st semester. Kei Sakaguchi
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1 0 s semeser MIMO Communicaion Sysems #5: MIMO Channel Capaciy Kei Sakaguchi <sakaguchi@mobile.ee.iech.ac.jp> ee ac May 7, 0
2 Schedule ( s half Dae Tex Conens # Apr. A-, B- Inroducion # Apr. 9 B-5, B-6 Fundamenals of wireless commun. #3 Apr. 6 B- OFDM for wireless broadband May 3 No class #4 May 0 B-7 Array signal processing #5 Nov. 7 A-3, B-0 MIMO channel capaciy #6 Nov. 4 B-, 3 Spaial channel model May 8 No class May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy
3 Agenda Aim of oday Derive hroughpu performance of MIMO communicaion sysem Conens SISO, SIMO/MISO channel capaciy MIMO channel capaciy Transmi & receive diversiy Spaial muliplexing, SVD-MIMO Waer filling power allocaion Measuremen on MIMO channel capaciy May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 3
4 Quesion Warming Up Calculae Singular Value Decomposiion (SVD of marix 0 3 Singular Value Decomposiion (SVD x h z 60 y h U Σ V u v u v m um v m Singular values: diag Singular marices: R r R May 7, 0 U Σ V V Σ U Σ m rank U U I V Σ U U Σ V V V U Λ U V Λ V I m Λ diag MIMO Commun. Sysems (MIMO Channel Capaciy m 4
5 SISO SSOSyse Sysem Received signal y( hs( n( Oupu SNR s h y E[ hs( ] h P E[ n ( ] PDF of oupu SNR in Rayleigh fading f ( exp Channel capaciy Average channel capaciy h P SISO log C SISO SISO f C C d May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 5
6 SISO Channel Capaciy 0 Capaciy vs. SNR channel capaciy [bi/s/ z] SNR [db] May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 6
7 SIMO Sysem Received signal vecor y( hs( n( Oupu SNR E[ w r hs max w r E[ w n ] r ] M r i h i P PDF of OSNR in independen Rayleigh fading f ( ( M M r M! r exp Channel capaciy Average channel capaciy M r P C SIMO log h SIMO SIMO C f C i s h h h M r y w r i d May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 7
8 MISO Sysem Received signal y T ( h w s( n( Oupu SNR T w E[ h s ] w M P max h i w E[ n ] i PDF of OSNR in independen Rayleigh fading f ( ( M! M M exp Channel capaciy Average channel capaciy C MISO M P log h i s w h h h M i C f C d MISO MISO y May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 8
9 SIMO/MISO Channel Cpaciy Chan nnel ca apaciy [bi/ /s/z] ]SNR vs. capaciy 4 SIMO/MISO x4/4x SIMO/MISO x/x SISO SNR [db] May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 9
10 SIMO/MISO SO Channel Capaciy Chan nnel ca apaciy [bi/ /s/z ]Anenna size vs. capaciy SNR=30[dB] SNR=0[dB] SNR=0[dB] Number of anennas May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 0
11 MIMO Communicaion Sysem Muli-Inpu & Muli-Oupu (MIMO a he same channel Uilizaion of rank m min M, M r effecive channels (ex. SISO, SIMO Benefis of MIMO = increase of hroughpu & area coverage MIMO ransmier Beamforming MIMO channel # # MIMO receiver Channel esimaion Spaial muliplexing Space-ime coding # M # M r Beamforming Inerference cancellaion May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy
12 Signal Model for MIMO Sysem Signal Model for MIMO Sysem Received signal vecor Transmi signal vecor ( ( ( n s y Received signal vecor Transmi signal vecor ( ( ( n s y Noise vecor MIMO channel marix M n s h h y y M r r r r M M M M M M n s h h y May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy
13 MIMO Diversiy Received signal vecor y( w s( n( w y w r Oupu SNR E[ w r w s max w, r w E[ w n ] r ] s u v P Channel capaciy C P P u P MD log Maximum singular value max u u, v v May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 3
14 Received signal vecor Spaial Muliplexing M si ( y( h i n( M i Inerference cancellaion w r i \ i Oupu SNR i E[ w ri h i E[ w ri si ( M n ] ] Null subspace inerference cancellaion h,, hi, hi, h \ i M \ i \ i EE Channel capaciy E e,, e M MD g i log C i e M \ i M May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 4
15 SVD-MIMO SVD MIMO Singular value decomposiion y, max v u v u v u ~ W W v u Eigenmodes m m m v u v u v u U Σ V m,, diag SVD MIMO r, min M M m SVD-MIMO ( ( ( r r n W W s W y ( ~ ( May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 5 ( ~ ( n Σs V W U W r if
16 SVD-MIMO Singular value decomposiion UV diag,, m MIMO channel capaciy C m MIMO log i P i m x y Tx ing daa S/P eigen-beam mforming x x 3 x 4 y y 3 y 4 Rx eigen n-beamform P/S daa V feedback channel channel esimaion SVD U May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 6
17 PDF of SVD-MIMO PDF of singular values (Wishar disribuion m m n m f (,, exp( m i i ( i j K K m, n Marginal probabiliy m, n i ij m (m n max M, M r m( n m ( m m minm, M r f ( f (,, m d dm May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 7
18 PDF of SVD-MIMO (Example o S O( a pe M x MIMO M Join disribuion (Wishar disribuion M M r Marginal probabiliy, ( e f Marginal probabiliy ( e e f 5 E 3. ( e f 5 E 0. Cumulaive probabiliy ~ ~ ~ ~ ~ ~ ~ ~ d ( ~ ~ 4 ~ ~ ~ 0 e e f f May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 8 0 ~ ~ d ( ~ e f f
19 CDF of SVD-MIMO Oupu SNR of SVD-MIMO 0 0 cumula aive dis sribuio on 0 - SISO MIMO ch. 4 MIMO ch. 3 MIMO ch. MIMO ch. 0 - MIMO oal normalized SNR [db] May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 9
20 MIMO Channel Capaciy Conribuions of differen eigenmodes May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 0
21 MIMO Channel Capaciy Chan nnel ca apaciy [bi/s s/z] Anenna size vs. capaciy SNR=0[dB] SNR=0[dB] SNR=30[dB] MIMO array size May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy
22 MIMO Channel Capaciy Chan nnel ca apaciy [bi/ /s/z] ]SNR vs. capaciy 35 MIMO 4x4 30 MIMO x SISO SNR [db] May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy
23 Transmi Power Opimizaion Cos funcion C m MISO log i m subjec o P P i i P i i Mehod of Lagrange mulipliers m P i i J log P i J 0 log Pi P i i Opimal MIMO channel capaciy P i m i m C WF log i i i e P i Waer filling May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 3
24 Opimal MIMO Channel Capaciy nnel cap paciy [b bis/s/ z] Ergo odic cha MIMO 4x4 MIMO 4x4 wf MIMO 4x MIMO 4x wf MIMO x MIMO x wf SISO SISO wf Average SNR per anenna [db] May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 4
25 Measuremen Sysem ULA ULA 4-ch 4-ch 4-ch 8-ch AWG ransmier vatt receiver DSO GPIB PC posiion conroller x-y posiioner May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 5
26 Phoos of Measuremen Sysem Rubidium -ch AWG x 8-ch DSO 4-elemen ULA Transmier x4 PC Receiver x 4 May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 6
27 Process of Measuremen Transmi frame upload Posiion conrol Frame daa acquisiion Channel esimaion Coheren deecion i y Ĥ ŝs Error coun END? May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 7
28 Measuremen Seup Cener freq. Array ype Tx. power Bandwidh Modulaion Frame 5. [Gz] 05λ 0.5λ spacing 4-elemen sleeve array 0 [dbm/channel] SNR = 5 [db] 87.5 [kz] 5 [ksps] α=0.5 BPSK,,Q QPSK, 6QAM 5 (3:raining 48:daa Meas. poins 56 poins ( [cm ] sep in [cm ] May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 8
29 Measuremen Environmen May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 9
30 Transmi Array Anenna (AP May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 30
31 Receive Array Anenna (UT May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 3
32 RF Transceiver RF IN BB OUT RF OUT BB IN Donaion from Samsung Yokohama Insiue of Technology May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 3
33 Received Signal of x MIMO wih QPSK Signaling Received signal Inerference cancellaion May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 33
34 Disribuion of Channel Capaciy SNR=0[dB] SNR=0[dB] May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 34
35 CDF of Channel Capaciy May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 35
36 Dependency on MIMO Array Size Channel capaciy increases linearly w.r.. array size in real environmen May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 36
37 MIMO channel capaciy Summary Transmi & receive diversiy o enhance reliabiliy Muli-sream spaial muliplexing o enhance specral efficiency SVD-MIMO & waer filling power conrol achieves bes performance MIMO channel capaciy increases linearly wih respec o he number of anenna elemens in IID fading environmen ow abou in realisic propagaion environmen? Double direcional spaial channel model May 7, 0 MIMO Commun. Sysems (MIMO Channel Capaciy 37
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