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6G does not exist, yet it is already here – II

The Shannon theorem, expanded, to take into account the use of several antennas. In the graphic W stands for the spectrum band, B in the original Shannon theorem, and SNR for the Signal Noise ratio. Image credit: Waveform

2. Spectrum efficiency

Over the last 40 years, since the very first analogue wireless systems, researchers have managed to increase the spectral efficiency, that is to pack more and more information in the radio waves. Actually, with the 4G they have reached the Shannon limit. Shannon (and Hartley) found a relation between the signal power and the noise on a channel that was limiting the capacity of that channel. Over that limit the errors will be such that the signal will no longer be useful (you can no longer distinguish the signal from the noise):

C=Blog(1+S/N)

where C is the theoretically available channel capacity (in bit/s), B is the spectrum band in Hz, S is the Signal power in W and N is the Noise power in W).

Since the spectral efficiency is a function of the signal power you cannot give an absolute number to it, by increasing the signal power you could overcome noise, hence pack more bit per Hz. In practice you have some limit to the power, dictated by the regulation (max V per meter allowed), the kind of average noise  in the transmission channel (very very low for optical fibre, much much higher from wireless in a urban area, even higher in a factory…) as well as to the use of battery power.

Today, in normal usage condition and with the best wireless system, the Shannon limit for wireless system is around 4 bit per Hz (that is for every available Hz in the spectrum range allocated to that wireless transmission you can squeeze in 4 bits. Notice that because of the complexity of the environment condition you can find numbers from 0.5 to 13 in spectral efficiency, what I am indicating is a “compromise” just to give an idea of where we are). A plain 3G system may have a 1 bit per Hz in spectral efficiency, a plain vanilla 4G reaches 2.5 and with QAM 64 reaches 4.

This limit has already been overcome using “tricks” like higher order modulation (like QAM 256 reaching 6.3 bit per Hz) and most importantly using MIMO, Multiple Input Multiple Output.

This latter is really a nice way to circumvent the Shannon limit. This limit is about the use of a single channel. Of course, if you use more channels you can increase the number of bits per Hz, as long as these channels do not interfere with one another. This is actually the key point! By using several antennas, in theory, I could create many channels. one for each antenna couple (transmitting and receiving). However these parallel transmission (using the same frequency and spectrum band) will be interfering with one another.

Here comes the nice thing: “interference” does not exist! Interference is not a property of waves. Waves do not interfere. If a wave meets another wave, it does not stop to shake hands, rather each one continues undisturbed and unaffected on its way. What really happens is that an observer will no longer be able to distinguish one wave from the other at the point where they meet/overlap. So, the interference is a problem in the detector, not of the waves. You can easily visualise this as you look at a calm sea. You will notice small waves and in some areas completely flat patches. These are areas where waves meet and overlap annihilating one another (a crest of one adds to the trough of the other resulting in a flat area). If you have “n” transmitting antennas and “n+1” receiving antennas (each separated from the others at least half-wavelength, then you can sort out the interference and get the signal. This is basically the principle of MIMO. To exploit it you need sufficient processing power to manage all signals received in parallel by the antennas and this is something I will address in a future post. For now it is good to know that there is a way to circumvent the Shannon limit and expand the capacity of a wireless system.

6G will not just exploit massive MIMO, it will be able to do something amazing: spread the signal processing across many devices, each one acting as an array of antennas. Rather than having a single access point in 6G, in theory at least, you can have an unlimited number of access points, thus multiplying the overall capacity. It would be like sending mails to many receivers. You may have a bottleneck in one point but the messages will get to other points that in turn will be able to relay them to the intended receiver once this is available.

About Roberto Saracco

Roberto Saracco fell in love with technology and its implications long time ago. His background is in math and computer science. Until April 2017 he led the EIT Digital Italian Node and then was head of the Industrial Doctoral School of EIT Digital up to September 2018. Previously, up to December 2011 he was the Director of the Telecom Italia Future Centre in Venice, looking at the interplay of technology evolution, economics and society. At the turn of the century he led a World Bank-Infodev project to stimulate entrepreneurship in Latin America. He is a senior member of IEEE where he leads the Industry Advisory Board within the Future Directions Committee and co-chairs the Digital Reality Initiative. He teaches a Master course on Technology Forecasting and Market impact at the University of Trento. He has published over 100 papers in journals and magazines and 14 books.