Carrier Recovery

Coherent Carrier RegenerationUsing a Long Loop PLL Technique

P. M. Rao, P. K. Jain and Padmavathy C.S.National Remote Sensing AgencyGovernment of India

Demodulation of QPSKmodulated data involvesthe regeneration of the

coherent carrier in a phase lockloop. Various schemes are usedfor this purpose in designing thedemodulators for tracking andreceiving very high data rate sig-nals from remote sensing satel-lites. A concept implementing thelong loop carrier tracking phaselock loop technique is describedhere, which is used for carrierrecovery in the demodulator. Theunit has been successfully devel-oped and tested in the groundstation. This concept has facili-tated a significant improvementin the loop performance for signalacquisition at very low signal tonoise ratios. Signal acquisitionand data retrieval at very low antenna elevationangles while tracking low altitude satellites hasbeen achieved through this scheme.

IntroductionThe design of the coherent carrier recovery

circuit for the demodulation of suppressed carri-er PSK signals is very critical and involves sev-eral performance considerations. Various carrierregeneration schemes have been developed andimplemented in this demodulator design foroptimal performance, in different applications.

A scheme implementing the long loop carriertracking phase lock loop along with even lawnon-linearity has been developed and used forthe design of a very high data rate QPSKdemodulator to receive data from remote sens-ing satellites. This scheme has provided betterlock threshold performance and loop stability inregenerating the coherent carrier for low input

signal to noise ratios at different QPSK modu-lated data rates, when compared to convention-al techniques.

The demodulator using this techniqueacquires the lock and starts regenerating thecoherent carrier at very low input S/N ratios, afeature very useful in remote sensing satelliteground station applications where a coherentcontinuous clock is required to be supplied tothe recording system, even from antenna angleslower than 1 degree in elevation.

This paper describes the design of the QPSKdemodulator using the long loop coherent carri-er regeneration scheme, and shows the merit ofits performance while demodulating the QPSKsignals at different data rates and varying signalto noise ratios.

Measured results regarding the unit’s coher-ent carrier acquisition performance are tabulat-ed and a comparison is provided with the theo-

28 Applied Microwave & Wireless

■ Figure 1. QPSK demodulator for remote sensing satellite datareception.

QPSK

Signal

Data Clock

BandpassFilter

CoherentDetector

BSSC

AutomaticGain

Control

PowerDivider

CoherentCarrier

Recovery

Carrier Recovery

30 Applied Microwave & Wireless

retically computed values. A compari-son is also provided with the perfor-mance of demodulators designed usingother techniques.

Configuration of the QPSK demodulator

The configuration of the demodula-tor used for the remote sensing satellitedata is shown in Figure 1. The inputQPSK modulated signals are bandpassfiltered in a broadband filter and givento a non-coherent AGC amplifier. Theconstant level signals from the AGCamplifier are power divided into twopaths. One path goes to the coherentcarrier recovery circuit and the otherpath goes to the coherent data detector.The I and Q data streams from thecoherent data detector are then inputto the bit synchronizer and signal con-ditioner unit, where the coherent sym-bol timing is recovered and the data issynchronized to the symbol timingclock. The outputs of this circuit are therequired serial data and bit rate clock.

The input broadband bandpass filterpasses the QPSK modulated signals with proper out ofband rejection. The automatic gain control circuit is anon-coherent AGC in order to assure that its transientbehavior is not a function of carrier regeneration acqui-sition time.

The coherent carrier recovery circuit employs non-linear squaring devices and a phase lock loop to regen-erate the coherent suppressed carrier from input modu-lation. This circuit is designed for handling a wide rangeof input data rates on QPSK modulation without signif-icant performance degradation. This feature hasenabled the demodulator to be adaptable for multi-satel-lite data reception in one unit with only a plug in changerequired for bit synchronization [1].

The coherent data detector extracts the in phase (I)and quadriphase (Q) data streams and lowpass filtersthem to isolate the carrier component. Proper care hasbeen taken in this circuit to avoid the crosstalk betweenthe I and Q channels by using circuit elements with verygood amplitude and phase balance specifications and bycompensating for the phase mismatch between the mod-ulated input and the regenerated carrier.

The bit synchronizer circuit has input matched fil-ters which are symbol rate specific, to optimize the sig-nal to noise ratio of the data streams before synchro-nization. The symbol timing is generated through aneven law nonlinearity coupled with a phase lock loop.The recovered symbol clock estimates the data pulses,and the synchronized parallel data streams are differ-entially decoded for resolving the carrier phase ambigu-ity. The decoded data are serialized and taken as outputof the unit.

Design options for carrier recoveryThe crucial circuit element which decides the perfor-

mance of the demodulator is the coherent carrier regen-eration circuit. Several schemes are developed for coher-ent carrier regeneration, among which are the followingdesign options discussed in this paper.

1. Carrier recovery through Costas loop.2. Carrier recovery through multiplication loop.

Implementation of the Costas loopHard limited Costas loop or polarity loop is one of the

popular approaches used in the demodulation of QPSKsignals [2]. This technique is unique in that it performsboth phase coherent suppressed carrier reconstructionand synchronous data detection within the loop. Figure2 shows the implementation of the polarity loop for aQPSK demodulator.

For any carrier tracking analysis, the description ofthe linear PLL model is inevitable [3]. Out of this work,a fundamental expression relates the root mean squaredphase error to the SNR in the loop:

( 1 )

where rL = SNR in the loop. Or,

( 2 )s f2 1= ◊

S N iBB

L

i/b g

srf

2 21=L

radb g

■ Figure 2. Hard limited Costas loop.

QPSK

Signal

Baseband Data - I

90°

SVCO

LPF

LPF

Limiter

Limiter

LoopFilter

Baseband Data - Q

Carrier Recovery

32 Applied Microwave & Wireless

where:

(S/N)i = input signal to noise ratio.BL = one sided loop band widthBi = one sided IF band width (arm filter band width)

The above relation concerns the carrier referencing forunmodulated or non-coherent modulation inputs.

The tracking performance of a suppressed carrierloop is analyzed by another relationship involving squar-ing loss SL:

(3)

The squaring loss describes the degradation in loopSNR due to S¥N and N¥N distortions occurring in thenon linearity in carrier regeneration. This depends uponthe shape of the arm-filter, the data waveform and theoperating Eb/N0.

Much work has been done in estimating the squaringloss. Simon [4] has derived a closed form expression forsquaring loss which is shown as

(4)

where:

Dm = modulation distortion factor fs = Data rate in symbols/secRd = Symbol signal to noise ratio KL= a constant dependent upon the filter type andcan be written as:

where ~Hc(w) is the filter transfer function. It is also

shown that

KL = (2n – 1)/2n for an n-pole Butterworth filter Kd = a constant dependent upon both baseband datapower spectrum and the filter type. This can be writ-ten as

where Sm(w) represents the data power spectrum.

The effects of signal suppression due to hard limiting

is also introduced into the above expression for squaringloss. Simon [2] has shown that inclusion of a limiterintroduces a signal suppression factor into the analysiswhich can affect the loop performance. For higher Eb/N0ratios (Eb/N0 >10 dB), there is an actual improvementin the loop's squaring loss while, at low S/N ratios, thelimiter degrades the loop performance. The expressionfor the squaring loss has also been derived in terms ofEb/N0 [5] and written as:

where

Tb = Bit duration

where

Hc(w) = Low pass equivalent of the input bandpassfilter transfer function.Sm(w) = Spectrum of the modulated signal.

Also, incorporating input Eb/N0 into the equation (3),we get:

(5)

where

sf2 = Max. allowable RMS phase jitter (rads).

Eb/N0 = Energy per bit to noise density ratio requiredfor desired bit error rate performance.

Having calculated the loop squaring loss, and know-ing the required SNR in the loop, RMS phase jitter inthe recovered carrier is calculated.

Implementation of multiplication loopThe explanation of this technique is similar to the

Costas loop, as both are identical in performance [6].The difference in the scheme is in the implementation ofthe non-linearity for modulation wipe-off as shown inFigure 3. The received QPSK signal plus noise is filteredand passed through the fourth power non-linearity. Theoutput after the non-linearity is given to a phase lockedloop which locks to the fourth harmonic of the receivedcarrier. The signal ¥ noise and noise ¥ noise distortionsoccuring in the carrier regeneration loop are controlled

s f2

0=

◊ ◊B

E N f SL

b s L/

ap

p

=

=

=

-•

•

-•

•

-•

•

zzz

12

12

2

1

4

2

4

S w H w dw

h S w H w dw

h H w dw

m c

m c

c

b g b g

b g b g

b g

~

~

~

Sh h T

E NLb

b= +LNM

OQP

-1 2

0

1

2aa/

/

KS w H w dw

S w H w dwD

m c

m c

@ -•

•

-•

•zz

b g b g

b g b g

~

~

4

2

KH w dw

H w dwL

c

c

@ -•

•

-•

•zz

~

~

b g

b g

4

2

SD

K KB fR D

Lm

d Li s

d m

=+ /

2

srf

2 1=L LS

Carrier Recovery

34 Applied Microwave & Wireless

mainly by the excess noisebandwidth in the input band-pass filter preceding the squar-ing devices. The jitter in carrierreferencing is hence deter-mined by the characteristics ofthis bandpass filter. Layland[7] has proposed an optimumsquaring loop filter consideringthe various factors contributingto squaring loss. However,design of the arm filters, or pre-filters to the squaring devices,need not be on the lines ofmatched filtering for optimiz-ing the data signal-to-noiseratio used before data estima-tion in bit and symbol timing synchronizers. The jitteror the SNR in the phase lock loop, and the static phaseerror in the regenerated carrier, are some of the degra-dation factors which contribute to overall losses in datadetection. Smith A. Rhodes [8] and V. K. Prabhu [9] havecalculated the QPSK losses due to imperfect carrier syn-chronization and plotted the curves of detection perfor-mance for QPSK as shown in Figure 4. The loss in detec-tion is derived as:

Z2 = effective loss in Eb/N0 caused by synchronizationerror f.

The plots show the values of the required S/N ratio inthe phase lock loop for given bit error rate performanceat different detection loss (LdB) values. It is seen from theabove equation and the plotsthat to keep the detection lossesto a minimum and achieve bitsynchronization for lower val-ues of loop SNR, it is essentialto reduce the jitter in carrierreferencing and minimize syn-chronization errors.

Coherent carrier regenerationby the long loop method

The squaring loop andCostas loop explained abovehave been considered for fixeddata rate input signals. In caseswhere the demodulator has tobe designed to be adaptable tosignals with varying input datarates, the effects of the excess

noise bandwidth of the pre-filter or arm filter beforesquaring will be quite significant. While the pre-filterbandwidth has to be optimized for highest baud rateinput signal, the signals with lower data rates facesevere reduction in signal-to-noise ratio in the widerpre-filter. Also, at the lower antenna elevation angles(less than 5 degrees), the signal reduction due to pathloss and terrain reflections causes further degradationin input S/N ratio to the carrier regeneration nonlin-earity. All these effects put together will reduce signal-to-noise ratio in the loop, thus resulting in a require-ment for higher system link margin for carrier lockacquisition.

One could use a narrow band pass filter to improvethe S/N ratio at the input of PLL in a short loop config-uration, but this would face minimum bandwidth limi-tation posed by the very high input Doppler offsets onthe received signal while tracking low earth orbitingsatellites. The Doppler offset for some circular orbitsmay be as high as 400 kHz. This results in the require-ment that the pre-PLL filter passband response be flatat least over ±2 MHz, resulting in a noise bandwidth

L

E N

L L

L

b

dB

SNR in the loop

= Z2

b g b g b g= + +

+FHG

IKJ

LNMM

OQPP

=

◊

4 341 2 1

1 2

2

0

.

/

rg

gr

r

g

■ Figure 3. Carrier recovery by a multiplication loop.

■ Figure 4. Loop SNR (vertical scale = 10 log[rrL]) versus bit error rate (horizontalscale) at different detection loss values (L).

BPF x4QPSK

SignalLoopFilter

x4 VCO

CoherentCarrier

BPF4 fc

BPF4 fc

35

30

25

20

15

10

5

010–2 10–3 10–4 10–5 10–6

35

30

25

20

15

10

5

010–2 10–3 10–4 10–5 10–6

35

30

25

20

15

10

5

010–2 10–3 10–4 10–5 10–6

L = 0.2 dB

BPSK

Offset QPSK

Offset QPSK

Offset QPSKConv. QPSK

Conv. QPSK

Conv. QPSK

BPSK

BPSK

L = 0.1 dB L = 0.05 dB

Carrier Recovery

36 Applied Microwave & Wireless

much larger than that.In order to maintain the pre-

PLL filter noise bandwidth at theminimum possible, carrier regen-eration using a long loop phaselock scheme has been implementedand the demodulator has been suc-cessfully developed.

The long loop technique forcoherent carrier regeneration froma QPSK modulated signal isdescribed with the help of Figure5. The received modulated QPSKsignal is passed through an auto-matic gain control circuit to pro-vide a constant output level inde-pendent of the larger signal levelvariations at the input. The inputmodulated RF signal is mixed witha VCO signal in the carrier refer-encing phase lock loop to providean IF signal. The IF signal is thenpassed through the bandpass filterwith the bandwidth that is selectedoptimally for minimum squaringloss for the highest input baudrate.

The filtered signal is thenpassed through the non-linearityto remove the modulation. Thefourth harmonic component of thisIF carrier frequency is then fil-tered through a very narrow band-pass filter, with the bandwidth assmall as possible and the signalalways centered at a fixed frequency. The output fromthe BPF is then phase locked with the ¥4 multipliedcomponent of a very highly stable crystal oscillatorsource. The crystal oscillator source frequency is cen-tered at the IF carrier frequency and becomes the coher-ent carrier reference for data detection after phase lock-ing. The source frequency after multiplication is passedthrough a bandpass filter with identical characteristicsas the one which is in the signal path at the input of thePLL. This ensures the correct phase referencing in thephase lock loop.

The PLL tracks the Doppler frequency variations ofthe input signal by correcting the VCO output frequen-cy accordingly, while maintaining the IF output of themixer at a constant frequency. The mixer output ispower divided, with one portion fed to the coherentdetector for data demodulation and the other portion fedto the loop. The VCO is swept for initial signal acquisi-tion and is designed for acquiring the signal with aDoppler shift as high as +500 kHz.

Tabulation & ResultsImprovement of the lock threshold performance of

the phase lock loop, in a long loop configuration with anarrowband filter, has been analyzed with the help of

the following equation (6). The equation relates the(S/N)i in the narrow band pre-PLL filter to the inputcarrier-to-noise ratio in the pre-filter prior to the non-linearity [10, 11]:

(6)

where

B = Noise bandwidth of pre-filter to the nonlinearityBN = Noise bandwidth of the narrowband pre-PLLfilter

The results in terms of threshold loop SNR have beentabulated for different lock threshold Eb/N0 values atdifferent data rates in Table 1. The results are also plot-ted in Figure 6.

The theoretically computed results are cross checkedwith measured values and found to be matching.However, the values deviate slightly from the theory, dueto the implementation margin of the modulator at thehigher data rates.

For measurement of (S/N)i, signal to noise density

S N iB B C C

C N C N C NN N/b g b gb gb g

b g b g b g=

+ + +- - -

1 16

1 4 5 6 151 2 3

/ / /

. / / . /

■ Figure 5. Coherent carrier regeneration by the long loop method.

BPF VCO

Limiter

LoopFilter

Narrow-band BPF

Narrow-band BPF

x4

x4PowerDivider

PowerDivider

HighStabilityCrystal

Oscillator

QPSKSignalInput

RF Signalfor

CoherentDetection

CoherentLO

Carrier

Carrier Recovery

38 Applied Microwave & Wireless

ratio S/N0 at the input of the narrow band fil-ter is measured, and (S/N)i is computed bydividing the S/N0 ratio with the noise band-width of the filter. The noise bandwidth ofboth filters is measured with the help of abroadband white Noise Generator with aknown noise power density.

For each measured value of (S/N)i at theinput of the phase lock loop or at the output ofthe narrowband pre-filter, the signal to noiseratio in the loop (SNR)L is calculated by:

(7)

where Bn and BL correspond to the noiseband width of pre-PLL filter and PLL loopband width respectively. These results arealso included in Table 1. The results in Table1 can be compared with the results tabulatedin Table 2 obtained by directly computing the(SNR)L with the help of equation (6), thecase where no pre-PLL filter is incorporated,or where the Costas loop is used for carrierrecovery.

These results are also plotted in Figure 6.It can be seen from the plots that there is an

SNRS N i B

BLn

L=

◊/b g

Data Lock Lock Threshold (S/N)i & SNRL (S/N)i & SNRLRate Threshold C/N0 measured at with measured calculated

Eb/N0 PLL input (output value of C/N0 theoretically withof narrowband filter) at PLL input eqns. (6) and (7)

(S/N)i SNRL (S/N)i SNRL(Mbps) (dB) (dB-Hz) (dB) (dB) (dB) (dB)

6 12.72 57 -10 7 -9.9 7.1

10 10.5 57 -10 7 -9.9 7.1

20 8.0 58 -9 8 -8.7 8.3

30 6.2 58 -9 8 -8.7 8.3

40 5.0 58 -9 8 -8.7 8.3

50 4.5 59 -8 9 -7.4 9.6

60 3.7 59 -8 9 -7.4 9.6

70 3.1 59 -8 9 -7.4 9.6

80 2.5 59 -8 9 -7.4 9.6

90 2.0 59 -8 9 -7.4 9.6

100 1.5 59 -8 9 -7.4 9.6

105 1.3 59 -8 9 -7.4 9.6

Notes: 1. Noise Bandwidth of the pre filter to multiplier = 116.14 MHz

2. Noise Bandwidth of the pre-PLL narrowband filter = 5.04 MHz

3. PLL loop Noise Bandwidth = 100 kHz

■ Table 1. Results with pre-PLL narrowband filter.

You can write for Applied Microwave & Wireless!

Take part in the technical interaction that is so important in the RF/Microwave/Wireless engineering profes-sion. Ideas need to be discussed, critiqued and nurtured to become answers to practical design problems!

Three types of articles can be presented:

1) Presentation and discussion of advanced design and analysis concepts.2) Specific design examples, including applications of particular devices or techniques.3) Tutorial articles on basic engineering subjects. New engineers need this type of instruction to gain

knowledge in a hurry.

Topics of current interest to us include:

mm-Wave technology Signal processing techniquesComplex modulation Interference reductionApplications of new ICs Manufacturing methodsOscillator design Test & measurement methods

We also want your “Design Ideas,” short notes with how-to hints or design shortcuts. If you have a favoriteidea that can be written up to fit on one or two pages, we’d like to publish it!

Just prepare a short description of your article idea and send it via mail, fax or E-mail. Send it to:

Gary Breed, Publisher, Applied Microwave & Wireless, 4772 Stone Drive, Tucker, GA 30084Fax: 770-939-0157, E-mail: amw@amwireless.com

Carrier Recovery

40 Applied Microwave & Wireless

improvement of more than 3 dB in the lockthreshold performance of long loop PLL con-figuration over a case where pre-PLL narrowband filter is not incorporated, or a Costasloop is used. This means the carrier acquisi-tion lock will occur at lesser input Eb/N0 val-ues in long loop PLL configuration. All theabove measurements were carried out with apre-PLL filter having a noise bandwidth of5.04 MHz. The improvement in the perfor-mance will be greater if the noise bandwidthis further reduced, as there is no limitation toits reduction.

ConclusionThe paper establishes the advantage of

long loop configuration over short loopschemes. The control of pre-PLL noise band-width in this technique has provided signifi-cant improvement in lock threshold of thedemodulator, thus facilitating its usage forcarrier acquisition from received modulatedsignals with very low S/N ratios.

The highly stable crystal oscillator sourcewith which the regenerated carrier signal islocked, forms the coherent reference with avery high S/N ratio, resulting in reduction ofdetection loss. The demodulator has been test-ed in practice at a satellite ground station bytracking and acquiring the signals from

remote sensing satellites. Carrier acquisition has beenpossible at antenna elevation angles as low as 0.5 degree,where the received signal has a low SNR and fluctuateswidely due to terrain reflections. The system margin forsignal acquisition has thus been extended. ■

References1. P. M. Rao, G. Uma Devi and P. K. Jain, “Design of

Multifunction Digital Data Demodulator and Bit syn-chronizer for Remote Sensing Satellite DataReception,” Institute of Electronic and Telecommunica-tion Engineers Technical Review, Vol. 13, Nos. 4 & 5,1996.

2. M. K. Simon, “Tracking performance of Costasloops with hard limited in phase channel,” IEEETransactions on Communications, Vol. COM-26, No.4,April 1978.

3. Floyd M. Gardner, Phase Lock Techniques, 2ndedition, John Wiley & Sons, New York, 1979.

4. M. K. Simon, “On the calculation of squaring lossin Costas loops with arbitrary arm filters,” IEEETransactions on Communications, Vol. COM-26, Jan1978.

5. Robert M. Gagliardi, Satellite Communications,Van Nostrand Reinhold Company Inc., 1987.

6. W. C. Lindsey and M. K. Simon, “Data AidedCarrier Tracking Loop,” IEEE Transactions onCommuni-cations, Vol. Com-19, April 1971.

7. J. Layland, “An Optimum Squaring Loop Filter,”IEEE Transactions on Communication Technology, Vol.

Data Lock Threshold Lock Threshold Threshold loop Threshold loopRate Eb/N0 at input C/N0 measured SNRL calculated SNRL calculated

of pre-filter at PLL input from the meas- from eqn. (6)to non-linearity ured value of C/N0 directly

at PLL input

(Mbps) (dB) (dB-Hz) (dB) (dB)

6 15.7 64 14 14.3

10 13.5 64 14 14.3

20 10.5 64 14 14.3

30 9.2 65 15 15.4

40 8.0 65 15 15.4

50 7.0 65 15 15.4

60 6.2 65 15 15.4

70 5.5 65 15 15.4

80 5.0 65 15 15.4

90 4.5 65 15 15.4

100 4.5 66 16 16.5

105 4.3 66 16 16.5

Notes: 1. Noise Bandwidth of pre-filter to nonlinearity = 116.14 MHz

2. Noise Band width of PLL = 100 kHz

3. SNRL calculated from equation(6) by replacing the noise bandwidth

Bn of pre-PLL filter with the loop bandwidth BL of PLL.

■ Table 2. Results without pre-PLL narrowband filter.

RF/MICROWAVE/WIRELESS COMPANIES:

Get Your Share of Attention!

Send information on your new product introduc-tions for our consideration. Applied Microwave &Wireless editors select product announcementsbased on interest to our readers, but we do ourbest to be sure that all companies get a chance tohave their products presented.

Send you new product information to:

New Products EditorApplied Microwave & Wireless4772 Stone DriveTucker, GA 30084

We prefer to receive material by mail with a colorprint or slide, if available. We will also accept E-mail and fax submissions:

E-mail: amw@amwireless.comFax: (770) 939-0157

Carrier Recovery

42 Applied Microwave & Wireless

COM-18, No.5, Oct. 1970.8. Smith A. Rhodes, “Effect of noisy phase reference

on coherent detection of offset-QPSK signals,” IEEETransactions on Communications, Vol. COM-22, Aug.1974.

9. V .K. Prabhu, “PSK performance with imperfectcarrier phase recovery,” IEEE Transactions onAerospace and Electronic Systems, Vol. AES-12, No.2,March 1976.

10. Tri Ti Ha, Digital Satellite Communications, 2ndEdition, Mc Graw-Hill Publishing Company, New York,1990.

11. S. A. Butman and J. R. Lesh, “The effects of band-pass limiters on n-phase tracking systems,” IEEETransactions on Communications, Vol. COM-25, No.6,June 1977.

Author informationP. Madhusudhan Rao is Head, Systems Development

and Maintenance Division of the National RemoteSensing Agency, Balanagar, Hyderabad - 500 037, India.P.K. Jain and Padmavathy C.S. are additionalresearchers involved with this project. All authors canbe reached at the above address, or by fax at +91 40277040.

20

15

10

5

020 40 60 80 100

With narrowband pre-PLL filter

Without narrowband pre-PLL filter

■ Figure 6. Plot of measured results using the data fromTables 1 and 2.