Photonic True-Time Delay Beamforming Based on Polarization-Domain Interferometers
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2492 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 28, NO. 17, SEPTEMBER 1, 2010
Photonic True-Time Delay Beamforming Based onPolarization-Domain Interferometers
Miguel V. Drummond, Student Member, IEEE, Paulo P. Monteiro, Member, IEEE, andRogrio N. Nogueira, Member, IEEE
AbstractIn this paper, we propose a novel photonic true-timedelay beamforming system for phased array antennas. The systemrelies on tunable delay lines which are based on MachZehnderdelay interferometers (MZDIs) with tunable coupling ratio. As theMZDIs are implemented on the polarization domain, a single op-tical source and a single piece of polarization maintaining fiber arerequired. The proposed implementation is theoretically assessedand beam squinting is investigated by simulation. A proof-of-con-cept experiment that validates the operation principle of the pro-posed delay lines is presented.
Index TermsMachZehnder delay interferometer (MZDI),phased array antennas, photonic true-time delay beamforming.
D EMANDING wireless applications such as electronicwarfare systems and broadband wireless networksrequire advanced antenna systems which can provide highsensitivity, broad bandwidth operation, and wide and preciseangular control . With this end, phased array antennas(PAAs) with photonic beamforming systems have been in-tensively investigated over the last years. Such systems sharethe advantages of microwave photonics, such as low losses,high time-bandwidth products, light weight and immunity toelectromagnetic interference. As broad bandwidth operation isrequired, photonic true-time delay (TTD) beamforming shouldbe used to avoid beam squinting.
Different photonic TTD beamforming techniques basedon different optical delay lines have been proposed .Optical fibers with different lengths can be used to providediscretely tunable delay lines . The photonic beamformingsystem therefore consists on a switchable fiber optic network.This approach has scalability problems. For a PAA composedby several antenna elements, a fiber optic network with manyfibers is required, which results in a bulky system. Another wellknown approach is to take advantage of chromatic dispersion. In , tunable laser sources are multiplexed and
Manuscript received January 18, 2010; revised June 20, 2010 and June 28,2010; accepted June 30, 2010. Date of publication July 15, 2010; date of currentversion August 18, 2010. This work was supported by the THRONE (PTDC/EEA-TEL/66840/2006) Fundao para a Cincia e Tecnologia (FCT) Project.The work of M. V. Drummond was supported by the FCT under the SFRH/BD/40250/2007 scholarship.
The authors are with the Instituto de Telecomuniaces, Universidadede Aveiro, 3810-193 Aveiro, Portugal (e-mail: firstname.lastname@example.org; email@example.com; firstname.lastname@example.org).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JLT.2010.2057408
modulated by the input RF signal, where is the number ofantenna elements of the PAA. The multiplexed signals are thenpropagated in a dispersive medium, thus acquiring a time delaydependent on their wavelength. Tunable delays among themodulated signals are achieved by tuning the wavelength of theoptical sources. This technique also has scalability problems,as the number of tunable lasers increases with the number ofantenna elements of the PAA. The dispersive medium can beimplemented with a chirped fiber Bragg grating (CFBG) or a dispersive optical fiber . A CFBG offers a compactimplementation. However, the group delay ripple must be lowto avoid signal distortion and beam squinting .
A novel technique based on ring resonators has recently in-troduced a new concept in . Instead of having a constant timedelay across the entire spectral bandwidth of the optical signal,the time delay only needs to be constant at the modulated RF car-rier, as long as the phase of the optical carrier is adjusted. Suchconcept relaxes the bandwidth requirement of the tunable delaylines down to the spectral bandwidth of the data signal mod-ulated onto the RF carrier. This is especially important whenhigh-frequency RF carriers are employed. However, this con-cept is limited to optical single sideband signals with monochro-matic optical carrier.
In this paper, we propose a novel photonic TTD beamformingtechnique based on an improved concept: the amplitude andgroup delay responses only need to be correct at the opticaland RF carriers. The proposed scheme allows using double orsingle sideband signals with monochromatic or modulated op-tical carrier. The tunable delay lines are implemented with po-larization-domain MachZehnder interferometers. Each inter-ferometer has a tunable coupling ratio, which allows tuning thetime delay between 0 and , where is the differential groupdelay (DGD) of the polarization-domain interferometer (PDI).The optical and RF carriers are set at different maxima of thePDIs amplitude response, thus sharing the same frequency re-sponse. As a result, the bandwidth requirement of the tunabledelay lines is relaxed down to the spectral bandwidth of the datasignal modulated onto the RF carrier. The proposed beamformerstructure uses only one optical source that needs not to be tun-able and a single birefringent medium.
The remainder of this paper is organized as follows. A math-ematical description of the proposed photonic beamformingsystem is presented in Section II. Section III presents sim-ulation results which analyze the impact of beam squinting.A proof-of-concept experiment with the purpose of assessingthe operation principle of one PDI is described in Section IV.Section V states the main conclusions of this work.
0733-8724/$26.00 2010 IEEE
DRUMMOND et al.: PHOTONIC TTD BEAMFORMING BASED ON POLARIZATION-DOMAIN INTERFEROMETERS 2493
Fig. 1. Photonic TTD beamforming scheme considering a PAA with antenna elements.
II. OPERATION PRINCIPLEThe photonic TTD beamforming scheme is depicted in Fig. 1.
A laser source provides a CW signal with a wavelength of .A MachZehnder modulator is used to modulate the CW signalwith the input RF signal. The polarization controller PC 0 setsthe state-of-polarization (SOP) of the modulated signal at 45with the slow axis of the polarization-maintaining fiber (PMF),which has a differential group delay of . Thus, at the output ofthe PMF there are two modulated signals delayed by , com-bined in orthogonal polarization. A 1: optical splitter is usedto replicate the PMF output signal, where is the number ofantenna elements of the PAA. Each output of the 1: opticalsplitter is connected to a polarization controller (PC) and a polar-izer. This allows performing a weighted addition of the polariza-tion combined signals, therefore resulting in a MachZehnderinterferometer with tunable coupling ratio. The output signal ofeach polarizer is converted to the electrical domain using a pho-todetector (PD) and then fed to the respective antenna element.The photonic beamformer is thus composed by PDIs. Thecoupling ratio of each PDI can be tuned by appropriately set-ting the corresponding PC.
The analysis of the beamforming scheme is divided in twosteps. Firstly, the beamformer is theoretically described. Sec-ondly, beam squinting analysis is conducted.
A. Theoretical AnalysisThe tuning principle of the tunable delay lines implemented
with PDIs is similar to the one presented in , with the dif-ference that in this work time delays are considered instead ofdispersive media.
The transfer function of one PDI is given by
(1)where is the angular difference between the slow axes of thePMF and polarizer . The value of can be set by the PC . Theamplitude and group delay responses of the PDI can be derivedfrom (1)
Fig. 2. Amplitude (a) and group delay (b) responses of the PDI for differentvalues of . As shown in (a), the carriers of the optical signal are centered atdifferent maxima of the PDIs amplitude response.
Both responses are depicted in Fig. 2. A periodical behavior witha period of is obtained. Fig. 2(b) shows that the group delaycan be changed with , however at the cost of also changingthe amplitude response. There are two options for centering theoptical signal with the response of the PDI. The first one is toset the optical signal within only one period of the frequency re-sponse. This approach limits the bandwidth of the optical signalto be lower than . Moreover, the attenuation of the RF carriersrelatively to the optical carrier depends on . The other optionis to center the optical and RF carriers at different maxima of thePDIs response, as depicted in Fig. 2(a). Mathematically this canbe written as
where is the frequency of the RF signal. In order to avoidsignal distortion, the bandwidth of the signal modulated ontothe RF carriers should be lower than . In comparison to thelatter option, this relaxes the PDIs bandwidth requirement asthe bandwidth of the optical signal is usually much higher than
2494 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 28, NO. 17, SEPTEMBER 1, 2010
Fig. 3. Amplitude and group delay responses of the PDI for .
the bandwidth of the signal modulated onto the RF carriers. An-other advantage is that the amplitude and group delay responsesare the same for all the carriers, for any value of . The varia-tion of the group delay and amplitude responses with for allcarriers is shown in Fig. 3.
The tunable time delay range required to achieve a beamsteering tuning range of 180 can be derived from the arrayfactor of a PAA, defined as
where is the spatial angle around the orientation axis of thePAA, is the amplitude of the RF signal, is thewavenumber of the RF signal, is the distance between twoadjacent antenna elements and is phase shift applied to therespective antenna element. In case of a TTD beamformer
where is the time delay. In order to achieve a phase shiftbetween 0 and for should have a tuning range of
. This corresponds to the maximum time delay betweentwo adjacent antennas. Therefore, the maximum delay requiredby the PAA is of
The tunable time delay range can be of , or of. In practice, the latter range only
requires an absolute maximum delay of . In
order to obtain positive delays one has, while for negative delays
, whereis a constant defined by the target beampointing angle
. The DGD of the PDI should therefore be of .This condition complies with (3). However, the exponentialterm in (1) assumes negative values for even values of , as
. In this case, the optical carrier is setat a minimum (maximum) of the amplitude response, whereasthe RF carriers are set at maxima (minima). This situationcan be resolved by considering a higher maximum delay of
. According to these considerations, the DGDof the PDI is
when is oddwhen is even. (7)
Equation (7) shows that the required is proportional to thenumber of antenna elements. On the other hand, the bandwidthof the amplitude response is inversely proportional to . Assuch, there is a tradeoff between maximum delay and band-width. Nonetheless, the bandwidth of the optical signal mod-ulated onto the RF carrier usually increases at the cost of alsoincreasing the RF carrier frequency, which according to (7) de-creases the required . In this case, high signal bandwidths canbe accommodated by the beamformer, since a low is required.
B. Beam Squinting AnalysisTTD operation can be demonstrated using the same analysis
as in . The modulated optical double sideband (DSB) signalsat the input of the PDs, , can be written as a sum of threespectral lines,
(8)where is the optical carrier frequency. After direct detectionof , the photocurrent can be expressed by
and (10), shown at the bottom of the page, where is thephase of . The phase of the photocurrent is given by(11), shown at the bottom of the page. As depicted in Fig. 2(a),
. From (1), it
DRUMMOND et al.: PHOTONIC TTD BEAMFORMING BASED ON POLARIZATION-DOMAIN INTERFEROMETERS 2495
Fig. 4. Group delay variation with , considering different values of .The group delay variation is given by .
can be seen that .Hence, (10) and (11) are simplified to
Equation (13) shows that TTD operation is achieved acrossa given bandwidth, at which the approximation is valid. Theobtained time delay depends on the optical carrier frequency.Fig. 4 shows that group delay error increases with the frequencyshift, defined as , where is the frequencyat which a maximum of the interferometer response shouldbe located. The error also depends on , being maximumfor of about 20 and 70 . Therefore, a frequency shift of theamplitude response maximum from causes beam squinting.This can be particularly serious if the PDIs have differentfrequency shifts. The amount of squinting also depends on theconsidered values of .
Equation (12) shows that the amplitude of the RF signal de-pends on the optical carrier frequency, i.e., ,and thus also of . Even when there is no frequency shift of theamplitude response, the amplitudes of the RF signals can differup to 3 dB depending on . This is depicted in Fig. 3. Equation(4) shows that target beampointing angle only depends on thephase of the RF signals, . Hence, deviations ofthe RF amplitudes do not cause beam squinting, although beamshaping is obtained.
For RF signals with broad data bandwidth or with an RF fre-quency not compliant with (3) the approximation done in (13) isnot valid. Under such conditions, the phase of the photocurrentis given by
where is the frequency of the PDIs amplitude responsemaximum nearest to . The phase of the detected RFsignal mainly depends on the group delay of the optical carrier,as . The first term corresponds to the phase
Fig. 5. Radiation diagrams for of (a) 0 , (b) 20 , (c) 45 , and (d) 60 .The solid line represents the proposed beamformer; the dashed line representsan ideal TTD beamformer.
shift originated by the frequency detuning between the RF car-rier and . If such detuning is zero, thenand . Under such condition (14) can be writtenas (13).
Finally, it should be noted that the analysis performed on(12)(14) is also valid for single sideband signals. By sup-pressing the RF carrier at , (12) and (13) become
III. SIMULATION RESULTS
The proposed beamformer was simulated considering a PAAwith antenna elements, GHz, and a distancebetween two adjacent antenna elements of mm.According to (7), ps. An optical DSB signalwas considered. Thus, the amplitude and phase of the RF signalswere obtained from (12) and (13). The radiation diagrams wereobtained using (4). Results considering different target beam-pointing angles are shown in Fig. 5. Beam squinting is not ob-served. However, beam shaping arises from the dependence ofthe RF amplitudes with the required time delays. Even thoughthe observed beam shaping is insignificant, it can be controlledusing variable optical attenuators at the outputs of the 1: op-tical splitter. Other option is to use RF amplifiers with variablegain after the PDs.