A Dual-Mode Synchronous/Asynchronous CORDIC Processor

Eckhard Grass, Bodhisatya Sarker and Koushik Maharatna IHP Im Technologiepark 25 15236 Frankfurt (Oder), Germany [email protected]

Abstract a frequency correction on the incoming signals. A Coordinate Rotation Digital Computer (CORDIC) offers For application in a software defined radio a CORDIC an elegant way of implementing an NCO. processor has been developed that can operate both in To open a broad market for consumer products, low synchronous and asynchronous mode. Each mode of cost of the required hardware is essential. One way to operation has advantages and drawbacks. Depending on realise low-cost systems is to reduce system complexity the actual application, an optimal trade-off can be and implement all functions of a wireless modem in a achieved by selecting the mode of operation that fits best single chip. Potentially, a single-chip solution is also with system demands. We believe that for a system advantageous in terms of performance and power developer this additional degree of freedom significantly dissipation when compared with multi-chip increases the application space. µ implementations. Fewer signals have to be routed via slow The design has been implemented on a 0.25 m SiGe:C and power-hungry pad drivers. In addition, short BiCMOS process. Simulation results using post-layout interconnections allow faster operation of the system. extracted parameters indicate that the design is µ competitive both with purely synchronous and purely Our in-house 0.25 m SiGe:C BiCMOS technology asynchronous implementations. enables the integration of complex digital baseband functionality together with the analog RF front-end (AFE). This process technology forms the basis for the single-chip 1. Introduction implementation of a complete wireless modem. This single-chip wireless modem will hence comprise analog Fourth generation (4G) wireless and mobile systems circuitry, processor cores as well as dedicated hardware. are currently the focus of research and development. They For the single-chip modem, a number of critical design will allow new types of services to be universally available problems have to be solved. One major issue is the to consumers and for industrial applications. Broadband reduction of crosstalk from the digital part to the analog wireless networks will enable packet based high datarate circuitry. The high energy which is delivered by clock communication suitable for video transmission and mobile drivers can influence the AFE and deteriorate its signal to Internet applications. noise (S/N) ratio. The most predominant crosstalk This paper is based on a project which aims to develop mechanisms are substrate noise, supply voltage variations a single-chip wireless broadband communication system in as well as electro-magnetic effects (EMR) [3]. Secondly, the 5 GHz band, compliant with the Hiperlan/2 [1] and system power dissipation is a critical issue. Since many IEEE 802.11a [2] standards. Both standards specify functional blocks are active for a limited period only, there broadband communication systems using Orthogonal is potential to reduce power dissipation drastically. A Frequency Division Multiplexing (OFDM) with data rates token-flow approach [4] is adopted by adding signals ranging from 6-54 Mbit/s. The duration of one OFDM which indicate the validity of data at inputs and outputs of symbol, which can carry 24 to 216 bits of information is functional blocks. Distributing the control of data flow, 4 µs. For such a system a large portion of the digital this token-flow approach allows easy implementation of baseband processor has to operate on complex signals clock gating and lends itself to asynchronous which are sampled at a rate of 20 MS/s. The most difficult implementations of blocks. to implement functional blocks of the baseband processor Currently a number of extensions to the standards for are FFT/IFFT processor, Viterbi Decoder, and Numeric 5 GHz broadband communication systems are being Controlled Oscillator (NCO). The NCO is used to perform discussed by the standardisation committee. Therefore, it w ou l d b e b e n e f i c i a l f o r c u s t o m e r s a n d s upp li e r s o f t ho s e a nd t h e v ec t o r i n g m od e w h e r e , v a r i a b l e s z a n d y a r e f o r c e d s y s t e m s i f h a r d w a r e w ou l d b e a b l e t o acc o m m od a t e f u t u r e t o ze r o r e s p ec ti v e l y . E ac h o f t h e s e m o d e s ca n b e u tili s e d i n c o mm un i ca ti o n s t a nd a r d s . A s o f t w a r e d e f i n e d r a d i o , i n c i r c u l a r , li n ea r a nd h yp e r bo li c c o o r d i n a t e s y s t e m s . T h i s p r i n c i p a l , o ff e r s t h i s n ee d e d f l e x i b ilit y . ill u s t r a t e s t h e v e r s a tilit y o f t h e C O R D I C a nd e xp l a i n s w hy H e r e w e e x t e nd t h e i d ea o f s o f t w a r e d e f i n e d r a d i o s u c h iti s r e g a r d e d a s on e o f t h e m a j o r t oo l s i n d i g it a l c o m p u t e r t h a t t h e s o f t w a r e d e v e l op e r ca n c ho s e ce r t a i n h a r d w a r e a r it h m e ti c . acce l e r a t o r s t o op e r a t e e it h e r s yn c h r o n ou s l y o r H o w e v e r , f o r o u r p u r p o s e it i s s u ff i c i e n t t o u s e t h e a s yn c h r o n ou s l y . T h i s a dd iti on a l d e g r ee o f fr e e do m r o t a ti on a n d v ec t o r i ng o p e r a ti on s i n t h e c i r c u l a r c oo r d i n a t e i n c r ea s e s t h e a pp li ca ti on s p ace o f t h e c o m p l e t e s y s t e m . s y s t e m on l y . H e n ce w e c o n ce n t r a t e on t h e r ea li za ti on o f a F u r t h e r m o r e , a l s o w it h a g i v e n s t a nd a r d , d i ff e r e n t c i r c u l a r C O R D I C p r o ce ss o r . I t ’ s op e r a ti on r e li e s on t h e a pp li ca ti on s ce n a r i o s r e q u i r e d i f f e r e n t p r o p e r ti e s o f t h e p r i n c i p l e o f v ec t o r r o t a ti on . T h e b a s i c op e r a ti on i s h a r d w a r e . W e a r e c onv i n c e d t h a t h a v i ng t h e fr ee d o m f o r d e s c r i b e d b e l o w : ce r t a i n k e y b l o c k s o f c h o o s i ng b e t w ee n s yn c h r o nou s a n d T h e r o t a ti on o f a v ec t o r [ x0 y 0 ] T i n t h e C a r t e s i a n c o - a s yn c h r o n ou s o p e r a ti on a ll o w s f i n d i ng a s u it a b l e t r a d e - o ff o r d i n a t e s y s t e m ca bn e d e s c r i b e d a s , b e t w ee n po w e r d i ss i p a ti on , c r o ss t a l k , d a t a t h r ou g hpu t , Ø x 1 ø Ø cos q sin q ø Ø x 0 ø l a t e n c y a nd ( s e l f-) t e s t a b ilit y . Œ œ = Œ œ Œ œ ( 1 ) A s a n e x a m p l e , it m a y b e d e s i r a b l e w it h v e r y s m a ll º y 1 ß º - sin q cos q ß º y 0 ß s i gn a l a m p lit ud e s on t h e r ece i v e r t o r e d u ce t h e i m p ac t o f w h e r e , [ x 1 y 1 ] T i s t h e f i n a l v ec t o r a n d q i s t h e a ng l e o f t h e C L K s i gn a l by op e r a ti ng t h e C O R D I C i n a s yn c h r o nou s r o t a ti on ( - 99 . 9 £ q £ 9 9 . 9 ) . I n t h e a bov e e qu a ti o n it w a s (‘ w h i s p e r’) m od e . O n t h e o t h e r h a nd , i f t h e r ece i v e s i g n a l a ss u m e d t h a t t h e r o t a ti o n t a k e s p l ace i n c l o c k w i s e i s v e r y s t r ong a nd f o r c on ti nu o u s r ece p ti o n o f d a t a , t h e d i r ec ti on . N o w , t h e t a r g e t a n g l e q ca n b e e xp r e ss e d a s t h e m o r e p o w e r e ff i c i e n t s y n c h r o n ou s op e r a ti o n i n c o n j un c ti o n s u mm a ti on o f a nu m b e r o f e l e m e n t a r y a ng l e s a s o t h a t w it h c l o c k - g a ti n g ca n b e u s e d . i T h e p a p e r d i s c u ss e s a du a l m od e i m p l e m e n t a ti on o f a b - 1 q = s a ( 2 ) C O R D I C p r o ce ss o r a nd c o m p a r e s t h e m a i n p a r a m e t e r s o f i i t h i s d e s i gn w it h a pu r e l y s yn c h r o n ou s a s w e ll a s a pu r e l y i = 0 a s yn c h r o n ou s i m p l e m e n t a ti on . I t i s d e m on s t r a t e d t h a t w h e r e , b i s t h e b it p r ec i s i on o f t h e m a c h i n e i n w h i c h s ˛ - a s yn c h r o n ou s c i r c u it s ca n b e i m p l e m e n t e d i n VHD L u s i ng t h e op e r a ti o n i s t o b e i m p l e m e n t e d a n d i { 1 , 1 } , i s s yn c h r o n ou s t oo l s . VHD L s yn t h e s i s a nd l a y ou t a r e kno w n a s t h e d i r ec ti on o f r o t a ti on . I n t h e c o nv e n ti o n a l s uppo r t e d by a nu m b e r o f a tt r i bu t e s a n d c on s t r a i n t s w h i c h c i r c u l a r C O R D I C op e r a ti on a i i s e xp r e ss e d a s , a r e s p ec i f i c t o t h e t o o l s u s e d . T h e h a r d w a r e ov e r h ea d o f a = tan - 1 ( 2 - i ) ( 3 ) t h e du a l m o d e C O R D I C p r o ce ss o r c o m p a r e d t o t h e i s yn c h r o n ou s v e r s i o n i s a bou t 1 2 % . I t s ho w s a s i m il a r S ub s tit u ti ng ( 2 ) i n ( 1 ) a ndu s i ng ( 3 ) o n e m a y w r it e b - 1 Ø - i ø p e rf o r m a n ce w h e n c o m p a r e d t o it s s yn c h r o n ou s Ø x 1 ø 1 s i 2 Ø x i ø c oun t e r p a r t . Œ œ = cos a i Œ œ Œ œ ( 4 ) y 1 - i y T h e r e m a i n i n g p a p e r i s s t r u c t u r e d a s f o ll o w s : I n º ß i = 0 ºŒ - s i 2 1 ßœ º i ß S ec ti on 2 t h e a r c h it ec t u r e o f t h e C O R D I C p r o ce ss o r i s i - 1 d e r i v e d f r o m t h e a l go r it h m i c s p ec i f i ca ti on . S ec ti on 3 a nd s i = Sign [ a - a r ] ( 5 ) d i s c u ss e s s t r a t e g i e s f o r i m p l e m e n ti n g t h e d e s i gn . I n r = 0 S ec ti on 4 , a n u m b e r o f i ss u e s r e l a t e d t o t h e d e s i gn f l o w f o r z = z + s 2 - i ( 6 ) a s yn c h r o n ou s i m p l e m e n t a ti on s a nd t h e u s e d t oo l s a r e i + 1 i i h i gh li gh t e d . F i n a ll y i n S ec ti on 5 t h e r e s u lt s o f o u r T h e p h y s i ca l m ea n i ng o f t h e s e e qu a ti o n s i s t h a t t h e i m p l e m e n t a ti on a r e r e p o r t e d a n d c on c l u s i on s a r e d r a w n i n t a r g e t a ng l e g i v e n a s t h e ‘ z ’ v a r i a b l e i s d r i v e n t o ze r o by S ec ti on 6 . t o - a nd - fr o m o ti on o f t h e v ec t o r . A t ea c h it e r a ti on s t e p t h e

s i gn o f t h e r e s i du a l a ng l e ( s i ) i s ca l c u l a t e d a n d acc o r d i ng l y 2. C O RD I C P r o c e ss o r A rc h i t e c t u re t h e v ec t o r i s r o t a t e d i n c l o c k w i s e o r c o u n t e r c l o c k w i s e d i r ec ti on . F r o m t h e h a r d w a r e i m p l e m e n t a ti on p o i n t o f T h e v e r s a tilit y o f C O R D I C s upp l e m e n t e d w it h it s v i e w , t h i s op e r a ti on c a n b e c a rr i e d ou t u s i ng on l y s h i f t - m u lti p li e r l e ss f ea t u r e h a s p r o p e ll e d d i g it a l d e s i gn e r s t o a nd - a d d iti on o p e r a ti on s s i n ce m u lti p li ca ti on o f a n y - i i n c o r p o r a t e iti n s e v e r a l a r it h m e ti c p r o ce ss o r s a s w e ll a s t o qu a n tit y b y 2 i s a s h i f t o f t h e b i n a r y r e p r e s e n t a ti on o f t h e f o r m u l a t e a n d i m p l e m e n t m a n y m od e r n D SP a l go r it h m s qu a n tit y b y i - b itt o t h e r i gh t . [ 5 - 9 ] t h a t r e qu i r e c o m p l e x n u m b e r m u lti p li ca ti on , H o w e v e r , t h e c onv e n ti on a l C O R D I C a l go r it h m s u ff e r s e l e m e n t a r y p l a n e r o t a ti ono r l a tti ce op e r a ti on s . fr o m t w o p r i n c i p a l d r a w b ac k s , v i z ., t h e r e qu i r e m e n t o f a I n e ss e n ce , t h e C O R D I C acce p t s t h r ee i npu t v a r i a b l e s s ca l e f ac t o r a nd t h e s l o w r a t e o f c onv e r g e n ce . I n o r d e r t o x0 , y 0 , a n d z 0 a nd g e n e r a t e s t h e o u t pu t x 1 , y 1 a n d z 1 . I t ov e r c o m e t h e s e d i ff i c u lti e s w e d e v e l o p e d a m od i f i e d ca n b e o p e r a t e d i n t w o d i ff e r e n t m o d e s v i z ., t h e r o t a ti o n C O R D I C a l go r it h m w h i c h i s d e s c r i b e bd e l o w . I n o u r s c h e m e , t h e t a r g e t a n g l e i s ac h i e v e d b y r o t a ti ng ca n b e e x t r a po l a t e d f r o m t h e r e s u lt o f a r o t a ti on t h e v ec t o r on l y i n on e d i r ec ti on ( e it h e r c l o c k w i s e o r c o rr e s po n d i ng t o [ 0 , 22 . 5 ] . c oun t e r c l o c k w i s e ) t h r o u gh s u ff i c i e n tl y s m a ll e l e m e n t a r y x ( i - 1 ) y ( i - 1 ) a ng l e s a i . T h e y c a n b e e xp r e ss e d b y t h e f o ll o w i ng e q u a ti on - i s i n a i @ a i = 2 ( 7 ) T h i s a ss u m p ti on i m po s e s a l o w e r li m it o n t h e v a l u e o f it e r a ti on i nd e x i . T h e l o w e r li m it o f i ca n b e ca l c u l a t e d fr o m t h e f ac t t h a t t h e l a r g e s t v a l u e n e g l ec t e d i n t h e x ( i - 1 ) y ( i - 1 ) e xp a n s i ono f t h e s i n e s e r i e s i s - 3 i - ( 3 i + log 6 ) - ( 3 i + 2 . 585 ) 2 / 6 = 2 2 = 2 . T hu s , t h e c o nd iti on f o r p r e s e r v i n g t h e acc u r ac y d u r i n g s u c h a pp r ox i m a ti onb ec o m e s 2 i + 1 - b it 2 i + 1 - b it s h i f t e r 3 i + 2 . 5 85 ‡ b o r s h i f t e r i i ‡ Ø ( b - 2 . 5 85 ) / 3 ø = p ( 13 ) ( s i n ce i ca n a d o p t on l y i n t e g e r v a l u e s ) . i - b it i - b it s h i f t e r s h i f t e r T h e u p p e r li m it o f i i s b - 1 s i n ce a r i gh t s h i f t o f a ny + - - + b - b it nu m b e r b y b - b it w ill r e s u lt i n m ac h i n e ze r o . U n d e r t h e a bov e c i r c u m s t a n ce s , t h e v a l u e s o f s i n a i a n d c o s a i ca n b e e xp r e ss e d a s , - i s i n a i = 2 ( 14 ) c o s a = 1 - 2 - ( 2 i + 1 ) ( 15 ) i + + C on s i d e r i ng t h e a p p r o x i m a ti on , s i = + 1 ( s i n ce t h e s i gn - + o f t h e r e s i du a l a ng l e i s a l w a y s t h e s a m e f o r a llit e r a ti on s ) a nd c l o c k w i s e r o t a ti o n o f t h e v ec t o r , e qu a ti o n ( 1 ) m a y b e r e w r itt e n a s b - 1 - ( 2 i + 1 ) - i Ø x 1 ø Ø 1 - 2 2 ø Ø x i ø Œ œ = Œ œ Œ œ ( 16 ) x ( i ) y ( i ) y 1 - i - ( 2 i + 1 ) y º ß i = p ºŒ - 2 1 - 2 ßœ º i ß F i gu r e 1 . B l o c k d i a g r a m o f a n e l e m e n t a r y E qu a ti on ( 16 ) ca n b e r ea li ze d i n p r ac ti ce u s i ng on l y d a t a p a t h c o m pon e n t( r o t o r s t a g e i ) . s h i f t - a nd - a d d op e r a ti on s . F u r t h e r m o r e , c on t r a r y t o e qu a ti on ( 4 ) , n o s ca li ng t e r m a p p ea r s i n e qu a ti o n ( 1 6 ) , T h e c o m p l e t e C O R D I C p r o ce ss o r ca p a b l e t o op e r a t e i n w h i c h i m p li e s a s ca li ng fr ee C O R D I C op e r a ti on . T h e t h e r o t a ti on a nd v ec t o r i ng m od e ov e r t h e e n ti r e c oo r d i n a t e e li m i n a ti on o f t h e s ca li ng t e r m i s a s i gn i f i ca n t s t e p , s i n ce it s p ace h a s t h r ee p a r t s , v i z ., s i gn a nd d o m a i n d e t ec ti o n a vo i d s t h e r e q u i r e m e n t o f e x t r a po s t - p r o ce ss i ng c i r c u it r y c i r c u it r y , b a s i c C O R D I C s ec t i on w it h c onv e r g e n ce r a ng e – a nd s a v e s p r o ce ss i ng ti m e . T h e d a t a p a t h c o m pon e n t s f o r 22 . 5 a n d t h e o u t pu t c i r c u it r y . T h i s i ss ho w n i n F i gu r e 2 . i m p l e m e n ti ng t h e op e r a ti o n o f e qu a ti o n ( 1 6 ) a r e s h o w n i n T h e s i gn a n d do m a i n d e t ec ti on c i r c u it r y ( d e s i gn a t e d a s F i gu r e 1 . T h i s ca n b e v i e w e d a s a n e l e m e n t a r y r o t a ti o n a l s gn_d e t ec t ) d e t ec t s t h e s i gn o f t h e i npu t a n g l e , q u a d r a n t a nd t h e d o m a i n ( po s iti on o f t h e v ec t o r i n a qu a d r a n t ) o f t h e s t a g e r e nd e r i n g a r o t a ti o n o f a i t o it s i npu t v ec t o r . T h i s r e qu i r e s f o u r s h i f t e r s , t w o s ub t r ac t o r s a n d t w o a dd e r / i npu t v ec t o r . A cc o r d i ng l y , t h e i n p u t v a r i a b l e s a r e s ub t r ac t o r s a s d a t a p a t h c o m po n e n t s . T hu s , c o m p a r e d t o t h e p r o ce ss e d a nd t h e y m a y b e r e g a r d e d a s t h e m o d i f i e d i n pu t d a t a p a t h o f t h e e l e m e n t a r y r o t a ti o n a l s t a g e o f a n un s ca l e d t o t h e b a s i c C O R D I C p r o ce ss o r . T h e d e t ec ti on o f s i gn a n d C O R D I C , it r e qu i r e s t w o s h i f t e r s a nd t w o s ub t r ac t o r s do m a i n , p r e - p r o ce ss i ng a n d a p p r o p r i a t e i npu t o p e r a ti on s m o r e . H o w e v e r , f o r t h e e l e m e n t a r y r o t a ti on a l s t a g e s r e qu i r e t w o c l o c k c y c l e s . T h e b a s i c C O R D I C p r o ce ss o r c o rr e s po n d i ng t o i ‡ b / 2 , t h e s e e x t r a s h i f t e r s a nd ( d e s i gn a t e d a s c o r d_p i p e ) i s a b it p a r a ll e l p i p e li n e d s ub t r ac t o r s ca n b e o m itt e d a s t h e r i g h t s h i f t o f t h e i n p u t i m p l e m e n t a ti on w it h i n t e r n a l w o r d l e n g t h o f 1 6 b it s . F r o m qu a n tit y b y ( 2 i + 1 ) b e c o m e s m ac h i n e z e r o a n d t hu s d o e s e qu a ti on ( 13 ) , t h e v a l u e o f ‘ p ’ f o r a 16 - b iti m p l e m e n t a ti o n no t a ff ec tt h e ac c u r ac y a ny m o r e . i s a pp r ox i m a t e l y 4 . T h e p i p e li n e i s 1 7 s t a g e s l ong w h e r e - 4 H o w e v e r , e q u a ti on ( 7 ) i m p li e s t h a t t h e c onv e r g e n ce t h e e l e m e n t a r y r o t a ti on a l s t a g e c o r r e s po n d i ng t o 2 i s r a ng e o f t h e C O R D I C w ill b e s m a ll . T h e c onv e r g e n ce r e p ea t e d 6 ti m e s . O u r a i m i s t o a p p r ox i m a t e z a nd y f o r t h e r a ng e ca n b e e x t e nd e d ov e r t h e e n ti r e c o o r d i n a t e s p ace by r o t a ti on a n d t h e v ec t o r i ng m od e r e s p ec ti v e l y w it h i n a n r e p ea ti ng ce r t a i n it e r a ti o n s t e p s a nd by e x p l o iti ng t h e acc u r ac y o f O ( 2 - 16 ) . I n t h e c on s t r u c ti o n o f t h e e l e m e n t a r y s y mm e t r y o f t h e c o o r d i n a t e a x e s . I n p r i n c i p l e , w e f o u nd r o t a ti on a l s ec ti on s , t h e c o nv e n ti o n a l t w o ’ s c o m p l e m e n t t h a tt o c ov e r t h e w ho l e c oo r d i n a t e s p ace , iti ss u ff i c i e n tt o a dd iti on i s u s e d . T h e i n f o r m a ti on a bou t t h e qu a d r a n t a nd c o m pu t e t h e a ng l e s i n t h e i n t e r v a l [ 0 , 22 . 5 ] . T h e r e s u lt s o f do m a i n o f t h e i n iti a l v ec t o r d e t ec t e d a t t h e s gn_d e t ec t C O R D I C r o t a ti on s f o r a n y a ng l e b e t w ee n 2 2 . 5 a n d 3 6 0 m odu l e i s t r a n s f e rr e d b e t w ee n t w o c on s ec u ti v e s ec ti on s o f t h e p i p e li n e a l o n g w it h t h e d a t a i n a l o ca l r e g i s t e r t r a n s f e r i m p l e m e n t e d u s i n g a d a t a p a t h a r c h it ec t u r e . T h e m o s t m a nn e r . T h i s m ea n s t h a t t h e d a t a i n d i ff e r e n t s ec ti on s o f c o m p l e x b l o c k s i n t h i s d a t a p a t h a r e C O R D I C - P r o ce ss o r , t h e p i p e li n e h a s a t o k e n a tt r i bu t e d t o it t h a t e ss e n ti a ll y FF T p r o ce ss o r a nd V it e r b i D ec o d e r . I ti s ou r go a lt o m a k e ca rr i e s t h e i n f o r m a ti on a b ou t it s i n iti a l qu a d r a n t a nd t h e d e s i gn o f t h e c o m p l e t e b a s e b a n d p r o ce ss o r a s m u c h a s do m a i n . A s i ng l e b it s i gn a l , ‘ s i gn ’ a nd t w o 2 - b it s i gn a l s po ss i b l e t ec hno l o g y i nd e p e nd e n t . T h e r e f o r e it h a s b ee n ‘ do m a i n ’ a nd ‘ qu a d ’ a r e u s e d t o t r a n s f e r t h i s i n f o r m a ti on d ec i d e d t uo s e VHD L f o r d e s i g n e n t r y t h r o ug h ou t . b e t w ee n s u cce ss i v e r o t a ti on a l s t a g e s . I n o r d e r t o d e - ce n t r a li s e c on t r o l , a t o k e n -f l o w a p p r o ac h i s u s e d . T h e v a li d it y o f d a t a t o k e n s i s i nd i ca t e d u s i n g x 0 y 0 z 0 m o d e d a t a _v a l i d a dd iti on a l s i gn a l s a t t h e i n p u t a nd ou t p u t o f f un c ti o n a l b l o c k s . 1 6 1 6 1 8 T o a ll o w p e r f o r m a n c e c o m p a r i s on , t h r ee d i ff e r e n t c i r c u it s w e r e d e s i gn e d : C i r c u it ‘ M I X - C O R D I C ’ ca n s gn_d e t e c t ( 2p i p e li n e s t a g e s ) op e r a t e b o t h s yn c h r o n ou s l y a s w e ll a s a s yn c h r o nou s l y , c i r c u it ‘ A S Y - C O R D I C ’ op e r a t e s a s yn c h r o n ou s l y a n d c i r c u it ‘ S YN - C O R D I C ’ i s a ‘ no r m a l ’ s yn c h r on o u s d e s i gn 1 6 1 6 1 8 2 2 w it h e x t r a s i gn a l s t o i nd i ca t e d a t a v a li d it y a t i npu t s a n d ou t pu t s . x_ i n y _ i n z _ i n q u a d d o m a i n m o d e _ i n d a t a _ v a li d _ i n Dual-mode circuit (MIX-CORDIC): A 4 - ph a s e h a nd s h a k e p r o t o c o l i s d e p l oy e d s i n ce it c o r d_p i p e ( 17p i p e li n e s t a g e s ) a ll o w s t h e u s e o f s i ng l e e dg e t r i gg e r e d f li p -f l op s . T h e h a nd s h a k e c i r c u it o f t h e M I X - C O R D I C d e s i gn i s i m p l e m e n t e d u s i n g t w o C - e l e m e n t s a ss ho w n i n F i gu r e 3 . 1 6 1 6 1 8 2 2 I n o r d e r t o a vo i d c on f u s i on b e t w ee n t h e t yp e o f t h e s i gn a l (‘ i npu t ’ o r ‘ ou t p u t ’) a nd t h e po r t o f t h e h a nd s h a k e c i r c u it , x_ o u t y _ou t z _ o u t q u a d d o m a i n m o d e _ ou t i n t h i s p a p e r w e d e f i n e t h e ‘ i npu t ’ p o r t o f t h e h a n d s h a k e d a t a _ v a li d _ o u t c i r c u it a s po r t ‘ a ’ a nd t h e ou t pu t p o r ti s l a b e ll e d p o r t ‘ b ’ . ou t pu t c i r c u it r y ( 1p i p e li n e s t a g e ) re q _a re q _b s t a g e ) 1 6 1 6 1 8 P o r t a C Element C Element P o r t b x 1 y 1 z 1 d a t a _v a l i d _ o u t

a c k _ a a c k _ b F i gu r e 2 . S t r u c t u r e o ft h e s y n c h r onou s p i p e li n e d C O RD I C p r o c ess o r F i gu r e 3 . H a nd s h a kec i r c u i tf o r c i r c u i t M I X - C O RD I C T h e ou t p u t c i r c u it r y c on s i s t s o f a f i x e d s ca li ng un it o f 1 / 2 a n d a c o up l e o f a dd e r / s ub t r ac t o r un it s . T h i s c i r c u it U n f o r t un a t e l y o u r ce llli b r a r y do e s n o t c on t a i n a ny C - po s t - p r o ce ss e s t h e ou t p u t v ec t o r e m e r g i n g f r o m t h e e l e m e n t s . R S f li p -f l op s a r e a l s o no t a v a il a b l e . c o r d _ p i p e s ec ti on i n ac c o r d a n ce w it h t h e i n f o r m a ti o n on C on s e qu e n tl y t h e C - e l e m e n t s h a d t o b e c on s t r u c t e d fr o m t h e i n iti a l v ec t o r d e r i v e d b y t h e s g n_d e t ec t c i r c u it r y a n d g a t e s . W e m od e ll e d t h e b e h a v i o u r o f t h e C - e l e m e n t s i n g e n e r a t e s t h e f i n a l ou t pu t . A llt h e op e r a ti o n s a tt h e ou t pu t VHD L a nd s yn t h e s i ze d t h e m . T h e y w e r e t h e n u s e d a s a r e c o m p l e t e d i n on e c l o c k c y c l e . c o m pon e n t s i n t h e VHD L d e s i gn . I t w a s f o u nd t h a t t h e A m od e s i gn a li s a l s o p r o v i d e d w it h t h e p r o ce ss o r . T h e S ynop s y s s yn t h e s i s e r do e s m e r g e t h e f un c ti on a lit y o f a l og i c ‘ H I GH ’ s t a t e o f t h e m od e s i gn a l m a k e s t h e p r o ce ss o r nu m b e r o f C - e l e m e n t s i n t o a s i ng l e c i r c u it d u r i ng t o op e r a t e i n r o t a ti on m od e w h e r ea s ;it s l og i c ‘ L O W ’ s t a t e op ti m i za ti on s t a g e . S i n ce i n t h i s p r o ce ss ti m i ng c on s t r a i n t s m ea n s t h e v ec t o r i n g m o d e o f op e r a ti on i s ca rr i e d ou t . a r e v i o l a t e d , t h e C - e l e m e n t c o m p on e n t s h a d t o b e p r o t ec t e d A p a r t fr o m t h e m o d e s i gn a l , t h e ( s yn c h r on o u s ) p r o ce ss o r i s fr o m o p ti m i s a ti on u s i ng ‘ do n ’ t t ou c h ’ a tt r i bu t e s . T h e a l s o e qu i pp e d w it h a n i n pu t ‘ d a t a _v a li d ’ a nd a n ou t p u t i nd i v i du a l C - e l e m e n t s w e r e e x t e n s i v e l y s i m u l a t e d u n d e r a ‘ d a t a _v a li d ’ s i g n a lt h a ti nd i ca t e s t h e v a li d it y o f i n pu t a n d v a r i e t y o f c ond iti o n s a nd w e r e f o u nd t o b e f un c ti on i n g ou t pu t d a t a r e s p ec ti v e l y . c o rr ec tl y t h r ou g hou t . B e f o r e a p p li ca ti on i n t h e C O R D I C p r o ce ss o r , o u r h a nd s h a k e c i r c u it w a s a l s o e x t e n s i v e l y 3. I m p l e m e n t a t i o n S t r a t e g i e s t e s t e d u s i ng a n a s yn c h r o n ou s F I F O .

T h e m a i n c o m p o n e n t s o f t h e O F D M b a s e b a nd p r o ce ss o r f o r H i p e r l a n / 2 a nd I EEE 8 02 . 1 1 a ca n ea s il y b e i n p u t C l o c k _g l o b a l s y n c r e q _ a _ t o p o u t p u t ...

F i gu r e 4 . S i ng l e s t a g e o f a n a s y mm e t r i c d e l ay e l e m e n t a c k _ a F o r c o m p l e ti o n d e t ec ti on a bo u nd e d d e l a y m e t h od w a s x 0 y0 z 0 u s e d d e p l o y i ng a s p ec i a l a s y mm e t r i c d e l a y e l e m e n t w it h s ho r t r ec ov e r y ti m e . A s i ng l e s t a g e o f t h i s d e l a y e l e m e n ti s 16 16 18 r e q _ a s ho w n i n F i gu r e 4 . A lt e r n a ti v e l y a ca s ca d e o f t w o - i npu t AND g a t e s ca n b e u s e d w h e r e b y t h e i npu t s i gn a l i s a c k _ a c onn ec t e d i n p a r a ll e lt o a ll AND g a t e s . H o w e v e r t h e i n p u t P i p e l i n e s t a g e 1 H a n d s h a k e 1 ca p ac it a n ce o f t h i s s t r u c t u r e s ca l e s w it h t h e l e ng t h o f t h e ca s ca d e w h i c h c r ea t e s a h i g h ca p ac iti v e l o a d on t h e i npu t r e q a c k s i gn a l m a k i ng t h e d e l a hy i gh l uny p r e d i c t a b l e . P i p e l i n e s t a g e 2 a c k _ a A ca s ca d e o f t e n s t a g e s o f t h e s t r u c t u r e s ho w n i n H a n d s h a k e 2 F i gu r e 4 d e li v e r s i n ou r c i r c u it a d e l a y o f 13 . 4 n s a nd r e q a c k 4 . 8 n s f o r a r i s i ng a nd a f a lli ng t r a n s iti on r e s p ec ti v e l y .. . . ( m ea s u r e d a f t e r b ac k a nno t a ti o n f r o m l a y o u t ) . T h e . . . r ec ov e r y ti m e f o r t h e f a lli n g t r a n s iti on o f s u c h a ca s ca d e i s . . . e qu i v a l e n tt o t h e d e l a y o f f ou r i nv e r t e r s o f a s i ng l e s t a g e . . . i . e . a pp r ox i m a t e l y 0 . 8 n s i n ou r ca s e . T h i s r ec ov e r y ti m e i s r e q a c k d i m e n s i on e d s u c h t h a t it i s w e ll b e l o w a ny p o ss i b l e P i p e l i n e s t a g e 2 0 a c k _ a r e s pon s e ti m e o f t h e h a n d s h a k e c i r c u it r y . T h e ac h i e v e d H a n d s h a k e 2 0 r a ti o b e t w ee n r i s e ti m e a n d f a llti m e o f n ea r l y 3 : 1 y i e l d s a 16 16 18 s ub s t a n ti a l s p ee dup o f t h e h a nd s h a k e c i r c u it w h e n c o m p a r e d t o u s i ng a ‘ n o r m a l ’ i n v e r t e r c h a i n . T h e c i r c u it x 1 y1 z 1 r e q _ b a c k _ b do e s no t s u ff e r f r o m h i gh i n pu t ca p ac it a n ce w h i c h a l s o k ee p s it s po w e r d i ss i p a ti on l o w . F i gu r e 5 . S c h e m a t i c d i a g r a m o f du a l - m od e T o a ll o w s w it c h i ng b e t w ee n s yn c h r o nou s a n d C O RD I C a s yn c h r o n ou s m o d e , f o r t h e du a l - m od e c i r c u it a dd iti on a l l og i c i s i n t r odu c e d t o e it h e r e n a b l e t h e a s yn c h r on o u s h a nd s h a k e c i r c u it o r t h e s yn c h r o n ou s c l o c k t o d r i v e t h e A s y n c h r o n o u s c i r c u i t u s i n g l a t c h e s ( A S Y - C O R D I C ): p i p e li n e s t a g e s a ss ho w n i n F i gu r e 5 . I f t h e ‘ s yn c ’ s i gn a li s A s ec ond v e r s i o n u s e s l a t c h e s i n s t ea d o f f li p -f l op s f o r i n l og i c h i g h s t a t e , t h e c l o c k s i gn a l ‘ C l o c k_g l o b a l ’ i s bu ff e r i ng t h e d a t a . S i n ce l a t c h e s a r e s m a ll e r a n d c on s u m e e n a b l e d v i a t h e NAND g a t e a tt h e i n p u t . T h e s t r u c t u r e i s l e ss po w e r , t h i s ca n po t e n ti a ll y r e du ce s ili c on a r ea a nd c on f i g u r e d t o w o r k i n s yn c h r o n ou s m od e . A t t h e s a m e po w e r d i ss i p a ti on . F o r ou r a pp li ca ti on , t h e s e m i - d ec o up l e d ti m e ‘r e q_ a _ t op ’ i s d i s a b l e d v i a t h e NO R g a t e d r i v i n g l a t c h c on t r o ll e r do e s r e p r e s e n t a r ea s on a b l e c o m p r o m i s e ‘r e q_ a ’ . T h e c o m p l e t e h a nd s h a k e c i r c u it i s d i s a b l e d by b e t w ee n h a r d w a r e c o m p l e x it y a n d p e r f o r m a n c e [ 1 1 ] . T h e f o r c i ng ‘r e q _ a ’ t o l og i c l o w . a s y mm e t r i c C - e l e m e n t s u s e d i n t h i s c on t r o ll e r w h e r e O n t h e c on t r a r y i ‘f s yn c ’ i s i n l o g i c l o w s t a t e , t h e g l o b a l d e s i gn e d i n t h e s a m e w a y a s d e s c r i b e d a bov e . T h e c l o c k ‘ C l o c k_g l ob a l ’ i s d i s a b l e d a nd t h e c i r c u it i s r e s u lti ng h a nd s h a k e c i r c u it r y w a s a g a i n t e s t e d i n a n c on f i g u r e d f o r a s yn c h r o nou s o p e r a ti on by e n a b li ng a s yn c h r o n ou s F I F O . P e rf o r m a n ce m ea s u r e m e n t s b a s e d o n ‘r e q_ a _ t op ’ t o d r i v e s i gn a l ‘r e q _ a ’ . C u r r e n tl y t h e r e i s no s i m u l a ti on s u s i ng po s t - l a y o u t e x t r ac t e d p a r a m e t e r s a r e dyn a m i c s w it c h i ng o f m o d e c o n s i d e r e d i . e . s i gn a l ‘ s yn c ’ i s g i v e n i n T a b l e 1 . a ll o w e d t o c h a n g e s t a t e on l y w h e n ‘ C l o c k _ g l ob a l ’ i s l o w S y n c h r o n o u s c i r c u it ( S Y N - C O R D I C ): a nd t h e p i p e li n e i s c o m p l e t e l y s e ttl e d . T h i s p r e v e n t s T h e s yn c h r on o u s i m p l e m e n t a ti on w a s d on e u s i n g po t e n ti a l h aza r d s d u r i n g m o d e - c h a n g e o p e r a ti on s w h i c h e x ac tl y t h e s a m e p i p e li n e a r c h it ec t u r e a s f o r t h e o t h e r t w o c ou l d r e s u lti undn e f i n e d s t a t e s o f t h e s y s t e m . d e s i gn s . I n o r d e r t o s up p o r tt h e t o k e n -f l o w a p p r o ac h ‘ d a t a v a li d ’ s i gn a l s w h e r e i n t r odu ce d a ti n p u t a nd ou t pu t po r t s o f t h e p i p e li n e . A p e rf o r m a n ce c o m p a r i s on o f t h e t h r ee d i ff e r e n ti m p l e m e n t a ti on s i s g i v e n i n T a b l e 1 . I n t e rf ac i n g o f t h e a s yn c h r onou s ou t p u t s w it h t h e s yn c h r o n ou s e n v i r on m e n t i s don e u s i ng a n a dd iti on a l ( s yn c h r o nou s ) D - t yp e f li p -f l o p f o r t h e r e q u e s t s i gn a l a tt h e ou t pu t ( ‘r e q _b ’ i n F i gu r e 5 ) . U s i ng a t yp i ca l c l o c k fr e qu e n c y o f 2 0 M H z f o r t h e s yn c h r o n ou s c i r c u it w ill c o m b i n a ti on a ll o g i c ) i n s e r t e d i n t o t h e i n pu t r e qu e s t s i gn a l . r e s u lti n a v e r y l o w p r ob a b ilit y o f m e t a s t a b ilit y o f P = 10 - 55 A ti m i ng m a r g i n o f 30 % w a s a dd e d t o gu a r a n t ee r e li a b l e o r a n M T B F o f 3x 1 0 39 y ea r s [ 12 ] . F o r t y p i ca l a pp li ca ti on s op e r a ti on a f t e r l a y o u t . T h e n t h e t o p l e v e l d e s i gn w a s t h i s w ill no t r e qu i r e a n y a d d iti on a l m ea s u r e s t o r e du ce s yn t h e s i ze d s e p a r a t e l y a nd t h e n e tli s t s o f t h e i nd i v i du a l m e t a s t a b ilit y p r ob a b ilit y f u r t h e r . p i p e li n e s t a g e s w h e r e i n t e g r a t e d i n t o t h e t op - l e v e l n e tli s t . T h e l a you t w a s ca rr i e d ou t u s i ng t h e s t a nd a r d ce ll 4. D e s i g n - F l o w Iss u e s a pp r o a c h o f S ili c on E n s e m b l e w it h 8 0 % r o w u tili za ti on . P o s t l a you t p a r a s iti c p a r a m e t e r s w e r e e x t r ac t e d a n d a A ll v e r s i on s o f t h e C O R D I C p r o ce ss o r w e r e m od e l e d V e r il og n e tli s tt og e t h e r w it h t h e po s tl a you t S D F f il e w e r e i n VHD L a nd a r e f u ll y s yn t h e s i ze d . F o r s i m u l a ti on a n d e xpo r t e d . T h i s V e r il og n e tli s t w a s a g a i n s i m u l a t e d u s i ng f un c ti on a l v e r i f i ca ti on w e u s e d M od e l s i m f r o m M e n t o r t h e s a m e VHD L t e s t b e n c h t h a t w a s u s e d f o r t h e G r a ph i c s . S yn t h e s i s w a s ca rr i e d ou t w it h S y n op s y s ’ b e h a v i o r a l m od e l . T h i s s i m u l a ti on c o n f i r m e d t h e c o rr ec t D e s i gn A n a l y ze r a n d t h e l a yo u t w a s g e n e r a t e d u s i ng op e r a ti on a nd f o r m s t h e b a s i s f o r t h e l a t e n c y a nd S ili c on E n s e m b l e fr o m C a d e n ce . T h e d e s i gn w a s m a p p e d t h r ou g hpu t m ea s u r e m e n t s r e p o r t e d i n t h e f o ll o w i n g S ec ti on . t o ou r i n - h o u s e 0 . 2 5 m m S i G e : C B i C M O S t ec hno l ogy u s i ng t h e I H P d i g it a l d e s i g n k it . T h e no m i n a l s u pp l y vo lt a g e f o r c o r e ce ll s i s 2 . 5 V . F ou r m e t a l l a y e r s a r e 5. R e s u l t s a nd C o m p a r i s o n a v a il a b l e f o r i n t e r c o n n ec t . T h e C O R D I C p r o ce ss o r u tili ze s on l y t h e C M O S p a r t o f o u r B i C M O S t ec hno l ogy . F o r m ea s u r i ng t h e p e r f o r m a n ce o f t h e a s yn c h r o n ou s B o t h , f o r s yn t h e s i s a nd l a you t s o m e a tt r i bu t e s a nd c i r c u it s t h e v a r i ou s h a nd s h a k e s i gn a l s a r e g e n e r a t e d fr o m c on s t r a i n t s w e r e a dd e d t o s up p o r t t h e a s yn c h r o nou s t h e t e s t b e n c h u s i ng a n i d ea l d a t a s o u r ce a n d a n i d ea l d a t a i m p l e m e n t a ti on . A f t e r s y n t h e s i s t h e g a t e l e v e l V e r il og s i nk . T h e i n p u t d a t a i s s upp li e d i n t h e t e s t b e n c h fr o m a n e tli s t g e n e r a t e d by t h e D e s i gn A n a l y ze r w a s r e - s i m u l a t e d f il e . F o r t h e a s yn c h r o n ou s m o d e o f op e r a ti o n , d a t a i s b e i ng i n c l ud i ng t h e ‘ S t a nd a r d D e l a y F o r m a t ’ ( S D F ) f il e . T h e s upp li e d t o t h e e n tit y w it h t h e r i s i ng e dg e o f i n p u t r e q u e s t c o rr ec t ti m i ng b e h a v i o r o f t h e p r o ce ss o r i n b o t h t h e s i gn a l ‘r e q_ a _ t op ’ s h o w n i n F i g u r e 5 . W it h t h e d e l a y i n t h e r o t a ti on a n d v ec t o r i ng m od e w a s ob s e r v e d . h a nd s h a k e c i r c u it b e i n g i n s e r t e d i n t h e p a t h o f s i gn a l F o r d r i v i n g t h e l o ca l c l o c k s i gn a l s o f t h e i nd i v i d u a l ‘r e q_ a _ t op ’ , t h e ac k no w l e dg e s i gn a l ‘ ac k_ a _ t op ’ go e s h i g h s t a g e s w e f itt e d t h e c l o c k s i gn a l o f e v e r y p i p e li n e s t a g e a f t e r t h e c o m b i n a ti on a l l o g i c b l o c k f i n i s h e s it ’ s w it h a n a pp r op r i a t e c l o c k b u ff e r . T h i s bu f f e r w a s c o m pu t a ti on . T h e l o ca l c l o c k s i gn a l i n ea c h o f t h e s yn t h e s i ze d s e p a r a t e l y a nd p r o t ec t e d w it h t h e h e l p o f c o m pon e n t s i s c onn ec t e d t o s i gn a l ‘ ac k _ a ’ o f eac h ‘ don ’ t t ou c h ’ a tt r i bu t e s . r e s p ec ti v e h a nd s h a k e c i r c u it . H e n ce , w it h t h e r i s i ng T h e a r ea o f a t r a n s p a r e n t l a t c h u s e d i n t h e A S Y - t r a n s iti on o f ‘ a c k_ a ’ , t h e c o m p u t e d d a t a i s l a t c h e d t o t h e C O R D I C d e s i gn i s 118 m m 2 a nd t h e a r ea o f t h e D - t y p e f li p - d a t a r e g i s t e r s . T h e l a t e n c y f o r a s y n c h r onou s op e r a ti o n i s f l op s u s e d i n M I X - C O R D I C a nd S YN - C O R D I C i s m ea s u r e d a s t h e ti m e i n t e r v a l f r o m t h e r i s i ng e dg e o f i n p u t 180 m m 2 ( acc o r d i n g t o I H P ce ll li b r a r y ) . T h e l a t c h b a s e d s i gn a l ‘r e q_ a _ t op ’ t o t h e r i s i ng e dg e o f o u t pu t s i gn a l v e r s i on ca n t h e r e f o r e po t e n ti a ll y r e s u lt i n s m a ll e r s ili c on ‘r e q_ b _ t o p ’ . T h i s m ea s u r e m e n t i s ca rr i e d o u t w it h a n a r ea . T h e d e s i g n f l o w f o r d e s i g n ‘ A S Y - C O R D I C ’ i s e m p t y p i p e li n e a s a n i n iti a l s t a t e a nd h e n ce a ss u m e s d e s c r i b e d i n d e t a il b e l o w . I n p r i n c i p a l , t h e s a m e a p p r o ac h op e r a ti on i n t h e d a t a li m it e d r e g i o n a s d e f i n e d i n [ 1 3 ] . w a s u s e d f o r t h e M I X - C O R D I C c i r c u it . T h e ‘ no r m a l ’ T h e m a x i m u m t h r o ug h pu t i s m ea s u r e d a s t h e nu m b e r s yn c h r o n ou s i m p l e m e n t a ti on d o e s no t r e q u i r e a n y e x t r a o f d a t a s a m p l e s e m e r g i ng a tt h e ou t p u t w h e n t h e i npu ti s m ea s u r e s a nd i s t h e r e f o r e g e n e r a t e d u s i n g t h e ‘ s t a nd a r d ’ d r i v e n by a n i d ea l s ou r ce a nd t h e ou t p u ti s c onn ec t e d t o a n s yn t h e s i s f l o w w it h c l o c k - t r ee g e n e r a ti on du r i n g l a y o u t i d ea l d a t a s i nk . ph a s e . F o r t h e s yn c h r o n ou s d e s i gn , t h e l a t e n c y i s d e p e nd e n t T h e l a t c h e s w it h i n eac h p i p e li n e s t a g e a r e c o n t r o ll e d on t h e c l o c k fr e qu e n c y . T h e c o r e a r ea f o r a llt h r ee d e s i gn s w it h a s i gn a l ‘ lt ’ w h i c h ca u s e s t h e l a t c h t o b e t r a n s p a r e n t i s m ea s u r e d fr o m t h e l a y o u t a n d r e p o r t e d i n T a b l e 1 w h e n l o w a n d i n h o l d s t a t e w h e n h i gh . S i n ce t h e d a t a p a t h t og e t h e r w it h p o w e r d i ss i p a ti on , l a t e n c y a nd t h r o u gh p u t . i s i n t o t a l 50 b it w i d e , t h e ‘ lt ’ s i gn a l m u s t h a v e a r ea s on a b l e d r i v e s t r e ng t h . T h e r e f o r e a bu ff e r i s u s e d f o r eac h p i p e li n e s t a g e t o d r i v e s i gn a l ‘ lt ’ . T o k ee p t h e s ili c on a r ea a s s m a ll a s po ss i b l e , w e u s e d l a t c h e s w it h a n a s yn c h r o n ou s r e s e t s i gn a l . T h i s i s ac h i e v e d by i n s e r ti n g t h e S yn t h e s i ze r s p ec i f i c a tt r i bu t e ‘ a s yn c _ s e t _ r e s e t ’ i n t h e VHD L s ou r ce c od e . A f t e r s e p a r a t e l y s yn t h e s i z i ng ea c h o f t h e 20 p i p e li n e s t a g e s , t h e y w e r e c onn ec t e d w it h t h e i r r e s p ec ti v e h a nd s h a k e c i r c u it . E a c h h a n d s h a k e c i r c u it h a d a d e l a y e l e m e n t ( t u n e d t o t h e c r iti ca l p a t h o f t h e T a b l e 1 . P e r f o r m a n c c e o m p a r i s ono ft h r ee 2 ) bu r i e d l a y e r s h i e l d , 3 ) n o p r o t ec ti on , a nd 4 ) G ND r i ng C O RD I C i m p l e m e n t a t i on s on l y . A d d iti on a ll y t h r e e s ub s t r a t e c on t ac t s f o r d i r ec t m ea s u r e m e n t o f s ub s t r a t e no i s e a r e p l ac e d a t t op e nd , A S Y - M I X - C O R D I C S YN - m i dd l e a nd bo tt o m e nd o f t h e r i gh t e d g e r e s p ec ti v e l y . W e C O R D I C S yn c h . A s yn c h . C O R D I C hop e t h a tt h i s d e s i g n w ill d e li v e r v a l u a b l e i n f o r m a ti on on m od e m od e t h e e ff i c i e n c y o f d i f f e r e n t m ea s u r e s f o r p r o t ec ti o n fr o m C o r e a r ea 1 . 8 2 . 6 2 . 3 s ub s t r a t e no i s e , bo t h f o r s y n c h r o nou s a n d a s yn c h r o n ou s ( i n mm 2 ) op e r a ti ono f t h e C O R D I C p r o ce ss o r . P o w e r ( 16 ) ( 9 . 4 ) ( 7 . 2 ) ( 9 . 8 ) ( i n m W ) L a t e n c y 370 444 320 500 C O R D I C ( i n n s ) c o r e T h r o u gh - 30 45 45 40 pu t ( M S / s ) s u b s t r a t e I t i s s ho w n i n T a b l e 1 t h a t t h e M I X - C O R D I C d e s i gn c o n t a c t s r e qu i r e s on l y 13 % m o r e s ili c on a r ea t h a n t h e S YN - C O R D I C . A s ub s t a n ti a l a dv a n t a g e i s t h e r e du c e d l a t e n c y . I n p a r ti c u l a r f o r t r a n s m itti ng ac k no w l e dg e m e n t fr a m e s w h i c h h a v e t o b e g e n e r a t e d a t a f i x e d ti m e i n t e r v a l o f 1 6 m s a f t e r r ece p ti o n o f a fr a m e , a ny r e du c ti o n i n l a t e n c y i n t h e d a t a p a t h i s w e l c o m e . T h e d a t a t h r ou g hpu t o f M I X - a n a l o g C O R D I C a nd S YN - C O R D I C a r e s i m il a r . T h e d i ff e r e n ce o f o s c i l l a t o r s 45 M S / s v e r s u s 40 M s / s i s p r ob a b l y du e t o t h e p a r ti c u l a r l a you t . F u r t h e r m o r e , t h e l e v e l o f m a n u a li n t e r ac ti on f o r t h e M I X - C O R D I C d e s i gn w a s h i gh e r , w it h b u ff e r s b e i ng e xp li c itl y i n s e r t e d i n t o e v e r py i p e li n e s t a g e . C i r c u it A S Y - C O R D I C h a ss i gn i f i ca n tl y s m a ll e r s ili c on F i gu r e 6 . L ay ou t o f c i r c u i t M I X - C O RD I C w i t h a r ea i . e . 22 % l e ss t h a n S YN - C O R D I C . T h i s i s p a r tl y du e t o a n a l og t es t c i r c u i t a s t r i gh t s i d e t h e s m a ll e r s i ze o f t r a n s p a r e n t l a t c h e s c o m p a r e d t o e d g e t r i gg e r e d f li p -f l o p s . F u r t h e r m o r e , i n c on t r a s t t o S YN - C O R D I C a nd M I X - C O R D I C , t h e A S Y - C O R D I C d e s i gn 6. C o n c l u s i o n s a nd F u t u re Wo r k do e s no t r e qu i r e a ny c l o c k t r ee . T h e u s e o f l o ca l i n t e r c onn ec t on l y , r e s u lt s i n c on s i d e r a b l e s a v i n g s i n s ili c on A p i p e li n e d C O R D I C p r o ce ss o r w h i c h ca n o p e r a t e b o t h a r ea . T h e h i gh e r l a t e n c y o f c i r c u it A S Y - C O R D I C i s du e t o s yn c h r o n ou s l y a s w e ll a s a s yn c h r o nou s l y h a s b ee n t h e m o r e c o m p l e x h a nd s h a k e c i r c u it f o r t h i s d e s i gn . T h e d e s i gn e d i n VHD L a n d i m p l e m e n t e d u s i ng a 0 . 2 5 m m t r a n s p a r e n t p h a s e o f t h e l a t c h e s r e qu i r e s c o u p li ng o f S i G e : C B i C M O S p r o ce ss . W i t h i n a ‘ s o f t w a r e d e f i n e d c on s ec u ti v e s t a g e s t h a ti s r e f l ec t e d by a dd iti on a l d e l a y s . r a d i o ’ f r a m e w o r k , t h e op p o r t un it y t o op e r a t e k e y h a r d w a r e T h e po w e r d i ss i p a ti on f i gu r e s g i v e n i n T a b l e 1 w e r e c o m pon e n t s e it h e r i n s yn c h r o n ou s o r a s yn c h r o n ou s m od e d e r i v e d f r o m t h e s yn t h e s i s t oo l . F r o m p r e v i ou s e xp e r i e n ce ca n o ff e r a dd iti o n a l fr ee d o m f o r t h e s y s t e m d e v e l op e r . t h e s e f i gu r e s a r e v e r y u n r e li a b l e . T h e d i s ti n c tl y h i gh e r U s i ng t h i s f ea t u r e , a m o r e o p ti m a l c o m p r o m i s e b e t w ee n po w e r d i ss i p a ti on o f A S Y - C O R D I C m a y r e s u lt fr o m t h e po w e r- d i ss i p a ti on , c r o ss t a l k , t h r o u gh p u t , l a t e n c y a nd S ynop s y s s o f t w a r e f a l s e l y e s ti m a ti ng h i g h g lit c h i n g ( s e l f -) t e s t a b ilit y ca n b e f o und . A s a n e x a m p l e , t o r e du ce ac ti v it y i n t h e do w n s t r ea m c i r c u it s du r i ng t h e t r a n s p a r e n t c r o ss t a l k , t h e c i r c u it ca n b e s w it c h e d i n t o a s yn c h r o n ou s ph a s e o f t h e l a t c h e s . C u r r e n tl y w o r k i s u n d e r w a y t o m od e w h e n t h e r ece i v e s i gn a l l e v e l i s v e r y l o w . F o r g e n e r a t e m o r e acc u r a t e f i gu r e s u s i n g t h e p o w e r s i m u l a t o r r ea s on a b l e s i gn a l s t r e ng t h a nd c on ti n u ou s op e r a ti on t h e ‘ P o w e r M ill ’ . m o r e p o w e r e ff i c i e n t s y n c h r o n ou s m od e ca n b e c h o s e n . A n T h e l a you t o f t h e M I X - C O R D I C p r o ce ss o r , f itt e d w it h a dd iti on a l a pp li ca ti o n o f ou r M I X - C O R D I C c i r c u it i s t o a n a l og t e s t c i r c u it s f o r c r o ss t a l k i nv e s ti g a ti on , i ss ho w n i n s e r v e a s a n v e h i c l e f o r d e t a il e d i nv e s ti g a ti ng o f t h e F i gu r e 6 . I n o r d e r t o p r e v e n t d i r ec t c oup li n g f r o m i n p u t i n t e rf e r e n ce c a u s e d by s y n c h r o n o u s a nd a s yn c h r o nou s s i gn a l s i n t o t h e a n a l og t e s t c i r c u it s a C - s h a p e d p l ace m e n t d i g it a l c i r c u it s on S i G e : C b i po l a r a nd C M O S a n a l og o f t h e d i g it a l p a d s w a s und e r t a k e n . F o u r i d e n ti ca l c i r c u it s . o s c ill a t o r s a r e p l ace d a tt h e ea s t s i d e o f t h i s l a you t , eac h F u r t h e r w o r k w ill f o c u s o n e x t e n d i ng ou r ce ll li b r a r y f itt e d w it h a d i ff e r e n t s t r u c t u r e f o r p r o t ec ti on fr o m a nd d e s i gn k it by a nu m b e r o f ce ll s c r u c i a l f o r s ub s t r a t e no i s e . F r o m t o p t o bo t t o m t h e d e p l oy e d a s yn c h r o n ou s d e s i gn . S u c h ce ll s a r e , f o r i n s t a n ce , v a r i ou s p r o t ec ti on s t r u c t u r e s a r e : 1 ) GND r i n g a n d n - w e ll r i n g , C - e l e m e n t s , c o m p l e t e h a nd s h a k e c i r c u it s a nd l o w - po w e r t un a b l e d e l a y e l e m e n t s . T h e ce ll s w ill b e d e s i gn e d on t r a n s i s t o r l e v e l , i n c l ud e d i n t o t h e ce ll li b r a r y a n d m a d e [ 5 ] D . S . C o c h r a n , “ A l go r i t h m s a n d acc u r ac y i n t h e H P – 35 ” , a v a il a b l e a s c o m p o n e n t s i n VHD L a nd V e r il o g . H e w l e tt P ac k a r d J ., pp . 1 0 – 11 , J u n e 1 9 7 2 . T h e M I X - C O R D I C d e s i gn r e po r t e d h e r e , i n c l u d i ng t h e a n a l og t e s t c i r c u it s , h a s b ee n t a p e d o u t f o r f a b r i ca ti o n o n [ 6 ] A . M . D e s p a i n , “ V e r y f a s t F ou r i e r t r a n s f o r m a l g o r i t h m s f o r i m p l e m e n t a ti o n ” , I E E E T r a n s . C o m p u t . , v o l . C – 28 , ou r i n - hou s e 0 . 2 5 m m S i G e : C B i C M O S p r o ce ss i n no . 5 , p p . 3 3 3 3– 4 1 , M a 1y 9 79 . D ece m b e r 2 0 01 . F i r s t r e s u lt s , i n c l ud i n g m ea s u r e m e n t s on i n t e rf e r e n ce o f t h e a n a l og c i r c u it s f o r s yn c h r o nou s a n d a s yn c h r o n ou s o p e r a ti on o f t h e M I X - C O R D I C d e s i gn w ill [ 7 ] D . T . L eea n d M . M o r f , “ G e n e r a li ze d C O R D I C f o r d i g it a l b e a v a il a b l e b y t h e m i d d l e o f M a r c h 2 002 . s i gn a l p r o ce ss i ng ” , P r o c . I C A SSP , v o l . 3 , p p . 1 7 4 8 – 17 5 1 , M a 1y 9 82 .

A c kn o w l e d g e m e n t s [ 8 ] M . C . M a nd a l , A . S . D h a r a n d S . B a n e r j ee , “ M u l ti p l i e r l e ss a rr a y a r c h it ec t u r e f o r c o m pu t i n g d i s c r e t e c o s i n e W e w ou l d li k e t o ac k n o w l e dg e t h e s upp o r t f r o m U l r i c h t r a n s f o r m ” , C o m p u t e r s E l ec . E ng . , v o l . 2 1 , n o . 1 , p p . 1 3 – J a gdho l d f o r g e n e r a ti n g t h e d i g it a ll a y ou t . 19 , 1 9 9 5 . F u r t h e r m o r e , w e a r e g r a t e f u l o f t h e s u p po r t fr o m W o l f g a ng W i nk l e r f o r d e s i g n a nd l a you t o f t h e a n a l ogu e [ 9 ] A . S . D h a r a nd S . B a n e r j ee , “ A n a rr a y a r c h it ec t u r e f o r f a s t t e s t c i r c u it s f o r t h e du a l - m od e C O R D I C i m p l e m e n t a ti on . c o m pu t a ti o n o f d i s c r e t e H a r tl e y t r a n s f o r m ” , I EE E T r a n s . C i r c u it s a n d S y s t ., vo l . 3 8 , n o . 9 , p p . 1 0 9 5 1– 0 98 , 1 9 9 1 . R e f e re n c e s [ 10 ] I . S u t h e r l a n d , “ M i c r o p i p e li n e s ” , C o mm u n i c a t i o n s o f t h e A C M , 32 ( 6 ) , pp . 7 20 - 7 3 8 , J un e 1 98 9 . [ 1 ] S t a nd a r d ET S I D T S / BR AN 0 3 0 0 0 3 - 1 , “ B r o a d b a n d R a d i o A cce ss N e t w o r k s ( BR AN ) ; H I P E R L AN T yp e 2 [ 11 ] P . D a y , J . V . W o o d s , “ I n v e s ti g a ti o n i n t o M i c r op i p e li n e F un c t i on a l S p ec i f i ca ti o n s . P a r t 1 – P hy s i ca l ( P HY ) l a y e r ” ; L a t c h D e s i gn S t y l e s ” , I E E E T r a n s . O n V L S I S y s t e m s , 3 J un e 1 9 9 9 . ( 2 ) , pp . 2 64 - 2 7 2 , 1 9 95 .

[ 2 ] S t a nd a r d I EEE P 8 02 . 11 a / D 7 . 0 , “ P a r t 1 1 : W i r e l e ss L AN [ 12 ] J . N . S e i z o v i c , “ P i p e l i n e S yn c h r o n i s a ti on ” , P r o c . M e d i u m A cce ss C on t r o l ( M A C ) a nd P h y s i ca l L a y e r I n t e r n a ti o n a l S y m po s i u m o n A d v a n ce d R e s ea r c h i n ( P HY ) s p ec i f i ca ti on s : H i gh S p ee d P h y s i ca l L a y e r i n t h e 5 A s yn c h r o n o u s C i r c u i t s a n d S y s t e m s , pp . 8 7 - 9 6 , N o v e m b e r GH z B a nd ” ; J u l 1y 9 9 9 . 19 9 4 .

[ 3 ] J . M . C a s a lt a , X . A r o g on e s a n d A . R ub i o , “ S ub s t r a t e [ 13 ] T . E . W illi a m s , “ P e rf o r m a n ce o f I t e r a t i v e C o m p u t a ti o n i n C ou p li n g e v a l u a ti o n i n B i C M O S T e c h n o l o gy ” , I EEE S e l f- T i m e d R i n g s ” J ou r n a l o f V L S I S i g n a l P r o ce ss i ng , J ou r n a l o f S o l i d S t a t e C i r c u it s , vo l . 3 2 , n o . 4 , p p . 5 9 8 – ( 7 ) , pp . 17 - 3 1 , 1 9 9 4 . 60 3 , A p r il 1 9 9 7 .

[ 4 ] J . B u c k a n d E . A . L ee , “ T h e t o k e n f l o w m o d e l ” , D a t a F l o w W o r k s h o p , H a m ilt o n I s l a n d , A u s t r a li a , p p . 2 6 7 – 29 0 , M a y 1 9 9 2 .