Non-Data Aided Approach for Carrier Recovery andModulation Identification of an M-ary PSK System

Imtiaz Ahmad Khokhar1, MIEEE Reeda Iftikhar2 Aitezaz Nawaz3 Khawar Shehzad4Dept. of Engineering Sciences, APCOMS, Ordnance Road, Rawalpindi, Pakistan

2. 3. 4.:

ABSTRACT Modulation identification and therecovery of the carrier lead to many applications in thedigital communication system. Techniques developed so

far for carrier recovery and modulation identificationare all statistical. In this paper efforts are made to use a

deterministic method rather than statistical. Zerocrossing detection method is recommended for use torecover carrier from frequency and amplitudemodulated systems. In this paper some modificationshave been suggested for the application of the same

system to make it useful for QAM and PSK as well.Based on the method presented by R. W. Wall, a

modified Zero Crossing Detection algorithm has beenused for carrier and phase extraction from an M-aryPSK (differential and non-differential) system. Inaddition, method has been developed for M-ary PSKsystem identification.

Key words: modulation identification, zero crossingdetection, M-ary PSK Identification

I. Introduction

Automatic recognition of digital modulation formats isbecoming increasingly important. Owing to rapid increasein the sophistication of the digital signaling system, theproblem of modulation classification within a set of knownconstellations has been fairly well studied in the recentliterature. Statistical and deterministic approaches are thebasis for the implementation of carrier recovery. The use ofFast Fourier Transform (FFT), peak amplitude and KalmanFiltering is one way which maybe used for the recovery ofcarrier [1]. Other methods include the Open Loop TanlockCarrier Recovery Structure [2], the Dual Mode CarrierRecovery Circuit for Adaptive Carrier Tracking [3],Constant Modulus Algorithm [4] and Maximum Likelihood(ML) Carrier Recovery [5].

Zero crossing detection is the most common method tomeasure the frequency and phase of any carrier [6]. Theonly problem here is that most zero crossing detectionschemes use multiple periods in order to extract thefrequency component [6].

The same approach of zero crossing detection has beenemployed for extracting the carrier frequency. In theproposed scheme, in addition to this, the analysis of thecomplete signal and identification of the phases usingdifferent mathematical concepts has been achieved. The

approach uses less number of symbols to achieve exactfrequency and phase tracking. It is a fast carrier tracker.

II. Signal Structure

The input signal to the receiver is of the type

r(x) = A sin(wc + $);

Where A is the amplitude, wc is the angular carrierfrequency and (D is the phase of the signal.

(D is the parameter used for detection of phase in M-aryPSK signal. While computing the carrier frequency, wc isof interest.

III. Zero Crossing Detection

The concept of 'Bisection Method' forms the basis of theproposed ZCD. Measuring the number of cycles over

multiple periods helps to reduce errors caused by phasenoise. This makes the perturbations in zero crossings smallrelative to the total period of the measurement.

The zero crossings have to be detected such that the twosampled points exist on both the negative and the positiveregions of a half cycle as shown in fig. 1.

nottdet eted

/

det ested

Fig. 1: Regions for Detection of Zero Crossings.

Taking into consideration, the change of regions frompositive to negative with time index 't1' and negative topositive with 't2'as depicted in fig 2.

The frequency extracted by this method is evaluated using:

fc = IAt22

where At= t2 -tl1

1-4244-1494-6/07/$25.00 C 2007 IEEE

l.i

:h de % -it

Fig. 4: Observation windowFig. 2: Zero Crossings of a Signal

The fc for all consecutive zero crossings are thus computedand the repeating value is retained. This enables theextraction of the carrier frequency for different phases ofthe signal, independent of the change in its phases.

IV. Phase Detector

d

......*

,.....................................................I

I'l)

As the algorithm computes for every change in the region,it automatically checks for any change in the distancebetween previous zero crossings. The repeating distance isconsidered and the deviating values are rejected.

The phases are identified using the inverse sine functionwhich converts the signal into its component phases. Thetranslation achieved manhandles a number of phases.Resulting from which, certain phase regions are notidentified correctly. The phase dimension is characterizedinto 4 regions, 0-90, 91-180,181-270 and 271-360. The sineinverse results are misleading in the way that a phase fromregion 2 is incorrectly mapped in region 1 and the same istrue for the other two regions. The problem arises betweenthe regions 1 and 2 as well as between the regions 3 and 4.

|v To eliminate this, the derivative of the phases is taken.Positive slopes dictate that the phase is either in the 1st orthe 4th region whereas negative slopes identify the regions 2or 3. Fig. 5 shows the actual received signal and the phasesextracted from it.

(A,ZC

Fig 3: Block diagram of the Proposed Scheme

All the phases of the received signal are calculated butsome are not conceived properly. The receiver is not able todistinguish some phases from each other. Comparison ofthese and their slopes is used to eradicate this problem. It isdiscussed in what follows.

V. Simulation and Results

The performance of the algorithm derived in the previoussection has been assessed by considering a randomsinusoidal signal consisting of a number of phasedeviations as can be seen in fig. 4. In the fig. 4 length of theobservation window is set to 3 symbols. The modulationformat considered is M-ary PSK.

Zero crossing detection enables the carrier extraction.Consecutive zero crossings are considered and theirdistance is calculated.

Fig.5: Top: Received phases after applyinginverse. Bottom: Received signal

q = sin '[sin(wc *t + s)](p represents the phase.

For the computation of slope:

d($)dt

VI. Decision Conditions:

1. If (p>0y >0

then

and

,l = abs(qp)2. If (p>0 and

y <0then

,8 =180-abs(9)

3. If (p<Oy <0

then

and

,8 =180+abs(9)

4. If (p<0y >0

then

and

,8 = 360 - abs(9p)where ,B is the correctly identified phase.

Thus, the above mathematical expressions enable thecorrect identification of the phase, ,B, for any M-ary PSKsignal.

Catering for the differential PSK scheme, a predefinedcyclic table is maintained for true recognition of phase.Initially the phase is set to be 0. On receiving the signal, thephase is calculated and the table is updated with the newvalue. This phase is subtracted from the previous phasekept in the table and this is considered to be the differentialphase. Each differential phase kept in the table is assigned aspecific numerical value. Upon calculating the differencebetween the current phase and the previous, thecorresponding numerical value is computed as:

= abs[/Jn-/,n1](360/M)

Where 11(n) is the current phase and 11(n 1) is theprevious phase, M is the value of the M-ary PSKmodulation technique.

This numerical value 'v' determines the number of hops tobe taken by the table from the previous phase to the currentphase which now becomes the top most value of the cyclictable. In the same way, the table updates dynamicallyaccording to the on coming phases. The table caters for upto 128 PSK, having 128 hops with an increment of 2.8125between two consecutive phases. The phases achieved canbe seen as in fig. 6.

Fig. 6: Received phases after identification

VII. CONCLUSION

Novel NDA algorithms for carrier phase and frequencyrecovery including modulation identification for M-aryPSK have been derived by applying a deterministicapproach. Development of this system is a step towards thedesign of universal transceiver system. The proposedestimation technique is suitable for digital implementation.Simulations indicate that the estimation algorithm providesa better performance than many other techniques.

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