gprs report
TRANSCRIPT
Impact of Interference on GPRS/EGPRSservices and Performance Optimization in a
Multi-cell Scenario
Francesca Tempesta - Emanuele de CarolisPhilipp Hagenhuber - Quentin Berder
Supervisor:Persefoni Kyritsi - Haibo Wang
8th semesterMay 2007
Contents
1 Introduction 41.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Report Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Theoretical Aspect 62.1 GPRS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 GPRS Architecture . . . . . . . . . . . . . . . . . . . . . . 72.1.2 GPRS Layers . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.3 GPRS Time slots . . . . . . . . . . . . . . . . . . . . . . . 92.1.4 GPRS Modulation . . . . . . . . . . . . . . . . . . . . . . 112.1.5 Mobile Station . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 EGPRS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.1 EGPRS Modulation . . . . . . . . . . . . . . . . . . . . . 132.2.2 EGPRS Coding Schemes . . . . . . . . . . . . . . . . . . . 14
2.3 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Problem Analysis 193.1 Problem definition . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2 Power control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.1 The Wireless Network . . . . . . . . . . . . . . . . . . . . 203.2.2 Distributed Power Control (DPC) . . . . . . . . . . . . . 223.2.3 Distributed Power Control with Active Link Protection
(DPC/ALP) . . . . . . . . . . . . . . . . . . . . . . . . . 233.3 Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 MMSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.2 Interference-plus-noise rejecter . . . . . . . . . . . . . . . 273.3.3 LCMV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.4 MCMV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.4.1 Scheduling in GPRS . . . . . . . . . . . . . . . . . . . . . 283.4.2 QoS in GPRS . . . . . . . . . . . . . . . . . . . . . . . . . 283.4.3 Explanation of scheduling techniques . . . . . . . . . . . . 30
4 Delimitation 314.1 Wireless channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.1 General characteristics . . . . . . . . . . . . . . . . . . . . 314.1.2 Path Loss: Deterministic parameter . . . . . . . . . . . . 334.1.3 Shadowing: Log-normal distribution . . . . . . . . . . . . 35
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4.1.4 Multipath: Rayleigh distribution . . . . . . . . . . . . . . 354.2 Throughput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5 Simulation Analysis 415.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.2 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.3 Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3.1 Creation of the cells and clusters . . . . . . . . . . . . . . 445.3.2 Wrap around . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.4 Mobility model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.5 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.5.1 Shadowing . . . . . . . . . . . . . . . . . . . . . . . . . . 495.5.2 Shadow fading correlation . . . . . . . . . . . . . . . . . . 505.5.3 Path loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.5.4 Short Scale Fading . . . . . . . . . . . . . . . . . . . . . . 525.5.5 CIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.6 Traffic generator . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.7 Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.7.1 Intercell scheduling . . . . . . . . . . . . . . . . . . . . . . 605.7.2 Intracell Scheduling . . . . . . . . . . . . . . . . . . . . . 60
5.8 Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.8.1 Basic Algorithm . . . . . . . . . . . . . . . . . . . . . . . 635.8.2 DPC Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 64
6 Simulation & Results 656.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.1.1 Simulation expectation . . . . . . . . . . . . . . . . . . . . 676.2 CIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.3 Throughput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7 Conclusion 74
Bibliography 74
List of Figures 77
List of Tables 79
A Glossar 80
Ålborg universityE-StudyboardMobile Communications 8th semester
TITLE:
Impact of Interference on GPRS/EGPRS services and PerformanceOptimization in a Multi-cell Scenario
THEME:
Communication, Signals and Systems
PROJECT PERIOD:
1st February - 31st May 2007
PROJECT GROUP:
07-gr-895
GROUP MEMBERS:
Berder QuentinDe Carolis EmanueleHagenhuber PhilippTempesta Francesca
SUPERVISORS:
Kyristi PersefoniWang Haibo
ABSTRACT:
With the development of multimedia application over Internet, the demand forhigh data rate connection is increasing. Obviously this happen also for mobilephones connected through GPRS/EDGE connections. Nevertheless interferenceis an important limitation to reach higher data rates. In this way, the aim ofthis project is to study and investigate several possibilities to reduce the effectsof those interference on GPRS/EGPRS services in a multi-cell scenario.
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Chapter 1
Introduction
1.1 BackgroundThe fast development of wireless technology and the increase of demand
for private usage and in business for a high data rate make of this technologyone of the most important fields of research in this decade. Furthermore theemergence of multimedia applications such as television or internet on mobilestations requires a high data rate.
Nevertheless, in order to obtain an efficient data rate, the interference hasto be taken in consideration. In the second generation of mobile phone, theGSM brought optimal improvement for the voice services. The circuit-switchedinterference on the GSM services has been exhaustively investigated. The voicecall traffic does not need a more advanced check for the interference because it isenough to reach the good enough level of quality to make the transmission withan acceptable quality. GPRS/EDGE services, which are packet switched ser-vices, are an evolution of the GSM which allow wireless data services with ratesup to 473 kbps. Because of those high rates, multimedia application can also berun on the mobile devices trough Internet. Nevertheless since those applicationcan be run on the mobile devices, the connection needs to be optimized in termsof traffic organization, performance optimization and interference attenuation.
Since circuit and packet switched services share the same physical resources,a notably increase in the interference level is appreciated in the whole system.On the other hand, in order to lessen this negative effect, they have more flexi-bility to make the system complex, improving the system capacity. The powercan be varied to improve the data rate. Different scheduling techniques can beused to have different user data rates; moreover, beam-forming can also be usedto achieve the best system performance.
This project analyzes a multi-cell scenario i.e. a certain amount of cells willbe considered in which a number of users will be modelized. All the effectsinherit in this the type of environment, such as buildings or trees and of theposition of the users in the cells, will be simulated in order to obtain a simulationas close as possible to the reality.
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1.2 Report OutlineThis report is based on the traffic analysis in GPRS connections. The aim of
this project is to analyze the impact of various technique such as scheduling andpower control in a multi-cell scenario during a download session. This report isdivided in five parts:
• Theorical aspect: Analysis of the theorical aspects of this project suchas GPRS, EGPRS and the interference. In this part, the background ofthis project will be analyzed.
• Problem analysis: Analysis of the problem and of the various tech-niques proposed to solve it. In this part, the physicals and mathematicalssolutions used for the simulation are developed.
• Delimitation: Delimitation of our scenario. In this part, the wirelesschannel and all its components such as path-loss, shadow fading or mul-tipath will be invetigate. And a mathematical approach of those effectswill be define to be used for the simulation.
• Simulation Analysis: Analysis of the simulation. In this part, the aimof the simulation will be define and all its components will be describe.
• Simulation & Results: Evolution and results of the simulation. Inthis part, the results of the simulation will be show and some partialconclusions will be propose.
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Chapter 2
Theoretical Aspect
2.1 GPRSGSM has been under very stable usage for mobile communication. GSM, in
addition to voice communication, provides mobile phone communication basedon digital data interchange. GSM is the core on which the second generationmobile phones are based. Actually, there are some limitations of GSM - namely,that is only provides voice services - that inhibit the widespread use of thistechnology GSM is a circuit switched connection. This means that the commu-nication between nodes and terminal is dedicated for each call session. Eachcircuit that is dedicated cannot be used by other callers until the circuit is re-leased and a new connection is set up. There is no incompatibility with theTCP/IP protocol and the mobile devices support just simply functions becauseof their easy hardware.
GPRS is a set of GSM-based services with provide packet mode transmissionwithin the GSM network, and it allows mobile devices to be connected viaInternet protocol addresses. As the name suggest GPRS’ data is broken intosmall packets at the transmitter and reassembled again at the receiver. Suchsystems do not require any particular connection between one user and another,the data are transmitted just when an user require it. GPRS is, for this reason, a2.5 generation wireless communication system. The transmission is digital and isup to 115 kbps, while GSM has transmission up to 9.6 Kbps. Another importantfeature of GPRS is that there is no dial-up connection to be completed for dataaccess. The bill charging is determined by the amount of effective transmittedand received information, and not by the connection’s time. That results in avery cost-effective service.[1]
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2.1.1 GPRS ArchitectureThe architecture of the GPRS network is shown in the following figure.
Figure 2.1: GPRS architecture
The items contained in the GPRS architecture are:
• BSS The Base Station Subsystem consists of the BTS and BSC. It hasbeen adapted to support the GPRS packets operations.
• BTS The Base Transceiver System handles all the radio transmission de-vices.
• BSC The Base Station Controller manages the resources in the communi-cation. Several BSCs can manage more than one BTS. It contains also thePacket Control Unit (PCU) which controls the data traffic in the GPRSnetwork.
The BSS consists of BTS and BSC. When voice or data needs to flow throughthe network, in the down link channel, it is transported over the air interface toBSC, and from the BSC to the BTS. The voice has is own path in the network,and the data passes through a new device called SGSN, via the PCU.
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• SGSN: The Serving GPRS Support Node maintains the logical connectionwith the Mobile Station (MS), forwarding incoming packets from the MSto the appropriate network node and vice-versa. Only one SGSN servesthe MS in its own service area.
• GGSN: Gateway GPRS Support Node provides the interface to externalpacket data network (PDN) and forwards packets destined for the MS tothe SGSN that is serving it.
The SGSN can be compared to a packet sorting center that delivers packetdata within its service area. SGSNs take care about the detection and the man-aging of new GPRS mobile station within their control area.
The GGSNs maintain routing information that is necessary to connect theProtocol Data Units (PDU) to the SGSNs that service particular mobile sta-tions.
The GPRS connection is based on protocols which assign network addressesto the devices within the network in order to manage the data path. TheGGSN is responsible in checking that the PDP address from the public packetdata network is forwarded. The network then routes the data to the specificmobile station through the SGSN. Each mobile station has is own PDP and isconstantly updated. Each time a mobile station wants to receive or send data ithas to communicate with the SGSN, then activate his PDP address and finallyget the PDP address from the GGSN to get the connection.
2.1.2 GPRS LayersFor a better understanding of the data flow, coding scheme and how the
packets are made in a GPRS connection, the following session focus on the differ-ent layers. The RF layer, layer at the bottom, manages the physical connectionbetween mobile station and base station. This layer is divided in Physical RFlayer, which includes modulation and demodulation, and Physical link layer,which manages the information for the physical channel such as error correc-tion, power control, cell location..etc etc.
The following up layers are the radio link control (RLC) and the mediumaccess control (MAC) which controls the logical connection between mobile sta-tion and base station. They are also the layer which will format the data topass to the upper layers, the logical link layer (LLC). The LLC is the layer whohandles the connection between SGSN, BSS, and mobile station. In this layerthe packets contain the user data. The LLC layer is important because in itthe authentication takes place, the mobile is attached to the SGSN through theLLC layer. The following figure 2.2 shows the position of the different layerswithin the GPRS communication.
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Figure 2.2: GPRS Layers organization
2.1.3 GPRS Time slotsThe multiple access methods used in GPRS is based on FDD and FDMA.
During a session, a user is assigned to one pair of up-link and down-link fre-quency channels. This is combined with time domain statistical multiplexingwhich makes it possible for several users to share the same channel. In this way,using the TDMA, different slots are assigned for the GPRS physical channels,while the remaining can be used for the voice communication. In this project,as will be outlined in the delimitation chapter, the voice data is not taken incount. Due to this, the channel allocation will be managed just with GPRSdata packets.
Figure 2.3: GPRS time slot
Examining it with more detail, it is possible to distinguish the entire sequenceof data transmitted in GPRS operations. The used physical channel is namedPacket Data Channel (PDCH) and is composed by burst structure (as shown infigure 2.3). The time slots are scheduled as 52 frames in a multi-frame. Eachframe contains eight slots and each slot is 0.577 ms, which means a frame lengthof 4.62 ms. The base station use one slot for the managing of the PDCH withthe information on the mobile station’s status, or timing information.
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Different classes of GPRS are made based on the number of up-link anddown-link available time slots. The table 2.1 is showing the different classes ofGPRS with the relative number of time slots.
Class Receiving Slots Sending Slots Maximum number of slots1 1 1 22 2 1 23 2 2 35 2 2 48 4 1 510 4 2 512 4 4 5
Table 2.1: Different classes in the GPRS connection
Within the same cell, different rates can be achieved by a single mobiledevice. The speed depends on the coding scheme used for the communication.It must be added that the maximum rate the is only available under the mostfavorable conditions. On the other hand, with the slowest transmission themaximum area of the cell (98% of the entire cell) is covered. The value, in thefigure 2.2, are shown in kilobits per second (Kbps).
Coding Scheme Number of slots1 2 3 4 5 6 7 8
CS-1 9.05 12.2 27.15 36.2 45.25 54.3 63.35 72.4CS-2 13.4 26.8 40.2 53.6 67 80.4 93.8 107.2CS-3 15.6 31.2 46.8 62.4 78 93.6 109.2 124.8CS-4 21.4 42.8 64.2 85.6 107 128.4 149.8 171.2
Table 2.2: List of different Coding Schemes
CS-1 provides for the most correction and detection capabilities for situa-tions in which the carrier-to-interference level are very low. The CS-2 and CS-3are something more balanced and, at last, CS-4 is used in the ideal situationwhere carrier-to-interference level are optimum. Here, no correction encoding isused at all. In the ideal conditions the maximum data rate for a GPRS frame,assuming that all slots are used for data, is 8 × 21.4K = 171,2Kbps. This rep-resents the most ideal location and situation, where there is no error correctionat all.
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2.1.4 GPRS ModulationThe modulation used for a GSM/GPRS connection is the Gaussian Minimum
Shift Keying (GMSK) [2]. This modulation comes directly from the FrequencyShift Keying (FSK) modulation in which the information is associated by par-ticular variation of the carrier signal frequency between two values f1 and f2.
By using the GMSK every symbol that is transmitted is composed by onebit, and its phase increment or decrement of π that is, each shift in the phaserepresents one bit.
Figure 2.4: GMSK modulation [2]
The probability of error of the GMSK, supposing an Additive White Gaus-sian Noise (AWGN) channel is:
PE = erfc
(√E
2N0
)(2.1)
where N0 is the spectral noise density and E is the energy of the received signaland it’s in relation with the received power PR and with the bit rate B by thefollow expression:
E =2PR
B(2.2)
The received power PR can be written as a function of transmission powery like:
PR = AyGc (2.3)
where A is the path loss coefficient (A < 1) and Gc the coding gain.
After these considerations, the energy E is equal to:
E =2AyGc
B(2.4)
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From the probability of error given by the equation 2.1 it is possible to havea probability of error per bit equal to:
Pb ≈PE
2(2.5)
Finally:
Pb =12erfc
(√AyGc
N0B
)(2.6)
2.1.5 Mobile StationDifferent states characterize the behavior of mobile devices:
• IDLEWhen a mobile device is in idle state it appears invisible to the network.The mobile device is not attached to the GPRS network, there is no in-formation in the SGSN routing list, and it is not possible to perform anydata transmission.
• STANDBYIf a mobile is in standby state, it is attached to the GPRS network butit is not possible to receive or transmit data. The SGSN contains all theinformation of the routing area regarding the mobile device. When themobile device is interrogated by the SGSN for starting a communication,the mobile goes to the ready state and the communication is established.If the time expires, it returns to the idle state.
• READYIn the ready state the mobile device can receive and send data. Duringthis state it also sends updates to the SGSN regarding the changes inrouting area. This state is timer controlled. Whenever the time expires,the mobile device goes in standby state.
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2.2 EGPRSA different modulation technique and error-tolerant transmission methods
make, starting from the GPRS’ bases, another type of connection named EG-PRS. The objective of this technology is to increase data transmission rates andspectrum efficiency using a new modulation technique and a new channel cod-ing and, due to this, to facilitate the use of new application on mobile devices.EDGE is used for the transmission of data on the same network as the GPRS’data, therefore it is an add-on to GPRS and cannot work alone. [3]
2.2.1 EGPRS ModulationIn addition to the modulation used in the GSM/GPRS connection, in the
EGPRS is also used the 8-Phase Shifting Keying (8PSK) modulation, that comesdirectly from a M-ary Phase Shifting Keying (M-PSK) modulation with M =8, in order to increase the size of the modulation using 8 different points in theconstellation. To achieve higher bit rates per time slot than the ones availablein the GPRS, the 8PSK modulation maps three consecutive bits in one symbol.
The symbol rate remains the same as the GMSK, but each symbol representsthree bits instead of only one. The increased number of possible symbols meansa shorter distance between each of them. Because of this, under poor radiocondition, the risk of misinterpretation is higher because for the radio receiverit is more difficult to detect which symbol has been received. Anyway, the extrabits are added to improve the error control coding, and the correct informationcan be recovered. Only under very poor radio environments the GMSK methodis more efficient.
Figure 2.5: 8-PSK modulation
The Probability of error for an 8-PSK modulation for a AWGN channel isgiven by a more general expression of the M-PSK modulation, as follow:
PE = erfc
(√E
N0sin( π
M
))(2.7)
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As said for the GMSK modulation, the energy of the received signal E isin relation with the received power PR and with the bit rate B by the followgeneral expression:
E =PR
Blog2(M) (2.8)
where
PR = AyGc (2.9)
Substituting these results in the expression 2.7, it results that the probabil-ity of error for a M-PSK modulation is:
PE = erfc
(√AyGc
N0Blog2(M)sin
( π
M
))(2.10)
In our case M = 8, so we have a probability of error for a 8-PSK modulationgiven by:
PE = erfc
(√3AyGc
N0Bsin(π
8
))(2.11)
2.2.2 EGPRS Coding SchemesAs said before, the GPRS coding scheme is composed of four different
schemes. Each of them is made for different environments and has differentrate. For the EGPRS there are nine different coding schemes which are chosenfrom MCS1 - MCS9 (Modulation Coding Scheme). The nine coding schemesof the EGPRS are based on both GMSK and 8PSK modulation. The firstfour MCS are based on the GMSK, and the upper five are based on 8-PSK.The following figure shows the different coding scheme of GPRS and EGPRScomparing each other in terms of rate.
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Figure 2.6: Modulation Coding scheme in EGPRS
The GPRS saturation limit is at 20 Kbps with the best coding scheme. Inthe best possible condition of EGPRS, it is possible to reach up to 59.2 Kbps.The two different technologies are based on the same GMSK modulation, butthe last five MCS of EGPRS are based on 8PSK modulation, which increase thethroughput. The difference in performance is partly due to the different headersize of the EGPRS packets. A packet sent with a fast MSC that is received withsome error, can be retransmitted again by using a more-secure MSC (more errorcorrection) if the radio environment requires it. This possibility of retransmit-ting by using different coding schemes is the reason why EGPRS and GPRS donot have the same performances: GPRS cannot support the re-segmentation.
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2.3 InterferenceIt is known that the capacity of a cellular system is determined by the in-
terference associated with it. In a multi-cell scenario the interference consists ofinter-cell interference arriving from neighbour cells. The intra-cell interferenceis avoided in GSM technology. The interference power received at a base stationof a given cell can be estimated by knowing the number of users within a cell(intra-cell interference), and the number of users and their locations in the adja-cents cells (inter-cell interference). In this report only the inter-cell interferencewill be treated. The possible sources of interference are shown in figure 2.7
Figure 2.7: Possible interference in multi-cell scenario
A lack of synchronization between the independent cells combined with animperfect channel isolation can lead to inter-cell interference. Inter-cell inter-ference can result in unsuccessfully received packets by the user due to thecombination of the wanted signal with the interfering signals.
Power control will be considered in the expression of the inter-cell interfer-ence. Power control is used to equalize MSs the received signal power at a givencell’s base station for all the mobile stations linked to this base station. Butinterference also arrives from mobile stations controlled by other cells base sta-tions. The signal arrives at the base station with a lower download power level.The interference comes from BSs that are using the same frequency in differentcells.
According to [4] it is possible to consider two cells i and j. The users poweris controlled by the base station of cell j at the distance rj(x, y). The distanceof the same user from the base station in cell i is ri(x, y). Assuming that in cellj there are nj users denoted by region Cj and area Aj = Area(Cj).
Figure 2.8: Multi-cell scenario & division of a cell for the integer
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According to [4], the relative average interference at cell i caused by nj usersin cell j can be written as
Iji = E
∫ ∫Cj
rmj (x, y)10
ξj10
rmi (x, y)/χ2
i
nj
AjdA(x, y)
(2.12)
where ξ is the decibel attenuation due to the shadowing which is a Gaussianrandom with zero mean and standard deviation sigma σs, m is the pass lossexponent and χi is a Rayleigh random variable that represents the fading onthe path from the user to cell i.
The equation 2.12 can be written as
Iji = e(γσs)2 nj
Aj
∫ ∫Cj
rmj (x, y)
rmi (x, y)
dA(x, y) (2.13)
where σ = ln(10)10 . In equations 2.12 and 2.13 the denominator represents the
propagation loss to the given base station and the numerator is the gain adjust-ment through power control by the nearest base station.
According to [4], to obtain the per-user inter-cell interference fji, Iji is di-vided by the total number of users in cell j. In this model, fii equals zero and fji
can be viewed as elements in a two dimensionnal matrix F with i, j = 1, ...,M ,where M is the total number of cells in the network. Each column i of F con-tains the per-user inter-cell interference radiated by cell j on every other celli. The relative average inter-cell interference in cell i is the summation of theproduct of number of users nj in cell j. The per-user interference factor fji
is the column vector i in F . It is possible to write the total relative averageinter-cell interference as
Ii =M∑
j=1
njF [j, i] (2.14)
It is possible to see that the interference in download caused by a user isindependent of its location within a given cell.
For a general mobile station distribution, the equation 2.12 becomes
Iji = E
∫ ∫Cj
rmj (x, y)10
ξj10
rmi (x, y)/χ2
i
nj
Ajw(x, y)dA(x, y)
(2.15)
where w(x, y) is the user density at (x, y). We can define kji as the per-userrelative inter-cell interference factor from cell j to base station i and write it as
Iji =e(γσs)2
Aj
∫ ∫Cj
rmj (x, y)
rmi (x, y)
w(x, y)dA(x, y) (2.16)
If the mobile station exact location is taken into account for the determina-tion of interference, the matrix F cannot be calculated in advance. For a userk in cell j, the relative interference offered by the mobile station to cell i is
(Uji)k = e(λσs)2(
rj
ri
)m
(2.17)
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Finally, the total inter-cell interference at cell i due to the nj mobile stationsin cell j can be written as
Ii =M∑
j=1
nj∑k=1
(Uji)k (2.18)
This vector represents the actual interference caused by each mobile stationon every cell.
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Chapter 3
Problem Analysis
3.1 Problem definitionThe GPRS and EGPRS technology permits improvements in the system ca-
pacity and so the data rate by using different techniques such as beamforming,scheduling or power control. Indeed, through the use of various coding schemes,the transmitting power can be varied to limit the effect of the interference. How-ever, the increase in power can degrade the carrier to interference ratio for a cellusing the same channel at the same time. The co-channel inteference i.e. theinterference of two MSs transmitting on the same frequency, which has alreadybeen treated, will not be discussed in this report.
Our problem will be solved by simulating a multi-cell urban scenario andcoordinate the base stations in term of power control, scheduling or beam-forming. The combination of those techniques will also be investigated to obtainthe best system performance.
3.2 Power controlOne of the most important things to consider in the design of wireless net-
work is Power Transmission Control, which minimizes the energy consumptionand reduces the interference, increasing the system capacity and, as a result,the Quality of Service (QoS).
If we consider a constant power transmission, the channel quality dependson the gain of the link between MS and BTS. This quality is reasonable if thereceived power is almost equal to an assigned value PRIF the eventual overloadof power isn’t necessary to obtain the minimum quality and, at the same time,it increase the interference.
Power control permits to change the MS’s and BTS’s transmission power,so that it is able to use the minimum required power to obtain a good qualityof transmission; in this way, if the MS is close to the BTS, it has to transmitwith a lower power, as shown in fig. 3.1
19
Figure 3.1: Ideal Power Control: (a) constant transmission power; in that case the receivedpower increases when MS approaches the BTS; (b) the transmission power is reduced whenthe MT approaches the BTS; in this way the received power is constant an equal to PRIF ,minimizing the interference [5].
If the interference is reduced by using Power Control, it is possible to havea more dense reutilization of frequencies (being able a reduction of cells’s num-ber in a cluster); in addiction it moderates MS’s power consumption in uplinkdirection, extending the life of the battery.[5]
3.2.1 The Wireless NetworkTo explain the power control algorithm about it is possible to consider the
wireless network like a set of radio-link in which every link stands for a transmis-sion single-hop in the channel. The QoS, expressed by Bit Error Rate (BER),is an increasing function of the Signal-to-Interference Ratio (SIR) observed atthe receiver.
Given N active links, the SIR of the i-th link is
Ri =GiiPi∑
j 6=i GijPj + ηi(3.1)
where Gij > o is the power gain (loss) from the BSj to the i-th receiver and itincludes the free space loss, the multi path fading and the shadowing; Pi andηi > 0 are the transmitted power on the i-th link and the thermal noise powerat its receiver node.
To guarantee the minimum QoS, every i-th link has to have a SIR more thana threshold value γi ≥ 0, so it’s required that
Ri ≥ γi for every i = 1, 2, ..., N (3.2)
It’s possible to rewrite equations 3.1 and 3.2 in matrix form
(I− F)P ≥ u and P > 0 (3.3)
20
where P = (P1, P2, ..., Pi, ...PN ) is the column vector of transmitted powersand
u =(
γ1η1
G11,γ2η2
G22,γ3η3
G33, ...,
γiηi
Gii, ...,
γNηN
GNN
)(3.4)
is the column vectors of normalized noise powers, and F is the matrix withelements
Fij =
{0 if i = j
γiGij
Gijif i 6= j
(3.5)
where i, j ∈ {1, 2, ..., N} and F is the matrix of cross-link normalized powergains. Its elements are nonnegative so it’s possible to assert that the matrix isirreducible. The maximum modulus eigenvalue ρF of F is positive and simple,while the corresponding eigenvector is positive component-wise.
From Matrix-theory it has that following statements are equivalent:
• It exists a vector P > 0 so that (I− F)P ≥ u;
• ρF < 1;
• There exists the matrix (I−F)−1 =∑+∞
k=0 Fk and its elements are positive.
If ρF < 1, it will be
limk→+∞
Fk = 0 (3.6)
Furthermore, if the equation 3.3 has solution, it is possible to have
P0 = (I− F)−1u (3.7)
This is a Pareto-optimal solution, that means that any other vector thatsatisfies the equation 3.3 is so that
P ≥ P0 (3.8)
If it is possible to satisfy the equation 3.2 for all links at the same time, itis a good strategy to set the power of transmitters to P0 in order to minimizethe power consumption [6].
21
3.2.2 Distributed Power Control (DPC)To describe in detail the DCP algorithm the word distributed must be de-
fined in the specific context of this analyzes.
In a distributed management of power control, every link, depending on ad-equate measurements, decide autonomously how modify its transmission power.This implies a less complex algorithm than the centralized case because bothdecision operations and the real adaptation of transmission power are performedby the link.
In the DCP algorithm every link increases autonomously its power when theSIR is under its threshold γi and decreases it otherwise.
DPC Algorithm
The following algorithm was proposed by Foschini and Miljanic in [7]. Inthis algorithm it is possible to observe that the iterative formula
P(k + 1) = FP(k) + u , k = 0, 1, 2, ... (3.9)
converges to P0 when it exists. As a matter of facts, substituting recursively inthe equation 3.9
P(k) = FkP(0) +
[k−1∑i=0
Fi
]u (3.10)
which can be used to obtain
limk→+∞
P(k) = limk→+∞
FkP(0) + limk→+∞
[k−1∑i=0
Fi
]u (3.11)
= 0 +
[k−1∑i=0
Fi
]u (3.12)
= (I− F)−1u = P0 (3.13)
The previous one is valid for ρF < 1, while if ρF ≥ 1 powers diverge toinfinite.
It is possible to simplify the DPC algorithm so that the local measurementsof interference
∑i 6=j GijPj , of the noise power ηi and of propagation gains Gii
are not necessary. The most important thing that the receiver has to know isthe SIR.
22
Considering the equation 3.9, the i-th link’s variation of the power is given by
Pi(k + 1) =γi
Gii
∑j 6=i
GijPj(k) + ηi
(3.14)
From equation 3.1 ∑j¬i
GijPj(k) + ηi =GiiPi(k)Ri(k)
(3.15)
so that 3.14 becomes
Pi(k + 1) =γi
Ri(k)Pi(k) , i ∈ {1, 2, 3, ..., N} (3.16)
where Ri(k) stands for the i-th link’s SIR at time k. Therefore every linkincreases its power independently from any other when the SIR is under itsthreshold value γi and decreases it in the opposite case. To do that, the receivertake a measure of interference and transmit this value to the transmitter, whichdecide how to modify the transmission power.
3.2.3 Distributed Power Control with Active Link Protec-tion (DPC/ALP)
The main problem of the described algorithm is that it may allow the SIR tobe below its threshold during its evolution, so the transmission power may fluc-tuate in the transient phase before convergence. When new links try to accessthe channel, established ones can be suppressed because of their SIR temporar-ily being under the threshold, even if they could be adjusted.
This is a serious problem that could be solved with the introduction of analternative power control scheme that protects both the currently active links,maintaining their SIRs over their thresholds γi, and new links that try to accessthe channel. Furthermore, if the latter cannot be adjusted, they will simply bedropped, maintaining the active links in the process. Let L be the set of alllinks. It’s possible to say that a link i ∈ L is active if, during the k-th step, itis that
Ri(k) ≥ γi (3.17)
Let Ak be the set of active links during the k-th step.
Moreover it is possible to define a non-active link or a new-link if, duringthe k-th step, it is that
Ri(k) < γi (3.18)
23
Let Bk be the set of non-active links during the k-th step. Finally, let δ bea control parameter bigger that 1, so that
δ = 1 + ε > 1 , ε > 0 (3.19)
The DPC/ALP algorithm updates transmission powers Pi(k + 1) in the(k + 1)-th step according to the following rule
Pi(k + 1) =
{δγi
Ri(k)Pi(k) , i ∈ Ak
δPi(k) = δ(k + 1)Pi(0) , i ∈ Bk
(3.20)
The previous equation shows that established links update their power fol-lowing the DPC Algorithm, while new ones increase gradually their power. TheSIR threshold is δγ and give a margin for the protection of the active link equalto ε = δ − 1 > 0; this means that latter ones can maintain the SIR over thethreshold γ also when other links try to access the channel.
DPC/ALP algorithm has following properties:
Proposition 1. Given δ ∈ (1,+∞), for each k ∈ {1, 2, 3, ...} and for eachi ∈ Ak, the result is
Ri(k) ≥ γi ⇒ Ri(k + 1) ≥ γi (3.21)
hence
i ∈ Ak ⇒ i ∈ Ak + 1 (3.22)
or, equivalently
Ak ⊆ Ak + 1 (3.23)
and
Bk ⊆ Bk + 1 (3.24)
This proposition says that active links at the beginning remain active duringthe whole evolution of DPC/ALP algorithm.
24
Proposition 1. Given δ ∈ (1,+∞), it results that
Pi(k + 1) ≤ δPi(k) (3.25)
for each k ∈ {1, 2, 3, ...} and for each i ∈ Ak
This proposition shows that Pi(k+1)Pi(k) ≤ δ = 1 + ε, where δ is slightly more
than 1, that is the active links power increases slowly so that it is able for newlinks to access the channel.
Proposition 1. Given a δ ∈ (1,+∞), it results that
Ri(k + 1) ≤ Ri(k + 1) (3.26)
for each k ∈ {1, 2, 3, ...} and for each i ∈ Bk.
From the last property it results that the SIR of every non-active link in-crease step-by-step and if its value crosses the threshold, that link becomesactive.
To improve this algorithm it is possible to consider two different strategiesthat can better be described the real world situation of a network situated in adynamic environment.
DPC/ALP with Voluntary Drop-Out (VDO)
When a new link detects a congestion of the channel and predicts fewprobabilities to access it, it voluntarily decides to drop out from the channel.In this way that link is non-active, it does not congest the channel and it alsogives other links the possibility to access that one.
DPC/ALP with Forced Drop-Out (FDO)
In this algorithm there is a restriction in the transmission power becausefor each i-th link it can’t exceed a certain value Pmax
i . If this limit is alreadyreached and new links increase their power to access the channel, the i-th linkobserves its SIR go down and it can become non-active. To avoid that situationthe Forced Drop-Out (FDO) mechanism can be used that pulls out new linksthat are the cause of the decrease in SIR of active links as written in [8]
25
3.3 BeamformingDue to the limitations of the channel bandwidth, the increase of data rate
increases interference. A way to reduce the interference is to use beamform-ing by the use of adaptive/smart antennas. Adaptive antennas are composedof a system of antenna arrays usually controlled by a signal processing algorithm.
Beamforming is divided into three parts. Firstly, the system estimates thedirections-of-arrival (DOAs) of the sources. This permits a signal-blocking (SB)transformation which removes from the coherent signal the interference and thenoise. The SB signal is then used to determine the Inteference blocking (IB)which permits determination the optimum beamforming. Optimum beamform-ing then maximizes the output SINR.
According to [9], [10] and [11] it is possible to construct a steering matrix inwhich each column correspond to the steering vector of a selective beam and aconstraint vector with each entry equal to the gain of a beam.
Assume a M -element antenna array from P coherent sources from directionsθdi and J uncorrelated interference from directions θui . It is also considered thatall the sources are narrow-band. The received array signal can be expressed as
x(t) = sd(t)P∑
t=1
αia(θdi) +
J∑i=1
si(t)a(θui) + n(t) (3.27)
where sd(t) represents the desired signal, αi represents the complex amplitudeof the coherent signal and a(θ) is the steering vector of the array. si(t) repre-sents the ith interference with power σ2
i = E|si(t)|2. n(t) is a spatially whitenoise vector power σ2
n. Assume that sd(t), si(t) and n(t) are not correlated witheach other.
The vector associated with the coherent sources can be written as
a =P∑
t=1
αia(θdi) = A.α (3.28)
where A = [a(θd1), ..., a(θdP)] and α = [α1, ..., αJ ]T . a is called the generalized
array manifold (GAM).
And the vector associated with the interference as
i(t) =J∑
i=1
si(t)a(θui) (3.29)
The expression 3.27 can be rewritten as
x(t) = sd(t)A.α + i(t) + n(t) (3.30)
Given A and x(t) beamforming consists in finding the optimum beamform-ing weight vector w.
26
Various beamformers are now possible: the minimum mean square error(MMSE), the interference-plus-noise rejecter, the linearly constrained minimumvariance (LCMV) or the multiple constrained minimum variance (MCMV). Thefirst two beamformers need a training signal which leads to a waste of bandwithand this training signal can be not available in pratical situation. The LCMVand the MCMV approaches require no training signal and can be called a blindbeamforming approach.
3.3.1 MMSETo use the MMSE combiner, the desired signal has to be known. The mean
square error function isE|sd(t)−wH .x(t)|2 (3.31)
The optimum weight vector is
min E|sd(t)−wH .x(t)|2 (3.32)
The solution iswMMSE = Rxx
−1rxs (3.33)
withrxs = E|x(t).s∗d(t)| (3.34)
3.3.2 Interference-plus-noise rejecterFor this beamformer the weight vector is chosen to maximally reject the
contribution of the interference and noise. The optimum weight vector is
wint = argminw(wHRinw) (3.35)
with wHa = 1, (3.36)
where Rin is the interference-plus-noise covariance. The solution is:
win =Rin
−1.aaH.Rin
−1.a(3.37)
3.3.3 LCMVIf we know the GAM, so the complex amplitudes and the DOAs of the
coherent signal, it is possible to use the LCMV. The optimum weight is
wLCMV = argminwE|wH.x(t)|2 (3.38)
withaHw = 1, (3.39)
Because the knowledge of a is not complete, α has to be estimated first. Thefirst step is to determine the signal-plus-interference subspace from the covari-ance matrix Rxx. The second step is to determine α from the noise subspace.
27
3.3.4 MCMVThis beamformer use the DOA to construct multiple constraints for the
minimum variance beamformer. The optimum weight is
wLCMV = argminwE|wH.x(t)|2 (3.40)
with AHw = f , (3.41)
where f is the unknown response vector depending on α. According to [11]the objective of the MCMV is "to optimize the receiver’s output energy whileconstraining the response of the user of interest to be constant".
3.4 ScheduleScheduling is a basic principle used in systems with different tasks/processes
at the same time, independent of their purpose. With different kinds of schedul-ing it is possible to change the behavior of the system regarding the tasks/processes(see [12]).
Scheduling is only for data information. The voice information can not bescheduled, because voice needs a dedicated bandwidth.
3.4.1 Scheduling in GPRSBecause GPRS is based on a packet switched system, one channel can be
used by several users. For this reason a scheduling technique is required.
Due to the fact that the channel has a different behavior in up- and downlink,different techniques are used (see [13]):
Downlink
“First-come first-serve” scheduling (see chapter 3.4.3) is used in the downlink.
Uplink
With slotted ALOHA (see chapter 3.4.3) the reservation of the timeslot inthe channel happens. Afterward the actual data is transmitted via “first-comefirst-serve” again.
3.4.2 QoS in GPRSQuality of service (QoS) describes the quality properties of a system. De-
pending on the goal of the specific application the parameters can have differentcharacteristic.
28
Important for the QoS in GPRS are following properties:
• priority
• reliability
• mean throughput
• peak throughput
• delay classes (see Table 3.1)
Because of the growing importance of data services (GPRS) and many dif-ferent user applications, a certin level of service quality was defined, the QoSprofile which goes hand in hand with the delay classes. The classes one, twoand three provide predictive services and require QoS management. Otherwise,class four offers the best-effort service.
delay class packed size- 128 octets 1024 octets- mean 95 % mean 95 %1.(predictive) 0.5 1.5 2 72.(predictive) 5 25 15 753.(predictive) 50 250 75 3754.(best effort) unspecified
Table 3.1: delay classes and requirements for different packet sizes (see [14])
For a useful performance measure with respect to the different delay classesand packet sizes the delays should be normalized.
Therefore the following method can be used:The first objective is to get an output independent from packet size and delayclass.
delaynormalized =experienced real delay of the packet
required delay of the packet(3.42)
and the mean normalized delay can be calculated by
mean delaynormalized =∑N
i=1 normalized delay of packet iN
(3.43)
With the mean delaynormalized (shown in formula 3.43) the performance re-quirement can be proved easily. If the mean delaynormalized is below 1 therequirement is met.
29
3.4.3 Explanation of scheduling techniques“First-come first-serve” scheduling
The tasks/processes are handled in order of their chronological appearance.If not enough capacity is available, the appearing task/process at this point oftime is shifted to the end of a waiting queue.
Static priority scheduling (SPS)
In this scheduling technique there is a buffer for every delay class reserved.Also a priority is assigned for every buffer - lowest priority for class 4 (besteffort), highest priority for class 1.
A downlink buffer timeslot will only be serviced if all higher prior buffersare empty.
Slotted ALOHA
The slotted ALOHA technique is based on the ALOHA technique:
1. If there is data to send, send the data.
2. If a collision with another message occurs, wait and attempt the transmis-sion later.
The main problem with this algorithm is, that the time which a task/processhas to wait is not defined. That can lead to unequal conditions, if one task/processuses a shorter delay than the others.
But in the case of GPRS this Problem disappear because of the timeslotsof the system –> slotted ALOHA. A transmission can only be started at thebeginning of a timeslot, and the delay time is given.This adaption also increases the maximum throughput because of the specifieddelay time.
Earliest deadline first (EDF)
Each packet has a given deadline (contains delay class and packet size). Andaccording to this deadline the packets will be controlled in a list.
Because of this sorted list a more difficult implementation is required. Thismeans that there are at least O(log N) operations for each packet (N is theamount of packets in the queue).
30
Chapter 4
Delimitation
4.1 Wireless channelThe environment of wireless communication is tightly constrained by the
complex variability of propagation parameters. Therefore is very important todescribe the characteristics of the wireless channel using representative models tounderstand the channel behavior in order to obtain peak performance followingthe planning choices.
4.1.1 General characteristicsA wireless transmission is a link between devices in which at least one of
them is not fixed in a known position. If one of the devices is fixed, it is calledBase Station (BS). A wireless system is a net of BS conveniently linked to givegood coverage for a service area. In the case of cellular wireless system, theservice area is separated in adjoining cells, each lead by a BS.
Let us consider a link between BTS and MS. The transmission channel forthat link has characteristics that can be modeled with just a statistic approach.
MS’s antenna is usually close to the ground and often not visible from theBTS because of many obstacles (shadowing). Furthermore it is possible to no-tice the presence of propagative phenomena diffraction, absorption (path loss)and diffusion as well as multiple ways to arrive at the receiver antenna (multi-path).
To describe the wireless channel it is possible to distinguish to differentphenomena:
• Slow fading: verifiable on long distance (some hundred times of wave-lengths), due to the sum of a deterministic parameter, function of distance(path loss), with a statistic one with mean equal to zero (shadowing);
• Fast fading: verifiable on short distance (some wavelength) due to mul-tipath;
31
In this case the i-th path suffer for:
– reduction;
– time delay;
– shift of carrier frequency (Doppler effect) fdi
We can define Doppler Spread as the quantity Fd = 2fd,max that is themeasure for channel frequency dispersion.
The difference between the minimum delay and the maximum is DelaySpread, which is a measure for channel time dispersion. Its mutual valueis defined as Coherence Bandwidth that is the limit for the bandwidthbeyond which the channel becomes frequency selective [2].
Figure 4.1: Channel Model
Figure 4.2: Received signal strength by MS [2].
32
4.1.2 Path Loss: Deterministic parameterThe pathloss is the amount of energy that gets lost from the signal during
transmission through a channel. It depends on the environment how much theinfluence of the pathloss is.
An easier description of a channel model is used to explain the behaviorof the channel. Regarding to the environment, i.e. rural, suburban, urban orheavy urban, the channel model uses different parameters (see [15]).
Okumura-Hata model
This model derives its name from its creators, Yoshihisa Okumura and Masa-haru Hata. It is quite easy to handle, built for frequencies up to 1000 MHZ anddistances between 1 and 20 km with higher locations for the transmit antennas(above 30m).
This is a more typical model for a rural area.
The pathloss is calculated as followed:
A(dB) = 69.55 + 26.16 log(F )− 13.82 log(H) + (44.9− 6.55 log(H)) log(D) + C(4.1)
The constants have the following meaning:
• F for frequency in MHz
• H for the efficient height of the BS-Antenna in m
• D for the distance between BS and MS in km
• C for the kind of environment:
– 0 for heavy urban
– -5 for urban
– -10 for suburban
– -17 for rural
COST- 231 HATA model
This propagation model is little similar to the Okumura-Hata model, butdesigned for frequencies around 1800MHz.
The pathloss is calculated as followed:
A(dB) = 46.3+33.9 log(F )−13.82 log(H)+(44.9−6.55 log(H)) log(D)+C (4.2)
The constants have the following meaning:
• F for frequency in MHz (1700 - 1900 MHz)
• H for the efficient height of the BS-Antenna in m
• D for the distance between BS and MS in km
• C for the kind of environment:
33
– -2 for heavy urban– -5 for urban– -10 for suburban– -20 for rural
Lee’s propagation model
This model was developed in 1982 in the United States and was a popularmodel for the early (analog) mobile operator.
If the frequency is above 450MHz and the efficient MS’s height is below3m, the pathloss for a distance between 1km to 10km can be calculated in alogarithmic format as followed:
P(E) = P0 − y log(d)− 3 log(f
900) + K0 (4.3)
With d as the distance between BS and MS in km and f for the frequencyin MHz. P0 (reference input power) and y (base attenuation) are depending onthe kind of environment and can be assumed as listed below:
environment P0 (dBm) y (dB/Decade)rural -41 20suburban -40 43,5urban -54 38,4heavy urban -55..-78 30..43
Table 4.1: assumed values for P0 and y for Lee’s propagation model (see [15])
The factor K0 is a correction factor which is dependent on the circumstancesof sender and receiver. It is calculated from the equations below:
K1 =(height of the BS)2
30.48m(4.4)
K2 =height of the MS’s antenna
3m(4.5)
K3 =transmission power
10W(4.6)
K4 =BS antenna gain over a λ/2-Dipol(lin)
4(4.7)
K5 = MS antenna gain over a λ/2-Dipol(lin) (4.8)
After the multiplication of the several factors (K1...K5) the linear factor Kis the result. To use the factor in formula 4.3 it has to be transformed into alogarithmic format:
K0 = 10 ∗ log(K) (4.9)
With this transformation all variables for the formula 4.3 are given and thecalculation can be progressed.
34
4.1.3 Shadowing: Log-normal distributionShadow fading, also called shadowing or slow fading, is defined as the fluc-
tuation in the received power averaged over a small area, typically a diameterof 10 to 50 wavelengths in an outdoor environment.
According to [16] the shadowing value X is characterized by a log-normaldistribution. The probability density function is
p(X) =1
σX
√2π
e− (X−µX )2
2σ2X (4.10)
where σX is the deviation of the local mean (in dB) due to the location variabil-ity, the shadowing of the signal, and µX is the average of the received loval meanlevel (in dB). The value of σX depends on the type of the terrain. According to[17] we can draw the following table
Environment σX (dB)Urban micro cell 2.3
Urban micro cell - Manhattan layout 3.1LOS fixed station (rooftop to rooftop) 3.4
Urban macro cell 8Sub-urban macro cell 8.2-10.6Indoor small office 12
Table 4.2: Some typical values for the deviation σX [17]
4.1.4 Multipath: Rayleigh distributionIt is possible to describe the multipath phenomena with a Rayleigh distri-
bution if we assume that there is not a component among all received signalsfrom the MS that has a bigger energy than the others.
Under these assumptions the received signal is the following:
c(t) = cR(t) + jcI(t) (4.11)
where the real component cR(t) and the imaginary one cI(t) are independentrandom variables with Gaussian statistic.
35
Expressing the same signal in a complex formula it is possible to write:
c(t) = α(t)ejϕ(t) (4.12)
with
α(t) =√
c2R(t) + c2
I(t) (4.13)
ϕ(t) = arctancI(t)cR(t)
(4.14)
It’s possible to demonstrate that:
• the phase ϕ(t) is a random variable uniformly distributed in [−π, π];
• the envelope α(t) of received signals is a random variable with densityprobability function that follows Rayleigh distribution, given by:
f(α) =
{ασ2 e−
α2
2σ2 if α > 00 if otherwise
s (4.15)
where σ represents the variance of the Rayleigh random variable.The corresponding distribution function is:
F (α) =
{1− e−
α2
2σ2 if α > 00 if otherwise
(4.16)
If we can make the approximation α2
2σ2 << 1 the expression 4.16 become:
F (α) ∼=α2
2σ2(4.17)
Probability of error
A non-selective channel is represented by an impulse response like:
h(t, τ) = α(t)δ(τ − τ0(t)) (4.18)
where α(t) follows the Rayleigh distribution at any time.
36
Assuming that the variations of α(t) and τ0(t) are unimportant in the sym-bol range T , the impulse response in 0 ≤ t ≤ T has the expression:
h(τ) = αδ(τ − τ0) (4.19)
where α is a Rayleigh variable.
A general expression for the probability of error, for every possible value ofα is:
Pb =∫ ∞
0
Pb(α)f(α)dα (4.20)
Solving this integral we have that:
Pb =12
[1−
√ρb
1 + ρb
](4.21)
where ρb is the average received SNR and is equal to:
ρb =Eb
N0E(α2) (4.22)
while E(α2) is the average value of the random Rayleigh variable α, so that:
E(α2) = 2σ2 (4.23)
Starting from the general expression is easy to find the expression for theprobability of error for modulations GMSK and MPSK [18].
For the GMSK modulation, from the equation 4.21, with
ρb =AyGc
N0B2σ2 (4.24)
we have that the probability of error per bit in a Rayleigh fading channel is:
Pb =12
1−
√√√√ AyGc
N0B 2σ2
1 + AyGc
N0B 2σ2
(4.25)
For the general M-PSK modulation, the probability of error per bit is givenby:
Pb =1
log2(M)
[1−
√ρb
1 + ρb
](4.26)
37
where
ρb =AyGc
N0Blog2(M)sin2
( π
M
)2σ2 (4.27)
In our case M = 8, so the final probability of error per bit for a 8-PSKmodulation is:
Pb =13
1−
√√√√ 3AyGc
N0B sin2(
π8
)2σ2
1 + 3AyGc
N0B sin2(
π8
)2σ2
(4.28)
4.2 ThroughputThe definition of the Steady-state Long Term Throughput f is:
f = limt→∞
Nt
t(4.29)
where Nt is the number of transmitted segments in the range [0, t]. To analyzethe throughput expression as function of the channel quality it is necessary todefine the probability to lose a segment, composed by J blocks, as follow:
PS = 1− (1− Pblock)J (4.30)
where Pblock is the probability to lose a block that can be approximated by:
Pblock = (1− (1− Pb)K)δ+1 (4.31)
In this case Pb is the probability of error per bit and it depends on the mod-ulation while δ is the maximum number of retransmissions that is possible, andit is given directly by the Link-Layer Protocol used.
After these conditions it is possible to write the final expression for thethroughput [19]:
f(PS) ≈ min
Wmax
RTT,
1
RTT√
2PS
3 + T0 min(
1, 3√
3PS
8
)PS(1 + 32P 2
S)
(4.32)
where Wmax is the maximum dimension of the congestion window, T0 is theTime-Out and RTT is the Round Trip Time given by the following expression:
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RTT = T + 2D + TS + (2D + Tb)J∑
i=0
δi (4.33)
in which T is the RTT of the wired part of the link, D is the propagation timeone-way, TS is the time for the transmission of one segment, Tb is the timefor the transmission of a block and δi is a random variable that stands for thenumber of retransmissions.
Given this expression, it could be analyzed by the following average value:
E(RTT ) = T + 2D + TS + (2D + Tb)J∑
i=0
E(δi) (4.34)
= T + 2D + TS + (2D + Tb)JE(δi) (4.35)
The expression of the average value of δi is given by [18]:
E(δi) =Pblock
1− Pblock−
(δ + 1)P δ+1block
1− P δ+1block
(4.36)
According to [20] the optimal choice of coding schemes can be described as afunction of the CIR of the channel. So if the CIR is known a CS that maximizesthe throughput can be chosen as shown as in figure 4.3.
Figure 4.3: Throughput vs CIR ratio
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In order to simulate this function it is possible to make a linear interpolationas shown as in figure 4.4.
Figure 4.4: Approximation of throughput vs CIR ratio
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Chapter 5
Simulation Analysis
5.1 DescriptionThe main objective of this project is to simulate users moving within a cell
representative of an urban area. The environment has been set to nine basestations. The number of users is changing, and each user is moving within itsown cell. Path-loss, shadowing and small scale fading will be evaluated based onstatistical distributions. Hence, this channel model will modify the value of gainfor all the users and for all the positions they pass trough. Spatial correlationwill also be taken in account.
Based on this situation, a certain amount of traffic will be generated for 2minutes and it will be carried to the users according to a certain schedulingalgorithm. The scheduling algorithm can be chosen between the different avail-able algorithms. At the same time, different Power Control algorithms can bechosen to reduce the interference problem of the multi-cell scenario. Inter-cellscheduling can also be part of the simulation.
41
The following diagram shows the different parts of the simulation.
Figure 5.1: Diagram of the simulation
42
5.2 InitializationThe different number of simulations will be based on different environmental
conditions. As was stated in the previous sub-chapter, the channel model willdefine the behavior of the gain and, based on this, different Coding Schemes willbe assigned to different users during their transmissions.All the parameters thatcan determine the network characteristics are determined by the environment.
Those parameters are showed in the following table.
Type of value ValueGeneral
Radius of a cell 650 mFrequency 1.8 GHzWavelength 0.16 m
Number of channel per cell 1Number of time slots 8
Number of cells within a cluster 25Number of mobile 5 to 25
Power level 1 WNoise level 1e−9
Training sequence 20 msChange position 5 s
Total time of simulation 120 sChannel model
Distance attenuation coefficient for the path gain 4 mStandard deviation for the lognormal faiding 20 dB
Gain at 1 m of distance from a BS -21 dBDownlink correlation 0.5Correlation distance 50 m
Mobility modelMean velocity of the users 1.38 m.s−1
Mean acceleration of the users 0.68 m.s−2
Table 5.1: Values used during the simulations
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5.3 EnvironmentRUNE (Rudimentary Network Emulator) is a collection of MATLAB func-
tions designed to simulate a cellular network and many of its features. It wasoriginally developed at Ericsson and later enhanced for the book "Radio Re-sources Management for Wireless Networks" [21] by the authors Magnus Alm-gren and Olav Queseth. RUNE functions permit the manipulation of variousaspects of a hypothetical cellular system environment such as the creation ofcells, base stations, propagation losses, interference, channel assignment or mo-bility of the MSs.
5.3.1 Creation of the cells and clustersWhen doing the cellular network simulations the first objective is to create
the cells. In reality these cells do not represent an organized shape, due to theenvironment, the terrain, the geography, etc. But it will be assumed that eachcell is of hexagonal geometry which will permit more simple calculations. Dueto this shape, the coordinates of the MSs and BSs are plotted in a hexagonalgeometry.
A cluster contains many cells and, after a cluster is created, it is replicated(number of clusters)2 times and then closely coupled to reuse in the cellularsystem.
Since the clusters are replicated situated in a patterned grid, it is importantthat the clusters fit together. If three rhombuses are created that have the sizekm2, lm2 and km.lm, and are put together, a geometric figure results. So eachcluster will contain km2+lm2+km.lm cells. The figure 5.2 demonstrates howRUNE is creating the clusters.
Figure 5.2: Creation of the clusters
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5.3.2 Wrap aroundThe main objective of cellular network simulations is to replicate reality as
closely as possible. These simulations require a lot of computer memory. If thesize of the cellular network increases, the computer memory needed increases aswell, as does the computing time. The best way to deal with this problem is tocreate and repeat a small amount of cells. A method to do this is to put thecells in a rhombus and then wrap the edges. That means that the top meets thebottom and the right meets the left. Illustration of a wrap around technique isshown in figure 5.3. It is also possible to refer to [22] to have more informationabout the wrap-around optimization in network simulation.
Figure 5.3: Illustration of wrap around
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5.4 Mobility modelThe mobility model is used to simulate a random walk of a pedestrian inside
a cell. This permits a more dynamic and realistic simulation.
During the initiation the number and size of the cells, the size of the clusterand the number of mobiles are given by the author of the source code as a testphase. In the further implementation the variables will be given by precedingroutines of the simulation itself.
The first part of the source code "Mobilitymobile.m" is to initialise the po-sition and velocity of the various MSs, respectively noted xym and xyv. It isperformed by the following code lines:
xym=nans(nmob,1);xyv=nans(nmob,1);
The velocity given to the users is in m.s−1. The coordinates are representedby a real component which represents East-West direction and an imaginarycomponent which represents the North-South direction.
The code line used to perform the movement of the MSs is:
[xym,xyv] = mobmove(xym,xyv,par.vmean,par.amean,par.dt,rombvec);
As INPUT parameters, we have:
• xym: last postion of the MSs;
• xyv: last velocity of the MSs;
• par.vmean: mean velocity of the MSs in m.s−1;
• par.amean: mean acceleration of the MSs in m.s−2;
• par.dt: time step in seconds;
• rombvec: two complex vectors determining the area within the mobileusers are folded;
As OUTPUT parameters, we have:
• xym: new position of the MSs;
• xyv: new velocity of the MSs;
The function mobmove found in RUNE permits, from a given position andvelocity, the calculation of a new position and velocity according to the follow-ing equations
ρ = exp(−dt.amean
vmean) (5.1)
vn = vn−1.ρ +√
1− ρ2.vmean.X (5.2)
46
where ρ is the correlation of the velocity between the times steps with dt thetime step, amean the mean acceleration in m.s−2, vmean the mean velocity. Xis the complex random number whose magnitude is Rayleigh distributed.
According to [23] the mean speed of a pedestrian in an urban scenario is 1,36m.s−1 and the mean acceleration is 0,6 m.s−2.
To avoid the handover between the BSs i.e. the movement of a MS from acell to another one, it is possible to constraint the MS to stay in its cell. Thebounce function is used in this way. If a MS is too far from its linked BS andcross the borders of its cell, it is automatically replaced near its linked BS.
Results
As a result of the simulation the figure 5.4 shows 100 MSs, uniformly dis-tributed, in a cluster containing 36 cells.
Figure 5.4: Mobility model for 100 MSs in a cluster containing 36 cells
It is possible to show the mobility of the MSs by zooming in on a certainamount of MSs as shown in the figure 5.5.
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Figure 5.5: Zoom in a cell to show the mobility model
It is also possible, as shown on the figure 5.6 to see the wrap effect -i.e.- if aMS go out from the cluster it will reappear in the other side of the cluster likea 3D-torus.
Figure 5.6: Wrap effect on the mobility label
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5.5 Channel ModelTo model the channel, taking into account just path-loss and Large Scale
Fading (or Shadowing) we use for our simulations the tool RUNE that gives ussome important functions useful for a cellular network.
As described in Chapter 4.1, to make an accurate model of our environment,it is important to consider three main aspects that contribute to change thereceived power at the mobile in a downlink connection: path-loss, shadowingand short scale fading.
The final result that must be obtained is a 3-Dimensional matrix in whicheach element represents the total path-gain for a specific mobile linked with acertain base station in a given time. This comes directly from the decision toobserve the channel for a period of time, taking measurements every 20ms, thatis the time range between two samples.
5.5.1 ShadowingTo generate a shadowing map that follows the log-normal distribution, is
still possible to use one of the RUNE’s functions:crelognmap.
The code is the following:
[lognmap, mapvec] = crelognmap(xyb,rombvec,par_corr.distance)
The INPUT parameters for this function are:
• xyb: the position of each base station, given by the mobility model, todetermine the size of the map;
• rombvec: a data structure that contains the size of the rhombus thatrepresents the service area of the system that is simulated; it is also usedto determine the size of the map;
• par_corr.distance: the correlation distance between two samples that con-trol how rapidly the value of the shadowing fading will change.
As OUTPUT parameters, we will have:
• lognmap: a square matrix of real values that contains, for each point, thefading value in dB;
• mapvec: two complex vector elements that are used to calculate the dis-tance at which the map will be repeated.
In the next figures the shadowing map is shown, and it is also applied to thecell map. It is possible to see how the shadowing map has to be calculated interms of cell’s border. The figure shows how the shadowing map covers the cellmap.
49
Figure 5.7: Shadowing map
5.5.2 Shadow fading correlationFor the radio links which have different propagation path, the shadow fading
experienced by each of them will not differ greatly. In order to obtain a modelthat approximates reality as closely as possible, the shadow correlation modelhas to be considered when simulating the shadow fading effect.
The correlation, as a function of space, can be written as
Rd(i) = σ2e−αX0|i| (5.3)
where σ2 is the process generalized power, X0 is the distance between themeasurements points, i is an integer number and e−α is the correlation coeffi-cient between two points spaced by a distance X0.
The correlation model in RUNE is created by generating a Gaussian whitenoise process and filtering through a first-order low-pass filter. It is known thata Gaussian white process has autocorrelation equal to zero. It is easy to findthe power spectral density of this process, which will be constant throughoutthe frequency band. At this the it is then passed from a first-order filter whichproduces a rect function whose Fourier transformation that will give a correlatedfunction, sinc here. This method is represented in figure 5.8.
5.5.3 Path lossWith respect to the loss that occurs over the path that the signal has to
cover, RUNE offers a function that puts together the shadowing gain alreadycalculated with the losses due to the distance between the mobile and the basestation in a matrix in which rows are the mobiles and columns are the different
50
Figure 5.8: Modelling correlated shadow fading using a Gaussian white processand a first order low filter
base stations.
The path-loss is calculated by the following equations:
Gatt = Gconst − 10αlog10(dist) (5.4)
The parameters that are used in this equation are calculated using the modeldiscussed in 4.1.2.
The RUNE function is:
g = pathgain (xym, xyb, fib, rombvec, par_attconst, par_alpha, par_sigma,par_raa, lobevector, lognmap, mapvec);
The INPUT parameters are:
• xym: a vector that contains the position for each mobile;
• xyb: the vector with the position of each base station;
• fib: a vector that points in the antenna direction;
• rombvec: as previous explanation, it’s a two complex vector elements thatare used to calculate the distance at which the map will be repeated;
• par_attconst: gain at 1 meter distance;
• par_alpha: a parameters that fixes the distance attenuation constant;
• par_sigma: standard deviation for the lognormal fading in dB;
• par_raa: this parameter determines the correlation for the lognormal fad-ing on the links between the base station and one mobile;
• lobevector: a column vector that contains the antenna gains for all direc-tions;
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• lognmap: given by the function crelognmap;
• mapvec: given by the function crelognmap.
The OUTPUT parameter is the matrix g with the total gain for each link.
The figure 5.9 shows the total pathgain between 3 different MSs and all theBSs. In this example the MS1 will be linked to the BS 3 which is the BS withthe highest total path-gain.
Figure 5.9: Total path-gain between 3 MSs and all the BSs
5.5.4 Short Scale FadingThe Short Scale Fading matrix is calculated based on the mobile’s position
with respect to the base station and the environment. This means that duringthe observation of the channel, the mobile changes its position within a spacedetermined by variation in the received power, which can be ignored in the cal-culation of the shadowing and the path-loss gain.
As shown in figure 5.10 the MS has a fixed path-loss and shadowing depend-ing on its position far R from the BS, but a different path-gain in respect totime given by localized movements of the user within a small space dR.
To take into account the small variation in positions of Short Scale Fading(SSF) that adds the third dimension to our path-gain matrix with respect tothe time must be considered.
To implement this aspect of the channel a vector of complex random vari-ables that follow the Rayleigh distribution and that have a fixed correlationbetween them is used.
52
Figure 5.10: Variation of the position of the MS responsible for the Rayleighfading
To create a set of correlated random variable a vector X must be consideredthat contains a number of uncorrelated complex random variables, in whichboth the real part and the imaginary part are normal distributed, equal to thenumber of samples that we want to consider.
X =
X1
X2
....XN
(5.5)
where
Xi = xQ,i + jxI,i (5.6)
and
xQ,i, xI,i ∼ N (0,12) (5.7)
Moreover the number of samples is given by the time that we observe thechannel divided by the time between each sample that can guarantee the corre-lation between two measurements:
N =Ttot
Tcorr(5.8)
To have a vector of complex random variables normally distributed with acertain correlation normalized to the power of one, the vector of uncorrelatedsamples X must be multiplied by the square root of a correlation matrix R:
Y = R1/2 ∗X (5.9)
53
In our case, the correlation matrix is given by a symmetric matrix given byBessel function as follows:
J =
1 J0
(2π v∗T
λ
)J0
(2π v∗2T
λ
)... J0
(2π v∗(N−1)T
λ
)J0
(2π v∗T
λ
)1 J0
(2π v∗T
λ
)... J0
(2π v∗(N−2)T
λ
)...
J0
(2π v∗(N−1)T
λ
)J0
(2π v∗(N−2)T
λ
)J0
(2π v∗(N−3)T
λ
)... 1
(5.10)
From that multiplication in 5.11, we have the desired randomly correlatedvariables and their envelope is Rayleigh distributed normalized to 1.
To obtain the correct samples of the path-gain for the context, this vector ismultiplied by the square-root of the power G, transformed in linear scale, givenby the matrix of path-gain obtained, considering only shadowing and path-loss.
Z =√
GY (5.11)
Repeating this process for every mobile station and base station, we havethe desired 3-dimensional matrix that contain the values of the path-gain foreach user, for each base station and for each time sample.
Figure 5.11 shows the total path gain, given by path-loss, shadowing andSSF, depending on the time for a MS linked to its BS. Figure 5.12 shows thedistance between the MS and its BS within the cell.
Figure 5.11: Variation of total path-gain of a MS linked to its BS
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Figure 5.12: Distance between the MS and its BS
5.5.5 CIRBased on the values of path-gain, it is easy to calculate the link between each
mobile and the base station to connect. This link is created with the base stationthat has the higher value of path-gain. This is possible to be implemented inRUNE using assign
[b,k,obk] = assign (b,k,g,obk,handover_margin));
As INPUT parameters, we have:
• b: a vector that is initialized to all zeros;
• k: a vector that is initialized to all zeros;
• g: the path-gain matrix;
• obk: a binary matrix that shows the occupied and the available channels;
• handover_margin: the standard deviation of the noise added to the gainmatrix.
In this case one may consider the path-gain matrix g given only by the shad-owing and the path-loss because the strongest component of the total gain isgiven by these two factors, so it’s enough to decide the base station to whichthe mobile must be linked.
The OUTPUT parameters are:
• b: a vector that contains, for each mobile, the number of the base stationthat is linked to;
• k: a vector that contains, for each mobile, the number of the channel thatthe mobile uses to communicate;
• obk: as told before, it’s a binary matrix that shows the busy and theavailable channels.
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After this assignment it becomes easy to calculate the CIR ratio for eachmobile, if it is supposed that every base station use the same channel (so thatwe will always have interference between two base stations), using the followingequation:
CIRMSi=
PBSj ∗ gBSj→MSi∑nk=1 PBSk
∗ gBSk→MSi− PBSj
∗ gBSj→MSi
(5.12)
in which we suppose that the i-th mobile is linked to the j-th base station andcapture the interference from the other base stations.
With this formula we can calculate this CIR for each mobile and for eachtime sample so that, at the end of our simulation, we will have another matrixthat contains the CIR referred to every mobile in every possiple time.
5.6 Traffic generatorThe traffic generator is used to create the amount of data needed for the
simulation. It is based on previously analyzed distributions associated withdifferent parameters of the traffic. The number of pages, length of waiting time,amount of data, etc. are calculated using standard distributions which can giverealistic results for the simulation. To recreate the realistic conditions, twodifferent types of data are analyzed: burst data and continuous data.
• WWW Model consists of requests for a certain number of pages in acertain moment. The number of requested pages follows a geometric dis-tribution. Each page is composed of a certain number of objects, each withits own size. All of the previous parameters have specific distributions witha certain mean and a certain variance. Another important characteristicis the time delay parameter between two different pages, which gives as aresult the total time for the entire session. A small number of objects perpage and a small size per object were chosen because clients with a GPRSconnection (mobile or PDA) do not have very high speed connections.
In the following diagrams, plots of a random scenario show the differentparameters that characterize the buffer of the traffic generation. Thescenario is simulated with four users. The number of pages generatedfrom the geometric distribution are shown in the following figure:
Then, the number of object generated for each page is following ageometric distribution and, the size of each of those objects follows aLog2-Erlang-k distribution. The plots of the objects characteristic are asfollows:
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Figure 5.13: Number of pages per single user
Figure 5.14: Number of object per single page
Moreover, the waiting time between one page and another has beenconsidered in the simulation. When the user is connected to the Inter-net, the request for downloading a page comes with some delay from theprevious one. This is due to the time required to read the page, checkinformation, or find the correct link to click. This waiting time, in statis-tical terms, follows a negative exponential distribution. The result of thiscomplete analysis of the traffic is the following plot 5.16. It is possible toobserve that the user 3, which is the user with largest number of pages, isthe last one to finish his WWW session.
57
Figure 5.15: Size of the object included in the pages
Figure 5.16: WWW traffic
• E-mail model is simulating the download of the e-mail data from a cer-tain server in the web. This traffic is applicable to a continuous amount ofdata downloadable from the network. The only parameter is the amountof data per e-mail. A mean value for the e-mail size is chosen with thepresupposition that no large attachments will be downloaded on the mo-bile devices. The distribution for the e-mail size is log2-normal and it hasdifferent mean values because of two different type of e-mail analyzed. Amean value of 1.7 kByte is chosen for a large number of e-mails. A smallnumber of e-mail are simulated using mean value of 16 kByte. This is dueto the simulation of larger attachments in the e-mail traffic.
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The figure 5.17 shows the behavior of the channel during a session of 1000e-mails.
Figure 5.17: e-mail traffic
The last table 5.2 is a resume of all the different distribution used for eachone of the relevant parameters into the traffic generator model [24].
WWW Traffic Distribution Mean VariancePages geometric 20 380
Interval between pages[s] neg.exponential 12 144Object per page geometric 2.5 3.75Object size[byte] log2-Erlang-k (k=17) 3700 4.67*109
e-mail Traffic Distribution Mean Variancee-mail size (80%) [byte] log2 normal 1700 5.5*106
e-mail size (60%) [byte] log2 normal 16000 71.3*109
Base quota [byte] constant 300 0
Table 5.2: First step of the simulation
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5.7 SchedulingScheduling is necessary if there is not enough capacity for all requests. It is
useful in guaranteeing that no request is lost.
The main purpose of the file “Scheduler.m” is to simulate different types ofscheduling techniques. So it is possible to measure the impact of the used tech-nique on the throughput.
During the initiation the occurring traffic and amount of users are given bythe author of the source code as a test phase. In the further implementationthe variables will be given by preceding subprograms of the simulation itself.
5.7.1 Intercell schedulingIn order to reduce the interference it is possible to coordinate the transmis-
sion among BSs. It involves the coordination of the activity phases of interferingBSs to increase the capacity gains.
An easy technique is to form two groups of BSs: one with the odd BSs andthe other with the even BSs. Then the times slots are divided in two parts, eachdedicated to a group of BSs. The figure 5.18 represents the cells used duringthe simulations and the two groups of BSs. More advanced techniques can befound in [25].
Figure 5.18: Intercell scheduling
5.7.2 Intracell SchedulingC/I scheduling
This technique first serves the user with the prime conditions. In this designthe rating is determined according to the coding scheme. A higher C/I equalsa higher ranking.
60
All the other requests are stored and handled as resources become availableagain. This means that the second highest rate is served immediately after thehighest rated buffer is empty, within the same channel.
“find2max.m”
This is a subprogram which searches for the actual highest and secondhighest active rating in the buffer and returns the indexes of the correspondingusers.
Result
As result of the C/I scheduling the figure 5.19 shows the state of the dif-ferent buffer of each user. It is also pictured that only the highest rate (codingscheme) is served and the other requests are delayed in the meanwhile.
Figure 5.19: result of the C/I scheduling
The rising edge marks the appearing traffic (here as amount of needed times-lots). The falling edge shows the current status of the buffer and therefore thetime needed to transfer all remaining packets.
FIFO scheduling
During this scheduling technique no user has priority. The only importantvariable is the point in time in which the traffic occurs. The first user is servedand all other user have to wait until the buffer of the first served user is empty.
All the other requests are stored and handled as resources become availableagain. This means that the next occurred traffic is served immediately after theprevious buffer is empty, within the same channel.
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“findFIFOorder.m”
This subprogram searches for the chronological occurrence of the differentuser, remembers the ranking and returns the first two users with active buffer.
Result
The figure 5.20 shows the current progress of the FIFO scheduling. As canbe seen the priority is given by the point in time the traffic occurs; the conditionof the users does not matter.
Figure 5.20: result of the FIFO scheduling
The rising edge marks the appearing traffic (here as amount of needed times-lots). The falling edge shows the current status of the buffer and therefore thetime needed to transfer all remaining packets.
“Proportional fair” scheduling
For this scheduling technique a more complex way to find the highest rateis used. The ratio between the C/I and the throughput of a user in a certainwindow is calculated for every user and used for the rating. A user who trans-mits for a shorter time get a higher chance to be served, more independent ofits C/I than the “C/I scheduling” in chapter 5.7.2.
All the other requests are stored and handled as resources become availableagain. This means that the second highest rate is served immediately after thehighest rated buffer is empty, within the same channel.
“findFAIRmax.m”
This is a subprogram that searches for the actual highest and second highestactive rating in the buffer and returns the indexes of the corresponding users.
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Result
As a result of the “proportional fair” scheduling, the figure 5.21 shows thestate of the different buffer of each user. It is also pictured that only the highestrate is served and the other requests are meanwhile delayed.
Figure 5.21: result of the “proportional fair” scheduling
The rising edge marks the appearing traffic (here as amount of needed times-lots). The falling edge shows the current status of the buffer and therefore thetime needed to transfer all remaining packets.
5.8 Power ControlPower Control is implemented in the total simulation to reduce the impact
of interference, giving more power to the BSs that have a bad path-gain, andconsequently a low CIR, with the linked MS and reducing the power to BSsthat boast good channel conditions in respect to the MS that is receiving data.
5.8.1 Basic AlgorithmThis algorithm is basic, and is based on the calculation of the power that
each MS should receive in accordance with the measure of its CIR, which isdependent on the channel conditions at the actual time.
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In particular, this power is decreased by a fixed amount δ if the measuredCIR is over a certain threshold γ and is increased by the same amount otherwise.
P (k + 1) ={
P (k)− δ if CIR ≥ γP (k) + δ if CIR < γ
(5.13)
5.8.2 Assignment of the power to BSsAfter the calculation of the power for each mobile present in our system, we
need to assign the power to the relative BS if a certain mobile is receiving data,and a null power otherwise. This way it is possible to calculate the new CIRduring the following step, as it is based on the transmitted power of all BSs.
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Chapter 6
Simulation & Results
In order to be able to see the effect of scheduling and power control on theinterference it is necessary to simulate various scenarios and compare them.
The first step of this simulation is to compare a scenario without any powercontrol or a particular scheduling technique, and compare it to a scenario us-ing power control. The scheduling technique used for all the simulations is theFIFO. Moreover, different scheduling algorithms will be evaluated to check thedifferent results they produce. As shown as in figure 6.1, it is possible to ’switch’between the various techniques to see their different influences and interactions.
The analysis of the different scenarios will be parametrized by the systemload. The different behavior of this parameter will give an idea of how muchthe system is busy in terms of carried data versus data. We can also comparethe various techniques in term of efficiency by visualizing the CIR over the users.
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The following diagram shows the simulation approach.
Figure 6.1: Diagram of the simulation techniques
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6.1 DescriptionThe simulation is built as a model of the real GPRS-system with some par-
ticular features. To get a statistically significant result, the simulation is basedon four different shadowing maps. Each of those maps has been used as a inde-pendent scenario to perform all the simulations. Moreover, for each shadowingmap a set of users position is calculated and, related to it, the set of correlationvalues of SSF is determined using the Bessel function.
For all the repetitions, with changing traffic, it was possible to use the samecorrelation values because always the same movement for all the users has beenused. Each user has a different starting position but has the same movementand velocity for every repetition. The position changes according to the mobil-ity model every 5 seconds.
All the different algorithms are simulated 10 times in order to have a statis-tical result. Afterwords, the mean value of all repetition is giving the averagebehavior of the entire system and different algorithm can be compared.
Therefore, the exspected results of the impact of the techniques are describedin advance.
6.1.1 Simulation expectationsOne of the main purposes of this project is to show how different tech-
niques and different combinations of these techniques influence or improve theperformance.
Comparison of the scheduling techniques
With different scheduling techniques the decision of the selected user, whoreceives data from the linked BS, changes.
Because of different positions of all the users, each of them has a differentdistance to it’s linked BS. This produces a different CIR and, based on the CIR,different Coding Schemes are chosen. This results in different throughput forall the users and, as a consequence, a different throughput for the entire system.
• C/I schedulingThis technique should achieve the best result because the user with thebest C/I, and therefore the highest data rate, is always served. So it isguaranteed that no resources lie idle.
• FIFO schedulingFor the rating in this technique only the time of arrival of the traffic isimportant. So the served user is independent of the C/I and the resultis not based on the C/I; for this reason the best throughput cannot beensured.
• Proportional fair schedulingWithin the proportional fair algorithm the C/I and the theoretical through-put of every user are taken into account. The theoretical throughput is
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calculated based on the Coding Scheme assigned to the user, indepen-dently of whether the user is transmitting or not. The unique throughputfor every user is also affected by the time since the traffic occurs. Forthat reason the user with the best conditions is not always the user whichreceives data. Thus is appears that this technique, though not the besttechnique in terms of throughput, is likely better than FIFO.
Influence of intercell-scheduling
In the realization of IS used in this simulation the BS are split into twogroups and the TSs of every channel are halved from eight into four TSs. Thebasic idea is to reach a higher C/I by avoiding the biggest interference from BSthat are close to each other.
IS will only show a positive effect if the improvement of the C/I and therespective throughput is bigger than the amount of data that is lost for thetransmission because of the reduced amount of TSs.
Influence of power control
With PC the transmitting powers of the BSs are affected. The aim ofthis technique, as in IS, is to reduce the intercell interference. But in this casea reduction in transmitting power instead of time division is deployed. Withspecific algorithms a predefined threshold of C/I can be achieved.
With this threshold the maximum C/I is also reduced. Because of this, themaximum possible throughput is equated for all BSs. Whether this techniqueenhances the overall throughput depends on how the remaining throughput canbe increased.
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6.2 CIRThe CIR shows the different behavior of the channel for every user’s connec-
tion. As one of the parameter of the project work, the CIR is calculated as meanvalue over the simulation time for every single user. Then, this mean value, isused to calculate the mean over all the user for all the repetitions. Checking thebehavior for different numbers of users it is possible to appreciate the changingof the CIR due to the different algorithms used and to the different number ofusers as shown as in figure 6.2.
Figure 6.2: Comparison of the CIR level for different simulations
In this figure we can see that the various techniques developed in this re-port permit to achieve a better CIR level. Comparing the case without anyPower Control with case with the Power Control, it is possible to appreciatehow much the PC can improve the CIR condition. This is possible due to thetheory predicted in chapter 3.2 where the PC algorithm is going to change thevalue of power for all the BS which are transmitting on the same channel atthe same timeslot. It is also possible to appreciate the different improvementsmade by Power Control and Intercell Scheduling. When the Intercell Schedul-ing is active, a better CIR is reached according on the aim of this algorithm.Due to the fewer timeslots available for each user, there is a smaller number ofusers transmitting at the same time and this is reducing the interference. Thisimprovement is smaller than the one obtained from the Power Control and thisis an important point for the improvement of the entire system.
However, the best results showed in the figure are related to the "PowerControl without Intercell Scheduling" algorithm, but in the real condition thiscould be a wrong result. The number of users considered during the entiresimulation is too small to appreciate the true behavior of the system. Because ofthis, the Intercell Scheduling is not having such importance for the interferenceoptimization because 25 users are a very small number in the studied area of 9cell.
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Furthermore, we can think that after a certain number of users, we will reacha physical limit in the BSs which will result at a constant level of CIR. We canalso think that as the number of users increase further, PC will not anymore beefficient and the CIR level will decrease.
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6.3 ThroughputThe throughput considered as a performance parameter, is used to establish
which is the most useful combination of algorithms in terms of sent data. Itis given by the carried traffic normalized to the capacity of the system as afunction of the load of the same system.
The most easy environment is given by a scenario in which there is neitherpower control nor inter-cell scheduling; with this kind of scenario we are ableto compare the three different scheduling algorithms to check which is the onethat performs better. The following figure 6.3 compares all the used schedulingtechnique within the system.
Figure 6.3: Throughput of scheduling algorithm
As said in 6.3, the system is not showing its entire features because of thetoo small number of users that are not able to raise the system load above 20%.This problem occurs also for the throughput representation. With a larger num-ber of users, the system load should increase and it would be possible to see howmuch traffic can be sent before reaching the saturation point. As the number ofuser is increasing, the number of users which are waiting is also increasing. Thismeans that after a certain point the load will keep growing while the throughputwill be constant.
Anyway, for the small amount of traffic we find a better performance for theFIFO algorithm. The second best algorithm is the CI technique. The differencebetween those two algorithms began to be bigger with increasing load. Thebehavior of the Proportional Fair Algorithm is different from our expectation
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because it appears clearly that it is not a function of the amount of load, so itremains always a constant value and this is not a proper behavior.
From figure 6.4 it is possible to compare the situation in which the inter-cellscheduling is applied with the case where the Power Control is applied.
Figure 6.4: Throughput of inter-cell scheduling with or without PC
In this figure we can not see a really different behavior between the twodifferent setting, so we can conclude that the Power Control algorithm does notinfluence the amount of carried traffic.
Another interesting comparison is between the system in which the sametime Power Control and inter-cell scheduling are implemented, with the onewith the same Power Control algorithm but without any inter-cell scheduling.Figure 6.5 shows a considerable difference between the two systems; it is easyto appreciate that the inter-cell scheduling decreases the throughput accordingto our expectation because of the different number of available time-slots.
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Figure 6.5: Throughput of inter-cell scheduling with or without PC
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Chapter 7
Conclusion
Based on the initial purpose of this project, we can say that the demandof high data rate is not a big problem for the GPRS/EDGE connection. Assaid in the beginning of the Report, the coming out of multimedia applicationssuch as television or Internet on mobile stations, requires an optimization of theconnection. Now we know that this could be reached by using additional tech-niques without having bad implications. Using algorithms in order to rise theCIR while having the same behavior of the throughput is a very good startingpoint for the optimization of the GPRS system.
The work done in this project has been based on two different algorithmsturned toward the interference optimization (PC and IS). After our simulationsit appears clear that the implementation of different algorithms has a consider-able effect on the performance of our system in terms of carried traffic and CIRlevel. One of the most important results is that a system in which there are noadded techniques, it is the most easy to create but is also the one that shows theworst performance. On the other hand, a system with an inter-cell scheduling(which is definitely not complex to obtain) can improve the CIR of the usershaving a very small payment in terms of throughput. Moreover, another obser-vation can be done about the Power Control algorithm: from our simulation itis possible to notice that the introduction of the PC do not have a big effect onthe throughput behavior, and at the same time it has a very high improvementof the CIR level; it means that its implementation, even if make the systemmore complex, gives better results in term of interference optimization.
Future Work
A future work based on this report can be to investigate deeper the effect ofbeamforming on interference in a multi-cell scenario. This will probably increasethe level of CIR as Power Control and inter-cell scheduling are doing. Moreover,Smart inter-cell scheduling can also be integrated in a multi-cell scenario con-taining more BSs to increase the CIR. Indeed in our scenario, containing 9 BSs,a smart inter-cell scheduling will not be worth in comparison with the increaseof the complexity of this system. Moreover, additional techniques in term ofpower control and scheduling can be implement and analyzed.
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List of Figures
2.1 GPRS architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 GPRS Layers organization . . . . . . . . . . . . . . . . . . . . . . 92.3 GPRS time slot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4 GMSK modulation [2] . . . . . . . . . . . . . . . . . . . . . . . . 112.5 8-PSK modulation . . . . . . . . . . . . . . . . . . . . . . . . . . 132.6 Modulation Coding scheme in EGPRS . . . . . . . . . . . . . . . 152.7 Possible interference in multi-cell scenario . . . . . . . . . . . . . 162.8 Multi-cell scenario & division of a cell for the integer . . . . . . . 16
3.1 Ideal Power Control: (a) constant transmission power; in that case the re-ceived power increases when MS approaches the BTS; (b) the transmissionpower is reduced when the MT approaches the BTS; in this way the receivedpower is constant an equal to PRIF , minimizing the interference [5]. . . . . 20
4.1 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.2 Received signal strength by MS [2]. . . . . . . . . . . . . . . . . . . . . 324.3 Throughput vs CIR ratio . . . . . . . . . . . . . . . . . . . . . . 394.4 Approximation of throughput vs CIR ratio . . . . . . . . . . . . 40
5.1 Diagram of the simulation . . . . . . . . . . . . . . . . . . . . . . 425.2 Creation of the clusters . . . . . . . . . . . . . . . . . . . . . . . 445.3 Illustration of wrap around . . . . . . . . . . . . . . . . . . . . . 455.4 Mobility model for 100 MSs in a cluster containing 36 cells . . . 475.5 Zoom in a cell to show the mobility model . . . . . . . . . . . . . 485.6 Wrap effect on the mobility label . . . . . . . . . . . . . . . . . . 485.7 Shadowing map . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.8 Modelling correlated shadow fading using a gaussian white pro-
cess and a first order low filter . . . . . . . . . . . . . . . . . . . 515.9 Total path-gain between 3 MSs and all the BSs . . . . . . . . . . 525.10 Variation of the position of the MS responsible for the Rayleigh
fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.11 Variation of total path-gain of a MS linked to its BS . . . . . . . 545.12 Distance between the MS and its BS . . . . . . . . . . . . . . . . 555.13 Number of pages per single user . . . . . . . . . . . . . . . . . . . 575.14 Number of object per single page . . . . . . . . . . . . . . . . . . 575.15 Size of the object included in the pages . . . . . . . . . . . . . . 585.16 WWW traffic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.17 e-mail traffic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.18 Intercell scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . 60
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5.19 result of the C/I scheduling . . . . . . . . . . . . . . . . . . . . . 615.20 result of the FIFO scheduling . . . . . . . . . . . . . . . . . . . . 625.21 result of the “proportional fair” scheduling . . . . . . . . . . . . . 63
6.1 Diagram of the simulation techniques . . . . . . . . . . . . . . . . 666.2 Comparison of the CIR level for different simulations . . . . . . . 696.3 Throughput of scheduling algorithm . . . . . . . . . . . . . . . . 716.4 Throughput of inter-cell scheduling with or without PC . . . . . 726.5 Throughput of inter-cell scheduling with or without PC . . . . . 73
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List of Tables
2.1 Different classes in the GPRS connection . . . . . . . . . . . . . 102.2 List of different Coding Schemes . . . . . . . . . . . . . . . . . . 10
3.1 delay classes and requirements for different packet sizes (see [14]) 29
4.1 assumed values for P0 and y for Lee’s propagation model (see [15]) 344.2 Some typical values for the deviation σX [17] . . . . . . . . . . . 35
5.1 Values used during the simulations . . . . . . . . . . . . . . . . . 435.2 First step of the simulation . . . . . . . . . . . . . . . . . . . . . 59
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Appendix A
Glossar
8PSK 8-Phase Shifting Keying
AWGN Additive White Gaussian Noise
BER Bit Error Rate
BS Base Station
DOAs Directions-of-arrival
EDF Earliest deadline first
EGPRS Enhanced GPRS
FDD Frequency Division Duplex
FSK Frequency Shift Keying
GAM Generalized array manifold
GMSK Gaussian Minimum Shift Keying
GPRS General Packet Radio Service
GSM Global System for Mobile Communications
IB Inteference blocking
LCMV Linearly constrained minimum variance
M-PSK M-ary Phase Shifting Keying
MCMV Multiple constrained minimum variance
MMSE Minimum mean square error
PDP Packet Data Protocol
QoS Quality of Service
QoS Quality of service
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SB Signal-blocking
SIR Signal-to-Interference Ratio
SPS Static priority scheduling
SSF Short Scale Fading
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