Thiết kế các modul trong FPGA

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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Modulation and Demodulation
Techniques for FPGAs
Ray Andraka P.E., president,
A
ndraka
C
onsulting
G
roup,
I
nc.
the
16 Arcadia Drive
•
North Kingstown, RI 02852-1666
•
USA
401/884-7930 FAX 401/884-7950
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
You can do Math
in them things???
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Overview
• Introduction
• Digital demodulation for FPGAs
• Filtering in FPGAs
• Comparison to other technologies

•Summary
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Digital Communications
• Historically only base-band processing
• High sample rates for down-converters
• Down-conversion traditionally analog
• Digital down-conversion with specialty chips
• FPGAs can compete
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Why Digital?
• Frequency agility
• Repeatability
• Cost
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Digital Challenges
• A to D converter
• High sample rates
• Arithmetic intensive
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
e
-
j
ω
c
t
=

cos(
ω
c
t)-
j
sin(
ω
c
t
)
Decimate
by R
Video
Bandpass
Filter
2
f
(t) cos(
ω
c
t)
Phase
Split
ω
c
-ω
c
-ω
c
ω

c
-2ω
c
00 0
√2f(t)e
j
ω
ct
Conventional Demodulator
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
-
j
sin(
ω
c
t)
cos (
ω
c
t)
Lowpass Filter
√
2
f
(t)
Lowpass Filter
√
2
f

(t)
I
Q
Decimate
by R
ω
c
-ω
c
-2ω
c
00
-2ω
c
0
e
-j
ω
ct
Re-arranged Demodulator
*
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Complex Mixer
Re[A
k
]
Im[A
k
]

Complex
Baseband
Signal
(Passband for
Demodulator)
Complex
Passband
Signal
(Baseband for
Demodulator)
Numerically
Controlled
Oscillator
sin(ω
c
t) cos(ω
c
t)
Re[S
k
]
Im[S
k
]
ω
c
Phase or
frequency
input
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Frequency
Synthesizer
Phase Angle
to Wave
Shape
Conversion
Waveform
Out
Phase Angle
Modulation
Waveform Synthesis (NCOs)
• Various Methods
– Look up table (LUT)
– Partial products
– Interpolation
– Algorithmic
• Most methods use a
frequency synthesizer
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
∆ Phase
(phase increment)
Sample Clock
Phase Accumulator Design
• “Direct Digital Synthesis”
• Essentially integrates phase increment
• Increment value may be modulated
– Frequency and PSK modulation
• Binary Angular Measure (BAMs)

– Most significant bit = π
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Addr
Data
Phase Angle
(BAMs)
Waveform
Out
Read Only
Memory
Waveform Synthesis by LUT
• Phase resolution limited
• Arbitrary waveshapes
• Sampled waveshape must be
band-limited
• Complex requires 2 lookups
• f
osc
= f
s
/4 special case
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Using Symmetry to Extend
LUT Phase Resolution
00NN 00NN
0N0N 0N0N
++
00 01 10 11

++
Q1 Sin
LUT
Q1 Sin
LUT
Q
MSB
MSB-1
remaining
bits
I
Phase MSB’s
Count
sequence
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Waveform Synthesizer plus Multiplier
• Obvious Solution
• Separate into functional
parts
• Treat each part
independently
Numerically
Controlled Oscillator
sin(ω
c
t)
cos
(ω
c

t)
Re[S
k
]
Im[S
k
]
ω
c
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
a Cos(
φ
) phase
signal
000 001 010 011 100 101 110 111
-4 -4 -2.8 0 2.8 -4 2.8 0 -2.8
-3 -3 -2.1 0 2.1 3 2.1 0 -2.1
-2 -2 -1.4 0 1.4 2 1.4 0 -1.4
-1 -1 -0.7 0 0.7 1 0.7 0 -0.7
0 00000000
1 1 0.7 0 -0.7 -1 -0.7 0 0.7
2 2 1.4 0 -1.4 -2 -1.4 0 1.4
3 3 2.1 0 -2.1 -3 -2.1 0 2.1
Look Up Table Modulator
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
6-LUT
A[1:0]
6-LUT

A[3:2]
6-LUT
A[5:4]
6-LUT
A[7:6]
<<2
<<2
<<4
Phase[3:0]
n+8
Partial Products Modulator
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
6-LUT
I[0]
6-LUT
I[1]
6-LUT
I[2]
6-LUT
I[3]
<<1
<<1
<<2
Phase[3:0]
n+8
Q[1]
Q[2]
Q[3]
Q[0]

Distributed Arithmetic Modulator
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
n+8
<<1
serial
inputs
6-LUT
Phase[3:0]
Q[3], Q[2], Q[1], Q[0]
I[3], I[2], I[1], I[0]
Distributed Arithmetic Modulator
(Serial Form)
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
CORDIC
Rotator
I
in
Q
in
Phase
Accumulator
I
out
Q
out
Signal In
Modulated
Signal Out

CORDIC Modulator
I
out
= I
in
cosφ - Q
in
sinφ
Q
out
= Q
in
* cosφ + I
in
sinφ
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
CORDIC Algorithm Explained
• Coordinate rotation in a plane:
x’ = xcos(φ) - ysin(φ)
y’ = ycos(φ) + xsin(φ)
• Rearranges to:
x’ = cos(φ) [x - ytan(φ)]
y’ = cos(φ) [y + xtan(φ)]
cosφ
sinφ
φ
I
Q
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
>>3
x
0
y
0
z
0
x
n
y
n
z
n
±± ±
>>3 const
sign
>>2
±± ±
>>2 const
sign
>>1
±± ±
>>1 const
sign
>>0
±± ±
>>0 const
sign
>>4

±± ±
>>4 const
sign
CORDIC Structure
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Digital Filtering
y[k]=Σx[k-i]•C
i
Z
-1
Z
-1
C
0
C
1
C
i-2
C
i-1
Z
-1
x[k]
• Many Constant
Multipliers
• Delay Queues
• Products Summed
• Advantages
– No tolerance drift

– Low cost
– precise characteristic
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Distributed Arithmetic Filter
Shift Reg
Shift Reg
Shift Reg
Shift Reg
C
0
C
1
C
2
C
3
<<1
Scaling Accum
Addr Data
0000 0
0001 C
0
0010 C
1
0011 C
0
+ C
1
1110 C

1
+ C
2
+ C
3
1111 C
0
+ C
1
+ C
2
+ C
3
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Take Advantage of Symmetry
SREG
X[k]
SREG
SREG
• Real filters are
symmetric
• Add bits with
like coef’s before
filtering
• Uses Serial
Adders
• Halves taps
SREG
SREG

SREG
SREG
x[k]+x[k-6]
x[k-1]+x[k-5]
x[k-2]+x[k-4]
x[k-3]
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copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved
Decimating FIR Filters
• Low pass filter then discard samples
• Keep only every 4th output
Y
n+0
=a
k
C
0
+a
k-1
C
1
+a
k-2
C
2
+ a
k-3
C
3
+a

k-4
C
4
+…
Y
n+4
= a
k+4
C
0
+a
k+3
C
1
+a
k+2
C
2
+a
k+1
C
3
+a
k
C
4
+…
Y
n+8
=a

k+8
C
0
+a
k+7
C
1
+a
k+6
C
2
+a
k+5
C
3
+a
k + 4
C
4
+…
• reduces to n parallel filters fed every nth sample
• sub-filter results summed to get result