Freq Hop (Bourjolly Et)

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Telecommunication Systems 21:24, 249260, 2002 2002 Kluwer Academic Publishers. Manufactured in The Netherlands.

Optimizing Frequency Hopping in GSM Cellular Phone

Networks

JEAN-MARIE BOURJOLLY and SOUHEYL TOUHAMI {brjolly;souheyl}@vax2.concordia.caConcordia University, John Molson School of Business, Department of Decision Sciences & MIS,

1455 de Maisonneuve Blvd., West Montreal, Qubec, Canada H3G IM8

LESLIE DJOIE, KE DING, OUMAR DIOUME and MICHEL LOMINYPrestige Telecom, 575 Morgan Boulevard, Baie dUrf, Qubec, Canada H9X 3T6

Abstract. The mobile telephony market has been undergoing a dramatic increase in the volume of demandas well as in the quality requirements. The limiting resource in this highly competitive market is the avail-able frequency spectrum. In GSM networks, frequency reuse has been the basic tool for optimizing thespectrum management. This method is sometimes insufficient, however, for the most congested networks.Frequency Hopping (FH) is a method that allows one to expand the available capacity of mobile networksor to improve the quality of service through interference averaging and frequency diversity. Current imple-mentations of FH are based on Random or Cyclic Hopping patterns. In this paper, we propose to optimizeFH. We describe a simple heuristic algorithm for allocating frequencies to cells and scheduling the fre-quency hopping for each mobile. The performance of the proposed approach in a synchronized networkis compared to Random and Cyclic FH and to the optimized static frequency reuse implementations. Weshow that hopping algorithms that use some form of controlled optimization beyond random and cyclichopping could significantly improve the quality of service and achieve interference averaging, should thetelecommunications equipment manufacturers decide to implement such a feature or to allow the operatorsto control frequency hopping by using their own algorithms.

1. Introduction

GSM, the European mobile communication system, is also widely used in Asia andAfrica. The rapid growth of the customer basis and competition increased the emphasison network capacity and service quality. Both of these issues are highly dependent on theefficient use of the available radio spectrum. GSM is based on Frequency Division andTime Division Multiple Access (FDMA/TDMA). The available bandwidth is partitionedinto frequencies (FDMA). The time horizon is divided into time frames, which in turn aredivided into eight time slots. Each time slot is used to handle the call of one subscriber(TDMA). Only a limited bandwidth is available for each network operator. This impliesthat inevitably a number of different mobile subscribers will use the same frequencyor adjacent frequencies. This results in Co-channel interference and Adjacent-channelinterference, respectively. Interference levels depend on the network configuration: thenumber ofTransceivers (the radios through which the mobile units communicate), and


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250 BOURJOLLY ET AL.

the location, transmission power and configuration of the antennas. They also dependon the position of the mobile users in the network.

An efficient use of the radio spectrum corresponds to an efficient allocation offrequencies to Transceivers so as to minimize interference. This problem has been tack-led as a combinatorial optimization problem, and several good algorithms for solvingit are already available (see [Borndrfer et al., 1], e.g.). However, the effectiveness ofthese methods is somewhat limited when applied to congested networks because the fre-quency allocation they provide is static: When two mobile subscribers are simultaneousallocated interfering frequencies for their respective communications, the interferenceremains as along as both communications are active since the frequencies on which thecommunications are established do not change. If, due to network characteristics, the

interference levels are high, the mobile subscribers may experience bad communicationquality or, even worse, one or both communications may be interrupted.

Frequency Hopping (FH) is a feature in GSM that aims at overcoming this problemthrough the introduction of frequency and interference diversity. Currently two types ofhopping patterns can be used: cyclic and random hopping. The objective of this paperis to propose an optimized version of FH. In section 2 we describe frequency hoppingin more detail. In section 3 we describe the proposed approach and a simple algorithmdesigned to illustrate the potential gain it may bring about. Section 4 contains someinitial results followed by a few concluding remarks.

2. Frequency hopping

GSM makes use of the inherent frequency agility of the transceivers and mobile units(ability to transmit and receive on different frequencies) to implement slow FrequencyHopping. FH is a technique where the frequency used by a given pair of a Base-Station(BS) and a mobile unit is allowed to change over time at a prescribed rate (217 times persecond). A Base-Station contains one or more cells. Each cell may contain one or moretransceivers (TRX). The first time slot in the first TRX of a cell is used as the BroadcastControl Channel (BCCH). The remaining time slots in that TRX and the time slots inthe other TRXs are used as Traffic Channels (TCH). The mobile allocation (MA) is theset of frequencies allocated to a cell. Under static allocation, the MA contains a numberof frequencies that is equal to the number of TRXs. Each TRX uses only one frequencyfor, say, the Down-Link, i.e., for transmission to the mobile unit. (The Up-Link, i.e.,communication from the mobile unit to the TRX, is processed symmetrically.)

From an implementation point of view, there are two types of FH: Baseband FHand Synthesized FH, and this depends on the type of equipment installed at the TRX. InBaseband FH, each TRX is tuned on a fixed frequency. Hopping is obtained by shiftingthe information from one TRX to another. As a consequence, the cell MA contains asmany frequencies as the number of TRXs in that cell. In Synthesized FH, the TRXsare capable of, and are allowed to, retune to different frequencies. Any given call goesthrough one TRX but the frequency used changes over time. This allows the number offrequencies in the MA to be larger than the number of TRXs (no more than 64, however).


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OPTIMIZING FREQUENCY HOPPING IN GSM 251

Two types of frequency hopping patterns can be used [2]. Under Random FH, thehopping sequence is randomly generated. Under Cyclic Hopping, the hopping sequencecycles through the available frequencies in the MA from the lowest index to the high-est index. The sequence length is equal to 64 TDMA Frames. In GSM, the HoppingSequence Number (HSN) is the parameter that determines the type of hopping patternto be used: If HSN is set equal to 0 then the Cyclic Hopping is active. If HSN is setto an integer value in the interval [1, 63], then random hopping is active and each valuecorresponds to a different seed for the random number generator. The Mobile AllocationIndex Offset (MAIO) is used to avoid that two TRXs with the same HSN (i.e., the samehopping sequence) interfere with each other. This index makes sure that the two TRXsstart hopping from different positions in the hopping sequence. This situation occurs in

the case of TRXs belonging to the same cell. Since these TRXs are part of the sameBase-Station, the interference level would be unacceptably high. To avoid this situa-tion, the hopping sequences for these TRXs are made orthogonal by adjusting them todifferent MAIOs.

Frequency hopping is often analyzed in light of elementary frequency re-useschemes according to which the cells are assumed to have an hexagonal shape with auniform propagation of radio waves [Ivanov et al., 3; Nielsen et al., 4]. These assump-tions are not realistic, especially in view of the fact that frequency hopping is most usefulfor large networks with a large number of interfering cells, or for networks with highlyirregular propagation patterns.

3. Optimized frequency hopping

This paper proposes a new frequency hopping approach: optimized hopping. Undercyclic or random hopping, the interference between any pair of TRXs occurs randomly.This is because calls arrive randomly to the system. Thus, the times at which the hoppingsequences are started are random. Therefore, regardless of the hopping pattern, theinterference incurred by the mobile subscribers will be random. Suppose now that it ispossible to synchronize the network so that all TRXs hop at exactly the same time andthat the TRXs remain hopping even if they are not involved in any communication. Insuch a case, interference levels would be random under random hopping. Under cyclichopping, however, interference would not be random but would depend on the indicesof the frequencies allocated to the MA of each cell. The proposed optimized hoppingwould be similar to cyclic hopping in a synchronized network with the difference thatthe sequences would not be based on the index of the frequencies in the MA but ratheron an order determined by an optimization algorithm. Optimization would occur intwo stages. First, the MAs of the cells need to be built so as to reduce interferencein an optimized way. This part does not require synchronization and could also beused to improve the performance of random or cyclic hopping. Second, the hoppingsequences need to be generated under an interference-minimizing objective function.This part requires that the network be synchronized. This is not the case in the currentGSM networks. However, this feature is likely to be introduced in the near future, to go


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along with the so-called third generation. The goal of the present paper is to show thatadditional capacity and quality of service gain could be made, should synchronizationbecome available.

Before describing the algorithm for optimized hopping in more detail, we mustidentify the required input. Under static frequency allocation, optimization problemsrequire as inputs the co-channel and adjacent-channel interference matrices. Each entryin these matrices corresponds to the interference level that one cell exerts on the other ifthey use the same frequency (or if adjacent frequencies are used in the case of adjacent-channel interference). One possible interference measure is expressed in terms of therelative size of the area in which the Carrier to Interferer Ratio (CIR) is lower than agiven threshold. The CIR is the ratio of the strength of signal carrying the communi-

cation to that of the sum of interfering signals. This data is also required for optimizedhopping.

In addition, static frequency allocation requires the separation matrix as input.Each entry in this matrix corresponds to the minimum frequency separation Sij be-tween a pair of cells (i,j). In other words, if frequency f is allocated to cell i, thenall frequencies g allocated to cell j must satisfy: |f g| > Sij . Minimum separa-tions are introduced in order to ensure sufficient service quality for specific links in thenetwork. The diagonal entries of the separation matrix (Sii ) represent the minimumseparation between frequencies allocated to the different TRXs of a same cell. Theproposed optimized FH algorithm uses a partially relaxed form of these separation con-straints to build the MA. The relaxation is later dropped when building the hopping

sequences. In this approach, we still require that the minimum within-cell separationbe satisfied at all times. In addition, in every cell, one TRX is responsible for carry-ing the Broadcast Control Channel (BCCH), which is not allowed to hop. Since thischannel is very important in establishing calls and ensuring synchronization and hand-over, we require that separation constraints between any TRX and all BCCH-carryingTRXs must be satisfied. Under synthesized FH, the number of frequencies allocatedto a cell can be larger than the number of TRXs. If the original separation constraintsare used, then the size of the MA will be bounded from above due to these constraints.However, at any time during the hopping process, only a subset of these frequencies isactive. Thus, the original separation constraints may be over-protective. Therefore, inthe relaxed-separation constraints, a frequency f is a candidate to be included in the MAof a cell i if, for each remaining cell j , the MA ofj contains a subset of frequencies suchthat:

All frequencies in this subset satisfy separation constraints with f, and

This subset contains a number of frequencies equal to the number of TRXs in cell j .

This frequency f still needs to satisfy minimum separation with all BCCH-carryingTRXs and with the other TRXs of cell i. This is justified because, in essence, FHworks against having high interference levels for several consecutive time periods, whichcould result in communication dropping. Therefore, the proposed relaxation is a wayof increasing communication capacity through a better use of the TCHs while pre-


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serving interference-free guarantee for the critical non-hopping service provided by theBCCHs.

Optimized hopping consists of two phases: MA construction and sequence gener-ation. In the first phase, the MAs are built. In the second phase, a hopping sequenceis generated for each hopping TRX. These sequences correspond to scheduling the useof the frequencies available in the MA of each cell. For this, we consider a time hori-zon H (in GSM this is equal to 64 TDMA frames but in our approach it is a givenparameter). The sequence of length H is then repeated indefinitely. We can view se-quence generation under optimized hopping as generating entries to fill a matrix whosecolumns corresponds to the TDMA frames in the horizon H and the rows correspond tothe hopping TRXs of the network. An entry in this matrix corresponds to the index of

the frequency that is to be used at a particular TRX at a particular TDMA frame overthe given horizon. These frequencies have to satisfy the separation constraints describedabove. Below, we describe a greedy algorithm for each phase. These algorithms aresolution construction algorithms, which could be further fine-tuned, and the solutionscould be even further improved through devising sophisticated solution improvementalgorithms (this is work-in-progress).

The objective typically used under static allocation is to minimize the sum or,equivalently, the average interference across all TRXs in the network. Because FH intro-duces the time dimension, this must be captured in the optimization objective function.In addition, the aim of frequency hopping is to achieve interference averaging acrossTRXs and across time. More specifically, its aim is to reduce the number of consecutive

TDMA frames in which interference is high so as to allow error-recovery algorithmsto function properly. Thus, the objective selected in our approach is to minimize themaximum cumulative interference incurred. In other words, for any given solution, theinterference incurred during each TDMA frame is computed for each TRX. These arethen summed across all frames in the horizon to produce the cumulative interferencefor each TRX. The quality of any solution is measured in terms of the maximum cu-mulative interference. The algorithm attempts to minimize this quantity. An alternativeobjective could have been to compute the average cumulative interference. This type ofobjective might produce a solution with lower average but with some TRXs having veryhigh interference, which might be considered as in conflict with the initial objective,i.e., interference averaging across TRXs. Moreover, using the maximum cumulativeinterference as an objective has the added advantage of producing solutions where highinterference levels are not incurred during consecutive TDMA frames, thus avoiding calldrops.

Greedy agorithm for phase 1: MA construction.

1. Initialization. Generate an MA for each cell, using static frequency allocation. DO-CAF1 is used to allocate frequencies to BCCH-carrying TRXs (which do not hop)

1 DOCAF is a commercial frequency allocation software package for GSM and AMPS networks, devel-oped by Prestige Telecom, Canada (www.prestige-tel.com).


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and provide an initial MA for each cell in such a way as to satisfy all separation con-straints. The size of a cells initial MA is equal to the number of TRXs in that cell.

2. Compute the amount of interference incurred by each cell: Each time two MAs con-tain the same frequency or adjacent frequencies, the interference levels of the cor-responding cells is augmented by the appropriate interference value (from the co-channel and adjacent-channel interference matrices).

3. Determine the number of passes (Nb_pass) which is the target increase in MA sizeover the initial MA obtained at step 1.This is a parameter that is determined by the user. Under Baseband FH, there wouldbe no increase (in this case the algorithm stops). This parameter is the same for all

cells. A potential improvement to this algorithm might be to allow this parameter tovary across cells.

4. For pass = 1 to Nb_pass Do

4.1. Order the cells in decreasing order of interference levels.

4.2. Select the cell with the highest interference level that has not been selected yetin the current pass. Call it cell i.

4.3. For each frequency f that satisfies the relaxed separation constraints with re-spect to cell i:

4.3.1. Evaluate the impact of adding f to the MA of cell i:

4.3.1.1. Let Cf denote the cell of the network that shows the highest in-terference level as a consequence of adding f to the MA of cell i.

4.3.1.2. Let Lf denote that interference level

4.3.2. f = argminf{Lf}

4.4. Add frequency f to the MA of cell i. (If no f is found, disregard cell i infuture executions of 4.2 during this pass and go to 4.1)

4.5. Update the interference levels as in 2. Go to 4.1.

Greedy algorithm for phase 2: Sequence generation.

1. Initialization.2. For t = 1, . . . , H Do:

2.1. Compute the interference level incurred by each TRX: Each time the same fre-quency is assigned to two TRXs, or adjacent frequencies are assigned to twoTRXs, the cumulative interference levels of these TRXs is augmented by the ap-propriate interference value (from co-channel and adjacent channel interferencematrices).

2.2. Order the TRXs in decreasing order of interference levels.


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2.3. Select the TRX with the highest cumulative interference level that has not beenselected yet in the current iteration t. Call it TRX i.

2.4. For each frequency f that satisfies the original separation constraints with re-spect to TRX i:

2.4.1. Evaluate the impact of using f at TRX i at time t:

2.4.1.1. Let Cf denote the TRX of the network that shows the highestinterference level as a consequence of using f at TRX i at time t.

2.4.1.2. Let Lf denote that interference level

2.4.2. f

= argminf{Lf}

2.5. Choose frequency f to be used by TRX i at time t.

2.6. Update the interference levels as in 2.1. Go to 2.2.

4. Results

The data set considered in these experiments corresponds to a real-life network with 337cells, and a total of 927 TRXs. A cell contains 1, 2 or 3 TRXs. The available band-width consists of 50 frequencies to be used both by the BCCH carrying TRXs and theTCH-carrying TRXs. We consider a hopping sequence of length 50. The separation con-

straints require a separation of 3 within a cell and a separation of 2 within a given site.In the experiments described below, optimized, random and cyclic hopping, and staticfrequency allocation under DOCAF are compared. The comparisons are based on thesame MAs, which were allocated using the procedure described above. Also, the staticfrequency allocation corresponds to the initial MA allocation used in step 1 of the MAconstruction algorithm. The evaluation assumes a 100% load (worst-case analysis). Inaddition, these comparisons assume a synchronized network. However, if this assump-tion were relaxed, it would still be possible to probabilistically determine the expectedinterference level for each TRX under random or cyclic hopping in an asynchronousnetwork. Experiments have shown that the expected interference level under random orcyclic hopping in an asynchronous network determined probabilistically is nearlyequal to the average interference level under random hopping in a synchronized network determined through simulation.

In order to investigate the impact of the MA size, it was allowed to vary from thenumber of TRXs of a cell to that number plus 10. Figures 1 and 2 show the impact of theMA size on the TRXs cumulative interference (averaged over time to allow comparisonwith static frequency allocation). In these figures, static corresponds to static allocation.OH, CH and RH correspond to optimized, cyclic and random hopping, respectively. Atthis point, it is important to note that the effect of hopping can only be fully appreciatedas a function of time, and that averaging over time may be misleading since a loweraverage over a network can hide the fact that several calls cannot be carried through


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Figure 1. Variation in average cumulative interference with MA size.

Figure 2. Variation in maximum cumulative interference with MA size.

Figure 3. Index of TRX carrying maximum cumulative interference.

because of some high interference being present at the corresponding TRXs over thewhole horizon; this is particularly true when comparing FH with static allocation: forinstance, figure 1 shows that for the data at hand, static allocation results in an averageTRX cumulative interference that is lower than what it is under frequency hopping,although it is not as good. Figure 2 shows that optimized frequency hopping outperformsall three other methods in terms of maximum cumulative interference. These figures alsoindicate that an MA size equal to the number of TRXs plus 5 provides a good balancefor OH in terms of deterioration in average and improvement in maximum cumulativeinterference. Beyond this value, the curves level off.


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Figure 3 shows the index of the TRX that incurred the maximum cumulative in-terference up to each of the 50 TDMA frames in the horizon that we consider, underoptimized hopping. Similarly, figure 4 shows the index of the TRX that incurred themaximum interference during each TDMA frame under optimized hopping. Note thatthe index of the TRX with the highest interference changes with time in both figures. Asimilar pattern is also observed under random and cyclic hopping. However, optimizedhopping outperforms cyclic and random hopping in terms of interference levels as shownin figures 5 and 6.

To illustrate the impact of hopping, figure 7 shows the interference incurred by arandomly selected TRX that is allowed to hop. Figure 8 shows the evolution of interfer-ence for a randomly selected non-hopping TRX (a BCCH-carrying TRX) that belongs tothe same cell as the one shown in figure 7. In both cases, optimized hopping shows lowerinterference levels than cyclic and random hopping. For these specific TRXs, static allo-cation often shows lower levels of interference than optimized hopping. The reason forthis is that OH reduces interference levels for some other TRXs for which interferencelevels under static allocation are high.

Figure 4. Index of TRX carrying maximum interference.

Figure 5. Maximum cumulative interference.


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In order to better capture the time dimension, the interference levels experiencedby each TRX during each TDMA frame are compared to the maximum interferencelevels experienced over the horizon. The maximum interference level determines theinterference range. This range is divided into 4 subranges or categories (the first being

Figure 6. Maximum interference.

Figure 7. Evolution of interference for a sample hopping TRX.

Figure 8. Evolution of interference for a sample non-hopping TRX.


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the best and the fourth being the worst). For each TDMA frame, each TRX is put in oneof the four categories. Figure 9 shows the average percentage of time spent by TRXsin each category. The interval shown in the legend of figure 9 is the range covered bythe four categories for each type of hopping. Although CH and RH have wider ranges,OH shows a higher percentage of time spent in category one. This indicates that OHsignificantly outperforms CH and RH. On the other hand, OH looks worse than staticallocation, which again is misleading.

Figure 9. Average percentage of time spent per category.

Figure 10. Number of 2 consecutive observations of a TRX being in category 3 or 4.

Figure 11. Number of times in category 3 or 4.


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It is also interesting to get an idea about how long a TRX would experience highinterference levels. Figure 10 shows the number of times each TRX in the networkexperienced interference levels of category 3 or 4 for two consecutive TDMA frames,under optimized hopping. This figure indicates that high levels of interference are expe-rienced for short periods of time. Figure 11 shows the number of TDMA frames duringwhich interference was in category 3 or 4 (out of a maximum of 50, which is the lengthof the horizon considered), for each TRX under optimized hopping. On the average aTRX would spend about 0.65 TDMA frames in category 3 or 4. Although not shown,optimized hopping outperforms the other types of hopping patterns.

5. Conclusion

On the overall, optimized hopping is seen to perform better than cyclic or random hop-ping both in terms of reducing the interference levels, maximum and average, and interms of reducing the time spent at high interference levels. The results presented aboveindicate that static frequency allocation may look better than frequency hopping in termsof average performance, which does not show the benefit over time of sharing interfer-ence between users; it is definitely worse in terms of interference sharing among TRXsand in terms of maximal interference levels. It is worth mentioning here that the staticfrequency allocation program used in this analysis is a powerful one, competitive withthe best tools available on the market, while Optimized hopping is based on a simplegreedy algorithm that could be improved significantly.

In analyzing the performance of frequency hopping, it is important to capture thetime dimension. It is difficult to visualize the impact of frequency hopping in two-dimensional graphs since this entails some form of data aggregation. A full appreciationof the effect of frequency hopping can only be achieved by looking at the variation ininterference over time for each TRX. It is also important to emphasize that the resultsshown here are only valid for the network examined. However, our experiments withdata corresponding to other networks provided similar indications.

References

[1] R. Borndrfer, A. Eisenbltter, M. Grtschel and A. Martin, Frequency assignment in cellular phones

networks, Annals of Operations Research 76 (1998).[2] GSM 05.02, Multiplexing and multiple access on the radio path, ETSI (1999).[3] K. Ivanov, N. Metzner, G. Spring, H. Winkler and P. Jung, Frequency hopping-spectral capacity en-

hancement of cellular networks, in: Proc. IEEE 4th Internat. Symposium on Spread Spectrum Tech-niques and Applications (ISSSTA96), Mainz, 1996, pp. 12671272.

[4] T.T. Nielsen, J. Wigard and P. Mogensen, On the capacity of a GSM frequency hopping network withintelligent underlay-overlay, presented at VTC97, Phoenix, USA.

[5] J. Wigard and P. Mogensen, A simple mapping from C/I to FER and BER for a GSM type of air-interface, presented at PIMRC96, Taipei, 1996.

[6] J. Wigard and P. Mogensen, Capacity of a GSM network with fractional loading and random frequencyhopping, presented at PIMRC96, Taipei, 1996.

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Freq Hop (Bourjolly Et)