A Tutorial on Microwave Photonic Filters

A Tutorial on Microwave Photonic Filters JoséCapmany,Senior Member,IEEE,Fellow,OSA,Beatriz Ortega,Member,IEEE,and
Daniel Pastor,Associate Member,IEEE
Tutorial
Abstract—Microwave photonicfilters are photonic subsystems designed with the aim of carrying equivalent tasks to those of an ordinary microwavefilter within a radio frequency(RF)system or link,bringing supplementary advantages inherent to photonics such as low loss,high bandwidth,immunity to electromagnetic interference(EMI),tunability,and reconfigurability.There is an increasing interest in this subject since,on one hand,emerg-ing broadband wireless access networks and standards spanning from universal mobile telecommunications system(UMTS)to fixed access picocellular networks and including wireless local area network(WLAN),World Interoperability for Microwave Ac-cess,Inc.(WIMAX),local multipoint distribution service(LMDS), etc.,require an increase in capacity by reducing the coverage area.An enabling technology to obtain this objective is based on radio-over-fiber(RoF)systems where signal processing is carried at a central office to where signals are carried from inexpensive remote antenna units(RAUs).On the other hand,microwave photonicfilters canfind applications in specializedfields such as radar and photonic beamsteering of phased-arrayed antennas, where dynamical reconfiguration is an added value.This paper provides a tutorial introduction of this subject to the reader not working directly in thefield but interested in getting an overall introduction of the subject and also to the researcher wishing to get a comprehensive background before working on the subject.
I.I NTRODUCTION
B Y MICROW A VE photonicfilter[1]–[5],we understand
a photonic subsystem designed with the aim of carrying equivalent tasks to those of an ordinary microwavefilter within a radio frequency(RF)system or link,bringing supplemen-tary advantages inherent to photonics such as low loss,high bandwidth,immunity to electromagnetic interference(EMI), tunability,and reconfigurability.The term microwave will be freely used throughout this paper to designate either RF,mi-crowave,or millimeter-wave signals.These terms will be used interchangeably.
The use and advantages of microwave photonicfilters have been thoroughly described in various references in the liter-ature.Here,we will use a simple example to illustrate this concept.Fig.1depicts a typical application configuration for a moving target identification(MTI)ground radar system[5].
Manuscript received July15,2005;revised September9,2005.This work was supported by TIC2002-04344-C02-01PROFECIA,IST-2001-37435 LABELS,the networks of excellence IST-EPIX,IST-EPHOTON/ONE,and IST NEFERTITI,and the Spanish government ayudas a parques científicos. The authors are with the Institute of Telecommunications and Multimedia (ITEAM),Universidad Politecnica de Valencia,Valencia46022,Spain(e-mail: jcapmany@dcom.upv.es).
Digital Object Identifier10.1109/JLT.2005.860478The MTI radar uses the Doppler effect to separate the targets
of interest from clutter(land,sea water,rain,etc.).To do
this,the radar sends a pulse sequence with pulse widthτ
and interpulse period PRI=1/PRF,where PRF identifies the
pulse repetition frequency.Any moving object will generate
a Doppler frequency shift∆νof the radar central frequency
f o accordin
g to its speed(dR/dt),where R(t)designates the time-varying distance from the target to the radar.The spectral
signature of each object repeats in the spectrum periodically
with a period given by the PRF,which obviously sets the limit
on determining an unambiguous Doppler shift.
Thus,focusing on a spectral region from f o to f o+PRF is enough to get all the information regarding moving targets and clutter,and what is required after signal detection is a signal processing stage to carry out thefiltering of clutter and noise(the unwanted signals)from the target(s).This is usually performed as shown in the upper part of Fig.2by using a digital notchfilter placed after frequency down-conversion to baseband and using analog to digital conversion(ADC). In order to distinguish the small echo from the target and the large echo from thefixed objects,high-performance(14-to18-bit resolution)ADCs are required,which represents a major bottleneck in the system.If the clutter can be removed before down-conversion,then the high-resolution requirements on the ADCs can be relaxed.For example,with a30-dB clutter attenuation,the required ADC resolution is reduced by5bits. This operation is difficult and costly in the microwave domain but is simple if the RF signal is modulated into an optical carrier and the whole signal is processed directly in the optical domain by means of a photonicfilter as shown in the lower part of Fig.2.
The former example illustrates the general concept behind
microwave photonicfilters[1]–[5],which is to replace the
traditional approach toward RF signal processing shown in the
upper part of Fig.3,where an RF signal originating at an RF
source or coming from an antenna is fed to an RF circuit that
performs the signal processing tasks(usually at an intermediate
frequency band after a down-conversion operation)by a novel
technique.In this approach,which is shown in the lower part
of Fig.3,the RF signal that was priorly made to modulate an
optical carrier is directly processed in the optical domain by a
photonicfilter based onfiber and integrated photonic devices
and circuits.
Adding extra photonic components implies increasedfilter
complexity on one hand but brings on the other several ad-
vantages as pointed out in most of the published literature
0733-8724/$20.00©2006IEEE
Fig.1.Example of application of a microwave photonicfilter to ground MTI
radar.
Fig.2.(Above)Typical signal processing configuration in an MTI radar system.(Below)Modified version including a microwave photonicfilter prior to down-conversion.
[6]–[44]:Optical delay lines have very low loss(independent of the RF signal frequency),provide very high time band-width products,are immune to EMI,are lightweight,and can provide very short delays that result in very-high-speed sam-pling frequencies(over100GHz in comparison with a few gigahertz with the available electronic technology).Finally,but not less important optics provides the possibility of spatial and wavelength parallelism using wavelength division multiplexing (WDM)techniques.
The purpose of this paper is to provide a tutorial introduction of this subject to the reader not working directly in thefield but interested in getting an overall introduction of the subject and also to the researcher wishing to get a comprehensive background before working on the subject.To this aim,we have structured the paper infive parts.
Section II provides an introduction to the theory of mi-crowave photonicfilters,including some very basic concepts to understand their operation as discrete timefilters and their applications,and a more detailed description of the opera-tion of single-source microwave photonicfilters(SSMPFs) and multiple-source microwave photonicfilters(MSMPFs). Section III presents and discusses their potential optical and electrical-driven limitations and the basic parameters used to evaluate their performance such as link gain,noisefigure, spurious free dynamic range(SFDR),etc.
In Section IV,we describe some of the main proposals for the implementation of microwave photonicfilters published in the literature.Obviously,there is a considerable amount of work carried by different research groups during the last years and it is impossible to describe them in detail,so we will concentrate on those that either are useful to understand the theoretical aspects,as described in Section II,or constitute a significant achievement.
Finally,Section V provides a summary,conclusions,and future challenges within thisfield of research.A complete ref-erence list of the subject including more than70bibliographical items is provided to assist the reader interested in getting more in-depth coverage of the subject.
CAPMANY et al.:TUTORIAL ON MICROW A VE PHOTONIC FILTERS
203 Fig.3.General concept behind microwave photonicfilters.The upper part shows the traditional configuration.The lower part shows the replacement of the RF filter by a microwave photonic
filter.
Fig.4.General reference layout of a microwave photonicfilter showing the relevant electrical and optical signals.
II.T HEORY OF M ICROWAVE P HOTONIC F ILTERS
A.General Concepts
A microwave photonicfilter is a photonic structure,the objective of which is to replace a standard microwavefilter used in an RF system,bringing a series of advantages(tun-ability,reconfigurability,electromagnetic immunity,etc.)that have been outlined in the prior section[1]–[5].Fig.4shows a general reference layout of a microwave photonicfilter that we will use to explain some of the basic concepts involved in its description.
Referring to the upper part of Fig.4,the RF to optical conversion is achieved by directly(or externally)modulating either a single continuous wave(CW)source or a CW source array.The input RF signal s i(t)is then conveyed by the optical carrier(s)and the composite signal is fed to a photonic circuit that samples the signal in the time domain,weights the samples, and combines them using optical delay lines and other photonic
204JOURNAL OF LIGHTW A VE TECHNOLOGY ,VOL.24,NO.1,JANUARY 2006
elements.At the output(s),the resulting signal(s)is optically RF converted by means of various optical receivers producing the output RF signal s o (t ).
The lower part of Fig.4shows an equivalent black-box repre-sentation of the aimed performance of the microwave photonic filter.In essence,it is expected to relate linearly the input and output RF signals by means of an impulse response h (t )in the time domain or by a frequency response H (Ω)in the frequency domain.In practice,however,this linear relationship can only be obtained under special operating conditions.Why this happens can be understood by observing Fig.4.Here,the only
guaranteed signal linearity is that relating the input E
i (w )and output E
o (w )optical fields to the optical subsystem by virtue of the linearity of Maxwell’s equations.This linear relationship is established through an optical field transfer function H o (w ),and hence
E
o (w )= E i (w )H o (w ).(1)
The conversion process from the input RF signal to the input
electric field to the optical subsystem is a nonlinear process since e i (t )∝ s i (t ),and similarly,the output RF signal is nonlinearly related to the output electric field from the optical subsystem since s o (t )∝ |e o (t )|2 ,where stands for the ensemble average over the possible signal fluctuations due to the coherence properties of the single or multiple optical CW sources that are employed to feed the filter.The two nonlinear operations described together with the linear relationship (1)do not yield under general circumstances an overall linear relationship between s i (t )and s o (t ),and in Sections II-B and C we will explore the conditions under which this overall linear relationship is obtained in practice.
Let us assume for the time being that this linear operation regime is possible,and therefore
s o (t )=
N r =−N
a r s i (t −rT )⇒s o (t )=s i (t )∗h (t )
h (t )=
N r =−N
a r δ(t −rT )=N n =−N
h (n )δ(t −nT ).(2)
According to the number of samples N in the impulse response sequence,the filter can be classified as either a finite impulse response (FIR)filter if N <∞or an infinite impulse response (IIR)filter if N <∞.
From (2),h (t )can be regarded as a discrete-time signal or sequence and thus the usual z and discrete-time Fourier (DTF)transform techniques developed for other filter technologies [45],[46]can be fully employed for its analysis.For instance,these are given by
H (z )=∞ n =−∞h (n )z −n H (Ω)=
∞ n =−∞
h (n )e −jn ΩT .
(3)
The operation of a microwave photonic filter can alterna-tively be described in terms of a system difference equation and
its corresponding system function
s o (t −nT )=b o s i (t )+b 1s i (t −T )+···+b M s i (t −MT )
−c 1s o (t −T )−···−c N s o (t −NT )
(4)
H (z )=
S o (z )S i (z )
=M
m =0
b M z −m 1+N
n =1
c N z −n
=
N (z )
D (z )
=Γz
N −M M
m =1
(z −z M )
N
n =1
(z −p N )
.
(5)
In (5),the system function is expressed as the quotient of
two polynomials N (z )and D (z )of the complex variable z ,the roots of which are known as the filter zeros and poles,re-spectively.The location of the filter zeros and poles depends on the values of the filter coefficients b i and c j and determine the modulus and phase response of the microwave photonic filter and whether this can be considered of minimum,maximum,or linear phase.
The observation of the microwave photonic transfer function given by (3)reveals that it is spectrally periodic with a period given by 2π/T in angular frequency units or 1/T in frequency unit.This period is known as the filter free spectral range (FSR).The spectrum of a microwave photonic filter is thus periodic,and Fig.5illustrates a typical example that we now employ to define some basic parameters related to its spectral characterization.
For bandpass filters,the spectral selectivity of any of its pass-bands (resonances)is given by the full width half maximum (or 3-dB bandwidth)denoted as ∆ΩFWHM .The filter selectivity of a given resonance is given by its quality or Q factor
Q =FSR
∆ΩFWHM
.
(6)
The value of the Q factor is related to the number of samples
(taps)used to implement it.If the number of taps is high (>10),the Q factor can be approximated for uniform filters by the number of taps Q ∼=N .This relation can be slightly corrected (Q <N )for windowed filters.Q factors as high as 237[32]and 938[11]have been reported for FIR and IIR microwave photonic filters,respectively.Recently,this figure has risen up to Q >3000[78]using a novel technique to obtain single resonance microwave filters.
Finally,the filter rejection of nonadjacent channels is mea-sured through the main to secondary sidelobe ratio (MSSR)also shown in Fig.5.
CAPMANY et al.:TUTORIAL ON MICROW A VE PHOTONIC FILTERS
205
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 source output electric field √I i e j (w o t +φ(t ))(where I i represents the optical intensity,w o the source central frequency,and φ(t )the source phase fluctuations)is modulated by the RF input signal s i (t )and the different filter samples are implemented by means of delayed and windowed replicas of the RF-modulated optical carrier.In Fig.6(a)and (b),we show two possible implementations of an FIR and an IIR SSMPF,respectively.In the first case,a transversal filter is shown where the electric field of the input RF-modulated optical signal is evenly divided into the N outputs of a 1×N coupler.Output port j ,for instance,is connected to an attenuator,providing a field attenuation
coefficient √
a j −1and an optical delay (j −1)T ,where T is the filter basic delay.Filter samples are then evenly combined by an output N ×1coupler.At the output port of this device,the overall electric field E o (t )is composed of the interference of all the delayed and this signal is fed to an output photodiode that converts the optical signal into the final output RF signal s o (t ).The overall filter structure thus relates the input and output microwave/RF signals given in volts or amperes.In the case of the IIR structure,infinite samples of the modulated electrical field are generated.Fig.6(b)shows,in particular,a microwave photonic filter based on a single cavity recirculating delay line formed by joining together two output ports of a fiber coupler,providing a basic delay per cavity recirculation given by 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.,
E 0(t )= I i
N −1 r =0
[a r s i (t −rT )]1
2e j (w 0(t −rT )+φ(t −rT )).(7)The upper number in the sum is N for the FIR case and N →∞for the IIR case.The output current from the photodiode is
(assuming a detector responsivity )
I 0(t )=
|E 0(t )|
2
= I i
N −1 r =0
[|a r |s i (t −rT )]
+ I i N −1 r =0N −1 s =r
a r a ∗s s i (t −rT )s i (t −sT )
×Γ((r −s )T ).
(8)
In the above expression, represents the ensemble average
over the signal fluctuations due to the stochastic process de-scribing the source phase noise,and Γstands for the optical source degree of coherence,and we assume as it is customary that phase fluctuations of the optical source are modeled by an ergodic process
Γ((r −s )T )∝e
−
|(r −s )T |τcoh
.(9)
τcoh =1/π∆νis the source coherence time,which is in-versely proportional to the source linewidth ∆νin the absence of modulation (i.e.,under CW operation).A crucial aspect that is connected with the filter operation is that of the optical source coherence,as we shall now discuss.
In principle,filter linearity is only guaranteed in the optical fields (due to the linearity of Maxwell equations)but not as far as optical powers are concerned.However,this last magnitude is related to the input and output currents or voltages of the RF signals since there is a linear relationship between the output optical power and the input current/voltage at the source and between the input optical power and the output electrical current/voltage at the optical receiver.
As shown in (8),the general shape of the output current is composed of two terms,an incoherent term where the output current/voltage is linearly related to the input RF signal and a coherent term that depends on the source degree of coherence and destroys,in principle,power linearity.
206JOURNAL OF LIGHTW A VE TECHNOLOGY,VOL.24,NO.1,JANUARY
2006
Fig.6.(a)Layout of an FIR SSMPF.(b)Layout of an IIR SSMPF.
If the optical source has a coherence time much smaller than
the basicfilter delay(τcoh T),then the second term in(8)
vanishes and a linear relationship between the input and output
RF signals results,i.e.,
I0(t)=s o(t)= I i N−1
r=0
[|a r|s i(t−rT)].(10)
Filters fulfilling this condition of operation are known as incoherentfilters and bring in principle several advantages. For instance,thefilter impulse response as seen in(10)does not depend on any optical phase.This makes thesefilters very stable against environmental conditions(i.e.,temperature variations,mechanical vibrations,etc.)and is the main reason why most of the implemented architectures so far are based on this paradigm.The main disadvantage is that thefilter coefficients are positive since,according to(8),the coefficients are given by|a r|=
|a r|2.Thus,in principle,onlyfilters with positive coefficients can be implemented using this approach. In the early1980s,Goodman,Moslehi,and others showed that filters with positive coefficients are severely limited since they always implement a resonance at baseband and,most notably, the range of transfer functions that can be implemented shows poor performance in terms offilter selectivity and roll-off. This limitation,however,has been overcome and,as we will see in the next section,today it is possible to implement
CAPMANY et al.:TUTORIAL ON MICROW A VE PHOTONIC FILTERS207 incoherentfilters with negative coefficients using a variety of
techniques.
On the other extreme,if the optical source has a coherence
time much bigger than the basicfilter delay(τcoh>T),then
thefilter works under coherent operation regime and(9)can be
approximated by
Γ((s−r)T)=e jw o(s−r)T.(11)
Therefore,(8)is now given by
s o(t)= I i N−1
r=0
[|a r|s i(t−rT)]
+ I i N−1
r=0
N−1
s=r
a r a∗s s i(t−rT)s i(t−sT)e jw o(s−r)T.
(12)
As it can be observed,the output RF signal is composed by
a set of weighted and delayed replicas of the RF-modulating
signal plus an interfering term which is optical phase sensitive.
Although the overall weight coefficient of a given output sam-
ple can now be negative,thefilter will now be very dependent
on environmentalfluctuations since part of the coefficients
depends on the evolution of optical phases.Coherent SSMPFs
are 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 signal
s i(t).The source array can be implemented either by using an array of independent lasers,the output spectrum of a low-
cost Fabry–Pérot laser,or by slicing the output of a broadband
source(i.e.,LED or SLED)by means of a periodic opticalfilter.
Regardless of the particular option,the electricfield prior to RF
modulation is given by
E S(t)=N−1
r=0
I r e j(w r t+φr(t))(13)
where I r,w r,andφr(t)represent,respectively,the optical in-tensity,the source central frequency,and the phasefluctuations of the r th component of the array.Each source implements a filter sample that is selectively delayed usually by employing a dispersive(i.e.,wavelength selective)delay line implemented either by afiber coil or by a linearly chirpedfiber Bragg grating (LCFBG).The dispersive delay element is chosen such that the differential group delay experienced by adjacent wavelengths of the source array is T.Sample windowing can be achieved using different techniques.If the MSMPF is based on an array of independent sources,then the simplest way is to control the output 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 basis and then multiplexed prior to RF modulation.Fig.7(a)and (b)show the two possible implementations of an MSMPF dis-cussed above.
The output electricfield from impinging on the photodiode in this case is given by
E0(t)=
N−1
r=0
a r s in(t−rT)e j(w r(t−rT)+φr(t−rT)).(14)
The output current from the photodiode is(assuming again a detector responsivity )
I0(t)=
|E0(t)|2
=
N−1
r=0
[|a r|s i(t−rT)]
+
N−1
r=0
N−1
s=r
a r a∗s s i(t−rT)s i(t−sT)
×e j(w r−w s)t e j(sw s−rw r)T
e j[φr(t−rT)−φs(t−sT)]
=
N−1
r=0
[|a r|s i(t−rT)].(15)
The second term in the above expression is zero since the output phase variations from different optical sources can be assumed to be always uncorrelated.Thus,a linear relationship between the input and output RF/microwave signal is obtained.
D.Applications of Microwave Photonic Filters
Apart from the application to thefield of ground radars[6] outlined in Section I,there are certainly a wide range of appli-cations where microwave photonicfilters can be of interest.For instance,in the emerging broadband wireless access networks and standards spanning from universal mobile telecommuni-cations system(UMTS)tofixed access picocellular networks and including wireless local area network(WLAN),World Interoperability for Microwave Access,Inc.(WIMAX),local multipoint distribution service(LMDS),etc.,there is a need to increase the capacity by reducing the coverage area[47].An enabling 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)usingfiber optic transmission as shown in the upper part of Fig.8.RoF makes it possible to centralize the RF signal processing functions in one shared location(headend).By so doing,RAUs are simpli-fied significantly as they only need to perform optoelectronic conversion and amplification functions.The centralization of RF signal processing functions enables equipment sharing,dy-namic allocation of resources,and simplified system operation and maintenance.The processing at the headend involves a prior frequency down-conversion,ADC,and baseband process-ing using a DSP as shown in the intermediate part of Fig.8, which illustrates a directfiber link joining a given RAU and the headend.The down-conversion operation can be eliminated or divided into two steps,putting less stringent requirements on the ADC and DSP operations if a microwave photonicfilter
208JOURNAL OF LIGHTW A VE TECHNOLOGY,VOL.24,NO.1,JANUARY
2006 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 part of Fig.8.
The microwave photonicfilter can be employed either for channel rejection[48],[49]or for channel selection applica-tions[50]–[52].In thefirst case,we deal with an optical link where not only the desired signal is carried by thefiber but also unwanted interfering signals that are also picked up by the antenna.A paradigmatic example can be found in radio astronomy applications[49],where signal transmission from several stations to a central site requires removing strong man-made interfering signals from astronomy bands.The ability to reject these interfering RF signals directly in the optical domain is a unique characteristic of these photonicfilters.Another application example is for noise suppression and channel in-terference mitigation in the front-end stage after the receiving antenna of an UMTS base station prior to a highly selective SAWfilter.In the second case[50],the signal carried by the optical link is composed of a frequency plan that comprises several disjoint parts of the RF spectrum(UMTS,HIPERLAN, LMDS,etc.).Here,a bandpass photonicfilter can be employed to select a given RF band or spectral region.Furthermore, the selected band can be changed if thefilter is tunable:a feature uncommon to traditional microwavefilters but possible in microwave photonicfilters,as we shall see in Section III. In both cases,the position of the frequency notch or thefilter bandpass can be as low as a few megahertz or as high as several tens of gigahertz due to the broadband characteristics of photonic delay lines.Microwave photonicfilters can also be of interest in applications where lightweight is a prime concern,for example,as analog notchfilters are also needed to achieve cochannel interference suppression in digital satellite communications systems[53].
Another important application of microwave photonicfilters is in thefield of true time delay beamsteering of antenna arrays [54].A photonic true time delay system for feeding an array of antennas is based on the use of broadband photonic delay lines.
CAPMANY et al.:TUTORIAL ON MICROW A VE PHOTONIC FILTERS
209 Fig.8.RoF access network(upper).Potential application of microwave photonicfilters at the head-end on the centralized station(lower)replacing the RFfilter of 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 transversal filter(see Fig.19).
The feeder network for an array of N antennas is essentially equivalent to an N-tap microwave photonic tunable FIRfilter where the basicfilter delay T can be altered,the only difference being that eachfilter sample is detected by a different optical receiver that is placed before each antenna unit in the array. Fig.9shows an example of a photonic beamsteering system that is based on using a dispersive delay line implemented by an LCFBG featuring a dispersion parameter of D ps/nm in combi-nation with a bank of N tunable laser sources.The wavelength distance∆λbetween adjacent sources is kept constant.The RF signal to be radiated modulates the whole set of optical sources and each wavelength is selectively delayed by the LCFBG and then directed to a particular optical receiver feeding an element of the array after being demultiplexed.The phase difference for an RF signal of frequencyΩbetween adjacent elements is given by∆Φ=ΩD∆λ,so it can be easily changed by changing∆λ. Tofinalize this list of potential applications,it should not be forgotten that the very high bandwidth and potentially low de-lays(5s/m)that can be achieved with optical delay lines make them an ideal technology option for the implementation of sig-nal correlators[55]for very high speed signals and incoherent optical code division multiplexing(OCDMA)applications.。