A theorem is not, indeed, a fact. It is rather, an idea that is deduced and supported by other proven facts. Thus, a theorem is generally believed a truth. It should be of interest to the “All Digital” AM (AKA Medium Wave) proponents that noise on the digital channel will reduce data throughput as a function of channel bandwidth and Signal to Noise Ratio. This is known as the Shannon-Hartley theorem:
C is the channel capacity in bits per second;
B is the bandwidth of the channel in hertz (passband bandwidth in case of a modulated signal);
S is the average received signal power over the bandwidth (in case of a modulated signal, often denoted C, i.e. modulated carrier), measured in watts (or volts squared);
N is the average noise or interference power over the bandwidth, measured in watts (or volts squared); and
S/N is the signal-to-noise ratio (SNR) or the carrier-to-noise ratio (CNR) of the communication signal to the Gaussian noise interference expressed as a linear power ratio (not as logarithmic decibels).
With this equation, one can discern a fundamental flaw in all digital logic. One of the main issues with AM Medium Wave broadcasting is the ever-increasing noise floor. Our society has changed drastically in the last one hundred years or so since AM was invented. Electrical noise generators; computers, plasma screen monitors, mobile phones, appliances, energy-efficient lighting, data over power line, street lights, poor utility line maintenance, and even electric cars, it seems, generate a cacophony of noise in the Medium Wave frequency band. A digital modulation scheme, be it HD Radio or DRM, will mask the noise to a certain extent, that is true. However, once the SNR exceeds the ability of the receiver to decode the necessary bits, the receiver will mute. While it is true, the listener will not hear noise, they may not hear anything at all.
I will also note; none of the current “AM improvement” schemes under consideration by the FCC addresses the noise issue on the AM band. Without addressing the noise issue, any digital modulation scheme will be a temporary fix at its very best. The noise floor will continue to rise and after it gets high enough, the all-digital modulation will simply not work.
It will be interesting to see the data from the all-digital HD Radio testing that is being done in various locations. That is, if the NAB, et al. does not decide to treat that data like some kind of state secret; they have become reticent of late. When somebody acts like they have something to hide, it makes me think they have something to hide…