Gallagher 1 P188/MAPLD2004

Accelerating DSP Algorithms Using FPGAs

Sean Gallagher

DSP Specialist

Xilinx Inc

Gallagher 2 P188/MAPLD2004

Why DSP in FPGAs

• Availability of fast analog-to-digital converters (ADCs) – Enables digital methods for functions

traditionally done in RF components

• Massive parallel processing – FPGAs may have several hundred embedded

multipliers on-chip– One FPGA can replace many DSP Processors

Gallagher 3 P188/MAPLD2004

Architectural Considerations

• FPGA architectures are vendor specific– Unlike ASICS, no two are alike

• FPGA vendors develop distinct competencies– In device architecture design

– In intellectual property (dsp functions, bus controllers, etc)

– In design tool flows

• Vendor independent HDL can be written but this usually achieves mediocre results in clock speed and design size instantiation

Gallagher 4 P188/MAPLD2004

FPGAs Are Massive Parallel Computing Machines

LPF

Multi ChannelFilter

80MHz Samples

ch1

ch2

ch3

ch4

LPF

LPF

LPF

LPF

20MHz Samples

• FPGAs are ideally suited for multi-channel DSP designs– Many low sample rate channels can be multiplexed (e.g. TDM) and

processed in the FPGA, at a high rate– Interpolation (using zeros) can also drive sample rates higher

Gallagher 5 P188/MAPLD2004

FPGAs Allow Space/Speed Trade-offs

Q = (A x B) + (C x D) + (E x F) + (G x H)

can be implemented in parallel

××

×× +

+

+

+

+

+

A

BC

DE

FG

H

Q

But is this the only way in the FPGA?

Gallagher 6 P188/MAPLD2004

××

×× +

+

+

+

+

+ ×+

+

D Q

××

+

+

+

+

D Q

Parallel Semi-Parallel Serial

Customize Architectures to Suit your Ideal Algorithms

FPGAs allow Area (cost) / Performance tradeoffs

Optimized for?Speed Area

Gallagher 7 P188/MAPLD2004

Exploitng The Xilinx Architecture For DSP Functions

• Memory Blocks that can be configured as ROMs, dual port RAMs, FIFOs

• Embedded 18x18 multipliers that can be ganged to form a 35x35 bit multiply

• SRL16 shift registers– A patented technique for turning the 4 input

lookup table (2 per slice) into an addressable shift register

Gallagher 8 P188/MAPLD2004

Using SRL16E to increase Compute Density

k3

‘0’ +

k2

+

k1

+

k0

+

99

9

918

20MHz

4 channels

9

20MHz

k3

‘0’ +

k2

+

9

9 channelsSRL16E takes the same area

as one LUT.

It can be used for up to 16 channels.

Gallagher 9 P188/MAPLD2004

Xilinx System Generator For DSP

– System Generator is a Block Set that resides in Simulink/Matlab environment.

– System Generator blocks are bit true and cycle true models of Xilinx’s DSP intellectual property (IP) cores.

– Hardware DSP design capture is significantly accelerated due to automatic code generation from Simulink

Gallagher 10 P188/MAPLD2004

Algorithm Instantiation Considerations

• There are cases where following a textbook approach does not necessarily translate into an efficient instantiation

• Manipulating the algorithm to exploit features of the architecture can lead to much more efficient instantiations

• Modification of a text book algorithm includes how the math is executed as well as over-clocking structures to allow the structures to be time division multiplexed

Gallagher 11 P188/MAPLD2004

Example 1: Digital Down Conversion

• In digital down conversion we need to filter before we decimate to prevent aliasing

• These filters can get rather large because the transition band is rather narrow in relation to the sample rate

• A text book solution is to step the sample rate down in steps

Gallagher 12 P188/MAPLD2004

Digital Down Conversion• The following 3 slides show three different filter designs for the down conversion of a .625 Mhz band of interest that is centered at 20 MHz and sampled at 61.44 MHz.

– The decimation rate is 25– The final sample rate will be 61.44/25= 2.4576MHz

• The next slide shows the filter design needed if decimating by 25 in one step– the total coefficient count is 184

• The two slides after the next show the two filters necessary to decimate in steps, decimating by 5 in each step– The total coefficient count is 11+43=54

Gallagher 13 P188/MAPLD2004

Gallagher 14 P188/MAPLD2004

Gallagher 15 P188/MAPLD2004

Gallagher 16 P188/MAPLD2004

Digital Down Conversion (DDC) Implementation

• The following design shows how the DDC function would be implemented using the FIR filter core from the Xilinx Library

• The coefficients are automatically loaded into the filter cores

• The design has been compiled and was found to use about 6000 logic slices

• The fir filter core is a legacy core and is built as an optimized lookup table of coefficients

Gallagher 17 P188/MAPLD2004

Digital Down Conversion Implementation

Gallagher 18 P188/MAPLD2004

DDC –Another Way• While we were able to exploit the math of DSP to

reduce our coefficient count, we did not necessarily exploit the Xilinx architecture.

• The next design shows a design that implements the 184 coefficient filter but is significantly smaller in instantiation size then the previous design

• This design exploits the memory, embedded multipliers, and SRL16s

Gallagher 19 P188/MAPLD2004

Gallagher 20 P188/MAPLD2004

Multiplexing I&Q multiplication so that just one filter is needed instead of two

Time Division Multiplexed Input

Gallagher 21 P188/MAPLD2004

Efficient Shift Registers via SRL16s

Delay line would require 16x50x7=5200 registers which would be 2800 logic slices.

Use of SRL16s reduces slice count to less then 700

Gallagher 22 P188/MAPLD2004

Clock Based Demuxing And Automatic Pipeline Balancing

Down sample block grabs last sample in a frame

Down sample block grabs next sample in a frame

Delay block “slide” frame

Balancing latencies is a common requirement in DSP designs. The Sync block uses SRL16s (very efficient) to automatically balance pipeline delays

Gallagher 23 P188/MAPLD2004

Notes on Previous Design

• One filter structure is used by clocking the filter at twice the rate of the incoming data

• The coefficients are stored in memory, 25 per rom. There are 200 coefficients but this approach allows storage of many more

• The delay between taps is built using SRL 16s. This would have taken 2800 slices alone without SRL16s but instead the entire design is less that 700 slices

Gallagher 24 P188/MAPLD2004

Channelizer Design • The following design is a 64 channel channelizer based on the

technique known as polyphase decimation filter with a DFT bank • The design basebands and decimates 64 channels simultaniously• The polyphase decimation is the same structure as the previous

design, hence very efficient device utilization.• This filter structure uses the on-chip ram blocks of the Xilinx device

to store the coefficients• This technique requires a tapped shift register that requires 6272

registers (3136 slices). However, Xilinx’s patented ability to turn the logic look-up table into a 16 bit register reduces this require by more than an order of magnitude. The whole design is less than 1700 slices.

• The DFT is implemented with a streaming fft core. The streaming mode allows the FFT to keep up with the data rate

• Individual channels out of the fft are demuxed using the implied clocking technique seen in the previous design

Gallagher 25 P188/MAPLD2004

512 Coefficients are stored in on chip block rams

64 pt FFT set to streaming mode

Gallagher 26 P188/MAPLD2004

Filter coefficients are stored in on-chip block rams. A new phase of the 64 phase-polyphase filter is rotated into the multipliers on every clock cycle. There are 64 phases x 8 taps =512 coefficients

Gallagher 27 P188/MAPLD2004

Gallagher 28 P188/MAPLD2004

Conclusion

• Efficient FPGA instantiation of DSP algorithms requires exploitation of the FPGA vendor’s architecture. Xilinx’s Virtex II architecture is especially amenable to systolic computation structures

• FPGA architectures may present non-obvious instantiation choices that are more efficient then a typical textbook approach

• Algorithms can and should be modified for parallelized data flow instantiation.