Subcarrier Assignment for OFDM Based Wireless Networks Using Multiple Base Stations

Transcription

1 Subcarrier Assignment for OFDM Based Wireless Networks Using Multiple Base Stations Jeroen Theeuwes, Frank H.P. Fitzek, Carl Wijting Center for TeleInFrastruktur (CTiF), Aalborg University Neils Jernes Vej 12, 9220 Aalborg Øst, Denmark phone: ; [theeuwes ff June 2004 Technical Report R ISBN ISSN c Aalborg University 2004

2 Abstract The goal of this report is to show the advantage of using subcarrier assignment for different base stations present in a cell. First this advantage is shown using dynamic assignment dynamic receiving (DADR) of subcarriers next the advantage is shown when using dynamic assignment static receiving (DASR) of subcarriers. Both the schedules are compared to the static assignment static receiving (SASR) case. Next these policies are compared with the scenario where we choose an optimal common receiving level for all the subcarriers of a wireless terminal to reduce the signalling. 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.

3 Contents Table of Contents i 1 Introduction 1 2 Optimizing Channel Quality Using Multiple Basestations System Model Static Assignment Static Receiving Dynamic Assignment Static Receiving Dynamic Assignment Dynamic Receiving Discussion of Results A Common Receiving Level for all Subcarriers of a Node Static Assignment Static Receiving Dynamic Assignment Static Receiving Dynamic Assignment Dynamic Receiving Multicast Using Multiple Base Stations Serving Multiple Nodes Binary Channel Model M-ary Gaussian Channel Model Discussion of results Conclusion 20 Bibliography 21 A Determining the Remaining Number of Nodes to Choose from for the DADR Scenario 22 c Aalborg University 2004 Technical Report: R Page i

4 Chapter 1 Introduction Tithin the last few years the demand for wireless communication systems has drastically increased. We not only see a much bigger demand for wireless connectivity, there is much more interest in broadband connections as well. New high speed wireless networks must be developed to make these demands possible. The multi-path propagation of a wireless channel often introduces Inter Symbol Interference (ISI ). ISI is a limiting factor on the maximum throughput. So it is desired to reduce or to totally remove this ISI. A possible way to do this is using multicarrier systems. In particular Orthogonal Frequency Division Multiplexing (OFDM ) is a promising method of such a multicarrier system. By using multicarrier techniques the frequency band is split up into many small frequency bands, so called subcarriers. A signal with a much lower bitrate is transmitted using one subcarrier. All the signals of the individual subcarriers add up to 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 one packet over several paths. When more than one base station is available in a cell, it is possible to let each base station send a part of the packet. This means that each base station sends only a set of all the subcarriers a wireless terminal will receive. In Chapter 2 it is described how this diversity can be exploited to optimize the connection quality. Here a way is described to divide the subcarriers over the different base stations when each wireless terminal receives its own unique packets. In Chapter 3 two different assignment scenarios are examined, in the first one the optimal connection of each single subcarrier is used, in the second one we choose one common receiving level for a total set of subcarriers of a wireless terminal. In chapter 4 the connection quality is examined when the same packets have to be send to multiple wireless terminals, using multiple 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 wireless station and base stations. This assignment is not modified during transmission. No interaction between the base stations is required. So in this case there is a fixed communication channel between the base stations and the WTs. Dynamic assignment static receiving A fixed subset of subcarriers is assigned to each wireless station. However now the base stations can communicate amongst each other and determine which base station should transmit using which subcarriers from the assigned subset of subcarriers, based on the quality of each subcarrier. c Aalborg University 2004 Technical Report: R Page 1

5 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 set of subcarriers is assigned to each WT and to each BS. So subcarriers are assigned both to WT and base stations in a dynamic way. In all schemes the same number of subcarriers per WT are assigned. c Aalborg University 2004 Technical Report: R Page 2

6 Chapter 2 Optimizing Channel Quality Using Multiple Basestations In this report multiple base stations are used to obtain macro diversity. An optimal subset of subcarriers is determined and used for transmission towards the wireless station. The wireless station 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 of the subcarriers may vary depending on the channel conditions. A performance increase can be obtained by using two base stations to communicate with the wireless station and selecting the the optimal subset of available subcarriers based on the link quality. In order to do this a new network entity to control the transmission of the base stations is introduced, the so called Inter Base station Subcarrier Selection Unit (IBSSU), as shown in Figure 2.1. The IBSSU is used to coordinate the subcarrier assignment of two or more base stations communicating simultaneously with the same wireless station. In Single Frequency Systems it has been proposed to transmit from several base stations simultaneously 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 sets of subcarriers, meaning that a subcarrier is only used by one base station, this helps in the geographical 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. The terminals can be relatively simple devices (low complexity terminals). The IBSSU is used to coordinate the transmission of the different base stations to a wireless terminal. The scheme is illustrated in Figure 2.1. Each base station sends on a set of subcarriers A i, which results from the allocation of the subcarriers. In the scheme the optimal subset of the available subcarriers is assigned for the communication between base stations and wireless stations A assigned A 1 A 2 A H. The assignment is done based on the subcarrier quality and optimizes the system throughput. The subsets are chosen orthogonally to each other, and the terminal 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. The wireless terminal however should correct / estimate the different phase offsets of the various transmitters, this is done in the channel estimation phase based on the pilot symbols in the c Aalborg University 2004 Technical Report: R Page 3

7 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 the terminal 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 sets of 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 network uses base stations to communicate with the Wireless Terminals (W T s). A cell is the total coverage 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 subcarriers for the communication with the WTs. We assume there are a total of N different subcarriers available. The received signal strength from all base stations is assumed to be equal, which corresponds to the WT being located in the center of the cell or the application of a power control scheme. There are several ways to connect the WTs to the base stations, in other words to assign subcarriers to the WTs. This can be done statically or dynamically. Each subcarrier reaches a WT in a different way than it was originally sent. It will arrive at the WT with a certain signal to 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 a state 0, when the subcarriers SNR is that low that there is no communication possible between a base station and a WT. It will have a state 1 when the subcarrier arrives with a SNR that allows the highest modulation and coding possible and so the best communication possible can c Aalborg University 2004 Technical Report: R Page 4

8 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 State none BPSK 1/2 6 1/6 1/6 BPSK 3/4 9 1/4 2/6 QPSK 1/2 12 1/3 3/6 QPSK 3/4 18 1/2 4/6 16QAM 9/ /4 5/6 16QAM 3/ 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 states at the receiver. Using this weight as a measure for the quality of a connection we assume a linear relation between a state (corresponding to a ceratin SNR) and the possible throughput. In Table 2.1 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 completely linear. We still use the linear model because in this way we can compare different assignment schemes. We define the normalized subcarrier vector weight, w n, as the subcarrier vector weight divided by the number of received subcarriers. So, when the state of subcarrier number n is S n : σ = N n=1 S n and w = σ/n (2.1) In this chapter we use statistical models for the state of a subcarrier. A binary channel model will be used. In this model the state of a subcarrier is either 1 or 0. The probability that a subcarrier has the state 1 at the receiver is called P g. This scenario, for one in stead of multiple base stations 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 the different scenarios. 2.2 Static Assignment Static Receiving The first scenario is the simplest. A set of N J 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... N J, WT 2 gets subcarrier N J N J etc. Furthermore each base station gets a set of subcarriers assigned. This is done in a predefined way as well and it is not necessary to assign each base station the same amount of subcarriers. No subcarriers are assigned twice and all subcarriers get assigned. In this case, called Static Assignment Static Receiving (SASR) the total subcarrier c Aalborg University 2004 Technical Report: R Page 5

9 weight of all the users together will be: And the normalized subcarrier vector weight is simply P g. σ SASR = N P g (2.2) 2.3 Dynamic Assignment Static Receiving The second scenario assumes more flexibility in assigning subcarriers to base stations. The subcarriers of each WT are assigned in the same way as in the SASR case. But in this case the base stations can communicate with each other about assigning subcarriers. Because base stations are usually wired inter-connected the extra signalling in this case is not an issue. We assume that the base stations are able to determine a division of subcarriers in such a way that the best possible connections are established. In this case, called Dynamic Assignment Static Receiving (DASR) we can say that the probability that a WT receives subcarrier n in a good state, is the same as the probability that at least one out of the H base stations can send this subcarrier in a good state to this WT. So, the total subcarrier weight of all WT is: σ DASR = N [1 (1 P g ) H] and w DASR = [ 1 (1 P g ) H] (2.3) 2.4 Dynamic Assignment Dynamic Receiving The third scenario assumes total flexibility in assigning subcarriers to base stations as well as assigning subcarriers to WTs. Each WT still gets N/J subcarriers assigned, but it is not predetermined which set of subcarriers is assigned to a WT. In this way an optimal set of subcarriers can be allocated to each WT. Further, just as in the DASR case, the base stations can communicate 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 to determine the subcarrier vector weight. First the probability that at least one out of the H base stations can send a given subcarrier to a WT in a good state is determined. This probability is already shown in the DASR case and is: P gh = [ 1 (1 P g ) H] (2.4) Now we have transformed the H base stations into one base station with a higher P g. So, to determine w we have to determine the subcarrier vector weight in the scenario of one base station and multiple WTs. This case is discussed in [3] and has the following approach. The base stations choose N/J subcarriers towards the first WT out of the total N subcarriers. According to this, for the second WT the base stations will then have to choose N/J subcarriers out of the N N/J remaining subcarriers. This process continues until the last terminal, where there c Aalborg University 2004 Technical Report: R Page 6

10 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 vector weight for each node. The expected subcarrier vector weight for each WT consists of two parts, w p and w h. For w p only good subcarriers are assigned to this WT, and for w h bad subcarriers are assigned to this WT as well. If v is the WT number: w p = 1 N/J 1 i=1 w h = ( ) (J v+1)n/j (p gh ) i (1 p gh ) (J v+1)n/j i N/J i N/J 1 i=1 ( (J v+1)n/j i ) (p gh ) i (1 p gh ) (J v+1)n/j i i (2.5) The total subcarrier vector weight will be the sum of all these vector weights: σ DADR = J w p,v + w h,v v=1 and w DADR = σ DADR N (2.6) 2.5 Discussion of Results In the following figures we can see the results for the different scenarios for different P g s. The DADR scenario is shown for different number of WTs. This is done to show the different behavior of this scheme for different numbers of WTs. The other schemes do not behave differently for different numbers of users, because predefined sets of subcarriers are assigned to them, that can not be changed later on, so only one line is shown for these scenarios. In the DADR case it is possible to divide the subcarriers in any possible way over the different WTs. When there are more WTs available it is more likely to find WT that can get good subcarriers assigned than when there are less WT available, so in this case σ depends on the number of WTs. Although the DADR case delivers (of course) the best results it should be pointed out that this case is quite complex. This complexity might reduce the possible throughput. In Figure 2.5 we can see that for three base stations or more the DASR and the DADR scheme deliver the same connection quality. These results all asume a binary channel model. In the next chapter the same investigations are done for a M-ary channel model as well. c Aalborg University 2004 Technical Report: R Page 7

11 Figure 2.2: The normalized weight of all WTs, P g = 0.1, and for different scenarios Figure 2.3: The normalized weight of all WTs, P g = 0.5, and for different scenarios c Aalborg University 2004 Technical Report: R Page 8

12 Figure 2.4: The normalized weight of all WTs, P g = 0.7, and for different scenarios Figure 2.5: The normalized weight of all WTs, P g = 0.9, and for different scenarios c Aalborg University 2004 Technical Report: R Page 9

13 Chapter 3 A Common Receiving Level for all Subcarriers of a Node In the previous sections the advantage of assigning certain sets of subcarriers to base stations and WTs is shown. In this way a node receives an optimal set of subcarriers, which means that for each individual subcarrier the best possible modulation and coding is used. This approach requires the signalling of the modulation and coding type of each subcarrier to a node. This means quite a lot of signalling. A possible way to decrease this signalling is to use one modulation and coding type for all subcarriers of a node. The disadvantage of this approach is that there are subcarriers which could use a better modulation and coding than the one used. Another disadvantage is that there are subcarriers which can not communicate at the chosen modulation and coding type and they are not used at all for communication. So this solution is a sub-optimal solution. 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 in the highest subcarrier vector weight. To determine the quality of this approach the binary channel model can not be used, because the optimal receiving level would always be the state S = 1. Since the subcarriers that are in a good state are the only ones who contribute to the subcarrier vector weight. So to determine the connection quality we use a M-ary channel model. The possible qualities of a subcarrier are now i 1 M 1 defined as M different discrete states. Each state has a weight, with i = 1... M. The probability of a terminal having a subcarrier in a given state towards a node is determined using the Gaussian distribution. For each state the probability of occurring is determined using the mean and the variance of the channel. The probability of a subcarrier being in state i or smaller is called P (S i). A total number of J nodes, M states, N subcarriers and H base stations is assumed. An example of this approach is shown in Figure 3.1, where N/J = 8 and M = 7. The weight would have been 30/6 when the optimal modulation per subcarrier would have been used. We can see that increasing the receiving level first increases the subcarrier vector weight and at one point the weight will decrease when the receiving level is further increased. So an optimal receiving level can be determined based on the states of the individual subcarriers of a node. In Figure 3.2 it the maximum throughput is shown for each receiving level, for different number of base 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-ary channel model. The σ is determined for each assignment scenario that is discussed earlier and for c Aalborg University 2004 Technical Report: R Page 10

14 Figure 3.1: An example of choosing one modulation type for all subcarriers of a node, with the total subcarrier vector weight of the node both choosing an optimal receiving level for each subcarrier and for the case where one common receiving level is chosen for a total set of subcarriers of a node. It is always assumed that each node gets exactly N/J subcarriers assigned. The derived equations all assume a Gaussian channel model 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 in normalized subcarrier vector weight) does not change with the number of base stations because it is predetermined which base station will send which subcarrier. First the probability of a subcarrier being in state n is determined: P (S = n). Furthermore the 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 normalized subcarrier vector weight will be: w = M i 1 P (S = i) M 1 i=1 In case we choose the modulation and coding resulting in the highest σ for the total set of subcarriers of a node the normalized σ will be: [ ] i 1 w = max P (S i) (3.2) i M Dynamic Assignment Static Receiving When we use Dynamic Assignment Static Receiving (DASR) we are able to choose the optimal base station for each subcarrier. First the probability that the best quality (out of all the base (3.1) c Aalborg University 2004 Technical Report: R Page 11

15 stations) of a given subcarrier towards a node is in state n or smaller is determined. P (S best bs n) = P (S n) H From this we can simply determine P (S best bs = n) and P (S best bs n). Next the normalized σ is determined in case we choose the best possible modulation and coding for each subcarrier: M i 1 w = P (S best bs = i) (3.3) M 1 i=1 In case we choose the modulation and coding resulting in the highest σ for the total set of subcarriers of a node the normalized σ will be: [ ] i 1 w = max P (S bs best i) (3.4) i M Dynamic Assignment Dynamic Receiving When we use dynamic assignment dynamic receiving we are not only able to choose the best base station for each subcarrier but also the best node for each subcarrier. For each subcarrier to be assigned there are equal or less nodes to choose from than the previous subcarrier that was assigned 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 (Jsc remaining = 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 (S opt,sc i) = J a=1 P (J remaining sc = a) [P (S i)] a H From this probability we can simply determine P (S opt,sc = i) and P (S opt,sc i). Next the normalized σ is determined as follows in case we choose the best possible modulation and coding for each subcarrier: w = 1 N M i=1 sc=1 N P (S opt,sc = i) i 1 M 1 In case we choose the modulation and coding resulting in the highest σ for the total set of subcarriers of a node the normalized σ will be: [ w = 1 N ] N max i 1 P (S opt,sc i) (3.6) i M 1 sc=1 In Figure 3.3 to 3.5 we can see what the normalized σ will be for the different assignment scenarios and for the two different receiving level scenarios. The vertical bars separate the different optimal receiving levels in the DASR case and next to the bars the optimal receiving level is shown. It can be seen that the DASR with an optimal receiving level for each subcarrier performs comparable to the case of DADR with one optimal receiving level for all subcarriers of a node. Furthermore it can be seen that for 4 base stations or more the DASR with one optimal receiving level for a total set of subcarriers outperforms the SASR with an optimal receiving level for each subcarrier. c Aalborg University 2004 Technical Report: R Page 12 (3.5)

16 Figure 3.2: The maximum relative throughput when choosing one receiving level for all subcarriers, for a M-ary channel model with an equal distribution Figure 3.3: The normalized subcarrier vector weight when using a common receiving level per subcarrier or per total set of subcarriers of one node, using a M-ary Gaussian channel model c Aalborg University 2004 Technical Report: R Page 13

17 Figure 3.4: The normalized subcarrier vector weight when using a common receiving level per subcarrier or per total set of subcarriers of one node, using a M-ary Gaussian channel model Figure 3.5: The normalized subcarrier vector weight when using a common receiving level per subcarrier or per total set of subcarriers of one node, using a M-ary Gaussian channel model c Aalborg University 2004 Technical Report: R Page 14

18 Chapter 4 Multicast Using Multiple Base Stations Serving Multiple Nodes In the previous chapters we have considered the case where several base stations send data to multiple nodes. In that case each node got its own unique data and its own unique set of subcarriers. In this case, multicasting is assumed, where all the users get the same content delivered. We assume a cell existing of J nodes that all should get the same packages. There are H different basestations which can communicate mutually about the assignment of subcarriers to the basestations. Note that there is no question of assigning subcarriers to nodes, because all the 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 a subcarrier is in a good state (perfect communication is possible) is P g. The normalized subcarrier vector weight of each node is the subcarrier vector weight as defined in 2.1. Now we define a new subcarrier vector weight, the normalized subcarrier vector weight per node, in case of multicasting, as follows: w m = 1 J J W i (4.1) i=1 This normalized subcarrier vector weight is the average subcarrier vector weight of all the nodes and therefore a measure of the quality of the connection in the case of multicasting. When the number of nodes increases, the quality of the connection will decrease because the probability that there is a basestation that has a subcarrier in a good state towards all nodes decreases as the number of nodes increases. When the number of basestation increases the quality of the connection will increase because the probability that there is a basestation that has a given subcarrier in a good state towards all nodes increases. To achieve the optimal channel quality each subcarrier is assigned to the basestation that can reach the most nodes in a good state for this subcarrier. A (simple) example of this can be seen in Figure 4.1, where J = 9, H = 5 and the subcarrier vector weight for this subcarrier per node will be w m = 7/9. c Aalborg University 2004 Technical Report: R Page 15

19 Figure 4.1: Assignment of a subcarrier to a basestation in the multicasting scenario To determine W m a few steps has to be taken. First the probability of a basestation having a given subcarrier in a good state towards n out of the J nodes is determined. ( ) J P (#G = n) = (1 P g ) J n Pg n (4.2) n Next the probability that a basestation has a given subcarrier in a good state towards n or less nodes is determined: P (#G n). This probability can be used to determine the probability that the best connection of all base stations for a given subcarrier can reach N or less nodes in a good state: P (#G n) H = P (#G n) H (4.3) From these probabilities the probability that the basestation with the best connection for a given subcarrier can reach exactly n nodes with this subcarrier in a good state can be determined: P (#G = N). Using these probabilities w m can be determined: w m = 1 J J N P (#G = n) (4.4) N=0 The results of this kind subcarrier assignment can be seen in the Figures 4.2 until M-ary Gaussian Channel Model To get a more realistic impression of the impact of subcarrier assignments in case of multicasting the M-ary Gaussian channel model is used to determine the σ. Each base station can reach each node with a given subcarrier in a given state. But only one modulation and coding scheme can be used for each subcarrier. So when one node can be reached in the best state and the others not it is probably not the best solution to use the highest modulation and coding. An optimal modulation and coding must be determined based on the different states a subcarrier arrives from a base station to the different nodes. We call the number of nodes a basestation can reach for a given state R. We call the probability that the base station with the best connection towards the total set of nodes for a given subcarrier can reach exactly n nodes in a state i or c Aalborg University 2004 Technical Report: R Page 16

20 higher P (S i; R = n). If we choose to use the modulation and coding type according to state i the expected subcarrier vector weight for this subcarrier will be: w m,i = J i 1 P (S i; R = n) n M 1 n=1 (4.5) So the optimal σ will be the one using that modulation and coding resulting in the highest σ: w m = max i J i 1 P (S i; R = n) n M 1 n=1 (4.6) To determine P (S i; R = n) we use the Gaussian probability distribution of the different states for a subcarrier from each base station to each node. First we determine the probability that a base station can reach exactly n out of the J WTs in a state i or higher as follows: ( ) J P 1 (S i; R = n) = P (S i) n P (S < i) J n+1 (4.7) i Next the probability that there is at least one out of the H base stations that can reach n or more out of the J nodes in a state i or higher. P H (S i; R n) = 1 (1 P 1 ( i; R n)) H (4.8) From this probability P H (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 weight per node gets close to P g, this is because in this case the probability that a basestation has a given subcarrier in a good state towards many nodes gets really small. It can be seen that the weight for small number of nodes depends strongly on the number of basestations. Further more it can be seen that if there are many nodes in one cell, increasing the number of basestations hardly increases the weight. It can also be seen that when P g is small (bad channel quality) the performance decreases more rapidly when the number of nodes is increased then when P g is close to 1. We can see that for a large number of nodes that need to receive the same packets the advantage of the multiple basestations vanishes totally. c Aalborg University 2004 Technical Report: R Page 17

21 Figure 4.2: The normalized weight per node in the case of multicasting with multiple basestations, P g = 0.1 Figure 4.3: The normalized weight per node in the case of multicasting with multiple basestations, P g = 0.5 c Aalborg University 2004 Technical Report: R Page 18

22 Figure 4.4: The normalized weight per node in the case of multicasting with multiple basestations, P g = 0.8 Figure 4.5: The normalized weight per node in the case of multicasting with multiple basestations, P g = 0.9 c Aalborg University 2004 Technical Report: R Page 19

23 Chapter 5 Conclusion As has been shown the connection quality can be drastically increased using subcarrier scheduling for multiple basestations and multiple wireless terminals (escpecially the DADR case). The cost 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 number of base stations. This advantage vanishes totally when multicasting is used. The approach with a common receiving level for all subcarriers of a wireless terminal is also a sub-optimal solution but has the big advantage that the signalling doesn t increase with the number of subcarriers per terminal. The results in this report do not include the signalling, so all of the performances will be 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 correlation between the different subcarriers, to get a more realistic impression of the impact of this kind of subcarrier scheduling. Further more it could be considered that the signal strengths from all base stations arriving at the WT are not equal, so the WT is no longer in the (by the use of power control possibly virtually) center of all base stations. A practical implementation of the different assignment policies can be developed. Rules should be made about the assignment of the subcarriers based on the information of the quality of 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 simulated in OFDM simulators. c Aalborg University 2004 Technical Report: R Page 20

24 Bibliography [1] T. T. Kokubo, S. Yamasaki, and M. Nakagawa, Transmission delay control for single frequency ofdm multi-base-station in a cell using position information, IEEE VTS-Fall VTC 2000, pp , September [2] M. Inoue and M. Nakagawa, Space time transmit site diversity for ofdm multi base station system, 4th International Workshop on Mobile and Wireless Communications Network, 2002, pp , September [3] J. Gross and F. Fitzek, Channel state dependent scheduling policies for an ofdm physical layer using a binary state model, Technical University Berlin, Tech. Rep., , 6, 20 [4] J. Gross and Fitzek, Channel state dependent scheduling policies for an ofdm physical layer using a m-ary state model, Technical University Berlin, Tech. Rep., c Aalborg University 2004 Technical Report: R Page 21

25 Appendix A Determining the Remaining Number of Nodes to Choose from for the DADR Scenario In the DADR scenario we are allowed to assign each subcarrier to a certain node as long as this node is not already fully assigned, thus has got S/J subcarriers already assigned to him. So to determine the σ we need to determine the remaining number of nodes that are not fully assigned when assigning a subcarrier. For example for the assignment of the last subcarrier (N) there can only be one node left to choose from and for the first subcarrier to be assigned there are always J nodes to choose from. But for the one but last subcarrier it is possible that there is only one node left to choose from but it is also possible that there are still 2 nodes left to choose from. For the assignment of subcarrier 1 to N we determine the number of possibilities that there are 1 to J nodes to choose from. The subcarrier that is to be assigned is called sc, the number of subcarriers per node is called S, so S = N/J. First the number of possibilities that there is only one node to choose from is determined: U 1 sc = ( ) ( J N (J 1)S J 1 sc 1 (J 1)S ) } {{ } R 1 (A.1) If the bottom part of the binomial coefficient is a negative integer the outcome of this binomial coefficient is 0. A part of U 1, R 1, is used to determine the number of possibilities that there are 2 nodes left to choose from: ( ) [( ) ( ] J N (J 2)S 2 Usc 2 = )R 1 (A.2) J 2 sc 1 (J 2)S 1 }{{} R 2 The number of possibilities that there are 3 nodes left to choose from is: ( ) [( ) ( ) ( ] J N (J 3)S 3 3 Usc 3 = R 1 )R 2 J 3 sc 1 (J 3)S 1 2 }{{} R 3 (A.3) c Aalborg University 2004 Technical Report: R Page 22

26 Table A.1: Number of possibilities that there are a nodes to choose from when assigning subcarrier number sc. sc a Total This process continues until the case that there are J nodes to choose from. The probability that there are a nodes to choose from for the assignment of subcarrier sc is determined using the total number of possibilities: P (Jsc remaining = a) = U sc a ) (A.4) ( N sc 1 So this probability can be determined as follows: [ ( P (Jsc remaining = a) = U a sc ) N (J a)s a 1 ( ] a ( N ) )R i sc 1 (J a)s i sc 1 i=1 }{{} R a (A.5) In table A the different possibilities are shown, the different probabilities can be determined by dividing the number of possibilities for this situation by the total number of different possibilities. c Aalborg University 2004 Technical Report: R Page 23