What is the formal definition of homogeneous noise field? Is there any example of it?
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Think of being at the center of sphere with a very large radius that has a very large number of uniformly distributed noise sources on its interior surface. What you receive at the center ls spherically isotropic noise. One can envision a similar cylinder for cylindrical isotopic noise.
These are ambient noise models. The interesting thing is that the noise is spatially correlated between two points and has a sin(x)/x form for spherically isotropic noise.
This is a model typically used in SONAR where the electronic thermal noise of each sensor is lower than the ambient noise.
This model is derived in a number of books or at least referenced in just about every SONAR or Underwater Acoustics book. I like the presentation in Underwater Acoustic System Analysis by William S. Burdic (first edition) because he also derives the half sphere and infinite plain models. The only criticism of Burdic's analysis is that it assumes straight line propagation. Van Trees, Detection Estimation and Modulation Theory, Vol 4, Array processing has a section on ambient noise fields with many references.
The really interesting thing of spherically isotropic noise is that for a given temporal frequency, the zeros of the spatial correlation function are separations of $\lambda/2$ which is also the spatial Nyquist criteria.