# Signal Analysis: What Would You Do With an Extra 9 dB?

Blog Post created by benz on Sep 15, 2016

Originally posted Jun 10, 2014

Mapping the benefits of noise subtraction to your own priorities

Otto von Bismarck said that “politics is the art of the possible” and he might as well have been speaking about RF engineering, where the art is to get the most possible from our circuits and our measurements.

The previous post on noise subtraction described a couple of ways that RF measurements could be improved by subtracting most of the noise power in a measuring instrument such as a spectrum or signal analyzer. In some instruments this process is now automated and it’s worth exploring the benefits and tradeoffs as a way to understand the limits of what’s possible.

In the last post I briefly mentioned sensitivity and potential speed improvements and in this post I’d like to discuss one example of what a potent technique noise subtraction can be. One diagram can summarize the benefits and tradeoffs for this example, but it’s an unusual format and a little bit complex so it deserves some explanation.

Accuracy vs. SNR for noise-like signals and a 95% coverage interval. The blue curves show the error bounds for measurements with noise subtraction and the red curves show the bounds without noise subtraction. Using subtraction provides a 9.1 dB improvement in the required SNR for a measurement with 1 dB error.

I didn’t produce this diagram and confess that I didn’t understand it very well at first glance. The 9.1 dB figure annotating the difference between two curves sounds impressive, but just what does it mean for real measurements?

Let me explain: This is a plot of accuracy (y-axis) vs. signal/noise ratio (SNR, x-axis) for a 95% error coverage interval and for noise-like signals. Many digitally modulated signals are good examples of noise-like signals.

The red curves and the yellow fill indicate the error bounds for measurements made without noise subtraction. Achieving 95% confidence that the measurement error will be less than 1 dB requires an SNR of 7.5 dB or better, keeping error below 2 dB requires an SNR of 3.5 dB, and so on. Note that the mean error is always positive and increases rapidly as SNR is degraded.

Now look at the blue curves and green fill to see the benefit of noise subtraction. In this example the effectiveness of the noise subtraction is sufficient to reduce noise level by about 8 dB, a conservative estimate of the performance of this technique, whether manual or automatic.

First, you can see that the mean error is now zero, removing a bias from the measurement error. Second, the required SNR for 1 dB error has been reduced to -1.6 dB, a 9.1 dB improvement from the measurement made without noise subtraction.

I have complained in the past about the effects of noise on RF measurements and it’s a frustration that many share. However, this example demonstrates the other side of the situation: Subtracting analyzer noise power, either manually or automatically, with technologies such as noise floor extension (NFE) provides big performance benefits.

What would you do with an extra 9 dB? You might use it to improve accuracy. You could trade some of it away for faster test time, improved manufacturing yields, a little increased attenuation to improve SWR, or perhaps eliminate the cost of a preamplifier. Use it well and pursue your own version of “the art of the possible.”