subcarrier assignment for ofdm based wireless networks

Subcarrier Assignment for OFDMBased Wireless Networks Using

Multiple Base Stations

Jeroen Theeuwes, Frank H.P. Fitzek, Carl Wijting

Center for TeleInFrastruktur (CTiF), Aalborg UniversityNeils Jernes Vej 12, 9220 Aalborg Øst, Denmark

phone: +45 9635 8688; e-mail: [theeuwes|ff|carl]@kom.aau.dk

June 2004

Technical Report R-04-1007

ISBN 87-90834-49-6

ISSN 0908-1224

c© Aalborg University 2004

Abstract

The goal of this report is to show the advantage of using subcarrier assignment for differentbase stations present in a cell. First this advantage is shown using dynamic assignment dynamicreceiving (DADR) of subcarriers next the advantage is shown when using dynamic assignmentstatic receiving (DASR) of subcarriers. Both the schedules are compared to the static assignmentstatic receiving (SASR) case. Next these policies are compared with the scenario where we choosean optimal common receiving level for all the subcarriers of a wireless terminal to reduce thesignalling. Finally the advantage of subcarrier scheduling is examined when data is broadcasted,thus the same packets are delivered to all wireless terminals in a cell.

Contents

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

1 Introduction 1

2 Optimizing Channel Quality Using Multiple Basestations 32.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Static Assignment Static Receiving . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Dynamic Assignment Static Receiving . . . . . . . . . . . . . . . . . . . . . . . . 62.4 Dynamic Assignment Dynamic Receiving . . . . . . . . . . . . . . . . . . . . . . 62.5 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 A Common Receiving Level for all Subcarriers of a Node 103.1 Static Assignment Static Receiving . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Dynamic Assignment Static Receiving . . . . . . . . . . . . . . . . . . . . . . . . 113.3 Dynamic Assignment Dynamic Receiving . . . . . . . . . . . . . . . . . . . . . . 12

4 Multicast Using Multiple Base Stations Serving Multiple Nodes 154.1 Binary Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2 M-ary Gaussian Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.3 Discussion of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5 Conclusion 20

Bibliography 21

A Determining the Remaining Number of Nodes to Choose from for the DADRScenario 22

c© Aalborg University 2004 Technical Report: R-04-1007 Page i

Chapter 1

Introduction

Tithin the last few years the demand for wireless communication systems has drastically in-creased. We not only see a much bigger demand for wireless connectivity, there is much moreinterest in broadband connections as well. New high–speed wireless networks must be developedto make these demands possible. The multi-path propagation of a wireless channel often intro-duces Inter Symbol Interference (ISI ). ISI is a limiting factor on the maximum throughput. Soit is desired to reduce or to totally remove this ISI. A possible way to do this is using multicar-rier systems. In particular Orthogonal Frequency Division Multiplexing (OFDM ) is a promisingmethod of such a multicarrier system. By using multicarrier techniques the frequency band issplit up into many small frequency bands, so called subcarriers. A signal with a much lowerbitrate is transmitted using one subcarrier. All the signals of the individual subcarriers add upto one signal with a high bitrate. Because symbol times of the individual signals become larger,ISI will not occur.

Because of the fact that multiple subcarriers are used it is possible to divide the data of onepacket over several paths. When more than one base station is available in a cell, it is possibleto let each base station send a part of the packet. This means that each base station sends onlya set of all the subcarriers a wireless terminal will receive. In Chapter 2 it is described howthis diversity can be exploited to optimize the connection quality. Here a way is described todivide the subcarriers over the different base stations when each wireless terminal receives its ownunique packets. In Chapter 3 two different assignment scenarios are examined, in the first onethe optimal connection of each single subcarrier is used, in the second one we choose one commonreceiving level for a total set of subcarriers of a wireless terminal. In chapter 4 the connectionquality is examined when the same packets have to be send to multiple wireless terminals, usingmultiple basestations. Finally in chapter 5 conclusions are drawn from this report.

We address the following three different schemes for assigning the subcarriers:

Static assignment static receiving A fixed subset of subcarriers is assigned to each wirelessstation and base stations. This assignment is not modified during transmission. No inter-action between the base stations is required. So in this case there is a fixed communicationchannel between the base stations and the WTs.

Dynamic assignment static receiving A fixed subset of subcarriers is assigned to each wire-less station. However now the base stations can communicate amongst each other anddetermine which base station should transmit using which subcarriers from the assignedsubset of subcarriers, based on the quality of each subcarrier.

c© Aalborg University 2004 Technical Report: R-04-1007 Page 1

Dynamic assignment dynamic receiving No predefined subset of subcarriers is assigned.Based on the quality of each subcarrier from each base station to each WT an optimal setof subcarriers is assigned to each WT and to each BS. So subcarriers are assigned both toWT and base stations in a dynamic way.

In all schemes the same number of subcarriers per WT are assigned.


Chapter 2

Optimizing Channel Quality UsingMultiple Basestations

In this report multiple base stations are used to obtain macro diversity. An optimal subset ofsubcarriers is determined and used for transmission towards the wireless station. The wirelessstation is unaware of the number of base stations involved, which simplifies the terminal design.

First consider the case where one base station is communicating with only one wireless station.Communication takes place using the channel available for base station one and the quality ofthe subcarriers may vary depending on the channel conditions. A performance increase can beobtained by using two base stations to communicate with the wireless station and selecting thethe optimal subset of available subcarriers based on the link quality. In order to do this a newnetwork entity to control the transmission of the base stations is introduced, the so called InterBase station Subcarrier Selection Unit (IBSSU), as shown in Figure 2.1. The IBSSU is used to co-ordinate the subcarrier assignment of two or more base stations communicating simultaneouslywith the same wireless station.

In Single Frequency Systems it has been proposed to transmit from several base stationssimultaneously while limiting the delay between the signal from these different base stations,allowing the various signals to be handled as multi path delay and so enhancing the performance[1]. In contrast to this, in this report the base stations transmit on mutually orthogonal setsof subcarriers, meaning that a subcarrier is only used by one base station, this helps in thegeographical reuse of frequencies and results in a more spectrum efficient solution.

Also advanced coding schemes on the different subcarriers can be used, see for example [2].Our scheme however does not require any complex decoding schemes at the terminal side. Theterminals can be relatively simple devices (low complexity terminals).

The IBSSU is used to coordinate the transmission of the different base stations to a wirelessterminal. The scheme is illustrated in Figure 2.1. Each base station sends on a set of subcarriersAi, which results from the allocation of the subcarriers. In the scheme the optimal subset ofthe available subcarriers is assigned for the communication between base stations and wirelessstations Aassigned ⊂ A1 ∪A2 ∪ · · · ∪AH . The assignment is done based on the subcarrier qualityand optimizes the system throughput. The subsets are chosen orthogonally to each other, and theterminal remains unaware of the exact number of base stations involved in the communication.This means that within the terminal no complex combining of different signals is required. Thewireless terminal however should correct / estimate the different phase offsets of the varioustransmitters, this is done in the channel estimation phase based on the pilot symbols in the


Figure 2.1: Exemplary configuration of three base stations communicating to a wireless terminal,co-ordinating the used subset of subcarriers using the IBSSU.

preamble. This means that the preamble and pilot symbols should be designed such that theterminal is able to resolve the different channels between base station and wireless terminal.Additionally they should be designed such that the IBSSU is able to select the appropriate setsof subcarriers.

The following schemes vary in complexity and flexibility in the optimization process.

2.1 System Model

Let us assume the following situation: we have a wireless network based on OFDM. The networkuses base stations to communicate with the Wireless Terminals (WTs). A cell is the totalcoverage area of the available base stations and there are H base stations in a cell, with H = 2.There are J different wireless terminals in the cell, with J = 1. OFDM uses different subcarriersfor the communication with the WTs. We assume there are a total of N different subcarriersavailable. The received signal strength from all base stations is assumed to be equal, whichcorresponds to the WT being located in the center of the cell or the application of a powercontrol scheme.

There are several ways to connect the WTs to the base stations, in other words to assignsubcarriers to the WTs. This can be done statically or dynamically. Each subcarrier reaches aWT in a different way than it was originally sent. It will arrive at the WT with a certain signalto noise ration (SNR). We can define a state for each subcarrier as it arrives at the receiver.This state corresponds with the SNR of a subcarrier at the WT. So, a subcarrier will have astate 0, when the subcarriers SNR is that low that there is no communication possible betweena base station and a WT. It will have a state 1 when the subcarrier arrives with a SNR thatallows the highest modulation and coding possible and so the best communication possible can


Table 2.1: Different modulation and coding schemes in comparison with the M-ary state model.

Modulation format Coding Rate, R Nominal Bitrate (MB/s) Actual State Used Statenone 0 0 0 0

BPSK 1/2 6 1/6 1/6BPSK 3/4 9 1/4 2/6QPSK 1/2 12 1/3 3/6QPSK 3/4 18 1/2 4/616QAM 9/16 27 3/4 5/616QAM 3/4 36 1 1

be established. When these two cases are the only cases we are considering a binary model.When there are intermediate states between 0 and 1 the used model is called a M-ary model(with M the number of different states).

We define the subcarrier vector weight, σ, as the sum of all the individual subcarrier statesat the receiver. Using this weight as a measure for the quality of a connection we assume a linearrelation between a state (corresponding to a ceratin SNR) and the possible throughput. In Table2.1 the relations between the modulation and coding and the states for IEE802.11a is shown.We can see that the relation between the states and the possible throughput is not completelylinear. We still use the linear model because in this way we can compare different assignmentschemes. We define the normalized subcarrier vector weight, wn, as the subcarrier vector weightdivided by the number of received subcarriers. So, when the state of subcarrier number n is Sn:

σ =N∑

n=1

Sn

and

w = σ/N (2.1)

In this chapter we use statistical models for the state of a subcarrier. A binary channel modelwill be used. In this model the state of a subcarrier is either 1 or 0. The probability that a sub-carrier has the state 1 at the receiver is called Pg. This scenario, for one in stead of multiple basestations is described in [3] for a binary channel model and in [4] for the M-ary channel model.This chapter compares the quality, in ways of subcarrier vector weights, and complexity of thedifferent scenarios.

2.2 Static Assignment Static Receiving

The first scenario is the simplest. A set of NJ subcarriers is assigned to each WT. This is done in

a predefined way and can not be changed afterwards, for example WT 1 gets subcarrier 1. . . NJ ,

WT 2 gets subcarrier NJ + 1 . . . 2N

J etc. Furthermore each base station gets a set of subcarriersassigned. This is done in a predefined way as well and it is not necessary to assign each basestation the same amount of subcarriers. No subcarriers are assigned twice and all subcarriers getassigned. In this case, called Static Assignment Static Receiving (SASR) the total subcarrier


weight of all the users together will be:

σSASR = N · Pg (2.2)

And the normalized subcarrier vector weight is simply Pg.

2.3 Dynamic Assignment Static Receiving

The second scenario assumes more flexibility in assigning subcarriers to base stations. Thesubcarriers of each WT are assigned in the same way as in the SASR case. But in this casethe base stations can communicate with each other about assigning subcarriers. Because basestations are usually wired inter-connected the extra signalling in this case is not an issue. Weassume that the base stations are able to determine a division of subcarriers in such a way thatthe best possible connections are established. In this case, called Dynamic Assignment StaticReceiving (DASR) we can say that the probability that a WT receives subcarrier n in a goodstate, is the same as the probability that at least one out of the H base stations can send thissubcarrier in a good state to this WT. So, the total subcarrier weight of all WT is:

σDASR = N ·[1− (1− Pg)H

]and

wDASR =[1− (1− Pg)H

](2.3)

2.4 Dynamic Assignment Dynamic Receiving

The third scenario assumes total flexibility in assigning subcarriers to base stations as wellas assigning subcarriers to WTs. Each WT still gets N/J subcarriers assigned, but it is notpredetermined which set of subcarriers is assigned to a WT. In this way an optimal set ofsubcarriers can be allocated to each WT. Further, just as in the DASR case, the base stations cancommunicate with each other about the assignment of subcarriers to the different base stations.In this case, called Dynamic Assignment Dynamic Receiving (DADR) it is more complex todetermine the subcarrier vector weight. First the probability that at least one out of the H basestations can send a given subcarrier to a WT in a good state is determined. This probability isalready shown in the DASR case and is:

Pgh =[1− (1− Pg)H

](2.4)

Now we have transformed the H base stations into one base station with a higher Pg. So,to determine w we have to determine the subcarrier vector weight in the scenario of one basestation and multiple WTs. This case is discussed in [3] and has the following approach. The basestations choose N/J subcarriers towards the first WT out of the total N subcarriers. Accordingto this, for the second WT the base stations will then have to choose N/J subcarriers out ofthe N −N/J remaining subcarriers. This process continues until the last terminal, where there


are no subcarriers to choose from. For this terminal there are exactly N/J subcarriers left.To determine the expected subcarrier vector weight we have to determine the subcarrier vectorweight for each node. The expected subcarrier vector weight for each WT consists of two parts,wp and wh. For wp only good subcarriers are assigned to this WT, and for wh bad subcarriersare assigned to this WT as well. If v is the WT number:

wp =

1−N/J−1∑

i=1

((J−v+1)N/J

i

)(pgh)i · (1− pgh)(J−v+1)N/J−i

·N/J

wh =N/J−1∑

i=1

((J−v+1)N/J

i

)(pgh)i · (1− pgh)(J−v+1)N/J−i · i (2.5)

The total subcarrier vector weight will be the sum of all these vector weights:

σDADR =J∑

v=1

wp,v + wh,v

and

wDADR =σDADR

N(2.6)

2.5 Discussion of Results

In the following figures we can see the results for the different scenarios for different Pg’s. TheDADR scenario is shown for different number of WTs. This is done to show the different behaviorof this scheme for different numbers of WTs. The other schemes do not behave differently fordifferent numbers of users, because predefined sets of subcarriers are assigned to them, that cannot be changed later on, so only one line is shown for these scenarios. In the DADR case it ispossible to divide the subcarriers in any possible way over the different WTs. When there aremore WTs available it is more likely to find WT that can get good subcarriers assigned thanwhen there are less WT available, so in this case σ depends on the number of WTs. Althoughthe DADR case delivers (of course) the best results it should be pointed out that this case isquite complex. This complexity might reduce the possible throughput. In Figure 2.5 we cansee that for three base stations or more the DASR and the DADR scheme deliver the sameconnection quality. These results all asume a binary channel model. In the next chapter thesame investigations are done for a M-ary channel model as well.


Figure 2.2: The normalized weight of all WTs, Pg = 0.1, and for different scenarios



Chapter 3

A Common Receiving Level for allSubcarriers of a Node

In the previous sections the advantage of assigning certain sets of subcarriers to base stationsand WTs is shown. In this way a node receives an optimal set of subcarriers, which means thatfor each individual subcarrier the best possible modulation and coding is used. This approachrequires the signalling of the modulation and coding type of each subcarrier to a node. Thismeans quite a lot of signalling. A possible way to decrease this signalling is to use one modulationand coding type for all subcarriers of a node. The disadvantage of this approach is that thereare subcarriers which could use a better modulation and coding than the one used. Anotherdisadvantage is that there are subcarriers which can not communicate at the chosen modulationand coding type and they are not used at all for communication. So this solution is a sub-optimalsolution. The big advantage is that only one modulation type has to be signalled to each node.The optimal receiving level that state corresponding to the modulation and coding resulting inthe highest subcarrier vector weight.

To determine the quality of this approach the binary channel model can not be used, becausethe optimal receiving level would always be the state S = 1. Since the subcarriers that are in agood state are the only ones who contribute to the subcarrier vector weight. So to determine theconnection quality we use a M-ary channel model. The possible qualities of a subcarrier are nowdefined as M different discrete states. Each state has a weight i−1

M−1 , with i = 1 . . .M . Theprobability of a terminal having a subcarrier in a given state towards a node is determined usingthe Gaussian distribution. For each state the probability of occurring is determined using themean and the variance of the channel. The probability of a subcarrier being in state i or smalleris called P (S 5 i). A total number of J nodes, M states, N subcarriers and H base stations isassumed.

An example of this approach is shown in Figure 3.1, where N/J = 8 and M = 7. The weightwould have been 30/6 when the optimal modulation per subcarrier would have been used. Wecan see that increasing the receiving level first increases the subcarrier vector weight and atone point the weight will decrease when the receiving level is further increased. So an optimalreceiving level can be determined based on the states of the individual subcarriers of a node. InFigure 3.2 it the maximum throughput is shown for each receiving level, for different number ofbase stations for a M-ary channel model with an equal distribution.

In the next sections the normalized subcarrier vector weights are determined for a M-arychannel model. The σ is determined for each assignment scenario that is discussed earlier and for


Figure 3.1: An example of choosing one modulation type for all subcarriers of a node, with thetotal subcarrier vector weight of the node

both choosing an optimal receiving level for each subcarrier and for the case where one commonreceiving level is chosen for a total set of subcarriers of a node. It is always assumed that eachnode gets exactly N/J subcarriers assigned. The derived equations all assume a Gaussian channelmodel but they are also valid for a M-ary channel model with an equal distribution.

3.1 Static Assignment Static Receiving

In case of Static Assignment Static Receiving (SASR) the connection quality (expressed innormalized subcarrier vector weight) does not change with the number of base stations becauseit is predetermined which base station will send which subcarrier.

First the probability of a subcarrier being in state n is determined: P (S = n). Furthermorethe probability of a subcarrier being in state n or larger is determined: P (S = n).

In case we choose the best possible modulation and coding for each subcarrier the normalizedsubcarrier vector weight will be:

w =M∑i=1

P (S = i) · i− 1M − 1

(3.1)

In case we choose the modulation and coding resulting in the highest σ for the total set ofsubcarriers of a node the normalized σ will be:

w = maxi

[P (S = i) · i− 1

M − 1

](3.2)

3.2 Dynamic Assignment Static Receiving

When we use Dynamic Assignment Static Receiving (DASR) we are able to choose the optimalbase station for each subcarrier. First the probability that the best quality (out of all the base


stations) of a given subcarrier towards a node is in state n or smaller is determined.

P (Sbest bs 5 n) = P (S 5 n)H

From this we can simply determine P (Sbest bs = n) and P (Sbest bs = n).Next the normalized σ is determined in case we choose the best possible modulation and

coding for each subcarrier:

w =M∑i=1

P (Sbest bs = i) · i− 1M − 1

(3.3)


w = maxi

[P (Sbs best = i) · i− 1

M − 1

](3.4)

3.3 Dynamic Assignment Dynamic Receiving

When we use dynamic assignment dynamic receiving we are not only able to choose the bestbase station for each subcarrier but also the best node for each subcarrier. For each subcarrierto be assigned there are equal or less nodes to choose from than the previous subcarrier that wasassigned because each node can only get N/J subcarriers assigned. For each single subcarrier(sc) to be assigned the probability that there are a remaining nodes to choose from is determined:P (Jremaining

sc = a), with a = 1 . . . J and sc = 1 . . . N . How this is done is shown in appendix A.Next for each subcarrier to be assigned the probability that the optimal connection is in state

i or smaller is determined as follows:

P (Sopt,sc 5 i) =J∑

a=1

P (Jremainingsc = a) · [P (S 5 i)]a·H

From this probability we can simply determine P (Sopt,sc = i) and P (Sopt,sc = i).Next the normalized σ is determined as follows in case we choose the best possible modulation

and coding for each subcarrier:

w =1N

M∑i=1

N∑sc=1

P (Sopt,sc = i) · i− 1M − 1

(3.5)


w =1N

maxi

[N∑

sc=1

P (Sopt,sc = i) · i− 1M − 1

](3.6)

In Figure 3.3 to 3.5 we can see what the normalized σ will be for the different assignmentscenarios and for the two different receiving level scenarios. The vertical bars separate thedifferent optimal receiving levels in the DASR case and next to the bars the optimal receivinglevel is shown. It can be seen that the DASR with an optimal receiving level for each subcarrierperforms comparable to the case of DADR with one optimal receiving level for all subcarriers ofa node. Furthermore it can be seen that for 4 base stations or more the DASR with one optimalreceiving level for a total set of subcarriers outperforms the SASR with an optimal receiving levelfor each subcarrier.


Figure 3.2: The maximum relative throughput when choosing one receiving level for all subcar-riers, for a M-ary channel model with an equal distribution

Figure 3.3: The normalized subcarrier vector weight when using a common receiving level persubcarrier or per total set of subcarriers of one node, using a M-ary Gaussian channel model


Chapter 4

Multicast Using Multiple BaseStations Serving Multiple Nodes

In the previous chapters we have considered the case where several base stations send data tomultiple nodes. In that case each node got its own unique data and its own unique set ofsubcarriers. In this case, multicasting is assumed, where all the users get the same contentdelivered. We assume a cell existing of J nodes that all should get the same packages. There areH different basestations which can communicate mutually about the assignment of subcarriersto the basestations. Note that there is no question of assigning subcarriers to nodes, because allthe nodes receive the same (complete) set of subcarriers.

4.1 Binary Channel Model

To evaluate this scenario we first assume a binary channel model where the probability that asubcarrier is in a good state (perfect communication is possible) is Pg. The normalized subcarriervector weight of each node is the subcarrier vector weight as defined in 2.1. Now we definea new subcarrier vector weight, the normalized subcarrier vector weight per node, in case ofmulticasting, as follows:

wm =1J

J∑i=1

Wi (4.1)

This normalized subcarrier vector weight is the average subcarrier vector weight of all thenodes and therefore a measure of the quality of the connection in the case of multicasting. Whenthe number of nodes increases, the quality of the connection will decrease because the probabilitythat there is a basestation that has a subcarrier in a good state towards all nodes decreases asthe number of nodes increases. When the number of basestation increases the quality of theconnection will increase because the probability that there is a basestation that has a givensubcarrier in a good state towards all nodes increases.

To achieve the optimal channel quality each subcarrier is assigned to the basestation thatcan reach the most nodes in a good state for this subcarrier. A (simple) example of this can beseen in Figure 4.1, where J = 9, H = 5 and the subcarrier vector weight for this subcarrier pernode will be wm = 7/9.


Figure 4.1: Assignment of a subcarrier to a basestation in the multicasting scenario

To determine Wm a few steps has to be taken. First the probability of a basestation havinga given subcarrier in a good state towards n out of the J nodes is determined.

P (#G = n) =(

J

n

)(1− Pg)J−n · P n

g (4.2)

Next the probability that a basestation has a given subcarrier in a good state towards n orless nodes is determined: P (#G 5 n). This probability can be used to determine the probabilitythat the best connection of all base stations for a given subcarrier can reach N or less nodes ina good state:

P (#G 5 n)H = P (#G 5 n)H (4.3)

From these probabilities the probability that the basestation with the best connection for agiven subcarrier can reach exactly n nodes with this subcarrier in a good state can be determined:P (#G = N). Using these probabilities wm can be determined:

wm =1J

J∑N=0

N · P (#G = n) (4.4)

The results of this kind subcarrier assignment can be seen in the Figures 4.2 until 4.5.

4.2 M-ary Gaussian Channel Model

To get a more realistic impression of the impact of subcarrier assignments in case of multicastingthe M-ary Gaussian channel model is used to determine the σ. Each base station can reacheach node with a given subcarrier in a given state. But only one modulation and coding schemecan be used for each subcarrier. So when one node can be reached in the best state and theothers not it is probably not the best solution to use the highest modulation and coding. Anoptimal modulation and coding must be determined based on the different states a subcarrierarrives from a base station to the different nodes. We call the number of nodes a basestation canreach for a given state R. We call the probability that the base station with the best connectiontowards the total set of nodes for a given subcarrier can reach exactly n nodes in a state i or


higher P (S = i;R = n). If we choose to use the modulation and coding type according to statei the expected subcarrier vector weight for this subcarrier will be:

wm,i =J∑

n=1

P (S = i;R = n) · n · i− 1M − 1

(4.5)

So the optimal σ will be the one using that modulation and coding resulting in the highest σ:

wm = maxi

J∑n=1

P (S = i;R = n) · n · i− 1M − 1

(4.6)

To determine P (S = i;R = n) we use the Gaussian probability distribution of the different statesfor a subcarrier from each base station to each node. First we determine the probability that abase station can reach exactly n out of the J WTs in a state i or higher as follows:

P 1(S = i;R = n) =(

J

i

)P (S = i)nP (S < i)J−n+1 (4.7)

Next the probability that there is at least one out of the H base stations that can reach n ormore out of the J nodes in a state i or higher.

PH(S = i;R = n) = 1− (1− P 1(= i;R = n))H (4.8)

From this probability PH(S = i;R = n) = P (S = i;R = n) can be easily determined.

4.3 Discussion of results

As can be seen in the figures, for a large number of nodes the normalized subcarrier vector weightper node gets close to Pg, this is because in this case the probability that a basestation has agiven subcarrier in a good state towards many nodes gets really small. It can be seen that theweight for small number of nodes depends strongly on the number of basestations. Further moreit can be seen that if there are many nodes in one cell, increasing the number of basestationshardly increases the weight. It can also be seen that when Pg is small (bad channel quality) theperformance decreases more rapidly when the number of nodes is increased then when Pg is closeto 1.

We can see that for a large number of nodes that need to receive the same packets theadvantage of the multiple basestations vanishes totally.


Figure 4.2: The normalized weight per node in the case of multicasting with multiple basestations,Pg = 0.1



Chapter 5

Conclusion

As has been shown the connection quality can be drastically increased using subcarrier schedul-ing for multiple basestations and multiple wireless terminals (escpecially the DADR case). Thecost for this increase is an increase in the signalling. When a suboptimal solution is chosen(DASR) the difference in the increase in the connection quality is only small for a large numberof base stations. This advantage vanishes totally when multicasting is used. The approach witha common receiving level for all subcarriers of a wireless terminal is also a sub-optimal solutionbut has the big advantage that the signalling doesn’t increase with the number of subcarriers perterminal. The results in this report do not include the signalling, so all of the performances willbe degraded more or less. Especially the DADR scenario will suffer from huge signalling losses.

To extend the research of this topic a channel model could be used that assumes correlationbetween the different subcarriers, to get a more realistic impression of the impact of this kindof subcarrier scheduling. Further more it could be considered that the signal strengths from allbase stations arriving at the WT are not equal, so the WT is no longer in the (by the use ofpower control possibly virtually) center of all base stations.

A practical implementation of the different assignment policies can be developed. Rulesshould be made about the assignment of the subcarriers based on the information of the qualityof the subcarriers towards wireless terminals. An example of such an implementation is given in[3], for the scenario when only one base statio is used. These scheduling policies can be simulatedin OFDM simulators.


Bibliography

[1] T. T. Kokubo, S. Yamasaki, and M. Nakagawa, “Transmission delay control for single fre-quency ofdm multi-base-station in a cell using position information,” IEEE VTS-Fall VTC2000, pp. 524 – 529, September 24-28 2000. 3

[2] M. Inoue and M. Nakagawa, “Space time transmit site diversity for ofdm multi base sta-tion system,” 4th International Workshop on Mobile and Wireless Communications Network,2002, pp. 30 – 34, September 9-11 2002. 3

[3] J. Gross and F. Fitzek, “Channel state dependent scheduling policies for an ofdm physicallayer using a binary state model,” Technical University Berlin, Tech. Rep., 2001. 5, 6, 20

[4] J. Gross and Fitzek, “Channel state dependent scheduling policies for an ofdm physical layerusing a m-ary state model,” Technical University Berlin, Tech. Rep., 2001. 5


Appendix A

Determining the Remaining Numberof Nodes to Choose from for theDADR Scenario

In the DADR scenario we are allowed to assign each subcarrier to a certain node as long as thisnode is not already fully assigned, thus has got S/J subcarriers already assigned to him. So todetermine the σ we need to determine the remaining number of nodes that are not fully assignedwhen assigning a subcarrier.

For example for the assignment of the last subcarrier (N) there can only be one node leftto choose from and for the first subcarrier to be assigned there are always J nodes to choosefrom. But for the one but last subcarrier it is possible that there is only one node left to choosefrom but it is also possible that there are still 2 nodes left to choose from. For the assignment ofsubcarrier 1 to N we determine the number of possibilities that there are 1 to J nodes to choosefrom.

The subcarrier that is to be assigned is called sc, the number of subcarriers per node is calledS, so S = N/J . First the number of possibilities that there is only one node to choose from isdetermined:

U1sc =

(J

J − 1

) (N − (J − 1)S

sc− 1− (J − 1)S

)︸︷︷︸

R1

(A.1)

If the bottom part of the binomial coefficient is a negative integer the outcome of this binomialcoefficient is 0. A part of U1, R1, is used to determine the number of possibilities that there are2 nodes left to choose from:

U2sc =

(J

J − 2

) [(N − (J − 2)S

sc− 1− (J − 2)S

)−

(21

)R1

]︸︷︷︸

R2

(A.2)

The number of possibilities that there are 3 nodes left to choose from is:

U3sc =

(J

J − 3

) [(N − (J − 3)S

sc− 1− (J − 3)S

)−

(31

)R1 −

(32

)R2

]︸︷︷︸

R3

(A.3)


Table A.1: Number of possibilities that there are a nodes to choose from when assigning subcar-rier number sc.

sc −→a ↓ 1 2 3 4 5 6 7 8 9 10 11 121 0 0 0 0 0 0 0 0 0 4 12 122 0 0 0 0 0 0 6 36 90 108 54 03 0 0 0 4 36 144 324 432 324 108 0 04 1 12 66 216 459 648 594 324 81 0 0 0

Total 1 12 66 220 495 792 924 792 495 220 66 12

This process continues until the case that there are J nodes to choose from. The probabilitythat there are a nodes to choose from for the assignment of subcarrier sc is determined using thetotal number of possibilities:

P (Jremainingsc = a) =

Uasc(

Nsc−1

) (A.4)

So this probability can be determined as follows:

P (Jremainingsc = a) =

U sca(

Nsc−1

) [(N − (J − a)S

sc− 1− (J − a)S

)−

a−1∑i=1

(a

i

)Ri

]︸︷︷︸

Ra

(A.5)

In table A the different possibilities are shown, the different probabilities can be determined bydividing the number of possibilities for this situation by the total number of different possibilities.


subcarrier assignment for ofdm based wireless networks

Documents