Modulation and Demodulation Techniques for FPGAs

Modulation and Demodulation Techniques for FPGAs Ray Andraka P.E., president, Andraka Consulting Group, Inc. the 16 Arcadia Drive • North Kingstow...
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Modulation and Demodulation Techniques for FPGAs

Ray Andraka P.E., president,

Andraka Consulting Group, Inc.

the

16 Arcadia Drive • North Kingstown, RI 02852-1666 • USA 401/884-7930 FAX 401/884-7950

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

1

You can do Math in them things???

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

2

Overview • Introduction • Digital demodulation for FPGAs • Filtering in FPGAs • Comparison to other technologies • Summary

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

3

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

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

4

Why Digital? • Frequency agility • Repeatability • Cost

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

5

Digital Challenges • A to D converter • High sample rates • Arithmetic intensive

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

6

Conventional Demodulator √2f(t)ejωct Video Bandpass Filter 2f(t) cos(ωct)

-ωc 0

ωc

-jωct

e

Decimate by R

Phase Split

-ωc 0

=cos(ωct)-jsin(ωct)

ωc

-2ωc

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

0 7

Re-arranged Demodulator cos (ωct)

*

e-jωct

Lowpass Filter √2 f(t)

Decimate by R

I

Lowpass Filter √2 f(t)

Q

-jsin(ωct)

-ωc 0

ωc

-2ωc

0

-2ωc

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

0 8

Complex Mixer Complex Baseband Signal (Passband for Demodulator) Phase or frequency input

Re[Sk]

Re[Ak]

Im[Sk]

Im[Ak]

sin(ωct) ωc

cos(ωct)

Complex Passband Signal (Baseband for Demodulator)

Numerically Controlled Oscillator

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

9

Waveform Synthesis (NCOs) • Various Methods – – – –

Look up table (LUT) Partial products Interpolation Algorithmic

• Most methods use a frequency synthesizer

Phase Angle to Wave Shape Conversion

Waveform Out

Frequency Synthesizer Phase Angle Modulation

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

10

Phase Accumulator Design Sample Clock

• “Direct Digital Synthesis” • Essentially integrates phase increment • Increment value may be modulated – Frequency and PSK modulation

• Binary Angular Measure (BAMs) – Most significant bit = π

∆ Phase (phase increment)

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

11

Waveform Synthesis by LUT • Phase resolution limited • Arbitrary waveshapes • Sampled waveshape must be band-limited • Complex requires 2 lookups • fosc= fs /4 special case

Read Only Memory Data

Waveform Out

Addr

Phase Angle (BAMs) copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

12

Using Symmetry to Extend LUT Phase Resolution remaining bits

-

+ +

+ +

-

-

Phase MSB’s 00 01 10 11 N 0 0 N N 0 0 N Count sequence 0 N N 0 0 N N 0

Q1 Sin LUT Q1 Sin LUT

I

Q

MSB

MSB-1

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

13

Waveform Synthesizer plus Multiplier • Obvious Solution • Separate into functional parts

Re[Sk] Im[Sk]

• Treat each part independently

sin(ωct) ωc

cos(ωct)

Numerically Controlled Oscillator

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

14

Look Up Table Modulator a Cos(φ) signal

-4 -3 -2 -1 0 1 2 3

000 -4 -3 -2 -1 0 1 2 3

001 -2.8 -2.1 -1.4 -0.7 0 0.7 1.4 2.1

010 0 0 0 0 0 0 0 0

phase 011 100 2.8 -4 2.1 3 1.4 2 0.7 1 0 0 -0.7 -1 -1.4 -2 -2.1 -3

101 2.8 2.1 1.4 0.7 0 -0.7 -1.4 -2.1

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

110 0 0 0 0 0 0 0 0

111 -2.8 -2.1 -1.4 -0.7 0 0.7 1.4 2.1 15

Partial Products Modulator A[1:0] A[3:2] A[5:4] A[7:6]

n+8

6-LUT 6-LUT

4

±

const

sign ±

yn

const

sign ±

±

const

sign

>>2

±

>>4

±

±

±

const

sign ±

±

>>2

z0

± zn

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

21

Digital Filtering • Many Constant Multipliers • Delay Queues • Products Summed • Advantages – No tolerance drift – Low cost – precise characteristic

x[k] C0

Z-1

Z-1

Z-1

C1

Ci-2

Ci-1

y[k]=Σx[k-i]•Ci

copyright  1998,1999,2000 Andraka Consulting Group, Inc. All Rights reserved

22

Distributed Arithmetic Filter C0

Scaling Accum

Shift Reg

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