The rise of AI computing, driven by tens of thousands of GPUs and AI accelerators in data centers, poses significant challenges for optical interconnects and networking technologies (Naffziger, 2023; Xie and Zhang, 2022). Current state-of-the-art optical interconnects utilize pluggable transceivers operating at 112 Gb/s and 224 Gb/s PAM-4 data rates with energy efficiencies of ∼ 25 pJ/b (Nagarajan et al., 2024). Next-generation transceivers aim to achieve data rates exceeding 400 Gb/s with improved energy efficiency (Nagarajan et al., 2021). However, with limited improvements in the speed and energy efficiency of mixed-signal circuitry in advanced CMOS technologies, and fiber dispersion constraints, further increases in data rates necessitate advanced modulation schemes. While PAM-6 and PAM-8 are under investigation, their significant SNR penalties (Li et al., 2019) make them less practical. Consequently, adopting advanced coherent modulation (e.g., 16-QAM) within data centers is inevitable for achieving energy-efficient links. Although wavelength and polarization division multiplexing (WDM and PDM) can increase aggregate bandwidth per fiber, boosting data rates per wavelength/polarization remains essential to reduce the number of laser lines and improve energy efficiency.

Coherent optical communication requires precise phase and frequency alignment between the received (Rx) signal and the local oscillator (LO). Long-haul coherent transceivers, such as the 800G-ZR/ZR + standards (Zhou et al., 2023), employ power-intensive digital signal processing (DSP) to handle channel impairments such as chromatic dispersion (CD), differential group delay (DGD), and carrier phase recovery (CPR) (Nagarajan et al., 2024; Ip et al., 2008). These DSP methods require oversampling ADCs, resulting in energy consumption around 50 pJ/b and increased system complexity. In short-reach interconnects (e.g., inter-rack links < 1 km), many DSP functionalities—such as dispersion compensation—are unnecessary and can be eliminated (Saleh et al., 2021). However, frequency and phase recovery remain essential. Therefore, performing CPR in analog front-end can eliminate or significantly simplify DSP, realizing the power efficiency requirements of data centers.

Previous studies have demonstrated DSP-free CPR systems for QPSK/4-QAM modulations (Valenzuela et al., 2022; Movaghar et al., 2023; Ashok et al., 2021b; Ashok et al., 2021a) using Costas loops (Chul Park et al., 2012; Dick et al., 2000). These systems utilize optical phase-locked loops (OPLLs) (Valenzuela et al., 2022), optical delay-locked loops (ODLLs) (Movaghar et al., 2023), and traditional PLLs (Ashok et al., 2021b) for phase and frequency mismatches in laser-forwarded links. However, as modulation schemes scale to higher orders (e.g., 16/64/256-QAM), Costas loops fail to correct phase errors due to varying symbol amplitudes (Rezaei et al., 2024).

For instance, using unmodified Costas loops for 16-QAM introduces symbol-dependent phase error detection, creating false I/Q locking points that deviate from n π 2 (Patil et al., 2016). A proposed solution involves sub-sampling the 16-QAM signal to form a 4-QAM constellation (Mizutori et al., 2017), but this relies on accurate symbol detection during CPR, which is impractical. Furthermore, sub-sampling reduces CPR loop bandwidth.

Another work (Liu et al., 2024) employed the pilot tone concept by adding a low-frequency test tone to the transmitted optical signal. At the receiver, phase error is detected and compensated based on the power of this tone. However, even after compensation, this low-power tone remains in the signal, interfering with the data and causing periodic jitter, ultimately impacting BER.

In this work, we propose a DSP-free carrier phase recovery system optimized for offset-QAM modulation. Offset-QAM is generated by leaking a portion of the LO signal into the modulated QAM signal at the transmitter, as shown in Figure 1. This can be achieved using Mach-Zehnder Modulators (MZMs) operating with an offset from the transmission null (Lu et al., 2010), or, as recently demonstrated, by employing micro-ring modulators (MRMs) (Sturm and Moazeni, 2024). In offset-QAM, the phase offset between the Rx signal and LO paths is detected based on the average power/voltage difference between the in-phase (I) and quadrature (Q) signals. This difference serves as an error signal to correct the phase error using a phase shifter (PS) in the LO path for laser-forwarded links. The laser-forwarding technique (Mehta et al., 2020) forwards a portion of the transmitter (Tx) laser to the receiver to serve as the LO, maintaining zero frequency mismatch, eliminating the need for an additional LO laser, and mitigating laser phase noise (PN). This approach reduces cost and enhances reliability. The proposed CPR system supports any offset-QAM modulation level (e.g., 4, 16, 256) without architectural modifications, making it highly scalable for future high-order modulations. Unlike Costas loops, our method avoids the need for high-speed analog devices (e.g., mixers, XORs) and does not suffer from π 2 phase ambiguity (Xiao and Cheng, 2006; Sadchenko and Kushnirenko, 2018).

The proposed receiver is modeled and simulated using GlobalFoundries (GF) 45 nm monolithic silicon photonics (GF45SPCLO) (Rakowski et al., 2020) PDK models, with circuit/system-level implementation at 100 GBaud. This approach paves the way for low-power QAM interconnects in future co-packaged optics (CPO) and coherent-lite (Lam et al., 2021) applications, enabling energy-efficient data rates exceeding 400 Gb/s per channel.

The paper is organized as follows: Section 2 introduces our DSP-free CPR techniques for offset-QAM modulation. Section 3 analyzes loop dynamics, including stability and laser phase noise. Section 4 discusses the circuit implementation. Section 5 presents simulation results and trade-offs. Finally, Section 6 concludes the paper.

Optical coherent communication relies on precise frequency and phase locking between the received signal and the local oscillator. Any phase error ( Δ ϕ ) between these paths induces I/Q cross-talk, severely impacting symbol/bit error rates (SER and BER) (Chang et al., 2009). Figure 1 presents the constellation diagrams for QPSK/4-QAM and 4-offset-QAM, highlighting the effects of phase offset between the Rx and LO signals. In QPSK/4-QAM, a Δ ϕ phase offset causes the entire constellation to rotate, which can be corrected using the Costas loop technique (Movaghar et al., 2023; Valenzuela et al., 2022; Ashok et al., 2021b). However, in offset-QAM, phase offset rotates the constellation center and distorts amplitudes with respect to the origin making the Costas loop approach ineffective (Rezaei et al., 2024). We have proposed a novel technique to detect the phase offset between the Rx signal and LO paths based on the average power or voltage difference between the in-phase (I) and quadrature (Q) signals in offset-QAM modulation. Figure 2a illustrates the CPR block diagram for laser-forwarded links using a tunable phase shifter in the LO path. In this approach, the Tx laser output is split, with one portion modulated with data and the other transmitted to the Rx as the LO signal. The phase error between the Rx and LO signals is detected in the CPR block and then compensated using a phase shifter in the LO path. Two techniques for phase error detection are shown in Figures 2b,c. The I and Q signals, before phase error compensation, are modeled in Equation 1: I ′ t = I t + A 0 cos Δ ϕ + Q t + A 0 sin Δ ϕ Q ′ t = Q t + A 0 cos Δ ϕ − I t + A 0 sin Δ ϕ (1) where A 0 is a constant due to offset-QAM modulation and I ( t ) and Q ( t ) are ± A OMA 2 . Then high-frequency portions of I ′ ( t ) and Q ′ ( t ) are filtered using low-pass filters, retaining the average voltage as shown in Equation 2: I avg Δ ϕ = A 0 cos Δ ϕ + A 0 ⁡ sin Δ ϕ Q avg Δ ϕ = A 0 cos Δ ϕ − A 0 ⁡ sin Δ ϕ (2)

In Method 1, the outputs of the low-pass filters in the I and Q paths are subtracted, generating an error signal equal to 2 A 0 ⁡ sin ( Δ ϕ ) . However, if the error signal is in the region where the slope is positive, the loop becomes unstable. To maintain stability, the summation of I avg ( Δ ϕ ) and Q avg ( Δ ϕ ) ( 2 A 0 ⁡ cos ( Δ ϕ ) ) is used as a select signal to choose between 2 A 0 ⁡ sin ( Δ ϕ ) and - 2 A 0 ⁡ sin ( Δ ϕ ) in different regions. For example, when − π 2 < Δ ϕ < π 2 , and the error signal’s slope is positive, cos ( Δ ϕ ) is positive and chooses − 2 A 0 ⁡ sin ( Δ ϕ ) , and vice versa. This ensures that the error signal matches what is depicted in Figure 3.

In Method 2, I avg ( Δ ϕ ) and Q avg ( Δ ϕ ) are sent to limiting amplifiers (SGN) and mixers, then subtracted, similar to the Costas loop technique, producing an error signal shown in Figure 3 (Movaghar et al., 2023). This method generates a sawtooth error signal that maintains constant gain over the entire range. However, the periodicity of π 2 introduces phase ambiguity between the I and Q signals at the receiver (Ashok et al., 2021b; Ashok et al., 2021a). To resolve this, differential coding during modulation and demodulation is required.

While Method 1 avoids the π 2 phase ambiguity, its gain diminishes near the peaks, affecting the loop bandwidth and phase error compensation time. In this work, we adopt the phase detection technique based on Method 1.

In this section, the CPR loop dynamics are analyzed in terms of stability, bandwidth, residual phase error, and phase noise performance.

In the transmitter, the electric field of the laser source can be expressed in Equation 3: E laser t = E 0 e j ω c t + ϕ 0 , l a s e r + ϕ p n t (3) where E 0 , ω c , ϕ 0 , l a s e r , and ϕ p n ( t ) denote the laser’s electric field magnitude, center frequency, initial phase, and phase noise, respectively. This signal is subsequently modulated with offset-QAM data and transmitted over fiber. At the receiver, the Rx signal ( E R x ) beats with the LO signal which is a portion of the Tx laser forwarded to the receiver and generates a beat signal proportional to E R x ( t ) E L O * ( t ) . Assuming a length mismatch of Δ L between the Rx signal and LO paths, the beat signal at the receiver has a phase noise expressed as ϕ p n ( t ) − ϕ p n ( t − τ Δ L ) ; where τ Δ L = n Δ L c , with n being the refractive index and c the speed of light (Zhou et al., 2021). Figure 4a illustrates the receiver’s phase linear model, where θ laser ( t ) = ω c t + ϕ laser,0 + ϕ p n ( t ) . In this context, ϕ data ( t ) denotes the modulation phase, ϕ offset refers to the phase offset caused by the length mismatch between the Rx signal and LO paths, ϕ err is the phase error detected by the CPR loop, and H ( s ) represents the open-loop transfer function of the CPR.

Since ϕ data ( t ) is initially filtered by low-pass filters, the loop model simplifies to the form shown in Figure 4b, where ϕ i n ( t ) = ϕ offset + ϕ p n ( t ) − ϕ p n ( t − τ Δ L ) . The linearized open-loop transfer function is expressed in Equation 4: H s = K P D K d r i v e r × H L F s × H P S s (4) H L F s = K L F 1 + s ω L F , z 1 + s ω L F , p H P S s = K P S 1 + s ω P S where K P D is the phase error detector gain expressed as 2 2 π I 0 K v , with I 0 indicating the average photocurrent of the I/Q signals, defined as I 0 = 4 | E I / Q ̄ | × | E 0 , L O | × R P D . Here, | E 0 , L O | and | E I / Q ̄ | correspond to the magnitudes of the electric field for the LO and the average I and Q signals, respectively. For DC-balanced I/Q data streams, | E I / Q ̄ | equals A 0 as shown in Figure 1. The photodiode responsivity is represented by R P D and K v is the current to voltage conversion gain. It is important to note that in Method 1, K P D is not constant and exhibits variations near the peak; however, for simplicity, it is approximated by its value in the linear region. K driver refers to the gain of the phase shifter driver and K L F , ω L F , z , and ω L F , p represent the gain, zero, and pole of the loop filter, respectively, while K P S and ω P S denote the gain and electrical 3-dB bandwidth of the phase shifter.

Figure 5 presents the Bode plot of the proposed CPR system, with parameters specified in Table 1. The system demonstrates a phase margin of 61 ° , a crossover frequency of 160 kHz, and a closed-loop bandwidth of 216 kHz.

We have designed and simulated the proposed laser-forwarded carrier phase recovery system using GlobalFoundries monolithic 45 nm silicon photonics PDK models in Cadence. The parameter values used in this design are listed in Table 1. The baud rate is 100 GBaud , corresponding to data rates of 200 Gb/s for 4-offset-QAM and 400 Gb/s for 16-offset-QAM. Eye diagrams artifacts are mainly due to the bandwidth limitations of the photodetectors ( 50  GHz with a ∼ 10 fF capacitance) which can be improved using equalization techniques. The laser has a linewidth of 1 MHz , and there is a 0.1 m length mismatch between the Rx signal and LO paths. The CPR loop bandwidth is 216 kHz . In these simulations, A 0 and A OMA are set to 25   μ A and 250   μ A , and the AFE first stage is modeled as a 220   Ω resistor.

To evaluate the functionality of the design, we performed closed-loop simulations for a phase offset of Δ ϕ = π / 4 between the Rx and LO signals which is applied by an extra phase shifter in the LO path. Figure 13A shows the eye diagram of I and Q signals for 4-offset-QAM at the PDs output (input of the AFE) under three different scenarios: without the CPR loop, with the CPR loop and no phase noise, and with the CPR loop in the presence of phase noise. It is worth mentioning that, to clearly observe the effect of laser phase noise on the eye diagrams, laser phase noise is the only noise source included in the simulation setup. As can be seen in this figure, the CPR loop is able to cancel the phase offset with less than 1 ° residual phase error. However, in the presence of phase noise, the eye opening is reduced.

Figure 13b presents the results for Δ ϕ = π / 4 for 16-offset-QAM. As seen in the figure, the proposed architecture successfully cancels the phase offset for 16-offset-QAM without requiring any changes to the design.

In the presence of phase noise, to achieve the same performance as in the absence of phase noise, we must reduce the phase noise power. This can be achieved by using a laser with a narrower linewidth, minimizing the length mismatch between the Rx signal and LO paths, or increasing the effective CPR closed-loop bandwidth, which is mainly limited by the thermal phase shifter bandwidth in this process.

We have proposed, modeled, and simulated a DSP-free offset-QAM coherent receiver architecture that can perform CPR for any offset-QAM modulation level (e.g., 4, 16, 64) without architectural adjustments that can solve the scalability problem of previously proposed DSP-free CPR systems for QAM modulation. Combined with laser-forwarding, we believe this method can become a solution for future low power coherent links inside data centers. We used electro-optical spectre models in Cadence using the GF45SPCLO for simulation. Received eye-diagram operating at a baud rate of 100Gbaud at the PD outputs are measured for both 4- and 16-offset-QAM. Additionally, we studied the effects of laser linewidths, LO/Rx signal fiber length mismatch, and CPR loop bandwidth on BER. We have also elaborated on the circuit block implementation of key loop components.

Realistic link scenarios assuming 1 MHz laser linewidth and 10 c m fiber length mismatch show that a 400 Gb/s 16-Offset-QAM link with an SNR of 19 d B can meet the KP4 FEC requirements. Our proposed approach can become a solution to realize DSP-free linear coherent optical transceivers (both pluggables and CPO) for 400 Gb/s links and beyond.