antennas resonating at the same frequency, fabricated on differentsubstrates. Variation in the percentage bandwidth with feed seg-ment length (S3) is shown in Figure 3.

Radiation patterns of the antenna at the operating band edgesand midband frequencies for the above feed parameters are shownin Figure 4. The HPBW of the antenna in the E and H planes are92° and 66°, respectively, at the resonant frequency. The crosspolarization of the antenna is better than �30 dB.

4. CONCLUSIONS

A microstrip antenna with an electromagnetically coupled L-stripfeed giving large bandwidth is presented. The remarkable featureof the proposed antenna is its compact structure to achieve en-hanced bandwidth. The feeding technique is very simple comparedto the other methods.

REFERENCES

1. A. Shackelford, K.F. Lee, D. Chatterjee, Y.X. Guo, K.M. Luk, and R.Chair, Small-size wide-bandwidth microstrip patch antennas, IEEEAP-S International Symposium, Boston, MA, Vol. 1, pp. 86–89, 2001.

2. M. Clent and L. Shafai, Wideband single layer microstrip antenna forarray applications, Electron Lett 35 (1999), 1292–1293.

3. C.L. Mak, K.M. Luk, K.F. Lee, and Y.L. Chow, Experimental study ofa microstrip patch antenna with an L-shaped probe, IEEE Trans An-tennas Propagat AP -48 (2000), 777–782.

© 2002 Wiley Periodicals, Inc.

ANALYSIS AND DESIGN OFAN ADAPTIVE POLYNOMIALPREDISTORTER WITHTHE LOOP DELAY ESTIMATOR

Donghyun Kim and Sangseol LeeDivision of Electronic and Computer EngineeringHanyang UniversitySeoul 133-791, Korea

Received 17 January 2002

ABSTRACT: Most adaptive linearization circuits for the nonlinear am-plifier have a feedback loop that returns the output signal of the ampli-fier to the linearizer. The loop delay of the linearizer must be controlledprecisely so that the convergence of the linearizer should be assured. Inthis Letter a delay control circuit is presented. It is a delay lock loop(DLL) with a modified early–late gate and can be easily applied to aDSP implementation. The proposed DLL circuit is applied to an adap-tive linearizer with the use of a polynomial predistorter, and the simula-tion for a 16-QAM signal is performed. The simulation results show thatthe proposed DLL eliminates the delay between the reference input sig-nal and the delayed feedback signal of the linearizing circuit perfectly,so that the predistorter polynomial coefficients converge into the opti-mum value and a high degree of linearization is achieved. © 2002Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 117–121, 2002;Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.10391

Key words: adaptive linearization; loop delay estimator; DLL

1. INTRODUCTION

Nowadays many communication systems adopt linear digital mod-ulation schemes that have high spectral efficiency. These modula-tion schemes require the linearity of the communication system.To maintain high-quality communications services, it is very im-

portant to eliminate distortion of the transmitted signal. Thereforethe nonlinearity of the power amplifier, which is a major contrib-utor of nonlinearities in the transmitter, should be eliminated.Nonlinearity in a power amplifier generates in-band and out-of-band distortion by spectral regrowth, which causes the adjacentchannel interference and degradation in the BER. Many lineariza-tion schemes, such as the backoff method, the LINC, the feedfor-ward amplifier, the envelope elimination and restoration, the pre-distortion and the postdistortion are proposed [1–5]. Recentlyadaptive methods are widely used to keep the linearity regardlessof ambient environments.

The structure of the adaptive linear power amplifier systemnecessarily has the part to compare the input signals of the linear-izer to the feedback signals of the high power amplifier (HPA)output. The feedback signals of the HPA output are delayed acertain amount of time compared to the input signal of the linear-izer. This delay must be eliminated so that the comparison of thefeedback signal of the HPA output to the corresponding input ofthe linearizer can be performed in the same phase. To adjust thisdelay, the analog delay circuit that is affected by the ambientenvironments are typically used to delay the input signal of lin-earizer. To reduce the effect of the ambient environments, the loopdelay estimator is proposed by Nagata [6] and Wright and Durtler[7]. The delay estimator proposed by Nagata is known to belacking in accuracy, and the one by Wright and Durtler estimatesthe delay by FFT, which requires a tedious and time-consumingcomputation. In this Letter the DLL circuit that uses the modifiedearly–late gate as the discriminator is proposed. The proposedDLL, which can easily be implemented in the DSP, is applied tothe linearizer proposed by Ghaderi, Kumar, and Dodds [8].

The linearizer structure proposed by Ghaderi et al. has a poly-nomial-type predistorter that is appropriate to a DSP applicationbecause it has low memory requirements and simple numericalcomputations. But Ghaderi’s work has the potential instabilitycaused by the delay variations. A modified structure is presentedand simulated. The simulated results show that the proposed DLLcan compensate the delay between the linearizer reference inputand the delayed feedback HPA output. The predistorter polynomialcoefficients also converge and a high degree of linearization can beachieved.

2. STRUCTURE AND OPERATION OFTHE POLYNOMIAL PREDISTORTER

Figure 1 shows the linear amplification system with an adaptivepredistorter. In this system, the inputs of the DSP block are thedigital-filtered baseband in-phase (I) and quadrature-phase (Q)signals and the first intermediate frequency (IF) local-oscillator(LO) signal. The DSP block includes the predistorter and the DLLdiscriminator to control the clock phase of the ADC (analog-to-digital converter) that samples the output of the HPA. In the DSPblock, the baseband I and Q signals are predistorted and thepredistorted signal is upconverted to the first IF band. Then theup-converted signal is applied to the DAC (digital-to-analog con-verter). It is converted to the second IF band and then to the RF

Figure 1 Linear amplification system with the adaptive predistorter

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 34, No. 2, July 20 2002 117

signal. This structure can filter the image signal of the mixer outputeasily. The output of the HPA is downconverted with the use of thesame RF LO through the directional coupler, and is filtered by theBPF through the feedback path. The BPF must have enoughbandwidth not to distort the coupled HPA output, which hasbroader bandwidth than the original bandwidth due to spectralregrowth. Then the downconverted signal by the RF LO is con-verted to the first IF band and is applied to the ADC. In thisprocedure, the clock phase of the ADC should be controlled so thatthe ADC can sample the feedback signal of the same phase as thatof the reference input signal to be compared. The structure of theadaptive predistortion part of the DSP block in Figure 1 is shownin Figure 2.

The baseband polynomial predistorter in Figure 2 is similar tothe Ghaderi’s predistorter. But in the present predistorter, aquadrature modulator (QM) is added, and the analog envelopedetector is replaced by the amplitude computation ri(n) ��I(n)2 Q(n)2, where I(n) is the inphase input signal of thelinearizer and Q(n) is the quadrature phase one. Also, the variableanalog delay element is replaced by the fixed delay element. Theinput of the DSP block is the first LO signal, which is used for theprecise operation of the quadrature demodulator (QDM). Thedifficult operation with a dc signal can be avoided, because thepredistorter output is the first IF band signal.

In Figure 2, the inputs I(n) and Q(n) of the predistorter aremultiplied by the predistortion gain GI,n(ri(n)) and GQ,n(ri(n)),respectively. These baseband predistorted signals are applied to theQM, which upconverts these signals to the first IF band. The D–Aconverted QM output is upconverted and amplified by the nonlin-ear HPA. The feedback signal from the HPA is applied to theQDM, the output of which is rotated by a certain amount � to raisethe convergence speed of the adaptation algorithm. These rotatedsignals xia(n) and xqa(n) are used to determine gains of thepostdistorter. YI,n(ro(n)) and YQ,n(ro(n)) are the in-phase andquadrature-phase gains of the postdistorter, respectively, wherero(n) is the amplitude of feedback signal. These postdistorter gainsare multiplied by ro(n), and are compared to predistorter gainsmultiplied by ri(n). The differences are eI(n) and eQ(n), whichare used as the error in the adaptation algorithm. The postdistortergain polynomial that minimizes these errors can be obtained, andthe predistorter gain polynomial is obtained from the relation ofYI,n(ro(n)), YQ,n(ro(n)) and GI,n(ri(n)), GQ,n(ri(n)).

The discriminator structure of the DLL is shown in Figure 3.The inputs of the DLL are ri(n) and ro(n), and the output of thediscriminator D�( ) is given by

D�� � � ro�t � Td��ri�t � Ts � Tdˆ� � ri�t � Ts � Td

ˆ��, (1)

where � �Td � Tdˆ �/Ts, Td is the delay time, Td

ˆ is the estimateddelay time, and Ts is the sample period. The discriminator inFigure 3(b) is similar to the conventional discriminator of Figure3(a), except that the delay having the symbol period T is replacedby the delay having the sample period Ts. The output of thediscriminator is filtered by the loop filter and is used as the controlvoltage of the VCXO in Figure 1. The phase of the VCXO clockis varied by the control voltage, so the sampling phase of the ADCthat sample ro is varied. By these controls, the delay in thefeedback signal of the HPA is eliminated. The phase error of theDLL is similar to that of the conventional DLL, and so can bewritten as [9]

Td�s� � Tdˆ�s�

Ts�

Td�s�

Ts� s

s � kdgcF�s�� , (2)

where kd is �2P(1 1/N) multiplied by the gain of multiplierused in the discriminator, where P is the input power of thelinearizer, and N is the noise power. In (2), gc is the gain of theVCXO, F(s) is the transfer function of the loop filter, and s isthe Laplace transform variable. In (2), the noise can be regardedas the difference between ri(n) and ro(n) caused by the distortionof the HPA. Therefore the SNR in the DLL circuit is given by

SNR � 10 log10

ri�n�2

ri�n� � ro�n�2 . (3)

3. ADAPTIVE ALGORITHM

The error of the RLS algorithm depends on the coefficients of thegain polynomials linearly. Also, the cost function given as the

Figure 3 Discriminator structure

Figure 2 Polynomial predistorter

118 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 34, No. 2, July 20 2002

square of the error can be minimized. The predistorter polynomialsare defined as [8]

GI,n�ri�n�� � �m�1

M

�i,m,nrim�1�n�, (4)

GQ,n�ri�n�� � �m�1

M

aq,m,nrim�1�n�, (5)

where n � 1, 2, 3, . . . , N. �i,m,n and �q,m,n are the mthcoefficient of the inphase and quadrature phase predistorter poly-nomial for the nth sample, respectively. Similarly, the postdistorterpolynomials are defined as

YI,n� xia�n�, xqa�n�� � �m�1

M

aii,m,nxiam�1�n� � �

m�1

M

aiq,m,nxqam�1�n�, (6)

YQ,n� xia�n�, xqa�n�� � �m�1

M

aqi,m,nxiam�1�n� � �

m�1

M

aqq,m,nxqam�1�n�, (7)

where n � 1, 2, 3, . . . , N. aii,m,n, aiq,m,n, aqi,m,n, and qqq,m,n

are mth coefficients of the postdistorter polynomial for the nthsample, and subscripts i and q denote inphase and quadraturephase, respectively. In (6) and (7), xia(n) and xqa(n) are given asxia(n) � ro(n) cos �o(n), xqa(n) � ro(n) sin �o(n), where�o(n) � �o(n) � �i(n) �. Here �i(n) is the phase of the inputsignals of the linearizer, and �o(n) is that of the feedback signal.If the amplifier has the monotonic increasing input–output rela-tion, after the convergence of the algorithm, ri(n) � ro(n),�i(n) � �o(n) can be obtained, and YI,n� � YI,n�1� andYQ,n� � YQ,n�1� result. From this, the following relations canbe obtained:

GI,n�ri�n�� � YI,n�1�ri�n� cos �, ri�n� sin ��, (8)

GQ,n�ri�n�� � YQ,n�1�ri�n� cos �, ri�n� sin ��. (9)

If (4)–(7) are applied to (8) and (9) the following relation isobtained:

�i,m,n � �cos ��m�1aii,m,n�1 � �sin ��m�1aiq,m,n�1, (10)

�q,m,n � �cos ��m�1aqi,m,n�1 � �sin ��m�1aqq,m,n�1, (11)

where m � 1, 2, 3, . . . , M. These equations show that thecoefficients of the predistorter are in linear relations to the coef-ficients of the postdistorter.

The cost function to find the polynomial coefficients that min-imize the error can be written as the following vector forms:

JI�n� � �l�1

n

�ri�l �GI,l�ri�l �� � AiT�n�uiq�l ��

2, (12)

JQ�n� � �l�1

n

�ri�l �GQ,l�ri�l �� � AqT�n�uiq�l ��

2, (13)

where the postdistorter coefficient vectors Ai(n), Aq(n), anduiq(n) are given by

Ai�n� � �aii,1,n, aii,2,n, aii,3,n, . . . ,

aii,M,n, aiq,1,n, aiq,2,n, aiq,3,n, . . . , aiq,M,n�T, (14)

Aq�n� � �aqi,1,n, aqi,2,n, aqi,3,n, . . . ,

aqi,M,n, aqq,1,n, aqq,2,n, aqq,3,n, . . . , aqq,M,n�T, (15)

uiq�l � � �ro�l �, ro�l �xia�l �, . . . ,

ro�l �xiaM�1�l �, ro�l �, ro�l �xqa�l �, . . . , ro�l �xqa

M�1�l ��T. (16)

The coefficient vectors Ai(n) and Aq(n) that minimize cost func-tions JI(n) and JQ(n) can be obtained by the following recursiveequations:

Ai�n� � Ai�n � 1� � kiq�n�e�I�n�, (17)

Aq�n� � Aq�n � 1� � kiq�n�e�Q�n�, (18)

where the gain vector kiq(n) and the errors of the algorithm e�I(n)and e�Q(n) are as follows:

kiq�n� �Piq�n � 1�uiq�n�

1 � uiqT �n�Piq�n � 1�uiq�n�

, (19)Figure 4 The transfer function of the power amplifier

Figure 5 PSD of the input and output of the HPA without predistorter

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 34, No. 2, July 20 2002 119

e�I�n� � ri�n�GI,l�ri�n�� � uiqT �n�Ai�n � 1�, (20)

e�Q�n� � ri�n�GQ,l�ri�n�� � uiqT �n�Aq�n � 1�. (21)

The update equation of the inverse correlation matrix is given by

Piq�n� � Piq�n � 1� � kiq�n�uiqT �n�Piq�n � 1�. (22)

The initialization value is

Piq�0� � c�1I, (23)

Ai�0� � Aq�0� � 0, (24)

where c is the very small positive constant. In conclusion, thepolynomial coefficients of the predistorter are obtained from (10)and (11).

4. SIMULATION RESULTS

The AM-AM and AM-PM distortion characteristics of the HPAused for the simulation are shown in Figure 4. The HPA model isthe model proposed by Saleh and Salz [10], which is similar to thatof the TWTA (traveling wave tube amplifier). The simulation isperformed for the 16-QAM raised cosine filtered signal with therolloff factor of 0.25. The symbol rate is 12.5 ksps and the sample

rate is 64 times the symbol rate, that is, 64 12.5 kHz. Theoperation of the quadrature modulator and demodulator is assumedto be perfect. And an input backoff of 2 dB from the saturationpoint of the amplifier and a rotation angle � � 50° is used [8]. Thepredistorter with the fourth-order gain polynomial is simulated.The initial values of the predistorter gain polynomial are given by�i,1,0 � 1, �i,2,0 � 0, �i,3,0 � 0, �i,4,0 � 0, �i,5,0 � 0,�q,1,0 � 0, �q,2,0 � 0, �q,3,0 � 0.1, �q,4,0 � 0, �q,5,0 � 0.For ADC and DAC, 14 bits are used, which is selected so that thespectral spreading due to quantization error can be avoided.

The normalized input and output power spectral density (PSD)of HPA for the 16-QAM signal is shown in Figure 5, which showsthe spectral regrowth. The characteristics of the proposed discrim-inator for the lead feedback signal and the lag feedback signal isshown in Figure 6, which shows the typical S curve. This meansthat the proposed discriminator can appropriately operate as thedelay discriminator. As noted by [6], the delay within 1

64symbol

can be tolerated by the algorithm, so the results are enough tosatisfy the required delay specification. Figure 7 shows the outputPSD of the HPA without the DLL for the delayed signal. Theresults show that the lag feedback signal has a worse influence onthe convergence of the algorithm than the lead one. Figure 8 showsthe output PSD of the HPA with the DLL for the delayed signal.Comparison of Figures 7 and 8 shows that more than 10-dBimprovement is achieved in Figure 8. Table 1 shows the predis-torter coefficients after convergence. Figure 9 shows the amplitudeand phase errors of the linearizer with DLL for a delayed signal. Itshows that the amplitude and phase errors are reduced to about 2%after five symbols.

5. CONCLUSION

In this Letter the polynomial predistortion linearizer with the DLLusing the modified discriminator is proposed and its performancesfor the 16 QAM signal have been simulated. The simulation resultsshow that the adaptive linearizer with the modified DLL keeps thestability despite the delay variation. Therefore the adaptive algo-rithm can maintain stable operation and the convergence. The

Figure 6 The characteristics of the proposed discriminator

Figure 7 PSD of the output of the HPA with the predistorter for thedelayed signals

Figure 8 PSD of the output of the HPA with the predistorter and theDLL

TABLE 1 Coefficients of the Predistorter Gain Polynomial

k 1 2 3 4 5

�i,k,n 0.504938 �0.057371 0.370701 �0.465841 0.380483�q,k,n �0.006459 0.103791 �0.660140 1.095246 �0.865855

120 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 34, No. 2, July 20 2002

proposed DLL can replace the analog delay circuit that has diffi-culty in tuning, so the delay variation by the environment such asthe ambient temperature can be overcome. More than 10-dB im-provement in the PSD is achieved, and the amplitude and phaseerrors are reduced to 2% after five symbols.

REFERENCES

1. P.B. Kenington, High-linearity RF amplifier design, Artech House,Dedham, MA, 2000, pp. 425–442.

2. J.K. Cavers, Amplifier linearization by adaptive predistortion, UnitedStates Patent No. 5,049,832, September 1991.

3. L.D. Quach and S.P. Stapleton, A postdistortion receiver for mobilecommunications, IEEE Trans Veh Tech VT-42 (1993), 604–616.

4. D.C. Cox, Linear amplification with nonlinear components, IEEETrans Commun COM-22 (1974), 1942–1945.

5. J.S. Cardinal, New adaptive double envelope feedback (ADEF) lin-earizer for solid state power amplifier, IEEE Trans Microwave TheoryTech MTT-43 (1995).

6. Y. Nagata, Linear amplification technique for digital mobile commu-nications, in Proc IEEE Veh Tech Conf, San Francisco, CA, 1989, pp.159–164.

7. A.S. Wright and W.G. Durlter, Experimental performance of an adap-tive digital linearized power amplifier, IEEE Trans Veh Tech VT-41(1992), 395–400.

8. M. Ghaderi, S. Kumar, and D.E. Dodds, Fast adaptive polynomial Iand Q predistorted with global optimisation, IEE Proc Commun 143(1996), 78–86.

9. R. Peterson et al., Introduction to spread spectrum communications,Prentice-Hall, Englewood Cliffs, NJ, 1995.

10. A.A.M. Saleh and J. Salz, Adaptive linearization of power amplifiersin digital radio systems, Bell Syst Tech J 62 (1983), 1019–1033.

© 2002 Wiley Periodicals, Inc.

OPTICAL WDM RINGSUSING A SMART WAVELENGTHROUTING ASSIGNMENT

Abelardo Podcameni and Marbey MossoCenter for the Telecommunications Studies of the Catholic Universityof Rio de JaneiroRua Marques de Sao Vicente 22522453-900 Rio de Janeiro, Brazil

Received 3 January 2002

ABSTRACT: Functionality is inserted into the physical layer of WDMoptical networks in order to provide for an efficient carrier routing andpacket-addressing scheme. No optoelectronic conversions are neededalong the network nodes, except at the source and destination nodes.Tuned transmitters or receivers are not used. The ancillary networkrouting management structure is dramatically reduced, together with thetotal network cost. Simple and efficient mechanisms to avoid optical car-rier modulation inefficiency and data collision are introduced. © 2002Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 121–125, 2002;Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.10392

Key words: optical networks; optical networking; optical fiber; opticalrings; wavelength routing; wavelength assignment; SONET; WDM; datacollision

1. INTRODUCTION

In classical optical WDM transport, a significant network costburden is the one associated with packet routing. Conversionbetween the optical and electrical domains, as well demultipl-exation, may be necessary for all carriers at each node. Thisconversion means extracting the specific data packets addressedto the said node [1] and properly rerouting the through traffic.In the future for instance, using (generalized) multiprotocollabel (Lambda) switching—(G)MPL(�)S—arrangements, willstill require substantial processing to read labels for properrouting and to deal with a complex multilevel protocol [2]. Theeffect will be to decrease data transmission efficiency and toincrease cost. When the network is finally put into service, anyfurther scalability operation, with new route branches and/orroute extensions, will affect each single node and dramaticallyincrease costs of the overall routing management [3, 4].

New architectures are being enthusiastically pursued to sim-plify the routing system or to reduce routing cost [5]. The presentscenario is such that there is a great expectation with respect toall-optical networks. However, all-optical networks are not yetfully commercially available. Network engineers are eager to seea wavelength (without suffering E/O conversions) cleverly findingits path through a quite simple network. Efficient and immediatesolutions, using well-established components, are then most wel-come.

A clever wavelength routing scheme may be one where acertain carrier finds its final destination by means of an ingeniousfunctionality added to the physical layer. An optical add-and-dropmultiplex (OADM) set, combined with a precise assignment of thelaunched wavelengths, is introduced and arranged in such a waythat a certain carrier will progress through the network, and find itsown way toward its designated node in a passive way.

These above arrangements have already been described [6],although only for very simple cases as a broadcast-and-select star.For an all-optical ring network, Marsan offered an elegant solution

Contract grant sponsor: CNPq; Contract grant number: 300019/92-0

Figure 9 The amplitude and phase error of the linearizer with the DLLfor a delayed signal

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 34, No. 2, July 20 2002 121