1. A Survey on Static Frequency Assignment
Karen I. Aardal, Stan P.M. Van Hoesel,
Arie M.C.A. Koster, Carlo Mannino, and Antonio Sassano,
Models and Solution Techniques for Frequency Assignment Problems, January 9, 2007.
Presented By Donghyun Kim On March 5, Mobile Computing and Wireless Networking Research Group
at University of Texas at Dallas

2. Electromagnetic Spectrum
Figure Source:
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

3. Availability of Frequencies
The availability of frequencies from the radio spectrum is regulated by the national governments, and world-wide by the International Telecommunication Union (ITU).
Operators of wireless services are licensed to use one or more frequency bands in specific parts of a country.
The frequency band for a provider is usually partitioned into a set of channels, all with the same bandwidth of frequencies.
Channels (open called frequencies) are usually numbered from 1 to a given maximum , where
The available channels are denoted by
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

4. Origin of Frequency Assignment Problem (FAP)
FAP appeared in 1960s.
Scarcity of usable frequencies in radio spectrum by the boom of wireless service businesses (i.e. cellular networks).
Frequencies were licensed by the government, which charges operators for the usage of each single frequency.
Operators want to develop a frequency plan to
service more people with the same amount of frequency.
avoid high interference level <= explained later.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

5. Growing Interest in FAP
Metzger suggested to use mathematical optimization, especially graph coloring techniques for this propose [1].
Until the early 1980s, most contributions on frequency assignment used heuristics based on the related graph coloring problem.
First lower bounds were derived by Gamst and Rave in 1982 for the most common problem of that time.
The development of GSM leads to the rapid increasing interest for FAP.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

6. Focus of This Survey
This paper only discuss Fixed Channel Assignment (FCA).
The set of connections remains stable over time.
Not cover…
Dynamic Channel Assignment (DCA) – the demand for frequencies at an antenna varies over time.
Hybrid Channel Assignment (HCA) – combination of FCA and DCA: a number of frequencies have to be assigned beforehand, but space in the spectrum has to be reserved for the online assignment of frequencies upon request.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

7. Common features of FAP instances
A set of wireless communication connections (i.e. antennae) must be assigned frequencies.
Two connections may incur interference to one another when following two conditions are fulfilled
The two frequencies must be close on the Electromagnetic band (i.e. same channel).
Connections must be geographically close to each other.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

8. Solutions
FAP arises with application specific characteristic and modeled differently based on
The handling of interference among radio signals
The availability of frequencies
The optimization criterion
The solution can be divided into largely two parts
Heuristic search techniques
Optimization and lower bounding techniques
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

9. Interference of Frequencies
Assume is the set of available channels to an antennae .
Not all channels from might be available.
At the border of a country, there can be a substantial reduction in channel availability.
Interference of signals is measured by the signal-to-noise ratio, or interference ratio, at the receiving end of a connection.
The actual signal-to-noise ratio at a receiver depends on
The choice of frequency
The strength of the signal
The direction it is transmitted to
The shape of the environment
Weather conditions
It is hard to obtain an accurate prediction of the signal-to- noise ratio at receivers => how to model interference?
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

10. Interference of Frequencies – cont’
One simplification
Ignore the environment and assume an omni- direction antenna.
Now, assume two signals at the same frequency channel. How to model interference?
The interference of the second signal at the receiver of the first signal is computed with the following formula: , where is the power of the interfering transmitter and is distance to the disturbed receiver. is a fading factor with values between 2 and 4 – which depends on the frequency used.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

11. Interference of Frequencies – cont’
Multiple source of weak noise can incur an interference.
In most models, this is ignored and only interference between pairs of connections or antennae is measured.
It is binary relation: only two connections or antenna are involved =>
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

12. Interference of Frequencies – cont’
In mobile telephony and radio-TV broadcasting, the receivers are spread within a certain area.
The standard approach of determining signal strength at all locations in the area is the followings.
A grid of squares of predetermined (small) size, the test points of pixels, is designed to overlap the area.
For each test point, the levels of the received signals generated by the serving transmitter, typically the one with the strongest received signal (best server), and by the interfering transmitters are predicted with a wave propagation model. Test points with same best server can be clustered to service areas.
For a single transmitter , and a given interfering transmitter , the noise generated by in each pixel of the service area of is aggregated to a single value, which represents the interference of over .
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

13. Interference of Frequencies – cont’
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

14. Interference of Frequencies – cont’
Pure co-channel Philadelphia instances
Interference of cells is characterized by a co- channel reuse distance .
No interference occurs iff the centers of two cells have mutual distance more than .
If it is less than , it is not allowed to assign the same frequency to both cells.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

15. Interference of Frequencies – cont’
Generalized Philadelphia instances
is replaced by a series of non-increasing value and corresponding forbidden set to
The following relation holds , whenever , where is the distance between the cell centers and denotes the set of forbidden differences for frequencies assigned to and .
For the original Philadelphia instance, the sets are take as For example, are
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

16. Interference of Frequencies – cont’
So, frequencies assigned to the same site should be separated by at least 4 other frequencies, whereas frequencies assigned to adjacent sites should be at a distance of at least 2, and frequencies assigned to a second and third ‘ring’ of cells should still differ.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

17. Interference of Frequencies – cont’
Two-way traffic
Except for radio and TV broadcasting all traffic is bidirectional, and one needs two channels, one for each direction.
Such characteristic can make a very special interference problem.
Usually, ignored in most models.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

18. Applications Mobile telephony Radio and Television
Military applications
Satellite communications
Wireless LAN
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

19. Divide frequency band into
Mobile Telephony
Moving agents
Antenna
Divide frequency band into
channels
Each antenna covers a certain region (cell) and can serve several mobile units concurrently.
Using TDMA, several mobile units can share the same frequency band – channel (i.e. 8 channels in GSM).
Multiple frequency band can be assigned to the same antenna.
More antenna can be mounted on a same physical support (site) to cover a number of adjacent regions.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

20. Mobile Telephony – cont’
The frequencies assigned to each antenna must satisfy a number of requirements depending on…
Availability, especially at country borders.
Interference levels.
Technological requirements.
Size of the area with unacceptable interference.
Four types of constraints can be specified.
Co-cell separation constraint.
Co-site separation constraint.
Interference constraint.
Hand-over separation constraint.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

21. Mobile Telephony – cont’
Co-cell separation constraint.
The frequencies assigned to the same antenna v must differ by at least (typically) 3 units.
Co-site separation constraint.
If u and v are co-site antennae, then the distance is typically 2 units.
Interference constraint.
The frequency difference between two antennae not at the same site has to be 1 or at least 2 units.
Co-channel constraints: forbid two cells to use the same frequency.
Adjacent channel constraints: forbid frequencies with distance 0 or 1.
Hand-over separation constraint.
As the mobile unit moves from a cell u to an adjacent one v, control must be switched from u to v (hand-over or hand-off).
Two antennas in the adjacent cells have to broadcast frequencies which have to be differ by at least one unit.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

22. Mobile Telephony – cont’
Problem Instances (Models)
Philadelphia
COST 259
CSELT
CNET
Bell Mobility
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

23. Radio and Television Resemble the mobile phone instances.
Differ in the used frequency distances.
UHF TV broadcasting
Constraints forbid certain differences in frequencies which are not consecutive.
For example, frequency distances 1, 2, 5, and 14 are forbidden.
Due to the inherent characteristic of the frequency band used.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

24. Military Applications
The usage of field phones leads to dynamic frequency assignment problems.
Each connection consists of two movable phone, which force two frequencies to be assigned at a fixed distance of each other.
The frequency assignment problem is extended with polarization constraints.
For every connection, a polarization direction (horizontal or vertical) is to be chosen.
The interference depends not only on the assigned frequencies but also on the choices for polarization.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

25. Satellite Communication
Transmitters and receivers are ground terminals and communicate with each other with the help of one or more satellites.
Uplink and downlink frequency are separated by a fixed distance.
We only have to assign frequencies to the uplink.
A set of consecutive frequencies has to be assigned to every transmitter.
To avoid interference, every frequency may be used only once.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

26. Wireless LANs
A Total 13 frequencies is available for communication using the g standard.
The center of the frequencies is only 5MHz apart from each other.
Typically 24MHz apart are considered to be non-overlapping (non- interfering).
Hence, only 3 frequencies can be used in the same physical neighborhood simultaneously without causing interference.
FAP in WLANs is often considered to be a three frequency problem.
Presented by Donghyun Kim on March 5, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas