoustic link is typically small, with reported dimensions of submillimeter and less than half a millimeter cube (mm 3 ) in recent literature [14,15]. The power delivery of the acoustic channel has an efficiency of 1.93%-0.23% [14,[16][17][18], and the data link for the acoustic link typically uses a backscatter approach to maintain the low power consumption in the internal part. The resonate frequency of the piezoelectric material is usually <2 MHz [16,17,19,20], so the optimal frequency for the acoustic channels is often below 5 MHz [21]. However, due to the backscatter approach used for data telemetry links, implementing modulation schemes like orthogonal frequency-division multiplexing (OFDM) is often challenging. As a result, ultrasound channels can only typically provide a few hundred kbit s −1 telemetry data links.
Inductive links use alternating magnetic fields through coils to transmit energy and data. The inductive link offers high power transfer efficiency when the distance between the source and receiver is less than 30 mm [22]. A reported efficiency of 95% is achievable when the distance is 10 mm [23]. Inductive links typically operate at a frequency below 20 MHz to maintain a balance between the transmitter's efficiency and the efficiency between the transmitter and receiver. These links can provide half-duplex bidirectional communication, and commercially available products report an 800 kbit s −1 data rate.
The capacitive link utilizes the tissue as a dielectric medium to form a capacitor. It builds the path to transfer data and power between tissues using a pair of capacitor plates between tissues [21]. The advantage of capacitive link for data and power telemetry includes the high-frequency pass character and the confined area of the energy field [24]. When using a capacitive link to transfer data and power through tissue, the electric field only impacts the tissue between the electrodes and does not broadcast widely like an electromagnetic field [25]. This character also enables the multichannel capacitive link to be built on the same implant to extend the bandwidth. The plates for capacitive link range from 5 × 5 mm 2 to 40 × 40 mm 2 and the carrier frequency ranges from 0.2 to 20 MHz [26][27][28][29][30][31]. The drawback of the capacitive link includes the potential damage to the living tissue caused by the electric field in a small area and the limitation of the miniaturization ability [30]. Another drawback of the capacitive link is the need for close contact of the plates on the tissue surface, which adds a challenge to applying a capacitive link at a site where the tissue surface, or contact in general, is not flat (e.g. hairs) [30].
From above, the most popular approach is the electromagnetic field, as it can easily achieve power delivery and have bi-directional data at the same time. There are two challenges when using an electromagnetic field to send high bandwidth data through tissue. One is that the living human tissue consists of a large among of water. A large amount of skin tissue is conductive, meaning the absorption rate increases exponentially with frequency. A large amount of energy will be absorbed by tissue when the radio frequency is over 2 GHz [32,33]. So, when carrying on high bandwidth data through tissue using electromagnetic, the human tissue becomes a questionable choice of the communication channel. Another challenge is that when the electromagnetic frequency increases, the analog radio frequency frontend becomes a power-hungry component and consumes more power than the neural signal recording sensor. Apart from the limitation originating from the physical property, another issue with RF transmission is the environment's interference, as many devices may operate at the same frequency that the implants are proposed to use.
Apart from optimizing the transmission channel to meet the requirement of uplink data telemetry of recorded neural signal, we can see a significant degree of efforts published each year to reduce the data rate by enabling more local data processing in the implant [34]. The popular solution includes spike thresholding, which only sends spike count over a certain threshold; another example is compressive sensing which adaptively compresses data by event, which turns the raw signal into a set of featured spikes [35,36]. The spike-related approaches have significantly lowered the high bandwidth requirement of the telemetry data link. The spike signal meets some targeted applications very well. However, transmitting a highfidelity signal is still needed for many applications such as brain disease monitoring, research on BCIs algorithms, and neural electrophysiological research.
The optical link is a promising solution for transmitting high-fidelity neural signal from high channel density sensors and has been explored by researchers in recent years [37][38][39]. The advantage of optical links includes small transducer size (relative to inductive and capacitive links), high bandwidth, multiple modulation approaches, high energy efficiency, magnetic resonance imaging (MRI) compatibility, and robustness against environmental EM noise.
Optical transcutaneous links have already achieved some promising results. One example has achieved a data rate of 300 Mbit s −1 , in which a vertical cavity surface emitting laser (VCSEL) is used as the transducer, and a super-fast photodiode is the receiver [40]. Other examples include modules that are demonstrated in-vivo in mice, where they used microscale inorganic light-emitting diode (LED) as the transducer and a group of photodiodes as the receiver. Benefit from the small size of the transducer, chronic recording of neural dynamics has been achieved in that work, but the maximum data rate in the in-vivo experiment only reached 27 kbit s −1 [41,42]. Hence, a better balance of high data rate, low power consumption, small volume, and robust to misalignment has not yet been demonstrated. Therefore, there is an excellent potential for using LEDs as the transducer to implement optical transcutaneous uplinks as it has a relatively small size and a high wall-plug efficiency.

System design overview
In this work, we present a novel design for an optical telemetry module that employs a single LED and addresses the challenges of high-speed data transfer, low power consumption, and minimal volume. Our module is well-suited for data transmission in multielectrode neural recording implants and is designed to operate subcutaneously to facilitate implant-tosurface data transfer. As this module is intended to be a part of the neural recording implant, we designed the entire system, taking into account power supply, energy harvesting, and usability for both the telemetry module and the recording implant.
The proposed system, as shown in figure 1, comprises an implant and an external unit. The external unit comprises a behind-ear unit and an over-the-head unit. The behind-ear unit houses the The system consists of internal implant, external unit with a behind ear unit. The proposed optical telemetry module is in the internal implant and aims to send high-speed data from the sensor to the external unit. The external unit include receiver and power delivery circuit, and the battery is in the behind ear unit to reduce the weight of the overhead unit. rechargeable battery, power management circuits, and data storage or transmission components. The over-the-head unit, which is smaller and lighter, is positioned over the site where the internal implant is located beneath the skin. This unit includes an optical receiver that retrieves high-bandwidth data from the implant. To demonstrate the concept, we used a coil that employed 13.56 MHz near-field coupling to provide power and less occupied forward control data link (downlink). This setup helped us showcase the potential of our proposed design.
This design utilizes the high efficiency of inductive power delivery and the high data rate of the optical link. Apart from optimizing power delivery efficiency, the extra forward data can be used to exchange control signals and send handshaking signals for the high bandwidth optical communication channel. This link will further enhance the channel stability, simplify the communication protocol and related hardware design, and lower the internal unit's power consumption. The overhead unit can also have a local data processing unit to implement applications, like controlling a brain stimulation device to achieve closedloop brain stimulation.
In figure 2, we present the critical component of our proposed system and demonstrate how the optical telemetry module works with the neural recording implant. In one possible implant configuration, high-density electrodes are positioned on the cortex to collect neural signals, while the analog frontend and ADC are located in a package that replaces a small part of the skull. The optical communication module is placed above the neural signal sensor under the skin tissue, minimizing internal connections. The transducer is a single 940 nm near-infrared InGaN LED, and an application-specific integrated circuit The main parts of the proposed system. Note that in our experiments we considered power harvesting via a conventional near-field antenna system. The power can be delivered also through optical energy harvesting and the device has a potential to achieve bidirectional communication via optical link.
(ASIC) is utilized to encode data and modulate the LED. A lens is positioned on top of the LED to focus the beam with an optimal emitting angle that matches the tissue thickness. A patch coil on a thin, flexible printed circuit is wrapped around the communication module to receive energy from the external coil through inductive link. The low power consumption of the proposed communication module is achieved through the high wall-plug efficiency of the LED and the low interference of the optical channel, which permits us to use a highly sensitive avalanche photodiode (APD) with high gain to recover the faint optical pulses from the internal unit with less concern about noise. With the advantage of the short wavelength of light, a high data rate can be achieved with a simple modulation approach that enables us to simplify the circuit and remove the power-hungry high-frequency analog part, thus further reducing power consumption.

Design and implementation 2.2.1. Design requirement analysis 2.2.1.1. Data rate requirement
The communication module is designed to stream high-fidelity neural signals throughout the skin tissue. Currently, the clinically available neural signal sensor has 100 (Utah array) [43] to 1024 (Neuralink) electrodes [44]. In order to identify a neural spike, both 0-1 mV magnitude local field potential and 0-10 µV extracellular action potential need to be recorded at the same time [45]. As a result, the minimal requirement of the effective number of bits of the ADC is eight-bits [45], which is usually achieved by an ADC with over ten-bits resolution [35,46]. As described above, the data transmission requirement can be calculated as follow: where H 0 is the encoding efficiency.
Take a neural-signal sensor with 100 channels as an example. When the sampling rate is 20 kSps, and the resolution of the ADC is 14 bits. When we use Manchester encoding with an efficiency of 50%, the data rate requirement will be 56 Mbit s −1 to send the raw neural signal out.

Noise analysis
For this proposed optical telemetry module, three main reasons will influence the signal quality. First is the environmental light interference. Compared to the electromagnetic (EM) field, fewer artificial signals work in the open-air optical domain, and the transmission of light has a specific direction that further reduces the chance of interference between different devices. Indoors, the light source is mainly visible (380 nm-700 nm wavelengths) and only have very limited energy in the near-inferred wavelength. However, sunlight covers a vast range of wavelengths, and the power in wavelengths from 900 nm to 1000 nm is much stronger than indoor light, which is the main challenge to this proposed optical telemetry module. As a result, the over-the-head unit also needs to be designed to block the sunlight shining into the internal unit.
The second source of the noise is from the receiver side. To convert the optical signal to an electronic signal that can be processed further, we need a photodiode with high speed and high sensitivity. The light from the internal LED can be feeble, and it needs to detect fast light intensity changes as the optical signal we designed is short period pluses. The photodiode will generate noise as the physic intrinsic. The signal from the photodiode is typically a small signal and needs to be further amplified to restore the information collected from the sensor. In most cases, the signal from the photodiode is a current signal requiring a trans-impedance amplifier (TIA) to turn it into a voltage signal and then send it to one or a few cascades amplifiers to increase voltage level further to help restore the data.
The third source of noise is the tissue impact. When the light travels through the skin, there is reflecting, refraction, and absorption of the light. The reflecting and refraction caused multipath effects generating noise and impacting the optical communication channel. The light wavelength ranging from 350 nm to 2000 nm are widely used in optical communication systems. For transcutaneous application, the distance between transmitter and receiver ranges from 0.5 mm (epidermal only) to over 10 mm (total skin thickness). With the short wavelength of light and the relatively short transmission distance, the multipath can be ignored for transcutaneous optical channels.
The total noise introduced to the optical communication module can be calculated as equation (2),

Power consumption analysis
The power consumption of the uplink data module is the sum of the power consumption of the transducer and the power consumption of the circuit to control and modulate the transducer. The higher the wall-plug efficiency of the transducer indicates the less energy dissipates during the transformation. Currently, LEDs have the highest wall-plug efficiency in generating photons from electrical power, and the integrated circuits that only consist of digital components can operate at GHz with sub-microwatt power consumption. Removing the high-frequency analog circuits in the design will lower the power consumption of the proposed communication modulation module.

Optical channel analysis
The human skin has three layers: epidermis, dermis, and subcutaneous fat. The skin tissue presents as a complex heterogeneous medium to lights [47]. The optical properties of human skin can be characterized by absorption and scattering coefficient [48]. The hemoglobin in the blood and the melanin in the epidermis are the substances that dominate the absorption. The scattering effect changes the direction and polarization of the light. Scattering can happen both on the contacting interface and within a small region where the optical property varies [49].
The main factors that contribute to scattering are filamentous proteins and the fibrous structure of the tissue. The scattering can happen at both a single fibril and a scattering centers as the interlacement of the proteins and bundles [49]. The distribution of the blood, pigments and protein bundles are inhomogeneous and random in the skin and varies over time, which makes the absorption and scattering coefficient change over time [47]. Both in vitro and in vivo studies showed that the lights with a wavelength between 800 nm and 1200 nm have lower absorption and scattering coefficient for the human skin tissue [50][51][52], which is suitable for optical power transfer through the skin and building a power-efficient telemetry link.
To design the optical components for the optical communication module, we did a skin simulation to check the transmitted light power on the skin surface at the receiver side. The light propagation in a tissue can be described using the scalar stationary radiation transfer theory, which is described in equation (3) [47], In equation (3), (⃗ r,⃗ s) is the specific intensity at the point ⃗ r in the given direction ⃗ s. ρ (⃗ s,⃗ s ′ ) is the scattering phase function. dΩ ′ is the unit solid angle about the direction ⃗ s, and µ t is the total attenuation coefficient. A least-squares Gaussian model can fit the distribution and approximate the shape of the power intensity at the receiver side when we assume the skin has an ideal smooth surface, which simplifies the simulation model and helps us analyze the light passthrough skin with different thicknesses. The Gaussian model in the form of equation (4) [37], According to [37], we use an exponential and quadratic random coefficient to represent the Gaussian parameters A and σ, respectively.
In figure 3, Dr is the light source size. For LED, Dr equals the emitting area in the diode.
α is the emitting beam angle that can be controlled by lens design.
Dd is the diameter of the projection light spot, which does not consider the tissue scatter effect.
Ds is the diameter of the light beam with the full width at half of the maximum (FWHM) energy of the Gaussian distribution on the skin surface.
Dn is the diameter of the lens to focalize the light to the photodiode to increase the receiving optical power on the receiver side.
Tn is the thickness of the skin tissue. With equation (3) and the quantitative measure of skin's optical property in [37], we write a Python code (available on the link) to simulate the effect of light passing through skin tissue. Figure 4 shows the simulation result with optical energy distribution on skin surface.
From the simulation, we can find for lights in 800-980 nm wavelength, the optical channel of tissue is dominated by the scattering effect. When tissue thickness is 3 mm, we can still observe the shape of the light emitting source. On the receiver side, the area that has the optical energy is around 90 times larger than the light emitting source size when the light passes the tissue. Compared with the laser source, the optical power distribution on the skin surface is a plateau shape, making it robust to the heterogeneous optical property of the tissue. For laser, the peak power on the receiver side is only in a small hot spot and decreases rapidly from the central point, increasing the misalignment challenges. For laser transmitters, the receiving power will significantly drop when the peak power point is a pigmentation area. Figure 5 shows the relationship of tissue thickness (Tn in figure 3), total optical power, affecting tissue area and light-emitting beam angles (α in figure 3). From the figure, we can find that with thicker tissue, a small emitting angle will have less energy attenuation, and with thin tissue, emitting angle less than 80 • , the total receiving power remains the same, but the collecting area increases linearly. The simulation can help us find the optimal emitting angle for the light emitting source to improve the power efficiency. Here we take 3 mm skin as an example. We can find that when the emitting angle is below 60 • , the total receiving power and optical energy collecting area will be balanced well. Figure 6 is the simulation result of the collected optical energy on the skin surface with different skin thicknesses and diameters of the lens. The solid curve is the receiving power on the photodiode. The dashed line is the FWHM diameter of the light beam on the skin surface. Figure 6 reveals that there has been a sharp rise when the lens diameter increases from 1 mm to a size that close to the spot diameter of the FWHM. With the increasing lens diameter, the attenuation caused by lens optical material overweight the benefit from the increasing diameter, and the collected energy gradually decreases. What can be clearly seen in this figure is when the skin thickness increases, the relative improvement of receiving energy from the help of a lens increases, and with thicker tissue, the amount of collected optical energy is projected to remain steady when the diameter of the lens reaches to a certain point. This trend indicates that a lens with  an optimal diameter that matches the tissue thickness will significantly improve the signal quality, and a bigger lens will have less alignment requirement when the optical source is in a thicker tissue.

Module and circuits design
The system design of the proposed system is presented in figure 7, which displays the block diagram of the internal unit. The internal unit consists of several components, including an analog front end, an ADC, a microcontroller unit (MCU), an Near field communication (NFC) power harvesting and communication module, an encoding unit, a power management unit, a pulse generator, and a dynamic voltage bias circuit. The crystal within the internal unit serves as a clock source, while a frequency multiplier multiplies the base clock for the pulse generator and encoding unit. The bias tracking unit provides a bias current to the LED, ensuring it can generate short period optical pulses with low current digital signals from the pulse generator while maintaining low power consumption. The optimal bias tracking circuit, consisting of two instrumental amplifiers and a low-power digitalto-analog converter (DAC), is designed to provide a dynamic bias voltage that stabilizes the LED's impedance, allowing the electrical pulse from the pulse generator to turn to an optical pulse successfully. This circuit provides a dynamic bias voltage, which keeps the LED's impedance at a constant level, regardless of changes in environmental light and temperature. Figure 8 is the proposed pulse generator's circuit block diagram that only uses digital components to ensure low power consumption. Instead of using plus amplitude, we use pulse density to encode digital logic. With this modified on-off-key modulation, the phase shift will not impact the signal's recovery and allows the phase locker removal.
The proposed pulse generator has five delay units with two different delay times, delay 1 and delay 2. The logic gates compute the data signal and clock signal, then output pluses with varying densities in a single clock circle. Here delay 1 is the output pulse width, and delay 2 equals two times of delay 1. From figure 8, we can find that when the data is logic high, then after the digital computing, the output signal is a double pulse shown as logic 1. When the data is logic low, the output is a single pulse shown as logic 0. When delay 1 ⩽1/4 of the clock signal circle, the signal and clock can be recovered on the receiver side. Here we set the delay 1 ⩽1/5 of the clock circle, so any phase shift of the delay unit will not influence the recovery of the data.
The block diagram of the circuit in the external unit showed in figure 9. A high gain low noise APD is chosen to collect optical signals. The TIA consists of two high-speed operational amplifiers (LTC 6268-10 and ADA4860) in a cascade connection. A booster with a low-side metal-oxide-semiconductor field-effect transistor (MOSFET) switch (TPS55340) is chosen to boost the voltage to provide voltage bias for the APD. The internal switch in the booster is directly connected to an inductor and a set of charge Figure 8. The schematic diagram of the proposed pulse generator for the LED to generate optical spikes. The input of the pulse generator is digital signal from the sensor with corresponding digital clock, and the output is short pulse to drive the LED to generate optical spikes. pump networks to further elevate the output voltage to increase the gain of the APD. After the amplifier, the signal from the APD is sent to two logic units to recover the clock and data signal.
The clock recovery is achieved in two steps. The first step is to recover a trigger signal for the cycle counter. The output of the first step is a periodically triggered signal which matches the optical pulse detected by the APD and works like a clock signal. As there is no phase locker for the pulse generator in the internal unit, the output of the first step only matches the optical pulse cycle but is not a stable clock signal. The duty cycle of the first step output is also not correct for clock synchronize that why a second step circuit is needed to recover the clock. The first step can be implemented with raising and falling edge detection and delay network circuits. The delay time is set to four times of the interval between every first rise and fall edge, which has been detected from the output of the TIA. When the edge detector detects the first rise edge, the output of the first step is set to logic high, and it reminded high until it reaches the delay time. The second step is designed to output a stable clock signal with the recovered data. The clock cycle of the second step output is the interval between every first rise edge that excluded all edges during the delay period, and the pulse width of the second step output is half of the delay time.
The data recovery is achieved by a cycle counter that continues count pulses when the output of first step clock recovery is logic high. When the pulse counter counts two pluses, the output of the data recovery is logic 1, and when the pulse counter result is one, the output is logic 0. The output level remained the same until a new counter cycle started. With the recovered clock signal, the digital logic can be processed further by a microcontroller and converted to a standard digital bus signal, for example, a serial peripheral interface.

LED module and impedance analysis at high frequency
The LEDs has high efficiency in generating optical signal within a small area from 25 µm 2 to around 1 mm 2 [53]. The challenge of LEDs for high-speed communication is the frequency response of LEDs follows the first order system with corresponding bandwidth up to hundreds of MHz [54]. When the frequency of the signal passing to the LED goes high, the parasitic capacitance lowers the LED efficiency and slows down the rising and falling time, significantly lowering the signal quality. Research on high-speed visible light communication systems has tested and modeled the LEDs for efficiency and signal quality improvement [54,55]. From the result, we can find when the bias current passing through a LED is much smaller than the saturation current of the diode, the parasitic capacitance decreases exponentially with the resistance decreasing linearly [54,55]. At the same time, the inductance of the LED remained at the same level, which means a high-power LED working at a low current will have a better efficiency performance at a higher frequency.
In figure 10, R g is the resistance of the signal source to the LED. R b is the bonding wire resistance. L b is the parallel bonding inductance. R s is the serial resistance. C b is the bonding wire and pad capacitance. C sc is the space-charge capacitance in the junction. C d is the diffusion capacitance in the junction. R j is the junction resistance. L e , C e , R e is the inductance, capacitance and resistance components in the Electrostatic discharge (ESD) diode. The impedance of the LED can be calculated as equation (5), The frequency response of the LED communication can be calculated by the following transfer function equation (6): hi is the gain of the photodiode at the receiver side. We measured the impedance of the LED using an impedance spectroscopy device and wrote Python code (available on the link) to estimate the model's parameters and then predict the LED's power consumption when delivering short-period pulses. To simplify the model, the intrinsic capacitance C d + C sc is represented with one parameter C j . Table 1 shows the estimated parameters at different currents. Figure 11 shows the prediction of the LED on high frequency using the estimated parameter. During the testing, we discovered that when there is no bias voltage applied to the LED or when the bias voltage does not generate a forward current over 50 nA, the LED's impedance fluctuates from each measurement. When we send short-period pulses with a low current under this situation, the LED will not generate a stable optical pulse that the APD can detect. As a result, we added a bias tracking circuit in the design to provide a minimal optimal forward current. With the small current bias, the impedance of the LED at high frequency is stable, and low current voltage electrical pulses can be converted to a detectable optical pulse by the LED.

Experiment setup
To evaluate the performance of our design, we conducted tests using a 940 nm wavelength LED, a lens, and a high-frequency arbitrary waveform generator (Keysight P9336A) to implement the circuit of the internal unit. The frontend of the external unit was implemented using discrete components, including an ultra-low-noise and high-gain APD (MTAPD-07-010), a low-noise APD voltage bias circuit, and a highspeed TIA circuit. We 3D printed a housing to hold an optical lens and a long-pass filter to implement the optical parts of the external unit. An oscilloscope equipped with a storage function was used to test the data recovery function and measure data transfer performance. Figure 12(a) depicts the experimental setup used to test the transmission distance and the impact of misalignment between the transmitter and receiver units, which were both mounted on optical stages. Figure 12(b) illustrates how the distance, misalignment, and angle were measured, with the green line representing the distance, the yellow line indicating the misalignment, and the angle between the two red lines representing the misalignment angle. A 3D printed frame was used to hold the tissue and test the data transfer performance with tissue in between, as shown in the sub-photo on the top right corner of figure 12(b). The transmission success judgment was achieved by the waveform matching function in the oscilloscope. In the experiment, we tested the data transfer in the air with and without the lens on the receiver side to verify the lens performance simulation results obtained in the design stage. We used extracted skin, fat, and muscle tissue with varying thickness to test the transmission performance with tissue between the transmitter and receiver. Data transfer experiment protocol is described in figure 13. To confirm the success of the data transfer, we generated a 64-bit random data segment, which we repeated 256 times to extend the data to 2 kB. We encoded the data using the proposed modified on-off-key encoding described in the design section and translated the data to a waveform file. We then uploaded the waveform file to the arbitrary waveform generator to generate periodically repeated pulses according to the data segment. When the arbitrary waveform generator started working, we recorded the waveform from the receiver side with no tissue in between. We exported the waveform data from the oscilloscope and used an edge detection function written in Python to implement the clock recovery and data decoding function described in the design section. If the decoding result matched the input data segment, we confirmed the   data transfer was successful; otherwise, we adjusted the pulse width and density and repeated the process until we obtained a positive outcome. Once the initial data transfer was confirmed, we added misalignment, distance, and tissue to verify if the waveform remained the same pattern with the recorded signal using the built-in waveform pattern matching function of the oscilloscope. If the matching was successful, we confirmed the transmission was successful, and vice versa. As the oscilloscope had limited storage to hold the receiving signal, we fixed the length of the random data segment at 64 bits to minimize the experiment challenge of synchronizing the waveform generator and oscilloscope waveform catch. The data transmission confirmation was done by the Python code that performed circular shift and tried to match the sending 64-bit data and the recovered data. Once the first 64 bits found a match, and the matching could last until the end of the recording, we regarded this as a successful transmission. As a result of the small data segment and the offline data transmission confirmation protocol used in the experiment, we were not able to measure the bit error rate (BER). The oscilloscope's memory could hold 4 Mpts, and the sampling rate was fixed at 5 G samples per second. Under this setting, we could only record the receiving data in 0.4 ms for transmission confirmation. We can estimate the BER by calculation. If the transmission passed confirmation checking, the BER must be lower than 1 data rate×0.4×10 −3 . For example, when the data rate is 108 Mbit s −1 , we can confirm the BER is lower than 2.31 × 10 −5 . Table 2 shows the successful data transfer testing result with different parameters and different thickness of tissue.

Power consumption estimation
The power consumption of the proposed design's internal unit is estimated by combining the transducer power consumption with the circuit power consumption. The transducer power consumption is calculated from our LED modeling and impedance testing. The circuit power consumption includes both the functional circuit power consumption and the power management circuit power consumption. The functional circuit comprises the pulse generator, encoder, and optimal bias tracking circuit. As the bias voltage is intended to generate <1 µA current and the circuit is operating at a frequency <500 Hz, the power consumption of the bias tracking circuit is a The setup and measurement of data transfer distance, misalignment angle and misalignment distance, and the frame to hold the tissue for testing. (c) The skin tissue from pork was used in the tests. The left part is the skin tissue, and the yellow part on the right side is a 3D-printed frame that holds the skin. A ruler shows the thickness of the tissue. (d) The fat tissue from pork was used in the tests. The tissue is held by a 3D printed frame (the grey base behind the tissue) and mounted on the PCB with the LED transmitter to ensure no light leaks from the side. (e) Same setup to test the performance with muscle tissue from pork. (f) Pork skin, fat, and muscle tissues were used in the tests, and were held in place by a 3D-printed frame. The picture shows the three-layer tissue arranged with skin on the left, fat in the middle, and muscle on the right. The muscle side was facing the LED during the experiment to simulate subcutaneous transmission. (g) The test setup with tissue. The left part is the data receiver. The right part is the transmitter with tissue. The tissue is held by the grey frame and mounted on the PCB with the LED transmitter. static value, with the testing result, this circuit consumes 90 µW.
The power consumption of the plus generator circuit and the encoder circuit is a dynamic number related to the transferring data rate. The encoder is a digital data processing circuit, and the power consumption is calculated with standard complementary metal-oxide-semiconductor (CMOS) power consumption as equation (7).
In equation (7) C PD is the power-dissipation capacitance, V CC is the supply voltage. Here we use 1.8 V for the calculation. f I is the input signal frequency, N SW is the number of bits switching, C L is the load capacitance and f O is the output signal frequency, The pulse generator we designed for this module only consist digital logic gate and delay or buffer unit. We estimate the power consumption by SPIC simulation in LTSPICE with TSMC's 350 nm model library under 1.8 V power supply.
We assume the efficiency of the DC-to-DC power management circuits in the internal unit is 80%, which is a reasonable number for a low-power system. The calculation result of the total power consumption of the internal unit under different data transmitting rates is listed in table 3.

Discussion
We compared the system performance with some state-of-the-art wireless communication approaches for bio-signal sensing implants. The result is shown in figure 14. The figure shows that the impulse radioultra wide band (IR-UWB) has the highest data rate, reaching 1.66 Gb s −1 for subcutaneous application [11]. The IR-UWB communication system's power consumption ranges from 6 mW to a few hundred milliwatts [56][57][58]. With the advantage of a high data rate, the power efficiency of IR-UWB technology is still at the top level among other technologies. The challenges remained in IR-UWB technology, including the big antenna size of close to 100 mm 2 , and the misalignment caused stability problems. For neural implants, if the antenna is on the skull, the individual curvature differences will require a custom antenna design for each recipient. Ultrasonic communication modules have the smallest size, lowest power consumption, and the best tissue penetration depth. The challenge with ultrasonic is the low data rate and limited modulation approach as it is a backscatter-based communication [59]. Radio frequency (RF) backscatter communication module also has sub-milliwatt power consumption for the internal unit, and a data rate can achieve 25 Mb s −1 [5]. Highspeed optical links reported in other works use VCSEL as the transducer [38,40,60] and conventional laser driver circuits to drive the laser diodes. The laserbased transducer has higher modulation bandwidth compared to LEDs and has reached a 300 Mbit s −1 data rate [40]. The drawbacks of lasers for implantable applications are the big volume and more complex driver circuits. From the comparison graph, we can find that this LED-based high-speed optical link has balanced both volume, speed, power consumption, and power efficiency very well, which is the optimal communication module for subcutaneous neural signal sensors.

Design trade-offs
The proposed module has balanced both volume, energy efficiency, data rate, and biosafety well, and the data transmission performance stands at the top of current state-of-the-art wireless communication systems for implantable devices. However, the current design and implementation still have some drawbacks. First, in the external unit, we use a high reverse voltage bias APD to detect short-period optical pulse with a very low optical energy. In this design, the bias voltage is 160-200 V, which is a risk to living tissue if  The misalignment is measured as described in figure 12(b), the first number in millimeter is the misalignment distance and the second number in degree is the misalignment angle. b Pulse density % refers to the maximum pulse duty cycle in each clock cycle, which calculated as following equation Pulse density = Pulse duration×Max(numberofper bit) Clock cycle × 100%. the high voltage part is not insulated well. Second, to transfer power into the internal part at high efficiency, we planned to use near field coupling, which includes a coil in the internal unit and will limit the miniaturization capability of the whole system as the coil efficiency drops with decreasing coil size. Thirdly, the LED-based transmitter has the potential to establish an optical downlink since it can detect light with a shorter wavelength than it emits. However, we did not implement bidirectional optical communication in this study because our experiment revealed that the LED's impedance fluctuated when we introduced a modulated external light source, causing the optical pulse to become unstable.

Future work
The optical telemetry module proposed in this work has a great potential to solve the challenge of bandwidth-hungry high-density neural recording implants. Thus, this work only presents a proofof-concept validation. There are still some engineering challenges that have not been solved in this work like the hardware level implementation of the low-power consumption pulse generator, the hardware level implementation of the data and clock signal recovery circuits, and the miniaturization of the whole system.

Conclusion
This paper presents a design of a subdermal optical telemetry module that balances high data rate, high power efficiency, and low volume. By simulating the optical property of the tissue, we optimized the optical design to improve power efficiency and signal quality. By choosing a high-saturation-current near inferred LED and driving it with a low amplitude voltage pulse with an optimal bias current, the LED can generate 1.5 ns short pulses with reasonable high efficiency. The proposed design is implemented with discrete components and tested with animal tissue. The proposed module can achieve a 108 Mbit s −1 data rate with 3 mm tissue and tolerance with misalignment up to 5 mm and ±15 • . The module's power consumption is below 1.57 mw, and the data transmission efficiency is 14.5 pJ per bit. The volume of the transducer in the proposed module is less than 1 mm 3 , which gives the proposed solution an excellent potential for miniaturization and a wide variety of applications. Modeling codes and data for this paper are available via https://dx.doi.org/10.6084/m9. figshare.22699279.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: https:// figshare.com/articles/journal_contribution/Data_ telemetry/22699279.