Multipath Fading Effect on Spatial Packet Loss Correlation in Wireless Networks

Transcription

1 Multipath Fading Effect on Spatial Packet Loss Correlation in Wireless Networks Hamid R. Tafvizi, Zhe Wang, Mahbub Hassan and Salil S. Kanhere School of Computer Science and Engineering The University of New South Wales Sydney, Australia Abstract Spatial packet loss correlation is important for error control protocols in wireless multicast and broadcast communications. This paper quantitatively studies the spatial packet loss correlation in wireless networks using a series of experiments conducted in different environments with different impact of multipath fading on wireless links. It is found that environments with more multipath opportunities exhibit less spatial correlation. It is also observed that spatial correlation is strongly dependent on the packet reception rate. Based on the experimental data, an empirical model is proposed to estimate the level of spatial loss correlation as a function of packet reception rate. It is shown that the empirical model yields accurate estimates of spatial packet loss correlation for different environments. I. INTRODUCTION Spatial packet loss correlation of wireless multicast and broadcast communications can be explained by the example in Fig. 1 in which a transmitter sends a broadcast (or multicast) packet to two receivers (R 1 and R 2 ). Let us define event A as the packet is lost by R 1 and event B as the packet is lost by R 2. The spatial packet loss correlation is a measure of the probabilistic dependency between A and B. If A and B are independent events, the packet loss is spatially uncorrelated, otherwise, the packet loss is spatially correlated. Spatial packet loss correlation is important in the design and evaluation of error control protocols for wireless broadcast and multicast communications. As an example, it has been shown in [1] that if packet loss is spatially uncorrelated, Forward Error Control (FEC) outperforms the Automatic Repeat-reQuest (ARQ), while the difference between the two error control protocols disappears if the packet loss is correlated. Researchers have demonstrated [2], [3] that it is possible to significantly improve the performance of retransmissions by using some forms of network coding providing that the spatial packet loss is not fully correlated. Due to these findings, it is important to better understand the phenomenon of spatial packet loss in wireless networks. Previous studies have presented somehow inconsistent results for spatial packet loss correlation. Reis et al. [4] observed that packet loss between receivers is roughly independent, while other studies ([1], [5] and [6]) found packet loss to be spatially correlated. The inconsistency of these observations calls for deeper studies to identify the circumstances under which spatial packet loss correlation exists and the factors affecting the level of this correlation. Figure 1. Example of wireless broadcast communication. A recent study [7] has found that the level of spatial packet loss correlation is a function of signal strength. When the signal strength is very low, the packet loss is uncorrelated while it becomes more correlated when the signal strength is increased. In this paper, we conducted more experiments in different indoor and outdoor environments to analyze the effect of multipath fading on spatial loss correlation. The contributions of this paper are twofold. First, we found that besides the signal strength, multipath fading is another factor affecting the spatial packet loss correlation. For the same signal strength, packet loss is spatially less correlated in environments with more multipath opportunities. Second, although the spatial packet loss correlation is affected by both signal strength and multipath fading, we found that the level of correlation can be estimated from the packet reception rate (PRR) alone without knowing the exact signal strength and multipath fading. We propose an empirical model to estimate spatial loss correlation as a function of PRR. The remainder of this paper is organized as follows. Section II describes the experiment setup. Section III presents and analyses the impact of multipath fading on spatial loss correlation. The empirical model to estimate spatial packet loss correlation as a function of PRR is derived in Section IV. Finally, the conclusion and future works are drawn in section V /11/$ IEEE

2 II. EXPERIMENT SETUP The experiment setup consisted of three Yawara ALIX3 single-board computers [8]. Each of these computers was equipped with a wireless card with Atheros AR5112 chipset and an omni directional antenna. The wireless cards were running at a mode and 5.18GHz. The bit rate was set to 6Mbps, which is the default value for broadcast packets in a standard. The three single-board computers were placed as shown in Fig. 2. The two receivers were located within 5cm of each other (less than the wavelength of the radio signal: 5.8cm) so that the communication channel conditions for the two receivers would remain as similar as possible. S Figure 2. Experiment Setup We conducted four experiments at three different locations. The first experiment (Indoor_1) was in a meeting room with a table, several chairs, a video projector and a screen. The distance between the transmitter and receivers (d) was 4m in this setting. The second experiment (Indoor_2) was in a student research lab with desks, office cubical walls, and large screen monitors. This time we moved the transmitter further and set the separation between the transmitter and receivers at d=9m. The third and fourth experiments (Outdoor_1 and Outdoor_2) were conducted in a quiet roof-less parking lot, with a few parked cars far away from the single board computers. The two outdoor experiments had different transmitter-receiver separation (d=4m in Outdoor_1 and d=9m in Outdoor_2). Table I summarizes the specifications of conducted experiments. In all experiments, the transmitter node was set to send broadcast packets at different power levels (TX_Power). The transmission sessions started at TX_Power= 16 dbm and decreased by 1dBm in every session until TX_Power = 5dBm. For each power level 20,000 packets, with a length of 100 bytes each, were transmitted. TABLE 1. The 4 experiments to study the effect of multipath fading. Experiment name Location Distance between sender and receivers Indoor_1 Meeting Room 4m Indoor_2 Student Lab 9m Outdoor_1 Parking lot 4m Outdoor_2 Parking lot 9m d d R 2 R 1 5cm The difference in the indoor and outdoor experiments was in the number of reflective objects which were surrounding the receiver nodes. This dissimilarity of physical obstacles imposes different multipath fading impacts on the packet reception patterns of receivers [9]. Hence, it would provide a setting for investigation of these effects. III. SPATIAL LOSS CORRELATION In order to study the packet loss correlation between receivers, we adopted the Entropy Correlation Coefficient (ECC) as the most appropriate metric [10]. This is because it indicates the mutual statistical dependency between two receivers and it is commutative (i.e. ρ12 = ρ21 ) [7]. Considering the packet loss or reception events for receivers R 1 and R 2 as X and Y respectively, the ECC can be defined as: ρ XY 2Ι XY = Η +Η Where respectively and Ι XY is mutual information between them. We have: X H X and HY are entropy of receivers R 1 and R 2 H ( X) = p( x)log p( x) x { 1,0} H ( Y) = p( y)log p( y) { } { } x 1,0 y 1,0 y { 1,0} p( xy, ) I( X; Y) = p( x, y)log p ( x ) p ( y ) X = 0 when a packet is received by receiver R 1 and X = 1 if it is lost, similarly Y = 0 or 1 if receiver R 2 receives or loses a packet respectfully. Having conducted the four experiments, shown in Table I, we observed the changes in the ECC as a result of the environmental change. Pairwise comparison of ECC versus transmission power in {indoor_1, Outdoor_1} (shown in Fig. 3) and {Indoor_2, Outdoor_2} (shown in Fig. 4), indicates that ECC rises when the transmission power increases. This is consistent with the observation made in [7], what is interesting here is that the ECC curves for outdoor locations are above those in indoors. Taking the average value of ECC across all transmission sessions, we found that the average correlation is higher by 73% and 63% in Outdoor_1 and Outdoor_2 respectively. These findings are still valid when comparing Indoor_1 against Outdoor_2 (Fig. 5), and Indoor_2 against Outdoor_1 (Fig. 6). The average ECC is remarkably higher (98%) in outdoor_2 when comparing it with Indoor_1. Similarly the average entropy correlation in Outdoor_1 is 43% higher than that in Indoor_2. Y (1) (2) (3) (4)

3 Figure 3. ECC in Indoor and Outdoor environments at d = 4m. Figure 4. ECC in Indoor and Outdoor environments at d = 9m. Figure 5. ECC in Indoor_1 and Outdoor_2 environments. Figure 6. ECC in Indoor_2 and Outdoor_1 environments. The difference between Indoor and outdoor experiments, conducted in this study, stems from the environmental differences. The higher density of obstacles indoors can cause the effect of multipath fading more severe in those locations. Less number of multipath components in outdoor can lead to more dependent packet loss (reception) patterns between the two receivers. To further investigate the accuracy of these findings, we analyzed the conditional entropy of the two receivers. Entropy can be defined for any probability distribution and it indicates the value of self-information about a random variable. The conditional entropy quantifies the remaining entropy of a random variable given that the value of another random variable is known. Furthermore mutual information between two random variables is a measure of the amount of information one random variable contains about the other [11]. It is defined as the relative entropy between the joint and the product distribution of random variables. This definition was given in (4). However, to find out how the knowledge of one receiver s packet loss entropy would affect their mutual information, we need to represent mutual information as a function of conditional entropy. By rewriting (4), using the definition of conditional probability, the relationship between mutual information and conditional entropy can be derived (proof in [11]) as: I( X; Y) = H( X) H( X Y) = H( Y) H( Y X) (5) In (5), H(X Y) represents the amount of reduction in the uncertainty of random variable X when calculating its mutual information with random variable Y. Fig. 7 illustrates H(X Y) in Indoor_1 and Outdoor_1, and Fig. 8 shows H(X Y) in Indoor_2 and Outdoor_2. The Conditional Entropy in both indoor environments is higher than those in outdoor. This shows the higher dependency of the packet loss (reception) events between the two receivers located outdoors. In the environment, which is less prone to multipath fading, the packet loss status of adjacent receivers seems to be more mutually related.

4 Figure 7. H(X Y) in Indoor_1 and Outdoor_1 at d = 4m. Figure 8. H(X Y) in Indoor_2 and Outdoor_2 at d = 9m. IV. PACKET RECEPTION RATE Evidence of our experiments showed that the spatial correlation can vary significantly as a result of multipath fading. Since practical measurement of multipath fading is not an easy task [12], it was of interest in our study to find an empirical model for representing the ECC which would be consistent for all types of transmission channels. For that, the ECC has to be defined as a function of a random variable which is not depended on the characteristics of the wireless link and environmental impacts. We found that ECC as a function of PRR satisfies such requirements and provides a reliable estimation of the spatial loss correlation in any given environment irrespective of the level of fading. Fig. 9 shows ECC as a function of PRR in all four experiments. Using MATLAB curve fitting toolbox [13], we found (6) as the best fit (SSE: , R-square: ) for estimating ECC as a function of PRR. y = x 2 α + βx+ γ The coefficients with 95% confidence bounds have been estimated as: α = β = γ = 1799 (-1.087e+005, 1.087e+005) (-3.528e+007, 3.528e+007) (-3.535e+007, 3.535e+007) (6) (7) For packet reception rate r, the ECC ( ρ ) can be represented as: ρ 5.527, r < , r = r r+ (8) Figure 9. Entropy correlation coefficient as a function of packet reception rate. Equation (8) indicates the threshold for which ECC follows the proportional relationship with PRR shown in (6). Mutual correlation goes to 1 when PRR is greater than or equal to this threshold. Conducting the same analyses for a wider range of experiments will lead to more accurate empirical models which can clarify ECC between receiver nodes in a cluster. This would be beneficial for proposing more practical local error recovery protocols.

5 V. CONCLUSION AND FUTURE WORKS We have studied spatial packet loss correlation for wireless broadcast communications in different environments with diverse impact of multipath fading. It has been found that with the same signal strength, packet loss is more correlated in environments with less multipath opportunities. Using experimental data, we have demonstrated that the spatial loss correlation for any environment, with different level of multipath fading, can be accurately estimated by simply observing the packet reception rate. Our conclusions are based on experiments involving only four different environments and two different receivers. As such, these should be considered as preliminary findings. More comprehensive experiments should be carried out in future to verify the validity of these preliminary findings. Also, at this stage, we do not have clear explanations for why signal strength, multipath, and packet reception rates impact spatial loss correlation. Further investigations therefore are needed to obtain these explanations. In particular, why the spatial correlation shoots up for very high packet reception rates (very small packet loss probabilities) remains an interesting observation to be explained. Mathematical Statistics and Probability, Tashkent, USSR, [11] T. M. Cover and J. A. Thomas, Elements of Information Theory, John Wiley & Sons, [12] D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, [13] Curve fitting toolbox 2.2. The MathWorks, Inc. [Online]. Available: REFERENCES [1] J. Lacan and T. Perennou, Evaluation of Error Control Mechanisms for b Multicast Transmissions, in 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, [2] D. Nguyen, T. Tuan, N. Thinh, and B. Bose, Wireless broadcast using network coding, in IEEE Transactions on Vehicular Technology, vol. 58, no. 2, pp , [3] Z. Wang, M. Hassan, and T. Moors, Efficient loss recovery using network coding in vehicular safety communication, in IEEE Wireless Communications and Networking Conference, WCNC 2010, Sydney, Australia, [4] C. Reis, R. Mahajan, M. Rodrig, D. Wetherall, and J. Zahorjan, Measurement-based models of delivery and interference in static wireless networks, in Proceedings of the 2006 conference on Applications, technologies, architectures, and protocols for computer communications. Pisa, Italy: (ACM SIGCOMM 06), [5] D. Salyers, A. Striegel, and C. Poellabauer, Wireless reliability: Rethinking packet loss, in International Symposium on a World of Wireless, Mobile and Multimedia Networks, WoWMoM 2008, pp. 1 4, June [6] J. Heide, M.V. Pedersen, and F.H.P. Fitzek, Know Your Neighbour: Packet Loss Correlation in IEEE b/g Multicast, in 4th International Mobile Multimedia Communications Conference (ACM MobiMedia 08), [7] Z. Wang, M. Hassan, and T. Moors, A study of spatial packet loss correlation in wireless networks, in 35th Annual IEEE Conference on Local Computer Networks (LCN 2010), Denver, Colorado, USA, [8] [9] D. Aguayo, J. Bicket, S. Biswas, G. Judd and R. Morris, Link-level Measurements from an b Mesh Network, SIGCOMM 04, Aug. 30 Sept. 3, 2004, Portland, Oregon, USA. [10] I. Virtanen and J. Astola, On entropy-based dependence measures for two and three dimensional categorical variable distributions, in Proceedings of The First World Congress of Bernoulli Society for