A Tutorial on Microwave Photonic Filters

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 1, JANUARY 2006 201

A Tutorial on Microwave Photonic FiltersJos Capmany, Senior Member, IEEE, Fellow, OSA, Beatriz Ortega, Member, IEEE, and

Daniel Pastor, Associate Member, IEEE

Tutorial

AbstractMicrowave photonic filters are photonic subsystemsdesigned with the aim of carrying equivalent tasks to those of anordinary microwave filter within a radio frequency (RF) systemor link, bringing supplementary advantages inherent to photonicssuch as low loss, high bandwidth, immunity to electromagneticinterference (EMI), tunability, and reconfigurability. There is anincreasing interest in this subject since, on one hand, emerg-ing broadband wireless access networks and standards spanningfrom universal mobile telecommunications system (UMTS) tofixed access picocellular networks and including wireless localarea network (WLAN), World Interoperability for Microwave Ac-cess, Inc. (WIMAX), local multipoint distribution service (LMDS),etc., require an increase in capacity by reducing the coveragearea. An enabling technology to obtain this objective is based onradio-over-fiber (RoF) systems where signal processing is carriedat a central office to where signals are carried from inexpensiveremote antenna units (RAUs). On the other hand, microwavephotonic filters can find applications in specialized fields such asradar and photonic beamsteering of phased-arrayed antennas,where dynamical reconfiguration is an added value. This paperprovides a tutorial introduction of this subject to the reader notworking directly in the field but interested in getting an overallintroduction of the subject and also to the researcher wishing toget a comprehensive background before working on the subject.

I. INTRODUCTION

BY MICROWAVE photonic filter [1][5], we understanda photonic subsystem designed with the aim of carryingequivalent tasks to those of an ordinary microwave filter withina radio frequency (RF) system or link, bringing supplemen-tary advantages inherent to photonics such as low loss, highbandwidth, immunity to electromagnetic interference (EMI),tunability, and reconfigurability. The term microwave will befreely used throughout this paper to designate either RF, mi-crowave, or millimeter-wave signals. These terms will be usedinterchangeably.

The use and advantages of microwave photonic filters havebeen thoroughly described in various references in the liter-ature. Here, we will use a simple example to illustrate thisconcept. Fig. 1 depicts a typical application configuration fora moving target identification (MTI) ground radar system [5].

Manuscript received July 15, 2005; revised September 9, 2005. Thiswork was supported by TIC2002-04344-C02-01 PROFECIA, IST-2001-37435LABELS, the networks of excellence IST-EPIX, IST-EPHOTON/ONE, andIST NEFERTITI, and the Spanish government ayudas a parques cientficos.

The authors are with the Institute of Telecommunications and Multimedia(ITEAM), Universidad Politecnica de Valencia, Valencia 46022, Spain (e-mail:[email protected]).

Digital Object Identifier 10.1109/JLT.2005.860478

The MTI radar uses the Doppler effect to separate the targetsof interest from clutter (land, sea water, rain, etc.). To dothis, the radar sends a pulse sequence with pulse width and interpulse period PRI = 1/PRF, where PRF identifies thepulse repetition frequency. Any moving object will generatea Doppler frequency shift of the radar central frequencyfo according to its speed (dR/dt), where R(t) designates thetime-varying distance from the target to the radar. The spectralsignature of each object repeats in the spectrum periodicallywith a period given by the PRF, which obviously sets the limiton determining an unambiguous Doppler shift.

Thus, focusing on a spectral region from fo to fo + PRFis enough to get all the information regarding moving targetsand clutter, and what is required after signal detection is asignal processing stage to carry out the filtering of clutterand noise (the unwanted signals) from the target(s). This isusually performed as shown in the upper part of Fig. 2 by usinga digital notch filter placed after frequency down-conversionto baseband and using analog to digital conversion (ADC).In order to distinguish the small echo from the target andthe large echo from the fixed objects, high-performance (14-to 18-bit resolution) ADCs are required, which represents amajor bottleneck in the system. If the clutter can be removedbefore down-conversion, then the high-resolution requirementson the ADCs can be relaxed. For example, with a 30-dB clutterattenuation, the required ADC resolution is reduced by 5 bits.This operation is difficult and costly in the microwave domainbut is simple if the RF signal is modulated into an optical carrierand the whole signal is processed directly in the optical domainby means of a photonic filter as shown in the lower part ofFig. 2.

The former example illustrates the general concept behindmicrowave photonic filters [1][5], which is to replace thetraditional approach toward RF signal processing shown in theupper part of Fig. 3, where an RF signal originating at an RFsource or coming from an antenna is fed to an RF circuit thatperforms the signal processing tasks (usually at an intermediatefrequency band after a down-conversion operation) by a noveltechnique. In this approach, which is shown in the lower partof Fig. 3, the RF signal that was priorly made to modulate anoptical carrier is directly processed in the optical domain by aphotonic filter based on fiber and integrated photonic devicesand circuits.

Adding extra photonic components implies increased filtercomplexity on one hand but brings on the other several ad-vantages as pointed out in most of the published literature

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202 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 1, JANUARY 2006

Fig. 1. Example of application of a microwave photonic filter to ground MTI radar.

Fig. 2. (Above) Typical signal processing configuration in an MTI radar system. (Below) Modified version including a microwave photonic filter prior todown-conversion.

[6][44]: Optical delay lines have very low loss (independentof the RF signal frequency), provide very high time band-width products, are immune to EMI, are lightweight, and canprovide very short delays that result in very-high-speed sam-pling frequencies (over 100 GHz in comparison with a fewgigahertz with the available electronic technology). Finally, butnot less important optics provides the possibility of spatial andwavelength parallelism using wavelength division multiplexing(WDM) techniques.

The purpose of this paper is to provide a tutorial introductionof this subject to the reader not working directly in the fieldbut interested in getting an overall introduction of the subjectand also to the researcher wishing to get a comprehensivebackground before working on the subject. To this aim, we havestructured the paper in five parts.

Section II provides an introduction to the theory of mi-crowave photonic filters, including some very basic conceptsto understand their operation as discrete time filters and theirapplications, and a more detailed description of the opera-

tion of single-source microwave photonic filters (SSMPFs)and multiple-source microwave photonic filters (MSMPFs).Section III presents and discusses their potential optical andelectrical-driven limitations and the basic parameters used toevaluate their performance such as link gain, noise figure,spurious free dynamic range (SFDR), etc.

In Section IV, we describe some of the main proposals for theimplementation of microwave photonic filters published in theliterature. Obviously, there is a considerable amount of workcarried by different research groups during the last years and itis impossible to describe them in detail, so we will concentrateon those that either are useful to understand the theoreticalaspects, as described in Section II, or constitute a significantachievement.

Finally, Section V provides a summary, conclusions, andfuture challenges within this field of research. A complete ref-erence list of the subject including more than 70 bibliographicalitems is provided to assist the reader interested in getting morein-depth coverage of the subject.


CAPMANY et al.: TUTORIAL ON MICROWAVE PHOTONIC FILTERS 203

Fig. 3. General concept behind microwave photonic filters. The upper part shows the traditional configuration. The lower part shows the replacement of the RFfilter by a microwave photonic filter.

Fig. 4. General reference layout of a microwave photonic filter showing the relevant electrical and optical signals.

II. THEORY OF MICROWAVE PHOTONIC FILTERS

A. General Concepts

A microwave photonic filter is a photonic structure, theobjective of which is to replace a standard microwave filterused in an RF system, bringing a series of advantages (tun-ability, reconfigurability, electromagnetic immunity, etc.) thathave been outlined in the prior section [1][5]. Fig. 4 shows ageneral reference layout of a microwave photonic filter that we

will use to explain some of the basic concepts involved in itsdescription.

Referring to the upper part of Fig. 4, the RF to opticalconversion is achieved by directly (or externally) modulatingeither a single continuous wave (CW) source or a CW sourcearray. The input RF signal si(t) is then conveyed by the opticalcarrier(s) and the composite signal is fed to a photonic circuitthat samples the signal in the time domain, weights the samples,and combines them using optical delay lines and other photonic



elements. At the output(s), the resulting signal(s) is opticallyRF converted by means of various optical receivers producingthe output RF signal so(t).

The lower part of Fig. 4 shows an equivalent black-box repre-sentation of the aimed performance of the microwave photonicfilter. In essence, it is expected to relate linearly the input andoutput RF signals by means of an impulse response h(t) in thetime domain or by a frequency response H() in the frequencydomain. In practice, however, this linear relationship canonly be obtained under special operating conditions. Why thishappens can be understood by observing Fig. 4. Here, the onlyguaranteed signal linearity is that relating the input Ei(w) andoutput Eo(w) optical fields to the optical subsystem by virtueof the linearity of Maxwells equations. This linear relationshipis established through an optical field transfer function Ho(w),and hence

Eo(w) = Ei(w)Ho(w). (1)

The conversion process from the input RF signal to the inputelectric field to the optical subsystem is a nonlinear processsince ei(t)

si(t), and similarly, the output RF signal is

nonlinearly related to the output electric field from the opticalsubsystem since so(t) |eo(t)|2, where stands for theensemble average over the possible signal fluctuations due tothe coherence properties of the single or multiple optical CWsources that are employed to feed the filter. The two nonlinearoperations described together with the linear relationship (1)do not yield under general circumstances an overall linearrelationship between si(t) and so(t), and in Sections II-B and Cwe will explore the conditions under which this overall linearrelationship is obtained in practice.

Let us assume for the time being that this linear operationregime is possible, and therefore

so(t) =N

r=Narsi(t rT ) so(t) = si(t) h(t)

h(t) =N

r=Nar(t rT ) =

Nn=N

h(n)(t nT ). (2)

According to the number of samples N in the impulseresponse sequence, the filter can be classified as either a finiteimpulse response (FIR) filter if N 3000 [78] using a novel technique to obtainsingle resonance microwave filters.

Finally, the filter rejection of nonadjacent channels is mea-sured through the main to secondary sidelobe ratio (MSSR) alsoshown in Fig. 5.



Fig. 5. Typical periodic spectrum of a microwave photonic filter showing the relevant parameters.

B. SSMPFs [6][15]SSMPFs are characterized, as its name indicates, by the

use of only one optical source to feed the filter. The sourceoutput electric field

Iie

j(wot+(t)) (where Ii represents theoptical intensity, wo the source central frequency, and (t)the source phase fluctuations) is modulated by the RF inputsignal si(t) and the different filter samples are implemented bymeans of delayed and windowed replicas of the RF-modulatedoptical carrier. In Fig. 6(a) and (b), we show two possibleimplementations of an FIR and an IIR SSMPF, respectively. Inthe first case, a transversal filter is shown where the electric fieldof the input RF-modulated optical signal is evenly divided intothe N outputs of a 1N coupler. Output port j, for instance,is connected to an attenuator, providing a field attenuationcoefficient aj1 and an optical delay (j 1)T , where T isthe filter basic delay. Filter samples are then evenly combinedby an output N 1 coupler. At the output port of this device,the overall electric field Eo(t) is composed of the interferenceof all the delayed and this signal is fed to an output photodiodethat converts the optical signal into the final output RF signalso(t). The overall filter structure thus relates the input andoutput microwave/RF signals given in volts or amperes. In thecase of the IIR structure, infinite samples of the modulatedelectrical field are generated. Fig. 6(b) shows, in particular, amicrowave photonic filter based on a single cavity recirculatingdelay line formed by joining together two output ports of a fibercoupler, providing a basic delay per cavity recirculation givenby T . The filter behavior is similar apart from the obvious dif-ference that in the first case, the structure produces N samples,whereas in the second, the number of samples is, in theory,infinite.

The filter operation in both cases is described by the follow-ing equation that gives the output electric field, i.e.,

E0(t) =Ii

N1r=0

[arsi(t rT )]12 ej(w0(trT )+(trT )). (7)

The upper number in the sum isN for the FIR case and N for the IIR case. The output current from the photodiode is

(assuming a detector responsivity )

I0(t) =|E0(t)|2

=IiN1r=0

[|ar|si(t rT )]

+ IiN1r=0

N1s =r

arassi(t rT )si(t sT )

((r s)T ) . (8)

In the above expression, represents the ensemble averageover the signal fluctuations due to the stochastic process de-scribing the source phase noise, and stands for the opticalsource degree of coherence, and we assume as it is customarythat phase fluctuations of the optical source are modeled by anergodic process

((r s)T ) e|(rs)T |coh . (9)

coh = 1/ is the source coherence time, which is in-versely proportional to the source linewidth in the absenceof modulation (i.e., under CW operation). A crucial aspect thatis connected with the filter operation is that of the optical sourcecoherence, as we shall now discuss.

In principle, filter linearity is only guaranteed in the opticalfields (due to the linearity of Maxwell equations) but not as faras optical powers are concerned. However, this last magnitudeis related to the input and output currents or voltages of theRF signals since there is a linear relationship between theoutput optical power and the input current/voltage at the sourceand between the input optical power and the output electricalcurrent/voltage at the optical receiver.

As shown in (8), the general shape of the output current iscomposed of two terms, an incoherent term where the outputcurrent/voltage is linearly related to the input RF signal and acoherent term that depends on the source degree of coherenceand destroys, in principle, power linearity.



Fig. 6. (a) Layout of an FIR SSMPF. (b) Layout of an IIR SSMPF.

If the optical source has a coherence time much smaller thanthe basic filter delay (coh T ), then the second term in (8)vanishes and a linear relationship between the input and outputRF signals results, i.e.,

I0(t) = so(t) = IiN1r=0

[|ar|si(t rT )] . (10)

Filters fulfilling this condition of operation are known asincoherent filters and bring in principle several advantages.For instance, the filter impulse response as seen in (10) doesnot depend on any optical phase. This makes these filtersvery stable against environmental conditions (i.e., temperature

variations, mechanical vibrations, etc.) and is the main reasonwhy most of the implemented architectures so far are basedon this paradigm. The main disadvantage is that the filtercoefficients are positive since, according to (8), the coefficientsare given by |ar| =

|ar|2. Thus, in principle, only filters withpositive coefficients can be implemented using this approach.In the early 1980s, Goodman, Moslehi, and others showed thatfilters with positive coefficients are severely limited since theyalways implement a resonance at baseband and, most notably,the range of transfer functions that can be implemented showspoor performance in terms of filter selectivity and roll-off.This limitation, however, has been overcome and, as we willsee in the next section, today it is possible to implement



incoherent filters with negative coefficients using a variety oftechniques.

On the other extreme, if the optical source has a coherencetime much bigger than the basic filter delay (coh > T ), thenthe filter works under coherent operation regime and (9) can beapproximated by

((s r)T ) = ejwo(sr)T . (11)

Therefore, (8) is now given by

so(t) = IiN1r=0

[|ar|si(t rT )]

+ IiN1r=0

N1s =r

arassi(t rT )si(t sT )ejwo(sr)T .

(12)

As it can be observed, the output RF signal is composed bya set of weighted and delayed replicas of the RF-modulatingsignal plus an interfering term which is optical phase sensitive.Although the overall weight coefficient of a given output sam-ple can now be negative, the filter will now be very dependenton environmental fluctuations since part of the coefficientsdepends on the evolution of optical phases. Coherent SSMPFsare thus potentially very difficult to stabilize and are not imple-mented in practice.

C. MSMPFs [16][31]In MSMPFs, the output of an array of optical CW sources

is optically combined and modulated by the RF input signalsi(t). The source array can be implemented either by usingan array of independent lasers, the output spectrum of a low-cost FabryProt laser, or by slicing the output of a broadbandsource (i.e., LED or SLED) by means of a periodic optical filter.Regardless of the particular option, the electric field prior to RFmodulation is given by

ES(t) =N1r=0

Ire

j(wrt+r(t)) (13)

where Ir, wr, and r(t) represent, respectively, the optical in-tensity, the source central frequency, and the phase fluctuationsof the rth component of the array. Each source implements afilter sample that is selectively delayed usually by employinga dispersive (i.e., wavelength selective) delay line implementedeither by a fiber coil or by a linearly chirped fiber Bragg grating(LCFBG). The dispersive delay element is chosen such that thedifferential group delay experienced by adjacent wavelengthsof the source array is T . Sample windowing can be achievedusing different techniques. If the MSMPF is based on an arrayof independent sources, then the simplest way is to control theoutput powers of the different sources. If a sliced source is em-ployed, then the wavelength components must be wavelength-demultiplexed, attenuated, or amplified on an individual basisand then multiplexed prior to RF modulation. Fig. 7(a) and

(b) show the two possible implementations of an MSMPF dis-cussed above.

The output electric field from impinging on the photodiodein this case is given by

E0(t) =N1r=0

arsin(t rT )ej(wr(trT )+r(trT )). (14)

The output current from the photodiode is (assuming again adetector responsivity )

I0(t) =|E0(t)|2

=

N1r=0

[|ar|si(t rT )]

+ N1r=0

N1s =r

arassi(t rT )si(t sT )

ej(wrws)tej(swsrwr)Tej[r(trT )s(tsT )]

=

N1r=0

[|ar|si(t rT )] . (15)

The second term in the above expression is zero since the outputphase variations from different optical sources can be assumedto be always uncorrelated. Thus, a linear relationship betweenthe input and output RF/microwave signal is obtained.

D. Applications of Microwave Photonic FiltersApart from the application to the field of ground radars [6]

outlined in Section I, there are certainly a wide range of appli-cations where microwave photonic filters can be of interest. Forinstance, in the emerging broadband wireless access networksand standards spanning from universal mobile telecommuni-cations system (UMTS) to fixed access picocellular networksand including wireless local area network (WLAN), WorldInteroperability for Microwave Access, Inc. (WIMAX), localmultipoint distribution service (LMDS), etc., there is a need toincrease the capacity by reducing the coverage area [47]. Anenabling technology to obtain this objective is radio-over-fiber(RoF) systems, where radio signals are distributed from a cen-tral location to remote antenna units (RAUs) using fiber optictransmission as shown in the upper part of Fig. 8. RoF makesit possible to centralize the RF signal processing functions inone shared location (headend). By so doing, RAUs are simpli-fied significantly as they only need to perform optoelectronicconversion and amplification functions. The centralization ofRF signal processing functions enables equipment sharing, dy-namic allocation of resources, and simplified system operationand maintenance. The processing at the headend involves aprior frequency down-conversion, ADC, and baseband process-ing using a DSP as shown in the intermediate part of Fig. 8,which illustrates a direct fiber link joining a given RAU andthe headend. The down-conversion operation can be eliminatedor divided into two steps, putting less stringent requirementson the ADC and DSP operations if a microwave photonic filter



Fig. 7. (a) Layout of an FIR MSMPF using a laser array. (b) Layout of an FIR MSMPF using a sliced broadband source.

is placed prior to optical detection as shown in the lower partof Fig. 8.

The microwave photonic filter can be employed either forchannel rejection [48], [49] or for channel selection applica-tions [50][52]. In the first case, we deal with an optical linkwhere not only the desired signal is carried by the fiber butalso unwanted interfering signals that are also picked up bythe antenna. A paradigmatic example can be found in radioastronomy applications [49], where signal transmission fromseveral stations to a central site requires removing strong man-made interfering signals from astronomy bands. The ability toreject these interfering RF signals directly in the optical domainis a unique characteristic of these photonic filters. Anotherapplication example is for noise suppression and channel in-terference mitigation in the front-end stage after the receivingantenna of an UMTS base station prior to a highly selectiveSAW filter. In the second case [50], the signal carried by theoptical link is composed of a frequency plan that comprises

several disjoint parts of the RF spectrum (UMTS, HIPERLAN,LMDS, etc.). Here, a bandpass photonic filter can be employedto select a given RF band or spectral region. Furthermore,the selected band can be changed if the filter is tunable: afeature uncommon to traditional microwave filters but possiblein microwave photonic filters, as we shall see in Section III.In both cases, the position of the frequency notch or the filterbandpass can be as low as a few megahertz or as high asseveral tens of gigahertz due to the broadband characteristicsof photonic delay lines. Microwave photonic filters can alsobe of interest in applications where lightweight is a primeconcern, for example, as analog notch filters are also needed toachieve cochannel interference suppression in digital satellitecommunications systems [53].

Another important application of microwave photonic filtersis in the field of true time delay beamsteering of antenna arrays[54]. A photonic true time delay system for feeding an array ofantennas is based on the use of broadband photonic delay lines.



Fig. 8. RoF access network (upper). Potential application of microwave photonic filters at the head-end on the centralized station (lower) replacing the RF filterof standard configuration (intermediate).

Fig. 9. Photonic beamsteering system based on a laser array feeding an LCFBG. The configuration is equivalent to that of a microwave photonic transversalfilter (see Fig. 19).

The feeder network for an array of N antennas is essentiallyequivalent to an N -tap microwave photonic tunable FIR filterwhere the basic filter delay T can be altered, the only differencebeing that each filter sample is detected by a different opticalreceiver that is placed before each antenna unit in the array.Fig. 9 shows an example of a photonic beamsteering systemthat is based on using a dispersive delay line implemented by anLCFBG featuring a dispersion parameter of D ps/nm in combi-nation with a bank of N tunable laser sources. The wavelengthdistance between adjacent sources is kept constant. The RFsignal to be radiated modulates the whole set of optical sources

and each wavelength is selectively delayed by the LCFBG andthen directed to a particular optical receiver feeding an elementof the array after being demultiplexed. The phase difference foran RF signal of frequency between adjacent elements is givenby = D, so it can be easily changed by changing .

To finalize this list of potential applications, it should not beforgotten that the very high bandwidth and potentially low de-lays (5 s/m) that can be achieved with optical delay lines makethem an ideal technology option for the implementation of sig-nal correlators [55] for very high speed signals and incoherentoptical code division multiplexing (OCDMA) applications.



III. LIMITATIONS AND PERFORMANCE PARAMETERS OFMICROWAVE PHOTONIC FILTERS

A. Optical Sources of Performance LimitationMicrowave photonic filters must overcome a series of poten-

tial limitations prior to their practical realization. We classifythese limitations into two groups according to whether theselimitations appear mainly in the optical domain or whether theymanifest in the electrical domain.

Limitations arising in the optical domain include nonlinearoptical effects, polarization, positive nature of the filter coef-ficients due to the incoherent operation, the limited range ofattainable spectral periods, spectral periodicity, filter reconfig-urability, and tunability.

Spectral Periodicity: The spectral periodicity of microwavephotonic filters limits the bandwidth of the RF signals to beprocessed to a fraction of the FSR in order to avoid spectraloverlapping. Single resonance (i.e., nonperiodic filters) is there-fore desired for certain applications. Section IV-D addressesthe techniques proposed to implement this class of filters[11], [32], [33].

Positive Coefcients: Filters working under the incoherentregime are linear in optical intensity, thus the coefficientsof their impulse responses are always positive. This has twoimportant implications as derived from the theory of positivesystems [4]. The first one and more important is that the rangeof transfer functions that can be implemented is quite limited.The second one is that regardless of its spectral period, thetransfer function always has a resonance place at baseband.This is not a serious limitation since a DC blocking filter can beinserted at the optical receiver output. Nevertheless, incoherentfilters with negative coefficients can be implemented by meansof different recently developed techniques [34][44] that arefurther discussed in Section IV.

Fiber Nonlinearities: Filter linearity can be compromised ifthe optical carriers used in filter implementation deliver enoughpower to stimulate fiber nonlinearities. The main sources ofoptical nonlinearities are self-phase modulation (SPM), cross-phase modulation (XPM), four-wave mixing (FWM), stimu-lated Brillouin scattering (SBS), and Raman scattering (SRS).The requirements for each one of these are the same as thosefor typical communication systems and can be found elsewherein the literature [56].

Polarization: Polarization effects are mainly important un-der coherent operation [2][4]. However, it has been outlinedand experimentally demonstrated that even under incoherentoperation the filter can be sensitive to signal polarization [57],[58]. The main cause for this apparent contradiction is thatsome signal samples experience exactly the same delay withinthe filter leading to a coherent interference between them evenif a broadband source is employed [57], [58]. Also, whenlaser sources and external modulators are used, care must betaken to adjust the source polarization to that required by themodulator. The use of polarization preserving fiber pigtails atthe modulator input helps to overcome this limitation.

Limited Spectral Period or FSR: As discussed inSection II-A, microwave photonic filters are periodic in spec-trum since they sample the input signal at a time rate given by

T . Thus, the spectral period or FSR is given by 1/T . If the filteris fed by only one optical source, then the source coherencetime (which is inversely related to the source linewidth) limitsthe maximum (minimum) value of the attainable FSR underincoherent (coherent) operation. MSMPFs have been proposedto overcome this limitation [15].

Recongurability: This property refers to the possibility todynamically change the values of ar and ck in (4). Passivestructures are incapable of this feature. Several solutions havebeen proposed to overcome this limitation including the useof optical amplifiers (OAs) [59][61], modulators [62], fibergratings, and laser arrays [15]. Some of these are addressedlater in Section IV.

Tunability: This property refers to the possibility to dynam-ically change the position of filter resonances or notches. Toprovide tunability, it is necessary to alter the value of thesampling period T . Solutions that include the use of switchedfiber delay lines [63], high dispersion fibers [64], and FBGs [6]have been proposed. In the last two options, a tunable source isrequired. Some of the main reported results are also reviewedin Section IV.

B. Electrical Sources of Performance LimitationMicrowave photonic filters are a particular case of an analog

fiber optic link and suffer from the same electrical limitationsources, including noise and intermodulation. The performancestudy of the complete microwave photonic filter from the pointof view of a black box with an RF input port and an RF outputport is therefore essential for the sake of comparison withother existing technologies and also in order to verify properlyits adequate fitting inside a real applications scenario withbounded gain, noise factor, and intermodulation characteristics.An important starting point for the analysis is the knowledge ofthe previously mentioned features in an RoF system [65][69].In fact, the more general structure of a microwave photonic(MWP) filter shown in Fig. 4 can be treated as an RoF systemwith direct intensity modulation (IM) or external modulation(EM), followed by an optical transmission section that in thiscase includes the necessary FIR or IIR tap replication scheme,and finally, the detection front-end. Nevertheless, MWP filterstructures can include additionally some specific optical com-ponents not specific of RoF as multiple optical source arraysinstead single-source broadband optical sources [LED, SLED,or ASE spectrum from erbium-doped fiber amplifiers (EDFAs)]or even sliced versions such as broadband sources. We now pro-ceed to present the gain and noise factor concepts applicable tothe general case of RoF and MWP systems and include the nec-essary specializations applicable to microwave photonic filters.

1) Gain: The total RF gain of the MWP filter can be derivedfrom the general set up in Fig. 10. The filter can be dividedinto the three main blocks from input to output, namely, theelectrooptical conversion module (EO), an all-optical process-ing part, and finally an optical to electronic conversion (OE)module. For the EO module, there are two main options, directIM of a semiconductor source, or EM employing a CW source.Both alternatives are equivalent from the point of view ofthe general operation concept of MWP filters since in both



Fig. 10. General MWP filter structure including electrooptical conversion, all-optical process, and optical detection. Definition of the optical span and RF gainreference planes.

amplitude modulation of the RF signal over the optical carrieris performed. The IM alternative can result interesting for lowcost and mediumlow frequency range applications due to theirlimited modulation bandwidth (< 1 GHz). The EM approachopens the possibility for RF modulation up to tens of gigahertzwith moderated cost. Electroabsortion modulators (EAMs) andelectrooptical modulator (EOMs) are the two main possibilities,EOMs being the more common option because of their moder-ate costs up to 10 GHz (they are very mature technologicallydue to the strong market of digital optical networks). EAMs,nevertheless, have also been demonstrated in a considerablenumber of RoF systems, and they represent a promising alter-native. On other hand, EMs require one additional device forCW light generation and also involve some additional opticallosses at the own EM.

The total RF gain or losses defined as the RF power ratiobetween input and output of the MWP filter (see Fig. 10) canbe approximated for the EOM case as

TRF =PRFoutPRFin

=(PoptToptZ0

2V)2

(16)

where Z0 is the effective EOM RF input impedance orresistance of the EOM electrode, V is the voltage for a-radian optical phase shift at the EOM arms that representthe voltage excursion between a minimum to a maximum ofits modulation response, [A/W] is the detector responsivity,Popt is the applied CW optical power to the EOM, and Topt isthe optical power transmission parameter that embraces all theoptical losses and/or gain along the optical processor includingthe EOM insertion losses as depicted in Fig. 10 (Gopt(dBo) =10 log10(Topt)). The biasing point along the standard nonlin-earized raised-cosine response of the EOM is supposed to bethe quadrature point (QB) that ensures the maximum linearityin optical amplitude modulation and the minimum even-orderdistortion terms. Equation (16) supposes also that the detectedphotocurrent is applied to load impedance RL equal to Z0, inother case, a factor RL/Z0 should multiply (16), i.e.,

GRF(dBe) = 10 log10(TRF)

= 2 (10 log10(Topt)) + 20 log10

(PoptZ02V

)

=2Gopt(dBo) +GEO&OE (dBe). (17)

The total RF gain can then be divided into two separate partsas shown in (17). The first term is the contribution of the pureoptical gain or losses to the RF gain, and the second term isthe contribution of the EO and OE conversion. Notice that theEOOE process can be divided also into two conversion slopeefficiency parameters, the detector responsivity [A/W ] andseom = PoptZ0/2V[W/A] for the EOM. Expressed in thatway, the slope efficiency for the EOM can be directly substi-tuted by the equivalent parameter if direct IM is employed,i.e., sIM = dP0/dI , which represents the slope of generatedoptical power versus the injected current when I > Ith, and itis proportional to the known differential quantum efficiency.

It is interesting to point out that sIM is independent of themean optical power delivered by the laser (I > Ith) and that itonly depends of the slope of the PI curve. This is in contrastwith seom that depends linearly with the CW power appliedto the EOM, and therefore TRF depends quadratically. This,in principle, allows the EOM-based systems to compensatefor their own EOM losses or even compensate optical inser-tion losses of the remaining optical processor if Popt can beincreased.

As an example of RF gain calculus: Popt = 10 mW, EOM:V = 6 V. Z0 = 50 , and Gopt = 10 dBo (including EOM,passive optical circuits like optical couplers, FBGs, circula-tors, optical delay lines, etc.). In that case, GEO&OE(dBe) =16 dBe, and the total gain GRF(dBe) = 36 dBe. This totalnegative gain can be compensated up to 0 dB by differentways: 1) by 36 dBe of electrical amplification (before, after,or at both places the MWP), 2) by pure optical gain (in thatcase the required gain will be half of the electrical gain, i.e.,18 dBo), or 3) a combination of electrical and optical amplifi-cation (for example, 12 dBo + 12 dBe). All these possibilitieshave important implications in terms of noise figure and distor-tion behavior of the MWP filter as it will be shown later.

The total RF gain has been calculated without any referenceto the particular frequency response of the MWP structurebecause it has to be considered as the absolute value to be addedto the normalized filter response independent of the number oftaps or particular optical process. In that sense, it has to bepointed out that Popt inside (16) and (17) should include thetotal optical power applied to the MWP structure by the set ofsources when the MWP filter is of the multiple-source type asdiscussed in Section II-C.

2) Noise Figure: The noise figure of the microwave pho-tonic filter can be defined as the ratio between the total noisepower spectral density at the device output Nout and the noisepower due to only the thermal noise spectral density applied tothe input at the reference temperature and affected by the devicegain. More specifically, in our case

NF (dB)

=10 log

[Nout

4kT0TRFR

]

=10 log

[NRIN +Nshot +Nsig-ASE +NPIIN +Nth(

4kT0TRFR

) ](18)



Fig. 11. EOM-based general MWP filter basic structure. Optical amplification can be included after or before optical processing. Noise sources are represented.(a) Optical intensity noise. (b) Shot noise. (c) ASE noise. (d) Thermal noise.

where k is the Boltzmanns constant, T0 is 298 K, and R isthe load resistance at the RF source applied to the MWP filter.The total noise spectral density at the output of the MWP filteris composed of different sources of noise generated along theMWP filter as we can see schematically represented in Fig. 11.

Relative intensity noise (RIN) produced in the optical source[case (a)] propagates along the optical processor up to thedetector and is one of the dominant sources of noise when directIM is employed. Its spectral power density is

NRIN = I2pRIN[A2/Hz

], Ip = PoptTopt (19)

where Ip is the average detected photocurrent and RIN [Hz1].Notice that this noise contribution increases with the square ofPopt. Also, for the case of multiple laser arrays feeding theMWP filter, the different sources can be considered in generaluncorrelated and with similar RIN values, and therefore, thetotal intensity noise is the adding of the individual ones, beingapplicable (19), where Popt contains the already mentionedaggregated array power. Notice also that intensity noise spec-tral density depends on the RF frequency under considerationRIN()[Hz1] and therefore the resultant noise figure. Externalmodulated systems relax the constraints over the laser sourceand the intensity noise features can be reduced employing CWsources with low RIN parameter. In that case, the dominantnoise source is the shot noise produced at the detector output,this being intrinsic to the quantum nature of lightwave withspectral density

Nshot = 2qIp[A2/Hz

]. (20)

OAs are indispensable in many cases to compensate highoptical losses of the passive components along the MWP filter.EDFAs or semiconductor OAs (SOAs) can be used dependingif their respective gain dynamics behavior is or not a limitationor whether this dynamic is used for some purpose [crossgain modulation (XGM), for example, to negative coefficientgeneration]. In the case of incorporating OAs, new sources ofnoise produced by the amplified spontaneous emission noise(ASE) should be considered. Detailed derivation of ASE noisesources and OA noise factor can be found in [70]. We willprovide here some summarized and useful expressions for theeasy calculation of the more general case with dominant signalASE beating contribution and the procedure to extend to anarbitrary chain of AO and optical losses [70].

According to the previous notation, the noise power spectraldensity due to signal to ASE beating is [7]

Nsig-ASE = 4qnspIp(GOA 1)T2[A2/Hz

] (21)where is the quantum efficiency of the detector [also inside = (q/h)], nsp is the population inversion parameter forthe amplifier that is related with the OA gain (G0A), and theOA noise factor (F0) through

F0 =(GOA 1)

GOA2nsp +

1GOA

. (22)

Notice also that (2) includes the term T2 that embraces theoptical transmission between the OA and the detector. In thisway, the expression can be applied to cover any location ofthe OA along the optical processing chain, leaving Topt =T1G0AT2, where T1 is the optical transmission before theOA (just between the source output up to the OA input). Toinclude the noise effect of more that one amplifier along theoptical process, we can use the equivalent OA gain (GOA,Eq)and OA noise factor (FO,Eq) of a chain of {GOA1, FO1}+intermediate losses (TINT) + {GOA2, FO2} being

GOA,Eq =GOA1TINTGOA2

FO,Eq =FO1 +FO2

GOA1TINT. (23)

Equation (23) assumes that GOA,Eq, GOA1, and GOA1 1,and therefore, (22) reduces to F0 = 2nsp. In other case,the cascading expression can be calculated also with slightmodifications [7]. Note that any OAs + optical losseschain combination can be calculated by recursive iterationemploying (23).

Phase-induced intensity noise (PIIN) is usually the dominantnoise source in single-source incoherent microwave photonicsignal processors. PIIN arises since, as mentioned previously,the incoherent regime implies the use of wide linewidth sourcesin order to obtain a robust transfer characteristic irrespectiveof environmental perturbations. The price to be paid is thatthe laser linewidth, which arises from random phase variationsof the optical output with time, is larger than the processorFSR. Inside the optical processor, the input power is tappedinto different paths (samples) and recombined at the output.



Fig. 12. (a) SFDR schematic definition and its relation with the system requirements. (b) IMD3 and C versus input RF power. Linearly extrapolated cross pointand its relation with SFDR.

The summation of multiple optical samples at the photodetectortransforms the laser phase fluctuations into intensity fluctua-tion noise (PIIN) at the output. PIIN noise has been studiedin passive structures [71] and active recirculating delay lines[72], [73]. Recently [74], an excellent and detailed considera-tion of its impact and the techniques to overcome the effect ofPIIN has been published in the literature [75]. Among these, itis worth mentioning the use of multiple-source architectures.

Finally, added to the optical-type noise sources, we also havethe thermal noise propagated along the MWP filter added tothat produced at the detector load resistance and the feasibleelectrical gain, i.e.,

Nth =(4kT0R

(F + TRF)) [

A2/Hz]. (24)

In the simplest case of thermal noise being dominant, if theMWP filter has considerable losses TRF 1, them NF(dB) =

F (dB) + LRF(dB), with LRF(dB) = GRF(dB). In the op-posite case, if TRF 1, then NF(dB) 0 dB, but this willbe very difficult to reach in practice because high TRF 1involves high optical power and therefore increase of RIN andshot noise or optical gain with added ASE.

3) Harmonic and Intermodulation Distortion: Harmonicand intermodulation distortion (IMD) features are the othergreat constraint that should be addressed for a real applicationof an MWP filter. The main source of signal distortion is nor-mally the E/O conversion stage. If we consider direct IM lasers,both static distortion produced by the PI curve and dynamicdistortion produced by the laser couple rate equation dynamicsare produced. EM is dominated by the static distortion anddepends on the E/O device employed (EOM or EAM) and ifa linearization technique was employed. Extensive compilationof all these possibilities can be found in [68] and [69]. Whateverthe E/O approach is finally used, the distortion will translateinto harmonic distorsion (HD) terms and IMD terms. From all



Fig. 13. RF notch filter based on a fiber optic MachZehnder and a linearly chirped FBG [8].

the intermodulation terms, the third-order terms (IMD3) aremore deleterious because they fall over the system frequencyband being difficult or impossible to avoid by simple filtering.In the case of EOM modulator (without liberalizer), the rise-cosine static PV curve implies distortion and traditionallythe biasing point QB that ensures maximum optical amplitudemodulation and minimum even-order distortion terms (IMD2,HD2). In that case, IMD3 can be reduced, decreasing theRF power and therefore the optical modulation index (m).Nevertheless, the m reduction will imply a reduction of thecarrier-to-noise ratio (CNR) at the MWP filter output due tothe noise floor. There are two aspects limiting the system inopposite directions, first the noise floor level and second the RFpower limit at the input due to intermodulation. This balanceis summarized into the known SFDR that is defined as thefundamental carrier to the two-tone third intermodulation prod-uct just when the IMD3 product power equals the total noisepower on the system bandwidth. Fig. 12(a) shows schematicallythe SFDR definition and how a specific application couldoperate with RF channels with maximum power difference Pbetween the strongest and weakest signals and SFDR should behigher than P + CNRmin, being CNRmin the minimum CNRfor the specific application. A general procedure to computeIMD3 output power versus output carrier power (C) for anarbitrary input RF power employs the linearly extrapolatedcross point IP3 [see Fig. 12(b)]. SFDR can be easily obtainedfrom the schematic of Fig. 12 as

SFDR = 2310 log

(IP3NoutR

) [dBHz 23

](25)

where NoutR is the power noise spectral density (watts perhertz). For the case of using EOMs without linearization [68],IP3 = 4I2pR, and

SFDR

=2310 log

(4I2p

RINI2p + 2qIp +NsigASE +Nth

) [dBHz 23

].

(26)

IV. PRACTICAL IMPLEMENTATION OF MICROWAVEPHOTONIC FILTERS

A. Introduction and Brief Historical SketchThe use of optical fiber as a delay medium in the context of

RF signal processing applications was proposed by Wilner andvan der Heuvel as early as 1976 [75]. They were the first tonote that fiber delay lines are attractive due to their low loss andlow dispersion. A year later, Ohlhaber and Wilner [76] reportedan experimental demonstration of an optical fiber transversalfilter based on three multimode fiber delay paths to generate andcorrelate a 4-bit 88 Mb/s coded sequence. Also, an optical fiberfrequency filter was demonstrated by Chang et al. [77], whoilluminated a bundle of 15 multimode fibers that provided 15different delays spaced by 5.2 ns, yielding a filter with a transferfunction having a fundamental passband at 193 MHz. Sincethen, different tapping elements and dispersive mechanismshave been investigated to develop advanced single-mode opticalfiber delay line architectures capable of synthesizing manysophisticated time- and frequency-domain filtering operationsfor basic signal processing functions. The most relevant initialactivity was carried by Goodman, Shaw, and others then at theUniversity of Stanford [4], [33]. However, most of these pro-posals presented filters relying on the implementation of timedelays by means of fiber strands. The use of novel componentssuch as FBGs to implement a programmable delay line based onoptical RF link technology [6] opened the perspectives towardthe implementation of fully reconfigurable and tunable discrete-time optical processing of microwave signals.

In this section, different approaches for the implementationof incoherent transversal filters are reviewed, attending to thetype of source(s) employed, and focusing on the main perfor-mance and limitations presented by each one. As discussed inprevious sections, there are two the main options for sourcesemployed to implement the optical taps: The first one is whereonly one modulated optical source is employed. The filter tapsare therefore generated from delayed versions of the outputsignal from this source, but a limitation of the maximumattainable filter FSR is found since interference effects need tobe avoided. The second one employs multiple sources, eitherby using multiwavelength optical sources (lasers) modulatedby the same RF signal or by using a sliced broadband source.In the first alternative, provided each source implements onlyone tap, there is no phase correlation between different taps,



Fig. 14. RF photonic filter architecture based on an EDF active cavity and two linearly chirped FBGs [9]. (Inset) Tunable bandpass frequency response.

so no limitation in the minimum time delay or maximumFSR is encountered. The second one consists of a modulatedbroadband optical source (LED, EDFA or SOA ASE source,etc.) with very low coherence time, which is sliced to generateall the filter taps. Since each tap is implemented by a differentpart of the sliced spectrum, there will be no limitations in thefilter FSR, provided each slice carries a portion of the opticalspectrum broad enough.

Finally, we have included a subsection on negative-co-efficient microwave filters due to the large interest they cur-rently attract to researchers. The main approaches proposed inthe literature for implementing these types of filters, which offerhigher flexibility in the transfer function, and also do not exhibita resonance at baseband, have also been reviewed in the section.

B. Implementation of SSMPFsThe first continuously tunable optical transversal filter was

reported in [7]. It was based on a single tunable modulatedlaser source and two long chirped gratings on separate portsof a coupler as tapping elements. By varying the wavelengthof the source over the chirp range of the gratings, the point ofreflection of the grating shifts linearly along the length of eachgrating, and this enables the time delay between both reflectedsignals (i.e., optical taps) to be controlled. Another exampleof an RF notch filter was proposed in [8], showing higherresolution filtering. It was based on a fiber optic MachZehndersection combined with a linearly chirped fiber grating, as shownin Fig. 13. In this structure, provided the fixed delay differenceis much larger than the tunable time delay, the shift of the notchfrequencies can be tuned linearly and precisely while the FSRis kept nearly unchanged, offering large flexibility for real-timesignal processing.

Another proposal featuring high Q filters with wide andcontinuous tunable center frequencies was presented in [9]. Theexperimental configuration for the tunable filter is shown inFig. 14. It consists of two chirped long Bragg gratings whosereflectivities are 50% and 100%, respectively, and a section ofactive fiber between them, which enables a large number oftaps to be generated in the impulse response. The modulatedlight launched into the cavity is reflected successively from both

Fig. 15. (a) Cascaded passive MachZehnder filters to select a desired fre-quency. (b) Filter frequency response of the hybrid structure based on an activefiber grating pair cavity and the passive section [10].

gratings by passing it back and forth through the active fiber.Tuning the wavelength of the optical carrier over the reflectionbandwidth of the gratings causes the point of reflection tochange linearly along the length of the gratings so the basic timedelay between taps is different, resulting in a tunable bandpassfrequency response (see inset in Fig. 14).

Further work on these structures presents hybrid approachescombining both active and passive sections to obtain a signifi-cant increase in the filtersQ factor [10], [11] The p-section pas-sive MachZehnder lattice see Fig.15(a)] is used to eliminate



Fig. 16. RF photonic transversal filter structure using four fiber grating arrays and doubling the number of coefficients using a MachZehnder stage [13].

Fig. 17. (a) Eight-tap filter response just after the circulator in Fig. 4.(b) Eight-tap filter response just after tap multiplexing stage in dashed box(Fig. 4). (c) Filter tunability.

the intermediate peaks and to select the multiple that corre-sponds to the desired filter frequency. Although this hybridstructure can only be implemented with uniform fiber gratings,

Fig. 18. FIR tunable RF filter architecture based on a fiber grating array [13].

and therefore, tunability has not been demonstrated, experi-mental results in [10] show a filter centered at a fundamentalfrequency of 1.1 GHz, exhibiting a Q factor of 801, as depictedin Fig. 15(b), and increased up to 983 when a third section isincluded, comprising a small-FSR long delay line differencepassive filter [11].

Another complex filter composed of a single tunable laserand eight fiber grating arrays was proposed in [12]. The systemconfiguration, shown in Fig. 16, uses a 1 8 splitter, and eachof the grating arrays is connected via an adjustable attenua-tor to provide the tap weighting (windowing of the impulseresponse) and, therefore, different bandpass spectral profiles.Each of the eight grating arrays, corresponding to eight tapsof the microwave photonics signal, has four gratings. Each ofthese four sets of Bragg gratings, selected by changing theoptical carrier wavelength, has a different spacing incrementof distance, providing different tunabilities of the bandpassresponses. However, the number of taps in this structure can beincreased by adding a MachZehnder section, as depicted in thedashed box in Fig. 16 [13]. One beam passes through directlyand the other is reflected at a grating with the same wavelength,and so placed that the optical path difference between thesetwo arms is exactly eight times that of the unit delay time,which is related to the spacing between the adjacent two taps.



Fig. 19. (Top) Tunable and reconfigurable RF photonic filter architecture based on a laser array and a linearly chirped FBG [16]. (Bottom) Experimental resultsfor a five-tap filter. (Left) Reconfigurability (reduction of sidelobes level). (Right) Tunability (different bandpass central frequency).

The impulse response, before and after this section, is alsoshown in Fig. 16. The frequency response of the filter measuredat the output of the optical circulator is shown in Fig. 17(a),whereas the response after the stage in the dashed box showsa narrower bandwidth of the passband while the FSR remainsthe same, confirming that the Q factor has been doubled [seeFig. 17(b)]. The bandpass profile optimization can achieve anMSSR of 30 dB by using a Hamming windowing function andfilter tunability is demonstrated by tuning the optical carrierwavelength from 1 to 2, as shown in Fig. 17(c).

Based on the fact that the optical fiber recirculating delayline is one of the most compact configuration to implementan IIR microwave photonic filter and can provide very steepnotch response, Zhang et al. proposed in 2001 [14] an opticalfiber recirculating structure incorporating a fiber grating arrayto achieve maximum notch depth and tunable FSR. As shownin Fig. 18, this filter consists of a fiber coupler and a length offiber to provide delayed feedback optical signal, which can bechanged in this structure by tuning the optical carrier.

Finally, it is worth mentioning that other approaches that arefound in the literature explore properties such as the polariza-tion synthesizing [15] in Bragg gratings to realize incoherent

optical transversal filters with large tunable FSR by using asingle optical source.

C. Implementation of MSMPFs1) Filters Based on Source Arrays: As described in

Section II, a class of MSMPFs is based on the use of laserarrays, aiming to provide a further step in the sense that thefilters proposed are completely flexible and allow fast andindependent reconfiguration and RF tunability, although themain drawback is related to the high cost of these structures.The first proposal was done in [16] and the layout of the filteris shown in the upper part of Fig. 19. It is composed of anN laser array, where the laser wavelengths and output powerscan be independently adjusted. Thus, spectrally equally spacedsignals representing RF signal samples can be fed to a linearlychirped fiber grating suffering different delays but keepingconstant the basic incremental delay T between two adjacentwavelengths. Furthermore, T can be changed by proper tuningof the central wavelengths emitted by the laser array, providingtunable transversal RF filters. Also, since the output powers ofthe lasers can be adjusted independently at high speed, impulse



Fig. 20. (Top) Architecture for a tunable RF photonic filter based on fixed optical sources and a tunable dispersive element [17]. (Top inset) Nonuniform magneticfield inside the electrical coil. (Bottom inset) Grating time delay response when chirp is induced: spectral location of the optical taps. (Bottom) Three-tap tunabletransversal filter response by using the filter architecture described in the upper part. Bandpass filter centered at (a) 6 GHz and (b) 9 GHz.

response windowing can be easily implemented, and therefore,the filter transfer function can be reconfigured at high speed.The reader at this point is invited to compare the structure inFig. 19 with that of Fig. 9 to verify the equivalence of thestructures required for microwave photonic transversal filtersand for photonic beamsteering of antenna arrays.

The lower left hand side part of Fig. 19 shows the responseof a five-tap uniform filter where the normalized output powersfrom the lasers in the array are [1 1 1 1 1] together withthe response of a truncated Gaussian windowed filter wherethe normalized output powers from the lasers in the array aregiven by [0.46 0.81 1 0.81 0.46], where a reduction on theMSSR down to 20 dB can be observed. The right hand sidedemonstrates resonance tunability, increasing the resonanceposition from approximately 2 up to 4 GHz. In addition, thisfigure shows the carrier suppression effect (CSE) suffered bythe second resonance in this specific case of dispersive mediaand wavelength spacing. CSE effect can be eliminated by usingsingle sideband (SSB) modulation.

Fig. 21. Multitap transversal bandpass filter implemented by spectrally slicinga broadband source with wavelength-multiplexed Bragg grating arrays equi-spaced in time [19].

A limitation of this technique is that since the tunability ofthese filters is based on the optical wavelength tuning of themultiwavelength laser, expensive sources must be employedfor them. A lower cost alternative was proposed in [17] based



Fig. 22. (Top left) UMTS filter layout based on a broadband slice source followed by a switched dispersive delay line. (Top right) Filter prototype developedwithin the IST-LABELS project. (Bottom) Filter response based on a fiber grating array [22] showing the tunability of the filter.

on dispersion variable devices. Fig. 20 shows the filter setupemploying the dynamic chirp of an original uniform FBG(UFBG) controlled by a nonuniform magnetic field, which isinduced by an electrical coil on a magnetostrictive transducer.The dispersion slope was changed from 300 to 900 ps/nm, andtherefore, by setting the optical wavelengths at fixed values, athree-tap tunable transversal filter is implemented, as shown inthe lower part of Fig. 20.

Other lower cost proposals for reconfigurable RF filtersbased on multiwavelength lasers are based on multimodeFabryProt lasers [18]. In these structures, the bias injectioncurrent to the laser is modified to change the emitted opticalspectra and, therefore, the optical taps. Although reconfigura-tion has been demonstrated, it is limited to the spectral charac-teristics to the modal distribution of the laser, and tunabilityis only achieved when used tunable dispersive elements, asdescribed above.

2) Filters Based on Sliced Broadband Sources: The lit-erature offers a large variety of microwave photonic filtersbased on sliced broadband optical sources, showing very lowcoherence time and low cost as their main advantages. In thissection, different slicing techniques required in these structuresto generate optical taps are reviewed focusing on the tunability

and reconfigurability properties of the filters. The incorporationof FBGs to microwave photonic filters has provided enhancedflexibility.

A simple discretely tunable notch filter was demonstrated[19] using two Bragg gratings written in series in one of thearms of a coupler. In such a structure, FBGs are used as tappingelements and the delay between taps is fixed by the distancebetween the gratings. In a further step [20], a multitap (29 taps)transversal bandpass filter was demonstrated by spectrally slic-ing a broadband source with wavelength-multiplexed Bragggrating arrays equispaced in time (see Fig. 21), showing thepossibility of shaping the tap element profile to obtain win-dowing for the design of the filter response. By apodizing thereflectivity of the gratings in the array according to a Kaiserwindow, the MSSR was lowered up to 18 dB. The accuracyof the tap weighting and time delays guaranteed by current massproduction techniques contributes to high sidelobe suppressionand excellent reproducibility of the grating-based filter [21].

An example of a filtering application implemented by usingthis approach is published in [22], where a tunable photonicfilter for noise suppression and channel interference mitigationin the front-end stage of a UMTS base station prior to the highlyselective SAW filter has been developed. As shown in Fig. 22,



Fig. 23. Architecture of the tunable stretched UFBG-based RF filter [24]. (Inset) FSR tunability dependence on the optical wavelength spacing of the opticalcarriers.

the slicing of the broadband optical source is performed byan array of FBGs, which also introduces a fixed time delaybetween the reflected slices of the signal. A 40-nm broadbandSLED centered at 1550 nm is RF modulated and tapped anddelayed by the N grating array. Finally, the spectral slices arefed to a reconfigurable chain of dispersive switched sectionsof standard fiber to vary the time delay between the slices.By varying the configuration of the switches, the time delaybetween the signals reflected from different gratings is changed,and thus, tunability of the filter RF response is achieved.

The UMTS channel filtering application requires a highQ factor (about 400) since the required 3-dB passband of thefilter should be less than 5 MHz and the operating frequencyof the filter lies within 19201980 MHz. Furthermore, UMTSchannel filtering also requires the tunability of the RF pass-band within the 12 channels allocated along the 60-MHz band(19201980 MHz). In order to achieve such a high Q factor, theFSR of the filter is an integer fraction of the UMTS operatingfrequency. The filter is tuned to the upper UMTS channelat 1977 MHz (18th resonance or FSR), when the dispersivemodule is switched off, the FSR of the filter has been set to109 MHz, and the corresponding spacing between adjacentgratings has been set to 930 mm. In order to meet the 3-dBbandwidth and 40-dB rejection level required by the applica-tion at the central RF frequency, 30 Gaussian apodized tapswere employed with a spectral spacing of 1 nm. The 5-MHztuning step between UMTS channels is achieved by sections of1.35 km of standard fiber for the 1719th resonances of the filterresponse. The small MSSR is mainly due to the spacing errorsbetween the gratings and has been subsequently optimized toover 20 dB.

More sophisticated continuously tunable systems based onFBGs have been recently presented [23], [24]. The tunableapproach was previously demonstrated to provide a simpletunable notch filter where the broadband optical source wassliced by means of only two FBGs, which can be tuned bymeans of a strain application stage [23]. Fig. 23 shows a filterconsisting of a broadband optical source, i.e., a superelectro-luminescent diode, SLED, and UFBGs as filtering elementsthat will be stretched to tune the reflection bandwidth, initiallycentered at init. Since the central optical frequency N ofdifferent gratings must be equidistant [24], each grating mustbe stretched over a different fiber length so that the totaldevice length is determined by the number of optical taps.The device employs identical Bragg gratings whose initialresponses have been tuned by tension before gluing the gratingson the mechanical stage. Provided one of the gratings is notglued on the stage but the others are glued over different fiberlengths, the filter tunability is demonstrated as a function of thebasic wavelength spacing between adjacent optical taps cor-responding to reflected signals by the gratings when differentelongations are applied. The inset of Fig. 23 shows the FSRtunability in the range of 16 GHz when three- and four-tapfilters are implemented by using a fiber length of 23 km asthe dispersive element. A similar configuration for a four-tapfilter where the gratings are written in a parallel configurationto achieve large sidelobe suppression by weighting the taps wasalso demonstrated.

Other solutions are based on the use of periodical spectralslicing elements such as fiber FabryProt, sampled fiber grat-ings, or arrayed waveguide grating (AWG) [25][29]. The firstone is based on the use of a transmissive low spectral period



Fig. 24. (Left) RF photonic filter architecture using a broadband optical source sliced by an SFBG [26]. (Right) Response of the RF photonic filter implementedfrom different spectral SFBG responses. (a) Asymmetric double sigmoidal. (b) Voigt function. (c) Lognormal function.

optical FabryProt filter to realize subnanometer-resolvedoptical sampling [25].

Superstructured fiber Bragg gratings (SFBGs) have alsobeen proposed as slicing elements in these type of structures[26], [27], as shown in Fig. 24, leading to high rejection level(> 45 dB) and with the potential of a big variety of filtertransfer functions to be synthesized by designing the properspectral response of that of the SFBG, such as asymmetricdouble sigmoidal, Voigt, or lognormal functions, as depictedin the left part of Fig. 24.

AWG devices have also been employed to implement broad-band source slicing with a high number of taps [28], [29].In Fig. 25, a recently proposed scheme that combines sourceslicing via AWG devices and signal tapping using an arrayof spatial light modulators (SLMs) to implement a 40-tap re-configurable microwave photonic filter is shown. This structurehas great potential because the spectrum slices can be indepen-dently adjusted or switched ON or OFF by optical components

as electronically operated attenuators providing fast tunabilityor reconfigurability. For instance, Fig. 26 shows different trans-fer functions obtained when programming standard windowingfunctions well known in the literature. These window functionswere dynamically loaded into the SLM array, thus demonstrat-ing the possibility of adaptive filtering.

Another recently reported slicing technique employs a bulkacoustooptic tunable filter (AOTF) to select certain wavelengthsfrom the broadband source to implement the transversal filtertaps with corresponding weights and separation determined bythe control signals applied to the AOTF [30]. A fiber imple-mentation of this approach is shown in Fig. 27 [31], where afiber Bragg grating and a longitudinal acoustic wave performthe slicing of the EDFA broadband source. The acoustic wavegenerated by a piezoelectric transducer driven by an RF createsa periodic strain perturbation that modulates periodically theperiod and the refractive index of the FBG, which has beenwritten at the neck of a symmetric tapered fiber in order to



Fig. 25. Forty-sample reconfigurable transversal filter using a two-stage 1 40 AWG configuration and a 40-SLM free space array [29].

Fig. 26. Filter response for different windowing functions [29].



Fig. 27. Transversal filter architecture based on a Bragg-grating-based acoustooptic superlattice modulator [30]. (Insets, a and b) Spectra of the optical signalgenerated by 0.755- and 1.444-MHz frequency, respectively. (c) and (d) Corresponding filter response.

increase the efficiency of the acoustic interaction. The inset ofFig. 27(a) and (b) shows the spectrally equispaced bands ofreflection on both sides of the original Bragg grating createdat 0.755 and 1.444 MHz, respectively, leading to filters with anFSR of 6.25 and 11.5 GHz (see insets c and d in Fig. 27) andan MSSR of up to 20 dB. The reconfigurability of the filter canbe obtained by applying different voltages to the piezoelectrictransducer since different degrees of apodization of the opticaltap intensities are achieved by controlling the acoustic power.

D. Single Resonance (Nonspectrally Periodic) MicrowavePhotonic Filters

As it has been pointed out in Section III-A, the periodicnature of the spectral response of microwave photonic filtersimposes a limitation over the bandwidth of the signals to beprocessed. In many practical implementations, particularly inthose based on the use of optical fibers as delay elements,the value of T can be considerable, yielding very low FSRvalues, sometimes below the gigahertz or even the hundreds ofmegahertz range. This is a serious drawback since the spectralrange where the filter can be employed is very limited.

To overcome the above drawback and obtain truly bandpasstransfer functions, Minasian has proposed to use incoherentstructures in cascade. The main idea is that by carefully choos-ing two filter configurations, one (that we call filter 1) witha low FSR and very selective resonances and a second with

broader resonances and higher FSR value, the overall filteryields a transfer function given by HF1()HF2(), whichfeatures the resonance selectivity of the first filter and the broadFSR value of the second. For instance, in [11], a filter composedof the cascade of a very low FSR active amplified recirculatingdelay line filter and a chain of MachZehnder interferometers(MZIs) was presented featuring Q factors of 801 and 938, re-spectively. The former approach has two limitations. First of all,both photonic filters must be carefully designed and stabilizedfor perfect spectral alignment, and second and most important,it is not clear that the transfer function of the cascade of twoincoherent filters is the product of the transfer functions of theirindividual constituents. In fact, it can be demonstrated that thisis not the general case, the main reason being the nonlinearrelationships between the input and output RF currents and theoptical field that propagates through the optical filters.

A second alternative, recently proposed [32], is based on afiber MZI used as a sinusoidally continuous slicing stage ofthe broadband spectrum emitted by the optical source used toimplement a tunable bandpass filter, showing a single bandpassfrequency response and large tunability, as shown in Fig. 28.By using a 3-dB bandwidth of 5.4-nm optical source and46-km fiber length as a dispersive element, the RF filter re-sponse shows a bandpass characteristic centered at a givenfrequency, which can be tuned varying the periodicity of theinterferometer MachZehnder output spectrum. The lower partof Fig. 28 shows how a periodic wavelength spacing in the



Fig. 28. (Top) Implementation of the RF single bandpass filter based on a broadband source and an MZI [32]. (Bottom) Tunability of the filter.

interferometer output of 0.237 and 0.173 nm leads to bandpassfilters at 7.9 and 12.2 GHz. A tuning range of several tens ofgigahertz has been achieved with an MSSR of over 20 dB anda maximum Q factor of 40, although potential high Q valuescan be obtained in this setup by choosing the appropriatedbroadband source and compensating the degradation effect ofthe dispersion slope.

Finally, a recent contribution proposes the implementationof single bandpass microwave photonic filter based on the useof tuned external modulators instead of broadband externalmodulators at the filter input, for instance, incorporating adiscrete bandpass microwave filter preceding the EOM. There-fore, a single resonance on the short RF spectral modulationregion of the tuned modulator will be shown by the filtertransfer function, but retaining the selectivity, tunability, andreconfigurability properties of the filter [33].

E. Microwave Photonic Filters With Negative CoefcientsAs discussed in Section III-A, incoherent structures that are

required to obtain a linear relationship between the input andoutput RF signals can only implement filters with positivecoefficients. This severely limits the range of impulse responses

or transfer functions that can be implemented. In this section,we briefly review some of the most important proposals toovercome this limitation.

The first technique, known as differential detection, wasproposed in [34] and was itself a particular case of an elegantsolution proposed in [35] to implement incoherent spatial filterswith complex coefficients. The impulse response of an arbitraryfilter can be decomposed into positive and negative taps con-tribution. Each part can be implemented by a different sectionwith only positive coefficients, but the output of each sectionis fed to a pair of photodiodes placed in a differential config-uration. Thus, signal subtraction is achieved in the final opto-electronic conversion. Although this approach was proposed inthe 1980s, the experimental demonstrations of its applicabilityon an RF photonic filter were performed in the last decade[36], [37]. Even though the differential detection techniqueallows the implementation of any kind of negative coefficientfilter, extra components are required because of the requiredstructure duplication. Furthermore, filter reconfigurability is notalways easy to implement.

The hybrid optoelectronic alternative [38], [39] consists ofthe electrical implementation of the taps, just after photodetec-tion. Light from a directly modulated injection laser is split by



Fig. 29. Two-tap RF filter implementing a negative coefficient using the RF signal inversion in XGMSOA-based wavelength conversion. (Inset) Spectrum ofthe notch filter [40].

a coupler to implement the different signal samples, which aredifferently delayed and converted in a photodetector. The mag-nitude and sign of the tap coefficients are implemented fromthe value and sign of the bias voltage to each photodetector[39]. Monolithic microwave integrated circuits (MMICs) [38]have also been proposed for sign and tap weighting with goodperformance, although the filter bandwidth is limited to that ofMMICs, and the thermal noise of these filters is increased.

All-optical approaches for implementing negative coeffi-cients are the preferred option since they overcome elec-tronic bandwidth limitations and electrical noise distortions.Coppinger et al. [40] made a first optical attempt by exploitingthe phase shift obtained in XGM and XPM wavelength con-version using SOAs in the modulating signal of the convertedcarrier, as depicted in Fig. 29, corresponding to the implemen-tation of a two-sample notch filter with negative coefficients. Byusing this approach, the filter bandwidth is limited by the band-width conversion of the SOA (which can be above 40 GHz),reconfigurability and multitap filter implementation are difficultto achieve, and polarization sensitivity of SOA devices must beovercome. Negative tapping was also demonstrated by usingthe carrier depletion effect in a DFB laser diode [41] in astructure that also contained cascaded FBGs. Discrete andcontinuous tuning was demonstrated with a linear FBG anda UFBG.

Other optical techniques for the implementation of negativecoefficients have been recently published. Mora et al. [42]proposed the use of tunable sources amplified by an EDFAfor implementing positive coefficients, whereas negative coef-ficients are obtained by carving the transmission spectrum of abroadband ASE source through UFBGs, as shown in Fig. 30.This technique offers phase inversion (negative coefficients)directly in the optical domain with no bandwidth limitation, andfilters can be easily reconfigured by tuning the sources and theFBGs. A main drawback of this approach is a DC componentalways present in the filter transfer function that arises from thenonzero average optical ASE radiation level, but it can be easilysuppressed at photodetection with a blocking filter. The inset

Fig. 30. RF photonic filter with negative taps based on a broadband ASEspectrum transmitted through UFBGs. (Inset) Filter response with the detailof the optical taps employed in this implementation [42].

of Fig. 30 shows the results obtained for a five-tap transversalfilter with three positive and two negative taps.

Other techniques recently reported [43][45] rely in thecounter-phase modulation in MachZehnder external modula-tor devices by means of employing the linear part of the transferfunction with positive and negative slopes in the output versusinput optical power sinusoidal transfer function of an EOM.As shown in the upper part of Fig. 31, two linear modula-tion regions with opposite slopes can be observed centeredat different bias voltages V BIAS and V

+BIAS, respectively. The

same RF modulation signal applied to the modulator at eachof the former bias points will produce an optical-modulatedoutput signal with the same average power but where the mod-ulating signals are shifted or have different signs (positiveand negative taps). Although, in principle, two modulators arerequired in the transmitter, each one biased at V +BIAS and V

BIAS,

to implement positive and negative taps, respectively, whoseoutputs are combined and sent to a dispersive element thatimplements the constant differential time delay between thefilter samples, in practice, the setup can be simplified to onlyone modulator if this device is provided with two input ports



Fig. 31. RF signal inversion in a dual-input EOM for the implementation of negative coefficients [43]. (Inset) RF signal inversion principle in the EOM response.

Fig. 32. Transfer function of an eight-coefficient filter with four negative coefficients and flat-top resonance shape: Theoretical (solid line) and experimental(dotted line) results.

[44], or a WDM architecture can be implemented by using themodulator transfer function dependence with wavelength [45].

Fig. 32 shows the transfer function of an eight-coefficientfilter with four negative coefficients and flat-top resonanceshape. Theoretical results in solid line and experimental resultsin dotted line are shown for reference and comparison. Asexpected, the filter resonance at baseband (typical of positivecoefficient filters) has been eliminated, thus confirming thefeasibility of the proposed scheme for the implementation of

negative coefficients. With this technique, phase inversion inthe modulation process is limited by the modulator bandwidth,which can be high enough so as to reach 40 GHz.

Finally, a new all-optical technique based on a dual-outputEOM connected to undergo double-pass modulation has beenused to obtain a frequency response equivalent to a two-tapnegative notch filter [46] under two different topologies. Thefirst one connects the two outputs via an isolator, and the secondone uses a reverse connection of the EOM together with a



grating reflector, which can be integrated on a planar circuit andextended to tunable filters when a chirped grating is employed.

V. SUMMARY AND CONCLUSION

We have provided a tutorial introduction to the subject ofmicrowave photonic filters to the reader not working directlyin the field but interested in getting an overall introductionof the subject and also to the researcher wishing to get acomprehensive background before working on the subject.The tutorial has covered both basic theoretical principles andpractical limitations and has also reviewed some of the principalachievements in the area of filter implementations.

Microwave photonic filters are photonic subsystems de-signed with the aim of carrying equivalent tasks to those of anordinary microwave filter within an RF system or link, bringingsupplementary advantages inherent to photonics such as lowloss, high bandwidth, immunity to EMI, tunability, and recon-figurability. There is an increasing interest in this subject since,on one hand, emerging broadband wireless access networks andstandards spanning from UMTS to fixed access picocellularnetworks and including WLAN, WIMAX, LMDS, etc., requirean increase in the capacity by reducing the coverage area. Anenabling technology to obtain this objective is based on RoFsystems, where signal processing is carried at a central officeto where signals are carried from inexpensive RAUs. On theother hand, microwave photonic filters can find applications inspecialized fields such as radar and photonic beamsteering ofphased arrayed antennas, where dynamic reconfiguration is anadded value.

Despite the intense research activity carried during the lastdecades, there is still a considerable room for improvement.Some highlights of the main current technological challengesare as follows.

1) Developing methods and techniques to obtain stable fil-ters with high Q values. This requires a) investigation innovel techniques for increasing the number of optical tapsin FIR structures possibly by combining guided wave andfree space architectures; b) developing techniques for tapvalue control in IIR structures, and c) investigating novelstructures composed by a cascade of incoherent filters.

2) Developing more compact techniques to obtain negativeand complex coefficient filters. This requires a) researchon novel MZM and electroabsorption modulator struc-tures and b) extending the SOA-based XGM techniqueto multiple taps.

3) Refining the techniques leading to filter tunability. Mainlyby a) developing flexible microwave FSR control by op-tical means, b) achieving stronger delays in small lengths(i.e., using photonic crystal fibers), and c) developingtechniques for a tighter bounding of the tolerances indelays and filter coefficients.

4) Overcoming the effects of coherence in filters with smallvalues of T with a view of circuit integration.

REFERENCES[1] A. Seeds, Microwave photonics, IEEE Trans. Microw. Theory Tech.,

vol. 50, no. 3, pp. 877887, Mar. 2002.

[2] J. Capmany, B. Ortega, D. Pastor, and S. Sales, Discrete-time opticalprocessing of microwave signals, J. Lightw. Technol., vol. 23, no. 2,pp. 702723, Feb. 2005.

[3] J. Capmany, D. Pastor, and B. Ortega, Microwave signal processing usingoptics, in Proc. Optical Fiber Conf. (OFC), Anaheim, CA, Mar. 611,2005, pp. 2376.

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A Tutorial on Microwave Photonic Filters