I searched a lot for a generalized equation or an algorithm that can be implemented on MATLAB. However, all that I found still theoretical analysis. Can you help with the algorithm or the code for wideband not narrowband?
Dear Amr,
CRB is a theoretical performance lower bound of the MSE of estimators (e.g. DOA estimator). It must then be theoretically computed, not through matlab, in my understanding. Matlab should be used to check the accuracy of any method through Monte-Carlo simulations compared with the theoretical results.
Best,
Vincent
Vincent Savaux I understand. My point is to add it to the RMSE figures to compare with the DOA methods. That is why I need to write a MatLab script for it.
If you recommend a good reference on how to drive it and understand it better, it would be much helpful for me.
First, you need to derive CRB for your reception scenario, based on its underlying assumptions. For example, are the signals of interest (SOI's) known (with or without an unknown gain), unknown, or random with a known distribution? What is your background interference distribution? If complex Gaussian, does it have a known or unknown spatial and frequency distribution? Assuming you are using a multielement antenna array, is it calibrated over azimuth and elevation? Is it cross-polarized? Are the SOI's subject to multipath, and if so is there a model for that?
For a wideband system, I would postulate a frequency-channelized reception system, such that narrowband array assumption holds on each channel, and assume that the interference is independent between channels and i.i.d. on each channel (not necessarily true based on your actual channelizer structure, but a good starting place). The extension from narrowband to wideband is straightforward under those assumptions.
Once you have derived DOA CRB for your system, then you can start using it to analyze performance of your system in Matlab.
Dear Amr
In addition to the preceding answers, when you code the CRB in Matlab (once you have your equation) you should use the true values of the parameters (of course without Monte-Carlo runs !).
See:
- DOI: 10.1109/GlobalSIP45357.2019.8969279
- https://ieeexplore.ieee.org/document/5406980
Mustapha Djeddou thanks for references. Brian G. Agee thanks for the explanation. I checked and read those references but what I want is a more detailed book or tutorial on how to drive CRB for any model. Any suggestions?
You can't find a reference for the CRB derivation for any model, you can find the theory behind the CRB. I recommend this book (the estimation volume):
Kay, Steven M. Fundamentals of statistical signal processing. Prentice-Hall PTR, 1993.
Just checked back on this thread. I'd also recommend H.L. Van Trees, "Detection, Estimation, and Modulation Theory, Part I," which provides a detailed general definition of Cramer-Rao bound, and provides a number of examples of use.
There are some important simplifications of CRB for Gaussian distributed random variables, which my version doesn't cover but I suspect is in the latest edition.
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