Calculation of the received voltage due to the radiation from multiple co-frequency sources

Transcription

1 Rec. ITU-R SM RECOMMENDATION ITU-R SM * EFFICIENT SPECTRUM UTILIZATION USING PROBABILISTIC METHODS Rec. ITU-R SM.1271 (1997) The ITU Radocommuncaton Assembly, consderng a) that communcatons technology has advanced rapdly durng the past decade and the use of radocommuncaton servces by admnstratons has multpled and placed new demands on the rado spectrum; b) that frequency sharng s one of the mportant aspects of effcent frequency spectrum utlzaton; c) that many gudelnes and sharng crtera are based on the most unfavourable nterference assumptons; d) that more effcent spectrum utlzaton may depend on the acceptance of performance crtera developed through the applcaton of probablstc methods; e) that the statstcal characterstcs of both the desred and nterference sgnals would be necessary to evaluate spectrum sharng stuatons and spectrum utlzaton aganst performance standards; recommends 1 that n order to acheve more effcent spectrum utlzaton, admnstratons should consder the use of the probablty of nterference and ts mpact on system performance. 2 that n order to assess fully the nterference potental of ntroducng a new system nto the envronment, the probablty of nterference due to multple nterference sources should be consdered usng technques such as those shown n Annex 1 and for calculaton a probablty of nterference for base to moble and moble to base nterference modes n a land moble duplex system a methodology gven n Annex 2 should be used. NOTE 1 Future examples wll be ncluded to explan how probablstc methods be used to estmate characterstcs of desred and nterferng sgnals wth the obectve of ncreasng spectrum utlzaton. ANNEX 1 (Example 1) Calculaton of the receved voltage due to the radaton from multple co-frequency sources 1 Introducton There are many frequency sharng stuatons where nterference may occur. In some stuatons the number and locaton of possble nterferng sources are not known (e.g. when the nterference s from land-moble rado transmtters). In these stuatons, nterference can be estmated usng probablstc methods. Ths example descrbes a method that clearly demonstrates the concept of calculatng nterference levels due to multple sources usng probablstc methods. Consder, for the sake of smplcty, the case of an arborne recever flyng over an urban area. In ths partcular case the effects of the earth curvature can be neglected. The arborne antenna wll be assumed to be a half-wave dpole wth a cosne pattern. The N nterferng sources are assumed to be unformly dstrbuted over the area whch s assumed to be crcular of radus R as shown n Fg. 1. * Radocommuncaton Study Group 1 made edtoral amendments to ths Recommendaton n the year 2018 n accordance wth Resoluton ITU R 1.

2 2 Rec. ITU-R SM FIGURE 1 Arborne recever over an urban area wth unformly dstrbuted nterference sources Arborne recever d h R r FIGURE 1..[ ] = 12 cm The obectve wll be to derve a smple expresson for the probablty densty functon of the receved r.m.s. voltage at the recevng antenna termnals. Ths example s based on several smplfyng assumptons as follows: The number of the nterferng transmtters, N, s large. The nterferng transmtters are unformly dstrbuted, n geographcal terms, over a crcular area of radus R. All nterferng transmtters have equal amount of radated power. The recever, whch s subected to nterference from all the mobles, s arborne at an alttude h, drectly above the centre of the crcular area that contans all the nterferng sources. The propagaton law from any nterferer to the arborne recever s approxmated by the free-space propagaton rule. 2 The method Consderng the arborne recever now flyng over the urban area, the voltage at the recevng antenna termnals can be wrtten as follows: N V C A d K 1 A e (1)

3 Rec. ITU-R SM C A s the relatonshp between the feld strength at an antenna and the voltage across ts termnals when matched to a 50 load: C A (2) A(d ) s the complex antenna factor whch s related to the nterferer-to-antenna dstance d as follows: ad A d ( d ) e (3) K and are the ampltude and phase of the feld at the recevng antenna due to nterferer and are defned as follows: K d L EL K s d (4) where E L s the specfed feld strength lmt (mv/m) at a dstance d L (m) from a sngle nterferng source. K s s the nterferer radaton pattern factor, accountng for the reducton of the mean level compared to the maxmum level. d s the nterferer-to-antenna dstance n (m). 0 2 d (5) where s the wavelength and (0) s the ntal phase of the sgnal as t leaves source. Equaton (1) can therefore be rewrtten as follows: N V v 1 e (6) where: V a( d ) CA EL K S dl (7) d 2 d ( 0) d (8) where s unformly dstrbuted between 0 and 2. It can be easly shown that v follows a Raylegh dstrbuton such that: p v v 2 v exp (9) where 2 (N/2). E(v 2 ) s the expected value of v2. The r.m.s. voltage s v r.m.s. 2. From the varables already stated, the r.m.s. voltage can be calculated as follows: v N C E K d E a d 2 ( ) r. m. s. A L S L d (10)

4 4 Rec. ITU-R SM The antenna/dstance factor: E a d 2 ( ) d s due to the combned effect of the recevng antenna pattern and the spread of the nterferng sources over a gven area and may be calculated by consderng the probablty dstrbuton of the nterferng sources. Assumng a unform dstrbuton for purposes of smplcty, referrng to Fg. 1, the probablty densty functon of the locaton r of the nterferng sources s gven by: p( r) ( 2r) r ( R ) R (11) Snce the earth curvature s neglgble, the nterferer-to-recevng antenna dstance s gven by: 2 2 d r h (12) Also snce we assumed a cosne law for the antenna: / a d h d (13) Thus the antenna factor s gven by: a( d ) / d h / d h / r h (14) of whch the expected value s: E a d 2 ( ) d R 2 h 2 2 r h 0 2r 1 d r (15) R R h The above expresson s sutable for computng the combned radaton from many sources over a relatvely small area, such as small towns where earth curvature can be neglected. For large ctes where the earth curvature cannot be neglected, a relatvely more complex formula can be obtaned. 3 Concluson In ths example, we can see that n order to estmate the effect of multple sources of nterference whch have unknown locatons, t s necessary to use probablstc methods under the assumptons gven n the Introducton. The two random varables, namely the receved voltage and the antenna factor, have to be consdered n ther expected value form. Equatons (10) and (15) are example formulae for computng the nterference voltage from the summaton of a relatvely large number of nterferng sources.

5 Rec. ITU-R SM ANNEX 2 (Example 2) A methodology to calculate a probablty of nterference for base staton to moble staton and moble staton to base staton nterference modes n a land moble duplex system 1 Introducton In land moble systems, the reuse dstance between co-channel base statons s tradtonally determned accordng to acceptable level of nterference at the vctm moble staton. Ths s a determnstc methodology n whch probablty of nterference s not consdered. Hence, the reuse dstance calculaton s based on worst case scenaros. Clearly, such systems do not frequently operate n such scenaros, hence leadng to neffcent use of spectrum. The methodology presented heren s based on a probablstc approach. It defnes a probablty of nterference that s dependent on dstance between co-channel base statons. Reuse dstance can hence be determned accordng to an acceptable level of nterference probablty, whch s a functon of specfc system parameters, and also to the off-channel reecton (OCR) whch s a measure of the capablty of a recever to reect nterference. Ths parameter was defned n Recommendaton ITU-R SM The probablty of nterference s defned as the rato of the area wthn the coverage area that would suffer nterference to the total coverage area. In ths example, the dstrbuton of mobles nsde both the vctm and the nterferng coverage areas s assumed to be unform. One would thnk that ths probablty would decrease as the dstance of separaton between base statons ncreases. The analyss n ths paper shows that ths s not always the case. For certan values of OCR, the probablty of nterference wll actually ncrease and then decrease as dstance ncreases. Usng the probablty curves, t s possble to select a smaller dstance of separaton at an acceptable probablty of nterference, hence ncreasng the utlzaton of the spectrum. Ths method of calculatng the probablty of nterference s ndependent of the modulaton technque used. It can also be appled to both analog and dgtal rado systems of dfferent channel wdths. 2 Interference crtera calculaton Ths example provdes a methodology to determne the probablty of nterference n a land moble duplex system. The base to moble nterference and the moble to base nterference are dealt wth separately. Frst, t s necessary to defne a crteron to determne f there s harmful nterference or not. In the nterference crteron, nterference s assumed to occur f the nterference power level P s hgher than the desred power level P r by a certan protecton rato, (db) (.e. f P P r ). By usng the 4th power law, t s possble to express the power levels n terms of dstances so that the nterference crteron becomes d 2 k d 1 where the parameters are defned as follows: d 1 : dstance n km, between the desred transmtter and the desred recever; d 2 : dstance n km, between the nterferng transmtter and the desred recever; k : nterference crteron factor and s gven by: k 10 hdtx G 20 log 10 log h G ITx 40 DTx ITx P P OCR tdtx titx where: h : antenna heght (m) G : sotropc antenna gan (db) P t : transmtted power (dbw) OCR : off-channel reecton (db) DTx : desred transmtter ITx : nterferng transmtter.

6 6 Rec. ITU-R SM Dependng on the values of these parameters, k can assume one of three possble values: 0 k 1, k 1, k 1. The nterference areas for the three values of k are shown n Fgs 2a), 2b) and 2c). Note that the shaded area corresponds to the area where nterference exsts and OCR 1 corresponds to an OCR value of 18 db. Analyss results n 6 show that small values of OCR correspond to hgh probablty of nterference and large values of OCR correspond to low probablty of nterference for the same dstance of separaton. FIGURE 2 Interference areas for the three values of k Interference area B D O B I a) k < 1 Interference area B D O B I b) k = 1 Interference area B D O B I FIGURE 2..[ ] = xx cm c) k >

7 Rec. ITU-R SM Probablstc model Fgure 3 shows the coverage areas or cells of two base statons separated some S km from each other. FIGURE 3 Desred and nterferng base statons Desred cell Interferer cell R D M D R I O B D M I B I S FIGURE 3..[ ] = xx cm Wthn both the desred and nterferer cells are moble statons. Here the desred base staton s referred to as B D, the nterferng base staton as B I and n the same way, the mobles staton as M D and M I. The constant R defnes the radus of the coverage areas. The base staton B D s at the orgn and the base staton B I s some S km away along the -axs. In both models d 1 s defned to be the dstance between the desred Rx and the desred Tx. Smlarly, d 2 s defned to be the dstance between the desred Rx and the nterferng Tx. All dstance parameters are n klometres. 4 Base to moble nterference Ths type of nterference occurs when a desred moble M D s nterfered wth by an nterferng base staton B I. To fnd the probablty of nterference, t s necessary to determne the overlappng area between the coverage and the nterferng area. Ths nterferng area s delmted by the boundary of the coverage area on one sde and the curve defned by d 2 k d 1 on the other. Dependng on the value of k, ths curve can be a crcle enclosng the nterference regon (k 1), a straght lne (k 1) or a crcle enclosng the nterference-free regon (k 1). The nterference crcles, whch are dfferent from the coverage areas, have a centre and radus that vary wth k and S. Once these areas are determned, the probablty of nterference can be obtaned by dvdng the nterference area by the coverage area.

8 8 Rec. ITU-R SM FIGURE 4 Base to moble nterference y M D d 1 d 2 Poston of B I O x S Poston of B D FIGURE 4..[ ] = xx cm 5 Moble to base nterference Ths type of nterference occurs when a desred base staton B D s nterfered wth by an nterferng moble M I. FIGURE 5 Moble to base nterference M D * d 1 d 2 M I * Poston of B I O S Poston of B D FIGURE 5..[ ] = xx cm

9 Rec. ITU-R SM For moble to base nterference to occur, the desred moble must be r km from B D and the nterferng moble must be less than k r km from B D. The probablty of nterference at the base staton recever s the product of the probabltes of these two events. 6 Results Based on ths methodology, the base to moble and moble to base nterference s calculated for varous values of OCR and S. The dfferent values of OCR take nto consderaton that dfferent land moble systems (both analog and dgtal wth dfferent channel wdths) may nterfere wth each other. The probablty curves for base to moble and moble to base nterference are plotted n Fgs. 6 and 7. As an example, the values: R D = R I = 32 km, 18 db have been assumed. Also, the sgnfcance of the OCR s descrbed n Table 1. FIGURE 6 Probablty of nterference from base to moble Probablty A B E C D F Dstance between base statons, S (km) Curves OCR (db) A 0.0 B 8.5 C 17.8 D 26.4 E 29.0 F FIGURE 6..[ ] = xx cm Wth these curves t s possble to determne the dstance of separaton between two land moble duplex systems when the OCR and an acceptable probablty of nterference are known. For example, gven an OCR value of 8.5 db and an acceptable probablty of nterference of 0.05, the curves gve us a dstance between transmtters of 73 km for the base to moble nterference and 68 km for the moble to base nterference. Hence, 73 km should be chosen, as t wll guarantee mnmum requrements for both types of nterference.

10 10 Rec. ITU-R SM FIGURE 7 Probablty of nterference from moble to base Probablty A B E C D F Dstance between base statons, S (km) Curves OCR (db) A 0.0 B 8.5 C 17.8 D 26.4 E 29.0 F FIGURE 7..[ ] = xx cm TABLE 1 Curve OCR (db) f (khz) Sgnfcance A One system type nterferng wth a smlar system B Two 12.5 khz systems nterferng each other C Two 25 khz systems nterferng each other D A 25 khz system nterferng nto a 12.5 khz one E A 12.5 khz system nterferng nto a 25 khz one F Two 12.5 khz systems nterferng each other 7 Concluson Ths example has presented a methodology to calculate the probablty of nterference for land moble duplex systems. By selectng an acceptable level of probablty of nterference, the dstance of separaton between two such systems can be determned. In ths way, the mnmum dstance of separaton requred can be determned, hence ncreasng spectrum utlzaton.