# Development of a numerical statistical model

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### Abstract

The reuse of the frequency of wireless WCDMA networks is an important feature, and because of this arrangement of the network, the intracell and the intercell interference are factors that play a major role in the attribution of such networks. The calculation of the amount of needed energy for each user, as well as the capacity of these users from the base stations of the network, carried out with a statistical basis. The aim of this paper is to develop a statistic model which will calculate the downlink power consumption. In order to further our study we need to make some alterations to certain constants due to environmental factors and then we will present the model which will take place in these measurements. With this model, we will calculate the average value of downlink power consumption compared with the distance that the UE (user equipment) occupied each time from the base station (BS). Some of the factors that we will pay attention for the calculations are: shadowing (sha), the orthogonality (ortho), angle (&theta;) and others. Next we will present a few diagrams and we will come to some certain conclusions after each chart will result from changes in prices of various factors (exa, sha, ortho, &theta;).

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The communication of the base station with the UE is interactive. When the signal transmitted by the user to the base station, it happens uplink. When the signal transmitted by the base station to the UE it happens downlink. The reuse of the same frequencies in WCDMA networks is due to the structure of the cell. Because of that, many users can simultaneously use their mobile phones. Due to the low power of base stations, the frequency reuse becomes easy, since the emissions do not get outside the bounds of the cell belonging to the base station and UE. For this reason, other neighboring base stations can use the same frequency. The energy which required for low-power emissions isn't so high. This leads to the consumption of a mobile phone is very low. To organize such a system with cells, should be many base stations with antennas broadcast throughout the area which will take place this wireless communication. We will study the downlink. In this link, the interference emits from the signals by his base stations or neighboring ones for all the UE located in the same or neighboring cells. The signal to interference ratio generated by each user, require an increase of transmitted power.

### Analysis of downlink interference

The total interference which a user can receive is the intracell and intercell interference. In the uplink, the intracell interference for a mobile user comes from all other mobile users, that served by the same base station. Here the intercell interference consists of all signals received by the entire mobile, unless of course the cell of its own mobile. This has as a conclusion that in the upper link, the position of the mobile does not play such an important role in interference, but the interference depends mainly on the load distribution network. In the downlink, the intracell interference which has a mobile user happens from a loss of the orthogonality between users.

The WCDMA networks use orthogonal codes. This happens in order the users to distinguish the downlink and thus does not appear intracell interference since orthogonality remains. The intercell interference is the power obtained from the mobile and the other stations, except from the station which serve the particular user wireless device. The intracell interference is the power for the common channels of downlink for other users in the same cell. With all the above, we conclude that the insertion of the downlink is necessarily linked to the position of mobile, as the source of interference is stable base stations.

For one user with a wireless device which is covered by a base station, the intracell interfere of downlink Iintra-cell which took from the base station is given by the following equation:

PT1: is the total power transmitted by base station

&alpha;: is the factor orthogonality, when &alpha; = 1 then we have perfect orthogonality and when &alpha; = 0, we have non-orthogonality

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d: distance from the base station

One conclusion that arises here is that the intracell interference as shown in the equations does not depend on the angle of the mobile but on the distance from the base station. On the other hand, the intercell interference depends on the angle from the surrounding base stations. So the distance from the other mobile stations is dependent on the angle &theta;.

#### Power consumption of downlink

In the case of the downlink of WCDMA channels, the quality of service (Qos) is constantly downgrading, due to interference from the transmission of signals both the same but and the neighboring channels. The algorithm for selecting the cell and the handover algorithms are constructed in such a way so as to have the best possible quality of service (Qos). The best choice for a station with better signal is being with the algorithms of selecting cells. The soft handover algorithm is responsible for the connection of neighboring channels which have a better signal. So, if a user needs to change station and go to someone else for better signal, then these stations are not working as interference, but as sources of useful information. Our aim in this work is to create a theoretical model of radio propagation; with formulas which will calculate the required energy consumption of a connection, with hard handover connections, but also intracell and intercell-interference.

### Hard handover analysis

In the previous section, we discussed the technical connections in GSM systems and the hard handover technique was reported. This technique has as the main feature, the transition of the UE by a radio frequency to another.

On the other hand, the UE stops using the original transmission frequency. The UE changes the frequency and operates in a new frequency. During the changing from one frequency to another, there is a communication gap between the UE and the network. The major problem in hard handover technique is that there is no way to address this gap throughout the duration of wireless communication which is generated by the change of frequency. This technique is also used when there isn't an interface between two RNCs to be able to make soft handover connection. Inter-frequency hard handover takes place when we want to transfer the operation of a mobile user from one frequency to another.

### Theoretical model of radio transmitting

The model which is analyzed below provides information on both the signal strength and interferences from a location within the cell. In this model, losses during transmission are calculated as the ath power of distance and loss of shadowing. The attenuations were omitted because the RAKE's receiver can compensate for such phenomena.

We consider a WCDMA network with 19 co-channel cells and are represented as a hexagonal grid. This structure contains the cell 1, which is the cell under study, and around that, two levels of cells, the cells 2-7 and cells 8-19. The base stations will eventually get the names BS1-BS19. The cell with the base station BS1 is the cell that we are interested in the scenario under study.

Let's suppose a UE which is located in the cell 1 with position r1. The interference as mentioned in the introduction of the presentation comes from the interference in the same cell and the interference from neighboring cells. Below, we will study with mathematical approach to calculate the interference in each case (inter and intra-cell interference).

In fact because of the semi orthogonal codes in WCDMA networks which are produced by base stations, each user is different so that the interference which is received by a UE (User Equipment) to a specific station, come from the contributions of many different UE. So, the UE receives a signal which has come from a combination of many signals, at the same base station that belongs. Part of its power signal belongs to the same UE and a low part of power belongs to the other neighboring UE. According to the above, the downlink interference that has come to a UE from the base station of the same cell that it belongs.

On the other hand we have the Iinter-cell interference caused by neighboring base stations. For our study and according to the structure that the 19 cells have (each cell has a hexagonal form) and regard to the distribution of these cells around the cell of interest.

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The two types of algorithms which are available for such studies are the soft handover and hard handover. In our case, the UE, because of its location, the user will receive additional signals from other stations located around it (apart from the same base station that belongs). So the RAKE receiver receives the various signals and aggregates them. The SIR in the RAKE output is the sum of all SIRs from all BSs connected with "hard handover". In this case, the SIR is expressed as (per bit interference). Assume that the UE is in cell 1 with the following position features r1, &theta;1. We will suppose that the UE communicates only with the base station BS1 in cell 1 which belongs.

### Assumptions for the downlink power consumption

For the downlink power consumption for a UE, it should become some exceptions and approaches. These make our calculations easier. A phenomenon that unfortunately exists in all the studies for designing a wireless network and it should be calculated approximately, of course, is the interferences as mentioned in our work all the time. This occurs because the problem varies from region to region. The energy per bit to interference ratio [Eb/Io]t is an estimate of the interferences depends on the conditions that will operate this service and the scenario we have mentioned in previous sections.

### Simulations with Matlab - Results - Discussion

For the simulation of the model under study, we will be described what data we shall use. We will define values for the Activity factor as "af", the Bit rate as "bit_rate", the Energy per bit as "en_per_bit", radio propagation conditions for losses as "exa", the Orthogonality factor as "ortho", the shadowing losses as "sha", the Chip rate as "c_r" for air interference, Active set size, Monitored set and Cell selection algorithm threshold as "cst". The part of the simulation code using the Matlab for the transmission of voice, for example, is described in the appendix of this work.

The value of CAT = 10000 (is the minimum number of results per case) is given until the results converge to a clear and interesting conclusions, covering several scenarios for investigation. The results are due to the scenario under study in our work and are reflect the average energy consumption compared to the distance. Some of the values and factors are mentioned above and will be used during our simulation are:

1. af= 0.5
2. bit_rate= 12.2
3. c_r= 3840
4. en_per_bit= 4.4 (db)
5. exa= 3
6. ortho= 0.9
7. sha= 8
8. cst= 3
9. thita= 30&deg;

In the simulation, we made some changes in the values of four factors. We made this move to see the impacts of the price of the average consumption according to the distance. The changed values are altered in each of the four cases in order of 'sha', 'exa', 'thita' and 'orth?'.

In the first case of simulation, all of values remain constant and we changed the shadowing (sha) putting three different values (sha = 8, sha = 4, sha = 3).

Three colored lines are simulated, each one says exactly what it represents. At the beginning, the three lines starts from almost the same spot and then the line with sha = 8 rises sharply faster than the others. By removing the UE from the cell, the sha = 8 falls sharply, followed by sha = 4 and sha = 3. When the distance r/Rmax gets value of about 0.7, then we see the three lines to obtain common average energy values. The trend of these lines justifies the theoretical part, which says that when the shadowing (for example when the objects surrounding a cell are many, there is great shadowing) increases, so the average power consumption should be higher to cover the interaction of the user. When the user is removed, namely the distance approaches the value of 1 means and is at the limits of its cell, and then the average power is reduced because the adjacent base station undertakes to cover it.

In the second case of simulation, all values remained constant and we changed the Radio propagation conditions for losses (exa) putting three different values (exa = 3, exa = 5, exa = 7).

Three colored lines are simulated, each one shows what it represents. At the beginning, the three straight starts from almost the same spot and then the line with exa = 3 goes up faster than other shadowings. By removing the UE from the cell and approaching the limits of the cell covered by base station, the average power consumption with exa = 3 is greater than the other radio propagation losses. This is because during the transfer of the mark in the air when conditions are not so good (therefore small exa), the base station needs more energy to transmit.

Three colored lines are simulated, each one shows what it represents. At the beginning, the three straight starts from almost the same spot. Then they go up almost with the same trend but the straight line corresponds to the angle thita = 30&deg; is above of both the other two lines. This is correct in theory, since as figure 7 shows and according to formula 9, as the angle increases, the distance of the UE by the cell increases too. So the energy, that the base station wants to serve the users, will be higher. Of course, this steep slope of the straight thita = 30, is not reasonable.

In the fourth case of simulation, all values remained constant and changed the shadowing (ortho) putting three different values (ortho = 0.9, ortho = 0.7, ortho = 0.5).

Three colored lines are simulated, each one shows what it represents. The values of orthogonality range from 0-1. In the beginning, the three lines start from a different point. All three lines grow at the same rate, with only line with ortho = 0.5 is higher than the two others and line with ortho = 0.7 and ortho = 0.9 follow. When the orthogonality is approaching the value 1, this means that for the propagation of the signal, the base station will require less energy.

### Conclusions

At this paper were presented and evaluated simulator multicell WCDMA systems for the calculation with a statistical way the energy consumption for the downlink direction. This calculation is conducted according to the position he holds in his cell where the UE and the factors responsible for the interference received from his own cell but also by neighboring cells. The simulated and the results come from measurements of learned; provide important information on the behavior of the network of treaties and proliferation signals from a base station to another, but from a UE to another. Improvements and comments above are making what interest the study and development of such technologies.

### References

1. Chen Yue, Soft Handover Issues in Radio Resource Management for WCDMA Networks, submitted for the degree of Doctor of Philosophy, Queen Mary University of London, 2003.
2. D. Staehle and A. M&auml;der, "Analytic Modelling of the WCDMA Downlink Capacity in Multi-Service Environment" Report No.330, University of Wurzburg, Department of computer Science, April 2004.
3. J. H. Winters. Optimum combining in digital mobile radio with cochannel interference. IEEE J. Select. Areas Commun, Vol. SAC-2, 1984, pp. 528-539.
4. J. Andrews, W. Choi and R. Heath. Overcoming interference in spatial multiplexing MIMO cellular networks. IEEE Wireless Communications Magazine, Vol. 14, issue 6, 2007, pp. 95-104.
5. Kin K. Leung, Arty Srivastava. Dynamic Allocation of Downlink and Uplink Resource for Broadband Services infixed Wireless Networks. IEEE Commun. Mag, Vol. 17, 1998, pp. 990-1006.
6. Steele R., Lee C., Gould P., GSM, cdmaOne and 3G Systems.Effects of Soft and Softer Handoffs on CDMA System Capacity, John Wiley & Sons Ltd, 2001.
7. S. Verdu. Minimum probability of error for asynchronous Gaussian multipleaccess channels. IEEE Trans. Inform. Theory, Vol. 32(1), 1986, pp. 85-96.
8. V. V. Veeravalli and A. Sendonaris. The coverage-capacity tradeoff in cellular CDMA systems. Transactions on Vehicular Technology, Vol. 48, 1999, pp. 1443-1450.
9. Viterbi, A.J. CDMA: Principles of Spread Spectrum Communication, Addison-Wesley, Reading, MA., 1995.
10. Viterbi A., Viterbi AM., Gilhousen K. Soft Handoff extends CDMA coverage and increase reverse link capacity. IEEE Journal of Selected Areas in Communications, Vol.14(9), 1994.
11. Venetas N., Development of a Numerical Statistical Model for WCDMA Downlink Performance Evaluation, Thesis for Kingston University, May 2006.