Photonic receiving and linearization of RF signals with improved spurious free dynamic range

Photonic receiving and linearization of RF signals with improved spurious free dynamic range

Optics Communications 423 (2018) 17–20 Contents lists available at ScienceDirect Optics Communications journal homepage: www.elsevier.com/locate/opt...

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Optics Communications 423 (2018) 17–20

Contents lists available at ScienceDirect

Optics Communications journal homepage: www.elsevier.com/locate/optcom

Photonic receiving and linearization of RF signals with improved spurious free dynamic range Xiang Zhu, Tao Jin *, Hao Chi, Guochuan Tong, Tianhao Lai, Dong Li College of Information Science and Electronic Engineering, Zhejiang University, 38 Zheda Road, Hangzhou, 310027, China

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Keywords: Microwave photonics Intermodulation distortion Intensity modulation Analog optical signal processing

ABSTRACT A linearization scheme for receiving broadband radio frequency (RF) is theoretically analyzed and experimentally demonstrated. The system uses three intensity modulators (IMs) to impose a two-tone RF signal on an optical carrier. We demonstrate that the linearization technique can be used to suppress the third-order intermodulation distortion (IMD3) and the five-order inter-modulation distortion (IMD5) components simultaneously. An improvement of the spurious free dynamic range (SFDR) as large as 112.13 dB in 1-Hz bandwidth is achieved, which is 13.5 dB higher than the SFDR of a conventional intensity-modulated scheme.

1. Introduction Analog photonic links have numerous advantages over conventional coaxial analog links, such as low propagation loss, large bandwidth, small size, low cost and immunity to electromagnetic interference [1,2]. Photonic-assisted techniques, therefore, are widely used in microwave receivers to overcome the bandwidth limitation. However, a modulator used in the link is known to be inherently nonlinear in response and may introduce highly nonlinear distortions to signals, such as harmonic distortion, cross-modulation distortion (XMD) and inter-modulation distortion (IMD). The IMD dominates spurious free dynamic range (SFDR) loss [3]. Many methods have been proposed to eliminate IMD [1–16]. Most of them focus on eliminating third-order IMD (IMD3) [1–14]. However, when IMD3 is suppressed, fifth-order IMD (IMD5) poses the limit to the link’s dynamic range. A digital multistage postprocessing technique has been proposed in [15] to suppress lowerorder and higher-order distortions. One of the disadvantages of the post-processing method is the narrow processing bandwidth. Another method to eliminate the IMD3 and any higher-order distortion is to utilize the nonlinear optical process of cascaded four-wave mixing [16]. The ambient temperature sensitivity of components such as the highly nonlinear fiber (HNLF) and the optical filter makes it difficult to maintain a given optical power ratio and path matching for a long time between the two branches needed to eliminate the distortions. In this paper, we propose a linearization scheme for receiving broadband radio frequency (RF). In the scheme, the received RF signal is divided into three branches and modulated by three intensity modulators (IMs). After being separately detected by three photodetectors *

(PDs), the beating signals are combined by two electrical couplers (ECs). By adjusting the IMs, the electrical attenuator and the optical attenuator, the system can simultaneously eliminate IMD3 and IMD5. 2. Theory The proposed linearized microwave photonic receiving scheme is shown in Fig. 1. The input RF signal is a two-tone signal (RF1 & RF2) with two center angular frequencies of 𝜔1 and 𝜔2 . Three IMs (IM1, IM2 and IM3) driven by the two-tone RF signal are used to modulate a continuous-wave laser carrier. The lower branch contains IM1, and the upper branch contains two cascaded IMs (IM2 and IM3). The outputs of the three IMs are photoelectrically converted, respectively. Before being combined, they are separately scaled in both magnitude and phase to meet several requirements. Then they are combined and bandpassfiltered to produce a linearized signal with the complete elimination of IMD3 and IMD5. Mathematically, the laser output field can be written as √ 𝐸𝐿𝑂 (𝑡) = 𝐴𝑒𝑗𝜔𝑐 𝑡 (1) √ where 𝐴 is the amplitude of the optical field, 𝜔𝑐 is the angular frequency of the laser carrier. After being modulated by the two-tone RF signal, the optical field at the output of IM1 can be expressed as √ √ ( ) 1√ √ 𝜂 𝐴1−𝑙𝑜𝑠𝑠 𝐴𝑒𝑗𝜔𝑐 𝑡 1 + 𝑒𝑗𝜑1 𝑒𝑗𝐹 (𝑡) 𝐸1 (𝑡) = (2) 2

Corresponding author. E-mail address: [email protected] (T. Jin).

https://doi.org/10.1016/j.optcom.2018.03.072 Received 30 January 2018; Received in revised form 26 March 2018; Accepted 27 March 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.

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Optics Communications 423 (2018) 17–20

√ √ where 𝜂 is the attenuation factor of the optical attenuator, 𝐴1−𝑙𝑜𝑠𝑠 is the insertion loss of IM1, 𝜑1 is the bias phase shift of IM1. 𝐹 (𝑡) = ( ) ( ) 𝑚1 sin 𝜔1 𝑡 + 𝑚2 sin 𝜔2 𝑡 , here 𝑚𝑖 is the modulation index, 𝑚1 = 𝜋𝑉1 ∕𝑉𝜋 and 𝑚2 = 𝜋𝑉2 ∕𝑉𝜋 , 𝑉1 and 𝑉2 are the amplitudes of the two-tone RF signal. The three IMs are assumed to have the identical half-wave voltage of 𝑉𝜋 . After photodetection, the received electrical signal at the output of PD1 is given by ( ( )) 𝑉1 (𝑡) = 𝜂𝑅𝐴1−𝑙𝑜𝑠𝑠 𝐴 1 + cos 𝜑1 + 𝐹 (𝑡)

(3)

where 𝑅 is the responsivity of PD. Applying the Jacobi–Anger expansion to (3), the components of the fundamental tones (𝜔1 , 𝜔2 ) are found to be ( ( ) ( ) ( ) ) ( ) 𝐽0 𝑚2 𝐽1 𝑚1 sin 𝜔1 𝑡 ( ) ( ) ( ) (4) 𝑉1−𝑏 (𝑡) = −2𝜂𝑅𝐴1−𝑙𝑜𝑠𝑠 𝐴 sin 𝜑1 ⋅ + 𝐽0 𝑚1 𝐽1 𝑚2 sin 𝜔2 𝑡 and the components of IMD3, IMD5 and IMD7 tones are ( ) 𝑉1−𝐼𝑀𝐷 (𝑡) = −4𝜂𝑅𝐴1−𝑙𝑜𝑠𝑠 𝐴 sin 𝜑1 ( ) ( ) ( ) ( ) ⎛𝐽1 𝑚1 𝐽2 𝑚2 sin 𝜔1 𝑡 sin 2𝜔2 𝑡 ⎞ ( ) ( ) ( ) ( ) ⎟ ⎜ ⎜+ 𝐽2 (𝑚1 ) 𝐽1 (𝑚2 ) sin (2𝜔1 𝑡) sin (𝜔2 𝑡 )⎟ ⎜+ 𝐽 𝑚 𝐽 𝑚 sin 3𝜔 𝑡 sin 2𝜔 𝑡 ⎟ 3 1 2 2 1 2 ⎟ ( ) ( ) ( ) ( ) ⋅⎜ ⎜+ 𝐽2 𝑚1 𝐽3 𝑚2 sin 2𝜔1 𝑡 sin 3𝜔2 𝑡 ⎟ ( ) ( ) ( ) ( )⎟ ⎜ ⎜+ 𝐽4 𝑚1 𝐽3 𝑚2 sin 4𝜔1 𝑡 sin 3𝜔2 𝑡 ⎟ ( ) ( ) ( ) ( )⎟ ⎜ ⎝+ 𝐽3 𝑚1 𝐽4 𝑚2 sin 3𝜔1 𝑡 sin 4𝜔2 𝑡 ⎠

Fig. 1. Block diagram of the proposed linearized microwave photonic receiving scheme. IM: intensity modulator, RF: radio-frequency, A: Erbium doped fiber amplifier, PD: photodetector, EC: electrical combiner, BPF: electrical bandpass filter, 𝛾: the attenuator factor of the electrical attenuator, 𝜂: the attenuation factor of the optical attenuator.

(5)

and the components of IMD3, IMD5 and IMD7 tones are ( ) 𝑉3−𝐼𝑀𝐷 (𝑡) = 2𝑅𝐴2−𝑙𝑜𝑠𝑠 𝐴3−𝑙𝑜𝑠𝑠 𝐴𝐸𝐷𝐹 𝐴 𝐴 sin 2𝜑1 ( ) ( ) ( ) ( ) ⎞ ⎛𝐽1 2𝛾𝑚1 𝐽2 2𝛾𝑚2 sin 𝜔1 𝑡 sin 2𝜔2 𝑡 ( ) ( ) ( ) ( ⎜+ 𝐽 2𝛾𝑚 𝐽 2𝛾𝑚 sin 2𝜔 𝑡 sin 𝜔 𝑡) ⎟ 2 1 1 2 1 2 ⎜ ⎟ ⎜+ 𝐽 (2𝛾𝑚 ) 𝐽 (2𝛾𝑚 ) sin (3𝜔 𝑡) sin (2𝜔 𝑡)⎟ 3 1 2 2 1 2 ⎟ ⎜ ⋅ ( ) ( ) ( ) ( ) ⎜+ 𝐽2 2𝛾𝑚1 𝐽3 2𝛾𝑚2 sin 2𝜔1 𝑡 sin 3𝜔2 𝑡 ⎟ ⎜ ( ) ( ) ( ) ( )⎟ ⎜+ 𝐽4 2𝛾𝑚1 𝐽3 2𝛾𝑚2 sin 4𝜔1 𝑡 sin 3𝜔2 𝑡 ⎟ ⎜ ( ) ( ) ( ) ( )⎟ ⎝+ 𝐽3 2𝛾𝑚1 𝐽4 2𝛾𝑚2 sin 3𝜔1 𝑡 sin 4𝜔2 𝑡 ⎠

where 𝐽𝑛 is the nth-order Bessel function of the first kind. Similarly, the optical field at the output of IM2 can be expressed as √ ( ) 1√ 𝐸2 (𝑡) = 𝐴2−𝑙𝑜𝑠𝑠 𝐴𝑒𝑗𝜔𝑐 𝑡 1 + 𝑒𝑗𝜑2 𝑒𝑗𝛾𝐹 (𝑡) (6) 2 √ where 𝐴2−𝑙𝑜𝑠𝑠 is the insertion loss of IM2, 𝜑2 is the bias phase shift of IM2, 𝛾 is the attenuator factor of the electrical attenuator. By setting 𝜑2 = 𝜑1 , the received electrical signal at the output of PD2 is then calculated to be ( )) 𝑅𝐴2−𝑙𝑜𝑠𝑠 𝐴 ( 𝑉2 (𝑡) = 1 + cos 𝜑1 + 𝛾𝐹 (𝑡) (7) 2 where the fundamental components are ( ( ) ( ) ( ) ) ( ) 𝐽0 𝛾𝑚2 𝐽1 𝛾𝑚1 sin 𝜔1 𝑡 ( ) ( ) ( ) 𝑉2−𝑏 (𝑡) = −𝑅𝐴2−𝑙𝑜𝑠𝑠 𝐴 sin 𝜑1 ⋅ (8) + 𝐽0 𝛾𝑚1 𝐽1 𝛾𝑚2 sin 𝜔2 𝑡 and the components of IMD3, IMD5 and IMD7 tones are ( ) 𝑉2−𝐼𝑀𝐷 (𝑡) = −2𝑅𝐴2−𝑙𝑜𝑠𝑠 𝐴 sin 𝜑1 ( ) ( ) ( ) ( ) ⎞ ⎛𝐽1 𝛾𝑚1 𝐽2 𝛾𝑚2 sin 𝜔1 𝑡 sin 2𝜔2 𝑡 ( ) ( ) ( ) ( ) ⎟ ⎜ + 𝐽 𝛾𝑚 𝐽 𝛾𝑚 sin 2𝜔 𝑡 sin 𝜔 𝑡 1 2 ⎟ ⎜ 2 ( 1) 1 ( 2) ⎜+ 𝐽 𝛾𝑚 𝐽 𝛾𝑚 sin (3𝜔 𝑡) sin (2𝜔 𝑡)⎟ 3 1 2 2 1 2 ( ) ( ) ( ) ( )⎟ ⋅⎜ ⎜+ 𝐽2 𝛾𝑚1 𝐽3 𝛾𝑚2 sin 2𝜔1 𝑡 sin 3𝜔2 𝑡 ⎟ ( ) ( ) ( ) ( )⎟ ⎜ ⎜+ 𝐽4 𝛾𝑚1 𝐽3 𝛾𝑚2 sin 4𝜔1 𝑡 sin 3𝜔2 𝑡 ⎟ ( ) ( ) ( ) ( )⎟ ⎜ ⎝+ 𝐽3 𝛾𝑚1 𝐽4 𝛾𝑚2 sin 3𝜔1 𝑡 sin 4𝜔2 𝑡 ⎠

The outputs of the three PDs are then combined using two electrical couplers (ECs). If 𝑚𝑖 ≪ 1, the high order Bessel functions (𝑛 > 1) can be neglected, and the fundamental components included in the combined signal can be approximated as 𝑉𝑏 (𝑡) = 𝑉1−𝑏 (𝑡) + 𝑉2−𝑏 (𝑡) + 𝑉3−𝑏 (𝑡) ( ) ) ( ( ) 4𝐴2−𝑙𝑜𝑠𝑠 𝐴3−𝑙𝑜𝑠𝑠 𝐴𝐸𝐷𝐹 𝐴 cos 𝜑1 𝛾 ≈ 𝑅𝐴 sin 𝜑1 −𝐴2−𝑙𝑜𝑠𝑠 𝛾 − 2𝜂𝐴1−𝑙𝑜𝑠𝑠 ( ( ) ( ) ( ) ( )) ⋅ 𝐽1 𝑚1 sin 𝜔1 𝑡 + 𝐽1 𝑚2 sin 𝜔2 𝑡

( )) 𝑅𝐴2−𝑙𝑜𝑠𝑠 𝐴3−𝑙𝑜𝑠𝑠 𝐴𝐸𝐷𝐹 𝐴 𝐴 ( 1 − cos 2𝜑1 + 2𝛾𝐹 (𝑡) 2 where the components of the fundamental tones are ( ) 𝑉3−𝑏 (𝑡) = 𝑅𝐴2−𝑙𝑜𝑠𝑠 𝐴3−𝑙𝑜𝑠𝑠 𝐴𝐸𝐷𝐹 𝐴 𝐴 sin 2𝜑1 ⋅ ) ( ) ( ) ) ( ( 𝐽0 2𝛾𝑚2 𝐽1 2𝛾𝑚1 sin 𝜔1 𝑡 ( ) ( ) ( ) + 𝐽0 2𝛾𝑚1 𝐽1 2𝛾𝑚2 sin 𝜔2 𝑡

(14)

and the components of IMD3, IMD5 and IMD7 tones can be approximated as 𝑉𝐼𝑀𝐷 (𝑡) = 𝑉1−𝐼𝑀𝐷 (𝑡) + 𝑉2−𝐼𝑀𝐷 (𝑡) + 𝑉3−𝐼𝑀𝐷 (𝑡) ( ) 3) ( ⎞ ⎛ 32𝐴2−𝑙𝑜𝑠𝑠 𝐴3−𝑙𝑜𝑠𝑠 𝐴𝐸𝐷𝐹 𝐴 cos 𝜑1 𝛾 3 ⎟ ⎜ − 2𝐴2−𝑙𝑜𝑠𝑠 𝛾 − 4𝜂𝐴1−𝑙𝑜𝑠𝑠 ⎜ ( ( ) ( ) ( ) ( ) ) ⎟ ⎟ ⎜ 𝐽1 𝑚1 𝐽2 𝑚2 sin 𝜔1 𝑡 sin 2𝜔2 𝑡 ( ) ( ) ( ) ( ) ⎟ ⎜⋅ + 𝐽 𝑚 𝐽 𝑚 sin 2𝜔 𝑡 sin 𝜔 𝑡 2 1 1 2 1 2 ⎜ ( ) ) ⎟ ⎜ (128𝐴 𝐴3−𝑙𝑜𝑠𝑠 𝐴𝐸𝐷𝐹 𝐴 cos 𝜑1 𝛾 5 ⎟ 2−𝑙𝑜𝑠𝑠 ⎟ ⎜+ − 2𝐴2−𝑙𝑜𝑠𝑠 𝛾 5 − 4𝜂𝐴1−𝑙𝑜𝑠𝑠 ( ) ⎜ ⎟ ≈ 𝑅𝐴 sin 𝜑1 ⋅ ⎜ ( ( ) ( ) ( ) ( ) )⎟ 3𝜔1 𝑡 sin 2𝜔2 𝑡 ⎜⋅ 𝐽3 𝑚(1 𝐽)2 𝑚(2 sin ) ( ) ( ) ⎟ ⎜ + 𝐽2 𝑚1 𝐽3 𝑚2 sin 2𝜔1 𝑡 sin 3𝜔2 𝑡 ⎟ ⎜ ( ( ) ) ⎟ ⎜ 512𝐴2−𝑙𝑜𝑠𝑠 𝐴3−𝑙𝑜𝑠𝑠 𝐴𝐸𝐷𝐹 𝐴 cos 𝜑1 𝛾 7 ⎟ ⎟ ⎜+ − 2𝐴 7 𝛾 − 4𝜂𝐴1−𝑙𝑜𝑠𝑠 ⎜ ( ( 2−𝑙𝑜𝑠𝑠 ) ( ) ( ) ( ) )⎟ ⎟ ⎜ 𝐽 𝑚 𝐽 𝑚 sin 4𝜔 𝑡 sin 3𝜔 𝑡 4 (1 )3 (2 ) (1 ) (2 ) ⎟ ⎜⋅ ⎝ + 𝐽3 𝑚1 𝐽4 𝑚2 sin 3𝜔1 𝑡 sin 4𝜔2 𝑡 ⎠

(9)

The optical field at the output of IM3 can be expressed as √ √ √ 1√ 𝐸3 (𝑡) = 𝐴2−𝑙𝑜𝑠𝑠 𝐴3−𝑙𝑜𝑠𝑠 𝐴𝐸𝐷𝐹 𝐴 𝐴𝑒𝑗𝜔𝑐 𝑡 (10) 2( )( ) ⋅ 1 + 𝑒𝑗𝜑2 𝑒𝑗𝛾𝐹 (𝑡) 1 + 𝑒𝑗𝜑3 𝑒𝑗𝛾𝐹 (𝑡) √ √ where 𝐴3−𝑙𝑜𝑠𝑠 is the insertion loss of IM3, 𝐴𝐸𝐷𝐹 𝐴 is the amplification factor of an Erbium doped fiber amplifier (EDFA), 𝜑3 is the bias phase shift of IM3. By setting 𝜑3 = 𝜋 + 𝜑1 , the received electrical signal at the output of PD3 is given by 𝑉3 (𝑡) =

(13)

(15)

where 𝐽0 (𝑚) ≈ 0, 𝐽𝑛 (𝛾𝑚) ≈ 𝛾 𝑛 𝐽𝑛 (𝑚). As can be seen from (15), when the value of 𝐴3−𝑙𝑜𝑠𝑠 𝐴𝐸𝐷𝐹 𝐴 is set to 1 by adjusting the gain of the EDFA, and the following equations: { ( ( ) ) 𝐴2−𝑙𝑜𝑠𝑠 16 cos 𝜑1 − 1 𝛾 3 − 2𝐴1−𝑙𝑜𝑠𝑠 𝜂 = 0 (16) ( ( ) ) 𝐴2−𝑙𝑜𝑠𝑠 64 cos 𝜑1 − 1 𝛾 5 − 2𝐴1−𝑙𝑜𝑠𝑠 𝜂 = 0

(11)

(12)

are satisfied, the IMD3 and the IMD5 products can be canceled. 18

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After linearization, the SFDR is limited by the IMD7 product. By calculating the fundamental output power from (14) and the distortion power from (15) and assuming 𝑚1 = 𝑚2 = 𝑚, we can express the seventhorder limited SFDR of the linearized scheme as )2 ) ) ( ) ( ( ))12∕7 ((( 4 cos 𝜑1 − 1 𝛾 − 2𝜂 𝐽1 (𝑚) 𝑅𝐴𝑙𝑜𝑠𝑠 𝐴 sin 𝜑1 (22) 𝑆𝐹 𝐷𝑅7 = ( )2∕7 ) ) ( ) 6∕7 1 (( 7 − 2𝜂 𝐽 (𝑚) 𝐽 (𝑚) 𝑁 − 1 𝛾 256 cos 𝜑 3 4 1 0 2 According to (20), the SFDR of a conventional intensity-modulated scheme can be calculated as )2 ( ( ))4∕3 ( 𝐽1 (𝑚) 4𝑅𝐴𝑙𝑜𝑠𝑠 𝐴 sin 𝜑1 𝑆𝐹 𝐷𝑅3 = (23) )2∕3 2∕3 ( 𝑁0 𝐽1 (𝑚) 𝐽2 (𝑚)

Fig. 2. Choices of 𝛾 and 𝜂.

The proposed scheme is simulated using Optisystem software. A continuous-wave light with a power of 18 dBm is modulated by a twotone RF signal with frequencies of 10 GHz and 10.5 GHz. The halfwave voltage, the insertion loss, and the extinction ratios for each IM are 4 V, 5 dB, and 100 dB, respectively. As shown in Fig. 3, the IMD3 can be observed in the conventional intensity-modulated scheme, but in the proposed linearized scheme, the above distortion is obviously eliminated by properly adjusting the gain of the EDFA, the attenuation factors of the electrical attenuator and the optical attenuator. The power difference at each fundamental tone between the two schemes is about 16.47 dB, which can be reduced by reducing optical insertion loss and increasing the injection RF power of each IM in the linearized scheme.

Fig. 3. Simulation results of (a) the conventional intensity-modulated scheme and (b) the proposed linearized scheme.

If 𝐴2−𝑙𝑜𝑠𝑠 = 𝐴1−𝑙𝑜𝑠𝑠 = 𝐴𝑙𝑜𝑠𝑠 , we obtain √( ( ) ) ( ( ) ) 16 cos 𝜑1 − 1 ∕ 64 cos 𝜑1 − 1 𝛾=

3. Results and discussions (17)

A proof-of-concept experiment is carried out and shown in Fig. 1. The laser has a center wavelength of 1550 nm. The frequencies of the two-tone signal are 10 GHz and 10.01 GHz. In comparison, Fig. 4(a) shows the measured output spectrum of the conventional intensitymodulated scheme, which contains the IMD3 and the IMD5 components. After linearization, the fundamental-to-IMD3 ratio reaches 54.37 dB, as shown in Fig. 4(b). This is an improvement over the conventional scheme of more than 21 dB. To further demonstrate the performance of our linearized approach, the fundamental and the IMD3 responses of our proposed scheme and the conventional intensity-modulated scheme are simulated independently, as shown in Fig. 5. The noise floor level occurs at −91.02 dBm. As can be seen from Fig. 5, the SFDR of the linearized scheme is 51.72 dB (112.13 dB for a bandwidth of 1 Hz), which is 3.5 dB (13.5 dB for a bandwidth of 1 Hz) higher than that of the conventional scheme. This indicates that this linearization technique can improve the dynamic range. Fig. 6 shows the SFDR as a function of the bias phase shift 𝜑1 . The simulations are carried out based on (22) and (23). Whether in the conventional intensity-modulated scheme or the proposed linearized scheme, the dynamic range varies with the bias phase shift. Fig. 6 again confirms that the proposed linearization scheme can improve the dynamic range.

and ( ( ) )5∕2 ( ( ( ) )3∕2 ) 𝜂 = 16 cos 𝜑1 − 1 ∕ 2 64 cos 𝜑1 − 1

(18)

As 0 < 𝛾 ≤ 1 and 0 < 𝜂 ≤ 1, 𝜑1 should be chosen to satisfy the following condition: ( ) ( ) 1 1 + 2𝑛𝜋 < 𝜑1 ≤ cos−1 + 2𝑛𝜋, 𝑛 = 0, 1, 2, … (19) − cos−1 16 16 Fig. 2 shows 𝛾 and 𝜂 as a function of the bias phase shift 𝜑1 when 𝑛 = 0. The value of 𝛾 is almost kept unchanged but that of 𝜂 decreases with increasing phase shift. The N th-order limited spurious-free dynamic range (SFDR) is defined as ( ) 𝑂𝐼𝑃𝑁 (𝑁−1)∕𝑁 𝑆𝐹 𝐷𝑅𝑁 = (20) 𝑁0 where 𝑁0 is the output noise power spectral density per unit bandwidth (W/Hz), 𝑂𝐼𝑃𝑁 is the output N th order intercept point, which is defined as ( 𝑁 )1∕(𝑁−1) 𝑃1 (21) 𝑂𝐼𝑃𝑁 = 𝑃𝑁

Fig. 4. Measured output spectra of (a) the conventional intensity-modulated link and (b) the proposed linearized scheme. 19

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Fig. 5. The fundamental and IMD3 responses versus input RF power of a conventional intensity-modulated scheme and the proposed linearized scheme.

Fig. 6. Calculated SFDRs versus 𝜑1 of (a) the conventional intensity-modulated scheme and (b) the proposed linearized scheme.

4. Conclusions In summary, a linearized microwave photonic receiving scheme is proposed. Theoretically, the linearization scheme could simultaneously eliminate the IMD3 and IMD5. A proof-of-concept experiment demonstrates the fundamental-to-IMD3 ratio has been improved more than 21 dB over the conventional scheme. Simulation results show that the SFDR is improved from 98.63 dB/Hz2∕3 to 112.13 dB/Hz6∕7 . The proposed scheme has potential applications in high performance radio over fiber transmission systems.

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