Simulate power of intermodulation products

Question

I would like to predict if in- and out-of-band interference will hurt my ability to read signals in the 902-928MHz spectrum.

I recorded the maximum received interference power from 10MHz to 3GHz with a spectrum analyzer connected to my antenna. I think if I model the input to my system as a two-tone signal made of the \$i^{th}\$ interferer and my desired signal, I will be able to predict the power of each of the intermodulation products and harmonics in my spectrum.

For example, with an uneven two-tone input to a non-linear system, the second-order IM products will be:

$$ V_{in} = Acos(\omega_1 t) + Bcos(\omega_2 t) \\ V_{out}(x) \approx a_0 + a_1 x + a_2 x^2 + a_3x^3 \\ V_{out, 2nd}(x) = (1/2~a_2A^2)cos(3\omega_1 t) + (1/2~a_2B^2)cos(3\omega_2 t) $$

However, I am not sure how to translate the last formula to "real life". The spec sheet for an LNA has measures like the IIP3 point, not the non-linear coefficients \$ a_0, a_1\$. I did find a formula to estimate the power of the 3rd order IM products, using the IIP3:

$$ P_{out} = 3 P_{in} - 2 IIP3 $$

Is there an IIP formula for predicting the power of other IM products and harmonics? Failing that, is there a way to simulate the power of all the products and harmonics with Matlab's RF Toolbox or Excel?

For context, I am an intern helping design the RF front end for a wireless networking startup. I don't have much experience with RF, but I've been doing some reading on interference and LNA design.

Answer 1

Given the 1:1 and 3:1 lines used in logPin and logPout for IP3, yield Pout = 3 * Pin - 2*IIP3,

Pout = 2 * Pin - IIP2, based on 1:1 and 2:1 lines.

Answer 2

Calculating this exactly, in particular if some of the interferers are modulated signals rather than tones, is difficult. Non-linear simulators generally use the Harmonic balance approach. Tools like Genesys, SystemVue, Visual System Simualtor, and MATLAB's RF toolbox will support this. For modelling a component like an amplifier they usually take parameters like intercept points, compression points, and saturation points to build a polynomial model of the amplifier's transfer characteristics as you are trying to do.

I don't know the architecture of your front end, but filtering will likely reject much of the interference away from your 902-928 MHz spectrum.