Mulipa 7. Mulipa Inroducion Tere are wo caracerisics o radio cannels a presen serious diiculies or elecommunicaion sysems. One is e remendous dynamic range a mus be accommodaed due o e large cange in pa loss wi disance. Anoer is e presence o muliple propagaion pas beween ransmier and receiver a produce ecoes o e ransmied signal in e received signal. Tis penomenon is called mulipa. Inererence beween mulipa signals can resul in ading. We ll cover ading in e nex lesson. Teory Consider an environmen lie a diagrammed in Figure 7. in wic ere exis objecs capable o relecing radio waves. Figure 7.. In e presence o relecing objecs ere can be many pas beween wo radios, eac aving a dieren propagaion disance. Te siuaion sown mig represen a op view o wo radios on eier side o a sree lined wi buildings. Maxwell s equaions are linear. I noing in e environmen is moving or oerwise canging wi ime en we ave a linear, ime-invarian sysem. For suc sysems e impulse response and ranser uncion conceps are applicable and generally very useul. Le s ae our sysem inpu o be e ransmied signal and e oupu o be e received signal. Concepually we could ransmi an elecromagneic impulse. Te impulse would ravel along e various pas rom ransmier o receiver. Te pa would produce a received impulse aer a ime delay. Due o e disance raveled and e ineracion wi relecing objecs, i will ave some ampliude a. Tereore e oal received ield, wic is e impulse response o e ransmier-receiver sysem will be N 0 ( ) a ( ) (7.) EE43: RF Engineering or Telecommunicaions Sco Hudson, Wasingon Sae Universiy 05//7
Mulipa 7. Te ranser uncion or requency response o e sysem is e Laplace ransorm o is evaluaed a s j j. H ( ) 0 ( ) e N 0 a e j j d (7.) Tis is a sum o pasors. For cerain requencies e pasors mig be in pase and add up o a large response. For oer requencies ey mig add ou o pase and give a low response. We see a e eec o mulipa is o creae a response a varies wi requency a ype o requency selecive iler. Mulipa Saisics Aloug in principle e impulse response is compleely deermined by e propagaion environmen, in pracice is environmen is so complex a we are inclined o rea e impulse response as a random process. Random processes are ypically caracerized by eir momens. Te irs and second momens are N a 0 N a 0 N a 0 N a 0 (7.3) (Because e a s represen volages we square em o ge power.) Te irs momen is jus e average ime o arrival. Te irs and second momens can be combined o ge e roo-meansquare delay spread: (7.4) I we coninued o calculae iger-order momens we would ge an increasingly accurae descripion o e impulse response. However, even wo momens provides us wi useul inormaion, namely, e average ime o arrival and e ime spread o e mulipas. One uncion a is compleely deermined by is irs wo momens is e Gaussian. So by sopping a e irs wo momens o () we are eecively modeling i as an equivalen Gaussian wi mean and variance. EE43: RF Engineering or Telecommunicaions Sco Hudson, Wasingon Sae Universiy 05//7
Mulipa 7.3 Consider a Gaussian uncion a () wi variance, and le s coose a ime origin so a e mean is zero. Te specrum o a Gaussian is also Gaussian: a( ) e A( ) e (7.5) Te specrum is down o ½ is pea value wen e /. Solving or e requency we ind / 5. We can ae is as e bandwid o e Gaussian. We will use is o deine e coerence bandwid o e impulse response: B c 5 (7.6) Te coerence bandwid speciies e minimum requency deviaion over wic e ranser uncion can cange signiicanly. In oer words, i wo signals dier in requency by muc less an Bc en ey experience essenially e same response roug e pysical cannel. I wo signals dier by muc more an Bc en ey may experience compleely dieren responses. Te relaion beween e signal bandwid B and e coerence bandwid o e pysical cannel Bc is imporan. I B Bc en all requency componens in e signal are essenially modiied in e same manner, and e received signal is simply a ime-delayed and aenuaed version o e ransmied signal. In eec e cannel is simply an aenuaor. Tis is reerred o as la ading. On e oer and i B c B en dieren requency componens are modiied dierenly by e cannel, and e received signal can be seriously disored. In eec e cannel is en a iler wi some complicaed ranser uncion. Tis is reerred o as requency selecive ading. In is case we oen mus ae seps o undo e disorion inroduced by e pysical cannel. Some ways o do is are roug e use o equalizers, or, in CDMA sysems, rae ilers. Bu, more abou a laer. Example 7. Assume N 0 ( ) a ( ) wi a 0, 0 0s, a 0.5, 0 s a 0.5,. 5s. Ten, () (0) (0.5) () (0.5) (.5) s 0.6s () (0.5) (0.5) () (0) (0.5) () (0.5) (.5) () (0.5) (0.5) s 0.98s so 0.98 0.6 0. 479s and B c 0. 48MHz. EE43: RF Engineering or Telecommunicaions Sco Hudson, Wasingon Sae Universiy 05//7
Mulipa 7.4 Simulaion Figure 7. sows a Macad program a simulaes a cannel in wic ere is a direc pa and our oer mulipas wi random imes o arrival spread over abou 00 ns and random ampliudes. You can see rom e plo a e requency response varies quie erraically over e 00 MHz bandwid sown. Dieren radio cannels in is bandwid mig experience as muc as a 30-dB dierence in ading response. Te coerence bandwid comes ou a a lile more an 0 MHz. You can see rom e plo a is is rougly e caracerisic wid o e bumps in e requency response. number o mulipas N 4 0 N maximum delay ime random ime delays and ampliudes ma x 0 7 0 0 rnd ma x a rnd( ) a 0 requency response a a H( ) a a a e j B 5 B.653 0 6 800 0 6 80 0 6 900 0 6 0 0 response (db) 0 0 30 800 80 840 860 880 900 requency (MHz) Figure 7.. Simulaion o requency response in a mulipa environmen. A direc pa and our mulipas wi random EE43: RF Engineering or Telecommunicaions Sco Hudson, Wasingon Sae Universiy 05//7
Mulipa 7.5 Experimen ampliudes and ime delays beween 0 and 0.s inerere o creae is response. A newor analyzer was used o measure () and H () in a laboraory in e EME building a WSU. Te requency band was 700 o 000 MHz resuling in -m resoluion. Figures 7.3-5 sow some resuls. Figure 7.3: Impulse and requency responses wen anennas are nex o eac oer. Te roll-o in requency response is primarily due o anenna resonance. EE43: RF Engineering or Telecommunicaions Sco Hudson, Wasingon Sae Universiy 05//7
Mulipa 7.6 Figure 7.4: Responses or anennas separaed by abou 0 and aving a clear line-o-sig pa beween em. Figure 7.5: Responses or anennas separaed by abou 30 and no line-o-sig pa beween em. From e above measuremens we can see a, even wi e ransmier and receiver in e same room, we can ge a very complicaed requency response. I you measured e requency response o a coaxial cable and saw someing lie is, you d ge a new cable. Bu in a wireless EE43: RF Engineering or Telecommunicaions Sco Hudson, Wasingon Sae Universiy 05//7
Mulipa 7.7 environmen is is e ype o pysical cannel we are suc wi. In ac, i ges worse, because as soon as e receiver sars o move, e.g., a mobile pone, is ugly requency response can rapidly cange in an essenially random manner. Our wireless communicaion sysems mus, ereore, be designed o uncion under suc non-ideal circumsances. Reerences. Rappapor, T. S., Wireless Communicaions: Principles and Pracice, Prenice Hall, 996, ISBN 0-3-375536-3. EE43: RF Engineering or Telecommunicaions Sco Hudson, Wasingon Sae Universiy 05//7