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1
Comparison of Bessel and RRC filters for DCS Platforms
Robert PetersStellar SolutionsJanuary 25, 2006
2
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?
3
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.
4
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)!
5
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
6
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
7
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
8
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
9
P3 Amplifier Response
10
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
11
Sidelobes for P3
Sidelobe regrowth makes Tx bandwidths equal.
Bessel RRC
12
8th Order RRC Tx Filter
13
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.
14
Added 3° Phase Noise
15
BER Measurements
16
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
17
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
18
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)
19
Saleth2
Saleth2 has same AM/AM as Saleth1, but greater AM/PM
AM/PM
20
Saleth1 Sidelobes
Narrower RRC filter advantage lost because sidelobe regrowth of amplifier.
Blue=before amplifier
Red=after amplifierRRC Bessel
21
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
22
Saleth 1 Medium Distortion
< RRC
< Bessel
23
Saleth2 (High Distortion)
24
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)
25
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).
26
2nd Order Comparison
Bessel RRC
27
3rd Order Comparison
28
4th Order Comparison
Bessel RRC
29
6th Order Comparison
Bessel RRC
30
8th Order Comparison
Bessel RRC
31
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).
32
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
33
Insertion Loss RRC, 8th
Order
34
Insertion Loss RRC, 8th Order
35
Insertion Loss RRC 4th Order
36
Insertion Loss RRC 4th Order
37
Insertion Loss RRC 2th Order
38
Insertion Loss RRC 2th Order
39
Insertion Loss RRC 2th Order
40
Insertion Loss RRC, 2th Order
41
Insertion Loss RRC, 1st order
42
RRC Implementation Loss for different orders
Saleth 1
43
RRC Implementation Loss for different orders
Saleth 2
44
Block Diagram NPR Simulated by 32 Channels
45
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).
46
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
47
Noise for 750, 1500 Hz Carrier Separation
1500 Hz
48
750 Carrier Spacing
49
1500 Carrier Spacing
50
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
51
Enlargement of RRC Tx - Bessel Rx Curve
Blue=RRC-RRC
Green=RRC-Bessel
52
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
53
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.
54
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
55
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