Multihopping for OFDM based Wireless Networks

Transcription

1 Multihopping for OFDM based Wireless Networks 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 how the multicarrier character of OFDM based wireless networks can be exploited when implementing multihopping. When it is not possible to establish a connection between a base station and a wireless terminal or when this connection is not of a satisfactory quality, multihopping can be used. In this report it is shown that with only a few multihopping nodes the connection quality with far away nodes can be drastically increased using subcarrier scheduling, based on the information of the quality of individual subcarriers. [3] First a binary model is used to show the results of this kind of multihopping. It is compared with the conventional case where the total signal follows the same path. It is assumed that the signals make 2 hops before arriving at the receiver. So there is one level of multihopping nodes. Further more it is assumed that the only degradation of the signal occurs between the sender and the intermediate nodes and not between the intermediate nodes and the receiver. This is done for simplification of the model. Secondly a M-ary model is used to see the impact of a more realistic channel model. And finally a M-ary Gaussian channel model is considered.

3 Contents 1 Introduction 1 2 Advanced Multihopping Binary Channel Model M-ary Channel Model with an Equal Distribution M-ary Channel Model with a Gaussian Distribution Conclusion 10 Bibliography 11 c Aalborg University 2004 Technical Report: R Page i

4 Chapter 1 Introduction The popularity of wireless local area networks (WLAN) increases rapidly. WLANs are currently deployed in many office buildings, but also gain interest for home networks and public access (hotspots). In a wireless network the signals that are send from a sender to a receiver can follow multiple paths with each its own characteristics (attenuation, delay, etc.). This is called multi-path propagation. This multi-path propagation of a wireless channel often introduces Inter Symbol Interference (ISI ). ISI is a limiting factor on the maximum throughput of a connection. 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 a multicarrier system. OFDM was invented in the mid sixties, when Chang published his paper on the synthesis of bandlimited signals for multichannel transmission [1]. However due to practical reasons it could not be applied in practical systems until recent times. Currently OFDM is being applied in several standards both for wired and wireless systems, such as Asymmetric Digital Subscriber Line (ADSL), Digital Video Broadcast systems and the IEEE WLAN standards a/g and a. An overview of the current OFDM techniques can be found in [2]. 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 subcarriers add up to one signal with a high bitrate. Because symbol times of the subcarriers are large, ISI will not occur. This report is focused on exploiting the fact that a signal in an OFDM network is split over different channels, each with its own characteristics. In this report it is shown how connectivity and connection quality can be increased using multihop by selecting the best path for each subcarrier. Three different channel models will be used to model the channel. First a binary channel model will be used where a subcarrier will either be perfect or not usable at all. The second used model is a M-ary model with an equal probability distribution, a subcarrier can have different states corresponding to different Signal to Noise Ratios (SN R), each with the same probability of occurring. And finally a M-ary Gaussian channel model will be used, this is the same as the former model, but now the probability of each state occurring follows a Gaussian distribution. c Aalborg University 2004 Technical Report: R Page 1

5 Chapter 2 Advanced Multihopping In a wireless network it is desired to let the Wireless Terminals (W T s) stay connected as long as possible. But, because of the limited power WTs can produce and the fact that interference with adjacent cells must be avoided this is quite a challenge. A possible way to achieve larger coverage areas is using multihopping. Multihopping is used when a base station, (BS), wants to send a package to a WT, but can not reach it or not in a satisfactory way. In stead of sending the package to the WT directly the BS sends the package through one or more intermediate nodes. In this way the coverage area of the BS is broadened. Assuming that the intermediate nodes have a better connection with the BS and the receiving WT than the BS directly with the receiving WT, the connection connection quality can be increased. See Figure 2.1 for an illustration of this approach. OFDM networks use different subcarriers to send data. For receiving a package it is not necessary that all the subcarriers come from the same node. When employing multihopping one could use this fact. It is possible to establish an optimal connection for each individual subcarrier in stead of choosing one way for all subcarriers. This approach is shown in Figure 2.2 and the increase in connection quality is shown in Figure 2.3, where S/R1 describes the quality from sender to receiver when path number one would be used and total describes the optimal connection. This chapter describes several scenarios in an OFDM network that utilize this fact. It is assumed that N subcarriers are used and that there are J intermediate nodes in a cell. 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 be established. We define the subcarrier vector weight, σ, as the sum of all the individual subcarrier states at the receiver. And we define the normalized subcarrier vector weight, w, as the subcarrier vector weight divided by the number of received subcarriers. So, when the state of subcarrier number c Aalborg University 2004 Technical Report: R Page 2

6 Figure 2.1: Multihopping in a wireless network, using 4 hops n is S n : σ = N n=1 S n and w = σ/n (2.1) To optimize the quality of a connection we try to optimize the subcarrier vector weight. Before thinking about implementing advanced multihopping in a network it first has to be proven that it improves the quality. This section describes three different channel models and the consequences of these models regarding channel quality between the sender and the receiver. The quality in case of normal connections and in the case of advanced multihopping is compared. The channel between the intermediate nodes and the receiver is presumed perfect. So the quality of the connection between the sender and the receiver is only influenced by the connection between the sender and the intermediate nodes. To be able to show the consequences of advanced multihopping a model of a wireless connection channel is made. This model is purely statistical. First a binary model is used, second an equally distributed M-ary model is used and finally a Gaussian distributed M-aray model is used, to show the gain in quality. The reason for assuming three different statistical channel models is to be able to compare subcarrier scheduling policies. When one develops a possible way to divide the subcarriers it is important to see how this policy performs for different channel models, because it is not known in front how a channel behaves. A scheduling policy should still work efficient if it is not aware of the specific channel behavior. So the throughput for different channel behaviors is important to observe when judging the flexibility of a scheduling policy. c Aalborg University 2004 Technical Report: R Page 3

7 Figure 2.2: Multihop approach Figure 2.3: Multihop connection quality 2.1 Binary Channel Model This channel model has been used before in [3]. For a subcarrier state we assume the following: when the SNR of a subcarrier is above a certain threshold the subcarrier is assumed to be good, called G. When the SNR is below this threshold the channel is assumed bad, called B. Over a good channel, communication with the highest bitrate is possible, if it is in a bad state there is no communication possible at all. A subcarrier in a good or a bad state towards a certain multihopping node has no effect on the state of this subcarrier towards another multihopping node. This means that we assume that there is no cross-correlation of a subcarrier between two nodes. State behavior of different subcarriers is also assumed to be completely independent of each other. Let S i be the state of a subcarrier at intermediate node i. The probability that a subcarrier is in a good state is: P (S i = G) = P g (2.2) and therefore P (S i = B) = 1 P (S i = G) = 1 P g = P b (2.3) An example of the probability distribution for the binary channel model is given in Figure 2.4. These probabilities are the same for each intermediate node and for each subcarrier. When several intermediate nodes receive a subcarrier, the node that receives that subcarrier the best will send this subcarrier through to the receiver. When the number of intermediate nodes is J, the probability that the state of a subcarrier at the receiver, using advanced relaying (S mi ) is good (this means that this subcarrier arrives at at least one of the intermediate nodes with state G) is: P (S mi = G) = 1 (P b ) J = 1 (1 P g ) J (2.4) The state of a good subcarrier is 1 and of a bad subcarrier is 0. The normalized subcarrier vector weight at the receiver, using advanced relaying will is called w a. For the binary case the following statement can be made about the weight: E(w a ) = P (S mi = G) (2.5) c Aalborg University 2004 Technical Report: R Page 4

8 Figure 2.4: Probability distribution for a binary channel model with P g = 0.7 When normal relaying would have been used the expectation of the normalized simple subcarrier vector weight w s would have been: E(w s ) = P (S i = G) (2.6) The gain of advanced relaying is the ratio of w a and w s. This is the ratio of the quality of the subcarriers in case of simple multihopping and advanced multihopping. The normalized subcarrier weight for advanced multihopping with two hops for different number of nodes and different P g s is shown in Figure 2.5. We can see in this figure that when the the probability of a good subcarrier is small, many nodes are needed to obtain a good quality. When the probability of a good subcarrier is greater only a few nodes are needed to get an almost perfect channel quality. 2.2 M-ary Channel Model with an Equal Distribution This channel model can be seen in [4]. Now we assume M different states a subcarrier can have in stead of the 2 in the binary model. Each state has the same probability of occurring. The minimum subcarrier state is 0 (no connection possible) and the maximum state is 1 (perfect connection). So the probabilities and the weights of each state x are: P (S = m) = 1 M and w(s = m) = m 1 M 1 (2.7) c Aalborg University 2004 Technical Report: R Page 5

9 Figure 2.5: The normalized subcarrier vector weight using advanced relaying and a binary channel model using two hops, for different number of nodes and P g s. An example of the probability distribution for the M-arry channel model is given in Figure 2.6. The probability that all intermediate nodes receive a subcarrier in a state equal to or smaller than m is: ( m ) J P (S m) = (2.8) M And the subcarrier vector weight can be determined as follows: E(σ) = N M m=1 ( [P (S m) P (S m 1)] m 1 ) M 1 (2.9) In equation 2.9 it can be seen that the subcarrier vector weight increases when the number of nodes increases and decreases when the number of states increases. The increase with the number of nodes is obvious because the probability that there is a node that receives a given subcarrier in a good state increases. The decrease of the subcarrier vector weight due to the increase of the number of states may be less obvious. When there are more states a subcarrier can have, the probability that a subcarrier has a given state decreases, see equation 2.7. Also, assuming the same number of nodes, when increasing the number of states, the probability that there is a node that can receive a given subcarrier in a given state, decreases, this can be seen in equation 2.8. Further more the probability of having perfect subcarriers decreases and therefore the subcarrier vector weight decreases. In Figure 2.7 the normalized subcarrier vector weight can be seen for different numbers of states and different numbers of multihopping nodes, for two hops. c Aalborg University 2004 Technical Report: R Page 6

10 Figure 2.6: Probability distribution for a M-ary channel model with M=5 Figure 2.7: Normailized subcarrier vector weight for a M-ary channel model c Aalborg University 2004 Technical Report: R Page 7

11 2.3 M-ary Channel Model with a Gaussian Distribution This channel model has been used before in [4]. In this case we assume again a channel model with M different states, but now these states do not have equal probabilities but they are Gaussian distributed. The weight of each state is still the same as in equation 2.7. The Gaussian distribution has a mean value of S mean and a variance of S var. As an illustration a possible subcarrier possibility distribution is shown in Figure 2.8. In this case the subcarrier vector weight will be the same as in equation 2.9, but the probabilities in this equation are different. These probabilities are now as in Figure 2.8 and they are not distributed as in Figure 2.6. This is a discrete case of a Gaussian distribution and therefore some changes have been made to the continuous version of it to make it suitable for our model. First of all the continuous scale has been made discrete by dividing it up into M + 2 portions. The first one starts at and ends at 0. Portion 2 until M + 1 all have width 1/M, so portion M + 1 ends at 1. The final portion M + 2 stretches from 1 to. First the probability of each portion occurring is determined using equation Next the first and the last portion are removed from the probability distribution and the sum of all the other probabilities is determined. Then all the remaining probabilities are divided by this sum, so the total probability is one again. These are the probabilities used in equation 2.9. Next we want the lowest state to have weight 0 and the highest state to have weight 1. This is done using equation 2.7. Determining the subcarrier vector weight for different numbers of states and different numbers of relaying nodes results in Figure 2.9. When we increase S mean or S var the normalized subcarrier vector weight increases, because it becomes more likely to have a subcarrier in the higher states. p i = iup e (x Smean)2 2 Svar dx (2.10) 2π Svar i low 1 c Aalborg University 2004 Technical Report: R Page 8

12 Figure 2.8: Subcarrier state probability distribution, with S mean = 0.5 and S var = 0.2 Figure 2.9: Normalized subcarrier vector weight for a Gaussian distributed M-ary channel model with S mean = 0.5 and S var = 0.2 c Aalborg University 2004 Technical Report: R Page 9

13 Chapter 3 Conclusion In this report it has been shown that the connectivity and throughput in an OFDM based wireless network can be drastically increased when using multihopping in combination with subcarrier scheduling. Different channel models have been used to show the advantage of enabling each subcarrier to follow a path resulting in the best possible connection for that subcarrier. This means that not all the subcarriers follow the same path from sender to receiver. First a binary model has been used, secondly a M-ary channel model with an equal probability distribution and finally a M-ary Gaussian channel model has been used. It is assumed that the only signal degradation occurs between the sender and the intermediate nodes. To further extend the research of this topic degradation of the signal between the intermediate nodes and the receiver should be included. Further more a channel model could be used assuming correlation between the different subcarriers. This will provide a more realistic impression of the impact of this kind of multihopping on the connectivity and throughput. In this report it is assumed that all the intermediate nodes are placed at the same distance of the sender and the receiver, resulting in similar signal degradations for each intermediate node. It could be investigated what happens when the intermediate nodes and the receiver are moving with respect to each other. c Aalborg University 2004 Technical Report: R Page 10

14 Bibliography [1] R.W. Chang, Synthesis of band-limited orthogonal signals for multichannel data transmission, Bell System Techn. J., vol. 45, pp , [2] R. V. Nee and R. Prasad, OFDM for Wireless Multimedia Communications. Artech House Publishers, [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., i, 4 [4], Channel state dependent scheduling policies for an ofdm physical layer using a m-ary state model, Technical University Berlin, Tech. Rep., , 8 c Aalborg University 2004 Technical Report: R Page 11