Shadowing Correlation Model for Indoor Multi-hop Radio Link in Office Environment

Transcription

1 JAVA, International Journal of Electrical Electronics Engineering Volume 4, Number, April 26 Shaowing Moel for Inoor Multi-hop Raio Link in Office Environment Mohamma Fahli Inustrial Engineering Department Universitas Putra Inonesia YPTK (UPI YPTK) Paang, Inonesia Puji Hayani, Gamantyo Henrantoro 2, Prasetiyono Hari Mukti 3 Electrical Engineering Department Institut Teknologi Sepuluh Nopember (ITS) Surabaya, Inonesia gamantyo@ee.its.ac.i, puji@ee.its.ac.i 2, prasetiyono@ee.its.ac.i 3 Abstract Propagation environment greatly affect the performance of wireless network. The existence of obstacles between transmitter receiver antennas provie shaowing effect to the transmitte signal. In multi-hop raio link, any link pairs experience shaowing effect that can be correlate if the links have a similar propagation environment. Various stuies have shown that correlate shaowing has significant impacts on wireless network s performance. This paper iscusses shaowing correlation of measure two-hop raio link. We propose moels that can be use to preict shaowing correlation coefficient of link pairs using eterministic stochastic formulas. Keywors shaowing, correlation, multi-hop raio link I. INTRODUCTION Wireless communication system is strongly affecte by propagation environment, so as in inoor office environment. Walls, furnitures equipments mae of material consisting metal will give rise to multipath propagation shaowing to the transmitte signal. So the receive signal will be romly fluctuate. Romly fluctuate receive signal cause by shaowing is ue to the existence of obstacles between transmitter receiver antennas. There are certain conitions where shaowing in a raio-link has correlation with the one in the other raio-link, e.g. shaowing is cause by the same obstacles []. Various stuies shown that correlate shaowing can affect the performance of a wireless network. Stuy [2] shown that when correlate shaowing in multi-hop network is ignore, then we will be get an inaccurate result of outage probability analysis. Therefore, we nee a mathematical moel of correlate shaowing so that we can estimate the correlation coefficient of shaowing effect for wireless networks in orer to analyze esign reliable communication system. Previous stuies have propose the correlation moels of shaowing with variety network scenarios. Stuy [3] have propose correlate shaowing moel in the form of istance as an exponential function at MHz 7 MHz. This moel verifie at outoor urban environment, so it cannot escribe the correlate shaowing in networks with inoor scenario. Correlate shaowing characteristics for inoor scenarios have verifie in [2], however the obstacles on these measurements were eliberately set in the environment. Other stuy about link correlation can be foun in [4] where the paper iscusse about correlation among converging raio link in terms of the irection of arrival (DOA) irection of eparture (DOD) of multipath signals. This paper iscusse the correlation of shaowing of two raio links which perform multi-hop correlate shaowing moels for multi-hop network that consisting of three noe at 2.4 GHz b in office environment. These three noes are noe i as transmitter, noe j as relay, noe k as receiver. Noe k can receive information from noe i in two ways. First, noe k receive information from noe i through relay k. The secon way is noe k receive information irectly from noe i. There are three raio link pairs that can be correlate in this situation. It can be seen in Figure that these link pairs are link with link, link with link, link with link. The moeling base on measurement ata of receive signal power in office environment. Basic statistical techniques are use to ekstract the shaowing values from the measure receive signal as istance function, correlating this values for all link pairs. All correlation coefficient that has been obtaine are moele as general form of statistical moel, so we can estimate correlation coefficient for other office or network moe. The correlation moels that will be propose are in the form of eterministic stochastic moels. Deterministic moels are base on istance, angle, arrival istance ratio. Shaowing measurements uses the inoor scenario at office environment. The obstacles in this measurements is natural, by allowing the conition of various kins of the furnitures in the location of measurements as it is. It aims to obtain a vali correlate shaowing characteristics for inoor location in the Figure. Multi-hop Network [2] 25

2 JAVA, International Journal of Electrical Electronics Engineering Volume 4, Number, April 26 office environment. In orer to construct the correlate shaowing moels for inoor multi-hop network, this stuy will first create a moel for shaowing it s average path loss. A. Average Path Loss Average path loss which represents average signal attenuation as a positive quantity measure in B, is efine as the average ifference (in B) between the effective transmitte power the receive power as istance function, can be expresse as [5]: PL ( B) PL( ) n log In equation (), PL ( ) is average path loss at reference istance, where reference istance shoul be at far fiel region of the transmitting antenna, n represents the path loss exsponent that relate to the attenuation s slope of signal power, are the istance of antennas istance of refference location respectively. Equation () is ientical to the equations of a straight line where PL (B) is the value at y axis, PL ( ) represents y axis intercept, n log(/ ) represents slope value at x axis respectively. B. Shaowing Average path loss moel provie loss preiction base on istance height of antenna, hence the loss on many channels having the same istance the same antennas height will be the same too. Actually, although in static conition, the loss variation is occure ue to the variation of objects near transmitter receiver objects that acts as obstacles. This loss variation is calle faing []. Faing can be consiere as small-scale faing or multipath faing large scale faing or shaowing. By consiering large scale faing cause by any obstacles, the loss at istance given by [2]: () PL ( B) PL ( B) Z ( B) (2) Where PL (B) enotes path loss at istance Z (B) enotes path loss fluctuation cause by large scale faing or shaowing. The variation of shaowing effect Z (B) will be occur after the istance between transmitter receiver change equally to the obstacle s imention [6]. By substituting equation () to (2), loss at istance is given by: C. Correlate Shaowing Shaowing in any of two links can be correlate if the links have obstacles which are similar [2]. This conition can bee seen in Figure 2. Accoring to Figure 2, link link 2 may have shaowing with strong correlation, because they have the same obstacle. Whereas link link 3, also link 2 link 3 can have shaowing with low correlation because they have ifferent obstacles. If there are two raio links X Y X 2Y2 with shaowing value S S 2 respectively, then shaowing correlation coefficient can be calculate by [7]: where enotes correlation coefficient of shaowing, 2 between link X Y 2Y2 S S 2 is the expectation of shaowing value in both links, VAR S X, VARS 2 enotes variance of shaowing in link X Y X 2Y2 respectively. In orer to estimate the shaowing correlation coefficient in a multi-hop network, it requires a moel that mathematically feasible, so that the moel can be use for simulations analysis [7]. In this stuy, the correlation of shaowing will be moelle as eterministic stochastic moels. With eterministic moel, the correlation coefficient of shaowing can be estimate base on some variables e.g absolute istance or angle. In stochastic moels, we can only estimate the probability of correlation coefficient of shaowing. Base on Figure 3, eterministic moel for correlate shaowing can be establishe in three variables: [7]:. Absolute istance of Y Y 2, r r2 2. Angle, r r 2 3. Arrival istance ratio, S S 2 S VARS,2 (4) VAR / lnln r 2 R log r r / r ln 2 2 PL ( B) PL( ) n log Z ( B) (3) Where PL (B) enotes path loss at istance, PL ( ) is average path loss at reference istance, n represents the path loss exsponent, are the istance of antennas istance of refference location respectively, Z (B) enotes the shaowing variations. Figure 2. Link Conition With Different Shaowing [2] 26

3 JAVA, International Journal of Electrical Electronics Engineering Volume 4, Number, April 26 TABLE I. Path Length (Meter) Arrival Distance Ratio (B) Figure 3. Variables of Determnistic Shaowing Moel [7] II. MEASUREMENT SYSTEM AND SET UP A. Measurement Set Up Multi-hop network which will be observe have three noes i, j, k as shown in Figure, where noe i assume to be a transmitter, noe j as relay noe k as receiver. So there Angle (Deg) are three link pairs that can be correlate, they are link with link, link with link, link with link. In orer to moeling shaowing correlation coefficient in angle, istance, the ratio of arrival istance, then the measurement will be performe on a wie variety of link moe, where link moe is the setup of transmitter, relay receiver position that we mae with variate angle, istance, the ratio of arrival istance (as shown on Figure 3). Variations of these three variables can be seen in Table. Each network scheme will be measure five times at ifferent positions, so that the measurement results can represent the real conition of signal propagation in inoor office environments. One example of measurement scheme can be seen in Figure 4. Distance (Meter) Path loss measurements carrie out on the 3r floor of builing B in electrical engineering ITS Surabaya. The aim of this location is to get a moel that can represent the real correlate shaowing in inoor office environment. Measurements site plan can be seen in Figure 4. DISTANCE, ANGLE, AND ARRIVAL DISTANCE RATIO VARIABLES ON VARIOUS NETWORK SCHEMES Scheme Data processing is base on transmitte receive power by WARP. Power output from WARP is.2 Bm. In orer measurements can be performe in a longer istance, then the signal power will be amplifie with a Wifi amplifier that has 5 B gain, so that the total transmit power is 34.2 Bm. The evices that will use to measure the path loss are: WARP (Wireless Open Access Research Platform) software efine raio, omniirectional antennas, a computer with MATLAB, Gigabit Ethernet switch, UTP cable, Wifi amplifier. B. Measurement Campaigns At each network scheme presente in Table, there are three links that shoul be measure. Due to limitations of the measurement evices, then each link is measure one by one, by terms conition of propagation environment oes not change uring the measurement process. The measuring process on each link can be illustrate in Figure 5. The Signal that will use to measure the path loss is a sinusoial signal at 2.4 GHz b. Accoring to IEEE 82. communications star, the 2.4 GHz b is ivie into fourteen channels. Base on the survey of frequency use in measurement location, it can be seen that the channel to channel 3 has been use for university s internet connection. In orer to avoi interference, measurements will be performe on channel 4 (2.484 GHz ) that is not use aroun the measurement locations. The use total frequency is sum of carrier frequency (channels 4) baseb frequency. The use baseb frequency is 8 MHz, so the total signal frequency is 2.42 GHz. The measurement process begins by iviing each link into several measurement points, inicate by point, 2,... n in Figure 5. It aims to get the variance of shaowing on each link. The istance of each measurement point at least 4λ. This istance is selecte because shaowing expecte to occur in the isplacement istances equally to the obstacle s imension that is expecte as far as 4λ. 27

4 JAVA, International Journal of Electrical Electronics Engineering Volume 4, Number, April 26 Figure 5. Distribution of Measurement Points Each measurement point is ivie into four subpoints with a istance of 5 cm each, represente by point na, nb, nc n in Figure 5. It aims to get local mean receive power averaging the effect of multipath. Local mean receive power obtaine by averaging the receive power in the four subpoints of measurement. The process of measurement ata collection begins by putting transmitter at point Tx receiver at point. Receiver antenna is place at subpoint a. Then the signal transmitte from the transmitter the signal power receive by receiving antenna is store into the computer. Once the measurement ata is store followe by moving the position of receiving antenna to subpoint b to. After the measurement is one at point a, b, c, receiver is move to point 2, its antenna is place at subpoint 2a. The measuring process such as at point is repeate. This process is continue until the receiver is at position n. Further measurements with the same process carrie out on other links network schemes. III. MEASUREMENT RESULTS AND DATA PROCESSING A. Average Path Loss Moel After all ata have been obtaine, then this ata is analyze to create it s relate shaowing moel. The first step is to compute the path loss exponent of average path loss moel. Average path loss moel is obtaine by processing the channel loss ata that obtaine from measurements using linear regression techniques, so we get a straight line equation that is ientical to equation (). Channel loss obtaine by fining the ifference of transmit power receive power in logarithmic scale. Result of linear regression of channel loss can be seen in Figure 6. Loss (B) Figure 4. Site Plan of Measurement Location Distance Log Measure Loss Average Path Loss.2 Figure 6. Path Loss as Distance Function 28.4

5 JAVA, International Journal of Electrical Electronics Engineering Volume 4, Number, April 26 The straight line at Figure 6 has a slope of intercept y axis at Base on this conition, obtaine an equation of average path loss moel as follows: PL ( B) log (5) From equation () (5), the path loss exponent value is This value is larger than free space conition, leaing to large channel loss with increasing istance between transmitter receiver antennas. This is cause by measurements conucte in a room with large number of obstacle objects, such as furnishings in the room. Moreover measurements also carrie out in two ifferent rooms, so the signal is blocke by a wall that restricts both rooms. B. Shaowing Moel Shaowing value in this stuy obtaine from the ifference between loss that has been obtaine from measurements loss from average path loss moel. The obtaine shaowing values will be moele base on average value, star eviation, it s relate probability function. Shaowing probability function can be etermine by plotting it s relate PDF (Probability Density Function) graphic. The istribution moel obtaine from this PDF chart will be verifie with Kolmogorov-Smirnov test methos (KS Test). The shaowing graphic in logarithmic function can be seen in Figure 7. Obtaine shaowing moel has an average value of B with a star eviation of 38 B. PDF chart of this shaowing moel can be seen in Figure 8. Base on Figure 8 it can be seen that the PDF of shaowing chart obtaine has a normal curve shape, so that it can be sai that the shaowing value obtaine has a normal istribution in logarithmic scale. This istribution moel is verifie by the KS test, which compares the CDF (Cumulative Distribution Function) of shaowing value with CDF of normal istribution theory, seek the maximum ifference. The CDF maximum ifference is fin using [8]: x F x D F (6) max 2 ( i) x ( i ) Where D 2 represent the maximum ifference of emprical theoritical CDF, F [x (i)] Fx[x (i)] represents empirical theoritical CDF respectively. The maximum ifference that allowe by KS test with large ata samples is efine with [8]:.22,. n.36 c,,.5 (7) n n.63,. n Where c n,α is the allowe maximum CDF ifference, n is the number of samples, α represents significant egree. When D 2 < c n,α it can be sai that the empirical CDF has a normal istribution. The maximum CDF ifference that was obtaine (D 2) is.2 from totally 648 samples of CDF values. The maximum Shaowing (B) Distance Log Figure 7. Shaowing Graphic ifference allowe by KS test with 648 samples significant Probability CDF Shaowing (B) Figure 8. Shaowing PDF Curve. Empirical CDF Theoritical CDF Shaowing (B) Figure. Shaowing CDF Empirical vs. Theoritical egree of,5 is.53. It can be seen that D 2 < c n,α. So Thus verifie that the obtaine shaowing moel has a normal istribution in logarithmic scale. This CDF graph can be seen in Figure. 2

6 JAVA, International Journal of Electrical Electronics Engineering Volume 4, Number, April 26 C. Correlate Shaowing After shaowing values has been obtaine, then calculate the correlation coefficient of shaowing on all link pairs using equation (4). Then shaowing correlation coefficient in all link pairs are moelle as eterministic stochastic moels. Deterministic moel of correlate shaowing in this paper is base on istance, angle, arrival istance ratio variables. The istribution of shaowing correlation coefficient to these three variables can be seen in Figure,, 2. Base on Figure,, 2 can be seen that shaowing correlation coefficient has a rom istribution to the istance, angle, arrival istance ratio variables. The resulting rom istribution cannot be etermine in mathematical moels, so it can be conclue that istance, angle, arrival istance ratio oes not affect the shaowing correlation coefficient on inoor multi-hop network in an office environment Distance (m) Figure. Shaowing Coefficient as Distance Function Arrival Distance Ratio (B) Figure 2. Shaowing Coefficient as Arrival Distance Ratio Function Stochastic moel of correlate shaowing is expresse by it s relate probability istribution. PDF chart of all shaowing correlation coefficients that has been obtaine can be seen in Figure 3. Base on Figure 3 it can be seen that the correlation coefficient of shaowing has a shape of PDF curve that similar to a truncate Gaussian istribution with an average of.2 a star eviation of.45. This istribution was verifie using the KS test with CDF graph in Figure 4. The maximum CDF ifference that was obtaine (D 2) is.56 from totally 87 samples of CDF values. The maximum ifference allowe by KS test with 87 samples significant egree of,5 is.458. It can be seen that D 2 < c n,α. So it can be verifie that the correlation coefficient of shaowing on inoor multi hop network in the office environment has a truncate Gaussian istribution, with mathematical expression in (8). 2.2 /.32 ρ Pr( ) exp,.45 2 (8) Angle (eg) Figure. Shaowing Coefficient as Angle Function Figure 3. Shaowing Coefficient PDF Curve 3

7 JAVA, International Journal of Electrical Electronics Engineering Volume 4, Number, April 26 CDF Empirical CDF Theoritical CDF Figure 4. Shaowing Coefficient CDF Empirical vs. Theoritical D. Verification of Channel Physical Conition Base on the correlate shaowing ata that has been obtaine, the amount of shaowing correlation coefficient in the office environment is very varie. There are link pairs that strongly correlate, either positive or negative correlation, there are also link pairs are almost uncorrelate. The variation of correlation coefficient is strongly influence by it s relate physical conition of propagation environment. Base on the measurement results, it is known that a link pair positively correlate ue to the similarity of obstacle s conition that passes by this link pair. For example, if a link pair together pass a wall, then shaowing effects that occur in that link pair can has a highly positive correlation. A highly negative correlation cause by the conition of the obstacles that passe by a link pair are very ifferent. For example when a link oes not pass an obstacle, while other link passes too many obstacles. Base on the measurement results can be known that high negative correlation also cause by the ifferences of link pair length. Shaowing effect on a link pair is not correlate if the obstacles on that link pair has ifferent characteristics, but the ifference is not as much on high negative correlation conition. For example, Shaowing effect on link link 2 are not correlate if link passes a wall as an obstacle while link 2 pass two walls respectively. IV. CONCLUSION Base on measurement ata processing results, obtaine a path loss moel with path loss exponent of Shaowing moel that has been obtaine has a log normal istribution with average of B star eviation of 38 B. The istance, angle arrival istance ratio are not affecte the shaowing correlation coefficient of inoor multihop network in office environment. The shaowing correlation of inoor multi-hop network in office environment has a stochastic moel with truncate Gaussian istribution. This moel has an average value of.2 star eviation of.45. ACKNOWLEDGMENT The authors wish to thank Ministry of Research, Technology Higher Eucation of the Republic of Inonesia that has supporte this research. REFERENCES [] Les Barclay, Propagation of Raiowaves, 2n e. Institution of Engineering Technology: Lonon, 28. [2] Neal Patwari, Piyush Agrawal. Effects of Correlate Shaowing: Connectivity, Localization, RF Tomography, Information Processing in Sensor Networks, 28. IPSN 8. International Conference on April 28. [3] M. Gumunson. Moel For Shaow Faing in Mobile Raio Systems, Electronics Letters, Vol. 27, No. 23, 7th November. [4] Puji Hayani, Gamantyo Henrantoro. Characterization of DOD DOA correlation among converging inoor raio links by applying reciprocity principle, ICT Convergence (ICTC), 2 International Conference on 28-3 Sept. 2. [5] Theoore S. Rappaport, Wireless Communications Principle Practice, 2n e. Prentice Hall: New Jersey, 22. [6] Anrea Golsmith, Wireless Communications. Cambrige University Press: New York, 25. [7] Sebastian S. Szyszkowicz, Halim Yanomeroglu, Jhon S. Thompson. On the Feasibility of Wireless Shaowing Moels, IEEE Transactions on Vehicular Technology, Vol. 5, No., November 2. [8] T. T. Soong. Funamentals of Probability Statistics for Engineers, Southern Gate, Chichester, Engl: John Wiley & Sons Lt, 24. 3