Broadband physical layer cognitive radio with an integrated photonic processor for blind source separation

The expansion of telecommunications incurs increasingly severe crosstalk and interference, and a physical layer cognitive method, called blind source separation (BSS), can effectively address these issues. BSS requires minimal prior knowledge to recover signals from their mixtures, agnostic to the carrier frequency, signal format, and channel conditions. However, previous electronic implementations did not fulfil this versatility due to the inherently narrow bandwidth of radio-frequency (RF) components, the high energy consumption of digital signal processors (DSP), and their shared weaknesses of low scalability. Here, we report a photonic BSS approach that inherits the advantages of optical devices and fully fulfils its “blindness” aspect. Using a microring weight bank integrated on a photonic chip, we demonstrate energy-efficient, wavelength-division multiplexing (WDM) scalable BSS across 19.2 GHz processing bandwidth. Our system also has a high (9-bit) resolution for signal demixing thanks to a recently developed dithering control method, resulting in higher signal-to-interference ratios (SIR) even for ill-conditioned mixtures.

the existing multiplexing schemes. However, this relies on a complicated software-layer radio-signal identification mechanism susceptible to privacy breaches 14,15 . Substantial signal processing and analysis are required to ascertain whether transmissions are attributable to specific users or others. In situations with many users in wide frequency bands, performing these computations in real time may not be possible. The only feasible way to oversee activity and enforce compliance from a regulatory standpoint may be to record spectral data for offline analysis, which introduces a serious risk to content privacy 16,17 . As soon as information is recorded to disk, its security is compromised. Even if the monitoring operator is deemed benign, it may be unknowingly harbouring malware that can access the content of all the spectrum users.
A physical layer cognitive technique called blind source separation (BSS) 6,18 can extract unknown signals (e.g., a signal of interest and an interferer) from their mixtures with minimal assumptions, as shown in Fig. 1b, c. Operating in the physical layer allows the isolation of unwanted transmissions in the analogue domain, reducing the risk of privacy leakage by eliminating the need to record the transmission content digitally 19 . Such a "blindness" feature is also critically demanded by recovering the scientific signals, for which no prior knowledge can be obtained. Another advantage is the agility in recovering sources with arbitrary characteristics. This means discarding substantial information before digitisation and total obliviousness to the frequency, modulation type, and power ratio. This advantage can only be realised when BSS is performed across a wide frequency range. Conventional BSS implementations by electronics are competent in separating narrow-band and low-frequency signals, such as audio signals 20 , but are challenging to achieve a broadband operation due to the limited bandwidth of RF technology. For example, the spectrum of ultrawideband (UWB) signals 21 covers up to 7.5 GHz, and that of Wi-Fi signals has expanded from 2.4 GHz (802.11) to 6 GHz (802.11ax). Having broadband coverage is challenging with a single RF system, as depicted in Fig. 1. Thus, alternative techniques other than conventional electronic processors are required to effectively process RF signals in next generation wireless systems 22 .
By upconverting to frequencies of hundreds of terahertz, photonic signal processors can deal with broadband information [23][24][25] , where GHz signals are regarded as narrowband. As a result, photonic processing can easily satisfy the demanded processing bandwidth requirements of incoming wireless technologies and comes with low energy consumption that does not scale with the signal frequency. A promising on-chip processor is the microring resonator (MRR) weight bank 26,27 , a bank of tunable filters implemented with tiny circular optical waveguides, which provides energy-efficient tuning 28 and scalable parallel processing through wavelength-division-multiplexing (WDM). Such an RF frontend powered by a photonic processor (Fig. 1b) can share the workload of signal processing with a digital signal processing (DSP) backend while enhancing overall performance. One key factor determining BSS performance is the resolution of the weights (the tuning accuracy of MRRs), which was reported up to 7 bits on MRRs 29,30 . We recently developed a dithering control method 31 that improves the tuning accuracy beyond 9 bits.
Here, we report a photonic implementation for BSS based on the dithering-controlled MRR weight bank. We also demonstrate a fully packaged photonic processor with a silicon photonic chip integrated with the MRR driver and control electronics on a single printed circuit board (PCB). We prove this setup can recover a weak transmitted signal in the presence of broadband jamming noise and successfully test it in real-time on a wireless transceiver system. In terms of performance, our setup fully realises the "blindness" agility by achieving a processing bandwidth of up to 19.2 GHz and signalto-interference ratios (SIR) of more than 40 dB in some cases. Besides, the dithering weight control enables a photonic processor with 9-bit accuracy beyond many electronic counterparts, enhancing the BSS with at least one-half reduced residual error than the setup without the dithering control. This work introduces a functional BSS system capable of operating at broad bandwidths. When included in transceiver circuits, it can help cancel interference signals, with potential implications in next-generation wireless cognitive radio to deal with signals across tens of Gigahertz. It also benefits radio astronomy in detecting unknown weak between electronic and photonic BSS implementation. a Frequency allocation for common bands (from 0.5 to 19 GHz) and example processing bandwidths for the two BSS implementations (photonics and electronics). Science service bands comprise the earth explorer satellite service (EESS) and radio astronomy service (RAS). Bands for civil and military applications include global positioning system (GPS), microwave oven, ultra-wideband (UWB), and standard frequency and time signal service (for the first row); broadcastingsatellite service, radar altimeter, Wi-Fi, and aircraft weather radar (for the second row); 5 G cellular networks and military radar (for the third row). b Photonic BSS system diagram. c Electronic BSS system diagram. In electronic BSS, covering the demanded bandwidth requires a complex switching system that consists of multiple electronic BSS setups (quantity of M) corresponding to distinct frequency regimes. Each one requires N ADCs (N is the number of receivers) and a dedicated DSP with N inputs to perform the multiply-accumulate (MAC) operation. Since ADC and DSP require power in scale with the signal frequency, the total power consumption of the electronic BSS approaches is proportional to N × M × f × ðE ADC + E MAC Þ. In contrast, achieving the same coverage requires only one photonic BSS setup consisting of N electrical-to-optical (E/O) converters with only one ADC and a low-end DSP with a single input. This architecture consumes much less power and is proportional to signals that require more than 30 dB signal-to-noise and distortion ratio (SINAD).

Photonic solution for BSS problem
The BSS problem can be formulated as separating an unknown mixture of unknown independent signals. The instantaneous model of generic mixing in a transmission channel is ½r 1 ,r 2 = H½s 1 ,s 2 , where ðs 1 ,s 2 Þ are the source signals, H is a mixing matrix representing the wireless channel, and ðr 1 ,r 2 Þ are the received signals. In the most general case, the source signals and their mixing matrix are unknown to the receiver. The goal of BSS is to estimate the corresponding demixing matrix, H −1 , and apply it to the received signals to arrive at ½s 0 1 ,s 0 2 = H À1 ½r 1 ,r 2 , where ðs 0 1 ,s 0 2 Þ is the estimated recovery of the source signals. In general, minimal prior assumptions are needed about signal characteristics. For example, s 1 and s 2 can occupy the same frequency band, meaning an implementation based on filtering would fail regardless of any receiver-side analysis. It is assumed that the two sources are statistically independent and that all mixing happened linearly. These assumptions are very realistic and are widely used in the radio community 32 .
For a given mixing matrix H, separating each signal component requires the mixtures to be weighted and summed with weights represented by each column of the inverse matrix H −1 . This operation can be implemented with a set of two MRR weight banks acting as an on-chip signal processor. Retaining the signal of interest and eliminating the other one utilises one of the two columns, which requires only one weight bank. As shown in Fig. 2a, c, the MRR weight bank consists of several microring resonators with slightly different radii; each has a Lorentzian-shaped transmission profile (as shown in Fig. 2c) centred at different wavelengths. Each MRR is equipped with a metal heater to allow thermo-optic displacement of the centre wavelength by varying the current applied 33 . The MRR weight bank independently weights the laser amplitudes of different wavelengths. The sum of all optical power can be obtained by a balanced photodetector (BPD) at the output. Utilising this ability of weighted addition, we develop a photonic BSS algorithm, which follows a pipeline consisting of three steps, including principal component analysis (PCA) 34 , whitening, and (bottom left), which also delivers the power for the whole PCB. e Estimation of weighing accuracy. The 2-MRR weight bank in a was tested to tune the weights represented by each grid. The dithering control yielded the red points, and the grey points were obtained without the dithering. f Errors of all the tested weights in d. A 9.0-bit of precision resulted from the dithering control and 6.7-bit for the control without the dithering. The precision is calculated by the standard deviation of the error. Quantitatively, there are 161 among the total 243 tested points inside the 9-bit bound (the solid circle). independent component analysis (ICA) (See details in ref. 35 ). For carrying out these analyses, an iterative algorithm is preferred because of its simplicity in that only one vector needs to be commanded to the MRR weight bank in each step. Essentially, a constrained Nelder-Mead algorithm 36 is carried out that performs an iterative projection-pursuit of the mixtures to search the optimised weighting vectors. The goal is to find the mixture that outputs a weighted addition (Σw i s i ,w i 2 À1,1 ½ ,i 2 ½1,2, Á Á Á N, N is the number of the mixtures) with maximal variance (the second-order statistic) for PCA and the maximal non-Gaussianity (the fourth-order statistic or kurtosis) for ICA.

Hardware implementation
The hardware realisation of this algorithm appears as a control loop (as shown in Fig. 2a). Apart from the photonic chip, also included are a BPD for electrical-to-optical (E/O) conversion (Discovery semiconductor DSC-R405ER), an analogue-to-digital converter (ADC) for signal digitisation (Tektronix DPO73304SX; sampling rate: 625 MS s −1 −100 GS s −1 ), a computer for statistical analysis and actuating weight commands, and a multi-channel current source for MRR tuning (custom-built as shown in Fig. 2d). The sampling rate of the ADC is set to the minimum of 625 MS s −1 for all the tested signals as the BSS method is agnostic to waveform frequencies, and it is switched to the maximum of 100 GS s −1 for recording resulted waveforms with the highest definition. The dithering control 31 implemented here allows tuning the MRRs with less complicated drivers instead of the sourcemeasurement unit (SMU) 29 . In this setup, the MRR driver is directly integrated into the PCB interposer, packaged close to the photonics chip with a much-reduced footprint and cable management 31 . The signal path starts from the Mach-Zehnder Modulator (MZM) and ends at the scope. The highest supported RF frequencies are determined at up to 20 GHz by the BPD and the transmission profile of the MRRs, providing coverage for many commonly used RF bands. Detailed discussion on the bandwidth of the MRR filtering function can be found in Supplementary Fig. 2. It is also worth noting that most of the signal path is in the optical domain, bringing about broadband and flat response and very low latency, which is estimated to be 15 ns by dividing the total waveguide length (3 m) by the speed of light in the waveguide (c 0 =n≈2 × 10 8 m s −1 ).
The photonic chip in this setup has a 4-channel MRR weight bank with resonance frequencies roughly spaced by 200 GHz. The spectra of the four MRRs (at 25 degrees) are shown in Fig. 2c, with the resonance peaks located at 1551.7, 1553.0, 1554.6, and 1555.7 nm. The waveguide of these MRRs is N-doped which can be efficiently thermaltuned from on to off positions with a power consumption of 10 mW 28 . Since this work recovers source signals from two mixtures, we use two MRRs (the leftmost and rightmost ones). The corresponding lasers (Pure Photonics PPCL500) are tuned to be 1551.5 and 1556 nm, then amplified (Pritel FA-23) and combined into a shared waveguide by a WDM multiplexer (Santec MDM-15-8) before coupling into the MRR weight bank through grating couplers.
The implemented dithering control method overcomes the low accuracy incurred by the high sensitivity of the weight bank. As shown in Fig. 2a, the lasers are modulated with either the received mixtures or pre-defined dithering signals. Each time a set of commanded weights are applied, the RF switch (Mini-Circuits RC-2SPDT-A26; DC − 26.5 GHz) passes the dithering signals into the photonic path, which helps adjust the driving currents of the MRRs until the output weights reach the demanded values. Then, the actual mixtures are switched into the weight bank and processed. The weight accuracy is reflected in the error between the target and actual weights. Usually, we quantify the accuracy in bits, which is calculated as log 2 ð2=ðw actual À w target ÞÞ. Figure 2e, f illustrates the weighting accuracy, showing the resulting weights (red dots) of the two MRRs being examined at the tested values represented by each grid point. The grey dots correspond to the same targeted weight without dithering control. An improvement of over 2 bits (from 6.7 to 9 bits) is observed, enabling the MRR weight bank to have competitive performance with its electronic counterparts.
While our setup included the demonstration of the wireless transceiver system, we also had a versatile control setup that provided flexibility and accuracy in controlling the carrier frequencies and the mixing matrix. In the control setup, the signal mixtures were generated by a high-speed multi-channel arbitrary waveform generator (Keysight N8196A; 92 GS s −1 ) and sent to each MZM directly. The generation of the two baseband signals, the up-conversion, and the signal mixing, are all performed via software tools (Python). The mixed signals are then transmitted to the photonic system.
Theoretical impact of weighting accuracy BSS must be able to deal with mixtures that are difficult to separate. Denoting the jth signal component in the ith mixture as y ij ðtÞ, the signal-to-interference ratio (SIR) 18 is defined as which is the ratio of the signal power (||y ij 0 t ð Þ 2 ||) to the rest interference power (Σ j≠j 0 || y ij t ð Þ 2 ||) of the ith mixture. Given a problem with N mixtures containing N sources to be separated, an often-used merit is the overall SIR, which is the average of the SIR of every mixture (1=N × Σ i SIR i , i = 1,2, Á Á Á N). The SIR captures the accuracy of the system, and it can also be stated as a function of carrier frequency, baseband bandwidth, or other metrics. A higher SIR means better suppression of the interference signals. This metric of SIR can be extended to any mixing H through the ill-condition number, κðHÞ 37 , defined as Eq. (2).
This describes the demixing difficulty calculated by the mixing matrix H. Mixtures with a small ill-condition number are easier to solve. Conversely, problems with a sizeable ill-condition number are challenging and prone to smaller SIR. An ill-conditioned BSS problem typically requires the weighting to represent the inverse matrix accurately.
To prove this, consider a simple case where the mixing matrix is symmetric, such that H = ½ 1,1 À a ½ ,½1 À a,a, a 2 ½0:5, 1, which is often the case when two receiver antennas and the two transmitter sources are symmetrically positioned and have identical power. The inverse of matrix H is given in Eq. (3).
And this can be further normalised to the form of Eq. (4), multiplying ð2a À 1Þ=a.
To introduce the weighting error, Eq. (5) describes the actual matrix of mixtures that is input to the photonic BSS, where d denotes the weight error caused by the inaccurate MRR control.

Demonstration on wireless transceivers
Based on the setup described above, we firstly demonstrated our proposed BSS photonic processor in a wireless transceiver system, which emulates the case where a communication link is deteriorated by nearby RF interference. As shown in Fig. 3i, two antennas (Southwest Antennas 1009-002; 1.7-2.5 GHz) transmit the signal of interest and a broadband jammer mixed over the air with a transmission distance of 0.75 m. Then, the mixtures are received by a 2 × 2 MIMO antenna (Southwest Antennas 1055-368; 1.7-2.5 GHz), with two outputs corresponding to the polarisation of 45-degree slant left and 45-degree slant right. The signals emitted from the transceivers have peak-to-peak voltages of 1 V and received signals are 150 and 140 mV peak-to-peak. The transmitted signal carries a repeating sequence of 200 random bits at a baud rate of 50 MHz with a binary phase-shift keying (BPSK) modulation format and a carrier frequency of 2.1 GHz. The interference is an instantaneous broadband jamming signal generated by adding 10,000 single tones with random phases and has a spectrum from 1.7 to 2.5 GHz, covering the entire bandwidth of the antennas. Thus, extracting the signal of interest is largely ineffective via spectral filtering even if the carrier frequency is known. If doable, the signal-to-noise ratio remained the same with the received mixtures at best. In contrast, photonic BSS can recover the communication link without prior assumptions and suppress the interference noise. Figure 3a-h illustrates the spectrum and the constellation diagram before and after the BSS process. The signal-to-noise ratio has almost a 15 dB improvement (20.8-35.5 dB), accompanied by a twofold increase of the Q value (5.84-12.6) from the constellation. This result demonstrates the effective suppression of nearby interference with high power and broadband coverage, maintaining the transmission quality of the wireless communication link.

Broadband capability
Next, we examined the proposed photonic BSS system under different scenarios, with different signal mixtures enabled by programming the arbitrary waveform generator (AWG). The original two signals are repeating patterns of 16 bits, and are in format of binary phase-shift keying (BPSK; bit pattern = [0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]) and on-off keying (OOK; bit pattern = [0,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0]), respectively. This configuration provided two short data periods that can be easily illustrated and also contributed all the potential bits combinations in their mixtures for a complete examination. Note that our BSS algorithm is based on the kurtosis analysis, independent of the modulation format (see Methods and Supplementary Fig. 1 for details). For consistency, all the experiments shown in the main content were performed on signals in the same digital modulation formats (BPSK or OOK). For reference, we performed an additional experiment showing similar BSS performance on analogue modulated signals (pulsed ultrawideband signal) in Supplementary Fig. 3. Based on this setup, we firstly tested the broadband capability by performing BSS on mixtures of signals from 20 MHz to 19.2 GHz by varying the carrier frequencies, as shown in Fig. 4. The baseband frequencies were also adjusted according to the carrier frequencies, which were 4 MHz for <80 MHz, 16 MHz for 80-480 MHz, 160 MHz for 0.48-1 GHz, 400 MHz for 1-3 GHz, 800 MHz for 3-6 GHz, and 1600 MHz for f carrier ≥ 6:4 GHz. In the spectrum, the transmitted signals are centred close to the carrier frequency with a width (instantaneous bandwidth) of approximately double the baseband. Annotating the two mixtures with M 1 and M 2 and the two sources with S 1 and S 2 , the mixing can be expressed as M 1 = 0:8 × S 1 + 0:2 × S 2 and M 2 = 0:2 × S 1 + 0:8 × S 2 , denoting an illcondition number of 2.26 (according to Eq. (2)). The two mixtures are identical in power, with both the peak-to-peak voltages set to 1 V.
As shown in Fig. 4d, the 27 tested carrier frequencies from 20 MHz to 19.2 GHz show SIR >30 dB. This result proves that our demonstrated photonic BSS system can process RF waveform with a carrier frequency lower than 19.2 GHz and a baseband of up to 1.6 GHz (an instantaneous band of 3.2 GHz). Compared with previous photonic demonstration 35 that dealt with problems of a similar ill-condition number, we obtain almost 55 times broader processing bandwidth (19.2 GHz versus previously 350 MHz centred at 900 MHz) while maintaining a clean signal separation across the entire band (SIR > 30 vs previously SIR≈14). This improvement in error suppression confirms the benefit of the improved dithering control method. Also, based on the Federal Communications Commission (FCC) frequency allocation chart (partly shown in Fig. 1a), this broadband coverage by a single silicon photonic chip translates into the agility of processing multiple commonly used bands. Examples of included bands are cellular (620 MHz-6.425 GHz), Wi-Fi (2.4 GHz, 5-7.125 GHz), military radar (extensive spectral usage above 8.5 GHz), and those for earth explorer satellite and radio astronomy (sparsely spread from 1.4-17.3 GHz). This wide processing bandwidth can also provide full coverage to some challenging bands, such as the ultra-wideband (UWB) services. Since signals remain narrowband at higher frequencies for photonic devices and the state-of-the-art BPD can be 100 GHz or more 38 , this system can easily expand the coverage to other important spectrums like millimetre-wave with just higher speed photodetectors. Due to the shape of the spectral profile (as shown in Fig. 2c), MRR weight banks apply uneven filtering on signals with large instantaneous bands, which could degrade the BSS performance to some extent. Additional discussion and experiments are included in Supplementary  Information, where we show that this BSS system maintains decent performance (SIR ≥ 33 dB) on two ultra-wideband (UWB) signals with a 7.5 GHz wide instantaneous spectral coverage (3.1-10.6 GHz). The practical device footprint on-chip is 0.13 mm × 0.42 mm, including four MRRs and the waveguide routing, which slowly scales up linearly with the number of sources.

Test on ill-conditioned mixing
Last, we investigated the performance of the proposed photonic BSS system in solving problems with different ill-condition numbers, which is to justify the significance of the improved weighting accuracy. Here, we fixed the carrier frequency at 1 GHz. The mixing matrix is of a symmetric form H = ½½a, 1 À a,½1 À a,a, where a is varied from 0.1 to 0.45, resulting in ill-condition numbers ranging from 2.05 to 10.1. Figure 5 shows the SIR of the mixtures obtained from the same setup but with the dithering control (compared to the previous control method without the dithering). Even in the presence of similar experimental noise levels, lower SIR is always obtained when not using dithering control. Conversely, the dithering controlled setup maintained constantly high SIR such that the influence of ill-conditioning was less distinguishable. The average SIR is above 35 dB for all tested cases, which generally shows around 20 dB improvement compared to the previous control method (the orange curve in Fig. 5), as expected in the analysis above. This improvement confirms the significance of accurate weight control for MRR-based applications, such as the BSS in this paper.

Discussion
In summary, we explored a physical layer cognitive radio solution based on BSS performed on a dithering-controlled silicon MRR weight bank. This solution is a complete RF frontend with a photonic signal processor that can do intelligent learning through the fully programmable and integrated electronic-photonic system. This setup has a large processing bandwidth of up to 19.2 GHz that can fully demonstrate the capability of the BSS technique. In addition, the high SIR observed for all the frequencies and ill-conditioned problems, together with an example of a wireless transceiver system, confirms the benefits of real-world applications brought by the improved MRR control method. Given the increasing carrier frequencies in the next generation of wireless communications technologies, the superior performance of this photonic approach illustrates the readiness to replace pure-electrical RF implementations, effectively addressing the incoming challenges, including bandwidth limitations, energy efficiency, and latency.
With the availability of higher speed modulators 39 and photodetectors 38 on the silicon platform, as well as the maturity of packaging, including photonic wire bonding 40 , laser integration 41 , and monolithic cointegration of complementary metal-oxide-semiconductor (CMOS) and silicon photonics 42 , this proposed photonic BSS can have future implementations with higher integration and broader bandwidth. With these, we envision a standalone BSS device of a small form factor that is field-deployable for various applications, including interference cancellation in autonomous vehicles and aviation.

Photonic BSS algorithm
The photonic BSS algorithm follows a pipeline of two steps, including principal component analysis (PCA) and independent component analysis (ICA). Firstly, PCA is to find the principal components (PC) from the received mixtures and construct a whitening matrix. In PCA, we use the MRR weight bank to perform a weighted addition of the received mixtures. Regarding all the applied weights as a vector, the PCA is to find the vector that the corresponding output weighted addition has the maximal possible variance. Finding the PC vectors is through the constrained Nelder-Mead (NM) method 43 . Starting from a random vector, the NM method iteratively tries new vectors and updates the old one if the new vector results in a larger variance. The new vectors are generated by manoeuvring the old ones in several different ways, including reflection, expansion, shrinking, etc. Usually, the search converges within 20 steps and takes no more than 5 minutes. Denoting this founded PC as the first PC, the vector  perpendicular to the first PC should associate with the minimum variance and is called the second PC. So, finding the first one can easily derive the other by a π=2 shift. With this, a whitening matrix can be constructed using the two PCs and their associated variances. Secondly, the ICA step follows a similar search procedure and finds the vector (denoted as the first independent component (IC)) corresponding to the maximal kurtosis. Based on the central limit theory, the mixture of two uncorrelated signals is more Gaussian-like than any original signals. The kurtosis is a metric describing the non-Gaussianity. Thus, the vector obtained by ICA is exactly one of the correct demixing weights that can recover the one original signal from the mixtures. Finally, using the first IC and the whitening matrix obtained in the PCA step, the second IC can be directly calculated and used to recover the second original signal. This BSS pipeline does not require explicit waveform digitisation but only the second-order and fourth-order statistics (variance and kurtosis) of weighted addition output, unlike conventional BSS solutions such as FastICA. This feature permits a low-cost ADC and DSP working at the sub-Nyquist sampling regime, generally more applicable to broadband BSS. Detailed pseudo codes regarding the algorithm mentioned above can be found in our previous works 34,44 .

Fully packaged photonic processor
We fully packaged the silicon photonic chip with its driver and control circuitry in the same interposer PCB in our experimental setup, as shown in Fig. 2d. This integration benefits a simplified lab setup, lower power consumption (<100 mW), and neat connectivity that a single USB cable handles both the digital interface and the power delivery. In terms of power management, the 5 V input (from the USB cable) generates isolated and low-noise power rails by several dedicated power management chips (Analog Devices LT1533CS and LT3042). These rails power up the precision current sources (Analog Devices LTC2662-16; 16-bit), which drive the MRRs on the photonic chip. The digital interface between the current source and the controller (Sparkfun Arduino Pro Micro) is built on the serial peripheral interface (SPI) protocol and isolated by a dedicated chip (Analog device ADUM4151). This fully isolated MRR driving circuity helps with noise suppression. The host computer commands the weights through serial communication via the USB cable. The onboard controller phrases the received command and talks to the current sources to adjust the current of each microring.

Device fabrication
The silicon photonic chip was fabricated on a silicon-on-insulator wafer with a silicon thickness of 220 nm and a buried oxide thickness of 2 µm. The waveguide is 500 nm wide. The weight bank consists of four MRRs (radius around r = 22 μm) coupled with two bus waveguides in an add/drop configuration, and two among the four were used in the experiments. A slight difference (Δr = 0:32 μm) was introduced in the ring radii to avoid resonance collision. The gap between the ring and bus waveguide is 200 nm, yielding a Q factor of about 6000. Circular metal heaters were built on top of each MRR for thermally weight tuning. Metal vias and traces were deposited to connect the heater contacts of the MRR weight bank to electrical metal pads.

Data availability
The source data generated in this study have been deposited in the Figshare database under accession code https://doi.org/10.6084/m9. figshare.21670880. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/.