Originally posted Jun 4, 2015
Lots of measurements of a stochastic process may provide the deterministic number you seek
For much of my measurement career, many measurement situations have been a search for The One True Number, or at least the closest approximation I could manage. I have complained about measurements that are more stochastic than deterministic and how noise makes my work life difficult in multiple ways, including excess consumption of my remaining days on this mortal coil.
To be fair, I have also had to recognize the occasional usefulness of noise, and generally accept that it’s an inescapable part of our universe. It’s similar to my views on insects: I don’t like most of them, but I’m pretty sure there would be big problems if they weren’t here.
Recently, I’ve been looking at tools and techniques for measuring RF pulses in radar applications, and it seemed that I had entered a kind of alternate measurement domain. In the past, I’ve made many measurements of individual radar pulses, usually with the 89600 VSA software. Using a wide range of RF front ends, this software quantifies anything you might want to know about a pulse: all kinds of frequency, amplitude (average power, power vs. time, on/off ratio), timing, and modulation parameters such as chirp linearity or modulation quality. With the VSA’s time capture and repeated playback capabilities, you can make most of these measurements on a single pulse (from one, many).
No matter how accurate or comprehensive those measurements may be, they are inadequate in one important respect for applications such as radar: They do not account for the consistency of the pulses in question. The VSA software has taken a pulse-by-pulse approach and generally does not indicate repeatability, stochastic characteristics, or trends in the pulse trains or sequences.
Understanding some aspects of radar performance requires a kind of meta-analysis, quantifying the trends or repeatability limits of various parameters of the signals in question. The recent addition of option BHQ to the 89600 VSA software adds this large-scale statistical view in the form of a measurement application for pulse analysis. One typical measurement, aggregating the behavior of a multitude of pulses, is the histogram.
This histogram of best-fit FM results summarizes the behavior of thousands of pulses, automatically identifying and quantifying outliers.
Radar is a prime example of a system in which repeatability is of critical importance, and where trend behavior can be invaluable in design optimization.
The inevitable question, however, is which parameter to analyze for trends or other statistical measures. This is where the experience, insight and intuition of the radar engineer come into play. As is true in wireless, this is another example of measurement software, powerful DSP and large multi-trace displays working together to leverage the talents of the design engineer.
The radar measurement application automatically identifies and measures large numbers of pulses. Multi-trace displays with both graphical and tabular data take advantage of an engineer’s pattern recognition to spot anomalous behavior or identify connections and causes.
Clever software and processing power is no substitute for engineering skill, but it helps distill the magnitude and complexity of pulse trains filled with complex signals. While it may not yield a single value as The One True Number, it can mitigate the risks of measuring too few pulses or analyzing too few parameters together.
If you’re interested in this sort of data reduction and analysis, please visitwww.keysight.com/find/radar.
* ”From many, one” is a common translation of “E pluribus unum” from the Great Seal of the United States