multiple-symbol differential detection scheme

8/9/2019 Multiple-Symbol Differential Detection Scheme

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M u l t i p l e - S y m b o l D i f fe r e n t ia l D e t e c t i o n S c h e m efo r D i f f e r e n t i a l A m p l i t u d e M o d u l a t i o n

T o s h i n o r i S u z u k i a n d T o s h i o M i z u n oK D D R &D La bora t o r i e s , 2 -1 -15 O ha raK a m i fukuoka - s h i , S a i t a m a 356 , J a pa n

A b s t r a c t . Th i s pa pe r a dd re ss e s a mu l t ip l e - s ymbo l d i f fe r e n ti a l de t e c t i onscheme for s t a r 16QAM. At the out se t , we ana ly t i ca l ly sc ru t in ized con-ven t iona l d i ffe rent ia l de te c t ion of s t a r 16QAM. As a resu l t, i t eme rgedt ha t t he e n e rgy pe na l t y o f d i f fe r e n ti a l a m pl i t ude de t e c t i on a s c om pa re dw i t h i de a l c ohe re n t de t e c t i on is l a rge r t ha n t ha t o f pha s e de t e c t i on . Th e nt o i mp rove t he ove ral l pe r fo rm a nc e o f s t a r 16Q A M , w e p ropos e a n M LS Ealgor i thm for a l a rge C/N a s w e l l a s a s ubop t i mum a l go r i t hm. B o t h o ft he m a llow mul t i p le - s ymbo l d i ff e r e n t ia l a m pl i t ude a nd pha s e de t e c t i on .Th e i r pe r fo rma nc e s a re a ls o e va l ua t e d t h rou gh c om pu t e r s i mu l a ti on .

1 In t roduc t i on

T h e m u l t i - l e v e l m o d u l a t i o n s c h e m e s a r e a g o o d c a n d i d a t e f o r i m p r o v i n g b a n de f fi ci en c y o n m o b i l e c o m m u n i c a t io n s s y s t e m . A m o n g t h e m , s t a r 1 6 Q A M o r1 6 D A P S K h a s b e e n g i v e n a t t e n t i o n [1 -3 ], b e c a u s e d i f fe r e n ti a l d e t e c t i o n i n s t e a do f c o h e r e n t d e t e c t i o n c a n b e e m p l o y e d a n d i ts p e r f o r m a n c e is b e t t e r t h a n t h a to f 1 6 D P S K . D i f f e r e n t i a l d e t e c t i o n h a s t h e f o l l o w i n g a d v a n t a g e s .( a ) r o b u s t n e s s u n d e r fa d i n g c o n d i t i o n s a n d f a s t p h a s e a c q u i s i ti o n .( b ) n o n e e d f o r c a r r i e r p h a s e t r a c k i n g .

D u e t o ( a ) , m a n y s tu d i e s o n s t a r 1 6 Q A M h a v e b e e n o r ie n t e d t o m o b i l e o rp e r s o n a l c o m n m n i c a t i o n s [ 4] . B e c a u s e o f (b ) , h o w e v e r , s t a r 1 6 Q A M is a ls o e co -n o m i c a ll y a t tr a c t i v e f o r h i g h r a t e d a t a t r a n s m i s s i o n w i t h le ss h a r d w a r e c o m p l e x -i ty.

S t a r 1 6 Q A M c o n s i st s o f 2 D A S K ( d if f er e n ti a ll y e n c o d e d 2 A S K ) a n d 8 D P S K( d if f er e n ti a ll y e n c o d e d 8 P S K ) . T h r e e o u t o f f o u r b i ts p e r o n e s y m b o l a r e m o d -u l a t e d b y 8 D P S K , a n d t h e re m a i n i n g b i t b y 2 D A S K . 2 D A S K m e a n s t h a t w h e ni n f o r m a t i o n b i t c h a n g e s f r o m a p r e v i o u s i n f o r m a t i o n b i t , t h e r i n g l e v e l s h o u l db e a l s o sw i t c h e d f r o m l o w t o h i g h o n e o r h i g h t o l ow o n e. W i t h o u t c h a n g e , t h er i n g l ev e l s h o u l d b e t h e s a m e a s t h a t o f t h e p r e v i o u s s y m b o l . I t is w e ll k n o w nt h a t t h e p e r f o r m a n c e o f d i ff e re n t ia l d e t e c t i o n is i n h e r e n t ly i n f e ri o r t o t h a t o fi d e a l c o h e r e n t d e t e c t i o n . T o f i l l t h e g a p b e t w e e n t h e m , a m u l t i p l e - s y m b o l d i f -f e r e n ti a l d e t e c t io n t e c h n i q u e m a y b e p r o m i s in g . H o w e v e r s o f a r, m o s t w o r k o nm u l t ip l e - s y m b o l d e t e c t io n h a s b e e n c a r r i e d o u t o n l y fo r M - D P S K [5 ,6]. M o r e -o v e r , i n m u l t i -l e v e l m o d u l a t i o n a n d d e m o d u l a t i o n , t h e c o m p l e x i t y is a ls o s u b j e c t


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to deliberation because it increases exponentially in proportion to the numberof observation symbols.

This paper proposes a multiple-symbol observation scheme for differentialamplitude detection to improve the performance of star 16QAM while retaininga modest hardware complexity. We obtain a posteriori probability analytically,considering a differential amplitude modulation and demodulat ion, and presenta maximum-likelihood sequence estimation (MLSE) method for star 16QAM fora large C / N . This method may be also applicable to general star QAM andsimple DASK.

It is manifested that, since the MLSE method makes amplitude and phasedecisions simultaneously, directly applying the MLSE method to star 16QAMcuhninates in an increase of complexity by the 16th power of the observed symbollength. To cope with this problem, an alternative method is considered in which amultiple-symbol detection is undertaken independently for 2DASK and 8DPSKin star 16QAM. While this doesn't make full use of the MLSE advantage, thecomplexity can be reduced significantly.

In Section 2, we develop an analytical expression of the bit error rate (BER)for a two-symbol-observed differential detection scheme of star 16QAM. It isshown that a multiple-symbol detection is more effective in amplitude detectionthan in phase detection. Section 3 proposes two algorithms of nmltiple-symboldetection for star 16QAM, and there performances are assessed by computersimulation.

2 S t a r 1 6 Q A M f o r C o n v e n t io n a l D i f f e r e n t i a l D e t e c t i o nIn star 16QAM, there are two levels of amplitude. Let the inner ring level beL, and the outer ring level be H, as shown in Figure 1. Then, an average C / Nis (L 2 + H 2 ) / 4 N , where N denotes the noise energy. There are two crucialparameters in the differential amplitude detection, amplitude decision thresholdsand the ring ratio. Let the former be flL and f i l l , and let the latter be H / L .Though some studies have been made [1,3], there still remains room for furtherconsideration of multiple-symbol detection of star 16QAM.

2.1 Amp lit ude Decision Thre shol dLet the received and transmitted symbols at time k are rk and sk, respectively,both of which have complex forms. We also define 7k and ACk as the following;

= I k l e = I k l ( 1 )7k = , AO k = Ok -- Ok-1 , ACk=r162 (2)

For an AWGN channel, a p o s t e r i o r i probability of and ASk given ak,ak-1 and ACk is derived by having recourse to [7] and [8], on the assumption of


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" I "L - "

F i g . 1 . S i n g a l c o n s t e l l a t i o n o f s t a r 1 6 Q A M

c o n s t a n t e n v e l o p l ev e l a n d u n k n o w n p h a s e o v e r a t w o - s y m b o l i n t er v a l. O n l y t h er e s u l ts a r e p r e s e n t e d .

p d f o ( ' / k , aOkla~, ak-1, ~r =7 k

( 1 + ' / ~ ) 2I 1 ]t- kTk q - 2a k - la k ' ) ' k COS1 "~ - 2 N ( 1 + ' / 2 ) { a~ '-I - ~ 2 2 (A O k A C k ) }- 1 { ~ k - ~ '~ k + a ~ - 2 a k - ~ k ' / k C os (z ~O k - - Z ~ r 2 N ( 1 + ' / ~ ) ( 3 )

pdfa ( T k l " k , " k - 1 ) = 2 2 227k ex p a~ ' - 17k---+-a~ ' "~( 1 + 7 2 ) 2 2 N ( 1 + 7 2 ) / /[ { ak_12 - t - a k ~ 2 } ( a k - l a k T k ' ~ a k . l a k T k I ~ a k - l a k ~ k ' ~ ] ( 4 ~x l + ~ - ~ i ~ _ - - ~ I o \ g ( l + 7 ~ . ) / + N ( l + 7 ~ ) 1 \ g ( l + 7 2 ) ] j , ,

( 4 ) i s d e r i v e d b y i n t e g r a t i o n o f (3 ) w i t h r e s p e c t t o A 0 k . I 0 (. ) a n d I 1 ( . ) a r e t h em o d i f ie d B e s se l fu n c t i o n s o f z e r o t h a n d f ir s t o r d e r , r e sp e c t iv e l y .

T o m a k e a d e c i si o n c o n c e r n i n g a n i n f o r m a t i o n b i t in d i f fe r e n t ia l a m p l i t u d e ,t h e d e m o d u l a t o r e m p l o y s t w o t h r e s h o l d s , i lL , f i l l . W h e n t h e f o l l ow i n g c o n d i t i o nis m e t , t h e r e c ei v e d i n f o r m a t i o n '0 ' i s d e c o d e d ;

~ L < 7 ~ < Z ~ ( 5 )O t h e r w i s e ' 1 ' i s d e c l a r e d .

T h e n t h e B E R o n a m p l i tu d e , Pb. .a~p , is d e r iv e d b y i n t e g r a t i o n o f (4 ) .:)b..amp


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1 9 91 1 , / ~ / ~ u~ + ~ - x d 7flz.{pdf~, ( ~ I L , H ) + pd.fa ( 7 1 H , L) - pd. fa ( ' d L , L ) - p d / o ( ~ IH , H ) } ( 6 )

B a s e d o n t h e a b o v e , w e c a n d e t e r m i n e t h e o p t i m u m t h r e s h o l d s t o m i n i m i z e t h eB E R as a ze ro -c ro s s p o i n t o f t h e fo l lo w i n g v a l u e .OP b~,-,,p _ OP b_,,mp

O f I , OPU1= - -- ~ { p d f a (f il L , H ) + p d f a ( f i l l , L ) - p d f a ( f l L , L ) - p d f a ( f l H , H ) }; f = / ~ L o r f . (7 )

Fi g u re 2 s h o w s t h e s en s i t i v i t y o f Pb_ ~,~p ag a i n s t t h r e s h o l d , f t . A t a h i g h C / N ,t h e o p t i m u m t h r e s h o l d s a r e a r o u n d (1 + H / L ) / 2 fo r fl H a n d 2 / ( 1 + H / L ) fo rf l z [ 1 ]. A l t h o u g h a n o p t i m u m t h r e s h o l d d e v i a t e s f l-o m t h e a b o v e v a l u e a t a l owC / N , t h e p e r f o r m a n c e b e c o m e s i n s e n s i t i v e t o t h r e s h o l d d e v i a t i o n .

I n t h i s p a p e r , a s t h e a m p l i t u d e d e c i si o n t h r e s h o l d s , ( 1 + H / L ) / 2 f o r f l ~ a n d2 / ( 1 + H / L ) fo r i lL , a r e e m p l o y e d t o e x a m i n e t h e p e r f o r m a n c e o f c o n v e n t io n a ld i f f e r en t i a l d e t ec t i o n .

iH

- 4

f [ X 1 /4 ] \ ., g , :. . C /N = 2 O d B2 I 2 / ( 1 + H / L ) ~ " , , , 4 . . . . . . lO d Bf / / . " X . - - 3 d B ( l + H / t . ) / 2

f . . . . .!

t h r e s h o l d s , 6H / L = 2

Fig . 2 . Sens i t iv i ty o f am pl i tude BE R w i th respec t to th resho lds

2 .2 R i n g R a t i oF o r t h e g i v e n si g n a l e n e r g y , h i g h r i n g r a t i o r e s u lt s in a d e g r a d a t i o n o f p h a s ed e t e c t i o n w h il e a n i m p r o v e m e n t i n a m p l i tu d e d e t e c t i o n . A l o w e r r in g r a t i o m a yl e a d t o a n i n v e r s e s i t u a t i o n . C o n s e q u e n t l y , t h e r e i s a n o p t i m u m r i n g r a t i o t oa c h i e v e a s u p e r i o r t o t a l p e r f o r m a n c e .


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I n idea l cohe r en t de t ec t ion , t he d i s t anc e be tw een s igna l cons t e l l a t ions i s g ivenb y t h e E u c l id i a n d i s t a n c e i n si g n al s p a c e . T h e r e f o r e , t h e m i n i m u m s q u a r e d d is -t ance i s :

d ~ , ~ . . s p s ~ : = 4 L 2 s i n 2 ( 8 )d ~ . ~ a s K = ( H - L ) 2

( 8 )( 9 )

A n o p t i m u m r i n g r a t i o H / L wo uld sa t is f y the co nd i t ion th a t ( 8 ) equa l s ( 9 ) ,leading to a round 1 .8 [3] .

H o w e v e r , i n d i f f e r e n t i a l d e t e c t i o n , t h e d i s t a n c e i s r e d u c e d f r o m t h e a b o v eva lue . Cons ide r ing a l a r ge C / N , w e c a n d e r iv e t h e m i n i m u m s q u a r e d d i s t a n c ef r o m t h e e x p o n e n t i a l p a r t o f ( 3 ), a s fo l lo w s :

( ~ ) ( l o )2m~,~_SDX, K = 8L 2 sin 2d ~ n ~ D A S ~ : - 4 ( H - L ) 2 (11)2

B y m a k i n g ( 1 0) e q u a l t o ( 1 1 ), t h e o p t i m u m r in g r a t io b e c o m e s a r o u n d 2 .0 . T h i sa p p r o x i m a t i o n i s s u p p o r t e d b y F i g u r e 3, w h e r e t h e s i m u l a t io n r e s u l ts o f B E R a sa flm c t ion o f r i ng r a t io a r e p lo t t ed . I n F igur e 3 , C / N = 2 0 d B an d t h e G r a y - c o d em a p p i n g a r e a s s u m e d . P b a n d P ~_ ph ,~ d e n o t e t h e o v e r al l B E P ~ p e r f o r m a n c e o fs t a r I 6 Q A M a n d i t s p h a s e p a r t , r e s p e c t i v e l y . P b i s c a l c u l a t e d f r o m

i 3 p (12)

i0 -I

o I 0 " z

m lO 3

10 41 . 4 1 . 6 1 .8 2 2.2 2.4ring ratio (H/L)Fi g. 3. BEP~ as a funct ion of r ing rat io

2.6


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W i t h t h e o p t i m u m r i n g r a t i o f o r e a c h d e t e c t i o n s c h e m e , t h e d e g r a d a t i o n o fd i f fe ren t i a l de t ec t i on f rom idea l cohe ren t de t ec t i on a t t he same ave rage C/N isr o u g h l y e s ti m a t e d a s

(2.0 2 + 1) sin 2 (~'/8)(1.82 + 1) 2 sin 2 (~r/16) 3.6dB (13)

T h i s e n e r g y p e n a l t y is l a rg e r t h a n t h a t a p p e a r e d i n 1 6 D P S K a g a i n s t 1 6 C P S K(cohe ren t P SK ) . O n th e o th e r s ide , once t he r i ng ra t i o i s f i xed to 2 . 0, t he ene rgyp e n a l t y i s a r o u n d 2 .S d B b e c a u s e t h e r i n g r a t i o o f 2.0 is n o t o p t i m u m f o r c o h e r e n tde t ec t ion . In t h i s s i t ua t i on , t he d i f fe ren t i a l ampl i t ude de t ec t ion sha l l pay ine x c es s o f 5d B , c o m p a r e d w i t h t h e c o h e r e n t d e t e c t i o n , a s c a l c u l a te d b y ( 9 ) a n d(11) w i th H/L = 2 . 0 . Ev iden t ly t he d i f fe ren t i a l ampl i t ude de t ec t ion w ou ld cos tmore t han the d i f fe ren t i a l phase de t ec t i on .

3 M u l t i p l e - s y m b o l D i f f e r e n t i a l D e t e c t i o n o f S t a r 1 6 Q A M

Th e p reced ing sec t ion show s a la rge r deg rada t ion in pe r fo rm ance o f d i f fe ren t ia la m p l i t u d e d e t e c t i o n , w h i c h i s 5 . i d B a s c o m p a r e d w i t h i d e a l c o h e r e n t a m p l i -t u d e d e t e c t io n . H o w e v e r , t h e r e m a y b e r o o m t o r e tr i ev e t h i s d e g r a d a t i o n b ya mul t i p l e - symbol obse rva t ion fo r d i f fe ren t i a l ampl i t ude de t ec t ion . To iden t i fyt h e i m p o r t a n c e o f m u l t i p le - s y m b o l o b s e r v a t io n o n a m p l i t u d e d e t e c t i o n r a t h e rt h a n o n p h a s e d e t ec t i o n , w e r o u g h l y e s ti m a t e a n u p p e r b o u n d o f i m p r o v e m e n tf o r s e l e c t e d d e m o d u l a t i o n s c h e m e s . F i g u r e 4 s h o w s t h e t h e o r e t i c a l B E R p e r -f o r m a n c e o f f o u r d if fe r en t d e t e c ti o n m e t h o d s , w h e r e a p r ef ix ' D E C ' m e a n s t h eidea l cohe re n t de t ec t i on w i th d i ffe ren ti a l encod ing and decod ing , and 'D ' d eno te sthe conven t iona l d i f fe ren t i a l de t ec t i on . N o te t ha t t he r i ng ra t i o fo r e ach de t ec -t io n m e t h o d is e q u a l t o 2.0 . A s s u m i n g t h a t t h e p e r f o r m a n c e o f m u l t ip l e - s y m b o lde t e c t ion u l t im a te ly reaches t ha t o f i dea l cohe ren t d e t ec t i on w i th d i f fe ren t ia le n c o d i n g a n d d e c o d i n g , w e c a n e x p e c t a n i m p r o v e m e n t b y a p p l y i n g m u l t i p l e -' s y m b o l o b s e r v a ti o n to a m p l i t u d e p a r t r a t h e r t h a n b y a p p l y i n g it to p h a s e p a r t .

Even w i th d i f fe ren t r i ng ra t i os fo r e ach de t ec t ion me thod , t he above specu la -t i o n w o u l d b e t r u e . T o r o u g h l y e s t i m a t e t h e o p t i m u m r i n g r a t i o f o r 2 D E C A S K+ 8D PSK , se t (9 ) equa l t o (10) . The r i ng ra t i o i s t hen a round 1 . 55 . S imi l a r ly ,w e o b t a i n a r i n g r a t io o f 2 .5 5 f o r 2 D A S K + 8 D E C P S K b y u si n g ( 8 ) a n d ( 1 1 ). B yh a v i n g r e c o u r s e t o ( 9) th r o u g h ( 1 2 ), th e a s y m p t o t i c i m p r o v e m e n t s o f 2 D E C A S K+ 8 D P S K a n d 2 D A S K + 8 D E C P S K a r e 1 . 7 d B a n d 1 . 1 d B , r e s p e c t i v e l y , a t t h es a m e a v e r a g e C/N.

O f c o u r s e , i f t h i s m u l t ip l e - s y m b o l d e t e c t i o n t e c h n i q u e c a n b e a p p l i ed s im u l -t a n e o u s l y t o b o t h 8 D P S K a n d 2 D A S K in s ta r 1 6 Q A M , th e n m o r e i m p r o v e m e n tc a n b e e x p e c t e d . I t is h o w e v e r n e c e s s a r y t o i m p r o v e t h e p e r f o r m a n c e o f a m p l i-t u d e d e t e c t i o n w h e n a p p l y i n g m u l t i p l e - s y m b o l d e t e c t i o n t o s t a r 1 6 Q A M .


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10-'=20 2

1 0 2

n-,=

1 0 . 3

1 0 - 412 14 16 18 20 22C/N [dB]

F i g . 4 . B E R s f o r v a r i o u s s c h e m e s

3 .1 M L S E o f S t a r 1 6 Q A M f o r a L a r g e C / NF o r s im p l ic i ty , l et t h e n u m b e r o f o b s e r v a t i o n w i n d o w s y m b o l s N s = 3 . R e f e r -r in g t o m a t h e m a t i c a l f o r m u l a [8], w e ca n d e r i v e t h e a poster ior i p r o b a b i l i t y o f( T a, ~ / k - i, A 0 k , A 0 k _ i ) g i v e n ( a k , a k - 1 , a k - 2 , A C k , A ~ r D u e t o t h e l i m i t e ds p a c e , o n l y t h e r e s u l ts a r e p r e s e n t e d h e r e . H e r e , w e a s s u m e t h a t t h e e n v e l o pl ev e l a n d t h e u n k n o w n p h a s e a r e c o n s t a n t o v e r t h e o b s e r v a t i o n w i n d o w l e n g t h .p d f ( 7~ , 7 k - i , A 0 k , AOl~_ilat:, a~ -i, ak -2, zlCk, Z l C k - 1 ) =

7r2 2 2 2 (u 2 -F 4u + 2) ex p u - - (14)\ 1 + 7 ~ _1 + % - ~ % 2 N1

2 2

a 2 2 + ak_iTi:_ i " l - ( a ~ 7 ~ - i " / ~ )x + 2 a ~ - i a ~ 7 ~ ._ i T ~ c o s ( A p u - Z Ir + 2 a ~ - 2 a ~ - i T ~ - i c o s ( A # ~ _ i - - A C e _ i )+ 2 a ~ - 2 a ~ 7 ~ - i T ~ c o s ( A 0 ~ - - A r + A t ~ _ i - A r

( 1 5 )F o r a l a r g e C / N , w e c a n p a y a t t e n t i o n o n l y to t h e e x p o n e n t i a l p a r t o f ( 14 ) .T h e r e f o r e , f in d i n g t h e s eq u e n c e ( a ~, a ~ _ l , a ~ - 2 , A r A C e _ i ) t o m a x i m i z e ( 14 )is a p p r o x i m a t e l y e q u i v a le n t t o m a x i m i z i n g t h e fo l l o w in g :

1+ 7k -17~

% - 2 a ~ -K Y k - 1 + (a k ~ ' k - l~ ' k ) 2X + 2 a ~ - t a k ~ _ t ~ ' k c o s (Z I0 ~ - - A C k ) + ~ a k - 2 a k - ~ ' k - ~ c o s (Z ~ 0~ _I - - Z ~ r+ 2ak -2a ~ 'k - l "Y k cos (Z~0k - - ZW'k + z~0k-~ - AC k- ~)_ [ a 2 a 2I k - 2 T k - l " l -~ % ~ ) ( 1 6 )


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o r

2 2

E *k--iSk-i 2- ( i w )m 3 = 2

i-----0

This gives an MLSE method for a large C / N , which shall be maintained toachieve an acceptable BER performance. Note that we cannot discriminate thetransmit ted amplitude sequences (H, H, H) and (L, L, L), since only the differ-ential amplitude is observed. Of course, there is no need to do so, because ofdifferential encoding. As a corollary, (16) is expanded for any N s of the obser-vation symbols.

N ~ - 1 2E Tk-iSk~ i t

- 2 ( i s )~ N o ~ N ~ - I [r~_/[2 i=0i-----0

3.2 Suboptimal Algori thm using Mult iple-symbol Detect i on ofD A S K

If an approximate MLSE method of (17) is directly applied to star 16QAM, itscomplexity increases by (2 N" - 1) x 8 y` -I , due to a combined decision on symbolswith their amplitude and phase at one time. Even three symbols observationtherefore leads to 448 considerable sequences. We call this an exhaustive searchalgorithm.

To avoid this problem, an independent detection of amplitude and phaseis introduced. A conventional differential detection originally uses this method.Together with conventional multiple-symbol detection of M-DPSK [5], by makinguse of (17) as a differential amplitude detection criterion, suboptimal approachcan be configured as shown in Figure 5. We call this suboptimal approach anindependent algorithm. The detection criterion of amplitude detection is:

to choose ( a k -N ,+ l , . . . , a ~ - l , a k ) to maximize (17) while (19)neglecting phase error, i.e. ACk-i- - A0k-i = 0 for i = 0,,~ N~-2

where N~ is the number of the observed symbols for 2DASK detection. Similarly,that of 8DPSK detection is Np. The complexity of the independent algorithm is(2 ~a - 1) + 8 Np-1. Table 1 shows each complexity, up to around 29, for variouscombinations of amplitude and phase observation period.


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3 .3 S i m u l a t i o n R e s u l t s a n d D i s c u s s i o n sT o a s s e ss t h e p e r f o r m a n c e o f t h e p r o p o s e d d e t e c t i o n s c h e m e , w e h a v e c a r r ie do u t a c o m p u t e r s i m u l at io n . T h e A W G N c h a n n e l a n d p e r fe c t ti m i n g fo r s a m p l i n gt h e r e c e i v e d s i g n a l w e r e a s s u m e d .A n o t h e r f a c t o r t h a t a f fe c t s t h e c o m p l e x i t y , p r o c e s s in g sp e e d a n d p e r fo r -m a n c e , is t h e n u m b e r o f s i m u l t a n e o u s l y d e t e c t e d s y m b o l s a t o n e o b s e r v a ti o nw i n d o w . H e r e w e s i m u l a t e d w i n d o w - b y - w i n d o w d e t e c t i o n a s o p p o s ed t o s y m b o l -b y - s y m b o l d e t e c ti o n .

I n F i g u r e 6 , t h e a m p l i t u d e B E R s a r e s h o w n f o r Na = 2 ( c o n v e n t i o n a l )t h r o u g h 9 b y t h e i n d e p e n d e n t a l g o r i t h m t o g e t h e r w i t h t h a t o f c o h e r en t d e t e c t i o nw i t h d i ff e re n t ia l e n c o d i n g a n d d e c o d i n g ( 2 D E C A S K ) . T h e s i m u l a t i o n ra n u n t i lm o r e t h a n 1 0 24 e rr o r sy m b o l s w e r e c o u n t e d f o r N ~ = 2 t h r o u g h 6 , m o r e t h a n5 12 e r r o r s y m b o l s fo r N ~ = 7 a n d 8 , a n d 2 5 6 e r r o r s y m b o l s f o r N ~ = 9 . T h e t o t a lp e r f o r m a n c e s o f e x h a u s t iv e a n d i n d e p e n d e n t a l g o r i th m s a r e s ho w n i n F i g u r e s 7a n d 8 , r e s p ec t iv e l y , w h e r e m o r e t h a n 2 56 e r r o r s y m b o l s w e r e c o u n t e d f o r N s = 4 ,a n d 512 o r 1024 f o r o the r s .

A s a r e s u l t, t h e o v e ra ll p e r f o r m a n c e o f s t a r 1 6 Q A M i s i m p r o v e d a s l i s te d i nT a b l e 1 . I n g e n e r a l , a s t h e t a r g e t B E R b e c o m e s l o w e r , a b e t t e r i m p r o v e m e n tw o u l d b e a c h i e v e d . N o t e t h a t , i n F i g u r e s 6 , 7, 8 a n d T a b l e 1 , t h e r i n g r a t i o w a ss e t a s 2 .0 t h a t m a y n o t b e o p t i m u m e x c e p t f o r c o n v e n t i o n a l d i f fe r e n ti a l d e t e c t i o n .F o r i n s t a n c e , i n a n i n d e p e n d e n t a l g o r i t h m w i t h ( N ~ , N p ) = (5 , 2 ), t h e o p t i m u mr i n g r a t i o i s a r o u n d 1 . 8 , t h e n t h e i m p r o v e m e n t g a i n i n c r e a s e s f r o m 0 . 9 d B t o1 .1dB a t P b = 10 - 3 .

r e c e i v e d Is ignal . ._ I- I s a m p l e r f 1 d e fe c to ,

conventional8DPSKdetector w ith Npobservationsymbols

p h a s e i n f o r m a t io nJ N a ~ ~ r I

a A ei n fo rma t ion

differentialamplitudedetectionbyNa symbolsobservation

F ig . 5 . S c he m a t i c d i a g ra m o f inde pe nde n t m u l t ip l e - sym bol de te c tion f o r s t a r 16QAM


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2 0 5

l 0 ~

l f f I

l f f~

10 3

1 0 41 2 1 4 1 6 1 8 2 0C/N [dB l

F i g . 6 . A m p l it u d e B E R o f i n d e p en d e n t m e t h o d2 2

l i f t

10 2

10"3

[0 "412 14 16 18 20 22

C/N [dB]Fig. 7 . Overal l perfor mance of exhaust ive algori thm

4 C o n c l u s i o n sA f t e r a n a l y t i c a l l y c o n s i d e r i n g t h e c o n v e n t i o n a l d i ff e r en t ia l d e t e c t i o n o f s t a r 1 6 Q A M ,w e p r o p o s e d a m u l t i p l e - s y m b o l d if f e r en t i a l d e t e c t i o n s c h e m e f o r a m p l i t u d e i n s t a r1 6 Q A M b a s ed o n a n M L S E f o r a la r g e C/N. T h i s a p p r o x i m a t e M L S E m e t h o dc a n a l so b e a p p l ie d t o g e n e r a l s t a r Q A M s a n d D A S K s . T h e c o m p l e x i t y o f a ne x h a u s t i v e a l g o r i t h m i n c r e a s e s q u i c k l y b y t h e 1 6 t h p o w e r o f t h e o b s e r v a t i o n s y m -b o l s, w h i le t h a t o f a n i n d e p e n d e n t a l g o r i t h m d o e s n o t i n c r e a s e so m u c h . W e a ls od e m o n s t r a t e d t h e p e r f o r m a n c e o f e ac h , a n d c o m p a r e d th e m t h r o u g h c o m p u t e rs i m u l a t i o n .

W i t h r e sp e c t t o t h e p e r f o r m a n c e im p r o v e m e n t o f b o t h a l g o ri th m s u n d e r t h e


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10 I206

10 2

10 3

l 0 412 14 16 18 20 22r [dB]Fig. 8. Overall performance of independent algorithm

same observation window length, for example, the improvement of the exhaustivealgorithm with N8 = 3 and tha t of the independent algorithm with (Na, Np) =(3, 3), are almost the same. Taking into account the complexity, the independentalgorithm has great advantages over the exhaustive algorithm. Moreover, theobservation window length should be longer in ampli tude detection than in phasedetection, i.e., Na > Np, to improve performance because of a lager energypenalty in differential amplitude detection. This may be easily achieved becausethe complexity in amplitude detection increases in proportional to 2 N~ whereasthat in phase detection does to 8Np.

As 16-level modulation, star 16QAM is an attractive scheme not only formobile / personal communications, but also for economical high rate data trans-mission. This is because of simpler hardware than square 16QAM and betterperformance than 16DPSK. A multiple-symbol differential detection proposedin this paper is deemed promising to fill the gap between ideal coherent anddifferential detections with a modest hardware complexity, which makes star16QAM more attractive.Acknowledgement The authors are grateful to Dr. Y. Urano, Dr. Y. Ito and Dr.H. Kobayashi in KDD R&D Laboratories for their suggestions and encourage-ment.

R e f e r e n c e s1. Webb, W. T., Hanzo, L., Steele, R.: Bandwidth efficient QAM schemes for Rayleighfading channels. IEE Proc. I, Vol. 138, No. 3, June 1991.2. Adachi, F., Sawahashi, M.: Performance analysis of various 16 level modulationschemes under Raylelgh fading. Electronics Letters, Vol. 28, No. 17, 13th August,1992.


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T a b l e 1 . C o m p le x i t y a n d p e r f o r m a n c e o f m u l t i p le s y m b o l d e t e c t io n

observation symbolsN s : exhaustive(Na ,Np ) : independent~ 2 .2 ) : c o n v e n t i o n a l( 3 . 2 ) : i n d e p e n d e n t( 4 , 2 ) : i n d e p e n d e n t( 5 . 2 ) : i n d e o e n d e n t( 2 , 3 ) : i n d e p e n d e n t( 3 ,3 ) : i n d e p e n d e n t

( 4 , 3 ) : i n d e p e n d e n t/ 5 , 3 ) : i n d e p e n d e n t

3 ) : e x h a u s t i v e

( 4 ) : e x h a u s t i v e

co mp l ex i t y improvementa t P b = 1 0 ""with H/L=2

1 11 5233 96 771

799 5

4 4 8

7 6 8 0

0 .000 , 5 50 .800 . 9 00.250 .90

1 . 2 51 . 4 5

0 . 9 5

1 . 2 5

[dBl

3 . Chow , Y . C. , N ix , A . R. , McG eehan , J . P . : Ana lys is o f 16 -A PSK m odu la t io n inAWGN and Ray le igh f ad ing channe l . E lec t ron ics Le t te r s , Vo l . 28 , No . 17 , 13 thAugust , 1992.

4 . W e b b , W . T . : M o d u la t i o n M e th o d s f o r P CN s . I E E E C o m m . M a g a z in e , D e c e m b e r ,1992.

5 . D iv s a l a r , D ., S im o n , M . K . : M u l t i p l e -S y m b o l D if fe r e nt ia l D e t e c t i o n o f M P S K . I E E ETran . on COM., Vol . 38 , No. 3 , March , 1991.

6 . S a m e j im a , S ., E n o m o to , K . , W a ta n a b e , Y . : D i f fe r e nt ia l P S K S y s t e m w i th N o n r e -dundan t Er ro r Cor rec t ion . IEEE Jou rna l on se lec ted a reas in COM. , Vo l . 1 , No . 1 ,January , 1983 .7 . P roak is , J . G . : Dig i ta l Comm unica t ions . McGraw-Hi l l , NewYork , 1983 .

8. Watson~ G. N.: A Treatise on the T heory of Bes sel Fun ctions. 2 n d e d . , Ca m b r id g eUniver s i ty P ress , 1962 .

9 . Gradsh teyn , I . S . , Ryzh ik , I . M. : Ta ble of Integrals, Series, and P roduc ts. 4 th ed . ,A c a d e m ic P r e s s , N e w Y o r k , 1 96 5.

multiple-symbol differential detection scheme

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