1

Comparison of Bessel and RRC filters for DCS Platforms

Robert PetersStellar SolutionsJanuary 25, 2006

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Problem

New requirement of meeting ITU -25 dB sidelobe specification calls for revision of NOAA requirements.

– Would a RRC or Bessel filter provide better performance?

– What impairment arises from a RRC Tx filter used with a Bessel Rx filter at DCS Rx station?

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Conclusions (1)

• Recommend using 2nd order RRC filter as performance is about the same as 8th

order Bessel filter

• DCS Rx station can use 8th order Bessel filter with 2nd order RRC DCS Tx filter without significant degradation.

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Conclusions (2)• 25 dB sidelobe requirement is driving factor in HPA

back-off, not type of filter.• For more linear amplifiers, RRC filters marginally better,

for less linear amplifiers, Bessel filters marginally better (both 8th order filters). But 8th Order Bessel filter needed to equal 2nd order RRC filter.

• RRC/Bessel filter differences in filter BW at -20 dBC (276 vs. 306 Hz) small compared to 100 Hz allowed frequency drift(+- 200 Hz spacing, both 8th order filters).

• Either 8th order filter can easily support half current spacing for 300 bps links. Filter sharpness not an issue (for 8th order filter)!

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Many Interacting Variables

• Over sample rate• Alpha of RRC filter (used NOAA

recommended alpha = 1)• Bandwidth of RRC and Bessel function• Order of RRC and Bessel filters• Type of Bessel filter (“analog” or digital)• AM/AM and AM/PM of platform amplifier• Output power back-off of amplifier

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Modeling (1)• Uncoded 450 bps, 8 PSK links. This gives correct bandwidth coded

300 bps but Eb/No high by 1.8 dB.• To determine oversample rate, filter bandwidth (BW), and filter

order:– Used Simulink RRC Tx and Rx filters which optimize filter BW.– Adjusted Bessel bandwidth to approximately match RRC BW at 3 dB

points– Modeled RRC link with no amplifier. Oversample rate increased until

performance leveled out. – Using oversample rate and BW from above, looked at scatter plots of

Rx of link using Bessel filter Tx and Rx and adjusting Bessel filter order to get good performance (found peaks in performance vs. order curve)

• Added platform amplifier, determined OPBO to exceed sidelobe specifications by 1 to 3 dB.

• Ran simulation to get BER curves for various back-offs to get implementation margin.– Found that OPBO drove backoff, not implementation margin

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Modeling (2)• Repeated simulation for two additional amplifiers with greater non-

linearity. – Found some changes in performance but no substantial change in

conclusions• Added Satellite SSPA with 18 dB NPR and 32 adjacent channels to

final simulation to determine impact on C/N. – Found minimal impact

• Investigated impact of lower order RRC and Bessel filters– RRC performance remains good while Bessel filter performance

deteriorated greatly.• Modeled NPR, examined the effect of decreased carrier spacing

– Noise constant as spacing decrease and equal to NPR• Modeled RRC transmit, Bessel Rx filter

– Found little difference from RRC Tx and RRC Rx in performance with 8th

order Bessel filter

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Determining Sampling Rate

Transmitted Power vs. Oversample

00.10.20.30.40.50.60.70.80.9

0 2 4 6 8 10OverSample

Tx P

ower

RRC PWRBessel PWR

Selected sampling rate (samples/ symbol) of 8 for single carrier simulations

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P3 Amplifier Response

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Setting Bessel BW for P3

Bessel Tx BW adjusted so as to be about equal to RRC. Note greater scatter on Bessel filter.

Both filters are 8th order

Red=RRC

Blue=Bessel

Bessel

RRC

RxTx

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Sidelobes for P3

Sidelobe regrowth makes Tx bandwidths equal.

Bessel RRC

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8th Order RRC Tx Filter

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Setting OPBO for P3

Side Lobe vs OPBO

-30

-29

-28

-27

-26

-25

-24

-23

-22

-21

-20

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0

OPBO

Side

Lob

e

RRC filterBessel Filter

RRC filter needs greater back-off to achieve same sidelobe. For this amplifier, difference is only about ½ dB for sidelobes of -26 dBC.

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Added 3° Phase Noise

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BER Measurements

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BER Plot RRC and Bessel Filters for P3

Linear AM/PM degrees/dB

The RRC filter has about 0.7 db less implementation loss. Thus the Bessel filter loses the ½ dB advantage it had with lower sidelobes.

Results consistent with scatter plot shown earlier

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Amplifiers

• P3 amplifier was fairly linear with linear phase change with amplitude which allowed operation very close to saturation.

• To determine effect of more realistic assumptions, two Saleth models, Saleth1 and Saleth2 developed which had greater nonlinearity than P3 model.– Saleth2 has similar AM/AM but higher AM/PM

than Saleth1

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Saleth1

Saleth1 has higher AM/PM and AM/AM than P3. Note AM/AM approximates a TWTA rather than an SSPA

AM/PM

AM/AM (dB)Power out vs. voltage in

Gain (dB)

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Saleth2

Saleth2 has same AM/AM as Saleth1, but greater AM/PM

AM/PM

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Saleth1 Sidelobes

Narrower RRC filter advantage lost because sidelobe regrowth of amplifier.

Blue=before amplifier

Red=after amplifierRRC Bessel

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Saleth 1(Lo phase) & Saleth 2 (Hi phase)

OPBO vs. Side Lobes

-45

-40

-35

-30

-25

-20

-15

-8 -7 -6 -5 -4 -3 -2 -1 0OPBO (dB)

App

rox

Side

lobe

s (d

BC

)

RRC Lo phaseBessel Lo phaseRRC Hi phaseBessel Hi Phase

Saleth2

Saleth1

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Saleth 1 Medium Distortion

< RRC

< Bessel

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Saleth2 (High Distortion)

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Reduced spacing

• 300 Hz from band center, out-of-band signal is > 25 dBC.

• This would allow 5x current spacing for 300 bps link and by scaling, 2X for 1200 bps link.

• However 200 Hz bandwidth allocated to accommodate frequency drift reduces capacity increases to only 2x for 300 bps and less than 2x for 1200 bps links (for overlap at < 25 dB)

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Why RRC Performance Does Not Degrade

• Acceptable use of lower order RRC filters unexpected as filter attenuation decreases as order decreases.

• Reason: The decrease in power of modulated signals as frequency increased from carrier band edge means that high filter attenuation not necessary. Note sharpness of RRC filter roll-off does not degrade significantly as filter order is decreased so sidelobe attenuation does not change (unlike Bessel filters).

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2nd Order Comparison

Bessel RRC

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3rd Order Comparison

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4th Order Comparison

Bessel RRC

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6th Order Comparison

Bessel RRC

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8th Order Comparison

Bessel RRC

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Filter Performance vs. Filter Order

Filter Performance vs. Order

-70

-60

-50

-40

-30

-20

-10

1 2 3 4 5 6 7 8

Bessel Filter Order (1/2 RRC Order)

dB

RRC 600 kHzRRC SidelobeBessel 600 kHzBessel Sidelobe

Best reason for using RRC filtersRRC filter performance remains good as order is reduced, Bessel deteriorates below 5th or 6th order. Note 4th

order Bessel cannot meet 25 dB sidelobe requirement without greatly increased backoff (and perhaps not at all).

600 Hz values shows “residual” signal (note 600 kHz should be 600 Hz).

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Bessel Filter Sidelobe Regrowth (expanded from last slide)

Bessel Sidelobe Regrowth

-27

-25

-23

-21

-19

-17

-15

0 1 2 3 4 5 6 7 8 9

Bessel Filter Order

Side

lobe

s (d

B)

Accuracy is about +- 1 dB

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Insertion Loss RRC, 8th

Order

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Insertion Loss RRC, 8th Order

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Insertion Loss RRC 4th Order

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Insertion Loss RRC 4th Order

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Insertion Loss RRC 2th Order

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Insertion Loss RRC 2th Order

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Insertion Loss RRC 2th Order

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Insertion Loss RRC, 2th Order

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Insertion Loss RRC, 1st order

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RRC Implementation Loss for different orders

Saleth 1

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RRC Implementation Loss for different orders

Saleth 2

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Block Diagram NPR Simulated by 32 Channels

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NPR Measurement

150 Symbols/sec with 160 Hz separation to approximate noise. Blue curve is before amplifier, red curve is after amplifier. Note “ripple” is actually individual carriers (not true noise).

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Noise for 160, 400 Hz Carrier Separation

160 Hz400 Hz

Note noise level unchanged as carrier separation increases. Only change in graphs in this and next slide is carrier separation

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Noise for 750, 1500 Hz Carrier Separation

1500 Hz

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750 Carrier Spacing

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1500 Carrier Spacing

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RRC Tx - Bessel Rx & RRC Tx and Rx

Used recommended RRC filter (65 coefficients, 2nd order) and 8th order Bessel function.

Blue=RRC-RRC

Green=RRC-Bessel

RRC-RRC

RRC-Bessel

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Enlargement of RRC Tx - Bessel Rx Curve

Blue=RRC-RRC

Green=RRC-Bessel

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Required Eb/No for BER=10E-3 Bessel=8, RRC=8th Order

RRC and Bessel Required Eb/No at BER=1E-3 Filter Order 8/16

11.5

12

12.5

13

13.5

14

14.5

0 1 2 3 4 5 6 7 8

OPBO

dB

RRCBessel

8

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Difficulties• Setting order of filters

– Bessel function can be calculated in different ways, most common for digital involves twice as many computations as RRC. Therefore we set the order of the RRC filter to be twice that of Bessel filter. But performance varied very non-linearly on over sampling, filter order and filter bandwidth. We chose bestcombination. RRC filter well behaved.

• Setting BW of filters– Bandwidth of Bessel filter set by approximately matching ~ 3 dB

bandwidth of both filters was not particularly accurate• DCS HPA used more like a TWTA than SSPA and did

not have good AM/PM curves. Better amplifier not available from Simulink.

• Suitable Bessel function filter not available in Simulink, MathWorks developed one for us.

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Coeff. For 2nd Order RRC Filter

-0.0017653261 -0.0013304488 0.0000000000 0.00152119420.0023085034 0.0017561925 0.0000000000 -0.0020503052-0.0031479591 -0.0024252182 0.0000000000 0.00291359160.0045470521 0.0035664973 0.0000000000 -0.0044675072-0.0071453676 -0.0057612649 0.0000000000 0.00771660330.0128616617 0.0108823893 0.0000000000 -0.0165355785-0.0300105439 -0.0282942121 0.0000000000 0.06063045450.1500527194 0.2546479089 0.3535533906 0.42441318160.4501581581 0.4244131816 0.3535533906 0.25464790890.1500527194 0.0606304545 0.0000000000 -0.0282942121-0.0300105439 -0.0165355785 0.0000000000 0.01088238930.0128616617 0.0077166033 0.0000000000 -0.0057612649-0.0071453676 -0.0044675072 0.0000000000 0.00356649730.0045470521 0.0029135916 0.0000000000 -0.0024252182-0.0031479591 -0.0020503052 0.0000000000 0.00175619250.0023085034 0.0015211942 0.0000000000 -0.0013304488-0.0017653261

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Coeff. For 4th Order RRC Filter

-0.0004400373 -0.0003211197 0.0000000000 0.00034254490.0005007321 0.0003661891 0.0000000000 -0.0003923697-0.0005749146 -0.0004214629 0.0000000000 0.00045391780.0006669010 0.0004902732 0.0000000000 -0.0005311805-0.0007828838 -0.0005774329 0.0000000000 0.00063000470.0009320045 0.0006901027 0.0000000000 -0.0007592365-0.0011282159 -0.0008393141 0.0000000000 0.00093277620.0013936785 0.0010427842 0.0000000000 -0.0011734927-0.0017653261 -0.0013304488 0.0000000000 0.00152119420.0023085034 0.0017561925 0.0000000000 -0.0020503052-0.0031479591 -0.0024252182 0.0000000000 0.00291359160.0045470521 0.0035664973 0.0000000000 -0.0044675072-0.0071453676 -0.0057612649 0.0000000000 0.00771660330.0128616617 0.0108823893 0.0000000000 -0.0165355785-0.0300105439 -0.0282942121 0.0000000000 0.06063045450.1500527194 0.2546479089 0.3535533906 0.42441318160.4501581581 0.4244131816 0.3535533906 0.25464790890.1500527194 0.0606304545 0.0000000000 -0.0282942121-0.0300105439 -0.0165355785 0.0000000000 0.01088238930.0128616617 0.0077166033 0.0000000000 -0.0057612649-0.0071453676 -0.0044675072 0.0000000000 0.00356649730.0045470521 0.0029135916 0.0000000000 -0.0024252182-0.0031479591 -0.0020503052 0.0000000000 0.00175619250.0023085034 0.0015211942 0.0000000000 -0.0013304488-0.0017653261 -0.0011734927 0.0000000000 0.00104278420.0013936785 0.0009327762 0.0000000000 -0.0008393141-0.0011282159 -0.0007592365 0.0000000000 0.00069010270.0009320045 0.0006300047 0.0000000000 -0.0005774329-0.0007828838 -0.0005311805 0.0000000000 0.00049027320.0006669010 0.0004539178 0.0000000000 -0.0004214629-0.0005749146 -0.0003923697 0.0000000000 0.00036618910.0005007321 0.0003425449 0.0000000000 -0.0003211197-0.0004400373