Free Spae Path Loss of UWB Communiations Pihaya Supanakoon 1, Sathit Aroonpraparat 1, Sathaporn Promwong 1 and Jun-ihi Takada 1 Department of Information Engineering, Faulty of Engineering, King Mongkut s Institute of Tehnology Ladkrabang, Chalongkrung Road, Ladkrabang, Bangkok 10, Thailand. E-mail: {kspihay,s8011,kpsathap}@kmitl.a.th Graduate Shool of Siene and Engineering, Tokyo Institute of Tehnology -1-1-S6-4, O-okayama, Meguro-ku, 15-85, Tokyo, Japan. E-mail: takada@ap.ide.titeh.a.jp Abstrat Although the Friis formula is widely used to alulate the free spae path loss of narrowband ommuniations, it is onsidered only single frequeny. Therefore, it should be extended to alulate the free spae path loss of ultra wideband (UWB) ommuniations by onsidering the frequeny bandwidth. In this paper, the free spae path loss of UWB ommuniations is studies. The Friis formula is extended in the omplex frequeny transfer funtion. The ideal and Gaussian lters are used for ltering the spei frequeny bandwidth. The UWB free spae path loss is derived based on average power and peak power losses. The example results are shown and disussed in the paper. Key words: Ultra wideband (UWB) ommuniation, free spae path loss, Friss formula. I. INTRODUCTION Reently, ultra wideband (UWB) radio tehnology has beome an important topi for mirowave ommuniation beause its potential is low ost and low power onsumption properties [1]-[5]. The Federal Communiations Commission (FCC) [6] spei ed that UWB has a frequeny spetrum ranging from 3.1 to 10.6 GHz and a frational bandwidth greater than 0.0 or oupied bandwidth greater than 0 MHz. The power density of the UWB signal is onsidered to be noise for other ommuniation systems beause its power spetral density is below the part 15 noise limit. Therefore, UWB radio tehnology an oexist with other RF tehnologies without interferene. Moreover, UWB radio tehnology an be utilized for ommerial, short-range, low power, low ost indoor ommuniation systems suh as wireless personal area networks (WPANs) [7]. Friis free spae path loss formula [8] is widely used to alulate the free spae path loss for narrow band system. For the UWB system, the free spae path loss model based on average power loss is proposed by IEEE 80.15.3a [9]. After that, the omplex form of Friis transmission formula is developed for UWB system [10]-[11]. The losed form expressions of the UWB path loss for the free spae hannel based on peak power loss are derived [1]-[13]. But these free spae path loss models are onsidered the spei frequeny bandwidth by using ideal lter, there are no researh about ausal lter. In this paper, the free spae path loss of UWB ommuniations is studies. The Friis formula is extended in the omplex frequeny transfer funtion. The ideal and Gaussian lters are used for ltering the spei frequeny bandwidth. The UWB free spae path loss is derived based on average power and peak power losses. This paper is organized as follows. Setion and 3, the onventional free spae path loss and that of UWB ommuniations are presented. The analysis results are illustrated and ompared in setion 4. Finally, onlusions are disussed in setion 5. II. CONVENTIONAL FREE SPACE PATH LOSS Friis free spae path loss [8] is widely used to alulate the free spae path loss for narrowband ommuniations. It an be written in the db as ( ) 4πf d P L f (d) = 0 log, (1) f = (f H + )/ is the enter frequeny, d is the transmitter-reeiver (T-R) separation distane, is the veloity of light, and f H are the lower and upper frequenies, respetively. III. FREE SPACE PATH LOSS OF UWB COMMUNICATIONS For UWB ommuniations, the free spae path loss an be de ned in the two meanings. The rst is based on the average power loss of the signal spetrum in the spei frequeny bandwidth. The seond is based on the peak power loss of the signal waveform in the spei frequeny bandwidth. Conveniently, the ideal lter is used for ltering the spei frequeny bandwidth. Unfortunately, the ideal lter is not ausal. Therefore, in this paper the Gaussian lter is additionally analyzed and the frequeny bandwidth is onsidered on positive frequeny axis. The Friis free spae path loss is extended in the omplex frequeny transfer funtion for onsidering the frequeny bandwidth instead of only single frequeny. That is H f (f, d) = 4πfd e jπfd/. ()
The ideal and Gaussian lters are used for ltering the spei frequeny bandwidth. The frequeny transfer funtions of ideal and Gaussian lters are respetively de ned as { 1 fl f f H i (f) = H, (3) 0 els H g (f) = e π d e (f f), (4) d e is the 1/e harateristi deay time and has the relation on the referene level l r that is used to onsider the frequeny bandwidth. The relation between d e and l r is d e = l r πf b 0 log(e), (5) f b = f H is the frequeny bandwidth. Here, l r is set to be 3 and 10 for onsidering the 3 and 10 db bandwidths, respetively. A. Free Spae Path Loss Based on Average Power Loss The free spae path loss based on average power loss is onsidered as the average power loss of the signal spetrum in the spei frequeny bandwidth. The ideal and Gaussian lters are onsidered. 1) Ideal lter: The free spae path loss based on average power loss by using ideal lter in db an be evaluated from P L a,i (d) = 10 log H f (f, d) H i (f) df. (6) H i (f) df This equation an be derived in the losed form, that is 4πfa,i d P L a,i (d) = 0 log, (7) f a,i = f H. (8) This free spae path loss formula orresponds with that proposed by IEEE 80.15.3a [9]. ) Gaussian Filter: The free spae path loss based on average power loss by using Gaussian lter in db an be evaluated from P L a,g (d) = 10 log H f (f, d) H g (f) df. (9) H g (f) df This equation an not be diretly derived in the losed form. Therefore, the Gaussian integration formula [14] is used to estimate this equation. The losed form formula obtained from - and 3-point Gaussian integration formulas respetively are 4πfa,g, d P L a,g, (d) = 0 log, (10) 4πfa,g,3 d P L a,g,3 (d) = 0 log, (11) 1f fb f a,g, =, (1) 36f + 3fb f a,g,3 = 1 4 + 5e 3 10 π d e f b. (13) + 5 0f +3f b (0f 3f e b ) 10 π d e f b 1 f B. Free Spae Path Loss Based on Peak Power Loss The free spae path loss based on peak power loss is onsidered as the peak power loss of the signal waveform in the spei frequeny bandwidth. The ideal and Gaussian lters are onsidered. 1) Ideal lter: The free spae path loss based on peak power loss by using ideal lter in db an be evaluated from P L p,i (d) = 0 log H f (f, d)h i (f) df. (14) H i (f) df This equation an be derived in the losed form, that is 4πfp,i d P L p,i (d) = 0 log, (15) f p,i = f b ln ( ). (16) This free spae path loss formula orresponds with that proposed in [1]-[13]. ) Gaussian Filter: The free spae path loss based on peak power loss by using Gaussian lter in db an be evaluated from P L p,g (d) = 0 log H f (f, d)h g (f) df. (17) H g (f) df This equation an not be diretly derived in the losed form. Therefore, the Gaussian integration formula [14] is used to estimate this equation. The losed form formula obtained from - and 3-point Gaussian integration formulas respetively are 4πfp,g, d P L p,g, (d) = 0 log, (18) 4πfp,g,3 d P L p,g,3 (d) = 0 log, (19) f p,g, = 1f f b 1f, (0) f p,g,3 = 4 f + 4 + 5e 3 0 π d e f b ). (1) e 3 0 π d e f b ( 100f 0f 3f b
.4.4...8.6.4..8.6.4..8.6 Frequeny bandwdith (GHz).8.6 Frequeny bandwidth (GHz) Fig. 1. free spae path losses based on average power loss with enter frequeny is f = 6.85 GHz and T-R separation distane is d = 1 m along frequeny Fig.. free spae path losses based on peak power loss with enter frequeny is f = 6.85 GHz and T-R separation distane is d = 1 m along frequeny IV. ANALYSIS RESULTS First ase, UWB free spae path loss is studies by setting the enter frequeny f to be 6.85 GHz. That is the enter frequeny of UWB bandwidth for ommuniations. The frequeny bandwidth f b is onsidered from 0 MHz to 7.5 GHz whih orresponds with minimum to maximum UWB bandwidth. The T-R separation distane d is set to be 1 m. Figure 1 and show the free spae path losses based on average and peak power loss for the rst ase, respetively. The ideal and Gaussian lters with l r = 3 and 10 are onsidered. In this ase, the free spae path loss obtained from the Friis formula is onstant about.16 db whih almost the same with eah UWB free spae path loss at the frequeny bandwidth about 0 MHz. Eah free spae path loss is dereased when the frequeny bandwidth is wider. The free spae path losses based on the average power loss are lower than that based on the peak power loss. The free spae path loss with ideal lter is lowest and it is higher when uses the 3 db and 10 db bandwidth Gaussian lters, respetively. Seond ase, the UWB free spae path loss is studied by setting the lower frequeny to be 3.1 GHz. That is lowest frequeny of UWB bandwidth for ommuniations. The same frequeny bandwidth f b range is onsidered that from 0 MHz to 7.5 GHz. The free spae path loss obtained from Friss formula is shown in Fig. 3. Figure 4 and 5 show the free spae path losses based on average and peak power loss for the seond ase, respetively. The ideal and Gaussian lters with l r = 3 and 10 are onsidered. Eah UWB free spae path loss at about 0 MHz frequeny bandwidth is almost the same that obtained from Friss formula. In this ase eah free spae path loss is inreased when the frequeny bandwidth is higher. That beause in this ase the enter frequeny is inreased when Frequeny bandwdith (GHz) Fig. 3. free spae path loss obtained from Friss formula with lower frequeny is = 3.1 GHz and T-R separation distane is d = 1 m along frequeny the frequeny bandwidth is wider while the lower frequeny is onstant. The harateristis of the free spae path losses based on average power loss respet that based on peak power loss are the same with the rst ase. That are the free spae path losses based on the average power loss are lower than that based on the peak power loss. The free spae path loss with ideal lter is lowest and it is higher when uses the 3 db and 10 db bandwidth Gaussian lters, respetively. The free spae path loss with Gaussian lter an not be diretly derived in the losed form formula. Therefore, the - and 3-point Gaussian integration formula [14] are used to estimate the equation. Hene, the auray of estimation are
Frequeny bandwdith (GHz) Fig. 4. free spae path losses based on average power loss with lower frequeny is = 3.1 GHz and T-R separation distane is d = 1 m along frequeny Frequeny bandwidth (GHz) Fig. 5. free spae path losses based on peak power loss with lower frequeny is = 3.1 GHz and T-R separation distane is d = 1 m along frequeny investigated. Figure 6 shows the free spae path losses based on average power loss for the rst ase. The formula of the 10 db bandwidth has the error more than that of the 3 db bandwidth. For the 3 db bandwidth, the maximum errors of - and 3-point Gaussian formula are about 0.08 db and 0.01 db, respetively. For the 10 db bandwidth, the maximum errors of - and 3- point Gaussian formula are inreased to about 0.51 db and 0.10 db, respetively. The free spae path losses based on peak power loss for the rst ase are shown in Fig. 7. For the 3 db bandwidth, the maximum errors of -point Gaussian formula is about 0.0.5.5.5.5 Frequeny bandwdith (GHz) Fig. 6. free spae path losses based on average power loss with enter frequeny is f = 6.85 GHz and T-R separation distane is d = 1 m along frequeny.5.5.5.5 Frequeny bandwidth (GHz) Fig. 7. free spae path losses based on peak power loss with enter frequeny is f = 6.85 GHz and T-R separation distane is d = 1 m along frequeny db while that of 3-point Gaussian formula is approahed to zero. For the 10 db bandwidth, the maximum errors of - and 3-point Gaussian formula are inreased to about 0.19 db and 0.0 db, respetively. Figure 8 shows the free spae path losses based on average power loss for the seond ase. For the 3 db and 10 bandwidth, the maximum errors of - and 3-point Gaussian formula are the same with rst ase. That is about 0.08 db and 0.01 db, respetively, for the 3 db bandwidth and 0.51 db and 0.10 db, respetively, for the 10 db bandwidth. The free spae path losses based on peak power loss for
Frequeny bandwdith (GHz) Frequeny bandwidth (GHz) Fig. 8. free spae path losses based on average power loss with lower frequeny is = 3.1 GHz and T-R separation distane is d = 1 m along frequeny Fig. 9. free spae path losses based on peak power loss with lower frequeny is = 3.1 GHz and T-R separation distane is d = 1 m along frequeny the seond ase are shown in Fig. 9. For the 3 db and 10 bandwidth, the maximum errors of - and 3-point Gaussian formula are the same with rst ase. V. CONCLUSIONS In this paper, the free spae path loss of UWB ommuniations is studies. From the analysis results, the UWB free spae path loss at the frequeny bandwidth about 0 MHz is almost the same with that obtained from Friss formula. When the frequeny bandwidth is inreased, the UWB free spae path loss is lower than that obtained from Friss formula. The free spae path loss based on the average power loss is lower that that based on the peak power loss. The free spae path loss with ideal lter is lowest and it is higher when uses the 3 db and 10 db bandwidth Gaussian lters, respetively. For the Gaussian integration formula whih is used to estimate the losed form formula of the free spae path loss with Gaussian lter. The - and 3-point Gaussian integration formula has very errors whih have maximum errors about 0.5 db, and 0.1 db, respetively. Therefore, the Gaussian integration formula proposed in this paper an be welly used for evaluating the UWB free spae path loss. [5] K. Siwiak, Impat of ultra wide band transmissions on a generi reeiver, 001 Spring IEEE Vehiular Tehnology Conferene (VTC), vol., pp. 1181-1183, May 001. [6] Federal Communiations Commission, Revision of Part 15 of the Commission s Rules Regarding UWB Transmission Systems, First Report, FCC 0-, Apr. 00. [7] J. Farserotu, A. Hutter, F. Platbrood, J. Gerrits and A. Pollini, UWB Transmission and MIMO Antenna Systems for Nomadi User and Mobile PAN, Wireless Personal Communiations, no., pp. 197-317, 00. [8] H. T. Friis, A Note on a Simple Transmission Formula, Pro. IRE, Vol 34, no 5, pp. 54-56, May 19. [9] J. Foerster, Channel Modeling Sub-ommittee Report Final, IEEE P80.15-0/368r5-SG3a, Nov. 00. [10] J. Takada, S. Promwong and W. Hahitani, Extension of Friis Transmission Formula for Ultra Wideband Systems, Tehnial Report of IEICE, WBS003-8/MW003-0, May 003. [11] S. Promwong and J. Takada, Free Spae Link Budget Estimation Sheme for Ultra Wideband Impulse Radio with Imperfet Antennas, IEICE Eletronis Express, vol. 1, no. 7, pp. 188-19, July 004. [1] S. Promwong, J. Takada, P. Supanakoon and P. Tangtisanon, Path Loss and Mathed Filter Gain for UWB System, 004 International Symposium on Antenna and Propagation (ISAP), pp. 97-100, Aug. 004. [13] S. Promwong, J. Takada, P. Supanakoon and P. Tangtisanon, Path Loss and Mathed Filter Gain of Free Spae and Ground Re etion Channels for UWB Radio Systems, IEEE TENCON 004 on Analog and Digital Tehniques in Eletrial Engineering, pp. 15-18, Nov. 004. [14] E. Kreyszig, Advaned Engineering Mathematis, John Wiley & Sons, In. 1993. REFERENCES [1] J. D. Taylor, Introdution to Ultra-Wideband Radar Systems, CRC press, London, UK, pp. 670, 1994. [] OSD/DARPA, Ultra-Wideband Radar Review Panel, Assessment of Ultra-Wideband (UWB) Tehnology. Arlington, VA.: DARPA, 1990. [3] K. Siwiak, Ultra-Wide Band Radio: Introduing a New Tehnology, 001 Spring IEEE Vehiular Tehnology Conferene (VTC), vol., pp. 1088-1093, May 001. [4] K. Siwiak, K. Siwiak, Ultra-Wide Band Radio: The emergene of an Important RF Tehnology, 001 Spring IEEE Vehiular Tehnology Conferene (VTC), vol., pp. 1169-117 May 001.