st semester. Kei Sakaguchi. ee ac May. 10, 2011

Transcription

1 0 s semeser IO Communcaon Sysems #4: Array Sgnal Processng Ke Sakaguc <sakaguc@moble.ee.ec.ac.jp> ee ac ay. 0, 0

2 Scedule s alf Dae Tex Conens # Apr. A-, B- Inroducon # Apr. 9 B-5, B-6 Fundamenals of wreless commun. #3 Apr. 6 B- OFD for wreless broadband ay 3 No class #4 ay 0 B-7 Array sgnal processng #5 Nov. 7 A-3, B-0 IO cannel capacy #6 Nov. 4 B-, 3 Spaal cannel model ay 8 No class ay 0, 0 IO Commun. Sysems Array Sgnal Processng

3 Agenda Am of oday Derve SNR and BER performance of maxmal rao dversy combnng Conens Plane wave sgnal model Beamformng & nerference cancellaon ul-pa sgnal model Dversy combnng Spaal correlaon & s effec ay 0, 0 IO Commun. Sysems Array Sgnal Processng 3

4 Queson Warmng Up Illusrae egen-vecors of correlaon marx R A 3 3 C B C z z y x Egen-value decomposon Cannel marx: x Egen vecors: y E e e e3 Correlaon marx: Egen-decomposon: R R E Λ E Egen values: Λ ay 0, 0 IO Commun. Sysems Array Sgnal Processng 4

5 Classfcaon of Array Processng Sac or oble corresponds o Fxed or Adapve RF conrol or BB conrol Beamformng, dversy, or Inerference cancellaon Average SNR, ouage SNR, or SIR w y x ay 0, 0 IO Commun. Sysems Array Sgnal Processng 5

6 Plane Wave Sgnal odel Plane wave sgnal model y s n Cannel response d a d Array manfold a, e jkd cos, e jk d cos,, e jk d cos k Anenna elemen drecvy d Omn-dreconal paern ay 0, 0 IO Commun. Sysems Array Sgnal Processng 6

7 Beamformng Beamformng s n a y Receved sgnal x w y Array combnng y y x y w Rero drecve beamformng y w w a n s x x 4 ] E[ ] E[ Oupu SNR Array gan 4 ] E[ ] E[ ] E[ ] E[ P P n s n s o o o ay 0, 0 7 IO Commun. Sysems Array Sgnal Processng

8 Beamformng Incden angle Beamwd Sde lobe level an lobe Sde lobes ay 0, 0 IO Commun. Sysems Array Sgnal Processng 8

9 Inerference Cancellaon Subspace decomposon R EΛE Λ dag[,, 3, 4 ] w y E [ e, e, e, e [ 3 e4 ] Sgnal space Null space e Re 0,3,4 Re x Inerference cancellaon x w y w,3,4 e Oupu SNR w o w w wp 0 ay 0, 0 IO Commun. Sysems Array Sgnal Processng 9

10 Inerference cancellaon Incden angle ay 0, 0 IO Commun. Sysems Array Sgnal Processng 0

11 ul-pa Sgnal odel ul-pa sgnal model y s n L l l Tme varan cannel response d a l l l l d v e l l jkv cos l ay 0, 0 IO Commun. Sysems Array Sgnal Processng

12 Dversy Combnng ul-pa sgnal model y s n axmum rao dversy combnng x w y w w y Oupu SNR o E[ s E[ n ] ] P P P x Sum of eac SNR ay 0, 0 IO Commun. Sysems Array Sgnal Processng

13 Dversy Combnng Power [d db] Branc # -5 Branc # RC Deep fadng f D ay 0, 0 IO Commun. Sysems Array Sgnal Processng 3

14 Caracersc Funcon PDF of sum of ndependen random varables f x f y f x, y f x f y z x y f z f x f z Caracersc funcon x dx f exp j d Convoluon 0 f exp j d Caracersc funcon on convoluon ay 0, 0 IO Commun. Sysems Array Sgnal Processng 4

15 PDF of dversy combnng PDF of dversy combnng Oupu SNR of RC C f f b f exp j Caracersc funcon of eac branc j PDF of oupu SNR n RC j exp! f ay 0, 0 X square dsrbuon Dversy gan 5 IO Commun. Sysems Array Sgnal Processng

16 CDF of Dversy Combnng Array gan on average SNR 0 0 = Cumu ulave ds rbuon = = 3 = 4 ay 0, Normalzed SNR [db] Dversy gan on ouage SNR IO Commun. Sysems Array Sgnal Processng 6

17 BER of dversy combnng Average BER Pe Pe f d 0 - Average BER performance 0 0 RC dversy, QPSK Sgnalng, Rayleg SISO SIO x, ISO x SIO 3x, ISO x3 SIO 4x, ISO x4 Insananeous BER for BPSK sgnalng P e erfc PDF of oupu SNR for RC f! Average BER for RC P e exp B Err ror Rae Average SNR per anenna [db] ay 0, 0 IO Commun. Sysems Array Sgnal Processng 7

18 Beam Paern Inerpreaon of Dversy = 4, L = = 4, L = = 4, L = 3 = 4, L = 4 ay 0, 0 IO Commun. Sysems Array Sgnal Processng 8

19 Dversy w Non-Idencal Elemens Non-dencal elemens d d j due o Caracersc funcon of oupu SNR w non-dencal elemens j PDF of oupu SNR n RC w non-dencal elemens exp f k k, k j Cumulave dsrbuon 0 0 = CDF of oupu SNR = 0. = Normalzed SNR [db] ay 0, 0 IO Commun. Sysems Array Sgnal Processng 9

20 Spaal Correlaon Correlaon marx of receved sgnals R E[ yy ] P E[ I y ] Correlaon marx of cannels -0 R * ] E * * E[ * g 0 0 g g * g g g Uncorrelaed Correlaed : Correlaon coeffcen beween brances -0 Pow wer [db] Power [d db] f D ay 0, 0 IO Commun. Sysems Array Sgnal Processng f D 0

21 Dversy Combnng w Correlaon Egen decomposon of correlaon marx R g * g g g Orogonal converson E EΛE g g R y E g 0 P I 0 g Dversy w non-dencal elemens f Cumulav ve dsrbuon 0 0 = 0 = 0.9 = exp exp CDF of oupu SNR Normalzed SNR [db] ay 0, 0 IO Commun. Sysems Array Sgnal Processng

22 Angular Profle & Spaal Correlaon Correlaon marx g R E g Uncorrelaed scaerng g * g L l e l jkvcos la l E jkv cos jkvcos e e 0 j for j Spaal correlaon L R E le l R g ay 0, 0 L l jkv cos L l l 0 l e l jkv cos l e jkd cos jkd cos l jkd cos e e 0 P e d jkd cos l d l d * P 0 IO Commun. Sysems Array Sgnal Processng Angular profle d

23 Angular Profle & Spaal Correlaon corr relaon coe effcen Unform dsrbuon P d J0 kd order Bessel funcon AS=[deg] AS=0[deg] AS=00[deg] cumu ulave dsr rbuon Gaussan dsrbuon 0 P exp sn d exp kd elemen ULA w / spacng 0 - SIO AS=00[deg] SIO AS=0[deg] SIO AS=[deg] - SISO anenna spacng [] normalzed SNR [db] ay 0, 0 IO Commun. Sysems Array Sgnal Processng 3

24 Dversy w Inerference Cancellaon y Receved sgnal w nerference # #N I I D D s s N n y # #N d Subspace decomposon,, N N C e e Q Inerference cancellaon Subspace decomposon IN I I I,,,,, N Q D s n Q Q y Q N C ~ ~ E E I I N N e e e e E,,,,, N C s D n Dversy combnng Null space D ~ w y Q w x Inerference cancellaon N order ay 0, 0 Dversy combnng -N order 4 IO Commun. Sysems Array Sgnal Processng

25 Summary Array sgnal processng Beamformng & nerference cancellaon for plane wave sgnal Dversy combnng for mul-pa sgnal Dversy combnng w nerference cancellaon Improvemen on SNR, SIR, and ouage SNR Furer revoluon Wa appen f array anennas are employed bo a Tx and Rx IO communcaon sysem ay 0, 0 IO Commun. Sysems Array Sgnal Processng 5