we consider more dimensions of the hyperellipsoid Y; we can add more balls adding dimensions until OK > E; the NDF is the largest k value such that Ok > E; in the example shown in the figure, NDF = 2 is a value k', such that Ok' becomes smaller than E making it impossible to add further spheres (see Fig. 2.5). Since Ok is a decreasing sequence of positive numbers, all the dimensions k > k' do not provide any contribution to the packing process. This intuitive explanation has its rigorous mathematical counterpart in the theory of Kolmogorov information theory and in the n-widths theory [35, 66]. Accordingly, the number of parallel spatial communication subchannels at the PL is limited by the NDFé at the DPL. Summarizing, the field can be approximated by the first NDFé basis functions (2.6) while the e-channel capacity turns out to be [9] (2.7) 2.3 Bandlimited Approximation in the Space Domain The analysis carried out in the above section is based on the Kolmogorov approach instead of Shannon's one usually adopted in Information Theory. The reason is related to a slight asymmetry between information in time domain and in space domain. 2 Information Flows at the DPL Level Loosely speaking, in the time domain, the information is associated with different time-varying waveforms chosen SO that they are distinguishable by the receiver even in the presence of noise. The bandwidth of the communication channels limits the set of waveforms that can be received. In practice, the bandlimiting operator plays a role equivalent to that played by the propagation operator in limiting the set of space-varying waveforms. Like the radiation operator, also the bandlimiting operator is a compact operator [67] whose singular values are almost constant up to a value after which an extremely rapid decrease occurs [68]. The number of singular values at the knee is called the Number of Degrees of Freedom of the (time domain) signal, and in the following it will be denoted as TNDF. In case of a signal having effective bandwidth B and observe