Correlation Analysis of Multiple-Input Multiple-Output Channels with Cross-Polarized Antennas

Transcription

1 Correlaton Analyss of Multple-Input Multple-Output Channels wth Cross-Polarzed Antennas Le Jang, Volker Jungnckel, Stephan Jaeckel, Lars Thele and Armn Brylka Fraunhofer Insttute for Telecommuncatons, Henrch-Hertz-Insttut Enstenufer 37, D-587 Berln,Germany Abstract In ths paper, we nvestgate the correlaton characterstcs of the multple-nput multple-output (MIMO) channels based on the outdoor measurement. The correlaton coeffcents for both co-polarzed and cross-polarzed channels are studed. Results show that the polarzaton decorrelaton performs better than spatal decorrelaton n strong lne of sght (LOS) scenaro. In non lne of sght (NLOS) scenaro, they are of the same order. The elope correlaton coeffcent s observed to be approxmately the same as the er correlaton coeffcent n both tme and frequency doman. The correlaton of the channels hghly depends on the propagaton scenaros, and t ncreases as the Rcean K factor ncreases. It s also found that the correlaton n the elevaton doman s much hgher than that n the azmuth doman. I. INTRODUCTION The multple-nput multple-output (MIMO) system has been shown to dramatcally ncrease the capacty of the wreless system and t draws ncreasng attentons n recent years [], [2]. An mportant condton for MIMO channels to acheve hgh capacty s that the ronment provdes suffcent multpath components. By explotng the multpath components, the MIMO lnk results n a hgh rank channel wth mproved capacty. However, because of the correlaton of the sub-channels, the rank of the channel may decrease n some propagaton scenaro such as LOS scenaro. Therefore, efforts are pad to reduce the correlaton of sub-channels, and technques such as polarzaton are employed n the MIMO communcaton system. Thus t s of great nterest to nvestgate the correlaton characterstcs of the MIMO channels. [3] studed the correlaton of the MIMO channels for ndoor ronment based on measurements. The spatal decorrelaton has been analyzed for both transmtter and recever. The ont advantage of spatal and polarzaton decorrelaton was not gven due to the lmtaton of the measurement. [4] nvestgated the cross correlaton values for dual-polarsed ndoor MIMO lnks at 5.2 GHz. The measurement was made manly n a NLOS corrdor and hall scenaro, and the correlaton coeffcents are calculated for dfferently polarzed lnks and co-polarzed array elements. In ths paper, we am at analyzng the correlaton characterstcs of the MIMO channels for outdoor propagaton ronments. Based on the measurement at 2.53GHz, the channel correlaton coeffcents for both cross-polarzed and co-polarzed channels wll be nvestgated n tme and frequency doman. Polarzaton and spatal decorrelaton are compared, and the scenaro dependency of the channel correlaton s also analyzed. For spatal decorrelaton, we further study the correlaton coeffcent n both azmuth and elevaton doman. II. MEASUREMENT SETUP Fg.. Transmt and receve antennas. Measurements were made on the campus of Techncal Unversty Berln (TUB) at 2.53 GHz wth the RUSK HyEff channel sounder n a 2 MHz band. The base staton s a unform lnear array (ULA) wth cross-polarzed patch antenna elements on t as shown n the top of Fg.. The four patches n each column are coupled to narrow the beam wdth and hence obtan hgher antenna gan. The left-most and rght-most columns of array are grounded va 5 Ω resstor to mnmze the edge effects. Therefore, altogether 8 columns of cross-polarzed antennas at λ/2 spacng,.e., 6 transmt antennas are used as actve elements. A +44 dbm er amplfer wth a 6 hgh er swtch s used for the multple antennas. The effectve transmt er s +37 dbm per antenna, due to the 4 db nserton loss of the swtch and -3 db antenna effcency. The nose fgure of the HyEff recever s 2.5 db. Low-loss feeder cables are used to reduce recever nose.

2 ( )( ) h mn (f,t ) h mn (f ) h m n (f,t ) h m n (f ) ρ (f )= (h mn (f,t ) h mn (f ) 2 ρ (t )= (h mn (f,t ) h mn (t ) 2 (2) h m n (f,t ) h m n (f ) 2 ( )( ) h mn (f,t ) h mn (t ) h m n (f,t ) h m n (t ) (3) h m n (f,t ) h m n (t ) 2 Altogether, the lnk margn s mproved by almost 2 db compared to [5]. All antennas are made of smlar patch elements wth two ponts of delvery feedng horzontal and vertcal polarzaton. Cross-polarzaton couplng s smaller than -2 db, measured back-to-back between two patches. The 3 db antenna aperture s about 9 both n azmuth and elevaton.the recevers are bult n two forms. One s a cylnder wth 8 cross-polarzed patch antennas on the surface arranged n a row. The other s a cylndrcal antenna made of two 2-patch elements arranged n tow rows. On top a cube antenna s mounted as shown n the lower part of Fg.. Fg. 2. Locatons of the base staton and termnal antennas. The base staton s mounted on the rooftop of the buldngs ndcated as BSx n Fg. 2, where BS s on Henrch-Hertz-Insttut (HHI), BS2 s on Deutsche Telekom (DTAG) and BS3 s on the man buldng of the TUB. The recever stes marked wth Rx use the cylndrcal antenna as shown n the bottom left of Fg.. Those marked wth Tx use the antenna shown n the bottom rght of Fg.. The recever s placed at the ground level for about 2 m hgh. Short tracks of m nsde campus area and long tracks wth a total length of approxmately 4.5 km outsde the campus area were measured. III. CORRELATION COEFFICIENTS For a seres of n measurements of X and Y, the Pearson product-moment correlaton coeffcents can be used to calculate the correlaton of X and Y. n x y x y ρ = ( ) 2 ( ) 2 n x 2 x n y 2 y () where x and y denote the measured samples. In the measurements, we sampled the sgnal at a frequency of 32MHz over 2MHz bandwdth along the measurng track. The over sampled data are removed durng the data processng. Hence the elope correlaton coeffcent for two arbtrary channels h mn (f,t ) and h m n (f,t ) n both frequency and tme doman are defned as n (2) and (3). Where m and m denote dfferent receve elements and n and n denote dfferent transmt elements. In (2) h mn (f ) and h m n (f ) are the sample mean values of the elopes of channels h mn (f,t ) and h m n (f,t ) over the tme nstances. We evaluate the correlaton coeffcents over all the snapshots of a selected sub traectory. In (3), the correlaton s evaluated over the whole bandwdth. h mn (t ) and h m n (t ) are the sample mean values of the elopes of channels n tme doman wth respect to the channel bandwdth. Smlar results can be obtaned for the er correlaton of the channels. (4) and (5) on the top of next page are the defntons of the er correlaton coeffcents of two arbtrary channels h mn (f,t ) and h m n (f,t ) n both frequency and tme doman. It has been shown n [6] n theory that, under certan assumptons, ρ ρ. (6) In the followng parts of our paper, we wll valdate ths approxmaton wth measurement data. IV. MEASUREMENT RESULTS A. Envelope and Power Correlaton Coeffcent The elope and er correlaton coeffcents versus the channel bandwdth and the samplng snapshots are plotted n Fg. 3 and Fg. 4 for strong LOS scenaro and NLOS scenaro. In Fg. 3, the measurement was taken along a track of 9.7 m n LOS scenaro. We can see that the cross-polarzed channels perform better than the copolarzed channels n LOS scenaro. It can be observed that the elope correlaton coeffcents are approxmately

3 (h mn (f,t ) 2 h mn (f ) 2)( h m n (f,t ) 2 h m n (f ) 2) ρ (f )= (h mn (f,t ) 2 h mn (f ) 2 2 h m n (f,t ) 2 h m n (f ) 2 2 (4) (h mn (f,t ) 2 h mn (t ) 2)( h m n (f,t ) 2 h m n (t ) 2) ρ (t )= (h mn (f,t ) 2 h mn (t ) 2 2 h m n (f,t ) 2 h m n (t ) 2 2 (5) Bandwdth (MHz) Snapshots LOS scenaro Bandwdth (MHz).5.3. ρ HH HH ρ HH HH Snapshots x Bandwdth (MHz).5.3. ρ HH VV ρ HH VV Snapshots x 4 Fg. 3. The elope and er correlaton coeffcents of co-polarzed channels and cross-polarzed channels n LOS scenaro. Fg. 4. The elope and er correlaton coeffcents of co-polarzed channels and cross-polarzed channels n NLOS scenaro. the same as the er correlaton coeffcents n both tme and frequency doman, whch valdates the statement n [6]. Furthermore, from the fgure we can also see that n the frequency doman, the correlaton coeffcents varatons are relatvely small, whch means that the correlaton coeffcents are not very frequency selectve n wdeband transmsson. In the measurement, we used a 2 MHz bandpass flter to smooth the channel. However, the channel correlaton coeffcents are hghly tme selectve as shown n the top fgure of Fg. 3, snce the channel correlaton depends on the propagaton ronment. In the NLOS scenaro, the channels are almost uncorrelated no matter usng co-polarzed antennas or crosspolarzed antennas as shown n Fg. 4. The elope correlaton coeffcents are also approxmately equal to the er correlaton coeffcents. In ths case, the dynamc range of correlaton coeffcents s also smaller n the frequency doman compared wth that n the tme doman. In the followng sectons, we only consder the elope correlaton coeffcents n the tme doman for the smplcty of analyss. B. The Correlaton Coeffcents of Channels wth Co- Polarzed and Cross-Polarzed Antennas In our measurement, we used cross-polarzed patch antennas as shown n Fg., on whch the vertcally and horzontally polarzed antennas are co-located. Therefore we are able to study the beneft due to polarzaton decorrelaton, whch extends the results n [3]. Snce here co-located antennas are used n the measurement, both spatal and polarzaton decorrelaton can be nvestgated. For MIMO channels wth cross-polarzed antennas, the channel matrx can be wrtten as below [ ] HVV H H = VH. (7) H HV H HH To study the polarzaton decorrelaton, we select one transmt antenna patch and one receve antenna patch, whchgvea2 2 MIMO channel, and check the correlaton coeffcent of the channel h VV and h HH, whch s denoted by ρ HH VV. For the correlaton of co-polarzed channels, we actually take the spatal decorrelaton nto account, two neghborng patches at both the transmtter and recever are chosen for analyss. The correlaton coeffcent s denoted by ρ HH HH or ρ VV VV, whch represents the correlaton coeffcent of a 2 2 MIMO channel wth only horzontally or vertcally polarzed antennas. The comparson between the correlaton coeffcents of the co-polarzed and cross-polarzed channels are plotted n Fg. 5. The evaluaton s done n both strong LOS and NLOS propagaton scenaros. It can be observed that the correlaton of the channels are generally hgher n LOS scenaro than n NLOS scenaro. In strong LOS scenaro, when usng co-polarzed antennas arranged on two spatally separated patches, the probablty of havng correlaton coeffcent lower than.5 s less than 2%,

4 whch means that the channels are hghly correlated. Wth the use of cross-polarzed antenna, 9% of the case the channels has correlaton coeffcent lower than.5, and 66% of the case, the correlaton coeffcent s lower than.3, where the channels can be consdered as uncorrelated. Ths mplcates that the polarzaton decorrelaton works better than spatal decorrelaton n LOS scenaro. In NLOS scenaro, 99% of the case the channels wll have correlaton coeffcent lower than.5, and probablty of havng correlaton coeffcent lower than.3 s 9%. Therefore the channels n NLOS scenaro can be approxmated as ndependent from each other. In NLOS scenaro, the crosspolarzed antennas have no advantage wth respect to polarzaton decorrelaton snce the polarzatons have been destroyed by multple reflectons, dffractons or scatterng durng propagaton..9.7 as the sde facng the transmt antenna). The effect of the polarzaton decorrelaton n such case has been reduced, but the effect of spatal decorrelaton ncreases. The of the mean value of the channel correlaton coeffcents ρ over all sub-channel pars s plotted n Fg. 6. It can be observed that, because of the spatal decorrelaton, the average channel correlaton s lower compared wth Fg. 5. However, n general, the correlaton of the crosspolarzed channels s stll smaller than that of the copolarzed channels. The cross-polarzed channels are now affected by both the spatal and polarzaton decorrelaton. Furthermore, the correlaton of the vertcally polarzed channels s smaller than that of the horzontally polarzed channels. C. Propagaton Scenaro Dependency From the analyss above we know that the channel correlaton coeffcent hghly depends on the propagaton ronment. In the top of Fg. 7, we plot the co-polarzed channel correlaton coeffcents aganst the measurng dstance along a longer track, whch experences dfferent propagaton scenaros. At the begnnng of the track, the.5.3 ρ HH HH (LOS) (LOS) ρ HH HH (NLOS). (NLOS) Fg. 5. The of the absolute value of the correlaton coeffcents of channels wth cross-polarzed and co-polarzed antennas Dstance (m).9 ρ HH HH ρ VV VV N HHI db Campus Telefunken Tower Ernst Reuter Platz Path Loss Techncal Unversty Man Buldng 2m Fg. 6. The of the mean values of over all sub-channel pars n LOS scenaro. In realstc communcaton systems, the performance of polarzaton decorrelaton s affected by spatal decorrelaton. Because of the cylnder geometry shape of the receve antenna as shown n the bottom of Fg., even though the antenna s n LOS scenaro, only one or two patches wll have drect LOS component wth the transmt antenna. For other antenna patches, the receved sgnal manly contans multpath components, especally those on the back sde of the antenna (the front sde s defned Fg. 7. The channel correlaton coeffcents and path loss measured along a track of 35 m. recever s n NLOS scenaro to the base staton, hence the channels are almost totally uncorrelated. As the recever moves, t receves stronger and stronger sgnal, untl t s n a weak LOS scenaro. The path loss of the channel n db s plotted n the bottom of Fg. 7. Snce the dfferent scenaros can be modeled usng dfferent Rcean K factors, we can come to the concluson that the channel correlaton coeffcents ncrease along the measurng track as the Rcean K factor ncreases. The larger value at around

5 m s caused by the empty spacng between buldngs as shown n the map of Fg. 7, where the shadow effect s weaker. D. Correlaton n the Azmuth and Elevaton doman In ths secton, we study the correlaton of the channels n the azmuth and elevaton doman. In the bottom rght of Fg., the antenna has two rows of receve patches on the cylnder surface. Therefore, we are able to nvestgate the correlaton effects of the antennas n the same row (azmuth doman) or n the same column (elevaton doman). The channel elope correlaton coeffcents n Fg ρ HH HH (upper row) ρ HH HH (lower row) ρ HH HH (same column) ρ VV VV (upper row) ρ VV VV (lower row) ρ VV VV (same column) The channel elope correlaton coeffcents n LOS scenaro. LOS scenaro s plotted n Fg. 8. From the fgure we can see that the channel correlaton n elevaton doman s qute hgh no matter for vertcally polarzed or horzontally polarzed channels. The correlaton of the channels n azmuth doman s much lower, especally for the vertcally polarzed channels. Ths s consstent wth the results n Fg. 6, where the correlaton of the vertcally polarzed channels s lower than that of the horzontally polarzed channels. Furthermore, t s also observed that the correlaton for the horzontally polarzed channels n the upper row s hgher than that n the lower row. However, for the vertcally polarzed channels, the channels n the lower row have hgher correlaton. V. CONCLUSION We nvestgated the correlaton of the MIMO channels wth cross-polarzed antennas for outdoor ronment. Results show that the polarzaton decorrelaton performs better than the spatal decorrelaton n LOS scenaro, and the cross-polarzed channels have smaller correlaton coeffcent than the co-polarzed channels. Furthermore, the horzontally polarzed channels tend to be more correlated than the vertcally polarzed channels. In both LOS and NLOS scenaro, the elope and er correlaton coeffcents are approxmately the same. The correlaton coeffcents vary less n the frequency doman, but change dramatcally n the tme doman dependng on the propagaton ronment where the channels undergo. It s also observed that, the correlaton of the co-polarzed channels ncreases as the Rcean K factor ncreases, and the channels have very hgh correlaton n the elevaton doman. In general, we can come to the concluson that the crosspolarzed channels are not affected by the ronment, whle the performance of the co-polarzed channels s scenaro dependent. ACKNOWLEDGMENT The authors would lke to thank the German Mnstry for Educaton and Research (BMBF) for the support n the proects 3GeT and EASY-C. The authors would also lke to thank Udo Krüger, Thomas Wrth, Yosa Hadsusanto, Matthas Mehlhose, Stefan Schffermüller and Ka Börner for preparng and performng the measurement. Efforts from Gerd Sommerkorn and Steffen Warzügel are also gratefully apprecated. REFERENCES [] M. A. Jensen and J. W. Wallace, A revew of antennas and propagaton for MIMO wreless communcatonss (nvted paper), IEEE Trans. Antennas Propagat., vol. 52, pp , Nov. 24. [2] G. F. Foschn and M. J. Gans, On lmts of wreless communcaton n a fadng ronment when usng multple antennas, Wreless Pers. Commun., vol. 6, no. 3, pp , 998. [3] P. Kyrts, D. C. Cox, R. A. Valenzuela, and P. W. Wolnansky, Correlaton analyss based on MIMO channel measurements n an ndoor ronment, IEEE J. Select. Areas Commun., vol. 2, pp , June 23. [4] W. A. T. Kotterman, G. Sommerkorn, and R. Thoma, Crosscorrelaton values for dual-polarsed ndoor MIMO lnks and realstc antenna elements, n 3rd Internatonal Symposum on Wreless Commun. Systems, pp , Sept. 26. [5] V. Jungnckel, V. Pohl, H. Nguyen, U. Küger, T. Hausten, and C. von Helmolt, Hgh capacty antennas for MIMO rado systems, n Proc. 5th WPMC, vol. 2, pp. 47 4, 22. [6] R. O. LaMare and M. Zorz, Effect of correlaton n dversty systems wth Raylegh fadng, shadowng, and er capture, IEEE J. Select. Areas Commun., vol. 4, pp , Apr. 996.