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58 www.rfdesign.com Ma y 2002

M i l l ime t e r - w a v e ( M M W ) , a l s o s o met imesloosely referred to as microwave, data linksare becoming an increasingly common means ofp r o vid in g c a r r ie r c l a s s s e r v i c e in den s e u r b a nareas. If a line-of-sight exists between two pointsand roof r igh t s and l icens ing can be secured, aMMW link provides a cost-effective alternative tothe s low and cost ly process of laying f iber . Thecarrier has two key factors tha t the l ink must sa t-isfy if t he link is g oing to provide fiber-like service:availability and bit error rate (BER). It is the jobof the radio and the link designers to ensure thatthese requirements are met.

System parametersA scan of Web sites of some of the equ ipment m a k-

ers provides some insight into the various types ofspecmanship. Some ma nufacturers provide a sensi-

tivity that is based on a residual (after correction)BER of 106 or 108. For the da ta ra tes involved (100Mb/s or grea ter), these kinds of error ra tes result inuncorrected err ors occurring only seconds apa rt .

That is hardly carrier-grade service. Thus, the firstorder of business is to determine the receiver thresh-old where the BER is at an acceptable level. Thisvalue may not be available from the manufacturerand may have to be est imated. Depending on thelevel of coding involved, an increase of 2 to 3 dBshould move the system into the clear operat ingregion wh ere the B ER w ill be 10 to 12 or better.

Once a usable threshold has been determined, thenext s tep is to determine the maximum transmitpower. Again, the user must be a wa re of what is actu-ally being specified. The number of interest is themaximum va lue of the average tra nsmit power a t theinput to the a ntenna. The manufacturer ma y specifythe maximum peak envelope power emitted from the

transmitter or delivered to the antenna. Most sys-tems using digital modulation and Nyquist filteringwill requir e any wh ere from 4 to 10 dB of output ba ck-off (OB O) for linea r operat ion1. Using the peak outputpower results in overstating t he tra nsmit capabilitiesof the radio, thereby overestimating the link perfor-mance. If the maximum average transmit power isnot given, the user may want to assume a reductionfrom the peak power between 4 and 8 dB, to includeOBO and any f i l t er or waveguide inser t ion lossbetween the transmitt er and the antenna.

The remaining hard wa re parameter to addr ess ist h e a n t e n n a g a i n . F or t h e 3 8 G H z b a n d , t h eFederal Communications Commission (FCC) pro-vides a minimum gain of 38 dB, w hich is generallymet with a 1-foot diameter or larger antenna 2. Forthe 28 GHz local mult ipoint dis tr ibut ion service(LMDS) band, there is no minimum gain require-ment only a ma ximum beamwidth requirement so there is a greater l ikelihood of a data sheetconta ining a mar keting or typical gain number. Inaddition to removing any fluff in the antenna gainnumbers, the link designer ma y a lso wa nt t o reducethe antenna gain by 1 dB to account for less-than-perfect alignment.

Once a sa tisfactory va lue for the antenna gain isd e t e r m i n e d , t h e h op d i s t a n c e a n d a v a i l a b i li t yanalysis can be performed. The system gain can bedefined as the maximum average transmit powerminus the receiver sensitivity expressed in dB ordB m. For dB, the formula is:

(1)

The link gain, which may also be referred to as sys-tem ga in, is defined as:

(2)

For the remainder of this article, the term systemgainwill refer to Eq ua tion 2.

G G P RL S T thresh= = ( )max + 2 GRxAnt dB

G P Rs T thresh= max dB

Figure 1. Five-nines hop distance chart, 39 GHz, ITU rain model.

Tx/Rx

Performance

prediction for fixedmicrowave data links

By J ohn S. Seybold

RF wir eless l in ks are becom in g a popul ar

al ter nat i ve to fiber. Gett i ng sol i d numbers that

wi l l perm it estim ation of l in k performance

w i th a hi gh degree of cer tai nt y is a mandate.

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This sys tem ga in determines howthe radios, and thus the link, will per-form during a rain fade. Depending ont h e e n v i r o n m e n t t h a t t h e l i n k i sdeployed in, the designer may elect toreduce the system gain by another dBto provide an interference margin. Ac o mmo n de f in i t i o n o f t h r es h o ld- t o -interference ratio uses a 1 dB degra da-t io n o f t h e s ys t em t h r es h o ld a s t h epoint where interference is considereda problem.

Availability is the percentage of timethat the l ink will be operat ional . Forwireless links, this is generally consid-ered to be exclusively due to rain out-ages and does not usually budget forequipment failures. This is a shortcom-ing of the rain availability analysis forwireless l inks because wireless l inksactually have more equipment in thecritical data path than a fiber link. Forthe remainder of this work, the terma v a i l a b i li t y w i l l be t a k e n t o a p p lyexclusively to link outages due to rain,wi th the unders t anding tha t an addi-t i on a l a n a l y s i s m a y b e r eq u i r e d t oaccount for availability limitations due

to equipment failures.Note the concept of the two or three-

s i g m a d e s i g n a s i t a p p l i e s t o r a d i oh a r d w a r e . W h i l e t h i s i s a c o m m o nmethod for system design, the conceptmust be addressed for the applicationto wireless data links. If a system ha s athree-s igma sys tem ga in , tha t mea nst h a t i t i s o n ly ex p ec t ed t o mee t t h especificat ion 99.87%of t he tim e. Thep r o b a b i l i t y o f h a v in g a s y s t em t h a tdoes not meet the specification is not

negligible when compared to a four- orfive-nines link availability.

Therefore, i t is important that thekey system parameters be known withb e t t e r t h a n a t h r ee-s igma c er t a in t y .This is best achieved by careful accep-tance testing either during productionor immediately prior to deployment. Ifthe uncerta inty in the system gain isnot addressed, then the availability ofthe l ink is l ikely to be less than thedesign target even if the ra in modelsa re correctly a pplied.

It should be stressed tha t ha ving lesst h a n t h e r e q u i r e d g a i n r e s u lt s i n areduction in availability. Thus, the link

will operate properly the majority ofthe t ime, but i t w i l l f a i l dur ing ra inevents th at it should be able to handle.

Rain models

There are two popular rain modelsc o m m o n l y u s e d f o r M M W R Fl i n k p l a n n i n g : T h e I n t e r n a t i o n a lT e l e c o m m u n i c a t i o n s U n i o n ( I T U )model3 and the Crane model4. Each hasa corresponding set of empirical ra ind a t a w i t h e a c h m o d e l . Wh i l e e a c hmodel can be applied using the otherset of rain data, that procedure is notdiscussed herein. Each set of rain datadivides the globe into rain regions thatcharacterize the rain conditions.

One recommendation for use of theITU model uses the ra in ra te, whichoccurs 0.01%of the time, or the 0.9999

rain rate. Table 1 shows the 0.9999 or0.01% rain ra te data for use with th eITU model. The rain rate data for thedes ired ra in region a re then used tocompute the path a ttenua tion using theexpression:

(3)

Where: RR= the 0.9999 ra in r a t e forthe chosen region, in mm/hr a nd disthe hop dista nce in km.

Furthermore:

(4)r d

d

=+

1

10

Atten a RR d rb0 01. = dB

Figure 2. Five-nines hop distance chart, 39 GHz, Crane rain model.

Figure 3. Four-nines hop distance chart, 39 GHz, Crane rain model.

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With :

(5)

Equat ion 3 provides an est imate oft h e p a t h a t t e n u a t i o n t h a t i s o n l yexceeded 0.01% of the time. The I TUmodel also provides an adjustment fac-tor for a vailability tha t is applied to the

path attenuation if availabilit ies otherthan 0.9999 are desired. The adjust-ment factor is applied to the a t tenua-tion (expressed in dB) that is computedby (3). The expression for the adjust-ment fa ctor is:

(6)

Where pis the desired outage proba-

bili ty expressed as a percentage (p=

0 . 0 1 f o r 0 . 9 9 9 9 a v a i l a b i l i t y ) . T h eadjustment fa ctor is validat ed for a vail-a bilities f rom 0.99 to 0.99999.

The aa n d bf ac tors a re empir ica lvalues that have been tabulated in thereferences a nd a re the sa me values forboth Crane and ITU models. The val-ues are a function of the frequency andpolarization of interest. Parameter val-

ues for frequencies that a re not tabulat -ed can be computed by interpolat ion,using a logarith mic frequency scale a ndlogar i thmic sca le for aa n d a l i n e a rscale for b.

The Crane model takes a dif ferentapproach to modeling ra in at tenuat ion.C r a n e d o es n o t u s e a n a v a i l a b i l i t yadjustment factor on the a t tenuat ion,b u t r a t h e r u s e s t h e r a i n d a t a f o r anumber o f d i f ferent ava i lab i l i t ies

some of which are shown in Table 2

along with th e rain ra tes. The rain ra teda t a f o r t h e des i r ed a v a i l a b i l i t y a r ethen used in Cranes empirical model todetermine the pa th a t tenua t ion as afunction of range. The Crane model is

divided into two segments, dependingon the actual ra in ra te involved. Thefirst segment is for distances between 0and (d) where:

(7)

In this region, the ra in at tenuat ion is:

(8)

Where:

(9)

For the other case, (RR)

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ad justment fa ctor (if any ) ar e fixed. Therain attenuation then becomes a func-tion of the dista nce, d, only.

Figure 1 shows a plot of the expectedra in fa de for a 0.99999 rain vs. hop dis-tance for several different rain regions.The colored curves represent the five-nines rain attenuation vs. distance forthe respective rain regions. The blacksystem gain curves represent the a vail-able fade margin for systems with dif-ferent system ga ins.

The Fr i is equa t ion g ives the f ree-space loss as a function of dista nce.

(12)

For terrestr ia l l inks a t frequenciesbelow about 55 GHz, gaseous absorp-tion can be ignored unless the link dis-tance is substant ia l . Mult ipath fadingis usually minimal because the l inksare s t a t ionary a nd the an tenna beamsare rela t ively narrow. Thus, the free-

space loss provides a good estimate ofthe path loss for a point-to-point link.The primary source of outages is pre-c i p i t a t i o n . T h e a v a i l a b l e r a i n f a d emargin for a g iven l ink can then becomputed as the sys tem ga in minusth e free-space loss.

By superimposing a plot of the sys-tem gain minus the free-space loss asa funct ion of range onto the ra in a t ten-uation curves, a hop distance chart isproduced. Figure 1 shows a hop dis-

t a n c e c h a r t f o r a 3 9 G H z , v er t i c a lpola r iza t ion l ink for three di f ferentsystem gains . The point where a sys-tem gain curve intersects a ra in a t ten-uation curve is the maximum 0.99999availabil i ty l ink dis tance for that sys-tem in the selected ra in region. Thepoint where they intersect is the rangewhere the ra in fade mar gin of the l inki s e q u a l t o t h e 0 . 9 9 9 9 9 r a i n - f a d edepth. For example, for a 170 dB sys-tem in ra in region A, the f ive-nineshop dista nce is 7.6 km.

Figure 2 shows a s imi la r hop dis-t a n c e ch a r t u s i n g t h e C r a n e m o d elan d da ta . Because the ra in regions forCra ne and ITU are defined different ly,it is not possible to make direct com-parisons between the two models. It isposs ib le to p ick a par t icu la r c i t y orgeo gr a p h ic r eg io n a n d c o mp a r e t h ep r ed ic t ed p er f o r ma n c e a t t h a t l o c a -tion. For instance, Orlando is in ITUregion N and Crane region E, so a170 dB system has an expected f ive-nines hop dista nce of 970 meters usingITU a nd 1000 meters using Cra ne. For

values of system gains not shown, t wocurves can be linearly interpolat ed.

The hop dis tance chart provides ag r a p h i c a l m e a n s o f d e t e r m i n i n g a twhat hop distance the rain attenuationis equal to the fade margin. The inter-section can be determined using itera-tion on a computer. Because the atten-uation model minus the free-space lossis a transcendental function, it cannotbe solved directly. While not a s precise,the graphical solut ion provides more

information than a numerical solution.F o r e x a m p l e , i n t h e d r i e r r e g i o n s ,where the ra in a t tenuat ion curve hasless slope, it can be seen that a smallchange in the system ga in can result in

a substant ia l change in the predictedh o p d i s t a n c e . T h i s b e c o m e s m o r eapparent a t lower ava ilabilit ies such ast h e f o u r -n i n e s h o p d i s t a n c e c h a r tshown in F igure 3.

F i g u r e 4 s h o w s a f i v e -n i n e s h o pchart a t 28 GHz. At the lower frequen-cy , the impact o f ra in a t tenua t ion isless severe tha n a t 39 GH z, so the cor-responding h op dista nces are longer. Itis a lso noteworthy th at the ra in a t ten-uat ion is s l ight ly greater on horizon-ta l ly pola r ized s igna ls than on ver t i-ca l ly pola r ized s igna ls . The aa n d bf ac tors in the a t tenua t ion model a re

d i f f er en t f o r h o r i z on t a l a n d v er t i c a lpola r iza t ion . This is a cons idera t ionfor dual polarization systems becausethe performance in rain will be limitedby the horizonta lly polarized signa l.

A common question encountered byradio vendors is : My hop dis tance islonger th an the ma ximum f ive-ninesh o p d i s t a n c e . W h a t w i l l t h e a c t u a lava ilabil ity be? This is a n importantquest ion. From an operat ional s tand-point, 0.99997 is not profoundly differ-ent from 0.99999 ava ilability. U sing th eITU model (wit h th e adjustment factor),a family of curves showing availabilityvs. hop distance can be generated for agiven sys tem ga in . F igure 5 shows asample availabil i ty chart for a systemgain of 170 dB. It must be rememberedtha t t his curve is only valid for the stat -ed system gain. Using such a curve, theava i lab i l i t y can be es t ima ted for anyhop distance once the rain region andsystem ga in have been esta blished.

SummaryThis art icle discussed how to look

past typical market ing specif ica t ionsand get to the solid numbers that willpermit estimation of link performancewith a high degree of certainty. Once a

set of solid radio specifications are inhand, the dominant l imita t ion of l inkava ilability is the ra in fade. Two popularmethods for modeling rain fa de and howthey rela te to availabil i ty were exam-ined. A hop distance chart was generat-ed a n d d i s c u s s ed . F in a l l y , a p lo t o fexpected availability vs. hop distance fora given system gain w as presented.

Ld

=

20

4log

dB

Figure 5. Availability vs. hop distance for vertical polarization, 39 GHz.

Contin ued on page 66

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References

[1] Output B ack-Off Requirementsfor Root Raised-Cosine Filtered DigitalS igna ls , J ohn S . Seybold , Ph .D. , RF

Design, 2001

[2] Code of Federal Regula tions, Title47, Volume 5, 101.517, Revised as ofOctober 1, 2000

[3] ITU Recommend a tion PN 837-1,Rec838, Rec.I TU -R P .530-7

[4 ] E l e c t r o m a g n e t i c Wa v eP r o p a ga t io n Th r o u gh R a in , R o ber tCra ne, J ohn Wiley & Sons, February1996.

About the authorJ ohn S. S eybold received his B.S .E.E . from the U niversity of Wisconsin in 1982,

his M.S.E.E. from California State University, Fullerton, in 1986 and his Ph.D.from the University of Central Florida in 1995. Seybold is an associate professorof electrical engineering at Florida Institute of Technology in Melbourne, FL,where he a lso serves as the associa te d irec tor o f their Wireless Center o fExcellence. Seybold held a variety of positions in the industry prior to joining thefaculty at Florida Tech. Most recently, he was a senior RF systems analyst at

Triton Network Systems, where he was responsible for RF network planning, linkoutage prediction and frequency r e-use ana lysis. Seybold ha s a lso worked in rada rsystems, synthetic aperture radar (SAR) and communications systems, includingspread spectrum. He is a licensed professional engineer in the state of Florida, asenior member of the IEEE and a member of Phi Ka ppa Phi a nd Tau B eta P i. Hecan be conta cted at :jseybol d@mpi net.net.

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