A SIMULATION STUDY OF THE COMBINED USE OF POWER CONTROL AND DYNAMIC CHANNEL ALLOCATION SCHEMES

Guilherme Zenkner Percia, JosC Roberto Boisson de Marca

CETUC - PUCI Rio de Janeiro - 22453-900, Rio de Janeiro - Brazil. e-mail: jrbm@cetuc.puc-rio. br

Abstract - This work investigates the behavior of a well known dynamic channel allocation scheme @CA), channel segregation, when associated to two different automatic uplink power control schemes. The two objectives sought with this association are improved capacity over the isolated use of the DCA scheme, and a better distribution of the Signal to Interference Ratio (SIR) due to an optimized use of transmission power. Simulation results show that indeed this can be achieved, but not without some costs.

I. INTRODUCTION

Throughout the world, the demand for cellular communications systems has increased geometrically in the last few years. To provide greater capacity and at the same time maintain the best possible communications quality, there are several techniques that are being attempted in the design of these systems. Two of the most promising alternatives to attain these objectives are automatic power control algorithms and dynamic channel allocation schemes. Both have been widely studied in the literature separately, but there are few articles in which they are employed together, and even fewer that present simulation results. This work proposes a combined application of those tools, and analyses the performance of the proposed procedure trough simulation, with focus on the effect of the automatic power control.

The dynamic channel allocation scheme considered in this work was the channel segregation. It is a pure DCA method, in the sense that all channels in the system can be made available to every cell. It also allows a hlly distributed implementation, i. e., no central controller is necessary to allocate the channels. Therefore, the network can adapt itself to environment changes that may occur, automatically solving the channel planning problem that often arises with the use of a fixed channel allocation (FCA) scheme. For comparison purposes, we have also considered the FCA scheme, without power control.

The type of power control algorithms studied here are those distributed methods that try to equalize the Signal to Interference Ratios (SIRS) of all users in the system, thus guaranteeing the same quality of communications for all of them, while at the same time minimizing the effects of the co- channel interference. Considering that cellular systems are

basically interference-limited, the use of power control alone already produces a capacity gain when compared to systems that do not employ it. As an added benefit, the power levels can be kept at the minimum necessary, resulting in battery savings for the mobile units.

The following section describes the two power control algorithms considered for comparison. Section I11 presents the channel allocation method chosen: the channel segregation. In section IVY we discuss the proposed combined procedure to employ simultaneously the tools described on the previous sections. Finally, in section V, we describe the simulation model and show the results obtained from it, drawing the conclusions in section VI.

11. AUTOMATIC POWER CONTROL ALGORITHMS

We have considered and compared two distributed automatic uplink power control algorithms: the one proposed by Zander in [ 11, and that proposed by Grandhi, Vijayan and Goodman (GVG) in [2].

The Zander algorithm is called the Distributed Balancing Algorithm, and the idea behind it is to equalize the SIR’S of all the users in a given channel. The following equations describe this algorithm, with the update of the user transmitter power given by the second one:

P@ =Pa, Pa>O

where is the power vector at the instant k, i.e., the vector whose entries are the values of the transmitting powers of the users, in the instant k. The dimension of this vector is equal to the number of users in the channel, and its i-th component, PIMY is the transmitter power of the i-th user at the instant k. Po is the initial value of the power vector. p is a positive constant that we chose equal to 0.9 in our simulation, and y,” is the signal-to-interference ratio in the uplink for the i-th

It is shown in [l] that this algorithm converges to the optimum values for P@ and E@. These values are those that maximize the minimum SIR over all channel users, and also minimize the maximum SIR Thus, it yields the same

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0-7803-3659-3/97 $1 0.00 0 1 997 IEEE 1470

optimum value of SIR for all the users in the channel, and its associated power vector. However, the convergence is slow when this optimum value of SIR is too high. In other words, this algorithm converges slowly when the system is not very loaded.

The GVG algorithm is called the Modified Distributed Balancing Algorithm, and is, as the name implies, a modified version of the Zander algorithm. Again the objective is to equalize all the SIR'S in a given channel. The algorithm, with the power updates, is given by:

P(O) =Po, Po 0

where the variables are the same as in the Zander algorithm, the only difference being that p, again a positive constant, can be regarded as the "target" SIR value. In this work, we have used p = 31.62, which corresponds to 15 dB.

It can be seen in [2] that, like Zander's, this algorithm converges to the optimum values of P" and E@. It also obtains the same optimum value of SIR for all users in the channel and its associated power vector. There is, nevertheless, an important difference in comparison to the Zander algorithm: the convergence is fast when the optimum SIR value is too high, or the system is not very loaded.

These two algorithms were compared when used in association with the dynamic channel allocation scheme chosen, namely the channel segregation method, which will be described in the next section.

111. CHANNEL ASSIGNMENT SCHEMES

The channel allocation method chosen was the channel segregation. In this technique, proposed by Furuya and Akaiwa in [3], all channels in the system are available at each cell. When a channel request is received, either due to a new call or to a handoff situation, the cell tries to assign the idle channel with the highest value, according to a priority function. Priority values are associated to each channel in the cell. The priority value increases with each successll allocation of the channel, and decreases when the channel cannot be employed. The criteria that determines if the highest-priority channel can be allocated is the signal-to- interference ratio (SIR) observed in that channel. If it is below some threshold value, the channel cannot be used. If it is above that value, the channel can be assigned. In the case where the highest-priority channel cannot be allocated, the cell tests the second highest-priority channel among the idle channels, and so on, until some channel can be assigned. If every channel is checked with no positive result, the call is blocked. The segregation method is a self-organized one, for the channels are ranked according to previous successful uses. Thus, channels with greater priority in a given cell are the ones which were most fiequently successfully used in that

cell. In other words, one can say that these are the channels that customarily have the best interference situation in the cell. In the original proposal by Furuya and Akaiwa [3], the equations used to update the priority pfi) of channel i in a base station are: 0 When the base station is successful in using the channel i

($6) must increase):

pfi) = [pfi)nfi) +I]/[nfi) + I ] (3) nfi) = nfi) +I (4)

0 When the base station cannot use the channel i (PO) must decrease):

where no) is the number of times channel i has been considered for use, and pfi) is a value between 0 and 1.

A drawback of these equations lies in the slow adaptation to changing conditions when the value of nfi) increases, and also in the relatively complex processing that the base station has to do. To eliminate those problems, we have proposed an alternative form for updating the priority function, that works in the basis of simple summation, and admits values outside the range (0, 1) for pfi?. The following equations show the alternative updating method: 0 Initially:

p(i) = N - i (7)

where N is the total number of channels. As can be seen fiom (7), at first the channel number 1 has the highest value of priority, and the channel number N has the lowest. 0 If the base can use the channel i, then:

pfi) =p(i) +N (8)

0 If the base cannot use channel i, then:

we have chosen the value N for the updates to guarantee that, if the channel cannot be used, it goes to the last position of the rank for that given cell, avoiding the possibility that it may be tested again before the other idle channels are tested. Also, we keeppfi) in the interval [-N, +N]. Everytime some channel has pfi) outside this interval, we subtract or add N to the priority values of all channels. The above procedure is the one implemented in our simulation.

IV. PROPOSED COMBINED PROCEDURE

The proposed joint algorithm for power control and channel allocation schemes is rather simple: once a user gets

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a channel, according to the segregation method (considering that he is not blocked), he starts adjusting his power following the power control algorithm in use. The initial power of the user was normalized and considered to be 1.0. The other terminals continue to update their powers as they were doing before the new user had entered. The users already allocated on the same channel as the one just admitted consider him as a new source of co-channel interference. If the SIR of any user in a given channel falls below the minimum acceptable level, that user is removed fiom the channel, and the system tries to reallocate him. If this is not possible, the call is lost due to excessive interference. Handoff attempts occur when the power received fiom another cell becomes stronger, and the user’s SIR is below the handoff threshold. If the system cannot accommodate the handoff, a handoff failure is said to have occurred. If neither one of the above is observed, the user completes his call normally. The flowchart in Fig. 1 shows the proposed procedure.

channel The request is blocked in the cell?

1 Yen

a n d g o t o l . than treshold?

I Yen

3. Assigns the channel and applie

power control

A , - perform handoff (in that case, a11 users above

finished

Fig. 1 Proposed combined procedure for joint application of power control and channel assignment schemes.

V. SIMULATION AND RESULTS

The simulation modeled a two-dimensional 49-cell system, and took into account the user mobility. Pedestrian users were considered, in a microcell environment (the distance between cell sites was 1000 meters). The users were uniformly distributed throughout the system. Wrap around was used to avoid border effects. For the baseline FCA system, a cluster of 7 cells was used, with 21 channels at each cell, in a total of 147 channels. For the segregation method, this was also the total number of channels available at each cell. The propagation model was deterministic and distance-dependent. The attenuation constant was equal to 4.0. Call statistics were modeled as a birth-death process. Mean duration of calls was equal to 3 minutes, and the mean interval between call arrival was varied in order to modify the mean traffic load. The minimum SIR for a call to be accepted was 16 dB, while the threshold for dropping a call due to interference was 14 dB. The handoff threshold was 15 dB.

b 18 20 22 24 2s Call am-1 rate (calls/s)

Fig. 2 Blocking probability.

The performance measures evaluated were: handoff failure probability (the probability that a handoff request cannot find a channel in the destination cell), outage probability (the probability that a call cannot be maintained due to co-channel interference), blocking probability (the probability that a new user cannot fmd a channel to handle his call), and the mean number of users served simultaneously by the system. Another important feature in the simulation is that the transmission power of each user was limited to the normalized interval EO.1, 1.01. By doing this, we have provided a more realistic environment, since in practice the terminal transmission power is indeed limited: above by the maximum terminal transmitter power, and below by their sensitivity and propagation conditions. The constants used with the power control algorithms were those mentioned in section 11. The results can be seen in Figs. 2 to 8, where PCO

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implies no power control, PC1, the Zander algorithm, and PC2, the GVG algorithm.

We can see that the channel segregation greatly improves the blocking probability when compared to FCA. Also, the use of power control gives an additional gain, especially in the case of the Zander algorithm, that yields very small blocking probabilities at these traffic levels.

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We see on Fig. 3 that channel segregation without power control also reduces the handoff failure probability significantly. Here we notice some of the negative effects of power control. Its use augments the handoff failure probability, because the power adjustments tend to provoke more handoff requests, due to users that do not achieve the minimum required SIR to stay associated with a given cell. This is especially true in the case of the Zander algorithm with lower traffic for, as it was noticed earlier, its convergence is slower. As the system becomes more loaded, the GVG algorithm becomes the worst, since it has now the slower convergence.

Considering Fig. 4, it is interesting to notice that FCA has no outage probability, due to the fact that its planning is made to allow no interference even in the worst case. The segregation method, as it has no planning, presents nonzero outage probability. This is because the users entering the system increase the co-channel interference sensed by the users that were there before, causing their SIRS go below the threshold. One more time the inclusion of power control only makes this worse, for there is a larger number of users that do not attain the minimum SIR to keep a given channel. Also, the upper limit imposed on the transmission powers has a clear influence here. For the case of the Zander algorithm, as a consequence of the smaller blocking probability, more users enter the system, and there is much more interference, and so the outage probability is the worst.

16 Is 20 22 24 2s call arriml rate (calls/s)

Fig. 4 Outage probability.

18 is 20 22 24 2s call aniwl rak? (CalldS)

Fig. 5 Mean number of users simultaneously in the system.

In Fig. 5, the gain of the segregation method over FCA is evaluated in terms of the mean number of users simultaneously served. At the arrival rate of 2.60 callds, we see that channel segregation accommodates 2.63 times the number of users of FCA. It is not shown in the graphic, but at 3.0 calls/s, this number grows to 3.06 times. Considering power control, these numbers are reduced a little: for the Zander algorithm, we have 2.395 times the number of users of FCA at 2.60 callds, and for the GVG algorithm we have 2.58 times FCA at the same point. It will be seen that this reduced gain is the price of the convergence of the SIR'S and the consequence of the increase in interference levels. The three following figures show the histograms of the SIR's for the channel segregation with and without power control.

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SIR (dB)

Fig. 6 Histogram of SIR’S for the channel segregation without power control.

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SIR (dB)

Fig. 7 Histogram of the SIR’S for the channel segregation with the Zander power control algorithm.

SIR (dB)

Fig. 8 Histogram of the SIR’S for the channel segregation with the GVG power control algorithm.

Zander algorithm has a smooth convergence, and the difference from Fig. 6 is almost imperceptible. We can notice, however, a slight convergence to 17 dB, against the two peeks at 16 and 18 dB with no power control. From Fig. 8, it is clear that the GVG algorithm has a more aggressive convergence, in that the absolute majority of the users presents a SIR of 15 dB, which is just the value chosen for the “target’7 SIR. The indirect consequence of this convergence is the lower gain, in comparison to no power control, observed in Fig. 5 . This is because the better distribution of the SIR’S allows more users to enter the system. Those users generate more interference, which the power control algorithm cannot handle appropriately. So, there will be a greater number of users expelled of the system, reducing the mean number of users in it. Also, the increase of the interference, shown in Fig. 4, is the main reason the Zander algorithm has the smallest gain between the two algorithms considered here.

VI. CONCLUSIONS

The use of power control together with channel segregation can improve some aspects of the system performance, such as blocking probability and SIR distribution. However, other performance parameters can be degraded, namely the outage probability, the handoff failure probability, and the mean number of users served. The level of this degradation depends on the power control algorithm in use, and on its convergence rate. One can conclude that the channel segregation method, due to its own nature, is extremely sensitive to power control, and there must be a tradeoff between the benefits and the degradation caused by such algorithms. In any case, the resulting capacity was never less, at a given traffic level, than about 140 % greater than that yielded by fixed channel allocation without power control. Further studies are currently being made regarding the joint application of those tools, involving other types of power control and allocation schemes, and in different propagation environments.

REFERENCES:

[ 13 Jens Zander, “Distributed CO-channel Interference Control in Cellular Radio Systems”, IEEE Transactions on Vehicular Technology, vol. 41, no. 3, August 1992.

[2] S . A. Grandhi, R Vijayan, D. J. Goodman, “Distributed Power Control”, Technical Report WINLAl3- TR-41, August 1992.

[3] Y. Furuya, Y. Akaiwa, “Channel Segregation, A Distributed Adaptive Channel Allocation Scheme for Mobile Communications Systems”, Second Nordic Seminar on Digital Land Mobile Radio Communications, October 1986.

Figs. 6, 7 and 8 clearly show the different effects of the two power control algorithms. In Fig. 7, we see that the

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