MUSIC algorithm terminology
Yeah, notation is not ideal.

It is not - he assumes that each of the $M$ antenna elements is connected to its own RF chain, i.e., there are also $M$ receivers available. If you have fewer receivers you need to modify your $A$, it needs to contain the response your $K$ receivers observe given a wave from a certain direction.

He doesn't put it but yeah, $F$ should have $N$ columns (and so should $X$ and $W$) that correspond to $N$ subsequent snapshots (i.e., samples in time) of the received RF data.

The received signal, i.e., the (basedband version of the) RF data at the ouput of the $M$ antennas observed in $N$ subsequent snapshots is the $M \times N$ matrix $X$. The matrix $F$ comprises only the waveforms itself, you could think of it as the signal &quot;before&quot; the antenna array. But that intuition is also slightly misleading. Point is that each antenna is observing a superposition of $D$ wavefronts corresponding to $D$ far-field sources. This can be written as $A F$.


Note that this data model is a gross oversimplification of the actual physics. It ignores near-field sources/reflections, multipath, diffuse components and many things more. It still works well enough in some applications. But the physical interpretation we can put into it has its limits.