Specification of APERTIF Polyphase Filter Bank in C aSH Rinse Wester - - PowerPoint PPT Presentation
Specification of APERTIF Polyphase Filter Bank in C aSH Rinse Wester a , Dimitrios Sarakiotis a , Eric Kooistra b , Jan Kuper a University of Twente, Enschede ASTRON, Dwingelo August 27, 2012 1 Monday, August 27, 12 Contents
August 27, 2012
Rinse Westera, Dimitrios Sarakiotisa, Eric Kooistrab, Jan Kupera University of Twente, Enschede ASTRON, Dwingelo
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✤ Introduction ✤ Background ✤ Describing the Filter bank using CλaSH ✤ Results ✤ Conclusions & Future Work
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✤ What is C흀aSH? ✤ Functional Language and Compiler for Concurrent Digital
Hardware Design
✤ Motivation? ✤ Testing C흀aSH on real life complex application ✤ Why APERTIF Polyphase filter bank? ✤ Strict specification on Throughput, Area and clock frequency
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✤ CλaSH ✤ A functional language and compiler for digital hardware design ✤ On the lowest level, everything is a Mealy machine f(s,i) = (s’,o) ✤ A CλaSH description is purely structural i.e. all operations are
performed in a single clock cycle
✤ Simulation is cycle accurate
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+
a
*
b
s' s
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fir cs (State us) inp = (State us0, out) where us0 = inp + us ws = vzipWith (⇤) us cs
+ *
in
+ * + *
cN-1 c0 c1
u0 u1 uN-1 w0 w1 wN-1
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✤ APERTIF Polyphase Filter bank ✤ Increasing field of view of Westerbork telescope using small array ✤ Each antenna in the array requires a polyphase filter bank ✤ Goals: Fclk = 200 MHz and throughput = 800 MS/s
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APERTIF project
k Monday, August 27, 12
✤ APERTIF Polyphase
Filter bank
✤ Polyphase FIR filter ✤ FFT
*
in
+ * + *
c(N-1)M c0 cM
↓M
* + * + *
c(N-1)M+1 c1 cM+1
↓M
* + * + *
cNM-1 cM-1 c2M-1
↓M M = 1024 N = 16 M-point FFT M = 1024
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✤ Design method ✤ Polyphase filter ✤ FFT pipeline
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✤ Design whole Architecture first in plain Haskell ✤ Perform small modification such that the code is accepted by C흀aSH ✤ Lists are replaced by vectors: lists with fixed length ✤ Fixed point representation for numbers ✤ A clear division between structure and low level hardware details
Design method
Functional description
Mathematics Haskell C훌aSH Hardware
Simulation/behavioral verification
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✤ A set of FIR filters
sequentially activated
✤ Parallelization of P=4
needed Polyphase Filter
FIR0 cntr inp
FIR1 FIRM-1 FIRcomb Coefficients States inp
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✤ A set of FIR filters
sequentially activated
✤ Parallelization of P=4
needed Polyphase Filter
FIR0 cntr inp
FIR1 FIRM-1 FIRcomb Coefficients States inp
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Monday, August 27, 12
✤ A set of FIR filters
sequentially activated
✤ Parallelization of P=4
needed Polyphase Filter
FIR0 cntr inp
FIR1 FIRM-1 FIRcomb Coefficients States inp
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Parallel Polyphase Filter
cntr FIRcomb Coefficients States inp0
cntr FIRcomb Coefficients States inp1
cntr FIRcomb Coefficients States inp2
cntr FIRcomb Coefficients States inp3
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fir :: [Double ] ! (State [Double ]) ! Double ! (State [Double ], Double) fir cs (State us) inp = (State us , out) where us = inp + us ws = zipWith (⇤) uscs
FIR filter: Haskell → CλaSH
13 + *
in
+ * + *
cN-1 c0 c1
u0 u1 uN-1 w0 w1 wN-1 Monday, August 27, 12
fir :: (Vector D16 S) ! (State (Vector D16 S)) ! S ! (State (Vector D16 S), S) fir cs (State us) inp = (State us,
where us = inp + us ws = vzipWith ‘fpmult‘ uscs
fir :: [Double ] ! (State [Double ]) ! Double ! (State [Double ], Double) fir cs (State us) inp = (State us , out) where us = inp + us ws = zipWith (⇤) uscs
FIR filter: Haskell → CλaSH
13 + *
in
+ * + *
cN-1 c0 c1
u0 u1 uN-1 w0 w1 wN-1 Monday, August 27, 12
fir :: (Vector D16 S) ! (State (Vector D16 S)) ! S ! (State (Vector D16 S), S) fir cs (State us) inp = (State us,
where us = inp + us ws = vzipWith ‘fpmult‘ uscs
fir :: [Double ] ! (State [Double ]) ! Double ! (State [Double ], Double) fir cs (State us) inp = (State us , out) where us = inp + us ws = zipWith (⇤) uscs
FIR filter: Haskell → CλaSH
13 + *
in
+ * + *
cN-1 c0 c1
u0 u1 uN-1 w0 w1 wN-1 Monday, August 27, 12
fir :: (Vector D16 S) ! (State (Vector D16 S)) ! S ! (State (Vector D16 S), S) fir cs (State us) inp = (State us,
where us = inp + us ws = vzipWith ‘fpmult‘ uscs
fir :: [Double ] ! (State [Double ]) ! Double ! (State [Double ], Double) fir cs (State us) inp = (State us , out) where us = inp + us ws = zipWith (⇤) uscs
FIR filter: Haskell → CλaSH
13 + *
in
+ * + *
cN-1 c0 c1
u0 u1 uN-1 w0 w1 wN-1 Monday, August 27, 12
FFT pipeline
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inp
*
8 BF2I 4 BF2II ws
*
2 BF2I 1 BF2II ws Monday, August 27, 12
✤ FFT is implemented using pipeline ✤ Two types of butterflies and Complex multiplier
FFT pipeline
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inp
*
8 BF2I 4 BF2II ws
*
2 BF2I 1 BF2II ws Monday, August 27, 12
FFT pipeline
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bf2i (cntr, lst) inp = ((cntr 0, lst0), out) where n = length lst cntr 0 = (cntr + 1) ‘mod‘ n lst0 = lstin + lst (out, lstin) = if cntr > n then (lstout + inp, lstout inp) else (lstout , inp ) lstout = last lst
lst
+
lstin lstout inp
inp
*
8 BF2I 4 BF2II ws
*
2 BF2I 1 BF2II ws Monday, August 27, 12
FFT pipeline
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cmult ws cntr inp = (cntr 0, out) where n = length ws cntr 0 = (cntr + 1) ‘mod‘ n w = ws ! cntr
= inp ⇤ w
inp
*
8 BF2I 4 BF2II ws
*
2 BF2I 1 BF2II ws Monday, August 27, 12
FFT pipeline
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fftbb ws (bf1state, bf2state, cmstate) inp = ((bf1state0, bf2state0, cmstate0), out) where (bf1state0, a) = bf2i bf1state inp (bf2state0, b) = bf2ii bf2state a (cmstate0, out) = cmult ws cmstate b
inp
*
8 BF2I 4 BF2II ws
*
2 BF2I 1 BF2II ws Monday, August 27, 12
FFT pipeline
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fftchain (ws1, ws2, ...) (bb1state, bb2state, ...) inp = ((bb1state0, bb2state0, ...), out) where (bb1state0, d1) = fftbb ws1 bb1state inp (bb2state0, d2) = fftbb ws2 bb2state d1
inp
*
8 BF2I 4 BF2II ws
*
2 BF2I 1 BF2II ws Monday, August 27, 12
FFT BF2I: Haskell → CλaSH
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bf2i (cntr, lst) inp = ((cntr 0, lst0), out) where n = length lst cntr 0 = (cntr + 1) ‘mod‘ n lst0 = lstin + lst (out, lstin) = if cntr > n then (lstout + inp, lstout inp) else (lstout , inp ) lstout = last lst
bf2i clash (cntr, lst) inp = ((cntr 0, lst0), out) where n = vlength lst cntr 0 = cntr + 1 lst0 = lstin + lst (out, lstin) = if cntr > n then (lstout + inp, lstout inp) else (lstout, inp) lstout = vlast lst
Monday, August 27, 12
FFT BF2I: Haskell → CλaSH
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bf2i (cntr, lst) inp = ((cntr 0, lst0), out) where n = length lst cntr 0 = (cntr + 1) ‘mod‘ n lst0 = lstin + lst (out, lstin) = if cntr > n then (lstout + inp, lstout inp) else (lstout , inp ) lstout = last lst
bf2i clash (cntr, lst) inp = ((cntr 0, lst0), out) where n = vlength lst cntr 0 = cntr + 1 lst0 = lstin + lst (out, lstin) = if cntr > n then (lstout + inp, lstout inp) else (lstout, inp) lstout = vlast lst
Monday, August 27, 12
FFT BF2I: Haskell → CλaSH
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bf2i (cntr, lst) inp = ((cntr 0, lst0), out) where n = length lst cntr 0 = (cntr + 1) ‘mod‘ n lst0 = lstin + lst (out, lstin) = if cntr > n then (lstout + inp, lstout inp) else (lstout , inp ) lstout = last lst
bf2i clash (cntr, lst) inp = ((cntr 0, lst0), out) where n = vlength lst cntr 0 = cntr + 1 lst0 = lstin + lst (out, lstin) = if cntr > n then (lstout + inp, lstout inp) else (lstout, inp) lstout = vlast lst
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✤ Polyphase filter bank has been fully implemented using C흀aSH ✤ Simulation shows that the PFB operates correctly ✤ Synthesis revealed some limitations of the current compiler
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Polyphase filter(256 elements) 1k-points FFT Logic utilization 91% 6% blockRAMS DSP blocks 128 70
114 MHz 195 MHz
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✤ The complete Polyphase Filter Bank has been implemented ✤ Haskell code needs only small modifications before it is accepted by
the C흀aSH compiler
✤ The description is purely parallel (structural) and cycle accurate ✤ Shortcomings of C흀aSH compiler ✤ Large coefficient vectors not supported ✤ BlockRAM not supported, limiting Fclk
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✤ Develop area vs time time trade off based on functional description ✤ Improvements for the C흀aSH compiler ✤ Support for blockRAMs on FPGA ✤ Support for memory initialization files for coefficient vectors
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