Genetic Algorithms for Optimal Channel
Assignments in Mobile Communications
Lipo Wang*, Sa Li, Sokwei Cindy Lay, Wen Hsin Yu, and Chunru Wan
School of Electrical and Electronic Engineering
Nanyang Technological University
Block S2, Nanyang Avenue, Singapore 639798
* Corresponding author
Phone: +65 6790 6372
Fax: +65 6792 0415
The demand for mobile communication has been steadily increasing in recent years. With
the limited frequency spectrum, the problem of channel assignment becomes increasingly
important, i.e., how do we assign the calls to the available channels so that the
interference is minimized while the demand is met? This problem is known to belong to a
class of very difficult combinatorial optimization problems. In this paper, we apply the
formulation of Ngo and Li with genetic algorithms to ten benchmarking problems.
Interference-free solutions cannot be found for some of these problems; however, the
approach is able to minimize the interference significantly. The results demonstrate the
effectiveness of genetic algorithms in searching for optimal solutions in this complex
Keywords: genetic algorithms, channel assignment, mobile communications, wireless
As cellular phones become ubiquitous, there is a continuously growing demand for
mobile communication. The rate of increase in the popularity of mobile usage has far
outpaced the availability of the usable frequencies which are necessary for the
communication between mobile users and the base stations of cellular radio networks.
This restriction constitutes an important bottleneck for the capacity of mobile cellular
systems. Careful design of a network is necessary to ensure efficient use of the limited
One of the most important issues on the design of a cellular radio network is to determine
a spectrum-efficient and conflict-free allocation of channels among the cells while
satisfying both the traffic demand and the electromagnetic compatibility (EMC)
constraints. This is usually referred to as channel assignment or frequency assignment.
There are three types of constraints corresponding to 3 types of interference , namely:
1) Co-channel constraint (CCC)
• where the same channel cannot be assigned to certain pairs of radio cells
2) Adjacent channel constraint (ACC)
• where channels adjacent in the frequency spectrum cannot be assigned to
adjacent radio cells simultaneously
3) Co-site constraint (CSC)
• where channels assigned in the same radio cell must have a minimal
separation in frequency between each other.
One of the earlier aims of the channel assignment problem (CAP) is to assign the
required number of channels to each region in such a way that interference is precluded
and the frequency spectrum is used efficiently. This problem (called CAP1 in ) can be
shown to be equivalent to a graph coloring problem and is thus NP-hard.
As demand for mobile communications grows further, interference-free channel
assignments often do not exist for a given set of available frequencies. Minimizing
interference while satisfying demand within a given frequency spectrum is another type
of channel assignment problem (called CAP2 in ).
Over the recent years, several heuristic approaches have been used to solve various
channel assignment problems, including simulated annealing , neural networks
, and genetic algorithms -. In particular, ,- used GA for CAP1.
, , and  formulated CAP2; however, they were interested only in interference-
free situations.  gives a unique formulation of CAP2 in terms of GA; however, no
simulation results were presented. Ngo and Li  developed an effective GA-based
approach that obtains interference-free channel assignment by minimizing interference in
a mobile network. They demonstrated that their approach efficiently converges to
conflict-free solutions in a number of benchmarking problems.
In this paper, we apply Ngo and Li's approach to several benchmarking channel
assignment problems where interference-free solutions do not exist. The organization of
this paper is as follows. Section 2 states the channel assignment problem (CAP). Section
3 summarizes Ngo and Li's approach to solving CAP with genetic algorithms. Section 4
describes the tests carried out and results obtained, with many choices of parameters.
Finally, we conclude the paper in section 5.
2 CHANNEL ASSIGNMENT PROBLEM
The channel assignment problem arises in cellular telephone networks where discrete
frequency ranges within the available radio frequency spectrum, called channels, need to
be allocated to different geographical regions in order to minimize the total frequency
span, subject to demand and interference-free constraints (CAP1), or to minimize the
overall interference, subject to demand constraints (CAP2). In this paper, we are
interested in CAP2, since it is more relevant in practice compared to CAP1.
There are essentially two kinds of channel allocation schemes - Fixed Channel Allocation
(FCA) and Dynamic Channel Allocation (DCA). In FCA the channels are permanently
allocated to each cell, while in DCA the channels are allocated dynamically upon request.
DCA is desirable, but under heavy traffic load conditions FCA outperforms most known
DCA schemes. Since heavy traffic conditions are expected in future generations of
cellular networks, efficient FCA schemes become more important . The fixed
channel assignment problem, or in other words, assigning channels to regions in order to
minimize the interference generated has been shown to be a graph coloring problem and
is therefore NP-hard.
A cellular network is assumed to consist of N arbitrary cells and the number of channels
available is given by M. The channel requirements (expected traffic) for cell j are given
by Dj. Assume that the radio frequency (RF) propagation and the spatial density of the
expected traffic have already been calculated. The 3 types of constraints can be
determined. The electromagnetic compatibility (EMC) constraints, specified by the
minimum distance by which two channels must be separated in order that an acceptably
strong S/I ratio can be guaranteed within the regions to which the channels have been
assigned, can be represented by an N × N matrix called the compatibility matrix C.
In this matrix C:
• Each diagonal element Cii represents the co-site constraint (CSC), which is the
minimum separation distance between any two channels at cell i.