Optimized planning of frequency hopping in cellular networks
Introduction
The radio spectrum has to be utilized efficiently in order to achieve high performance in cellular networks. For GSM networks, previous research in resource management has focused on the frequency assignment problem (FAP). The objective of FAP is to assign the available frequencies to the transmission facilities, such that the network performance, often measured in the total interference, is optimized.
We consider a generalization of FAP that arises in GSM networks using the frequency hopping technique. Frequency hopping means that a traffic channel shifts its frequency in a certain pattern. In GSM networks, frequency hopping has become a standard feature for improving the network performance in terms of interference. Our focus is to take into account the impact of frequency hopping in modeling and solving the problem of frequency assignment. In this paper, we show how the interference improvements provided by frequency hopping can be modeled mathematically. The optimization problem that we consider concerns assigning lists of frequencies to blocks of transceivers, such that the total interference is minimized. We refer to this problem as the frequency assignment problem with frequency hopping (FAPH). The classical frequency assignment problem, FAP, is a special case of FAPH. To solve FAPH, we present a simulated annealing algorithm. As a feature of the algorithm, a frequency list for one transceiver block is generated in each iteration. Moreover, generating the optimal frequency list for one transceiver block can be formulated using a linear integer program, for which our computational experiments show that a greedy procedure finds optimal or near-optimal solutions.
The remainder of the paper is organized as follows. In Section 2 we give a brief description of the classical FAP. A discussion of the frequency hopping technique and a problem definition of FAPH are given in Section 3. We present a mathematical model in Section 4, and describe the simulated annealing algorithm in Section 5. Computational results are reported in Section 6. Finally, we draw some conclusions in Section 7.
Section snippets
The classical frequency assignment problem
The infrastructure of a GSM network comprises of base transceiver stations (BTS) located at a number of sites. A BTS site consists of one or several cells. A transmission facility is often referred to as a transceiver (TRX). Typically, a cell has several TRXs, and one frequency is allocated to each TRX. The capacity of a cell can therefore be measured in the number of TRXs. The capacity of a frequency is divided into eight time slots using time division multiple access (TDMA), where each time
Frequency hopping
Frequency hopping has become a standard feature in GSM networks (see, for example, [22], [23], [24], [25], [26], [27]). Using frequency hopping, a TRX shifts its frequency among a set of frequencies. This frequency shift occurs for every time slot, and follows a defined sequence. To implement frequency hopping, a so-called mobile allocation list (MAL), containing a number of frequencies, is used by each TRX. The hopping sequence is determined by a parameter called the hopping sequence number
A mathematical model
To formulate FAPH mathematically, we introduce the following parameters:the co-channel interference between STRX p and STRX q, where p is the interfering STRX the adjacent channel interference between STRX p and STRX q, where p is the interfering STRX the distance between MALs i and j in the frequency spectrum the minimum distance between the MALs at STRX p and STRX q the minimum distance between the frequencies in the MAL assigned to STRX p the set of feasible frequencies at
Algorithm outline
Simulated annealing is one of the meta heuristics, a class of methods that are frequently used to find high-quality solutions for hard combinatorial optimization problems. The basic idea of simulated annealing is to equip a local search method with a mechanism of accepting inferior solutions at certain probabilities. For detailed treatments of simulated annealing, see Aarts et al. [30], Dowsland [31], Eglese [32], and Vidal [33].
A key issue of the algorithm is the so-called neighborhood
Instances
Table 1 summarizes the networks instances. The first instance (Urban) originates from a real-life GSM network. The networks in the other instances are synthesized. Note that in the table, the last three columns are associated with the traffic channels (TCH), not the control channels (BCCH). This is because frequency hopping is only performed for TCH, and separate frequency bands are allocated to TCH and BCCH in these instances.
All the instances have the following characteristics:
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For each cell,
Conclusions and future work
We have considered the frequency assignment problem with frequency hopping (FAPH), which is a generalization of the classical frequency assignment problem (FAP). We have presented a mathematical formulation and a simulated annealing algorithm for FAPH. The key operation in the algorithm is to generate a list of frequencies to a STRX. The algorithm has been applied to real-life and synthesized networks. Our computational study shows that the algorithm is able to achieve significant interference
Acknowledgements
We deeply appreciate the conversational feedback and the test data given by Joachim Samuelsson, ComOpt AB, Sweden. We thank the editor of Computers & Operations Research and the two anonymous referees for the valuable comments and suggestions. This work is partially financed by CENIIT (Center for Industrial Information Technology), Linköping Institute of Technology, Sweden.
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