When I was a kid I wondered how radio stations avoided interfering with each other. "Different frequencies" was an obscure concept, when even audio frequency was still obscure.

Phase array radar and holograms are explained and probably invented in terms of wave concepts. They collectively seem in conflict with the inverse square law that seems like one of those laws of nature that you shouldn't try to cheat on.

When FM radio became common in cars the phenomenon of fading and null spots became widely known.

There are germs of several ideas mixed in with the above comments. I want to introduce a scheme that draws on these ideas. What would it take to build a radio transmission system that put the strong spots where the only intended receiver was? By strong spot I mean where the signal is near a maximum—the opposite of a null spot. This is a bit like phase array radar where by regulating the phases of many transmitting elements, signal energy is delivered to a small part of the space that would receive the signal of any one of the elements transmitting in isolation. Think of it as phase array radar with ad-hoc empirical phases.

Instead of transmitters and receivers, I will refer to stations and mobile units (MUs) for we want to design a two way system. Both would transmit and receive.

The idea is to install many permanent stations each operating on the same very narrow band. Each station would be a transmitting and receiving element. This is like phase array systems except that the stations are distributed hundreds of meters apart, where ever sites are conveniently available. Their phase would be adjusted to maximize the signal at the intended MU. This is far more energy efficient than current schemes where the signal energy is delivered over the entire cell. It saves both bandwidth and energy. The stations can simultaneously transmit different signals to several MUs, each MU located near its own strong spot. As in phase array radar, receiving is a variation on transmitting.

My intuition is that the stations would need to be spread in clumps of just a few, a few clumps per cell. The stations of a clump would need to be a wavelength or so apart. If all of the stations are within a few wavelengths of each other and those distances are small compared with the distance to the MU, then the strong spots will all have at least one long dimension. It will be a lobe that is long along the radius vector. If stations are spread apart at distances comparable with the distance to the MU then the strong spots may be small in all dimensions. (Well if the stations are distributed in mainly two dimensions, then the lobes will have a large vertical extent.)

There are several obvious, perhaps fatal problems with this scheme. Three I address here are (1) the ability to control phase to a few picoseconds, (2) the discovery of the correct phase for each combination of element and MU, (3) tracking these phases as the transmission paths change slowly.

Several times each second, all stations but one would shut up and listen to the remaining element that would set the standard phase for the neighborhood. Still, a highly stable oscillator is required.

The determination of the phase for each combination of station and MU would be empirical. If the frequency is used half-duplex then by reciprocity the transmit and receive phases are the same. I think that the phase information would need to be recomputed or adjusted a few times per second due to changes in the multipath configurations. The simplest scheme would be to reserve 1 microsecond a few times per second for any particular active MU. During that time just that unit would transmit a pure carrier. Each base station would then know its phase relationship with the MU. The oscillator on the MU is not so good but the relative phases between the base stations, regarding that MU, would be accurate. I do not anticipate that this would work well for moving cars, but that it could compensate for a few people milling around an MU.

Problem with Receiving

It may not be feasible to require such stable oscillators in the MUs. The stations would not know what phase to receive from an MU. The signal addition might have to be done centrally by digitally transmitting over land lines time averaged signal strength for two orthogonal phases. Such transmission would cover the needs of several MUs, however. Such time averaging would be over durations of a large fraction of a baud. I think that the phase relationship between stations and MUs might be a byproduct of this calculation.

Math Annex

There is some surprising math here. Consider a phase array radar with 100 elements. You are a cloud that the radar has decided to ping. The radar runs each element with the same frequency but with the phases adjusted so that the 100 signals will be all in phase as they reach you. If your distance from the radar is r then the strength of the individual signals is each 1/r2 and you might think that the total strength would be 100/r2. That would about right except that it does not take into account that the signals are in phase. The field strength due to each element goes down as 1/r, and the energy (power) is the square of the field strength. The collective field strength of the elements is thus 100/r and the square of that is 10000/r2. Big difference! The signals at the neighboring cloud systematically out of phase and the strength there is much less than 100/r2. In some sense the strength averaged over all directions is 100/r2

Direct Sequence Spread Spectrum

These ideas could be applied to DSSS except I wouldn't know how to come up with effective inverses of the transfer function. This would likely be required several times per second for each MU and each base station. Tricks with the precomputed FFT of the sequence might reduce this problem to the previous solution.

This does not seem promising with frequency hopping.

See this for some different ideas based on the same physics.