An Investigation on the Performance of Receiving Optical Beam-Forming Networks

Mostafa Shabani*(1,2), Mahmood Akbari(1,3)

(1) Department of Electrical Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran,

P.O. Box 11365-9363 (2)Email: m_shabani@ee.sharif.ir

(3)Email: makbari@ee.sharif.ir

ABSTRACT: Next generation wideband and ultra-wideband radar antenna arrays need efficient true-time delay networks for array control. Following the great interest for optical control of antenna array beam steering, performance analysis of optical beam-formers is a must. In this paper signal to noise ratio and dynamic range of simple optical beam-forming structures with components off the shelf are investigated theoretically. Especially the effects of certain power combining components such as arrayed wave guide gratings, broadband passive optical combiners and microwave combiners inspected. It turns up that an efficient microwave combiner would surpass the optical combiners in both SNR and dynamic range. INTRODUCTION Next generation phased array radars require efficient true time delay beam-formers to process wideband transmitted and/or received signals [1]. Many Optical Beam-Forming Networks (OBFN), have been proposed as promising solutions especially in transmitting arrays [2, 3]. The authors found few reports to discuss the performance of OBFNs in receive mode [4, 5]. In [4] some rather new definitions for effective beam-former gain and noise-figure are proposed and different microwave and optical power combining methods are quantified through these definitions. But this reference does not discuss dynamic range limitations in OBFNs. Despite the very useful approach of this reference, some presented illustrations are not clearly characterized. Reference [5] discusses the effect of systematic noises on a wideband OBFN receiver. The receiver performance is inspected with integrated antenna pattern and impulse response benchmarks in the context of wideband arrays. This latter reference discusses neither any specific optical noise source nor any dynamic range limitation factors. The goal of this paper is to discuss the effects of different power combining methods, optical noise sources and also optical modulator and detector nonlinearities on the performance of a receiving mode OBFN. We will consider thermal noise, shot noise, Relative Intensity noise (RIN) and the optical amplifier added noise on the received Signal to Noise Ratio (SNR). Especially we are interested to evaluate the performance of networks developed with Components off the Shelf (COTS). The structure of the paper is as follow: First we will introduce our OBFN structures of interest. Then we will obtain equations for signal to noise ratio calculations. Applying these equations to different structures and components provides us with SNR comparison plots. Finally some Investigation on an OBFN Inter-Modulation-Free Dynamic Range (IMFDR) is provided. OBFN STRUCTURES In a receiving OBFN some optical sources outputs are modulated with the received signals from the array antennas. The received RF signals are often amplified by Low Noise Amplifiers (LNAs) before the optical modulation. Then in each channel a proper tunable true time optical delay mechanism is utilized to steer the antenna array pattern to a desired direction. A great amount of work on OBFNs is devoted to the way the optical true time delays are realized. Switching between different delay lines [6] or using dispersive delay lines with tunable lasers [7] are a couple of common instances. But from a performance point of view, the structure of the OBFN plays the determinant role [4]. In Fig. 1 two OBFN structures are demonstrated with the focus put on the way the signals from different channels are combined:

1- Combining channel signals after the channel optical detectors with a microwave power combiner (Fig. 1-a) 2- Combining channel signals before a single optical detector with an optical power combiner (Fig. 1-b)

978-1-4244-4885-2/10/$25.00 ©2010 IEEE

(a) (b)

Fig. 1 Microwave (a) and optical (b) power combining in OBFN structures

SIGNAL TO NOISE RATIO ANALYSIS If we represent the i’th optical source with I cos ω t φ t θ , the relevant modulator output is [8]:

1 (1)

Where is the modulator optical loss, is the intensity modulation index and is the RF signal at the modulator input. With an optical power combiner the detectors output current equals:

1 (2)

Where is the i’th time delay value and and are optical losses of the time delay and the combiner, respectively. The optional Erbium-Doped Fiber Amplifier (EDFA) gain is represented by and the optical detector responsivity is A W⁄ . Expanding (2) produces some terms around DC, , 2 , and ω ω frequencies where the 2 and ones are easily filtered out by the detector frequency response. With proper selection of the spacing between optical source wavelengths and also the detector output filter bandwidth, the last term is also filtered out and the following DC and RF terms remain:

I 2 2 (3)

For a focused array all the channel time delays compensate for the propagation delay, i.e. v v t , i and the mean square signal current equals:

2 I (4)

Obviously for an uncorrelated signal, the mean square current is 1/N of the above value. Following standard equations for noise power in analog optical links [9] the thermal, shot, RIN and signal-spontaneous beat noise powers for an OBFN with optical combiner is obtained to equal the followings:

2 I R 2⁄ , I 10 / R 2⁄ , . 4 ⁄ 1 R 2⁄ (5)

I 1 N⁄ I 1 1 (6)

Where and are the LNAs gain and noise-figure, is the input correlated noise power density in (W/Hz), is the optical source relative intensity fluctuations mean square value (in dB/Hz), R is the detector output resistance, is the optical power incident on the EDFA, is the EDFA spontaneous emission factor and is the EDFA gain. Lossless impedance matching circuits are assumed at modulator input and detector output. Using (4) to (6) the SNR of an OBFN with optical combiner can be calculated. Two available choices for the optical combiner are the Arrayed Waveguide Grating (AWG) and broadband Passive Optical Combiner (POC). AWGs are used extensively in Wavelength Division Multiplexing (WDM) systems in fiber communications. POCs are used in last mile fiber to the home solutions and are made from the combination of 2x2

fused optical fiber pairs. The extracted loss values from the Samsung™ and Zhon™ product datasheets in Tab. 1 shows the 1/N splitting loss plus some excess loss of POCs. On the other hand AWGs loss values do not scale with the number of channels. Many available 8, 16 and 40 channel AWGs with similar Gaussian or flat-top profiles show very similar loss values. By inspection we have assigned 4dB loss to 2, 4 and 8 channel AWGs and 8dB loss to 16, 32 and 64 channel AWGs. In Fig. 2 per Hz SNR of an OBFN with WDM and POC optical combiners are plotted. The superior performance of the WDM combiner is clear in the plots. It is also demonstrated that addition of an EDFA before the detector cannot increase the performance of the POC. The considered EDFA is an OFC-17F3500CA model from JDSU™ with 17dBm output power and −28 to 12dBm input power range. It was not possible to use this EDFA in combination with the WDM combiner as the input power would be higher than the mentioned limit for N>16.

Tab. 1 POC loss values extracted from Samsung™ and Zhon™ product datasheets

1x64 1x32 1x16 1x8 1x4 1x2 Number of channels

20.3 17.4 14.110.97.74.3 Samsung™ Insertion Loss(dB) 21.5 18 14.3117.53.6 Zhon™

Tab. 2 Proposed values for different optical

components characteristics

Laser output powers 20 mw

0.9 0.7 A/W

0.1

1.5dB

−165 dB/Hz

5dB

Fig. 2 SNR of a receiving OBFN with different optical combining components: WDM and wideband passive photonic combiners (POC) and also microwave

stripline combiner (MWC)

Although microwave combiners are heavier and bulkier- especially for large values of N, it improves the SNR performance of the OBFN. Similar to (1) through (6) the signal and noise powers may be obtained for a microwave combining OBFN. In Fig. 1 SNR values for a microwave combing (MWC) OBFN is also shown. The loss values for the microwave combiner are those of X-band stripline combiners from MCLI™. INTER-MODULATION-FREE DYNAMIC RANGE Optical modulators seem to be the dominant nonlinear component in an analog optical link [9]. But in an OBFN with an optical combiner and a large number of channels the amount of photodetector (PD) current may be much higher than a single optical link. Thus the nonlinear effects of PDs may start to show up with increasing number of channels. As LNAs may appear in any other beam-former we will not consider its effects on dynamic range not to mask the effects of the OBFN itself. As the quadrature biased Mach-Zehnder modulator is the general option for optical intensity modulation we will focus on this kind of modulator here. No linearization technique is considered for the modulator. “Photodetector linearity is a complex function of illumination conditions and photodetector structure” [10]. Thus it is wise to consider its effects on OBFN dynamic range with a parametric approach. The performance of a cascade of multiple nonlinear components is well understood [11]. The contour plot in Fig. 3 depicts the dependence of the output 3 order intercept point ( ) of an optical link on the PD current and the PD . The more the PD current the

more the PD dominates. In small PD currents the modulator nonlinearity is limiting. Knowing the output noise power density in an OBFN with a WDM optical combiner one may easily find the 3 order IMFDR of the OBFN using MFDR dB. Hz N [9]. This is plotted in Fig. 4 for the same parameters of Fig. 2. The plot shows

the dynamic range degradation with increasing number of channels (due to increased noise) but no remarkable dependence on the PD nonlinearities. Thus with no linearization techniques applied to the modulator, it limits the dynamic range of the OBFN with similar trends in optical and microwave power combining structures. But any linearization on the modulator side will push the limits to the detector side, where the microwave combining structure will surpass the race again. This is not discussed further in this short paper. CONCLUSIONS SNR and IMFDR for some simple OBFN structure are investigated. Especially the effects of optical and microwave power combining methods are compared considering off the shelf components. It turns up that a microwave power combining structure surpass in both SNR and dynamic range benchmarks due to smaller PD currents.

Fig. 3 Contour plot of an optical link in

terms of the optical detector and PD current Fig. 4 order IMFDR for an OBFN with an optical

power combiner

REFERENCES [1] R. J. Mailloux, "Technology for array control," in IEEE International Symposium on Phased Array Systems

and Technology, 2003. , 2003, pp. 35-39. [2] P. J. Matthews, "Photonics for phased array systems," in IEEE International Conference on Phased Array

Systems and Technology, 2000, pp. 349-352. [3] P. Ritosa and B. Batagelj, "Overview of optically driven antenna systems," in Proceedings of SPIE - The

International Society for Optical Engineering, Yalta, 2008. [4] N. M. Froberg, E. I. Ackerman, and C. H. Cox III, "Analysis of signal to noise ratio in photonic beamformers,"

in IEEE Aerospace Conference Proceedings, Big Sky, MT, 2006. [5] R. Rotman, S. Rotman, and M. Tur, "Noise considerations for wideband true time delay photonic

beamformers," in Radar Conference, 2008. RADAR '08. IEEE, 2008, pp. 1-6. [6] J. J. Lee, R. Y. Loo, S. Livingston, V. I. Jones, J. B. Lewis, Y. Huan-Wun, G. L. Tangonan, and M.

Wechsberg, "Photonic wideband array antennas," Antennas and Propagation, IEEE Transactions on, vol. 43, pp. 966-982, 1995.

[7] H. Zmuda, R. A. Soref, P. Payson, S. Johns, and E. N. Toughlian, "Photonic beamformer for phased array antennas using a fiber grating prism," Photonics Technology Letters, IEEE, vol. 9, pp. 241-243, 1997.

[8] Y. L. Guennec, G. Maury, and B. Cabon, "Performance of interferometric systems for optical processing of microwave signals: influence of laser- and microwave-phase noises," Photonics Technology Letters, IEEE, vol. 16, pp. 2120-2122, 2004.

[9] C. H. Cox, Analog optical links: theory and practice: Cambridge University Press, 2004. [10] K. J. Williams, L. T. Nichols, and R. D. Esman, "Photodetector nonlinearity limitations on a high-dynamic

range 3 GHz fiber optic link," Journal of Lightwave Technology, vol. 16, p. 192, 1998. [11] D. C. Scott, T. A. Vang, J. Elliott, D. Forbes, J. Lacey, K. Everett, F. Alvarez, R. Johnson, A. Krispin, and J.

Brock, "Measurement of IP3 in pin photodetectors and proposed performance requirements for RF fiber-optic links," IEEE Photonics Technology Letters, vol. 12, pp. 422-424, 2000.