Multidimensional Uncertainty Quantification of Microwave/RF Networks Using Linear Regression and Optimal Design of Experiments

I was attracted to this paper because I'm interested in polynomial chaos (PC) as well as Design of Experiments (DOE)

• MC is not optimum approach
• PC is good but literature is dominated by "highly accurate but intrusive stochastic Galerkin (SG) approach"  And if the network is nonlinear then the PC "inner product operations need to be approximated using a quadrature method where each quadrature term is represented busing a large number of additional voltage/current sources".  These approaches can not use SPICE simulators.
• non-intrusive PC approaches include stochastic collocation (SC), pseudo-spectral collocation approach, PC linear regression approach.  These approaches can use SPICE simulators.
• They are advocating an DOE approach to get the PC coefficients.  Apparently, "blindly choosing the DoE can lead to inaccurate evaluation of the PC coefficient" and says that no guidance is given in literature.  I think that they aim to remedy this.
• They introduce some D-optimal approach to find a good DoE for PC applications.   It sounds like they get a whole set of separate DoE's and quantify their quality (D-optimal), discard the worst ones, generate new ones and continue until the best D-optimal one is found. They say that they give lots of details on how to do this.  It sounds exactly like what JMP does, so I'm not terribly impressed.
• If I was trying to write my own D-Optimal DoE creation script I would certainly read and use this paper.
• II. Review of PC Approaches for Microwave/RF Circuit Simulation
• "the goal of uncertainty quantification is to compute all statistical moments of the unknown network response in an accurate yet efficient manner."
• represent the output network response with PC expansion (a projection using orthogonal multivariate polynomials).  This results in the PC coefficients.
• Approaches to obtain PC coefficients
• nonintrusive linear regression with DoE (their approach)
• Once the PC coefficients are known, the mean and variance of the a given network output can be calculated.
• They give lots of good examples of applications

A. K. Prasad, M. Ahadi and S. Roy, "Multidimensional Uncertainty Quantification of Microwave/RF Networks Using Linear Regression and Optimal Design of Experiments," in IEEE Transactions on Microwave Theory and Techniques, vol. 64, no. 8, pp. 2433-2446, Aug. 2016.

NOTE: I just noticed that I reviewed this paper on 8/16/16 as well.  I had this paper in my browser tab for a long time and thought that I needed to review it.

REDUCED NOISE SENSITIVITY IN INVERSE SCATTERING THROUGH FILTERING

These guys have an improvement of the TDR impedance peeling algorithm to deal with the inherit measurement or numerical round-off noise

• They call the peeling algorithm "inverse scattering, modified deconvolution"
• "multiple reflections" column 4, line 19
• Reference "Inverse Scattering for Discrete Transmission-line Models", 51 AM Rev., 1987,
• This might be an interesting read

Reduced noise sensitivity in inverse scattering through filtering
US 5321365 A
1994 - Textronix

https://www.google.com/patents/US5321365

OVERCOMING MULTIPLE REFLECTIONS IN PACKAGES AND CONNECTORS AT HIGH SPEED BROADBAND SIGNAL ROUTING

• concerned with "multiple reflections" -- abstract
• "cause multi-frequency reflections to destructively interfere" -- abstract
• add a stub to a trace where "the stub is configured to reduce broadband reflections in the trace by causing multi-frequency reflections that destructively interfere with at least some broadband reflections"  Paragraph [0005] see also [0044]
• the stub length, impedance and position are key [0006]
• "Due to the above stated impedance discontinuities, a high speed broadband signal propagating through the transmission line 120 is severely degraded. The signal degradation is caused by frequency dependent distortion that is introduced by the multiple reflections between the trace 120 and discontinuities along or at both ends of the trace such as introduced by 130 and 110. Specifically, the discontinuities cause multiple reflections of the broadband signal within the trace, which results in signal distortion and degrades the output signal quality. To mitigate this effect, stubs 107A and 107B are formed along the trace transmission line, such as along a longitudinal length of the transmission line 120 -- 0025
• "For each stub 107A and 107B, the stub length, stub impedance, stub width as well as the location of the stub along the longitudinal length of the transmission line 120 is selected such that the stubs are configured to reduce broadband reflections in the trace by causing multi-frequency reflections that destructively interfere with at least some broadband reflections, to be added to signals transmitted along the trace 120 --026
• "It is noted that numerous techniques can be used to determine stub parameters to overcome broadband reflections of a broadband signal that propagates through a trace of a semiconductor package. FIG. 5 is a flowchart depicting one representative technique."
• They don't really describe an optimization technique, the summary of the described approach is to twiddle the inputs and select outputs which look good.  

Summary, insert a stub in a transmission line which improves low frequency loss at the cost of increasing high frequency loss.  This is due to multiple reflections.  The reflections cancel at low frequency and combine catastrophically at high frequencies.

Overcoming multiple reflections in packages and connectors at high speed broadband signal routing
US 20140016686 A1
https://www.google.com/patents/US20140016686

CMOS ADC-based receivers for high-speed electrical and optical links

• They contrast ADC receivers to mixed-signal receivers.  They state that ADC receiver can more easily support PAM4 and robustness to PVT variations.  
• The downside of ADC receivers is that they consume more power.  
• Their research is about "techniques to improve ADC energy efficiency and novel approaches to reduce DSP complexity and power consumption."
• TI (time-interleaving) converters
• partial embedded analog equalization -- sounds interesting
• SNDR - signal-to-noise-plus-distortion ratio -- also sounds interesting
• SAR converters - successive approximation registers, a piece of the ADC
• TI (time-interleaving)
• When you do time-interleaving, conversion errors can occur due to mismataches between the parallel sub-ADC.  They note that these effects are typically calibrated out.
• Also need to calibrate/correct the sampling offset error.
• Also bandwidth mismatches between the parallel sub-ADC.  One benefit of an ADC is that each branch can be equalized independently which somewhat addresses any bandwidth mismatch.
• skew errors
• Equalization
• "After quantization, ADC-based receivers typically remove ISI in the digital domain with combination of a FFE and a DFE before symbol detection."
• "A major difference between ADC-based and mixed-signal receivers is the quantization noise introduced by the ADC, which can ultimately limit the BER."
• partial analog equalization means that they do some analog equalization (such as a FFE) before the ADC where they do more equalization.
• The quality of the equalization impacts the required ADC resolution.
• "A higher ADC resolution is required as channel loss increases due to reduced signal power and the impact of quantization noise amplification by the stronger FFE tap settings, with the DSP-only receiver requiring an 8-bit ADC resolution to compensate for the highest loss channel.
• " High-speed linearity is of particular importance with more spectrally efficient modulation, such as PAM4, further motivating ADCbased front-ends that allow for precise digital FFE and DFE computation"
• Hybrid ADC-Based Receiver

S. Palermo et al., "CMOS ADC-based receivers for high-speed electrical and optical links," in IEEE Communications Magazine, vol. 54, no. 10, pp. 168-175, October 2016.

Exerpts from --> Sapiens: A Brief History of Humankind

This is a provocative book which I am attracted to because my interests in understanding and building cultures.

• 87 - One of history's few iron laws is that luxuries tend to become necessities and to spawn new obligations.
• 164 - Equality and liberty, cognitive dissonance, the best way to understand a culture is to understand its cognitive dissonance.

The first section of chapter 9:

After the agricultural revolution, human societies grew larger and more complex, while the imagined constructs sustaining the social order also became more elaborate.  Myths and fictions accustomed people, nearly from the moment of birth, to think in certain ways, to behave in accordance with certain standards, to want certain things, and to observe certain rules. They thereby created artificial instincts that enable millions of strangers to cooperate effectively.  This network of artificial instincts is called 'culture'.

• 179 - Us and Them
• 172 - Potential universal orders 1) Monetary 2) Political 3) religion
• 180 - Money is the most universal and most efficient system of mutual trust ever devised.
• 185 - Christians and Muslims who could not agree on religious beliefs could nevertheless agree on a monetary belief, because whereas religion asks us to believe in something, money asks us to believe that other people believe in something.
• 259 - In 1620 Francis Bacon published a scientific manifesto titled The New Instrument.  In it he argued that 'knowledge is power'.  The real test of 'knowledge' is not whether it is true, but whether it empowers us.  Scientists usually assume that no theory is 100% correct.  Consequently, truth is a poor test for knowledge.  The real test is utility.  A theory that enables us to do new things constitutes knowledge.
• 264 - Until the scientific revolution most human cultures did not believe in progress.  They thought the golden age was in the past, and that the world was stagnant, if not deteriorating. 
• 273 - To channel limited resources we must answer questions such as 'What is more Important?' and 'What is good?' And these are not scientific questions.  Science can explain what exists in the world, how things work, and what must be in the future.  By definition, it has no pretensions to knowing what should be in the future.  Only religions and ideologies see to answer such questions.
• 274 - scientific research can flourish only in alliance with some religion or ideology.
• 282 - The Chinese and Persians did not lack technical inventions such as steam engines (which could be freely copied or bought).  They lacked the values, myths, judicial apparatus and sociopolitical structures that took centuries to form and mature in the West and which could not be copied and internalized rapidly.  France and the United States quickly followed in Britains's footsteps because the French and Americans already shared the most important British myths and social structures.  The Chinese and Persians could not catch up as quickly because they thought and organized their societies differently.  . . .  [the difference was ] modern science and capitalism.
• 283 - The key factor was that the plant seeking botanist and the colony seeking naval officer shared a similar mindset.  Both scientist and conqueror began by admitting ignorance - they both said, 'I don't know what's out there.' They both felt compelled to go out and make new discoveries.  And they both hoped the new knowledge acquired would make them masters of the world.
• 303 - People continue to conduct a heroic struggle against racism without noticing that the battlefront has shifted, and that the place of racism in imperial ideology has now been replaced by 'culturism'.  . . . Among today's elites, assertions about the contrasting merits of diverse human groups are almost always couched in terms of historical differences between cultures rather than biological differences between races.
• 309 - If the global pie stayed the same size, there was no margin for credit.  Credit is the difference between today's pie and tomorrow's pie.  If the pie stays the same, why extend credit?

Sapiens: A Brief History of Humankind (By: Yuval Noah Harari) [published: September, 2014]