Crosstalk is unwanted noise from structures coupled to a signal link that degrade the useful signal and may reduce the data transmission rate and even cause complete link failure. All possible signal degradation effects, including the crosstalk, can be expressed with the balance of power as follows:

P_out = P_in - P_absorbed - P_reflected - P_leaked + P_coupled

The formula is valid in the time domain and in the frequency domain over the bandwidth of the signal.¹ Here, P_out is the power of signal at a receiver. The power from a driver (P_in) is absorbed in dielectrics and conductors (P_absorbed),² reflected back to the driver (P_reflected)^3,4 and, possibly, leaked (P_leaked) to coupled structures. P_leaked is a type of loss that includes local leaks to other signal links5 and leaks to power distribution systems and radiation that happen mostly at the unlocalized via-holes.⁶  The leaked power can be predicted or prevented relatively well; it requires analysis of a link with potentially coupled links (local coupling) and analysis of via-holes with absorbing boundary conditions. Only small leaks on via-holes can be accurately predicted with the analysis in isolation from the rest of the board, and the large leaks must be prevented. Overall, the effects of leakage on a signal can be predicted relatively well in links with vias localized up to a target frequency. This is unlike the last term in the balance of power: the power gained from the coupled structures or P_coupled. 

There are a lot of uncertainties related to P_coupled and, as the result, there are multiple ways to characterize it. This is because of a signal from the coupled links or aggressors involved in the analysis.¹⁰ It can be one or multiple aggressors, signals similar to the victim signal as in parallel buses, or signals with different data rates and/or rise time in cases of accidental or distant coupling. Peaks of crosstalk are defined by the aggressor signal; the timing of the peaks and victim signals are not synchronized, but they are not completely random as well. The impact of the coupling also depends on the strength of the signal in the victim link and the location of the coupling. Very small coupling at the victim receiver where the useful signal is already degraded by the absorption and reflection losses may have much greater impact on the signal compared to larger coupling at the driver end of the victim link. As a consequence of that uncertainty, there are multiple ways to quantify the crosstalk phenomenon, and this article discusses most of them. Overall, the crosstalk simulation and quantification can be separated into four categories: 

1. Coupling Coefficients: Analysis of transmission line cross-sections at one frequency point and use of approximate equations for backward and forward coupling (Kb and Kf) 
2. Frequency Domain: Extraction of S-parameters with coupling in frequency domain and use of crosstalk metrics PSXT, ICR, and ICN
3. Time Domain: Simulation in time domain with step, pulse or PRBS excitation signals (peak voltages or eye distortion)
4. Probabilistic: Statistical evaluation of crosstalk impact on bit error rate (BER) and channel operating margin (COM).

The first approach, coupling coefficients, is useful only for the evaluation of local coupling in parallel or nearly parallel traces and can be effectively used for quick pre-layout investigations or to find the locations of crosstalk in post-layout analysis. The second approach, frequency domain, is the most universal and is the foundation for the time domain and probabilistic approaches. It can be used for both local and distant coupling.⁵ The third approach, time-domain analysis, is also universal and, technically, is the most accurate evaluation of the actual crosstalk values. The time-domain response is usually computed from the frequency domain S-parameters, to account for the frequency-dependent dispersion. But the results are useful on its own, especially for understanding the phenomenon. The time-domain analysis is useful for evaluation of the crosstalk from a step or pulse (single bit or symbol) excitation. It can be used to simulate a crosstalk from pseudo-random bit streams (PRBS), but the bits in a victim signal and the bits in possible aggressor signals are not correlated, and the timing of the rise and fall edges in aggressors and victims are not synchronized; different bit sequences and timing produces different crosstalk impact. To handle these uncertainties, the crosstalk can be treated as a noise with a bounded probability density function identified from the time-domain analysis. The fourth approach is the most modern probabilistic option in terms of aligning with the crosstalk treatment in the IEEE 802.3 and OIF-CEI signaling standards. It may be also the most pessimistic crosstalk model. 

Simbeor software is used to generate all examples for this article. Crosstalk validation platform XTALK-28/32 from Wild River Technology is used to illustrate the crosstalk quantification for the post-layout examples.¹¹ 

Crosstalk Quantification with Coupling Coefficients

The fastest and the simplest way to quantify crosstalk is to simulate a cross-section of coupled traces with a field solver at one frequency point and use approximate equations for evaluation of forward and backward coupling. With this approach, capacitance (C) and inductance matrices per unit length are computed for a cross-section with the coupled traces first. Then an equation is used to evaluate possible backward (Kb) and forward (Kf) coupling coefficients for a transmission line segment with length, l, for a step signal with unit amplitude and rise time, t_r. Jarvis derived such formulas⁷ for single-ended symmetric traces. The Jarvis formulas were further improved for small segments and for non-symmetric coupling cases by Bracken⁸:  

Here, C₂₁ and L₂₁ are mutual capacitance and inductance,  T₁ and T₂ are flight times, and ζ₁ and ζ₂ are impedances of the coupled traces or impedances of differential modes for differential traces. The coefficients are the voltage step responses at the near-end (Kb) and the far-end (Kf) of the coupled transmission line segment, assuming 1 V step excitation in the aggressor. If only one coupled segment is involved, Kb is the voltage of near-end crosstalk (NEXT) and Kf is the voltage of far-end crosstalk (FEXT). The equations are relatively accurate for lossless or low loss cases. However, they do not work well with high losses or long segments (it may overestimate the forward crosstalk that is attenuated by the losses). 

The formulas can be used as an estimate of the maximal possible step crosstalk. The formulas also assume ideal transmission line segment termination and do not account for possible reflections (yes, the crosstalk is reflected, too). Note that the reflected NEXT can be observed as FEXT and the formulas provided above can be further improved.⁹ However, the frequency or time-domain simulation of crosstalk is always preferable to account for the reflections. Additionally, it should be noted that the step excitation may underestimate the actual peak-to-peak crosstalk for short links by up to 2x or by up to +6 dB.

The coupling coefficients is a convenient tool for both pre-layout and post-layout crosstalk investigation. Different kinds of sweeps can be used to define design rules in the pre-layout process for instance. A static or quasi-static field solver is needed to begin such an investigation (such as Simbeor SFS, available in Simbeor software). This can be done by scripting in MATLAB or Python and using the Simbeor SFS field solver through Simbeor SDK.¹⁰

The coupling coefficients can be used for preliminary investigation of an existing PCB layout to find the location where the coupling coefficients exceed some threshold. It can be done with one button click using the advanced simulation-based Electrical Rule Checking (ERC) mode in Simbeor SI Compliance Analyzer tool (only signal rise time is required for this type of analysis). The crosstalk validation platform XTALK-28/32 from Wild River Technology is a perfect tool to validate and illustrate different ways to analyze the crosstalk. (This is in addition to the investigation of interconnects predictability with the analysis to measurement correlation). The results of the crosstalk analysis for four 2-in. coupled differential segments and long link coupled to short link are shown in Figure 1. The insert shows details of the crosstalk evaluation for a 2-in. structure with 1w separation between the pairs; the forward coupling Kf = -69.69 mV dominates the backward coupling Kb = 21.37 mV for the bottom differential pair. The stackup for the XTALK-28/32 board¹¹ is practically the same as for the CMP-28 validation platform featured in¹². Trace widths are 13.5 mil (wide traces are used to reduce the effect of manufacturing variations). As can be seen in Figure 1, the larger separation results in less coupling.

Figure 1.  Example of crosstalk evaluation on XTALK-28/32 platform in Simbeor SI Compliance Analyzer for five 2-in. differential microstrip structures with the edge-to-edge separation from 1 to 5 trace widths and for long to short link coupling structure (bottom), 25 ps rise time (10% to 90%).

Crosstalk Quantification in Frequency Domain

A more accurate way to quantify the crosstalk is to simulate a segment of multi-conductor transmission line in frequency domain over a signal spectrum bandwidth. S-parameters of a coupled line segment can be either extracted separately for an analysis in isolation (to generate rules in pre-layout process) or used as an element of a model for coupled links that contains segments of coupled traces. Note that the S-parameters with coupling can be directly used to quantify the crosstalk. For instance, a transmission parameter between two ports from different links is a coupling parameter that describes the crosstalk. S-parameters of coupled links can be directly used to simulate the effect of coupling in time domain or evaluate the probability density function of crosstalk.^13,14 Though, a metric called Power Sum Crosstalk (PSXT) may be useful for preliminary evaluation of overall crosstalk in a link with multiple aggressors.¹³ It can be defined as follows (for additional information, please refer to OIF-CEI and IEEE 802.3 standards):

PSXT is the total power sum crosstalk. PSNEXT and PSFEXT are PSXTs from the near- and far-end aggressors. PSXTs are functions of frequency and are computed from the S-parameters at a set of frequency points. The PSXT is just a sum of squares of S-matrix elements from all possible aggressors at a victim receiver port, expressed in dB. If there is just one aggressor, PSXT sum contains one S-parameter element. In this case, PSXT is equal to corresponding S-parameter magnitude, expressed in dB. PSXT is different from S-parameters only if there are multiple disturbers or aggressors. In such cases, PSXT may be called Multiple Disturber PSXT (MDXT, MDFEXT, and MDNEXT, respectively). 

As an example of the post-layout crosstalk analysis, let’s compute PSXTs for some differential coupled links from XTALK-28/32 platform. Very similar to ERC, it can be done with one button click in Simbeor SI Compliance Analyzer tool (either Fast SI or 3D EM analysis can be used for the crosstalk modeling). However, this requires additional setup for the transmitters and receivers in order to properly define victims and aggressors. The bit rate and rise time must be also defined; the frequency sweep is auto-defined from these data, but it can be manually re-defined, if necessary. Simbeor uses decompositional electromagnetic analysis¹⁵ that accounts for the coupling between transmission lines. 

The results of PSXT analyses for two structures with three differential links coupled over 2 in. parallel segments are shown in Figure 2. Those are two structures from Figure 1 marked as s =1w and s = 4w. The differential trace width is 13.5 mil and the differential trace pitch is 37 mil. Those are loosely coupled microstrip differential pairs, which are very susceptible to interference, as we can see from these examples. In each case, two links have transmitters on one side (TX1 and TX2) and one link has transmitter on the opposite side (TX3). Each receiver has multiple disturbers, in this case. Crosstalk on the victim receiver (RX2) is also shown in Figure 2. RX2 has one near-end aggressor, TX3, and one far-end aggressor, TX1. As in the case of pre-layout example, the corresponding PSNEXT and PSFEXT are exactly the magnitudes of corresponding transmission parameters. The total PSXT is the sum of squares of magnitudes expressed in dB. PSXT is a superposition of the aggressor’s signals and does not account for the phases of signal harmonics. The PSFEXT dominates in both cases. PSNEXT is also substantial for the case with smaller separation between coupled differential pairs. 

Figure 2. Examples of post-layout PSXT analysis on XTALK-28/32 platform in Simbeor SI Compliance Analyzer for 2-in. differential microstrip structures with the edge-to-edge separation equal to a) 1 trace width and b) 4 trace widths. TX1-TX3 are the transmitter sides and RX1-RX3 are the receiver sides.

where IL_i,j = 20 ⋅ log (|S_i,j (f )|) is the insertion loss at port i and PSXT_i is the power sum crosstalk at the same port (both values are expressed in dB).

ICR is a king of signal to noise ratio13 (IL is the signal at a receiver and PSXT is the noise). The larger values of ICR mean smaller impact of the crosstalk on the signal. To understand the ICR, let’s use structure with coupled long and short links from XTALK-28/32 platform. The results of the analysis are shown in Figure 3. ICR at RX1 is computed for longer link, and ICR at RX2 is computed for the shorter link. It can be observed that the shorter link has much larger ICR, which means smaller impact of the crosstalk. This is because of much smaller insertion loss in the shorter link. PSXT and IL for both links are also shown in Figure 3 for comparison.

Figure 3. Examples of post-layout ICR analysis on XTALK-28/32 platform in Simbeor SI Compliance Analyzer for long and short coupled links. TX1-RX1 is the long link and TX2-RX2 is the short link. ICRs for both receivers are shown at both receiver ports together with corresponding PSXT and IL. The PSXT and ICR are useful metrics for a preliminary crosstalk evaluation. However, those are pure frequency domain metrics. The actual amount of crosstalk noise for a particular signal depends on the signal spectrum and may be also altered by filtering properties of a transmitter and a receiver package. Integrated crosstalk noise (ICN) metric was introduced to account for the signal spectrum and filtering properties of a transmitter and a receiver.¹³ ICN is just RMS of weighted PSFEXT and PSNEXT, computed as follows: 

The frequency-dependent weights W_NEXT and   W_FEXT account for spectrum of random bit sequence. They are computed with the rise and fall time of the near- and far-end transmitters (aggressors), baud rate (bit or symbol rate), reference receiver and transmitter bandwidth, and amplitudes of the near- and far-end aggressors.¹³ The result of the ICN computation is near-end σ_NEXT, far-end σ_FEXT, and total crosstalk σ_XTK estimated in volts (rms value). The total ICN is one number that is very convenient for qualitative assessments of the crosstalk impact.

The limit on the ICN is usually set and plotted versus the insertion loss at the Nyquist frequency. An example of ICN computation and plotting for three differential links coupled over 2-in. length with 4 widths separation between the differential pairs is shown in Figure 4. The ICN values are plotted together with a typical compliance mask. The mask allows larger crosstalk in links with smaller insertion losses. The aggressor signals are set to 1 V, in this case; the other parameters for computation of ICN are shown in Figure 4. It can be observed that the receivers RX3 and RX2 have almost the same insertion losses at Nyquist frequency, but the crosstalk at RX2 is larger; the corresponding dot is in the failure area of the compliance mask. In this case, RX3 has only near-end crosstalk from two transmitters, TX1 and TX2. Receiver RX2 has both far-end crosstalk from TX1 and near-end crosstalk from TX3. Note that the ICN is sometimes explained as an average value of expected crosstalk, or even as a standard deviation for a crosstalk with the normal probability distribution.¹³ Thus, it is usually the bottom estimate.

Figure 4. Examples of total ICN analysis on XTALK-28/32 platform in Simbeor SI Compliance Analyzer for 28 Gbps signal in 2-in. differential microstrip structure with the edge-to-edge separation between differential pairs equal to 4 trace widths. TX1-TX3 are transmitter sides and RX1-RX3 are receiver sides.

Crosstalk Quantification in Time Domain

Yet another way to quantify crosstalk is to compute the step or pulse response of a link with coupling and measure the crosstalk values directly in time domain as maximal peak-to-peak value of a voltage response at a victim input/output (IO) with a stimulus attached to the aggressor transmitter IO. This type of analysis can be done with more realistic models of the transmitter and receiver, and also accounts for the reflections from non-ideal terminations. Additionally, the analysis of a victim link in time domain with one or multiple aggressors is useful to understand the “evasive” nature of the crosstalk. If the aggressor signals are not synchronous with the victim signal, the crosstalk does not correlate in time with the single bit response.5 Thus, it cannot be mitigated as the other types of signal degradation factors such as reflection and losses. The time-domain analysis in Simbeor is done with the rational approximation of S-parameters computed for a segment or a complete link.

As an example of the post-layout crosstalk analysis, let’s simulate differential coupled links from the XTALK-28/32 platform that were previously investigated with coupling coefficients and frequency domain. (Again, it can be done with just one button click in the Simbeor SI Compliance Analyzer tool). However, in addition to setting up the transmitters and receivers, time-domain stimuluses should be defined before the crosstalk simulation. The minimal setup requires the bit rate and rise time. Amplitudes of the sources, type of bit stream, and possible jitter parameters may also need adjustments. 

The results of step and pulse crosstalk analyses for two structures with three differential links coupled over 2 in. parallel segments are shown in Figure 5. Those are two structures from Figure 1 marked as s = 1w and s = 4w. Differential trace width is 13.5 mil and differential trace pitch is 37 mil. In each case, two links have transmitters on one side (TX1 and TX2) and one link has a transmitter on the opposite side (TX3). The pulse and step crosstalk are shown at receivers RX2 and RX3. RX2 has two aggressors: far-end, TX1, (blue lines on the plots) and near-end, TX3 (green lines on the plots). RX3 has two near-end aggressors, TX2 and TX1. Overall, crosstalk at RX3 is much smaller compared to RX2. Also, the far-end crosstalk at RX2 dominates, which is consistent with the investigation in frequency domain that was shown in Figure 2.

Figure 5. Examples of post-layout time-domain crosstalk analysis with step and pulse responses (25 ps rise time) on XTALK-28/32 platform in Simbeor SI Compliance Analyzer for 2-in. differential microstrip structures with the edge-to-edge separation equal to a) 1 trace width and b) 4 trace widths. TX1-TX3 are the transmitter sides and RX1-RX3 are the receiver sides.

 Notice that the peak-to-peak far-end crosstalk computed from the pulse response is almost 2x larger than computed from the step response. It peaks at the rising and falling edge of the pulse. However, this is not always the case, and each coupled link should be simulated to find actual values of the crosstalk. Considering the crosstalk values, it can be observed that the FEXT peak-to-peak value is about 110 mV while the NEXT is about 30 mV for the structure with 1width separation between the differential links. Both are below the “upper limit” 126 mV evaluated from PSXT. A possible superposition of the FEXT and NEXT peaks provides a new upper boundary of 140 mV for the crosstalk. The value is specific to the rise time and happens when the peaks of crosstalk from the NEXT and FEXT aggressors coincide in time; it is highly unlikely, but possible. 

The step and pulse response may be useful for a preliminary quantification of the crosstalk and the upper bound evaluation. The actual signals in the links are sequences of bits for NRZ/PAM2 signal or symbols for PAM4 signals; eye diagrams are typically used to evaluate the signal distortion. Examples of eye diagrams with and without crosstalk computed at RX2 for two links, with different separations between the links, are shown in Figure 6. The crosstalk impact on the eye is clearly visible in case of strong coupling (see Figure 6a). The eye height is reduced by about 90 mV and the width by about 0.16 of UI. This is below our upper bound estimate 140 mV; this particular sequence of bits did not include the worst-case condition that could produce ideal superposition of the FEXT and NEXT peaks at the middle of the victim eye. A smaller reduction of the eye size is observed for the links separated by 4 widths (see Figure 6b); about 10 mV reduction in eye height and about 0.016 UI reduction in width. In both cases, crosstalk is observed as additional jitter (eye width reduction) and amplitude noise (eye height reduction). That is not the worst case as well. 

Figure 6. Eye diagrams at RX2 without and with crosstalk, computed in SI Compliance Analyzer for 2-in. differential microstrip structures from XTALK-28/32 platform with the edge-to-edge separation equal to a) 1 trace width and b) 4 trace widths. 28 Gbps, 20 ps rise/fall time (10% to 90%).

In this example, the eyes were computed directly in time domain, with PRBS32 bit stream signals in the victim as well as in the receivers. The sequences of bits in different links are not correlated and the phase or time offset of the bit rise times is defined randomly at the beginning of the analysis. The result of such analysis will depend on the particular phase and bit sequence, as illustrated in Figure 7.

Figure 7. Signal and crosstalk superposition example. Bit sequences in three links are shown in top plot and the corresponding eye diagrams are shown on the right for 28 Gbps PRBS32, 20 ps rise/fall time (10% to 90%). The bottom plot shows bits at RX2 and the crosstalk noise from bits in the coupled links alongside the corresponding eye diagram, which depicts the location of the crosstalk noise.

The top time domain plot shows a small subset of bits at the receiver ends in three coupled links. The bit sequences are not correlated and the offset between switching time is selected randomly at the beginning of the analysis. At RX2, the useful signal and the crosstalk noise are shown in the bottom plots in Figure 7. The peaks in the noise are defined by the bit sequences and timing in the aggressors, which are not correlated with the victim signal. As a result, peak crosstalk can be observed at any time within the eye, as illustrated by eye diagrams. All graphs show the eye diagrams without the crosstalk. The eye diagram with the crosstalk for that case is shown in Figure 6a. Some bit sequences and timing offsets may degrade the eye more, and some may degrade the eye less. In fact, the crosstalk may even improve the eye opening or reduce the jitter. This is possible, but highly unlikely. In this case, the probability of the worst case is of more interest than the chance of improvement, and statistical methods should be used to quantify this.

Statistical Crosstalk Quantification

The frequency and time domain analyses of the crosstalk are useful tools, but the ultimate metric for a link performance is the BER or eye diagram height at a specified BER. Statistical methods are usually used to evaluate BER or the eye diagram opening. The statistical approach to the BER evaluation requires a statistical model for a crosstalk. However, the crosstalk is not random in general and is bounded by our worst-case estimates. A possible superposition of the victim signal with crosstalk from two aggressor links is illustrated in Figure 8. 

Figure 8. Signal and crosstalk superposition example. The following are depicted: an eye diagram without crosstalk (left), near and far end crosstalk components from the aggressor links (middle, where green is FEXT and blue is NEXT), and a plot displaying possible superposition of signal and crosstalk noise (right).

This is the same middle link case with two aggressors as seen in in Figure 6a. The near-end crosstalk looks like a noise, but the far-end crosstalk does not look like a random signal. What is the probability to have the peak noise from FEXT and NEXT? Using time-domain analysis, the probability density function (PDF) can be evaluated for both cases, as shown in Figure 9.

Figure 9. Crosstalk probability density functions for 2-in. differential microstrip structures from XTALK-28/32 platform with the edge-to-edge separation equal to a) 1 trace width and b) 4 trace widths. 28 Gbps, 20 ps rise/fall time (10% to 90%), PRBS32, time step 2 ps.

PDFs are computed for the tightly coupled links (s = 1w, top plots) and for loosely coupled links (s = 4w, bottom plots). It can be observed that the NEXT distribution looks like normal; this is similar to what is observed in Reference 13. It is getting more “normal” for the loosely coupled links, though the normality test is required to evaluate it. However, the FEXT distribution does not look as normal at all (as seen in the PDFs on the left side in Figure 9) and the probability to have maximal possible values is not negligible. Both distributions are bounded by the maximal possible values for a particular rise time. Though the NEXT and FEXT are independent, as the total crosstalk PDF is a convolution of the two distributions, it is also bounded by the maximal possible value observed from the pulse crosstalk analysis.  

The PDFs of the crosstalk can be used to evaluate the effect of the crosstalk on BER or on detector error rate (DER), which is the COM.^13,14 This is the most “modern” method of the crosstalk quantification and may be considered as the next step in evolution of the crosstalk quantification. COM^13,14 is a signal to noise ratio defined as follows:  

Where A_Signal is the peak signal and A_Noise is the peak BER or DER noise defined through the peak signal minus the peak eye opening at a specified BER/DER level. “Signal” in this context includes all losses and dispersion in the link from chip to chip and the effect of equalization. It includes the reference transmitter and receiver models as well. “Noise” in this context includes all possible signal degradation effects with some assumptions. It includes absorption losses and dispersion, return loss, reflections and crosstalk as well as equalization by TX and RX. The COM metric is computed in the time domain as the voltage ratio of signal available in a reference signaling architecture (TX and RX) to noise at the reference receiver’s sampler; essentially, it characterizes the complete link from chip to chip. The noise is calculated for the specified DER. DER is a generalization of BER for NRZ and of SER for PAM4. Equalized single bit or symbol responses of the signal link and crosstalk aggressor links are used to calculate the vertical slice of the eye diagram centered at the sampling point where the DER is minimal. The crosstalk in COM is assumed to be in the middle of the eye, but that is highly unlikely. 

To evaluate the crosstalk contribution, COM uses S-parameters of the crosstalk paths. The crosstalk in COM is treated as an additional bounded uncorrelated noise similar to the inter-symbol interference. For each crosstalk source, COM computes PDFs and convolves them with the bit PDF to compute the overall crosstalk effect. An example of such analysis is shown in Figure 10.

Figure 10. Example of COM computation for 2-in. differential microstrip structures from XTALK-28/32 platform with the edge-to-edge separation equal to 1 trace width (left) and 4 trace widths (right). 28 Gbps signal; all other parameters are from IEEE 802.3 spreadsheet.

The IEEE COM tool was used for this computation with default reference transmitter and receiver parameters. In this case, the limit of the DER is 1e-4 and the pass value of the COM is 3 dB. As seen in Figure 10, the middle link with 4 widths separation between differential links has a COM of about 8.7 dB. However, the eye at DER = 1e-4 would be almost completely closed if the links have only 1 width separation. The eye closure due to the crosstalk is highly unlikely in this case. Thus, the COM is, probably, the most pessimistic crosstalk metric.

Conclusion

As Ransom Stephens perfectly stated, “The crosstalk problems are back.”¹⁶ They are here to stay as long as interconnects are designed as the open waveguiding systems. Thus, understanding and proper quantification of the crosstalk and mitigation of the consequences are important. This article outlines multiple possible ways to quantify the crosstalk: coupling coefficients, frequency domain metrics, time-domain analysis of crosstalk, and a modern statistical approach. The ultimate metric of the crosstalk effect is the reduction of BER due to crosstalk. The local crosstalk is deterministic, but usually treated as a part of bounded uncorrelated jitter. This is because of the uncertainties in timing between the victim and aggressor signals. The most modern methods are statistical and are applicable to both local and distant crosstalk evaluation. 

References

1.  Y. Shlepnev, “How Interconnects Work: Bandwidth for Modeling and Measurements,” Simberian App. Note #2021_09, November 8, 2021.
2.  Y. Shlepnev, “How Interconnects Work: Absorption, Dissipation and Dispersion,” Simberian App. Note #2021_10, November 26, 2021.
3.  Y. Shlepnev, “How Interconnects Work: Impedance and Reflections,” Simberian App. Note #2021_11, December 22, 2021.
4.  Y. Shlepnev, “How Interconnects Work: Reflections from Discontinuities,” Simberian App. Note #2022_01, January 10, 2022.
5.  Y. Shlepnev, “How Interconnects Work: Anatomy of Crosstalk,” Simberian App. Note #2023_04, December 27, 2023.
6.  Y. Shlepnev, “Life beyond 10 Gbps: Localize or Fail!,” Simberian App. Note #2018_03, April 13, 2018.
7.  D. B. Jarvis, “The Effect of Interconnections on High-Speed Logic Circuits,” IEEE Trans. On Electronic Computers, Vol. EC-12, 1963, N. 5, pp.   476–487.
8.  J. E. Bracken, “Improved Formulas for Crosstalk Coefficients,” DesignCon 2016.
9.  S. Yong, V. Khilkevich, X.-D. Cai, C. Sui, B. Sen, and J. Fan, “Comprehensive and Practical Way to Look at Far-End Crosstalk for Transmission   Lines With Lossy Conductor and Dielectric,” IEEE Trans. on EMC, Vol. 62, No. 2, 2020, pp. 510–520.
10.  Y. Shlepnev, “How Interconnects Work: Crosstalk Quantification,” Simberian App Note #2024_01, February 14, 2024.
11.  Wild River Technology, Web: https://wildrivertech.com.
12.  Y. Shlepnev, “Sink or Swim at 28 Gbps,” The PCB Design Magazine, October 2014, pp. 12–23.
13.  M. Shimanouchi, H. Wu, and M. P. Li, “Evolution of Various Crosstalk Metrics and Evaluation Methods for High-Speed Serial Link and Their   Complementary Characteristics,” DesignCon 2019.
14.  R. M. Mellitz, A. Ran, M. P. Li, and V. Ragavassamy, “Channel Operating Margin (COM): Evolution of Channel Specifications for 25 Gbps and   Beyond,” DesignCon 2013.
15.  Y. Shlepnev, “Decompositional Electromagnetic Analysis of Digital Interconnects,” IEEE International Symposium on Electromagnetic   Compatibility (EMC2013), Denver, Colo., 2013, pp. 563-568.
16.  R. Stephens, “Crosstalk Problems are Back,” Test & Measurement World, July 2012.