Is the radio spectrum a six-dimensional problem space?
Dec 20, 2012 by Richard Womersley



There have been a myriad of attempts to define spectrum usage and spectrum rights. For fun(!) I have been trying to bring these all together into a single framework for defining interference and, by dint, sharing. The result appears to point to the radio spectrum being a six-dimensional problem space…

Over the
past couple of months, as a result of work I have been undertaking, I have been
led into thinking about how to define metrics for technical spectrum efficiency
as well as considering how spectrum can best be shared.  One thing that I have come to realise is that
sharing and efficiency go hand-in-hand insofar as that although spectrum
efficiency can be considered purely in terms of ‘how much output can be gotten
from a certain input’ it should also take into account that across the whole
radio spectrum there are a multitude of users whose outputs need to be
accommodated within the available input.
Efficiency, therefore, must be cognisant that, as controversial 18th
Century philosopher Jeremy Bentham had it, ‘It is the greatest good to the
greatest number of people which is the measure of right and wrong
’ (or as Mr.
Spock interpreted it in The Wrath of Khan, ‘the needs of the many outweigh the
needs of the few
’). As a result of these activities, I have come to develop a
model for defining spectrum usage which I believe captures all the possible
parameters which come to play and which might form the basis for a full and
holistic framework for assessing spectrum efficiency.

For a long
time, various sages have identified that spectrum use can be shared by:

  • Time
    – different users can use the same spectrum at different times without causing
    each other interference.
  • Frequency
    – as with time, using different frequencies from other users does not cause them
    undue interference.
  • Location
    – depending on the coverage of a transmission, spectrum can generally be
    re-used in different locations without causing interference.


small gaps need to be left in time (guard intervals), frequency (guard bands)
and location (sterilisation areas) in order for spectrum to be effectively
shared between users.  The bigger these
gaps, the less efficiently the spectrum is being used and it therefore follows
that if they can be reduced or eliminated, spectrum efficiency is increasing.

These first
three parameters are relatively straightforward and well documented, but there
are at least a further two methods by which spectrum can be shared:

  • Directionality
    – spectrum can be used in one place, time and frequency, in different
    directions (or at different angles).
    Think of a satellite dish: by moving it just a few degrees, you can
    receive many different signals.
  • Polarisation
    – in some controlled environments (satellite remains a good example) the same
    spectrum can be re-used with orthogonal polarisation (eg vertical versus


But for
each of these parameters there are both ‘intentional’ and ‘unwanted’
effects.  Intentional effects determine
how well the spectrum is used within a given parameter, that is to say when a
system is meant to be using the spectrum.
Unwanted effects are products that are generated in such a way as to
occur when the system in question is using spectrum that it is not meant to be.
Intentional effects might also be considered as ‘contributors’ in that the
greater the extent to which a system operates at the limits of these effects
(the smaller the gaps), the better the contribution it is making to efficient use
of the spectrum.  Unwanted effects might
be seen as ‘detractors’ in that any system generating these unwanted effects
will be detracting from the ability of other systems to use the spectrum

These are
perhaps difficult concepts to describe. The table below gives examples of
intentional effects (contributors) and unwanted effects (detractors) for each
of the five parameters identified so far.

Parameter Intentional / Contributor Unwanted / Detractor Example causes of unwanted effects
Time Emissions that occur within a defined time period. Emissions that occur outside of a defined time period. The need for time to elapse to turn a transmitter on or off. Delays caused by distance and the finite speed of light.
Frequency Emissions that occur within a defined channel. Emissions that occur outside of a defined channel (out of band emissions). Imperfections in digital modulation techniques or circuitry. Doppler shift.
Location Emissions that occur within a defined area. Emissions that spill outside of a defined area. There are no means to stop radio signals at any boundary and such spill over is therefore difficult to control.
Directionality Emissions that occur in a defined direction. Emissions that are not in the defined direction. Even the best directional antennas radiate some signal either side of the direction in which they are pointing.
Polarisation Emissions that occur in a defined polarisation. Emissions which are on the orthogonal polarisation to the one intended. Generally, antennas can only discriminate between orthogonal polarisations by around 20 dB (100:1 ratio). Another difficulty here is that multi-path signals cause polarisation to be scrambled.


This table focuses on emissions from transmitters but the same concepts can equally be applied to receivers.  A receiver’s ability to discriminate between signals that it is intended to receive and those which are unwanted also contributes to the efficient use of spectrum.  Whilst there are questions about the economic benefits of enforcing receiver characteristics, there is no technical question as to whether or not it would improve spectrum efficiency.

If use of the spectrum to the maximum extent within all of the five intentional effects can be obtained, spectrum is being utilised effectively.  Similarly, if all five unwanted effects can be minimised, there should be no significant impact on the efficiency of other systems.  This has to be the case both for transmitters and for receivers for the ultimate in efficiency to be achieved.

In theory, all ten parameter/effect combinations could be used and indeed in some advanced mobile networks, most of these ten are already in use to maximise spectrum efficiency.

Parameter Way exploited in LTE
Time Timeslots are used to share spectrum between users (TDMA). Timing advance is used to minimise any ‘guard intervals’ required between users who are different distances away from a base station.
Frequency The available spectrum is shared between different users (OFDMA on the downlink and SC-FDMA on the uplink). This provides mitigation against some kinds of fading and shares spectrum between users.
Location The frequency re-use factor can be ‘1’ meaning that all cells are on the same frequency and as such there are no sterilisation areas around a cell in which a frequency cannot be re-employed.
Directionality Multiple antennas can be used at both the base stations and potentially in the handsets to form electronically steerable directional beams (MIMO) which can both focus energy in the wanted direction and can form notches in directions where interference is present.
Polarisation Cross-polarised antennas can be used in MIMO systems and have been shown to provide better throughput than co-polarised antennas.(see


But is there a sixth parameter, interference?  The ITU definition of harmful interference includes some relatively qualitative assessments such as ‘endangers’ and ‘obstructs’, neither of which are truly measurable.  Nonetheless, the use of harmful interference as a reference to mean ‘interference which degrades the operation of a system beyond that which it can safely operate’ or ‘… beyond which it is able to provide a pre-agreed level of service’ at least provides some means of categorising the effect.

Some systems already balance interference from various users to operate just short of it being harmful. Take a typical CDMA network.  At the base station, the signals coming from mobile devices interfere with each other as they are on the same frequency at the same time (and may be coming from the same direction).  In this instance, power control is used to ensure that each user transmits at the power necessary to overcome interference from other users. At the same time, power levels can be increased to improve the speed of connection between the base station and a user if doing so would not cause harmful interference to other users.  If these rules are maintained, it is possible for the base station receiver to use signal processing to separate users and the system therefore continues to operate.  The network therefore maximises (not minimises) interference and by doing so, maximises the efficiency with which it uses the spectrum.

In many GSM handsets, a technique called ‘Single Antenna Interference Cancellation’ (SAIC)  is used to remove some interference from an incoming signal using knowledge of what that interference looks like (it happens to look like another GSM signal).  It effectively changes the level at which interference becomes harmful and in doing so makes use of spectrum more efficient.  It does not change time, frequency, location, direction or polarisation.

I therefore posit that there is another row to the table of parameters.

Parameter Intentional / Contributor Unwanted / Detractor Example causes of unwanted effects
Interference Emissions that are below a defined interference threshold. Emissions that exceed a defined interference threshold. Using more power than is necessary to communicate.


As with other parameters, it is the transmitter which determines the amount of interference that is generated.  This could just be using a higher transmitter power than is necessary, or could be to do with the waveform used. Ultra Wide Band (UWB) transmitters are meant to use a waveform that causes minimal interference to other spectrum users.  Use the same power as UWB, but a different waveform, and interference to a different system could easily manifest. Equally, a receiver that is better able to cope with interference (as in the SAIC example above) can also contribute to efficiency.  The concept of VFDM which I discussed in an earlier blog post, is effectively just another means of managing or controlling interference.

Unless my musings have passed over some additional parameter (which they quite easily could have done) then the framework for spectrum efficiency and sharing is a six dimensional problem space (noting that two of those dimensions – location and direction – are in themselves already three dimensional parameters).  Is it therefore any wonder that spectrum regulators, policymakers and strategists, let alone mere mortals, find it difficult to get to grips with whether, when and how spectrum is being used and/or shared efficiently?

The framework outlined above is more a sujet de conversation than a fait accompli but I would be interested to hear whether anyone else has views on what the complete set of parameters for defining a framework for technical spectrum efficiency might be. Obviously I have carefully sidestepped any discussion of economic or social efficiency, as these would require years of continuous academic study and debate before any agreement on how to measure them in such staunchly quantitative terms would ever be reached. Nonetheless, have I missed anything?  Are there better parameters?  Do leave your thoughts.  Like the aforementioned Mr. Spock, I’m all ears!