% '( )* +, - .%( / 0. "$12# !"#$" (& "%& * ( ) ' 23"$! (& "4 4$$" ! " !#!$ % & "'( % ) * & + ,*&+- . / 0 ,./0- ./0 1 , !" #$!%" & !' ( )Æ * +,''!% % ++% % '#- & . &.( ( /&0 1" 2 3 - Æ ! " # ! $ % # $ Æ & ! ' ( $ # ! ) " # * # % + ! % , - " Æ % . & / ! 0 )/ * ,1- ! & Æ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Æ ! . Æ % ! " Æ " ! ! # <)$ " ! ? . ! G H G # 8 1 Æ # 2 8 2 # B * " # " G # , - G # &@0 G G #, 1 ,1- H - , H - G 1 3 G # ( ,1- G G G ? # ? # , - G & # ! ! & ? # 1 G # Ë G G ; . 1 # ; #/ +$ * / " ? + $ & +$ $# $ ; ( / I J ( $ ( G / 2 ( ! % # 2 # " . 7" 3 H ( G 1 H H . G G , - , 9 - 7 7" 9 $ ) A $ $# + ( . 1 5&6>=$) ; 8 C=$) 9=$) . C=$) ! =$) " ,18- $ " 9=$) . " " # =$) ,18- A ! . 1 G 8 1 > =5&6 * # > " > C=$) C5&6 % 9 (1,1) (1+ √ 3 ,0) (1,-1) (a) 8QAM (b) 16QAM . =$) 1.8 1.6 2 BPSK QPSK 8PSK 8QAM 16QAM unconstrained input 1.8 1.6 BPSK QPSK 8PSK 8QAM 16QAM unconstrained input 1.4 1.4 bits/channel use bits/channel use 1.2 1 1.2 1 0.8 0.8 0.6 0.6 0.4 0.2 −2 0.4 0 2 4 E /N (dB) s 6 0.2 −2 8 0 0 2 4 E /N (dB) s 6 8 0 . 1 @ ( / & 3 ' & 31K3? & 31 & 33 % )<5&6 +)<5&6 & 3? : . 3 ! " " " " )5&6 ! 2 " " ! ! 7 ! ! $ # ! ! $55 5&6 &" $55 $55 & 31 I#J $55 # $ 5&6 # ! . # $55 ( $ # bi ∧ bi channel encoder SISO decoder ηb ci channel interleaver MPSK gray mapping channel deinterleaver non-coherent demodulator ∧b ζ w modulation coder y x transmit filter block fading channel receive filter b λ channel interleaver . 3 $ ! < / )5&6 $ # G 8 G G # 1 G )5&6 < C G . G )5&6 < G 7 G # )5&6 G ( ! < Æ ' ! ! ! B G G ! 7 )5&6 # @ G 8 H G G & G G $55 I#J $55 L G G ! L $55 )5&6 * G 1 ( $55 " # ! G G G , - G , - , , - ,- , - , - : % ,- G ,- $ ( 7" : % ! D A , - ! Æ & 31 311 3 $55 # L $55 1 G G G 8 / G 8 H G G # L G G G L G G G G G G H G G G 8 @# Æ 7" : 7" 3 5&6 , - G C H . 7" : " 1 # ( ! , C # , - 7" - 7" C $55 # ( # " # # / ! Æ G ! L L G # 8 " 1 8 D 4 L ! # ' " ! $ L . # 83 8? + ! # 5&6 "/ ! " ) , 1- + + ! ' ! ! # ,8 1- ! M G 8 # < G 1 8 $ % # # , , - , G ,! G 1 8 - L- G L- G , G L ! G - @ 7" 1 # 1 1 # # ,! G G L- , # G L ! G - 7" : G G # , # 1 + " 7" 1 +A ! E!0 +AE0 , ?- ,1 - " # # +AE0 ! + ! & B ,11- ) , 1- % &@0 * ! % ( / ' # . &@0 Æ @# # ( 7" 1 ! ) % ! )<5&6 G 8 G H % & ! Æ ,8 1- ! " "/ # 7" 1 ( "/ ! ,8 1- 7" 8 "/ ,8 - "/ "/ # " # $ 8 $G # H $ 8 % 8 $ # % $ % # 7" 1 " 7" 3 G G G # G # # # 3 # Æ +AE0 $ )<5&6 H B 7 1 ! ! 8 " # G ! G 8 + G ! ! G ! G ! G H * 1 . ? ( " 7" 3 1 " # 8 G G ( % ! # ( ! # +AE0 ,13- $ ! ! ! ) % ! +)<5&6 . +<5&6 G G 8 H % . 7" C ! G " G 8 / G 8 % ( ! $ +)<5&6 ! +)<5&6 H B * " "/ M G 8 G M 7 ! "/ " # + ! ! ! G ! ( 1 . ? " # G 8 G G 8 @ " # G # * # +AE0 +)<5&6 )<5&6 3 0 ( θ i = 0 ¸ xi ) 1 0 • 1 M L′ ¸ xi ) 1 0 • 0 • 2π ( θi+1 = ¸x i+1 ) M L′ 1 θ i = 2π θi+1 = 0 L • θi+1 = 1 • • M-1 • 0 • 2π ( L′ 1) x 1 ( θi+1 = M L′ ¸ i+1 ) θ = 2π i 1 ( L 1) L • 0 1 … M-1 • M-1 2π L M-1 0 M-1 M-1 0 • M-2 1 • 0 0 • • 1 θi = 0 2 M-1 • ( θ = 2π ( L′ 1)¸ xi ) i M L′ 1 M-1 1 M-1 M-1 0 • M-2 0 • ( θi+1 = 0 ¸x i+1 ) 0 0 • 1 1 … ( θi = • … 0 0 2 M-1 • 2π • 1 M-1 M-1 0 • M-2 θi+1 = 2π ( L 1) L • M-1 2 0 • M-1 (a) MDPSK (b) B-MDPSK . ? !" ( % + & (& 4 &(&4 +AE0 &(&4 &(&4 &(&4 * &(&4 ' < . + 2# ,3- 0$ < E )7 ,1?- $ &(&4 + , - ( ' . 3 N 0$ ? 9888 >? 0$ ,1?- . % . >3 >1 >? . ? )<5&6 +)<5&6 =5&6 >? ,1; 1: 33 3:- >? ,18 1; 1: 33- >3 ,1; 33 3:- >1 ,13 3;- 5 ! " # $% ( ! 7" D "/ 7" 8 0 10 RA B−MDPSK T=20 amplitude estimate RA B−MDPSK T=20 amplitude known RA B−MDPSK T=50 amplitude estimate RA B−MDPSK T=50 amplitude known −1 BER 10 −2 10 −3 10 −4 10 0 0.5 1 1.5 2 Eb/N0 (dB) 2.5 3 3.5 . ; 5 ( . ; / ! # 0$ 9888 +)<5&6 18 $ G ;8 O 83 + . G 18 8? + ! . 9 "/ % . 9 0$ 9888 +)<5&6 ; 18 N "/ 8 ?8 # "/ 18 . )<5&6 "/ +)<5&6 . 9 )<5&6 "/ A ? ; "/ Æ 0 0 10 10 quantization level 10 quantization level 20 quantization level 30 quantization level 40 quantization level 3 quantization level 4 quantization level 5 −1 10 −1 10 −2 BER BER 10 −2 10 −3 10 −3 10 −4 10 −4 10 −5 1 1.5 2 2.5 3 10 3.5 1 1.5 Eb/N0 (dB) 2 2.5 3 3.5 Eb/N0 (dB) /0 43+15 6 /0 7 3+15 6 . 9 7% "/ ! & 4 ( . : % 0$ )<5&6 +)<5&6 ! 9888 18 0$ +)<5&6 )<5&6 +)<5&6 ! )<5&6 +)<5&6 )<5&6 ! ! +)<5&6 ( +)<5&6 ! ( ' ! 7P( ,1;- . C ## # 9 9 0 10 turbo B−MDPSK noncoh T=20 turbo MDPSK noncohT=20 conv MDPSK noncoh T=20 conv B−MDPSK noncoh T=20 RA B−MDPSK noncoh T=20 RA MDPSK noncoh T=20 −1 BER 10 −2 10 −3 10 −4 10 2 2.5 3 3.5 Eb/N0 (dB) 4 4.5 5 . : 5 % 7 " Pc,demod: probability of a correct bit decision at the output of the demodulator 0.9 0.85 turbo B−MDPSK SNR=3.6dB RA MDPSK SNR=3.6dB RA B−MDPSK SNR=3.6dB turbo MDPSK SNR=3.6dB convol MDPSK SNR=3.6dB convol B−MDPSK SNR=3.6dB 0.8 0.75 0.7 0.65 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 Pc,decoder: probability of a correct bit decision at the output of the channel decoder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conv non−recursive MDPSK noncoh conv recursive MDPSK noncoh turbo B−MDPSK coh turbo B−MDPSK noncoh RA B−MDPSK coh RA B−MDPSK noncoh conv non−recursive MDPSK noncoh conv recursive MDPSK noncoh turbo B−MDPSK coh turbo B−MDPSK noncoh RA B−MDPSK coh RA B−MDPSK noncoh −1 −1 10 10 BER BER non−recursive conv DPSK noncoh −2 10 −2 10 RA DPSK noncoh −3 −3 10 10 noncoherent channel capacity −4 10 −4 1 1.5 2 2.5 3 Eb/N0 (dB) 3.5 4 4.5 10 5 0 1 2 3 E /N (dB) b /0 6% " * % 4 5 6 0 /0 6 " * % 0 0 10 10 conv MDPSK noncoh turbo B−MDPSK coh turbo B−MDPSK noncoh RA B−MDPSK coh RA B−MDPSK noncoh conv MDPSK noncoh turbo B−MDPSK coh turbo B−MDPSK noncoh RA B−MDPSK coh RA B−MDPSK noncoh −1 −1 10 10 BER BER turbo DPSK noncoh noncoherent channel capacity −2 10 −3 −2 10 −3 10 10 noncoherent channel capacity −4 10 −4 0 0.5 1 1.5 Eb/N0 (dB) 2 2.5 3 10 0 0.5 1 1.5 2 2.5 E /N (dB) b /0 6' " * % 3 3.5 4 4.5 0 /0 6 " * . D 5 % # ! & ! ' . >1 +70 8 9 : + & ! 18 ! ! # ( ( / 0 ! ! # 2 ! / . % / * # 2 # &@0 ( 1 " 8 . =5&6 =5&6 . =5&6 )<5&6 +)<5&6 =5&6 % 4 > 5&6 1 ) Æ . ' ! " 1 ! # Æ "/ ! # 1 / ( # # C5&6 C=$) 9=$) ( ! =$) " / 5&6 ! / % =$) , 3- 3 ( / . N 0$ * % % % # 0$ +)<5&6 +)<5&6 )<5&6 . 9 : + $ 838? + + $ / % # )<5&6 +)<5&6 * # . ! $2@ ! ! < +) * < B )/ ) +$ , - < < ) & I) % )5&6J 3C 388K38C ) DD8 ,1- )/ + * IA ! 0 O J ?; 3DK ;: E DDD 11 ,3- 2 + $ 2# 5 ' I@ J 89?K 8:8 ) DD3 ,?- ) 5 & & I( <5&6J 33 8 CK 818 E 1888 ,;- ) 5 & & I4 !J 8 9;K:3 . DDD ,9- ) 5 & & & 2Q I( )5&6 $2@ J ?: C:KD; $ 1888 ,:- 0 A < $ ) I@ J ! " #$$$ % ! % %% #$$$ ) 1888 ,C- 5 * E B I <5&6 % 5&6 J ?: C3:KC?1 E DDD ,D- ( ) 5 ) I4 )5&6 J ?C ;CCK;D9 $ 1888 , 8- ( < ) 5 ) I) % 0 J & % ! ' 9 19;K1:? . DDC , - & + < < 2 ) . 5 I$ # )$5 J & ( !( '( & )' " * +##, @ DD9 , 1- < ) I& Æ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Ë G G $ + ,19- . + ,19- 1? / 0 8 ! 1 '( ( ' G G ' G ' G $1 2 " 3 G H # # ( ' $3 2 G ! 0 0 1 ! ( ( ' 4! 3 ' G G , G G - $? 1 ! '( ( ' 4! 3 # G # G ' G G ' G & ' # G # 2 G ,8 3 G G $; 0 5 ' ( $9 G +$ / 0 8 1 ! ( G # G G G ! 0 !! G 1; 8( 5 $: ! $C ! ) ) ) 2 G 0" " " " 0 ! $ # 7" $: )/ * ,1- G # * + + H H $D G 1 * G + , G - . G H , S - , H , / / 1 # 7" $D T B ( 0 # # G T G 8 ( G G 1T 1 G 8 0 G ( 0 T < 1 # # ,T * -, + - , + - H H G G @ 7" $ G 19 " ! # 7" 9 ) A )5&6 & " =$) < G 7" 9 G G G , - , , ! G G G ! - - , , - + - " , - " * G H * G , - $ Æ * @# 0 2 " # 7" + 0 G " * G 0 * 2 +1 ( Æ , - , - ( # , - , - G G G G + G ! , - , - +3 ! ," - + ! ," - 7" +3 # ) A 7" +1 1: