Digital Backend MeetingDigital Backend MeetingMPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

TunableTunable Digital Filter Digital Filter for the ALMAfor the ALMA CorrelatorCorrelator

Gianni ComorettoGianni Comoretto INAF INAF -- Osservatorio di ArcetriOsservatorio di ArcetriAlainAlain BaudryBaudry, Philippe, Philippe CaisCais, ,

BenjaminBenjamin QuertierQuertier ObservatoireObservatoire de Bordeauxde BordeauxAndreAndre GunstGunst ASTRON ASTRON -- DwingelooDwingeloo

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

TheThe AtacamaAtacama LargeLarge MillimeterMillimeter ArrayArray

• 64 12m dishes on the Atacama highland (5000 m elevation)• 15m -> 12 Km baselines• 9 bands from 32 to 850 Ghz• 2 polarization * 8 GHz instantaneous bandwidth• 3 bit sampler, 2 bit correlator

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

The ALMAThe ALMA CorrelatorCorrelator

Original design

• 4 units, each analyzing an IF: 2 polarizations * 2GHz BW• 125 Mhz clock: x32 time multiplexed• Digital filter to reduce bandwidth and increase resolution• 64 channels/IF @ 2GHz BW, 4 polarization• 256 channels/IF @ 2GHz BW, 1 polarization• 8192 channels/IF @ 31 Mhz BW, 1 polarization• Reasonable resolution/bandwidth up to 210 Ghz• Wideband modes usable only for pseudo-continuum

NRAO filterboard (one channel) on test fixture

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

ALMAALMA CorrelatorCorrelator (2)(2)Hybrid correlator (F-X-F) architecture

• Digital filterbank to split the input bandwidth into 32 sub-channels• One or more correlator planes analyze each sub-channel• 8192 usable spectral channels (for all polarizations)• Each sub-channel can be independently tuned => zooming

Problems• Sub-channel stitching and platforming => overlapping sub-

channels• Digital filter architecture => economically implement 32 filters• Multiple quantization effects• Increased data rate to control computer => keep original TM mode

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

HybridHybrid correlatorcorrelatorGeneral architectureGeneral architecture

32 x62.5 MHz bw• Hybrid correlator concept:

• Filterbank to adapt input bandwidth to correlatorspeed

• Conventional correlatorto analyze the output of each filter

• Increased resolution & flexibility

• Sub-bands must be joined together

2 GHz bandwidth

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

General problems with hybridGeneral problems with hybrid correlatorscorrelators●Edge effects important

● aliasing & filter rolloff● different response for real and

imaginary components● different "barycenter shift"● phase errors near band edge

●To reduce effects:● Fourier transform on semi-integer

channel freqs.● Band filter: Ntaps=2xNchans.

4Ktaps, but should increase with resolution

● Correct for channel shift

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

Nonoverlapping subchannelsNonoverlapping subchannelsExample simulation.

correlated pseudo-random noise with defined amplitude and phase spectrumprocessed through hybrid,nonoverlapping correlator, with 64 pts/sub-band

Green: Original spectrumRed: continuous sub-band

spectrumx: spectral pointsPhase cancels at band edges

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

SubchannelSubchannel edge errorsedge errors

Red: corrected for amplitude response

blue: corrected for channelbarycenter shift

Correcting only for amplitude response leaves errors of ~25% and ~10 deg. in phase

Dynamic range limited to ~15dBCorrecting for channel shift

improves by a factor of 2Error is confined on 2 edge

channels.

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

OverlappingOverlapping subchannelssubchannels

• An overlap of 1-2 channels improve dramatically the spectral accuracy

• Some band lost at the edges of the whole 2 GHz band• In principle can be done with polyphase, but requires change of

rate in the data clock or radix-17 FFT• Adopted solution: complete digital receiver with tunable LO

• filter requirements less stringent (2Ktaps) • further simplified using a 2-stage FIR• Amplitude accuracy ~0.2%• Phase ~0.5 deg

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

SubchannelSubchannel stitchingstitchingThe problemThe problem

- Subchannels in the hybrid correlator are separatelydigitized

- Quantization errors are different for different subchannels- Multiple quantizations present in the systemThus: Sub-channel alignment problems- Must measure total power in each subchannel- Level-dependent quantization correction- Validate with simulations

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

SubchannelSubchannel stitchingstitchingSimulation data setSimulation data set

• Gaussian noise: completely stochastic signal to simulate real data• Independent uncorrelated noise and correlated signal• Variable phase relation between the two signals• Maximum correlation coefficient ~0.3• 65 Msample: 16 ms of real data• Reference cross spectrum obtained using a 2048 ch. continuous

correlator

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

SubchannelSubchannel stitchingstitchingResult analysisResult analysis

• Result from hybrid correlatorcompared to reference spectrum

• Hybrid spectrum both withand without final 2-bitquantization to discriminate effects

Difference within noise except corresponding to strong linesNo difference except excess noise in spectrum with 2-bit quantization35 dB of measured dynamic range, despite unrealistc strong spectral lines

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

TunableTunable digital filterdigital filter• Conceptually a SSB digital receiver

• Complex LO and mixer• Low pass filter for band selection

• Implementation using a 2-stage complex low-pass filter• 1st stage: minimum selectivity required for correct decimation• 2nd stage operates at 125 MHz, determines bandshape & final width

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

TunableTunable digital filter architecture (1)digital filter architecture (1)

Signal processingTest signal with random noise + 2 strong spectral lines

Input band rotated in order to have the desired frequency around zeroFirst filter: complex low-pass

few taps, wide transition regionstap encoding with 8 bit rejection ~ 47-50 dB

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

TunableTunable digital filter architecture (2)digital filter architecture (2)

Resampling to final frequencytransition regions aliasedback, but passband is clean

Second filter: equivalent number of taps multiplied by decimation factor.Compensates for 1st filterrolloff

Conversion to real outputTotal power measurement and re-quantization

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

Implementation parametersImplementation parameters• Local Oscillator:

• 16 bit (5+11) frequency register, 30 KHz step, 0-2 GHz range• 9 bit sin/cos table implemented in 512x6 LUT (block RAM)• output 6 bit: 0.9% loss, > 50 dB spurious free dynamic range

• 1st stage filter: • symmetric 128 taps, implemented with 64 LUTs (each branch)• 8 bits frozen coefficients (LUT optimization) ~ 48 dB rejection• output re-quantized to 8 bits (0.2% sensitivity loss)• 1:32 decimation

• 2nd stage filter:• symmetric 64 taps (loadable)• implemented with 16 9x9 bit multipliers (each branch)• 9 bits coefficients: >40 dB rejection, 0.3 dB peak-to-peak ripple

• Real output, quantized to 2 bits

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

QuantizationQuantization effects effects -- LOLOPhase resolution in mixer sin/cos table determines SFDRMixer output requantization determines SFDR and lossFor > 50 dB SFDR at least 6 bits of mixer output are neededSin/cos generation, mixing, requantization can be implemented in a single LUT memory

# Bits Loss SFDR3 3,3% 31 dB4 1,5% 38 dB6 0,9% 52 dB

Performance of quantized mixers(3 bit input, N bit output)

LO leakage very well rejected. Main source of unwanted harmonics is sampler DC offset

Filter responseDigital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

8 bit taps in 1st filter and 9 in 2nd adequate for 47 dB minimum stopband rejection

Filter responseDigital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

In-band ripple

Composite stopband rejection(8+9 bit)

2nd FIR tap width: 9 bit10 bitmany bits

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

Operation modesOperation modes

• Basic mode: 62.5 MHz band, 32 independently tunable filters

• Bypass mode: each filter outputs omeof the 32 input samples, requantizedto 2 bit

• Reduced bandwidth: 31.25 MHz (to be used with correlator oversamplemode) - 27.3 MHz usable BW

• 4x2 and 4x4 bit modes for increased sensitivity

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

• Tunable filter board is compatible with existing filter board

• Interface chip (CPLD2) for programming and personality download

• Delay with 3 XilinxSpartan FPGAs – 8µsdelay range

• 32 filters implemented on 16 Altera Stratix FPGAs

• Final version usingAltera 1S40 Hardcopy

• Signal distribution using point-to-point 1.8V

• Estimated power consumption: ~60W 40W for Hardcopy

Filter board implementationFilter board implementation

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

PrePre--prototype boardprototype board

• 6 channels (3 FPGAs)• Delay and distribution

logic identical to final board

• Single-ended and LVDS interconnections

• Selectable I/O voltage • A/D and D/A converter

+ speed-up memory • Standalone tests or used

with test fixture

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

Design statusDesign status• Pre-prototype board built and

under test• Test fixture from NRAO for

signal generation and analysis– Digital noise + 2 tones – A/D and D/A converter +

speed-up memory– Socket for ALMA sampler – ALMA correlator chip – C167 controller – Control program on PC

• Prototype board designed and awaiting test results

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

Alternate design Alternate design -- undecimatedundecimated LOLO

Reversing LO and 1st filter LO operates at decimated speed. Full (N bit) multiplication possible1st filter must be recomputed/reloaded every time band changes2nd filter identical

Digital Backend MeetingDigital Backend Meeting MPIfRMPIfR Bonn Bonn -- Sep 6, 2004Sep 6, 2004

Alternate design signal processingAlternate design signal processingSame test signal

1st filter: complex coefficientsbandpass.

Frequency rotated version of prototype LPF Coefficient truncation cannot be optimized for all freqs.

Decimation produces desired band in an arbitrary positionComplex LO/mixer recovers correct frequency orderingSuccessive processing identical