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( & & $ B ' " $% A Chapter 1: "Introduction" Chapter 2: "An Overview of Design Strategies in Multi-Antenna Systems" Chapter 3: "Joint Beamforming Design in MIMO-OFDM SingleUser Communications" Chapter 4: "Joint Beamforming Design in MIMO-OFDM MultiUser Communications" Chapter 5: "Sources of Imperfections in the CSI and Robustness Strategies" Chapter 6: "Robust Maximin Design of MIMO Single-User Communications" Chapter 7: "Conclusions and Future Work" Preceding block is required Preceding block is recommended : $ A ( , . ' $% & # H% ( %. " $ : $% ' " R & . $% $ B G ) ( $% ' ( ) $ C R # ( " ( & ( ! ' $ B " (& . ! ' $ < ' ;B G ! ! ! ! $% #)( ' $% # / K@AL . . 2 & 0 . 3 =2 & O ! C . % ( % 0 + ' %P B B F@FF?@ ?@@A K@;L . . 3 =2 & . 2 & 0 O% . %9 * $P !"#$ B ;;<D;;F? % ?@@; K@;L . . 2 & 0 . 3 =2 & O ) $ . =*+3.0I? ' P % & ' !"#$ BF % ?@@; K@? L . . 2 & 0 . 3 =2 & O6 ) ( (!")$ % ' %P B ?FA:?FAF ?@@? 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G / M U BF , B: '' $ & M U ( % U BD " . $ $ 9 BD 9 + M U B;@ ## "# A? bp(0) s0(m) bp(1) s1(m) IFFT modulation + P/S + CP addition s(m) xT(p)(m,n) bp(N-1) sN-1(m) (a) a1*(k) xR(1)(mP+n) yk(1)(m) CP removal + S/P + FFT demodulation a2*(k) xR(2)(mP+n) xR (nR ) (mP+n) yk(2)(m) CP removal + S/P + FFT demodulation rk(m) + yk CP removal + S/P + FFT demodulation ( nR )(m) dec{·} QAM demodulator sk(n) a n *(k) R (b) %& ( % & . 9 % % % % B;; ! ) *##% % &+ %&, ## '' Æ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umulative Density Function of the Maximum Eigenvalues. As=30º (TX), 15º (RX). channel A. 1 0.9 0.8 Cumulative Density Function 0.7 0.6 0.5 0.4 0.3 0.2 1+1 antennas 2+2 antennas 3+4 antennas 5+5 antennas 0.1 0 0 5 10 15 Maximum eigenvalue 20 25 !0 12Ó 34Ó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Æ # Æ . ( K)@A @BL & $G / % " & ( " BAC # B?A , K@BL * G / ) M ( ? @ U ) BA< B?A . $. %* & $G G M @ ) , =.+ .>0 G @ ) M 9 ( ) BAF " / M ; BAD ! 5 * & ! , Q Æ - # :? ) 7 ) ) 23 ( 8 M #1 ( 8 9* ( 8 M % M M ( M M ; M ; ( @ 31 ( 8 @ ) 3 ( 8 - ( 8 M ( ( ( M ; "& 2& , B; ! ! # % % =3.0I? * J3.0 K*%@@L " CA ' :? A & $ ! ! )%E M ?@ =& M B? ) M A ! ) M ;C S )*+ " BAA & & M ; & " *% K*%DFL " ( %0+ ' B< ( & BUA " " . K*%DFL :@ B@ ;: ? . .J50 ' B< F :: ) *##% % &+ %&, ## :B Maximum eigenvalues vs frequency 22 20 18 Maximum eigenvalues 16 14 12 10 8 6 4 2 0 0 10 20 30 Subcarrier index (k) 40 50 60 ½ %& 8 19: $ ' BF BD B;@ %0+ ! 5*$. =.+%* .>0* / M ; J M ;@@ J $. %* * ' BF BD B;@ ! . ( 5* " %0+ ( ' BF ' =.+ .>0 ! ! ' BD B;@ G $. %* * .>0 !& %0+ %0+ (& M ;@@ J 5* ! G %* * ! $ $. 5* ! ' BF - # :A Power allocation − GEOM − low P0 SNR − GEOM − low P0 1 0.04 0.8 SNR power Pk 0.05 0.03 0.6 0.02 0.4 0.01 0.2 0 0 20 40 Subcarrier index (k) 0 60 0 Power allocation − CAP − low P0 0.04 0.8 SNR power Pk 1 0.03 0.6 0.02 0.4 0.01 0.2 0 20 40 Subcarrier index (k) 60 SNR − CAP − low P0 0.05 0 20 40 Subcarrier index (k) 0 60 0 20 40 Subcarrier index (k) 60 Power allocation − GEOM − high P0 SNR − GEOM − high P0 30 2 25 power Pk 2.5 SNR 1.5 20 15 1 10 0.5 0 5 0 20 40 Subcarrier index (k) 0 60 0 Power allocation − CAP − high P 60 SNR − CAP − high P 0 0 2.5 30 2 25 power Pk 20 40 Subcarrier index (k) SNR 1.5 20 15 1 10 0.5 0 5 0 20 40 Subcarrier index (k) 0 60 0 20 40 Subcarrier index (k) 60 * /. !$* 7 %& # %¼ ; 3 <& % & = %¼ ; 322 <& ) *##% % &+ %&, ## Power allocation − HARM − low P0 SNR − HARM − low P0 1 0.04 0.8 SNR power Pk 0.05 0.03 0.6 0.02 0.4 0.01 0.2 0 0 20 40 Subcarrier index (k) 0 60 0 Power allocation − MMSE − low P0 0.04 0.8 SNR power Pk 1 0.03 0.4 0.01 0.2 20 40 Subcarrier index (k) 60 0.6 0.02 0 20 40 Subcarrier index (k) SNR − MMSE − low P0 0.05 0 :: 0 60 0 20 40 Subcarrier index (k) 60 Power allocation − HARM − high P0 SNR − HARM − high P0 30 2 25 power Pk 2.5 SNR 1.5 20 15 1 10 0.5 0 5 0 20 40 Subcarrier index (k) 0 60 0 Power allocation − MMSE − high P 60 SNR − MMSE − high P 0 0 2.5 30 2 25 power Pk 20 40 Subcarrier index (k) SNR 1.5 20 15 1 10 0.5 0 5 0 20 40 Subcarrier index (k) 0 60 0 20 40 Subcarrier index (k) 60 * /. =$. 7 %& # %¼ ; 3 <& % & = %¼ ; 322 <& - # :C Power allocation − MAXMIN − low P0 SNR − MAXMIN − low P0 1 0.04 0.8 SNR power Pk 0.05 0.03 0.6 0.02 0.4 0.01 0.2 0 0 20 40 Subcarrier index (k) 0 60 0 Power allocation − MEP − low P0 0.04 0.8 SNR power Pk 1 0.03 0.6 0.02 0.4 0.01 0.2 0 20 40 Subcarrier index (k) 60 SNR − MEP − low P0 0.05 0 20 40 Subcarrier index (k) 0 60 0 20 40 Subcarrier index (k) 60 Power allocation − MAXMIN − high P0 SNR − MAXMIN − high P0 30 2 25 power Pk 2.5 SNR 1.5 20 15 1 10 0.5 0 5 0 20 40 Subcarrier index (k) 0 60 0 Power allocation − MEP − high P 60 SNR − MEP − high P 0 0 2.5 30 2 25 power Pk 20 40 Subcarrier index (k) SNR 1.5 20 15 1 10 0.5 0 5 0 20 40 Subcarrier index (k) 0 60 0 20 40 Subcarrier index (k) 60 * /. $>/ * 7 %& # %¼ ; 3 <& % & = %¼ ; 322 <& ) *##% % &+ %&, ## :< 3+4 antennas. BPSK. GEOM, CAP techniques. channel E. 2 interferences. −1 uncoded effective BER 10 −2 10 CAP − SNR=5 dB − As=30º(TX), 15º(RX) CAP − SNR=5 dB − As=40º(TX), 60º(RX) GEOM − SNR=5 dB − As=30º(TX), 15º(RX) GEOM − SNR=5 dB − As=40º(TX), 60º(RX) CAP − SNR=10 dB − As=30º(TX), 15º(RX) GEOM − SNR=10 dB − As=30º(TX), 15º(RX) CAP − SNR=10 dB − As=40º(TX), 60º(RX) GEOM − SNR=10 dB − As=40º(TX), 60º(RX) −3 10 −15 −10 −5 0 SIR (dB) 5 10 15 ! !$* 7 . . /. ? 4 32 5 1 : " ) 6 " ? 12Ó 34Ó 5 :2Ó @2Ó " A 7 ( BB; ! =.+%* .>0* BB? ' BD B;@ BBB " ! )*+ " %0+ %+ " / %0+ M - %+ M - .J50 ' ' B;; 5* $. )*+ BUA " * ! ?:@ %+ ? ! %0+ / : ;@ ) G B@ C@ ;: A@ ' " 5* $. , 5* - # :F 2+2 antennas. BPSK. HARM, MMSE techniques. channel E. −1 10 −2 uncoded effective BER 10 −3 10 MMSE − 1 interf. SIR=−5 dB − As=30º(TX), 15º(RX) HARM − 1 interf. SIR=−5 dB − As=30º(TX), 15º(RX) MMSE − 1 interf. SIR=−5 dB − As=40º(TX), 60º(RX) HARM − 1 interf. SIR=−5 dB − As=40º(TX), 60º(RX) MMSE − 0 interf. − As=30º(TX), 15º(RX) HARM − 0 interf. − As=30º(TX), 15º(RX) MMSE − 0 interf. − As=40º(TX), 60º(RX) HARM − 0 interf. − As=40º(TX), 60º(RX) −4 10 0 2 4 6 8 10 12 14 SNR (dB) ! =$. 7 . /. ? 3 ( . ; 4 5 A A " ) 6 " ? 12Ó 34Ó 5 :2Ó @2Ó . )*+ =.+ %* ! ' B;? ?U? )*+ %0+ / %+ ! : ) " " " =.+ ! %0+ ) %* BB? =.+ %* =.+ ' %* + )*+ ' B;B .>0 * )*+ . ( * & $G )*+ ) *##% % &+ %&, ## :D 2+2 antennas. BPSK. MAXMIN, MEP techniques. channel E. −1 10 −2 uncoded effective BER 10 −3 10 MAXMIN − 1 interf. SIR=−5 dB − As=30º(TX), 15º(RX) MEP − 1 interf. SIR=−5 dB − As=30º(TX), 15º(RX) MAXMIN − 1 interf. SIR=−5 dB − As=40º(TX), 60º(RX) MEP − 1 interf. SIR=−5 dB − As=40º(TX), 60º(RX) MAXMIN − 0 interf. − As=30º(TX), 15º(RX) MEP − 0 interf. − As=30º(TX), 15º(RX) MAXMIN − 0 interf. − As=40º(TX), 60º(RX) MEP − 0 interf. − As=40º(TX), 60º(RX) −4 10 0 2 4 6 8 10 12 14 SNR (dB) ! $>/ * 7 . /. ? 3 ( . ; 4 5 A A " ) 6 " ? 12Ó 34Ó 5 :2Ó @2Ó .>0 0 ( G ! ; ) %0+ .>0 * ' * ! ( .>0 . )*+ ' B;A B;: 5* %* =.+ .>0 ?U? ! B@ ;: / %+ ! : ) ' B;A " . ! :@ ' B;: $ ! ;:@ ' " ! 5* ! .>0 =.+ ! 0 %0+ - # C@ 2+2 antennas. BPSK. As=30º (TX), 15º (RX). channel A. −1 10 −2 uncoded effective BER 10 −3 10 GEOM − 1 interf. SIR=−5 dB MAXMIN − 1 interf. SIR=−5 dB MMSE − 1 interf. SIR=−5 dB HARM − 1 interf. SIR=−5 dB GEOM − 0 interf. MMSE − 0 interf. HARM − 0 interf. MAXMIN − 0 interf. −4 10 0 2 4 6 8 10 12 14 SNR (dB) ! 5 5 =$.5 $>/ 7 . /. ? 3 ( . ; 4 5 A A " ) 6 $ " 12Ó 34Ó .>0 =.+ 5 #" $G .>0 & )*+ BBB 0 5 .>0 =.+ %0+ %+ 0 %0+ .>0 )*+ 5* %* .>0 ' ! J ! ' B;A B;: ' 5* ! .>0 =.+ $. %* * ) *##% % &+ %&, ## C; 2+2 antennas. BPSK. As=30º (TX), 15º (RX). channel C. −1 10 −2 uncoded effective BER 10 −3 10 GEOM − 1 interf. SIR=−5 dB MMSE − 1 interf. SIR=−5 dB MAXMIN − 1 interf. SIR=−5 dB HARM − 1 interf. SIR=−5 dB GEOM − 0 interf. MMSE − 0 interf. HARM − 0 interf. MAXMIN − 0 interf. −4 10 0 2 4 6 8 10 12 14 SNR (dB) ! 5 5 =$.5 $>/ 7 . /. ? 3 ( . ; 4 5 A A " ) 6 ! " 12Ó 34Ó & # ' ( , , ) # " # (& %0+ . " G / 5* =.+ .>0 / $. %* * .>0 =.+ ! G $ .>0 (& %0+ . ##" C? %0+ ! G ( ! ! * & $G )*+ * ' ) *##% % &+ %&, ## CB #' "! '( ) * %0+ %0+ M M B:@ ( @ ! @ = ( " . M . ; A M ; / ; M $ M # ; AA B:? B:B = ( " M K L / / ! ( , %0+ B:; . . / / + + + . 0 / M M ; 9 B:? = ( ; M . ( " . / " M # @ K; $%& ;L B:A ! + M (& ( & B:@ * /' ($ /#0% 1# CA (& & / & # S M @ ; B:: M @ @ 3 U B:C EE / . S M . ; M . U ! @ BC; M @ @ M @ ; B:< ; B:F B:D M @ M @ ; BC@ M @ M @ ; BC; $! @ M @ @ M @ ; ! 9 # B:D / + M #' "! * ; %0+ ; M @ ; BC? '( , %0+ M BCB ( @ ! @ ) *##% % &+ %&, ## = ( " Æ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Æ & ( . %. ! & " & ( G , 5% . ! " ( ) , " ! " , , , # K3,@@L , $$ . ! . & ! H% %0+ ( )*+ ( & 5% ! 3 KJ@;L ' & . ! # "( " & - ) *##% % &+ &, ## %0+ CD H% " , R & K$@?L Q )%Q G & " & %0+ "( # (& %0+ # " ! ( & , & G K+@AL , )% Q H% K%@AL # & %* # ! " . . , )% Q & K)@?L & %0+ # , , ( # & K7DDL & )%Q Q . ( ' K)@?L )%Q Q . . ! # H% %0+ & ! R & ! ' % A? & %. ! % AB %. % AA ! 5% - (#' # % %# <@ . % A: % AC ' % A< % " $ # K@A @? @?L %. K.FD 3F<L %. & & " & ( G ! 5% . 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" 3 & & & ?< ?BB ( / / @ M ; M @ , " & S OP ( U U & M ; AF " / AD " & , @ " " A? A? " & @ J , % %. & " & 5 & O P & (/ & M U 0 -" A;@ ( 5 & ( G ( %. K.FDL & - / "# &, ## <C @ K7FAL ( %. ( = ( = ( & V K$FA JF: EFC %&F<L G G ' ( K%&F<L $ KD;L ! % -' # ./ . $ ( 3 . , ! B $ ' . I * , % ++(!+ +"(4 & + . $ B , G # G G Q .Q )%Q I . ! G , ' A? 3 ,4 4 , ' 4 ' A? ( , ( # , # 4 $ B ' - ) *##% % &+ &, ## #1 3 1)=3 #2 1, r(2 t(2)= 1 #5 (5)= r 2, )= t(5 )=4 t(4 )= #4 3, r(4 )= 2 t(1)=1, r( 1 << #3 t(3)=3, r(3)=4 4 ; ;; ; ;; 2 term. #4 i sig nter na fer l ( ing M AI ) ed de term. #1 al t(1) = 1 ign ds sir ire link #1 r(3) = 5 r(2) = 4 des sig na l r(1) = 4 term. #5 link #2 de sir ed link #3 sig na l t(3) = 3 t(2) = 2 term. #3 term. #2 %& 6 ) 5 4 : % & 6 ) 1 + " 45 1 "0 A 0 - / "# &, ## <F & 4 , $# % M ' 9 $# + $# U A;; & ( B;@ B;@ A;; 3 M ; $# # ( ( ' 9 $# ,# ' 4 $ B ( # 9 0 M 4 # + & ' $# & M ; & ( B $# ' 4 $# $# ( ! " , % ' , , " (4 , ," , $ B 4 ' # $# # ' # $# M A;? # 9# $# +# # # " # U % # # ' 9 $# + # $# # ' U ! %0+ A;B B?B J - ) *##% % &+ &, ## <D " "/ # *# *# 4 *# 9# $# +# % $# B 9 $# + + 9 $# # M M U A;A A;: # ( , 4 G Æ %0+ & ! 0 # # 9# $# +# M ; %0+ I %0+ 4 # +# 9# $# *# 9# $# +# M , ( *# + # A;C B?B A;A # + % # G , Æ & A;A %0+ . AA # , ( G J ' G 4 # ( # # ; ( 5 ( # % M # " , % KD:L )%E A;< $ # %0+ % A;F M ; # M ? %0+ A;C A;A ,-./ % ! 0 -- # % #0 (!# F@ %% # " ( ( A;A # J # & " . # & , Q . ( $ B 4 + ) # ) ) ) B?B , " ! ) + # & / # + # M % ) ) ) # ) # + M % # # # & / + # M + + A;D 0 4 = , " H% , ( = 1 ( G # 5 # 5 # ( 4 M ; 3 ( A?@ 4 & & K3,@@L $$ . K$@? )@? 7DD )@?L R H% %0+ G KJ@; +@A %@AL "( " # & ! , %* H% & ( )%Q Q - ) *##% % &+ &, ## Æ " F; / 1 H% ( Q 3 W , ) % + ) ) # ) ## ( W A?; , , %& & # % ) # ) ) ) + # # 5 # 4 M ; A?? 3 W $ ( ( & ( K)@AL . ( & + # # ( 3 M ; ' M ; ( G ! %0+ 3 9 M B M ( . H% + + %0+ %0+ ! %0+ ( ( ( + 5% . " % 5% ! K3,@@L . KJ@; $@? %@A 7DD )@?L G , . K$@?L # " & %. ) 5% . ! Æ , %. ( -- # % #0 (!# F? %" 5% ! G %. ( " & A?? %. %. & + %. ( # 5 ! O / P OP @ & ( A?; O O " & P P OP " , A;D A?? " " & . " %. & A?? ' " " % 5 5 1 & + # S # + U % # # 5 # U A?B " ! ! , G " ( ) - ) *##% % &+ &, ## FB OP " " % & , & " . ! # M ;@@ G ( , ( 0 , 1 +&# +# # M # 0 -& U M @ ; 4 M ; -& ( A?B @; : 5 A?A ( 5 & 3 ( - & ' @D:- & ( && 1 + # & * + + , + + - ; ( # + K.FD 3F<L ( & # + & +# & # & +# & + & A?: A?? ()& ( ' G ! . %. Æ " ( -- # % #0 (!# FA 1 . ' ( M @DD A?C ! ( ( ( A?? A< ' A; ( . A?: $! J , ( %. 0 & ! & " %. & ;@@ & -& ! ! H% ( G , . $ B # D: ;@@ X % ' AB R & %. %. & ;@@ A?C ;@ X : 5 -& ' @D:- , & ! @ % ' AB R %. - ) *##% % &+ &, ## F: Main iteration BEGIN Initialization 2 b 0.95 2 b Lar = 5 Initialization Lar ? T=1 = mean transmit power with no MAI (u) bk = 0 2 b T 0.9T Lar < 5 Propose 100 solutions. Na = number of nonaccepted solutions Lar Propose 100 solutions. Na = number of nonaccepted solutions Lar = 0 T Lar+1 T 2T 0 < Na < 10 Na = 100 Na ? Na < 95 95 < Na < 100 0.99T Na ? Na > 10 Na = 0 no convergence ? END yes END (a) (b) ( $ %& 8 $ % & $ -. !## 2 FC %& $0 AA %. ! " & A?? 0 5% . %* . 2 . G %. ! , %. ! 3 ! K3,@@ )F?L ! " 3 ( , ( A?@ " ! 9 3 ( + # S # + % U U 5 ! A?< , ! K3,@@L/ +# ' +# ) A?F ) ' % U ) & U 5 A?D # G . $ B ! @ ( , Q )% )%E , ! 4 9 Q # )% ( ( Æ " - ) *##% % &+ &, ## Æ 4 M ; 4 W +# M U ? ' $ M 4 5 ?6 U / ( W ' ; 4 # ; M M @ % ( Æ 4 F< # %0+ +# Æ 4? # M 4/ # # # # 9 * 9 + # ; AB@ ' # # AB; ?%0+ ( ( K5DCL / %0+ M ; ?6 ( %0+ # ; ?%0+ %0+ AB? . . . # # # . 9 * 9 + . 9 * 9 + .. $ % .+ # # # # # + 9 * 9 + # # # + # 9 # * # 9 +# # 9# *# 9 + + 9 * 9 + % B 9 + + 9 # M # # ;U ABB ;U *# M U ABA # ( .( A. . , 5% ! G 0 %* 2 5 + 2 ' KJ@; %@A 7DD )@?L . %0+ , ( A;: A;C . ! "( -. !## 2 FF Initialization Set all the transmit beamvectors equal to the maximum eigenvectors of (t(u),r(u)) H Hk (r(u)) O In -1 (k)Hk(t(u),r(u)) (without taking into account the MAI). Calculate the power allocation: GEOM or MAXMIN. Calculate the covariance matrices: (u) {Rk } Calculate the transmit beamvectors as the maximum eigenvectors of (t(u),r(u)) H Hk -1 (u) (t(u),r(u)) Rk H k Calculate the power allocation: GEOM or MAXMIN. no convergence ? yes END ( $ ( , ( ! . , ( ( Æ (& %0+ ( ( 9# $# *# 9# $# ! B?B B?? ) ' H% ( " G / 5* - ) *##% % &+ &, ## Simulated Annealing. MT’s power. Scenario 1. 10 power 10 FD 1 10 5 10 0 10 8.5 9 9.5 user 1 user 2 user 3 10 x 10 0 10 0 1 2 3 4 5 flops 6 7 8 9 10 10 x 10 Simulated Annealing. Mean BER. Scenario 1. 0 10 mean BER −100 −2 10 10 −200 10 −3 10 user 1 user 2 user 3 8.5 −300 10 0 1 2 3 4 5 flops 6 7 9 8 9.5 9 10 x 10 10 10 x 10 * $ 3 1 "0 3 + 6 5 4 " / ( 3@ .0 C .>0 ! %0+ ! BB & . G ( $ B % ' AA R . K%@A 7DD )@?L ) . G & 0 %1 , B Q )% : ' M ;C -3 # D@ Simulated Annealing. MTs power. Scenario 1. 10 1 10 power 10 5 10 0 10 8.5 user 1 user 2 user 3 9 9.5 10 x 10 0 10 0 1 2 3 4 5 flops 6 7 8 9 10 10 x 10 Simulated Annealing. Mean BER. Scenario 1. 0 10 −2 mean BER −100 10 10 −200 10 −3 10 user 1 user 2 user 3 −300 8.5 10 9 9.5 10 0 1 2 3 4 5 flops 6 7 8 9 x 10 10 10 x 10 * $ 3 1 "0 3 + 6 5 4 " " 6 D < ( 3@ .0 C )% Q , H% ;@ ;@ ( G / ;@ A?B ;@@ & ! ; B $# M 4 & ' ( , " ' A: )*+Q %. ! " " H% " FA: J ?@; J " ! F J ' AC %. <C J " - ) *##% % &+ &, ## 2 Simulated Annealing. MT’s power. Scenario 2. 10 D; 10 power 10 5 10 0 10 user 1 user 2 user 3 8.5 9 9.5 10 x 10 0 10 0 1 2 3 4 5 flops 6 7 8 9 10 10 x 10 Simulated Annealing. Mean BER. Scenario 2. 0 10 mean BER −100 10 −2 10 −200 10 −3 10 user 1 user 2 user 3 −300 8.5 10 9 9.5 10 0 1 2 3 4 5 flops 6 7 8 9 x10 10 10 x 10 * $ A 1 "0 3 + 6 5 4 " 7 3A ( 3@ .0 C . ?@F J ( ( & " ' A< AF " ! ;? ) ' A< %. ' AF 5% & ! ) M @@@; R %. " 5% ! 3 ( A?< ! " & % . G / 5* .>0 BB; BBB ' . -4 ##" D? Gradient based method. MT’s power. Scenario 2. 2 10 power user 3 user 1 1 10 user 2 user 1 user 2 user 3 0 10 0 1 2 3 4 5 flops 6 7 8 9 10 10 x 10 Gradient based method. Mean BER. Scenario 2. −1 10 user 1 user 2 user 3 mean BER user 3 −2 10 users 1,2 −3 10 0 1 2 3 4 5 flops 6 7 8 9 10 10 x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¾ ¾ ½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rror power due to the channel variability 3 Power of the error in the CSI Power of the error in the CSI 2.5 2 1.5 1 0.5 0 0 0.5 1 1.5 delay (normalized by 1/fD) * ! ) 7 6 5 ) 8 ) 7 ) " 85 5 ¾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Æ U Æ 9 * 9 9 * 9 Æ M . .>0 M / M :BC 9 * 9 ) ) )9 * 9 ) ) ) ) ) :B< :BF BBB % # ( %0+ :BC/ # Æ M # M U Æ # $ M :BD :A@ , %0+ .>0 $% %0+ BBB ( BAB/ M %0+ M ( %0+ %0+ %0+ U Æ U U M U Æ U :A; :A? Æ Æ Æ U :AB Æ Æ U Æ U Æ :AA . % &+ %&, "# ;@F . " ( %0+ %0+ $% %0+ %0+ . . %0+ .. M Æ Æ Æ :A: . " ( ( .( :.. " (/ Æ Æ U Æ # M ; ! Æ # U Æ " ; # # :AC ( KÆ L M K L M 0 / 1 0 KÆ L M 1 :A< :AF ! 6Q ! 9 ! KÆ L/ KÆ L , M 9 * 9 M , U ?- , ?- K L K L :AD .( :.) ) , :AD " ( %0+ ; 9 * # 9 ?- ! ?- 9 * # 9 - 9 * # 9 9 * # 9 " 9 * 9 - 9 * 9 # * # 9 9 * 9 9 U? U ::@ U? ; $% 43 '* '* ' * '678* ' * 5 . # ! % ;@D %0+ - - . .>0 ( ' ( =.+ BB? BB? M ; %0+ ::; .>0 %0+ ; Æ ::? . .>0 =.+ ( %0+ %0+ ( %0+ , ( :BD :A@ , %0+ $% %0+ %0+ BB? BBB Æ U U Æ U U M M ::B Æ U U Æ Æ U Æ Æ ::A U Æ ( U Æ Æ U Æ " " ( .( :.$ / %0+ . .. . %0+ %0+ ; ? Æ Æ U ; Æ ? ::: ( Æ - K L - %0+ . % &+ %&, "# ;;@ 1 2+2 and 4+4 antennas. As=30º (TX), 15º (RX). channel A. No interferences. 10 worst relative degradation of the SNR 0 10 −1 10 −2 10 Theoretical upper−bound degradation. 2+2 antennas. Estimated degradation. 2+2 antennas. Theoretical upper−bound degradation. 4+4 antennas. Estimated degradation. 4+4 antennas. −3 10 −10 0 10 20 30 estimation SNR (dB) 40 50 60 /. /. $>/ ) ! ) 5 A9A :9: " ) 6 $ " 12Ó 34Ó " * " ," & ! $% . BA $ B " =3.0I? K*%@@L , " . K*%DFL ! :@ & M ; & BA B@ ;: %0+ " BA %0+ M - . - .J50 5 ! %0+ " %0+ ;- 9 - . . # ! % ;;; 2+2 antennas. BPSK. As=30º (TX), 15º (RX). channel A. Noise in the CSI. −1 10 −2 uncoded effective BER 10 −3 10 −4 10 Estimation SNR=5 dB Estimation SNR=10 dB Estimation SNR=15 dB Estimation SNR=20 dB Estimation SNR=25 dB Perfect CSI −5 10 0 2 4 6 8 10 12 14 SNR (dB) ) ! . /. $>/ ) /. ? 45 325 345 A25 A4 5 ! 5 A A " ) 6 $ " 12Ó 34Ó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s0(m) P1 s1(m) IFFT ... S/P P/S xT(n) CP addition ... information symbols PN 1 sN-1(m) " ) ( ** +" -/, 2 (!+ " $ B A ' , %% # ' ' 3 ) @ ; % ' ; ! ' " ( " M ) ::D . ' :A ( " ( % " %% M J :C@ $ B B?A , $ . # ! % ' $ M % & U ;;< M ; :C; ' .J50 - %0+ %0+ M % M % - M - ) ( M ) ) :C? - 0 ( %0+ & B?? %% G " BAA % %0+ :CB ( , " )%E H%E & G ! ! & $G ( %0+ $G M % %0+ " %0+ M " :CA ( G ! ' . , ( ) !! ! !9 ¾¾ 2 7 .. # /# *" % ;;F *+ 1 % & % % M = ( % ) M @ @ M & # & ; :C: BBB BA< 9 ( ) M ?- ( % % @ U ) :CC :C@ *+ 1 J , ( ) 3 ) ) ) U Æ :C< Æ ! % % ( ' ) M % U Æ ) 5 ( ( @ @ )) ) M ; @ 6 " $! & ( ) @ ) ) :CF Æ & 5 ( E ÆÆ )S . # ! % ;;D Æ Æ M ; E 6 ( Æ EÆ :CD 9 Q )) M M )) :A; / ) ) ) ; Æ ) ; ; ) 6 ) E / ( :<@ ) ) E ) ) )) ) ) M / M ; @ 6 ( ) @) ) ) ) ) Æ :<; # & ( $G G / ; / ) + M ?- ( ( & ( ) ) ) ) "* Æ ( ) ( :<? "* # :C@ ! ( & .( :) !/ & # * * @ M M @ ; :<B M , M . @ E . . E E).. . @ U U :<A :<: .( :$ ) EE ( :<B .. # /# *" % ;?@ Actual channel frequency response 10 5 Channel gain (dB) 0 −5 −10 −15 −20 −25 10 20 30 40 Subcarrier index (k) 50 60 (7 ) 5 5 85 * % " %% & M ; " ( & ! B ' M CA ' :: ! & ;@ ( ' :C :C & %0+ ! ;: ) G E M @@; " ! E M @: ! ! $% " $% . # ! % ;?; Power allocation − Non−robust design 30 20 k power P (dB) 25 15 10 5 0 10 20 30 40 Subcarrier index (k) 50 60 50 60 50 60 50 60 Power allocation − Robust design 30 20 k power P (dB) 25 15 10 5 0 10 20 30 40 Subcarrier index (k) Power allocation − Non−robust design 30 20 k power P (dB) 25 15 10 5 0 10 20 30 40 Subcarrier index (k) Power allocation − Robust design 30 20 k power P (dB) 25 15 10 5 0 10 20 30 40 Subcarrier index (k) . %& = /. % ; 223& % & # /. % ; 24& .. # /# *" % ;?? Robust and non−robust solutions. Channel estimates length: 3 taps. 0 10 −1 uncoded effective BER 10 −2 10 −3 10 Estim. noise power=0.5 − Non−robust Estim. noise power=0.5 − Robust Estim. noise power=0.1 − Non−robust Estim. noise power=0.1 − Robust Estim. noise power=0.01 − Non−robust Estim. noise power=0.01 − Robust −5 0 5 10 SNR (dB) 15 20 25 ! 7 . /. 8 )5 ) 7 1 5 ? 245 235 223 " 7 1 ' :< :F G )*+ )%E " " " B ( ;@ ' G / @@; @; @: ' " " ( . " " , ( ( " @ :CF " . # ! % ;?B Robust and non−robust solutions. Channel estimates length: 10 taps. 0 10 −1 uncoded effective BER 10 −2 10 −3 10 Estim. noise power=0.5 − Non−robust Estim. noise power=0.5 − Robust Estim. noise power=0.1 − Non−robust Estim. noise power=0.1 − Robust Estim. noise power=0.01 − Non−robust Estim. noise power=0.01 − Robust −5 0 5 10 SNR (dB) 15 20 25 ! 7 . /. 8 )5 ) 7 1 5 ? 245 235 223 " 7 32 ** " !, ! + !8"& " ) ' ) , % , '+ " G " . G 3 / 7 %* ' :D , ' 0 .. # /# *" % ;?A SIGNAL DETECTOR h1 z, h, h z1 h2 hn ... z2 T a R* xR(n) ... s(n) s(n) hD MLSE (Viterbi) e(n) zn s(n) heq T Channel estimator h Quantization FEEDBACK CHANNEL ) ) + (. 6 ! ( 3 ) @ ; ) " ) ) ) @ ) ) ) K ) M ; @ 6 ( . ) ) ) @ ) L " $! . ::; ( 5 ( / ( ) ( :<C ) ) M U Æ :<< Æ ) Æ Æ $! Æ & ( Æ Æ E M ( )) M ) ) Æ 5 Æ 0 E/ ; 6 E ( Æ EÆ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Æ -Æ . # ! % ;?D MMSE technique −1 10 uncoded BER −2 10 4 TX ant. Delay diversity. MLSE receiver 2 TX ant. Quant. (6 bits). Non−robust 2 TX ant. Quant. (6 bits). Robust 4 TX ant. Quant. (4 bits). Non−robust 4 TX ant. Quant. (4 bits). Robust 4 TX ant. Gauss. noise power=0.01 − Non−robust 4 TX ant. Gauss. noise power=0.01 − Robust 8 TX ant. Gauss. noise power=0.01 − Non−robust 8 TX ant. Gauss. noise power=0.01 − Robust −3 10 −4 10 −5 0 5 10 SNR (dB) ! ) ) 6 . /. 8 )5 ) 7 1 5 7 ) ? 7 2235 7 8 : @ " 7 4 5 7 8 6 E 32 5 ) " 12Ó5 A5 :5 D . " , $% )*+ %0+ ) )*+ %0+ !& ) ' :;@ K%DBL ( " G ! ! , , ' :;; ! 3%* ! A 5 " .3 ##" ;B@ MLSE technique −1 10 −2 uncoded BER 10 −3 10 −4 10 1 TX ant. MLSE receiver 4 TX ant. Delay diversity. MLSE receiver 4 TX ant. Gaussian noise power=0.5. Non−robust 4 TX ant. Gaussian noise power=0.5. Robust 4 TX ant. Gaussian noise power=0.1. Non−robust 4 TX ant. Gaussian noise power=0.1. Robust −5 10 −5 0 5 SNR (dB) 10 15 ! ) )5 )5 /. . /. " 7 ' # " 8 )5 ) 7 1 " ? 24 23 " 7 1 " 12Ó5 : . " ) %* 7 !& %* %0+ ) ( )*+ $% ! &1 # 3%* G $% & . " G G ( . # ! % ;B; ' , $% $ B ' , ( G ( &/ ) # , ( ! G & ) # & ( # & ' ( ) %%' # & $G % / , '+ " # (& %0+ & %* " , . /' / % ;B? & #' -' * # ) 3( F$8%&G ) - 5 )A :AC " " ( ( %0+ :AA Y%0+ ) * M %0+ , " ( %0+ ; ; Æ * ;/ Y%0+ M M M M M Æ U Æ Æ ;U Æ ; Æ U Y%0+ %0+ M M Æ Æ ; % Æ :;@? $ ; " Æ U Æ $ # ; Æ Æ :;@A Æ % :;@: :;@C " Æ Æ :;@< :;@F U :;@B % # # % " ! Æ Æ Æ Æ :;@; ; Æ ! # U ; % Æ 9 ( ( :AC ; $ Æ Æ Æ $ Æ Æ ! # $ :;@@ Æ U ; U Æ ; :DD Æ ; Æ U ; ;U U Æ U Æ Æ U " ; # # :;@D . # ! % ) "(( Æ K C * 9 KÆ L . :AF * L * ;BB U M 9 * C 9 9 U U / C C M M C C C C C , M M M M - 0 :;;@ :;;; - 0 :;;? :;;B 5 ( 9 * C C * 9 C M ? 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C ( 5 M C( M 5 " 1% ' 3 ' / " ( & , ! :? , & " G # & ( ! & . 9% / ." . 5 , , # ( , 5 3 9& 9 3 U 3 & & 0 G C 9 3 C 9& 3 C 9 9& 3- / ," % ;:A 3 " ) 9 9 , 3 3 ) . # 5 0 # ' #' ) ) . 5 KEDBL/ ))& '' #'' ))& '' M ; #'' . 6 . ." . CBB '' #'' ' #'#' #)& ' #' # M U M U U '' ) CB: , %* ) KEDBL ) CBA $! CBB ) 9 " '' Æ C ! ) '' . ( " ! C;? !/ C M / Æ M C Æ 5 Æ ' Æ # '' Æ #''Æ ' M CBC ; ( ! ! H% %0+ %0+ ! )*+ ( )*+ ' M 8 & 8 ! ? CBB & ( ' M - 9 ' 9 - , #''Æ ( 5 3 ) C C 9 9 / & ( ' & ;? ' M ' -' ; U /. CB< /. -' - %0+ ! ( 3 ! /# % %&, ## 9% ;:: 6" / ' , % , ( !& $% . , ! Y /. 9 C- Y ' 9 ' ( M 9 !& !& , !& %0+ " - 9 9 $! ( C " . .+ K / C .. L 5 " ( ! / .. Y ? C .. K L Y ? CBF 9 !& ! C , & , 9% & M B%0+ %0+ , !& & $ / 6" / G 5 !& ( " ( ( M C C C . C 9. . . C . . M U / + K ( 0 ( L C K . . L CBD 5 ( !& . & C;? ! / & # , 9 C C 9 C C C C. 9 . . . . C . . C . , U U U U CA@ + K L K L & 3- / ," % ;:C i i i r r r (a) (b) (c) ) F5 F ; . F F ; F %& 5 % & 7 8 5 %& 7 8 ' CB Y Y 9%% $ M + Y Y M Y 4& , , ( ( / ; () ;( > ' C 9 Æ #''Æ 5 ? B . . <? > C .. .. C .. #+ 2 . . A? > . . C C C 9 . C . . C . + K L K L U + K L K L . , ( 9 9 C M !& !& % ( E3 K6FDL $ " ) % "( ( ( " M , )) "" M 5 3 ! /# % %&, ## ;:< . Hi G) 7 8 5 + / , ) M ) M ) M , Æ 9 9 M ( 9 "( , CA; ( I!& 9 M Æ Æ 9 9 ÆM M C Æ M 9 Æ 9 A : " Æ K)@AL / () ;( ) > <? ) > C ( ( M ( Æ CA? #+ % $8 ' : Æ Æ Æ + 3. &+# ," % ;:F !& !&S !& $ 9 ( U 9 9 ( U 9 ( , ! * ( 9 " " ' CA ( / < 7 A?> 9 9 M C ( ( . ( !& K0DFL 3 K5D?L " (& %0+ % % K3@AL !& ! " , 1& #.4 / ( C;? ( " 1( & BC$ ( C 9 9 9 " ., & M & / +/ & / & * , M - % $ ) ; @ CAB / ) ; / 51 $ M % 9 CAA / 1 18 ? U ( 9 M @ CA: 9 C ( / 9 9 " C C" CAC 3 ! /# % %&, ## ;:D ( C " 9 C 9 C" M U U ( M 9 C 9 C U U ( CA< C C 9 C C 9 0 " ( " C ( M / ! ) ( 9 ( C< & ' ' ( U U CAF 9 C 9 C U ( 9 C 9 C C 9 # 3 ? ( M ( ; ( & ) U ) ) ) M ) U Æ ) $ Æ ( C ) U Æ)) Æ M +)) 9 & Æ Æ & ' 9 C + & U M ) ) 9 C U ( M ) $ ) ) ; ) ) ; ) %) ) + ) ) . CAF & M + # , ) $ ; ; ) % + ) + M CAD ! ( C:@ M 0 ) + 9 + C 9 , + + + 9 M ) ) ) ) ! " , ) ; M / E "1 , ? + M ) ) M 9 @ %0+ E & 1 C 9 9 M M 9 G @ ! 3. &+# ," % ;C@ h1 h2 c1 himax c2 cimax t ... h nT ... i =1 i =2 P0 imax i =nT active eigenmodes . ) C:@ " ! + @ ( ( " ! , " ) 9 + , + ) + + $ @ M $! + , M 9 ' C: ( , ( ( ! " M Æ + ) ) 9 ! @ + + M @ / M + ( ) + ) + " 9 C:; " , ( 9/ ( , ' C: + M ) ) U + M ; C:? , 3 ! /# % %&, ## ! + U? + ) ) M + 0 C ( C U C C 9/ M + ) ) 9 M 9 " M @ C:B " 1 + " C:A ( ) ) + M U + $ ;C; " EE 3 C) S " 9 C 9 C" U U ( U ) C C 9 C:: EE 9 C" U ( " U ) C 0 " 9 C " ( 9 C ( C M U U " ' ! " ) * ) ; * M ) M @ " ) + + M $ + ; M C:C M C:< % ) )) )+ * * , ) * M @ ; - ) @ M M + M ) " C:B ? ! CA: 11 + ; & M U Æ U ) Æ U ) ) C" 0 ) C 0 U # -' ( 33 / ;C? 99 +" " ( ' EE C;DC?? ( C;? 5 C ( C M $! " 9 C 9 C " U U 5 C:F & %0+ %0+ & # ! , 5 ! 99 M %0+ - " 9 C 9 C" U U 5 C:D 2 2 + " +" -/, (& . K$<? J D: 5D< $@;L # )*+ # (& ! ( )*+ $ %0+ )*+ H. )*+ . )*+ %0+ %0+ , , / ; " H% ( )*+ ? 5 & 9 ( 3 C 5 3 ! /# % %&, ## ;CB B $ ( %0+ C:D/ %0+ - M " 9 C 9 C " U A $ ( U " )*+ 5 %0+ CC@ )*+ , %0+ ! )*+ & " ! M @ H% " " ( C:D : ' 0 ! " )*+ ! ( %& . ! (& H% 99 / , ( 3 * ( " (& %0+ " 9 * 9" %0+ M 9 ( 9 * 9 9 9 M 9 * B?B B;: " M " 9 9" 9 * 9 " 9 * 9 9 9 ( " M M ( CC; ( 0 ( %0+ ! C: ( (& ( C ) "/ M * " 9 C 9 C" U U ( CC? 33 / ;CA C 9 9 9 C M U CCB . " C ( ( ( ( 99% C * * M ( 9 * ( ( ( M ( 9 ( C * C C ( M / CCA ( C / !+ + " R ! $! ( . ! ' K)D@ 0DF J@@L # ( ! 3 M @ 9 ; ( ' C 9 9 3 ( M " C ( ' G ( ' CC " ( M " / 9 9 % %0+ ( . ( CC: 3 ! /# % %&, ## power allocation ;C: beamforming ... ... p0,1 ... u 0, nT S/P pN beamforming 1,1 ... ... ... s(n) power allocation uN ... 1, nT ... pN ... ... OSTBC R symbols 1,1 ... ... {sN-1(l )(m)}Rl=1 #1 ... ... R symbols p0, nT IFFT P/S CP ... OSTBC ... R {s0(1)(m)}l=1 ... ... u 0,1 uN IFFT P/S CP # nT 1, nT " ( ( 0 ( M ; - " 9 C 9 C " U . U 5 " # M ( & .>0 CCC BBB . M ; ( , CC< %0+ 12 ! %)$ 34 # ;CC Mean value of the normalized robust power allocation 1 Mean value of γ1 Mean value of γ2 Mean value of γ3 Mean value of γ4 0.9 0.8 0.7 Mean value of γi 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Parameter g 0.7 0.8 0.9 1 8 ) . CB ( ! , M ! M @ M ? J " A C & 9 9 9 9 C $ 0 C ( M ! M U @ M 5 ; 0 ! @ % M A A ' C< & . ( . 5 M @ " 0 %)$ ! M ;A M @?: ; A . ' C< & ; K5@;L 3 ! /# % %&, ## ;C< Cumulative density functions of the minimum transmit power 1 0.9 0.8 0.7 g = 0.1 Probability 0.6 g = 0.65 0.5 g = 0.8 0.4 0.3 g = 0.9 0.2 0.1 0 Robust maximin approach Non−robust approach Pure OSTBC 5 10 15 20 25 Minimum transmit power (dB) 30 35 40 ! ) 7 8 ) 5 /. 7 /.¼ ; 32 %)$ ( , / ( & M ( 9 9 ; / ; 0 9 0 M M ; G %)$ ( ! . M ; CC; ( %0+ ! ' CF ! %0+ M;@ ) M ? M ? G !/ %)$ , G @C: @F @D . / @; %)$ ( J & " H% ! 0 ( ! %)$ $% 34 # ;CF Mean value of the minimum transmitted power (dB). TDD system. Spherical uncertainty regions. Robust. P =0.85. n =2, n =2 in T R Non−robust. Pin=0.85. nT=2, nR=2 Pure OSTBC. Pin=0.85. nT=2, nR=2 Robust. Pin=0.6. nT=2, nR=2 Mean value of the minimum transmit power (dB) 22 20 18 16 14 12 10 8 9 10 11 Estimation SNR (dB) 12 13 14 7 " ) % 5 ) & /. 7 /.¼ ; 32 %)$ 0 ! ! ' CD C;@ ! %0+ M;@ ) ' & !& %0+ CA ' G H% " CA; M @C / M @F: " !& %0+ %)$ ( , . !& %0+ ! " %0+ ! & 0 ! ! . !& %0+ %)$ ! , ( 3 ! /# % %&, ## ;CD Mean value of the minimum transmit power (dB). FDD system. Cubic uncertainty regions. 11 Robust. nT=4, nR=4 Non−robust. nT=4, nR=4 Pure OSTBC. nT=4, nR=4 Robust. nT=6, nR=6 Mean value of the minimum transmit power (dB) 10 9 8 7 6 5 4 3 2 1 5 6 7 8 9 10 Quantization SNR (dB) 11 12 13 14 7 ( ) %7 8 5 ) & /. 7 /.¼ ; 32 H% ! & ' " ' ( ) A ) M ? M A M ? %0+ M ;; M A %0+ M : ) B ) . ( %0+ 9 0 M && ' C;; C;? H% ! 9 C $ 0 C ( U M !& %0+ ' G . !& %0+ ( H% ! H% ( 9 0 M H% 39 ##" ;<@ Probability of service provision 1 0.9 Probability of service provision 0.8 0.7 0.6 0.5 0.4 0.3 nT=4, nR=4, SNRest=6 dB nT=4, nR=4, SNRest=4 dB nT=4, nR=4, SNRest=3 dB nT=4, nR=4, SNRest=2 dB nT=4, nR=4, SNRest=0 dB nT=2, nR=2, SNRest=6 dB 0.2 0.1 0 −5 10 −4 −3 10 −2 −1 10 10 1−Pin (Probability of no QoS) 10 0 10 * ) 3 5 ) , ) . ( CC? (& ( )*+ C;B ! ;@ ! 9 ' ( )*+ M 9 ! ' ! ( ) "( H%E ;CH. ' " , ( & ( " 18 # $% 3 ! /# % %&, ## ;<; Probability of service provision 1 0.9 Probability of service provision 0.8 0.7 0.6 0.5 0.4 0.3 nT=8, nR=8 nT=6, nR=6 nT=4, nR=4 nT=3, nR=3 nT=2, nR=2 n =1, n =1 0.2 0.1 T 0 −4 −2 0 2 Quantization SNR (dB) 4 R 6 8 * ) 7 8 /.5 7 8 ) G 5 !& , ( ( & %0+ & $% %)$ , %)$ ! , & %0+ & ( ( & 3 & 0 39 ##" ;<? System throughput with maximum BER constraints 8 Robust AM, nT=8, nR=8, g=0.4 Non−robust AM, nT=8, nR=8, g=0.4 Robust AM, nT=4, nR=4, g=0.6 Non−robust AM, nT=4, nR=4, g=0.6 Fixed modulation − Robust nT=4, nR=4, g=0.6 7 Throughput (bits/s/Hz) 6 5 4 16−QAM 3 2 QPSK 1 0 5 10 15 20 25 Maximum available power (dB) 30 35 $ + .¼ ; 32 ¿ ( Æ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Æ 9 % . ' $P ( K0DFL + 0 + = )I3 ; ;C F ;A?BZ;ABC - ;DDF +?E% % & % . ;DDF K0DAL 8 0 . 0, O $( P (% ( % ;B ;DDA K@BL * 0 . % ) 7 7 O*Æ % % J % J $ 9 $ % P F K DAL ;DDA :? ; ;Z;B 6 ?@@B . + ( > $ *!%" ;FA K@;L . 3 =2 & . . 2 & 0 O 6 + % + ' ( (!"#$ P :?;Z:?A . ?@@; K@BL 6 $Æ . 3 =2 & O6 (+( ) $/ 9" ', $( &P :; D ?BF;Z?A@; % ?@@B K@B L 6 $Æ . 3 =2 & O9 . $/ . 5 .P AD < ;<@<Z;<?< 6 ?@@B K@AL . 3 =2 & 6 $Æ O 3 6 + $ H% $P :? : ;;<DZ;;D< ?@@A K@:L . 6 $Æ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Æ O% $ J $P AC B B:<ZBCC ;DDF K+@?L ' + 3 5 72 &!& O. 6 + % + $ 9 J3.0 .P !")$ % & ' 6 ?@@? K+@? L ' + 3 5 72 &!& O . $ E %P ? F!")$ F A ?;?;Z?;?: % ?@@? 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P F F!AA$ ; F:;ZF:C ;DDD K7@;L * 7, 9 O% J ' ,P A< C ?CB?Z?CBD % ?@@; K7@BL % . 7 . ) 5 NH 3 O+ . ) 9 J$ &/ . % % P V KN@@L :; ? B;BZB?A ' ?@@B V % N,2 $ O. . $ % $ $ (P ( + , DD :DZ<< ?@@@ KJ@@L N J 5 ) 5, OJ $P %; KJ D:L J J ;< B ?DZAF ?@@@ + % O7 + H. +P AB < ???BZ??B@ 6 ;DD: KJF:L 3 J 6 7, O* * & P - (1 % > % . ;F ;< 3;;;BZ;;;< ;DF: KJD:L . J O > P ><+7+%!AH$ > & ;BZ;< 0 ;DD: *!%" ;D@ KJ@;L E E J + % E $ E ) 3 + O. . ) % ' I . %P AD ; ;D:Z?@C 6 ?@@; KJD<L 5 J J O*Æ % ! *( . ' $P A: ; ;D;Z?@: 6 ;DD< K>@AL > % N 5 ) 5, O. ' ) $ % P :? ; ?@?Z?;B 6 ?@@A K8DAL 6 8 % + O6 + & % ' ,P A@ : ;BBAZ;B< % ;DDA K8DA L 6 8 % + O 6 + & %P A? ;? B??;ZB?B; ;DDA KNDCL E N 6 $ E 5 , & + = 9 % + 06 ;DDC KN@?L % N 5 ) 5, O *) % ), $ $ ' ,P :@ ;@ ?:DDZ?C;B ?@@? KN@BL % N 5 ) 5, O *) % ), $ $ $P AD < ;C<BZ;CD@ 6 ?@@B KN@AL % N 5 ) 5, O= . $ 0 ) . + $[P B A ;?F:Z;?DA 6 ?@@A