Radi Siene, Vlume 36, Number 6, Pages 1393-1403, Nvember-Deember 2001 Experimental and mputer simulatin studies f frequeny seletive fading in terrestrial line-f-sight mirwave links Xingwen Zha, 1 Yerng Zhang, 2 Pertti Vainikainen, and Xie Yixi 3 Abstrat. Rummler's three-ray mdel is used fr multipath prpagatin in mdified spherial stratified air. The time delays f the three rays are btained by using the ray traing methd. Bth the time delays and the amplitudes are related t the mdified refrative index gradients inside and utside the layer. Beause f the randm variatins f the mdified refrative index gradients, the mputer simulatin methd f multipath fading is studied by using the Mnte Carl methd. The experiments f frequeny seletive fading are perfrmed in China n a 48.4 km terrestrial mirwave link. The statistial distributins f flat fading, in-band dispersin and the effet f diversity reeptin and their rrelatins are studied bth by mputer simulatins and by experiment. On the basis f data measured in China and Japan, and mputer simulatin results, the rrelatin between the equal prbability values f the in-band linear amplitude dispersin and flat-fading depth due t multipath prpagatin is analyzed. An exellent linear relatinship is fund between them. 1. Intrdutin harateristis f the signal fading in theretial Multipath prpagatin during anmalus atm- studies. The analyti expressins are hard t develp, spheri nditins an give rise t destrutive inter- and thus many assumptins and apprximatins must ferene at the reeiving antenna. The resultant signal be made. Cmputer simulatin has brught new flutuates and may be redued t pratially zer fr sends at a time. The multipath prpagatin, being pssibilities t study FSF. It an nt nly make it pssible t avid mpliated mathematial analysis an interferene phenmenn, auses frequeny sele- and unneessary assumptins and apprximatins but tive fading (FSF) whih is in-band amplitude disper- als prvide the fading and dispersin statistis easily sin. FSF is the main fatr in the quality degradatin [Zhang, 1990; Zhang and Xie, 1991; Zha et al., 1996]. f medium- and high-apaity digital mirwave mmuniatin systems. It has been shwn that the bit Sine 1970, in Frane, Ameria, Japan, and China, muh theretial and experimental wrk n FSF has errr rate (BER) f a ertain mirwave mmuni- been perfrmed. Fr example, Sandtrg [1980] simuatin system is lsely rrelated t in-band linear amplitude dispersin (LAD), whih is defined as the abslute value f the pwer differene between the lated the amplitude and relative time delays f the three rays n the basis f experimental samples f transfer funtin; Sylvain and Lavergnat [1985] studmaximal and minimal frequenies in band [Serizawa ied the statistial mdel f transfer funtin by using and Takeshita, 1983]. The typial physial ray mdels experimental data; Vigants [1975] studied spae and are given by Rurnrnler [1979] and Greenstein and frequeny diversity reeptin theretially and exper- Czekaj [1980], but it is diffiult t btain the statistial imentally and shwed the diversity imprvement t FSF. Higuti and Mrita [1982] studied the diversity effets during multipath fading; the pwer distribu- 1Radi Labratry-Institute f Digital Cmmuniatins, Hel- tins with single- and diversity signal reeptin were sinki University f Tehnlgy, Esp, Finland. fund. Sine 1985, sme prgress has been ahieved 2Labratry f Wireless Cmmuniatin and Eletrmagneti in this field f researh in China. At first, mputer Cmpatibility, Nanjing University f Psts and Telemmuniasimulatin methds have been develped and prtins, Nanjing, China. 3China Researh Institute f Radiwave Prpagatin, Xinxiang, grammed fr the researh f FSF [Zhang, 1990; China. Zhang and Xie, 1991; Zhang et al., 1994; Zha et al., 1995, 1996]. Crrespnding t the mputer simula- Cpyright 2001 by the Amerian Gephysial Unin. Paper number 2000RS002608. 0048-6604/01/2000RS002608511.00 tin results, large-sale FSF experiments were perfrmed during the summer f 1992 [Zhang et al., 1994]. The statistial harateristis f flat fading (the 1393
1394 ZHAO ET AL.' FREQUENCY SELECTIVE FADING STUDIES 84 m 84 m 49.3 m (Xintai) Figure 1. Prfile f the experimental mirwave link. 48.4 km (Handan) fading at the enter frequeny), in-band LAD, inband maximal amplitude dispersin (MAD) (whih is defined as the differene between the deepest and shallwest fading in band), diversity effet, and the rrelatins amng them have been btained bth by experiments and mputer simulatins. Zhang [1990] used the Paem 2 measurement data frm Frane 2. Experiment Setup The prfile f the experimentalink with the path length f 48.4 km is presented in Figure 1. The height f the transmitting antenna is 84 m. Spae diversity is used fr the reeiving antennas by using tw vertially lated antennas with heights f 84 m and 49.3 m, respetively, and the maximal rati mbining tehnique is used in the diversity reeptin. Bth transmitting and reeiving antennas are f parabli shape with a diameter f 4 m. The enter frequeny is 2.2 GHz with a bandwidth f 24.2 MHz. The measurement setup is shwn in Figures 2a and 2b. The signal is reeived by using frequeny nversin t the intermediate frequeny amplifier (IFA). The IFA has tw utputs: One ges t A/D nversin and finally t the mputer fr deteting flat fading. Anther utput ges t a narrwband reeiver whih has five narrwband signal utputs at different frequenie stred by the mputer. The main parameters f the narrwband reeiver are as fllws: number f hannels, 5; enter frequenies, 57.7, 64.7, 70, 75.7, and 81.9 MHz; frequeny interval, -5.3-7 MHz; bandwidth,-15-20 khz; dynami range, 40 db; hannel islatin, ->50 db; and measurement auray, 1 db. [Gle et al., 1987] t mpare with the mputer simulatin results. Using the data measured in China [Zhang et al., 1994], measurement results frm Japan [Sakagami and Hsya, 1982], and mputer simula- 3. Cmputer Simulatin f Multipath tin results, the rrelatin between equal prbability Fading values f the in-band linear amplitude dispersin and flat fading due t multipath prpagatin is analyzed. 3.1. Transfer Funtin f Multipath Channel It is shwn that there is an exellent linear relatin- Arding t ray thery the multipath transfer ship between them, whih prvides a simple and funtin an be expressed as valuable methd fr prediting the seletive fading by N means f the flat-fading depth. (1) H(f) = ane -j2vrf 'n n=l where a n and q'n are the amplitude and time delay f path n and f is the frequeny. Regarding the three-ray mdel, when the superrefrative ray is mpletely refleted by the layer, the phase must have a hange f,r/2 [Jin et al., 1985; Zhang, 1990]. The grund refletin is near grazing inidene, whih an be regarded t ause the phase hange vt. Therefre the mplex vltage transfer funtin is H(f) = a + a2e -jt -2+j(,/2) + a3e -jtt3q-j,(2) where t = 2,rf. As a result the pwer transfer funtin is Pr(f) = H(f)l 2= a 2 + a22 + a + 2a a2 sin (60'1'2) -- 2ala3 COS (6'1'3) q- 2a2a3 sin [60('1' 3 -- '1'2)], (3)
ZHAO ET AL.' FREQUENCY SELECTIVE FADING STUDIES 1395 I PN-gen. ] digital mdulatr transmitter I fi'equeny nversin amplifier demdulatr analy, I detetr ] er narrwband reeiver narrwband reeiver,/d m --{detetr] ' ' fxequeny nversin amplifier demdulatr anal[ Figure 2. Measurement setup: (a) the transmitting system and (b) the reeiving system. where a 1, a2, and a3 are the amplitudes fr the rn = m + Gz, (5) diret, the superrefrative, and refletin rays, respetively. rn = m + Gh + G(z - h), (6) where m is the mdified refrative index near the 3.2. Time Delays f the Rays grund, G and G are the mdified refrative index In this paper, the plane Earth is under nsidergradients utside and inside the layer, respetively, atin, and the mdified refrative index m is used and h is the lwer height f the layer frm the grund. instead f the refrative index n in a spherial Earth; The time delays f the superrefrative ray and the their relatinship is refleted ray relative t the diret ray are m(z) = n(z)(1 + z/r), (4) *2 = *s - *a, (7) where r 0 is the radius f the Earth and z is height. The mdified refrativity gradient rn shwn in Figure 3 '1'3-- 'l'r-- 'I'd, (8) has a linear relatin with the height z, whih an be expressed as the fllwing equatins utside and inside the layer, respetively: where rs, rr, and ra are the abslute time delays f the refrated, refleted, and diret rays, respetively. They an be alulated by
1396 ZHAO ET AL.: FREQUENCY SELECTIVE FADING STUDIES k Z z layer Figure 3. The m-prfile. 4" ' T h h}t ß d > x z = - m dl, (9) where is the speed f light and dl is the differential length alng the trak. Figure 4a shws the prpagatin trak f the superrefrative ray in the layer, where 0[ and 0 are the transmitting and arriving angles, respetively. Here, 01 is the angle between the ray and the layer, h r and h R are the heights f the transmitting and reeiving antennas frm the grund, and d is the hrizntal path length. The time delay is derived as k (XT R ß d v b x 1 's = -[(m0 + GhT + s 0 )0 - sin O ](R - R) 1 + -[(me + GehR + s 0 )01 - sin Oi](R - Re) Jt R Re Re +- (me + GehT + s 0[)0[-- sin 0[ < d > x Re +- (me + G ehr + s 0 )0 -- where 0[, 0, and 01 satisfy h = h r + Re(s 01 - s 0 ), Re sin 0, ( 0) h = h + Re(s 01 - s 0 ), (11) d = Re(sin 0[ + sin 0 ) + 2(R - Re)sin 01, where R and R0 are the urvature radii f the rays inside and utside the layer, respetively, written as Figure 4. Traks f the multipath rays: (a) the superrefrative ray, (b) the diret ray, and () the refletin ray. R = -l/g, R = -1/G. (12) Figure 4b shws the prpagatin trak f the diret ray. Here, a T and a R are the transmitting and arriving angles, respetively. Time delay za is alu- lated as fllws:
ZHAO ET AL.: FREQUENCY SELECTIVE FADING STUDIES 1397 R R ß a = (rn + Ghr + s at)at sin ar R R + (m + Gha + s aa)aa - sin aa, sin at = Ah + 2R ' ( 3) sin aa = Ah - --, (14) 2R Ah = ha - hr. Figure 4 shws the prpagatin trak f the refletin ray, and the time delay T r is R --[(m0 + Ghr + s 0e) ( - 00) - r Oe r (sin Oe r R R R - sin 0)] +- [(rn + Gha + s 0 )(0-0) - (sin O a - sin 00)], (15) where 0f, 0e, and 00 are the transmitting, arriving, and refletin angles expressed as ht sin 0f = dl 2R0 hr d2 - +, (16) sin 0ff- d2 2R0 sin 0 = ht d d 2R where dl is the distane frm refletin pint A t the transmitting antenna and d2 = d -dl. 3.3. Amplitude f the Rays The nrmalize diretivity f a parabli antenna is J ('n'd sin 0/X) F(O)=(1 +s0),rdsin0/x ' (17) where D is the aperture diameter, 0 is the ff-axis angle, and J1 (x) is a Bessel funtin f the first kind. Fr nveniene, let us assume the amplitude f the diret ray t be unity; ne has a2 = F(O - ar)f(0 - aa), ( 8) a3 = ReF(Oe T- ar)f(o - ar), (19) where R e is the effetive grund refletin effiient, whih is affeted by the grund rughness. 3.4. Cmputer Simulatin f FSF 3.4.1. Statistial distributins f mdified refrative index gradient. The umulative distributin f refrative index gradient (dn/dz) in the lwer atmsphere hanges with different seasns, regins, and meterlgial nditins. Based n bserved data ver many years, the umulative distributins f refrative index gradient in the lwer atmsphere were given by Yang et al. [1980] fr different regins and seasns in China. Yang et al. [1980] shw that the expnential distributin has gd agreement with the refrative index gradient and the nrmal distributin applies utside the layer. In this paper, we use the mdified refrative index gradient drn/dz. Frm (4), drn/dz = dn/dz + 157 x 10-6 km -1. Therefre, inside the layer the umulative density funtin (CDF) f G is P(G' < G) = 1 exp {4(G-S)} 3V ' (20) where parameters S and V an be fitted by using the bserved data. Outside the layer, G fllws nrmal distributin P(G' < G)= 5 erf X/ r r (21) where G and r are the mean value and standard deviatin, whih an als be derived frm the bserved data. Beause f absene f real measured meterlgial data during the experiments the CDF f the refrative index gradient in the lwer atmsphere [Yang et al., 1980] fr the summer seasn f Shijiazhuang, China, near the experimentalink is used here t fit the abve parameters by means f the least squares methd. As a result, we btain V = 0.906 x 10-4 S = 1.64 x 10-4 0.350 x 10-4 O0 = 0.950 x 10-4 3.4.2. Statistial methd f fiat fading and inband dispersin. The randm values f G and G0 an be prdued by the fllwing sampling equatins:
1398 ZHAO ET AL.: FREQUENCY SELECTIVE FADING STUDIES 3 G - In (2RW)V + S, (22) G = 4-2 In R1 s (2 rr2)tr + 0, (23) where W = exp (-4S/3V) and R, R 1, and R 2 are unifrmly distributed randm numbers in [0,1]. Let the enter frequeny be f0 and the bandwidth be fr a medium- r large-apaity mirwave link. Then, the flat fading is the fading f f0, the LAD is defined as the abslute value f the pwer differene between the maximal and minimal frequenies in band, and the MAD is the differene between the deepest and shallwest fading in band. The in-band dispersin dependent n /xf by its definitin, and the interferene f the multipath rays an ause deep fading at sme frequeny pints in band, whih means that it prdues in-band dispersin, namely, frequeny seletive fading. A flwhart f the mputer simulatin is shwn in Figure 5, where fl, f2, ---, fn are the enter frequenies fr the narrwband hannels. In the simulatin, five hannels are used. Zh, Z l, and Z are the in-band dispersins fr the upper and lwer antennas and fr the diversity reeptin, respetively. 4. Cmparisn f Cmputer Simulatin With Experimental Results In this setin, the mparisns between the mputer simulatin results and experimental results are presented. The experimental results used here inlude Xintai t Handan (China), Paem 2 (Frane), and Bukk t Okunsawa (Japan) mirwave links. 4.1. Xintai t Handan Experimental Results (China) In the mputer simulatins the effetive grund refletin effiient is estimated t be 0.3 fr the Xintai t Handan mirwave link shwn in Figure 1, beause the refletin pint is lated at the middle f the path, whih is a plain regin with rps. 4.1.1. Cumulative distributin f 1tat fading. The umulative distributins f the upper and lwer antennas and the diversity reeptin are presented in Figure 6 and Table 1. In Table 1, gd agreement between experiment and simulatin is ntied at several typial prbability pints. The maximal abslute errr is less than 6 db. There is a signifiant imprvement due t spae diversity, with a gain f 23.8 db fr the upper antenna and 19.8 db fr the lwer antenna at the prbability level f 0.0001. N upper ant. I RN in [0'11 I nrmal RN G expnent RN G lwer ant. I narrw-band hannels narrw-band hannels I fl f2 ''' fn in-band dispersin =201øg{ abs[h(f i )] Z t =20lg{ abs[h(fi)] I spae diversity Z=min ( Z h, Z t) statistis Z h I I statistis Z I statistis Z l Figure 5. Flwhart f the mputer simulatin. RN, randm number. The diversity imprvement is mre bvius fr the deep fading. 4.1.2. Cumulative distributins f LAD and MAD in band. Figure 7 and Table 2 present the LAD umulative distributins and the dispersin mparisn at typial prbability pints. It is seen that diversity reeptin imprves LAD signifiantly. It has been reprted that 4 db in-band LAD an result in 10-3 BER fr a 16 quatrature amplitude mdulatin (QAM) system and 8 db LAD an result in the same high BER fr an 8 phase shift keying (PSK) system [Zha et al., 1996]. The maximal imprvement is 16.8 db when the prbability is 0.0001. Clearly, diversity reeptin is ne f the mst effetive ways t ver-
ZHAO ET AL.: FREQUENCY SELECTIVE FADING STUDIES 1399 10 0 10 0 1 0 '2 10-4 k_ ".. upper ant. '.( line with markers: simulatin "%'m. øø øß disrete markers: experiment, d,v si % ø ø øo / ' '. d pper ant' 10 '2 ßß line with markers: 10-4 1 0 '6 ß e ',, simulatin ' ß disrete markers: experiment ø ß - > øøø ß dive rs ity ß 0 10 '6 10-6 0 1 '0 2 '0 3'0 4 '0 50 0 Fading depth (db) 1 '0 2 '0 3 '0 LAD (db) 4O Figure 6. Cumulative distributin f flat fading. Figure 7. Cumulative distributin f in-band LAD. me FSF. Hwever, LAD is in the range f 7.2-9.3 db at a prbability f 0.0001 when diversity reeptin has already been used, s use f diversity reeptin is nt enugh t redue the BER f the system fr terrestrial mirwave links with severe FSF. It is neessary t take ther antifading measures, suh as adaptive equalizers. Figure 8 and Table 3 present the MAD umulative distributins and the dispersin mparisn at typial prbability pints fr upper and lwer antennas and diversity reeptin. The results shw the advantage f diversity tehniques as well. 4.1.3. Crrelatin studies f flat fading and inband dispersin. It is imprtant t study the rre- latin f flat fading and in-band dispersin t see if there are sme relatinships between them and between the dispersin in upper and lwer antennas. If flat fading and in-band LAD have gd rrelatin, we may use flat fading t predit in-band LAD and, further, t predit the BER f the system. It an be seen frm Table 4 that the rrelatin effiients f flat fading between the upper and lwer antennas are -0.119 and 0.002 fr experiment and simulatin, respetively. The rrelatin is lw; in ther wrds, when ne antenna is in deep fading, the signal f anther antenna is prbably stable. This is why the diversity reeptin wrks. The narrwband hannels f upper antennas have gd rrelatin, as d thse f lwer antennas. Hwever, the rrelatin effiients f in-band LAD r MAD are small between the upper and lwer antennas, and thus the diversity reeptin an redue the in-band dispersin and the BER f the system. Frm Table 4 it is als seen that there exists a definite rrelatin between instantaneus values f flat fading and in-band LAD fr bth antennas. 4.1.4. Crrelatin between multipath dispersin and ttat fading. It is well knwn that there are mature methds t predit flat fading [Sylvain, 1995; Lavergnat and Gle, 1991]. These are based n large amunts f bserved data and have high reliability. If Table 1. Cmparisn f Flat Fading at Typial Prbability Pints a Prbability f 0.01 Prbability f 0.001 Prbability f 0.0001 Simulatin Experiment Simulatin Experiment Simulatin Experiment Upper antenna 18.5 21.5 28.4 28.6 39.0 39.0 Lwer antenna 16.5 14.8 26.2 21.8 35.0 30.0 Diversity reeptin 8.2 10.3 12.2 14.3 15.2 21.0 Diversity imprvement Upper antenna 10.3 11.2 16.3 14.3 23.8 18.0 Lwer antenna 8.3 4.5 14.0 7.5 19.8 9.0 avalues are given in deibels.
1400 ZHAO ET AL.' FREQUENCY SELECTIVE FADING STUDIES Table 2. In-Band LAD Cmparisn at Typial Prbability Pints a Prbability f 0.01 Prbability f 0.001 Prbability f 0.0001 Simulatin Experiment Simulatin Experiment Simulatin Experiment Upper antenna 6.8 9.5 15.3 16.5 24.0 23.0 Lwer antenna 3.5 7.0 9.2 11.5 16.4 19.8 Diversity reeptin 2.6 4.3 6.1 8.0 7.2 9.3 Diversity imprvement Upper antenna 4.2 5.2 11.2 8.5 16.8 12.2 Lwer antenna 0.9 2.7 5.1 3.5 9.2 10.5 avalues are given in deibels. rrelatin between the flat fading and in-band LAD an be btained, we an use fiat fading t predit in-band LAD and, further, t predit the BER f the system. As seen in Figures 7 and 8, the prbability pints f 0.03, 0.01, 0.003, 0.001, 0.0003, and 0.0001 are nsidered here. The rrelatin between the equal prbability values f in-band LAD and fiat-fading depth is analyzed by using 100 1 0 '2 LL 0 4 1 0 '6,[ 0 -e diversity D = af + b, (24) D = 0.79F- 4.95, (26) upper ant. line with markers' ø ß simulatin disrete markers' experiment ß ß ß 1 '5 2'0 2'5 3'0 3'5 MAD (ds) 10 40 Figure 8. Cumulative distributin f in-band MAD. ß D = 0.49F- 0.59. (27) The rrelatin effiients are 0.99, 0.99, and 0.98, and the standard deviatins f D fr the equatins are 0.96 db, 0.82 db, and 0.49 db, respetively. The rrespnding regressin equatins based n mputer simulatins are D = 0.83F- 8.53, (28) D = 0.63F- 6.78, (29) where D is LAD in-band (deibels), F is the flat- D = 0.31F- 0.70, (30) fading depth (deibels), and a and b are regressin the rrelatin effiients are 0.99, 0.98, and 0.97, effiients. Fr upper and lwer antennas and diver- and the standard deviatins f D are 0.29 db, 1.14 db, sity reeptin the fllwing regressin equatins have and 0.52 db, respetively. been derived frm experiments, respetively, 4.2. Paem 2 (Frane) and Bukk t Okunsawa D = 0.82F- 8.04, (25) (Japan) Experimental Results 4.2.1. Cumulative distributin f LAD in band fr the Paein 2 experiment. The Paem 2 experiment [Gle et al., 1987] was perfrmed in the Beaue regin, whih is 100 km frm Paris. The path frm Buffy t Viabn is 50 km lng with tw reeiving antennas at heights f 78.5 m and 93.5 m, respetively. The frequeny was -11.123-11.187 GHz. It is reprted that the experiments lasted fr several years. Zhang's [1990] Paem 2 experimental results f the LAD in band fr the ttal fading perid f 1985 were used t mpare with ur simulatin results, and gd agreement was shwn. Beause we had n meterlgial data frm the experiment, the data fr the Paris regin were used t estimate the parameters in (20) and (21) in the mputer simulatin. 4.2.2. Analysis f Okunsawa t Bukk experimental results. In rder t test the quality f the 16 QAM digital mirwave mmuniatin system a fading experiment was perfrmed in April 1979 and in June 1980 in Japan [Sakagarni and Hsya, 1982].
ZHAO ET AL.: FREQUENCY SELECTIVE FADING STUDIES 1401 Table 3. In-Band MAD Cmparisn at Typial Prbability Pints a Prbability f 0.01 Prbability f 0.001 Prbability f 0.0001 Simulatin Experiment Simulatin Experiment Simulatin Experiment Upper antenna 9.0 18.0 Lwer antenna 4.0 9.3 Diversity reeptin 3.0 8.0 Diversity imprvement Upper antenna 6.0 10.0 Lwer antenna 1.0 1.3 18.5 22.8 28.2 28.5 11.0 14.0 20.5 20.5 4.8 10.2 10.5 12.3 13.7 12.6 17.7 16.2 6.2 3.8 10.0 8.2 avalues are given in deibels. The experimental path extended arss the sea with large relative learane. It was a tilted path with hrizntal distane f 63.4 km. The frequeny was in the -- 4.44-4.50 GHz band, and the vertial diversity distane was 17 m. The refletin pint was in a frest near the Bukk statin. On the basis f data given by Sakagami and Hsya [1982], where an adaptive amplitude equalizer was nt used, the prbability pints 0.02, 0.01, 0.002, 0.001, 0.0002, and 0.0001 are nsidered here. The rrelatin f the equal prbability values f in-band LAD and flat-fading depth an be written as D = 0.63F- 6.33. (31) The rrelatin effiient is 0.99 with a standard deviatin f 0.27 db fr D. It was reprted that the data fr diversity reeptin were als btained by using adaptive amplitude equalizers in the Okunsawa t Bukk mirwave link [Kmaki et al., 1979]. The prbability pints 0.3, 0.1, 0.03, 0.01, 0.003, 0.001, and 0.0003 are nsidered by using the available data frm Kmaki et al. [1979], and the rrelatin f the equal prbability f in-band LAD and flat-fading depth is D = 0.34F- 0.23. (32) The rrelatin effiient is 0.99 with a standard deviatin f 0.23 db fr D. It an be seen fi'm regressin equatins (25)-(32) and Figures 9a, 9b, and 9 that in-band LAD and flat fading have exellent rrelatin. As the flat fading inreases, the in-band LAD inreases with the slpe Table 4. Crrelatin Ceffiients Simulatin Experiment Flat fading between upper and lwer antennas Narrwband signals f different hannels in upper antenna First hannel t send hannel First hannel t third hannel First hannel t furth hannel First hannel t fifth hannel Narrwband signals f different hannels in lwer antenna First hannel t send hannel First hannel t third hannel First hannel t furth hannel First hannel t fifth hannel In-band LAD between upper and lwer antennas In-band MAD between upper and lwer antennas Flat fading and in-band LAD Upper antenna Lwer antenna Between in-band LAD and MAD Upper antenna Lwer antenna 0.002-0.119 0.995 0.925 0.986 0.607 0.975 0.815 0.960 0.915 0.999 0.827 0.997 0.819 0.995 0.614 0.991 0.769 0.132 0.055 0.147 0.035 0.643 0.616 0.448 0.203 0.956 0.604 0.959 0.641
1402 ZHAO ET AL.' FREQUENCY SELECTIVE FADING STUDIES less than unity. The slpe f diversity reeptin is smaller than that fr a single-antenna reeptin. This shws that diversity reeptin an redue the in-band dispersin. It must be pinted ut that the Japanese experiments were quite different frm ur Xintai t Handan experiments in bandwidth, mdulatin system, transmissin rate, and path prfile. In the Japanese experiments [Sakagami and Hsya, 1982; Kmaki et al., 1979] the path was an versea link, whih uld have made the transmissin heavily affeted by the evapratin dut. Nevertheless, the equal prbability values f in-band linear amplitude dispersin and flat fading satisfy a linear relatin. 5. Cnlusins By the mparisn f the mputer simulatin with experiment results it is shwn that the mputer simulatin methd is a very effetive way t study frequeny seletive fading. Diversity reeptin redues signifiantly flat fading and in-band dispersin, and it is ne f the mst imprtant antifading methds. Fading and dispersin are severe during a small perentage f the time. The narrwband signals f different hannels f the upper r lwer antennas have a high rrelatin. The in-band linear amplitude dispersin (LAD), as well as the in-band maximal amplitude dispersin (MAD), have a relatively high rrelatin. The instantaneus values f flat fading and in-band linear amplitude dispersin have a definite rrelatin. The equal prbability values f inband linear amplitude dispersin and flat-fading depth have an exellent linear relatinship with the slpe less than unity. This is demnstrated by experiments dne in China and Japan and the mputer simulatins. This linear relatin wuld enable us t intrdue a simple and valuable methd fr prediting the frequeny seletive fading by means f the preditin f flat fading. Hwever, the parameters f these relatinships are different fr different paths and fr peratin with and withut diversity. There are sme prbable sures f errr fr ur experiments and mputer simulatins. First, we did nt have real meterlgial data during the time f ding the experiment; the height f the layer is just estimated. Send, bth transmitting and reeiving antenna heights were assumed t be belw the layer, but smetimes they may be in the layer. The mputer simulatin methd intrdued in this paper needs mre verifiatin bth experimentally and theretially. 30 40 35-25.: '.- 20 30 '15 10 40 35-25._ ',- 20-20 15 10 25 u_1o /', / i // Itl I up e r ant. (e xp e rim e nt, Chhiinn;)) /,' J upper ant. (experiment, Japan) 5 10 15 20 25 In-band LAD (db) /, lwer ant. (simulatin) J 5 10 15 20 25 In-band LAD (db) b /// diversity (experiment, Japan) China / diversity, diversity (simulatin) 0 2 4 6 8 10 12 In-band LAD (db) Figure 9. Linear relatinship between flat fading and in-band LAD: (a) experimental results fr single-antenna reeptin, (b) simulatin results fr single-antenna reeptin, and () diversity reeptin. 30
ZHAO ET AL.: FREQUENCY SELECTIVE FADING STUDIES 1403 Aknwledgments. The authrs wuld like t thank the reviewers very muh fr their helpful suggestins. We als wish t thank Antti Rfiisfinen fr his enuragement and supprt, Wei Zhang fr his helpful suggestins n the riginal manusript, and the CRIRP lleagues fr their hard wrk and effrt during the experimental ampaign. Referenes Gle, P., J. Lavergnat, and M. Sylvain, Desriptin and preliminary results f the Paem 2 experimental prgram, paper presented at IEEE Glbal Cmmuniatins Cnferene, Inst. f Eletr. and Eletrn. Eng., Tky, 1987. Greenstein, L. J., and B. A. Czekaj, A plynmial mdel fr multipath fading respnses, Bell Syst. Teh. J., 59(8), 1197-1125, 1980. Higuti, I., and K. Mrita, Diversity effets f prpagatin harateristis during multipath fading in mirwave links, Rev. Eletr. Crnrnun. Lab., 30(3), 544-551, 1982. Jin, H., Z. Sha, and Y. Xie, The statistial distributins f XPD and CPA in multipath prpagatin (in Chinese), Chin. J. Radi Si., 1 (1), 46-56, 1985. Kmaki, S., I. Hrikawa, K. Mrita, and Y. Okamt, Charateristis f high apaity 16QAM digital radi system in multipath fading, IEEE Trans. Crnrnun., 27(12), 1854-1861, 1979. Lavergnat, J., and P. Gle, Statistial behaviur f a simulated mirwave multipath hannel, IEEE Trans. Antennas Prpag., 39(12), 1697-1706, 1991. Lavergnat, J., M. Sylvain, and J. Bi, A methd t predit multipath effets n line-f-sight link, IEEE Trans. Crnmun., 38(10), 1810-1822, 1990. Rummler, W. D., A new seletive fading mdel: Appliatin t prpagatin data, Bell Syst. Teh. J., 58(5), 1037-1071, 1979. Rummler, W. D., et al., Multipath fading hannel mdels fr mirwave digital radi, in Mirwave and Digital Radi, edited by L. J. Greenstein and M. Shaft, pp. 67-77, IEEE Press, Pisataway, N.J., 1998. Sakagami, S., and Y. Hsya, Sme experimental results n in-band amplitude dispersin and a methd fr estimatin in-band linear amplitude dispersin, IEEE Trans. Cmmun., 30(8), 1875-1887, 1982. Sandtrg, J., Extratin f multipath parameters frm swept measurements n a line-f-sight path, IEEE Trans. Antennas Prpag., 28(6), 743-750, 1980. Serizawa, Y., and S. Takeshita, A simplified methd fr preditin f multipath fading utage f digital radi, IEEE Trans. Cmmun., 31(8), 1017-1021, 1983. Sylvain, M., Extensin f the nrmalized tw-ray transferfuntin mdel t a spae diversity line-f-sight link, IEEE Trans. Cmmun., 43(7), 2271-2280, 1995. Sylvain, M., and J. Lavergnat, Mdelling the transfer fun- tin medium bandwidth radi hannels during multipath prpagatin, Ann. Telemmun., 40(11-12), 584-603, 1985. Vigants, A., Spae diversity engineering, Bell Syst. Teh. J., 54(1), 103-142, 1975. Yang, G., et al., The graphis f refrativity at lw atmsphere in China (in Chinese), tehnial reprt, China Res. Inst. Radiwave Prpag., Xinxiang, China, 1980. Zhang, R., Cmputer randm simulatin n multipath fading, paper presented at SBT/IEEE Internatinal Telemmuniatins Sympsium, Inst. f Eletr. and Eletrn. Eng., Ri de Janeir, Brazil, 1990. Zhang, R., and Y. Xie, Cmputer randm simulatin f frequeny seletive fading f mirwave line-f-sight links (in Chinese), J. China Inst. Cmmun., 12(5), 31-36, 1991. Zhang, R., X. Zha, Y. Xie, and G. Han, The experimental study f frequeny seletive fading (in Chinese), J. China Inst. Cmmun., 15(6), 1-8, 1994. Zha, X., Y. Xie, and Y. Zhang, The relatinship between frequeny seletive fading and the variatins f meterlgial nditins (in Chinese), Chin. J. Radi Si., 10(4), 61-65, 1995. Zha, X., et al., The prgress n the study f frequeny seletive fading and deplarisatin due t multipath prpagatin in China (in Chinese), J. China Inst. Cmmun., 17(3), 8-14, 1996. P. Vainikainen and X. Zha, Radi Labratry, Helsinki University f Tehnlgy, P.O. X 3000, FIN-02015 Esp, Finland. (xzh@radi.hut.fi) Y. Zhang, Labratry f Wireless Cmmuniatin and Eletrmagneti Cmpatibility, Nanjing University f Psts and Telemmuniatins, 210003 Nanjing, China. Y. Xie, China Researh Institute f Radiwave Prpagatin, 453003 Xinxiang, China. (Reeived January 22, 2001; revised May 29, 2001; aepted June 5, 2001.)