## 2 Fundamental Methods
### Channel Operating Margin  
The COM method is a high-speed serial link characterization method recommended by the IEEE 802.3 working group for channel compliance testing. The official definition states that a \"COM is a figure of merit (FOM) for channels determined from a minimum reference PHY architecture and channel s-parameters\" [29]. This approach provides a relatively accurate and fair environment for the physical design of channels by considering various factors such as loss, reflection, inter-symbol interference (ISI), dispersion ISI, crosstalk, and device specifications, enabling a relatively accurate assessment of channel performance and the impact of aggressor channels on victim channels. The impact of equalizers has been considered in subsequent versions of the COM method, and the value of a COM based on the FOM can be improved by selecting equalizer parameter settings. Consequently, calculating the COM can also determine whether the channel quality meets the transceiver's SI requirements [30]. As shown in Equation (1), the COM can be expressed by the ratio of available signal amplitude \(A_{s}\) to statistical noise amplitude \(A_{n}\).  
\[\text{COM}=20\times\log_{10}\left(\frac{A_{s}}{A_{n}}\right) \tag{1}\]  
The process of deriving the COM involves several essential steps, including determining the transfer function, converting the transfer function into the impulse response, applying transmitter and receiver equalizer algorithms, and performing statistical noise calculations. Figure 3 presents a flowchart of COM model derivation and depicts two paths for the victim and aggressor channels. Additionally, the model also considers transmitter and receiver package interference S (tp/rp), termination resistance Rd, equalizers, and filters. To better simulate actual channels, the COM model incorporates Gaussian white noise and jitter at the receiver end. Figure 4 shows the detailed process of COM value calculation.  
Figure 2: (a) FD. (b) TD. Illustration of two different simulation methods for detecting SI.  
The equalizer parameters are mainly set based on the channel loss. The FOM serves as a quantitative metric for assessing channel quality and equalizer performance. It takes into account several factors affecting SI, including ISI, jitter, crosstalk, and noise. The FOM calculation formula can be expressed as follows:  
\[\text{FOM}=10\times\text{log}_{10}\Bigg{(}\frac{A_{s}^{2}}{\sigma_{TX}^{2}+ \sigma_{ISI}^{2}+\sigma_{J}^{2}+\sigma_{XTK}^{2}+\sigma_{N}^{2}}\Bigg{)} \tag{2}\]  
The numerator \(A_{s}\) is derived from the amplitude of the impulse response at \(t_{s}\), which corresponds to the main cursor of the impulse response \(h(t)\). The denominator includes the sum of variances from all noise, jitter, and interference components. \(\sigma_{TX}^{2}\) represents the noise variance at the transmitter, \(\sigma_{ISI}^{2}\) denotes the variance in the residual ISI amplitude, and \(\sigma_{J}^{2}\) indicates the variance in jitter amplitude. In COM analysis, jitter is accounted for by converting horizontal jitter into vertical noise at the sampling instant \(t_{s}\). Additionally, \(\sigma_{XTK}^{2}\) represents the total crosstalk variance from all interference paths, while \(\sigma_{N}^{2}\) denotes the Gaussian white noise at the receiver sampling point.  
The COM approach entails exploring all possible parameter combinations of the TX and RX equalizers within a set range to find the configuration that maximizes the FOM. This process determines the values of \(A_{s}\) and \(A_{n}\) that result in the optimal FOM.  
Traditional methods rely on various indicators such as jitter, eye height, and eye width, but the COM serves as a comprehensive metric for evaluating a serial link. It can significantly reduce the computation time and number of iterations, and provides an accurate evaluation of channel performance both before and after equalization.  
Figure 4: COM calculation process.  
Figure 3: A typical COM model.