Photonic simultaneous frequency identification of radio-frequency signals with multiple tones

Transcription

1 Photonic simultaneous frequency identification of radio-frequency signals with multile tones Hossein Emami,, * Niusha Sarkhosh, and Mohsen Ashourian Deartment of Electrical Engineering, Majlesi Branch, Islamic Azad University, Isfahan , Iran Deartment of Electrical Engineering, University of California Los Angeles, Los Angeles, California 9004, USA *Corresonding author: h.emami@iaumajlesi.ac.ir Received May 3; revised 9 June 3; acceted 9 June 3; osted July 3 (Doc. ID 9096); ublished July 3 A hotonic aroach to instantaneously identify frequency comonents of microwave signals with multile tones is conceived and ractically demonstrated. A mathematical model was first develoed to redict the behavior of the system. Then the system oeration was tested in ractice. The system emloys a double mixing technique that enables high-frequency measurement without the need for any highfrequency RF comonent or broadband hotodetector. The system oeration was demonstrated over a frequency range of 0. GHz. Frequency measurement of two simultaneous RF tones is demonstrated; however, the system has the otential to be exanded to measure a larger number of simultaneous RF tones. It also has the otential to oerate over a wider frequency range. 3 Otical Society of America OCIS codes: ( ) Radio frequency hotonics; (350.0) Microwaves. htt://dx.doi.org/0.364/ao Introduction In the harsh electronic warfare environment, both sides emloy electromagnetic waves to attack, sy, and detect the enemy s signals sent for the same urose. To be victorious in the battle, it is imortant to detect threat signals instantly. Instantaneous frequency measurement (IFM) receivers are designed for such urose; however, traditional IFM receivers are not able to identify more than one RF tone at once. Receiving more than one signal will lead to false frequency identification. One solution is to divide the oerating frequency range into many smaller sub-bands using a bank of band ass filters with incrementing central frequencies or using a channelized receiver with the same oeration basics. At each of these small bands, an IFM receiver will be oerating. This way, the robability of receiving two signals in one 559-X/3/550-0$5.00/0 3 Otical Society of America band will be decreased tremendously. A simultaneous signal detector also oerates in arallel with the IFM system [,]. In case of having two RF tones at the inut of an IFM receiver, the detector will generate a false signature to void the measurement made by the IFM receiver. Frequency measurement of simultaneous RF tones has thus attracted much attention in recent years. Comressive sensing has recently attracted much attention as a means of multitone RF detection. In this method, signal acquisition beyond Nyquist samling constraints becomes ossible. This way, ultrahigh-frequency comonents can be identified without the need for high-frequency comonents. In an attemt to utilize comressive sensing, the feasibility of hardware imlementation of sub- Nyquist random samling was demonstrated [3]. The system oerated based on the theory of information recovery from random samles using an efficient information recovery algorithm to comute the sectrogram of the signal. Reconstruction of signals 550 APPLIED OPTICS / Vol. 5, No. / August 3

2 samled at half the Nyquist rate with u to 5 db SNR was demonstrated. In another work, a rototye of a comressive analog-to-digital converter suitable for wideband signals that are sarse in the time-frequency lane was imlemented [4]. The imlementation was based on random demodulation architecture. This led to a maximum of 7.5% savings in bandwidth and storage memory. Microwave hotonics aroaches to measure RF frequency comonents have been of interest, too. Broadband oeration range and immunity to electromagnetic interference rovided by microwave hotonics technology [5 9] have made it an excellent candidate for electronic warfare alications. A hotonic technique for frequency measurement of simultaneous RF signals was resented in [0]. Using a disersive medium, frequency information of inut signals was maed to relative time delays. This way, measurement of the time delay led to measurement of the value of the inut signal frequency, demonstrating the caability of the technique to oerate in a sectrally cluttered environment. Frequency comonents of a microwave signal consisting two RF tones with 5 and 0 GHz frequency were identified successfully. Simultaneous measurement of frequency and ower of several microwave signals was resented in []. The system was based on the rocessing of an interferogram generated by integrating the microwave ower over the measurement band at the outut of a tunable hotonic microwave notch filter. The system exhibited a resolution of 5 MHz. The microwave hotonics techniques mentioned above are serial in nature, and are therefore unable to identify all signal frequency comonents at once. We have develoed a category of wideband yet cost-effective IFM receivers based on the hotonic aroach []. In this aer we resent a technique to measure the frequency of microwave signals comosed of multile RF tones. A roof-of-concet demonstration was resented with frequency comonent identification of two RF tones. This way, the number of band ass filters and also IFM receivers located after each filter could be reduced to half in a radar warning receiver. This is imortant since the cost of such a system could also reduce to half. The system also has the otential to be extended to measure more RF tones at once.. IFM Concet Figure (a) shows a block diagram of a basic IFM system. An RF tone with angular frequency Ω was divided into two equal ortions. One ortion is delayed relative to the other by time τ. The two RF tones were then multilied together, and the result was low-ass filtered. The outut can be described as V DC 4 cos Ωτ, which varies with inut RF frequency. The angular frequency Ω can then be calculated as Ω τ cos 4V DC. cosωt (a) cosω t + cosω t (b) Fig.. cosωt τ cosωt Module Module 90º cosω( t τ ) τ τ This system can thus be used to imlement an IFM receiver; however, in case of having two RF tones (with angular frequencies Ω and Ω ) at the inut, frequency measurement is not ossible since V DC will be a function of both Ω and Ω. Figure (b) resents a configuration that enables frequency measurement of two RF tones. Two single RF tones with angular frequencies (Ω and Ω ) was divided into two equal ortions feeding two modules; Module and Module; within each module, the RF tones were further divided into two equal ortions. One ortion was delayed relative to the other by time τ. The two ortions were then multilied together, and the outut was low-ass filtered. The outut of each module was a sinusoidal function of frequency. A 90 hase shift was introduced in one arm of Module, causing its outut to have a sine resonse, while Module exhibited a cosine resonse. The outut voltages of Modules and can thus be described as VDC cos Ω τ cos Ω τ V DC sin Ω τ sin Ω τ : Equation () is a set of two indeendent equations with two unknowns (Ω and Ω ), and thus it can be emloyed to identify both Ω and Ω indeendently. Therefore, the system of Fig. (b) could be emloyed to imlement an IFM system caable of frequency measurement of two simultaneous RF tones. 3. IFM Setu Figure shows the exerimental setu of the roosed hotonic IFM system. Two RF signal generators (SG and SG) roduced two single RF tones with angular frequencies of Ω and Ω. The signals were then combined and divided into two equal ortions. Each ortion fed one of the IFM system arms. These arms were labeled RF ath and otical ath in Fig.. The RF signal in the otical ath modulated three otical carriers roduced by a laser array. These otical carriers are emloyed to imlement a Hilbert transformer [3]. The Hilbert transformer LPF LPF V DC cosωτ LPF 4 + cos(ωt Ωτ ) 4 V DC V DC = cos Ωτ 4 = cosωτ + cosωτ = sin Ωτ + sin Ωτ (a) Basic IFM system. (b) Dual-tone IFM system. August 3 / Vol. 5, No. / APPLIED OPTICS 5509

3 Fig.. Proosed IFM setu. will act as a quadrature hybrid couler that rovides two identical signals at its oututs with 90 hase shift difference. Imlementation of this Hilbert transformer was achieved via emloying a transversal filter in which the otical carriers λ and λ layed the role of transversal tas, which were basically samles of the imulse resonse of the Hilbert transformer. Carrier λ o was emloyed as a reference to rovide 0 hase shift to which the 90 hase shift was comared. Carriers λ and λ were combined using a 3 db otical couler. This signal together with λ was modulated in ush ull mode by a Mach Zehnder modulator (MZM) to make the desired combination as shown in Fig. (a). The modulated signal was then inut to ort of an otical circulator. Port of the circulator was connected to a cascaded grating. The cascaded grating reflected each wavelength with different but uniformly incremented delays (τ 0 ). This delay was required to imlement the transversal filter. The disersed signal was outut from ort3 and inut to MZM fed with the original RF signal traversed through a coaxial cable. To ensure correct olarization at the MZM inut, both the cascaded grating and the otical circulator were selected to be olarization maintaining. The outut of MZM was then amlified by an erbium-doed fiber amlifier (EDFA) and inut to an arrayed waveguide grating (AWG) that searated all wavelengths. Carrier λ o remained searated and was used as the reference [Fig. (b)]. Carriers λ and λ were again combined using a 3 db couler to make the two-ta transversal filter [Fig. (c)]. Both signals were then detected by low-frequency hotodetectors (PD and PD), low-ass filtered, and finally measured by digital voltmeters. Having conceived an exerimental setu for the IFM system, it is now time to model the behavior of the IFM system. 4. IFM Model As shown in Aendix A, the outut voltages of the system of Fig. (V and V ) can be described as V rgp o Z L f 4a 4 4a 4a 4 M M a M M a a M M a M cos Ω τ a a M M a M cos Ω τg; () V rgp Z L f 4a 4 4a 4a 4 M M a M M 6a a M M a M sin Ω τ 0 sin Ω τ 6a a M M a M sin Ω τ 0 sin Ω τg; (3) where r denotes the hotodetectors resonsivity. P o is the otical ower level of λ o. P is the otical ower of carriers λ and λ. Z L denotes the load imedance of each hotodetector. τ and τ 0 are the differential delay between the RF ath and the otical ath and the cascaded grating delay, resectively (Fig. ). Parameter G is defined as G G LPFG EDFA L AWG L MZM L circl FBG ; (4) where G LPF, G EDFA, L AWG, L MZM, L circ, and L FBG are the low-ass filter gain, gain of the EDFA, insertion loss of the AWG, insertion loss of each MZM, insertion loss of the circulator, and insertion loss of the cascaded grating, resectively. Parameter a is defined as a π Z in P RF V π ; (5) where Z in, and V π denote the inut imedance and half-wave voltage of each MZM, resectively. P RF is the RF ower of each tone. Equations () and (3) form a set of equations with two unknowns (Ω and Ω ). 550 APPLIED OPTICS / Vol. 5, No. / August 3

4 Therefore by solving these equations, frequencies Ω and Ω can be identified indeendently. Having develoed a model that enables simultaneous frequency calculation of two inut microwave signals via solving a set of indeendent equations, it is now time to demonstrate the IFM receiver. 5. System Demonstration The system was configured as deicted in Fig.. The wavelengths of lasers were set to λ o 550, λ 55., and λ nm. The otical ower of laser sources was set to.7, 5, and.7 mw, resectively. The half-wave voltage of both MZMs was V π 5 v, and the delay τ 0 was 50 s. The factor G was 0.9. Both the hotodetectors load imedance and the MZMs inut imedance were Z PD Z in 50 Ω. P RF was set to 0 mw. Measurements were then conducted as follows. The outut frequency of SG was first set to f 0 MHz. Then SG swet a frequency range of f 0.0 GHz with 0 MHz stes while outut voltages (V, and V ) were recorded at each ste. This rocedure was conducted again with 0 MHz incremental stes for f. This was continued until f reached GHz. The measurements were then used to calculate outut frequencies using Eqs. () and (3). These results together with redicted results are shown in Fig. 3. Excellent agreement between rediction and measurement is evident. Some minor deviations can be seen at higher frequencies (after GHz), which could be attributed to the coaxial cable loss in these frequencies. To quantify the frequency measurement error, the frequency measurement rocedure was reeated 00 times and the data were recorded. For each inut frequency (f ), a maximum measurement error was then calculated (the maximum amount among the data of 00 reetitions when a band of 0.0 GHz was swet for f ). The results are shown in Fig. 4. As the inut frequency increases, the measurement error increases as exected. Secifically, after GHz, the sloe of the error curve increases with a higher Measured frequency (GHz) Fig Ω (measured) Ω (measured) Ω (redicted) Ω (redicted) Inut frequency (GHz) Measured frequency as a function of inut frequency Measurement error (MHz) Frequency (GHz) Fig. 4. Maximum frequency measurement error. rate. As stated before, this could be due to coaxial cable loss, which increases nonlinearly at this region. A maximum frequency measurement error of 93 MHz was observed. In this demonstration we have assumed the same RF ower at the inut of the system based on the assumtion that there are RF amlifiers and limiters before the system that equalize the amlitude of any received RF signal. The stand-alone system, however, is not able to identify the frequency comonents with different RF owers. But there is the ossibility to extend this design such that it becomes caable of measuring both the amlitude and frequency of each RF comonent. This would be ossible via utilizing an orthogonal measurement concet [4]. Obviously it will be at the cost of more comlexity. It would be ossible to identify frequency comonents of an RF signal with more than two tones. Figure 5 deicts a simle diagram showing a ossible extension to measure another two RF comonents (quadrule-tone IFM system). Comared to Fig., another air of modules was added with a different delay in each air. Therefore another air of measurements (V DC3 and V DC4 ) could be emloyed to quantify four frequency comonents. The amounts of τ and τ must be selected carefully such that they would not be multiles of each other. Note that these new airs could be easily integrated into the hotonic setu of Fig. by the following rocedure. Two lasers (otical carriers) would be required to imlement a new Hilbert transformer, lus another otical carrier to act as a reference for the new system. Two channels must be introduced to the cascaded grating. The recent commercial cascaded gratings have u to 50 channels. The new otical carriers would need to become combined at the outut of the AWG. Again the commercial AWGs have u to 50 channels; thus there would be no need to add another AWG. An otical couler, however, has to be used to combine the new otical carriers at the outut of the AWG. August 3 / Vol. 5, No. / APPLIED OPTICS 55

5 Module Module 90º τ τ v f Low-ass filter v f Low-ass filter V DC V DC 6. Conclusion We have demonstrated a hotonic IFM system caable of frequency measurement of dual-tone RF signals. The system oeration was demonstrated over a frequency range of 0.0 GHz with the ossibility of imrovement using all-otical mixing. Suggestions to achieve simultaneous frequency measurement of a larger number of signals were also rovided. 4-tone inut Module3 τ v f Low-ass filter V DC3 Aendix A: Calculation of V and V The IFM setu shown in Fig. has two oututs (V and V ). We therefore need to find a relationshi between these oututs and the RF inuts. Module4 90º f Low-ass filter The outut of the couler must then feed a hotodetector and finally a low-ass filter. The limitation of such architecture would thus be the number of channels of the cascaded grating and the AWG. For instance, 6 simultaneous tones could be measured using a 50-channel (only 4 channels used) AWG. The frequency measurement range could also be imroved. The oeration frequency range of the RF signal generator we used was 0 MHz to GHz. However, the lower frequency limitation is basically constrained by the MZM RF inut cut-off frequency, which is due to the couling caacitor laced at the RF inut. The cutoff frequency of this caacitor is aroximately khz; thus the system oeration frequency could be as low as khz. The uer frequency limitation is constrained by a number of factors. The MZM high-frequency resonse is a limit. To our knowledge, commercial MZMs have a maximum of GHz oeration frequency limit. However, a rototye 0 GHz MZM was reorted in [5] that could be emloyed for such a urose. The bandwidth of the cascaded grating is another limit. The cascaded grating used in this demonstration has an aroximately 0. nm bandwidth in each channel. This will lead to an aroximately 50 GHz bandwidth at 550 nm. A wider fiber Bragg grating must thus be emloyed if frequencies beyond this limit are aimed to be measured. The third limit is the RF coaxial cable resonse. Utilization of allotical mixing would remove the need for the cable [6]. Although current all-otical mixers such a semiconductor otical amlifiers or highly nonlinear fibers exhibit frequency-deendent conversion gain roblems, their frequency resonse would be higher than GHz. Integration could also be considered as another solution for removing the coaxial cable. τ v V DC 4 Fig. 5. Block diagram of a ossible extension of the dual-tone IFM system to a quadrule-tone system. Calculation of V To redict the first outut of our IFM receiver (V ) when two RF tones are inut to the system, we start with otical carrier λ o. This otical carrier has an angular frequency ω and ower of P o, and therefore can be exressed as Et E o e jωt, where E o P o. Each RF tone can also be reresented as V RF t V o cos Ωt, where Ω is the angular frequency and V o is thesignal amlitude, which can be reresented as V o Z in P RF, where Z in and P RF are the MZM inut imedance and RF ower, resectively. Assuming the same ower level for two RF tones, the inut voltage resent at the inut of MZM can thus be described as V in t V o cos Ω t cos Ω t, where Ω and Ω are the angular frequencies of each RF tone. The outut of MZM is πvin V E t Et L MZM cos B ; (A) V π where L MZM, V π, and V B are the insertion loss, half-wave voltage, and DC bias voltage of MZM, resectively: E t L MZM E o e jωt πvo cos Ω cos t cos Ω tv B : (A) V π Since MZM is biased at ositive quadrature, V B V π. Substituting the amount of V B and exanding the cosine function in Eq. (A), it can be written as E t E o e jωt cos πv o cos Ω t V o cos Ω t L MZM V π cos π 4 sin πv o cos Ω t V o cos Ω t sin π ; V π 4 (A3) where V π, and V π are half-wave voltages of MZM and MZM, resectively. Equation (A3) can also be further exanded as below: 55 APPLIED OPTICS / Vol. 5, No. / August 3

6 E t b E o e jωt fcosa cos Ω t cosa cos Ω t sina cos Ω t sina cos Ω t sina cos Ω t cosa cos Ω t cosa cos Ω t sina cos Ω tg; (A4) where a π Z in P RF V π and b L MZM. To extract all harmonics of the electrical field, we need to exand Eq. (A4) using Fourier series. Substituting the Fourier series of each term using Bessel functions of the first kind, Eq. (A4) can be exanded as E tb E o e jωt J 0 a X J 0 a X X n X n X n n J 0 a X n n J n acosnω t n J n acosnω t n J n acosn Ω t n J n acosn Ω t n J n acosn Ω t n J 0 a X X n n n J n acosnω t n J n acosnω t n J n acosn Ω t : (A5) In the electronic warfare environment the enemy s radar signal has to travel several kilometers to reach to the target, and as a result the RF signal received by the IFM system, is usually weak. Therefore, in ractice V o V π, and as a result a πv o V π. Thus for the Bessel function of the first kind, the values of J n a and J n a terms in Eq. (A5) are much smaller than J 0 a and J a, and thus they can be ignored. Note that in the case of a strong signal received by the receiver, RF limiters will ensure a small amount for the arameter a. Note that this is not only an assumtion, but also a serious issue since if the received signal is not limited, the system behaves nonlinearly and the rest of the calculations would not be valid any longer, secifically due to a third-order intermodulation roduct occurring in the system. Care also has to be taken to ensure correct bias of the MZMs since any significant drift from the quadrature oint will result in secondharmonic generation. With the assumtion above, Eq. (A5) can be simlified as E t b E o e jωt J 0 a 4J a cos Ω t cos Ω t J 0 aj acos Ω t cos Ω t: (A6) This signal traversed trough the otical circulator and cascaded grating, and the results became the inut of MZM. The otical signal at the inut of MZM can thus be described as E t b E o e jωt J 0 a 4J a cos Ω t cos Ω t J 0 aj acos Ω t cos Ω t; (A7) where b L circ L FBG b,andl circ and L FBG are the insertion loss of the circulator and the cascaded grating, resectively. At MZM, the otical signal was again modulated by the same RF signal delayed by time τ. Since the RF signal traversed through the coaxial cable, a frequency-deendent loss was also exerienced. Therefore the RF signal at the inut of MZM can be described as V in t V o MΩ cos Ω t τ MΩ cos Ω t τ; (A) where MΩ and MΩ are the absolute magnitude resonses of the coaxial cable at angular frequencies Ω and Ω, resectively. For brevity, we will use M and M instead of MΩ and MΩ. The outut of MZM can thus be written as E 3 t b 3 E o e jωt J 0 a 4J a cos Ω t cos Ω t J 0 aj acos Ω t cos Ω t J 0 am J 0 am 4J am J am cos Ω t τ cos Ω t τ J am J 0 am cos Ω t τ J am J 0 am cos Ω t τ; (A9) where b 3 L MZM b. Note that the same insertion loss was assumed for both MZMs. As mentioned before a. Also note that M and M <. The Bessel terms in Eq. (A9) can thus be aroximated as J 0 a ; J am ; J 0 am ; J a a; J am am ; J am am : (A0) Substituting Eq. (A0) in Eq. (A9), we have August 3 / Vol. 5, No. / APPLIED OPTICS 553

7 E 3 t b 3 E o e jωt 4a cos Ω t cos Ω t acos Ω t cos Ω t f 4a M M cos Ω t τ cos Ω t τ am cos Ω t τm cos Ω t τg: (A) The outut of MZM was then amlified by the EDFA, and searated using the AWG. The otical signal resent at the inut of PD can thus be written as E 3 t b 4 E o e jωt 4a cos Ω t cos Ω t acos Ω t cos Ω t f 4a M M cos Ω t τ cos Ω t τ am cos Ω t τm cos Ω t τg; (A) where b 4 G EDFA L AWG b 3, and G EDFA and L AWG are the gain of EDFA and insertion loss of AWG, resectively. The otical signal was finally detected by PD ; thus the outut current of PD can be written as I re 3 E 3 ; (A3) V rge oz L f 4a 4 4a 4a 4 M M a M M a a M M a M cos Ω τ a a M M a M cos Ω τ a 4 M a a M cos Ω τ a 4 M a a M cos Ω τ a M M cos Ω Ω τ cos Ω Ω τ a 6 M M M cosω Ω τ M cosω Ω τm cosω Ω τ M cosω Ω τg; (A6) where G G LPF b 4, and G LPF is the voltage gain of the low-ass filter. As mentioned before, the amount of a is much smaller than ; thus the last four terms can be neglected comared with the first four terms. Therefore, Eq. (A6) can be simlified as V rge oz L f 4a 4 4a 4a 4 M M a M M a a M M a M cos Ω τ a a M M a M cos Ω τg: (A7) where r is the resonsivity of PD, and denotes the comlex conjugate. I can thus be written as Finally, by substituting the amount of b 4 Eq. (A7), we have in I t rb 4 E o 4a cos Ω t cos Ω t acos Ω t cos Ω t f 4a M M cos Ω t τ cos Ω t τ am cos Ω t τm cos Ω t τg : (A4) The inut voltage of the low-ass filter can thus be calculated as V in;lpf trb 4 E oz L 4a cos Ω t cos Ω t acos Ω t cos Ω t f 4a M M cos Ω t τ cos Ω t τ am cos Ω t τm cos Ω t τg ; (A5) where Z L is the load imedance of the PD. The lowass filter will remove all harmonics excet the DC comonent. Therefore, the outut voltage of the lowass filter can be calculated by exanding Eq. (A5), and extracting the DC comonent as below: V rgp o Z L f 4a 4 4a 4a 4 M M a M M a a M M a M cos Ω τ a a M M a M cos Ω τg; (A) where the amount of factor G can be calculated as G G LPFG EDFA L AWG L MZM L circl FBG : (A9) Calculation of V To calculate the voltage V, it has to be taken into account that two otical carriers (λ and λ ) roduced this voltage. These carriers were modulated in ush ull mode; thus the electrical fields corresonding to λ and λ [E 0 t and E00 t] can be described as < E 0 t E0 t : E 00 t E00 t L MZM L MZM cos cos h πvin V B i V π h πvin V B V π i; A 554 APPLIED OPTICS / Vol. 5, No. / August 3

8 where E 0 t and E 00 t denote the electrical fields made by carriers λ and λ launched at the inut of MZM. Carrier λ was ahead in time by an amount of τ 0 comared to carrier λ o, while carrier λ was behind by an amount of τ 0 comared to carrier λ o. By following the same rocedure, the outut voltage made by each carrier can be calculated as V λ rgp Z L f 4a 4 4a 4a 4 M M a M M a a M M a M cos Ω τ τ 0 a a M M a M cos Ω τ τ 0 g; (A) V λ rgp Z L f 4a 4 4a 4a 4 M M a M M a a M M a M cos Ω τ τ 0 a a M M a M cos Ω τ τ 0 g: (A) Assuming linear behavior for PD, the amount of V can be derived by using the suerosition rincile: V V λ V rgp Z L f 4a 4 4a 4a 4 M M a M M a a M M a M cos Ω τ τ 0 a a M M a M cos Ω τ τ 0 g rgp Z L f 4a 4 4a 4a 4 M M a M M a a M M a M cos Ω τ τ 0 a a M M a M cos Ω τ τ 0 g: (A3) Equation (A3) can be simlified using trigonometric identities as below: V rgp Z L f 4a 4 4a 4a 4 M M a M M 6a a M M a M sin Ω τ 0 sin Ω τ 6a a M M a M sin Ω τ 0 sin Ω τg: (A4) References. J. B. Tsui, Simultaneous signal detector for an instantaneous frequency measurement receiver, U.S. atent 4,336,54 ( June 9).. J. B. Y. Tsui, Simultaneous signal detection for IFM receivers by detecting intermodulation roducts, U.S. atent 4,46,64 (7 January 94). 3. S. Pfetsch, T. Ragheb, J. Laska, H. Nejati, A. Gilbert, M. Strauss, R. Baraniuk, and Y. Massoud, On the feasibility of hardware imlementation of sub-nyquist random-samling based analog-to-information conversion, in Proceedings of 0 IEEE-ISCAS International Symosium on Circuits and Systems, (Institute of Electrical and Electronics Engineers, Seattle, Washington, 0), T. Ragheb, J. Laska, H. Nejati, S. Kirolos, R. Baraniuk, and Y. Massoud, A rototye hardware for random demodulation based comressive analog-to-digital conversion, in Proceedings of 0 MWSCAS Midwest Symosium on Circuits and Systems (MWSCAS) (Institute of Electrical and Electronics Engineers, 0), J. Camany and D. Novak, Microwave hotonics combines two worlds, Nat. Photonics, 39 3 (07). 6. J. Yao, Microwave hotonics, J. Lightwave Technol. 7, (09). 7. A. J. Seeds and K. J. Williams, Microwave hotonics, J. Lightwave Technol. 4, (06).. R. A. Minasian, Photonic signal rocessing of microwave signals, IEEE Trans. Microwave Theor. Tech. 54, 3 46 (06). 9. H. Emami, N. Sarkhosh, E. Loez, and A. Mitchell, Photonic feed for sinuous antenna, J. Lightwave Technol., (). 0. L. V. T. Nguyen, Microwave hotonic technique for frequency measurement of simultaneous signals, IEEE Photon. Technol. Lett., (09).. B. Vidal, T. Mengual, and J. Marti, Photonic technique for the measurement of frequency and ower of multile microwave signals, IEEE Trans. Microwave Theor. Tech. 5, 3 (0).. N. Sarkhosh, H. Emami, L. A. Bui, and A. Mitchell, Reduced cost microwave hotonic instantaneous frequency measurement system, IEEE Photon. Technol. Lett., 5 53 (0). 3. H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, Wideband RF hotonic in-hase and quadrature-hase generation, Ot. Lett. 33, 9 00 (0). 4. L. A. Bui and A. Mitchell, All otical instantaneous frequency measurement incororating otical Hilbert transformer, in Proceedings of MWP International Toical Meeting on Microwave Photonics (MWP) (Institute of Electrical and Electronics Engineers, 0), H. Kiuchi, T. Kawanishi, M. Yamada, T. Sakamato, M. Tsuchiya, J. Amagai, and M. Izutsu, High extinction ration Mach-Zehnder modulator alied to a highly stable otical signal generator, IEEE Trans. Microwave Theor. Tech. 55, (07). 6. N. Sarkhosh, H. Emami, L. A. Bui, and A. Mitchell, Photonic instantaneous frequency measurement using non-linear otical mixing, in Proceedings of 0 IEEE-MTT-S International Microwave Symosium Digest (MTT) (Institute of Electrical and Electronics Engineers, 0), August 3 / Vol. 5, No. / APPLIED OPTICS 555