I am following this book "Theory and Applications of Spherical Microphone Array Processing", as well as this paper on DOA estimation "Eigenbeam-ESPRIT for DOA-Vector Estimation".
My dataset is composed of a small number of channels (4) from the Eigenmike32. The book states "all spatial sampling schemes require at least $(L_f + 1)^2$ microphones to sample a sound field of order Lf without aliasing.", where $L_f$ is the order of the sound field (3.4 Spatial Sampling). Both the paper and the book use 32 microphones in their implementations.
First, I do not find any information on what is the order of the sound field. It sounds to me that this is a signal-dependent quantity, much like a sampling rate is lower bounded by the highest frequency of the signal you want to sample. Did I get this right? Can anyone elaborate please?
Second, does that mean that I can do very little with 4 microphones? Is there a lower limit on the number of microphones for a DOA estimation and for a number of active sources estimation?
What other, none neural network, methods can I use to estimate the number of active sources and DOA with (no necessarily by the same model)?