N-BEB: New Binary Exponential Back-off Algorithm for IEEE

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N-BEB: New Binary Exponential Back-off Algorithm for IEEE 802.11 Mohammad Shurman 1, Bilal Al-Shua'b 2 (1) Jordan University of Science and Technology/Network Engineering and Security Department, Irbid, Jordan (2) Jordan University of Science and Technology/Computer Engineering Department, Irbid, Jordan alshurman@just.edu.jo, ambilal12@cit.just.edu.jo Abstract: In recent years, wireless ad-hoc networks have become increasingly popular because they are considered a de-facto alternative for infrastructure-less environments. These networks are formed by a collection of independent wireless mobile nodes that can communicate and operate directly over wireless media without the need for a preexisting communication infrastructure. Along with the hidden and exposed terminal problems, it has been observed that the fairness issue is responsible for DCF' performance-degradation. The IEEE 802.11 DCF (Distributed Coordination Function) is considered the most popular technique used for the physical and MAC layers in ad-hoc networks. DCF is based on Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) mechanism. Since the IEEE 802.11 is the most implemented protocol, there has been countless research aimed at enhancing its performance in different ways, including modifying the Medium Access Control (MAC) algorithm (i.e. back-off algorithm). In this paper, a novel mechanism is suggested to resolve the IEEE 802.11 standard fairness problem, which results an unfair channel sharing between the stations due to the duplication of CW each time an unsuccessful transmission occurs, while resets CW value in case of a successful transmission. To impose fairness in ad-hoc networks, our proposed idea dynamically tunes the CW value based on the previous transmission status of each node attempts to transmit. By studying the characteristics of the proposed algorithm using the NS2 simulator, we found that our proposed algorithm improves the fairness by fairly distributing channel between the competing nodes as well as a remarkable reduction in the number of dropped packets. In addition, our proposed algorithm has a considerable improvement in the packet delivery ratio as well. Keywords: IEEE802.11 back off, BEB, QoS, chancel fairness, wireless MAC. An earlier version of this research paper was presented in MIPRO2014.

1. INTRODUCTION M obile Ad Hoc Network (MANET) is a collection of mobile nodes that can communicate directly over wireless media without the need for a preexisting communication infrastructure. Nodes in these networks act as a transmitter, receiver, and a router for others to forward the communication packets until reaching the desired destination [1]. Two mechanisms are provided for the MAC protocol in IEEE 802.11 standard: the point coordination function (PCF), and the distributed coordination function (DCF). The major difference between them is that PCF utilizes a basic access mechanism that supports contention-free services, which in turn require a coordinator (or a central point) to coordinate the channel access between the nodes. On the contrary, the distributed coordination function (DCF) utilizes the contentionbased services, in which, all nodes have the same priority to access the channel without the need of a central point [2] [3]. DCF is a Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) mechanism in which a station wishing to transmit a packet first senses the channel status. If the channel is free for a time greater than or equal to predetermined DIFS (Distributed Inter Frame Space), then the station is allowed to transmit if its back-off counter (the number of idle slots a node should wait before it can transmit) equals zero. Otherwise, the node should decrements the counter (back-off counter) for each time slot that passes. The back-off counter value is randomly picked from the range [0, CW] size as in equation 1, where CW denotes the contention window size which is initialized to CW min, and is doubled after each collision until it reached to a maximum value CW max [3][4]. Back-off time Random CW SlotTime

In order to send a packet, a wireless node should wait until the medium becomes idle, and then wait for DIFS period followed by back-off time. After that, if the medium is still idle, the station can send its packet, but if the medium becomes busy before back-off time expiration, the wireless node waits until the medium becomes idle again. It then waits for DIFS period followed by the residual of the previous back-off time before it starts to transmit [4][5][6]. The collision occurs when two stations are transmitting at the same time with no ACK is received. This will increases the value of CW to reduce the collision probability as in equation 2 [5]. CW new min CW old 1 CW max Each time the transmission fails due to a collision or other reason, the retry counter is incremented and the CW is duplicated as in equation 2. If the retry counter reaches a specific limit of 7 as defined by the standard IEEE.802.11, the packet will be dropped. However, if the transmission succeeds, the CW is reset to CW min, and a new back-off counter is chosen randomly as in equation 1. The default back-off scheme in IEEE 802.11 is the binary exponential back-off (BEB) which suffers from fairness problem. Fairness is one of the major problems where some nodes obtain most of the channel s bandwidth while others starve [6] [7], and thus, some nodes can achieve significantly larger throughput than others. Many researchers have proposed algorithms to improve back-off performance (i.e., fairness), these algorithms can be divided into two categories: Adjusting the CW size based on the number of collisions that have occurred during the transmissions [2][5]. Adjusting the CW size dynamically based on changes occur within the network environment [3].

In the first category, adjusting the CW is performed after a collision happened, which means that the cost of collision (such as packet retransmission and power drain caused by retransmitting packets) has already been paid. In contrast, approaches of the second category can immediately adjust the CW to the most appropriate CW size, based on network environment changes without paying the cost of the collision. This option clearly outperforms the first category. For these reasons, this paper proposes a novel algorithm, New Binary Exponential Back-off (N-BEB), to solve the fairness problem. Unlike other algorithms, our proposed algorithm adjusts the CW by taking into account the number of successful and unsuccessful transmissions. In addition, it also takes into account the state of channel occupation in order to guarantee fair access to the communication medium to all competing nodes. 2. RELATED WORK Authors of [1] proposed a History Based Adaptive Back-off (HBAB) algorithm that attempts to improve the QoS by modifying the original BEB algorithm. The history of successive packet transmit trials is taken into account. To accomplish this task, HBAB defines three variables: the contention window size (CW) which holds most recent CW value, the multiplicative factor α which is used to update CW value, and the ChannelState which represents channels states. Their proposed algorithm was tested using QualNet and Linux-based testbed simulators. The results showed that their algorithm outperforms the original IEEE 802.11 with up to a 33.51% improvement in delay, and a 7.36% improvement in packet delivery ratio. A new algorithm that modifies DCF procedure to reduce the bandwidth as well as end-to-end delay caused by retransmitting the collided packets is proposed in [2]. This algorithm adopts a new mathematical model to increment the value of the CW. This proposed approach is implemented and tested using NS2 Simulator. The

obtained results showed significant improvements in the number of sent packets, packets lost, and the average throughput. Improving the short-term fairness (fairness over short time scales) in IEEE 802.11 networks without any adjustment to CW size is presented in [8]. Basically, the main idea is forcing all nodes in the network to choose their CW value randomly within the initial CW size, which is equal to 512. When a collision happens, the CW of the collided nodes is decreased to gain higher channel access priority, therefore increasing the short-term fairness. Compared with the original standard, the results showed that their approach achieved a high level of short-term fairness, higher throughput, and lower collision probability. An improved collision back-off algorithm that considers the node access fairness is presented in [9]. In Node Access Fairness Back-off (NAFB) algorithm, the sending and non-sending stations adjust their CW based on the sensed collided stations. In case of a successful transmission of any sending node in the network, its CW value will be decreased slowly. At the same time, the CW values of the other non-sending stations are decreased faster. In case of an unsuccessful transmission, the CW value of the sending node is increased faster than the CW values of the non-sending stations. Simulation results showed that NAFB algorithm can improve the network throughput, packet drop rate, and packet delay. Both unfair bandwidth sharing, and station-to-station communication efficiency problems in the IEEE infrastructure 802.11 WLAN are discussed in [10]. In addition, a new mechanism to improve the fairness of IEEE 802.11 protocol is presented. Since the probability of transmitting packets from all stations is considerably larger than the probability that AP has to transmit a packet, this algorithm considers dual queues and multiple transmission opportunities to tackle the unfair bandwidth sharing problem

between the AP, and other stations. The results showed that their proposed approach can improve the efficiency and fairness of IEEE 802.11 protocol, as well as enhance the throughput of station-to-station traffic. 3. PROPOSED APPROACH In our proposed approach a new procedure enhances the opportunity for any given node intending to access the channel. In an instance when the node cannot access the channel, the proposed algorithm allows the CW to increase its value two times consecutively. After two unsuccessful transmissions, the node starts decreasing the value of the CW. This is contrary to the original protocol which doubled the CW value each time an unsuccessful transmission occurred. When a transmission is successful, the CW is calculated by CW = CW/ 2 as shown in Fig. 1. This operation is repeated during the first nine successful transmissions. Afterwards, we set the number of successful transmissions to 1 and CW is set to CW 1.3. The CW value is incremented in order to give the other nodes more opportunity to access the channel, especially the nodes that collided more than two times. This step demonstrates an efficient fairness between the nodes. In case of an unsuccessful transmission as explained in Fig. 2, the CW is calculated by CW = CW 2. This operation will be repeated during the first two unsuccessful transmissions. Thereafter, the number of unsuccessful transmissions is set to 1, and CW is set to CW/1.5. This reduction in CW value gives the node an opportunity to retransmit its data successfully. However, the parameters of 2, 1.3, and 1.5 in both successful and unsuccessful transmissions are chosen carefuly based on intensive simulation experiments to achieve the best results.

Start counter =1 Backoff=random(0,CW) *slot time Successful transmission No Counter >9 Yes Counter++ Counter=1 CW=CW/ 2 CW=CW * 1.3 No CW<CW min CW>CW max Yes Yes No CW=CW min CW=CW max Figure 1: Proposed algorithm (Successful case)

Start counter =1 Backoff=random(0,CW) *slot time unsuccessful transmission No Counter > 2 Yes Counter++ Counter=1 CW=CW* 2 CW=CW/1.5 No CW>CW max Yes Yes CW<CW min No CW=CW max CW=CW min Figure 2: Proposed algorithm (Unsuccessful case) 4. SIMULATION RESULTS AND DISCUSSIONS The NS-2 simulator [13] is used to test our approach. We build three experimental scenarios using the above proposed parameters. Scenario1 is used to test our approach

against the following four metrics: PDR, end-to-end delay, number of dropped packets, and number of lost packets. The simulation was run over multiple trials to observe how our algorithm will behave in the network. Scenario 2 and Scenario 3 are used to test our approach, Fairness Index (FI) metric. Scenario 2 is used in many research papers such as [11][12], and it tests the fairness between the nodes while they are static. Finally, we use scenario 3 to test our approach in case of mobile nodes, which is more realistic for comparison. The proposed algorithm is compared with the original Binary Exponential Back-off (BEB), Improved Binary Exponential Back-off (I-BEB)[11], and Enhanced Binary Exponential Back-off (E-BEB) [12] using different metrics in this comparison. 4.A Performance Metrics Packet Delivery Ratio: the number of correctly received packets at the intended destination to the number of sent packets at the source node, which is defined as: PDR =Packets Received / Packets Sent (3) Where larger packet delivery ratio means better performance of the protocol. The number of dropped packets during the network lifetime: the total number of packets that were dropped by all nodes in the network during the network lifetime. It is defined by TraceGraph [14] as the number of dropped events (D) that appear in the trace file. End-to-End Delay: the average time taken by a data packet to be transmitted across a network until it reaches the destination. This also includes the delay caused by route discovery process, and the queue in data packet transmission. Only the data packets that are successfully received by destinations are considered.

End-to-End Delay = ( arrive time send time )/ Number of connections (4) This contains the transmission delay, propagation delay, processing delay, and queuing delay. Fairness index: which is defined as: Fairness index (FI) = ( n i=1 x i) 2 n (x i ) 2 n i=1 (5) Where n is the number of the same priority flows and X i is the throughput of flow i. Therefore, FI < 1 and it reaches 1 when all X i are equal, which corresponds to the highest fairness that can be achieved between the nodes. Number of lost packets during the network lifetime: represents the total number of the packets that were sent by the sender nodes, but were not received by receiver nodes during the network lifetime. 4.B Performance Evaluation In this section a deeper understanding of the impact of our scheme on the system performance, as well as the fairness among nodes through the simulation study is presented. The above 3 scenarios are used for this purpose. To achieve a fair comparison we implemented BEB, I-BEB, and E-BEB algorithms as a baseline for comparison with our proposed algorithm, New Binary Exponential Back-off (N- BEB). Table1: Simulation parameters Transport Protocol UDP Max-speed 10m/s Area (100*100) m 2 Simulation time 600s Number of nodes 30,40,50,60... 100 Traffic type CBR Pause Time 0 Slot time 20 µs Packet size 512 bytes DIFS 40 µs SIFS 10 µs

CW min 31 CW max 1023 All experiments were performed in a 100m 100m area consisting of different number of nodes ranging from 30 to 100, distributed randomly within the chosen area. Also, the source/destination pairs were chosen at random from the set of available nodes in the network. Each point in every presented graph is an average of the result of 5 trials using different seed values. For all experiments we chose the pause time to be 0. This means each node moves continuously throughout the simulation without stopping. The same generated scenarios are tested against the original BEB, N-BEB, E-BIB and I-BEB. Scenario (1): There are 30, 40, 50,, 100 nodes distributed randomly on 100 100 m 2 planar domain. The maximum connections are chosen to be 30, 40, 50,, 100 respectively, and the transport layer adopts the UDP protocol. In the application layer, CBR (Constant Bit Rate) is adopted, the top speed of each node is 10 m/s, the simulation time is 600 sec. In addition to scenario 1, scenarios 2 and 3 are used to estimate fairness. Scenario 2 is when all nodes are static and distributed carefully, and is used in almost all research papers, and scenario 3 is when all nodes are mobile and distributed randomly. Scenario 3 is more realistic when used for comparison than scenario 2. Scenario (2): 10 nodes share the same channel in an area equal 100 100 m 2, and the nodes are static. All nodes are the single-hop type to make sure that each node only communicates with its neighboring node. At 1.0 second simulation time, nodes (0, 2, 4, 6 and 8) simultaneously start sending data to their neighboring nodes (1, 3, 5, 7 and 9) as shown in figure 3.

Scenario (3): In this scenario 10 nodes share the same channel randomly distributed in 100x100 m 2 planar domains. We assume that all nodes are mobile continuously with a top speed of 10 m/s. By the time of 1.0 second, nodes start sending data to their neighboring nodes. Figure 3: scenario 2. N-BEB algorithm is a bit more complex than I-BEB and BEB since the original BEB has two cases, a successful case, and an unsuccessful case. In the successful case, the CW is reset to CW min, so the node can access the channel as soon as possible, and in the unsuccessful case BEB algorithm simply duplicates the CW. I- BEB algorithm focuses primarily on success by accessing the number of successful transmissions to determine whether to increase or decrease the CW. However, in cases where the transmission is not attained in a successfully consecutive manner, the CW is reset to minimum, making both of these algorithms simpler than N-BEB algorithm. In N-BEB algorithm, we considered both cases of successful and unsuccessful transmissions. We take into consideration the number of unsuccessful and successful transmissions, and adjust the value of CW accordingly. Thus, N-BEB is considered slightly more complex than BEB and I-BEB. In E-BEB algorithm, we note that it has the highest complexity since it continually calculates a threshold value to adjust the CW value as well as it maintains

a counter to calculate the number of successful transmissions to achieve more fairness. By doing so, this algorithm adds a new computational complexity. This computational complexity increases power consumption which is a critical issue in ad-hoc network. A. Dropped Packets Parameter One of the factors in which our approach outperforms BEB, E-BEB, and I-BEB algorithms is in the total number of dropped packets. With respect to scenario 1, figure 4 demonstrates that N-BEB algorithm has the lowest number of dropped packets among the comparative algorithms for all network sizes, which results in significant reduction in the channel overhead. Thereby, this results in having a higher network utilization as lower number of packets will be retransmitted. Reducing the number of dropped packets can be attributed to the reduction in the collision probability as a result of the randomization process that is followed by N-BEB algorithm. Also, our approach takes into account the unlucky nodes that could not send their data successfully in a consecutive manner. By increasing their chance to gain successful transmission before the max retry count is reached the chance of dropping the packets is decreased. Thus, our approach saves the packets from being dropped.

Figure.4 Number of Dropped packets From figure.4, we noticed that our approach (N-BEB) reduced the number of dropped packets by 50% relative to the BEB approach when the network size is 30 nodes. This reduction is increased, as the network size increased, until it reaches 65% when the number of nodes are 100. Also N-BEB overcomes I-BEB approach by a 72% reduction in the number of dropped packets when the network size is 30 nodes. This reduction is increased as the network size increased until it reaches 85% when the network size is 100 nodes. By comparing the N-BEB approach with the E-BEB approach we found that N-BEB overcomes E-BEB approach by a 50% reduction in the number of dropped packets when the network size is 30 nodes. This reduction is increased as the network size increased to 85% when the network size is 100 nodes. B. Lost Packets Parameter Another factor that N-BEB outperforms BEB, E-BEB and I-BEB approaches, is the total number of lost packets. Figure 5 compares the lost packets in different network sizes. It is clear that our proposed algorithm has a significant reduction in the number of lost packets, thereby having higher network utilization and lower energy drain caused by retransmissions. This reduction can be attributed to the reduction in the average time the transmitted packet spends in the buffer before it is successfully received by the destination. Lost packet could happen due to node movement, which changes the network topology before the packet received successfully, so our approach saves the packets from being lost. From figure.5, we can see that our approach (N-BEB) reduced the number of lost packets by 83% relative to BEB approach when the network size is 30 nodes. This reduction is decreased until it reaches 68% at 100 nodes network size. Compared to I- BEB approach, N-BEB reduced the number of lost packets by 86% when the network

size is 30 nodes. This reduction is decreased until it reaches 74% at 100 nodes network size. N-BEB also overcomes E-BEB approach with a 69% reduction in the number of lost packets when the network size is 40 nodes. This reduction is decreased until it reaches 2% at 100 nodes network size. Figure.5 Number of lost packets C. Packet Delivery Ratio Parameter Figure 6 shows the delivery ratio for the proposed algorithm, N-BEB, compared to BEB, E-BEB and I-BEB algorithms with different network sizes. Each value in the presented graph is an average of 5 trials using different seed values. It is clear that N- BEB algorithm has the highest delivery ratio among the other algorithms since the channel availability for the sender is higher than the other algorithms, due to retransmissions reduction. When the number of nodes increased, we notice that the PDR for all approaches decreased. Increasing number of nodes in the network will decrease the distance between nodes and thus increase the impact of interference between the nodes, which leads to increase the number of dropped packets and reduce the PDR.

Figure.6 Packet Delivery Ratio (PDR) Figure.6 demonstrates that our N-BEB increased the PDR by 7% relative to BEB approach when the network size is 50. This improvement in the PDR is continuously increased, as the network size increased, until it reaches 11% when the network size is 100 nodes. When we compared N-BEB with I-BEB we found that N-BEB increased the PDR by 5% when the network size is 30 nodes. This improvement in the PDR is continuously increased, as the network size increased, until it reaches 10% when the network size is 100 nodes. Relative to E-BEB approach we found that N-BEB outperforms E-BEB by 2% improvement in PDR value when the network size is 40. This improvement in the PDR value is continuously increased, as the network size increased, until it reaches 15% when the network size is 100 nodes. D. End To End Delay Parameter End-to-End delay for N-BEB, BEB, E-BEB, and I-BEB algorithms are shown in Figure 7. For all network loads, E-BEB algorithm has the highest End-to-End delay value among the other algorithms since E-BEB increases its threshold value when the number of nodes is small, which increases the End-to-End delay. It decreases its

threshold value in case of high network load, which leads to a collision probability increase, thereby increasing the End-to-End delay. When the network load is low, BEB algorithm has the lowest End-to-End delay value compared to the other algorithms. End-to-End delay value for N-BEB algorithm is higher than BEB algorithm when the number of nodes is less than 70 nodes. The reason behind this is the original algorithm resets the value of the CW when a node attains successful transmission, which increases the probability of another packet to be also successfully transmitted within short time interval. The N-BEB approach tries to delay the node that already has a successful data packet transmission from transmitting again to give the starving nodes more opportunity to transmit. Figure.7 End-to-End delay We can see that our approach (N-BEB) increased the end-to-end delay value by 34% to 37% when the network size varied from 30 to 70 nodes relative to BEB approach. It outperformed BEB by 5% up to 15% when the network size varied from 80 to 100 nodes. Compared to I-BEB approach, N-BEB had significant reduction by 2% up to 29% as the network size varied from 60 to 100 nodes. While at network size, 30 nodes to 50 nodes, I-BEB approach had a better end-to-end delay value by

30% at 30 nodes, down to 10 % at 50 nodes. Relative to E-BEB approach we noticed that N-BEB approach decreased the end-to-end delay value by 33% when the network size is 30 nodes. This reduction is decreased until it reaches 28% when the network size equals 100 nodes. E. Fairness Index Parameter By adjusting the CW value carefully and reducing the starvation in the network, as well as minimizing the capturing problem, fairness can be significantly improved as in figure 8. By comparing our proposed algorithm (N-BEB) with the other mentioned algorithms, namely BEB, I-BEB, and E-BEB according to scenario 2, it is clear that N-BEB algorithm has better FI metric value than both BEB, and I-BEB algorithms, while it has almost the same FI value as E-BEB. To be more realistic and fair in our comparison, we applied scenario 3, and the obtained results are shown in figure 9. Figure.8 Fairness Index of static node From Figure.8 we can see that our approach (N-BEB) increased the fairness index value by 1.4%, relative to BEB approach, and 3% compared to I-BEB approach. The value of fairness index of N-BEB is being compared to the original standard,

and another two algorithms according to scenario 3, and equation 5, is shown in figure 9. It is clear that the value of fairness index of N-BEB remains better than BEB and I-BEB algorithms, while it has the same FI value as E-BEB algorithm, which indicates how stable our proposed approach is. There is a significant reduction in FI metric value for BEB algorithm, which can be attributed to the capturing problem in which one node captures the channel continually while the others starve. Our improvement in fairness is due to the dynamic way in adjusting the CW value since each node can be assigned a CW based on its transmission status which prevents channel capturing by a greedy node. Figure.9 Fairness Index of mobile nodes N-BEB approach increased the FI value by 27% relative to BEB approach and 4% compared to I-BEB approach. FI clearly shows how fairly the channel is shared between all active nodes. Therefore, FI indicates that our proposed algorithm, N- BEB, achieved the fairness requirements more efficiently than the I-BEB and BEB, and has the same FI value as E-BEB for scenario 1, and scenario 2.

5. CONCLUSION AND FUTURE WORK In this paper, we focused on solving the fairness issue to enhance the Qos of the existing IEEE 802.11 protocol by dynamically adjusting the value of the CW based on the transmission status of each node. We presented a novel mechanism for improving fairness in the IEEE 802.11 protocol called N-BEB algorithm. N-BEB algorithm aims to solve the problem of fairness by counting the number of successful and unsuccessful data packet transmissions, and adjusting the CW accordingly. In addition to attaining better fairness than the original standard (BEB) algorithm and I-BEB algorithm, N-BEB also achieves a higher packet delivery ratio, a lower number of lost packets, and a lower number of dropped packets than BEB, I- BEB, and E-BEB algorithms. It deserves pointing out that our proposed algorithm manages a massive improvement in the end-to-end delay when the network size is large. When making a comprehensive evaluation and as far as the complexity is concerned, we found that N-BEB algorithm is less complex than E-BEB, but more complex than I-BEB and BEB. REFERENCES [1] Maali Albalt, Qassim Nasir, Adaptive Backoff Algorithm for IEEE 802.11 MAC Protocol, International Journal of Communications, Network and System Sciences, vol. 4, 2009. [2] Sedrati Maamar, Maamri Ramdane, Contention Window Optimization: an enhancement to IEEE 802.11 DCF to improve Quality ofservice, International Journal of Digital Information and Wireless Communications, vol. 2, 2011. [3] Yi-Hung Huang, Chao-Yu Kuo Dynamic tuning of the IEEE 802.11 distributed coordination function to derive a theoretical throughput limit, EURASIP Journal on Wireless Communications and Networking, vol. 1, 2011. [4] Mustafa Ergen, IEEE 802.11 Tutorial, Report of Electrical Engineering and Computer Science Department, University of California-Berkeley, 2012. [5] Amine Berqia, Blaise Angoma Fairness and QoS in Ad-Hoc Networks, IEEE Vehicular Technology Conference, Singapore, 2008.. [6] Ying Jian, Ming Zhang, Achieving MAC-Layer Fairness in CSMA/CA Networks, IEEE/ACM Transactions on Networking, Vol. 19, 2011. [7] Ying Jian, Shigang Chen, Can CSMA/CA networks be made fair?, Proceedings of the 14th ACM international conference on Mobile computing and networking, MobiCom 08, New York, 2008. [8] Almotairi, Khaled Hatem Inverse Binary Exponential Backoff: Enhancing Short-term Fairness for IEEE 802.11 Networks, Proceedings of the Tenth International Symposium on Wireless Communication Systems (ISWCS 2013), Germany, 3013.

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