Over the past few years, a dramatic increase in data traffic within communication networks has been driven by the rapid development of emerging services, such as big data, cloud computing, Internet of Things (IoT), artificial intelligence (AI), and extended reality (XR)^[1–3]. This requires data centers (DCs) to support high-speed processing of large amounts of data, which further brings challenges to data center interconnects (DCIs)^[4]. Traditional electrical interconnects based on copper cables have drawbacks, such as short connection distances, low fan-out densities, high power consumption, and significant thermal effects^[5]. As a result, optical interconnects are attracting increasing attention to achieve high-speed DCIs. Conventional fiber-based optical interconnects often encounter installation and operational difficulties because of cabling complexity problems, which leads to several issues, including prolonged installation times, dust accumulation and loss at connectors, excessive power consumption, oversubscription, limited scalability, micro-bending, fiber breakage, and traffic offload burden^[6,7]. Therefore, optical wireless communication (OWC) is considered an efficient approach to tackling the above issues. Compared with other OWC technologies, free-space optics (FSO) provides advantages, such as low cost, high capacity, license-free, high security, compact antenna size, and tolerance to interference and multi-path fading^[6,7].

Visible light communication (VLC) has become a research hotspot during the last ten years, which inherits the advantages of FSO^[8]. In the early stage of research, VLC systems are dominated by communications based on light-emitting diodes (LEDs). However, the system data rates are restricted by the inherent modulation bandwidth of the LEDs. Recently, laser diode (LD)-based VLC, which is also known as visible light laser communication (VLLC), is gaining attention to improve the speed^[8]. Compared with traditional infrared LDs, visible LDs have a smaller Auger recombination due to higher Auger activation energy^[9–11], which leads to higher thermal stability^[12]. In addition, one benefit of using short wavelength visible light for chip-to-chip optical interconnects is that good performance can be achieved with integrated photodetectors or trans-impedance amplifiers (TIAs) in silicon. For example, the absorption length of blue light is short in silicon, which enables the photodetector structures to have very low capacitance per unit area. The reduced capacitance can facilitate high gain in the TIA and low power consumption and thus decrease packaging cost^[13]. Wavelength division multiplexing (WDM) has been demonstrated as an efficient way to increase the data rates for VLLC systems, which proves that WDM-based VLLC has the potential to implement highly parallel optical interconnects to achieve high capacity and wide data links for chip-to-chip optical interconnect^[14]. Considering the above advantages, it is reasonable to regard WDM-based VLLC as a candidate solution for optical interconnects, especially for short-distance applications.

Figure 1 shows the recent representative research advances for VLLC systems^[15–32], which contain systems based on single wavelength, multiple-input multiple-output (MIMO), and WDM. Over the past decade, VLLC systems have primarily focused on single-wavelength point-to-point communication, achieving speeds from 1 to 10 Gbps with transmission distances concentrated in scenarios within 10 m. In the past two years, there has been a shift toward higher-speed, longer-distance, and larger-capacity VLLC systems. In 2016, the Industrial Technology Research Institute achieved 11.1 Gbps communication over a short distance of 1.2 m using a 682 nm LD^[15]. In our previous work, we implemented speeds of 6 and 11.2 Gbps over up to 100 m using blue and green LDs in 2021 and 2023, respectively^[22,25].

To further enhance the capacity and spectral efficiency of VLLC systems, various studies have investigated MIMO and WDM technologies in VLLC. In 2023, Guru Nanak Dev University realized a 500-m MIMO VLLC system using red, green, and blue (RGB) LDs and increased the transmission rate to 60 Gbps^[26]. In 2024, Cambridge University achieved an indoor communication rate of 105.36 Gbps using a 10-wavelength laser module^[27]. In the same year, we developed a multi-wavelength VLLC prototype and successively achieved ultra-high-speed communication systems of 113^[28], 519.21^[31], and 534.51 Gbps^[33]. However, the free space distance of the beyond 500 Gbps record is only 17 cm, which severely restricts the application scenarios of this system in optical interconnects. Additionally, a quasi-balanced detection was proposed in Ref. [34], which can be applied to improve the sensitivity of the receiver by 3 dB. Nevertheless, the effective data rate is reduced by half due to the opposite symbols in the same block.

In this Letter, to the best of our knowledge, for the first time we propose to apply a novel differential pilot coding (DPC) scheme to achieve a high-speed VLLC system, which can improve system performance by supporting precise channel estimation and compensation for linear impairments without halving the effective data rate. A data rate of 601.46 Gbps with a constellation size of up to 1024QAM over a 1 m multimode fiber (MMF)-1 m FSO-1 m MMF link is successfully achieved based on a 50-channel WDM VLLC system utilizing DPC. To the best of our knowledge, this is the highest data rate and constellation size ever the reported for a WDM VLLC system, which validates that VLLC is a promising solution for implementing high-capacity and cost-effective optical interconnects.

Discrete multitone (DMT) modulation is chosen to be utilized in this VLLC system. The transmitting QAM symbol of the kth subchannel in the mth block is denoted as xk,m (where k=0,1,…,N−1,m=1,2,…,M). Here, N is the number of subchannels, and M is the number of data blocks. To ensure that the generated waveform data is real, the QAM symbols are conjugate-expanded as follows: $$\begin{gathered} xk,m=x2N−k−1,m*, \\ k=0,1,…,N−1,m=1,2,…,M. \end{gathered}$$(1)

Subsequently, a 2N-point inverse discrete Fourier transform (IDFT) is applied to the expanded symbols, $$\begin{gathered} sm(n)=∑k=02N−1xk,mej2π2Nkn=∑k=02N−1xk,mejπknN, \\ n=0,1,…,2N−1, \end{gathered}$$(2)where sm(n) is the nth time-domain sample of the mth block. It is worth noting that some blocks of symbols are designated as the pilot for DPC, which is used to estimate and compensate for signal degradation caused by the VLLC channel. For each pilot block, a corresponding opposite pilot block is appended. An example is provided in Fig. 2, the inset (i), i.e., an opposite pilot block −xk,1 is added after the positive pilot block xk,1.

After digital-to-analog conversion, the transmitting pilot signal s(t) is generated to drive the lasers, which includes two opposite parts, s+(t)=∑k=02N−1xk,mej2πfkt,(3)s−(t)=∑k=02N−1(−xk,m)ej2πfkt=−∑k=02N−1xk,mej2πfkt,(4)where fk denotes the frequency of the kth subcarrier and xk,m denotes the symbols in the pilot. It is noted that the maximum value of m is M′ here, where M′ represents the number of pilot blocks.

The corresponding positive and negative pilot signals modulated onto the laser light through a bias-tee can be expressed as w+(t)=(V0−V1)ej2πfct+αej2πfcts+(t),(5)w−(t)=(V0−V1)ej2πfct+αej2πfcts−(t),(6)where fc represents the optical carrier frequency, V0 and V1 denote the bias voltage and reverse voltage of the laser, respectively, and α corresponds to the ratio of the DMT signal amplitude to the main carrier. After passing through the VLLC channel, the received pilot signal can be expressed as $$\begin{gathered} r+(t)=(V0−V1)ej[2π(fc+Δf)t+ϕ(t)] \\ +αej[2π(fc+Δf)t+ϕ(t)]s+(t)+n+(t), \end{gathered}$$(7)$$\begin{gathered} r−(t)=(V0−V1)ej[2π(fc+Δf)t+ϕ(t)] \\ +αej[2π(fc+Δf)t+ϕ(t)]s−(t)+n−(t), \end{gathered}$$(8)where Δf is the frequency deviation, ϕ(t) is the phase noise, and n+(t) and n−(t) represent the additive white Gaussian noises (AWGNs). After square-law detection by the photodetector (PD), the detected signal can be expressed as $$\begin{gathered} I+(t)=|r+(t)|2+nr+(t)=r+(t)·r+*(t)+nr+(t) \\ =Is+Ib+Inl+In+, \end{gathered}$$(9)$$\begin{gathered} I−(t)=|r−(t)|2+nr−(t)=r−(t)·r−*(t)+nr−(t) \\ =Is+Ib+Inl+In−, \end{gathered}$$(10)where Is=2α(V0−V1)s+(t),(11)Ib=|V0−V1|2,(12)Inl=α2s+2(t),(13)$$\begin{gathered} In+=2(V0−V1)Re{e−j[2π(fc+Δf)t+ϕ(t)]n+(t)} \\ +2α⁢Re{e−j[2π(fc+Δf)t+ϕ(t)]s+(t)n+(t)}+n+2(t)+nr+(t), \end{gathered}$$(14)$$\begin{gathered} In−=2(V0−V1)Re{e−j[2π(fc+Δf)t+ϕ(t)]n−(t)} \\ −2α⁢Re{e−j[2π(fc+Δf)t+ϕ(t)]s+(t)n−(t)}+n−2(t)+nr−(t). \end{gathered}$$(15)Here, nr+(t) and nr−(t) represent the receiver noises, Is corresponds to the transmitting signal s+(t), Ib is the DC component, Inl denotes the signal-to-signal beating interference (SSBI), and In+ and In− account for the inference related to the noise. The results of the differential pilot decoding (DPD) is given by I+(t)−I−(t)=2Is+In+−In−.(16)

Therefore, the DC component and SSBI of the receiving pilot signal are eliminated, which leads to more accurate channel estimation.

As shown in Fig. 2, the positive receiving pilot symbol of the kth subchannel in the mth block is denoted as yk,m, and the corresponding negatively received pilot symbol is −yk,m. After DPD, the final receiving pilot symbol is yk,m′, which is obtained through the 2N-point discrete Fourier transform (DFT) of I+(t)−I−(t). Therefore, the estimated channel frequency response can be expressed as HEST=y′x.(17)

Accurate channel estimation is crucial for subsequent zero-forcing equalization. Utilizing DPC can eliminate the impact of SSBI and DC effect on the channel estimation, which results in a more precise channel estimation and compensation for linear impairments, and further improves the system performance.

Figure 3 illustrates the experimental setup of the 50-channel WDM VLLC system that employs DPC and adaptive bit-power-loading DMT modulation. This system comprises three parts, including a transmitter, a VLLC channel, and a receiver. The digital signal processing (DSP) at both the transmitter (TX) and receiver (RX) is conducted by offline MATLAB programs.

The transmitted bit-power-loading DMT signal generated by an offline MATLAB program is fed into an arbitrary waveform generator (AWG, M8190A, Keysight) to produce an analog electrical signal output. Then, the signal is input into the transmitter module, which is an integration of five 4U chassis, and each chassis is a 10-λ transmitter unit. Thus, there are 50 channels in total. Each 10-λ transmitter unit is equipped with hardware pre-equalizers, amplifiers, adjustable DC power supply devices, bias tees (RCBT-63+, mini-circuits), lasers coupled with multimode fibers (MMF, OM3, 50 µm core diameter), micro lenses, and thermoelectric cooler (TEC) modules. The TEC modules are applied to achieve precise temperature control for the lasers. The lasers are coupled to 1 m MMFs through microlenses. GRIN lenses are employed between the MMFs and free space to achieve 50 parallel beams in free space to reduce inter-channel crosstalk. After 1-m free-space transmission, the optical signals are guided to an array of 50 PDs (DET025AFC, Thorlabs) via 1 m MMFs (105 µm core diameter) at the receiver. Subsequently, the detected signal is sampled by an oscilloscope (OSC, MSO9404A) for offline DSP. It is noted that the nonlinearity caused by the MMFs is not significant in this system due to the large effective area and parallel usage of multiple MMFs. The primary source of nonlinearity in this system arises from the photon-to-electron conversion during internal modulation and direct detection, for example, the nonlinearity of the electro-optical characteristics of the lasers and the PDs. In addition, high driving currents are required to drive the lasers, which may also cause nonlinearity.

Figure 4 shows the spectra of the 50 lasers employed in this system. The light of the lasers distributes on the visible spectrum. It is noted that only 34 unique wavelengths are utilized for the 50 lasers. The reused wavelengths include 637.536, 637.658, 637.903, 638.147, 638.757, and 638.879 nm. The number of red lasers is the largest, which is 25 out of 34, with wavelengths ranging around 690, 660–670, and 635–645 nm. Red lasers are favored because of their lower operation voltage and power consumption due to their intrinsic AlGaInP material systems. The remaining lasers adopt InGaN/GaN material systems to emit short wavelength visible light from 405 to 520 nm to ease the crowdedness of the red spectrum and increase the total capacity of the system. Therefore, the employed lasers cover the entire visible light spectrum, with wavelengths ranging from 405 to 690 nm, except for the region between 520 and 635 nm. This is because thus far it has been extremely challenging to fabricate efficient yellow lasers using InGaN/GaN materials.

To generate an adaptive bit-power-loading DMT signal, a QPSK DMT test signal is transmitted at first to estimate the signal-to-noise ratio (SNR) distribution of each subcarrier. The bit number for each subcarrier is allocated utilizing the Levin–Campello (LC) algorithm. Then, the input data is mapped to the QAM symbols of the corresponding modulation order based on the bit number allocation for 512 subcarriers. After the signal is combined with its conjugation, DPC is carried out with a pilot block number of 6. Both the signal and the differential pilot are up-sampled by a factor of 4 and transformed using inverse fast Fourier transform (IFFT). A cyclic prefix (CP) of 16 samples is added to mitigate intersymbol interference (ISI). During the offline DSP at the receiver side, DPD is performed after removing the CP, down-sampling, and fast Fourier transform (FFT). Subsequently, channel estimation and zero-forcing equalization are applied. Finally, QAM de-mapping is performed according to the modulation order of each subcarrier, and the recovered bit sequence is used for bit-error-rate (BER) calculation.

Figure 5 shows the achievable information rates (AIRs) of three wavelengths of lasers as a function of the bias current and the output peak-to-peak voltage (Vpp) of the AWG with a fixed operational bandwidth of 2 GHz. Figures 5(a), 5(b), and 5(c) represent the results for the three wavelengths, including 638.757 (red), 486.238 (blue), and 520.679 nm (green), respectively. The results for all three wavelengths exhibit a similar trend, that is, when the Vpp is held constant, the AIR initially increases and then decreases as the bias current increases. Similarly, when the bias current is fixed, the AIR increases and then decreases as the Vpp increases. The reason for this phenomenon is that when either the Vpp or the bias current is too low, the optical power is insufficient, causing the system to be primarily limited by noise. In contrast, when Vpp or bias current is too high, the nonlinearity of the system becomes significant, leading to a decline in transmission quality. The maximum achievable rates for the red, blue, and green wavelengths are 15.66, 12.74, and 11.72 Gbps, respectively. The optimal working points are 0.5 V Vpp and 90 mA current for the red wavelength, 0.5 V Vpp and 70 mA current for the blue wavelength, and 0.5 V Vpp and 100 mA current for the green wavelength.

The AIR performance versus different bias currents with and without DPC is presented in Fig. 6. The signal Vpps are set to the optimal values corresponding to the laser wavelengths. According to the results, the overall trends remain similar regardless of the employment of DPC. At first, the achievable AIRs increase as the bias current increases due to higher optical power, and after the optimal point, the AIRs decrease with further increases in bias current because of higher nonlinearity. Applying DPC does not impact the optimal bias current for each wavelength. For all three wavelengths, employing DPC can improve the achievable AIR. For red, blue, and green wavelengths, the improvements at their individual optimal bias currents are 1.83, 1.22, and 1.49 Gbps, respectively.

Figure 7 shows the estimated channel frequency response comparison with and without DPC. The amplitude of the estimated channel estimation frequency response with DPC is higher than that without DPC because the received pilot signal becomes larger after differential decoding. However, the difference decreases as the frequency increases. This phenomenon can be further explained based on the difference ratio. According to Eq. (16), the difference ratio of the channel frequency response between using DPC and not using DPC should be 2 in an ideal scenario without any noise. In the low frequency range, the proportion of the pilot signal is larger. Thus, the ratio is closer to 2. In the high-frequency range, the ratio tends to decrease due to greater noise interference. Since the subsequent zero-forcing equalization is applied based on the estimated channel frequency response, it is obvious that the compensation of liner impairments for low and high frequency components is different due to different ratios. The compensation after using DPC is more accurate because the influences of SSBI and DC effect on the channel estimation are erased.

Figure 8 illustrates the bit allocation schemes for three typical wavelengths operating at the corresponding optimal points. The modulation order of each subcarrier is determined based on the SNR estimation results, where higher SNR results in a higher modulation order. As shown in Fig. 8, the average bit number is 7.83, 6.37, and 5.86 for the red, blue, and green wavelengths, respectively. The constellation diagrams are presented in the subfigures. It is noted that the highest bit number for the red wavelength is 10, which corresponds to 1024QAM. Finally, the data rates and the corresponding BERs of all the 50 channels are measured, which are shown in Fig. 9. The maximum channel data rate reaches 15.66 Gbps, and the minimum rate is 7.69 Gbps. The differences in data rate with different channels are caused by the diversity of laser characteristics and different responsivities of PDs to different wavelengths. This system achieves an aggregate data rate of 601.46 Gbps, with an average of more than 12 Gbps per channel. As shown in Fig. 9(b), the BER for all the channels is under the 7% FEC threshold of 3.8 × 10^-3. To the best of our knowledge, this is the first time that beyond 600 Gbps transmission with a constellation size of up to 1024QAM is experimentally demonstrated in a WDM VLLC system.

In this Letter, a novel DPC scheme is proposed to mitigate the effects of SSBI and DC effect on the channel estimation, which enables more accurate estimation and compensation for linear impairments and ultimately improves system performance without halving the effective data rate. The estimation differences between the low-frequency and the high-frequency ranges are explored. The difference ratio is closer to 2 in the low-frequency range and tends to decrease in the high-frequency range. This indicates that more compensation is applied to the high-frequency components of the signal. A data rate of 601.46 Gbps with a constellation size of up to 1024QAM over a 1 m MMF-1 m FSO-1 m MMF link is successfully achieved based on a 50-channel WDM VLLC system utilizing DPC and bit-power-loading DMT modulation. To the best of our knowledge, this is the highest data rate and constellation size ever reported for a WDM VLLC system, which proves that VLLC is a highly viable candidate solution for achieving high-capacity and cost-effective optical interconnects in DCs.