## Abstract

We propose and demonstrate a novel scheme to effectively suppress the cross modulation distortion (XMD) and the third-order inter-modulation distortion (IMD3) which exist in wide-band, multi-carrier analog photonic link (APL) system. Such nonlinearities, which are caused by the out-of-band and in-band signals, respectively, constrain the link’s performance severely. Instead of building an extra nonlinear path in hardware, the XMD and IMD3 compensation information is extracted from the received distorted signal, and both distortions are then suppressed by digitally multiplying the distorted signal with the compensation information. After compensation in the digital domain, the down-converted XMD and IMD3 distortions are experimentally suppressed with 33 dB and 25 dB, respectively, resulting in an improved upper limit for the SFDR.

© 2014 Optical Society of America

## 1. Introduction

Taking advantage of the low insertion loss, broad bandwidth and immunity to electromagnetic interference, the analog photonic link (APL) has become the heart of an emerging field of microwave photonics, in which various functionalities like generation, distribution, control, and processing of radio frequency (RF) signals have been explored and applied [1]. The unique capabilities offered by photonics for processing ultra-wideband, high frequency and multi-carrier signals make it a promising alternative for wideband microwave signal processing [2]. For most photonic systems, analog processing application is an embedded APL due to the indispensable E/O and O/E conversion. Therefore, the system performance is susceptible to the distortions which are induced by the nonlinear conversion [3]. In the traditional intensity modulation and direct detection (IMDD) APL, the harmonic crosstalk, third-order inter-modulation distortion (IMD3), and cross modulation distortion (XMD), which are all caused by the nonlinear transfer curve of intensity modulator, deteriorate the spurious free dynamic range (SFDR) severely. It is a great challenge on the components and designing of the link to extend the linearity and acquire high signal fidelity.

Notably, in narrow-band or single carrier operation, the generated harmonic distortions can be suppressed by choosing appropriate RF filters or sub-octave spectral occupation [4]. IMD3 lies very close to or overlaps with the RF carriers and then dominates the nonlinearities within the signal band. Numerous innovative linearization techniques, in both electronic and optical ways, for IMD3 reduction have been devised, such as pre-distortion, post digital signal processing (DSP) [5,6], multiple wavelength architecture [7], optical carrier processing [8], cascaded or parallel Mach-Zehnder modulators (MZMs) [9], optical single sideband (SSB) with carrier modulation [10], and coherent link with a polymeric DP-MZM [11]. By generating a well-designed and matched distorted path to cancel out exactly the existing one, reduction of the IMD3 has been achieved by the above schemes. The hardware is usually required to be carefully designed. Clearly, once the distortion is not precisely matched, the compensation methods result in significant imperfections otherwise.

Different from the single-carrier photonic link, additional nonlinear behavior is derived in the multi-carrier operation. The modulated in-band signals are not only distorted by IMD3, but also affected by the out-of-band interfering carrier components. This kind of distortion is referred as XMD and has been demonstrated the same magnitude as IMD3. The more powerful the interferer is, the more prominent the XMD becomes. Under certain circumstance, the XMD can be the dominant nonlinearity and its correction is urgent. Obviously, for the high fidelity APL applications, both XMD and IMD3 nonlinearities are demanded to be eliminated. Pioneering researches have been conducted to address the mitigation of XMD in coherent channelized photonic systems [12–14]. In [12], the dynamic range is still limited by IMD after XMD is suppressed by pre-distortion technique. In [13], IMD3 and XMD are mitigated through inverting the link response. However the entire output signals of all channels are recorded and synchronized to compensate the link nonlinearity and reconstruct the original signal, which increases the configuration complexity largely and requires heavy computation in DSP module. In [14], an extra well-designed O/E path is introduced to gather the compensation information, which requires careful synchronization between the distortion and compensation signals. Note that all of the previous works are for APLs with coherent detection.

In this paper, we propose and demonstrate an efficient digital suppression of both cross and inter-modulation distortions in multi-carrier incoherent IMDD link with down-conversion. The incoherent detection decreases the system operation complexity and increases its stability. Meanwhile, due to its flexibility and superior linearization ability, the technique of optical down-conversion combined with DSP has been considered as a promising strategy. Rather than construct a critical nonlinear path in hardware, we directly extract the nonlinear sidebands from the received signal to linearize the distorted signal in the DSP unit, avoiding the less XMD suppression caused by the non-synchronization between compensate and distorted signals. Experimentally, simultaneous suppression of XMD and IMD3 by about 33 dB and 25 dB, respectively, is achieved and the SFDR is greatly improved.

## 2. Operation principle

Figure 1 shows the experimental setup and the flow diagram of the proposed digital signal post-processing linearization algorithm. A continuous optical source is firstly injected into a low-biased MZM_{1} and modulated by the multi-carrier RF signal. After a short single mode fiber delivery, the target carrier that we concern is down-converted to the intermediate frequency (IF) by a proper local oscillator (LO), which is achieved by the second MZM_{2}. So it can be digitalized by a low speed data acquisition card with high resolution. Note that MZM_{2} should be biased at its quadrature point to maximize the down-conversion efficiency. The generated sum-frequency of RF signal and LO as well as other spurious frequency by MZM_{2} is beyond the operational bandwidth of the system, while the difference-frequency refers as target carrier. Afterward, the down-converted IF signal is received by a photo-detector (PD), and then the distorted IF signal is fed forward to a post-compensation module after digitization, as illustrated in Fig. 1(b). The proposed linearization technique obeys sequentially the following two strategies: XMD suppression is the first and then the IMD3. Eventually, both XMD and IMD3 nonlinearities caused by the external modulator are removed numerically, and the output of the DSP module is the linearized IF signal.

The modulated wideband RF signal consists of multiple frequency components, each of which is centered at *ω _{k}* with amplitude of

*A*(

_{k}*t*) and phase of

*φ*(

_{k}*t*), respectively. Mathematically, the voltage of the wide-band, multi-carrier signal can be expressed as

*x*(

*t*) . Generally, the power series are expressed as

*a*(

_{i}*i*= 0, 1, 2, 3…) are the coefficients of the power series, which are determined by the specific parameters of the given APL. With small-signal approximation, higher order harmonics than three are ignored since their minor contributions. Substitute Eq. (1) into Eq. (2) and the normalized optical power signal before down-conversion follows the expression

As can be seen in the Eq. (3), the XMD is induced by the $\sum _{m}{A}_{m}^{2}(t)$ in the 2nd term, which also shows as $\sum _{k}{A}_{k}^{2}(t)$ in the 1st term. That is, the XMD is contained in the 1st term, i.e. the baseband. After optical down-conversion, the 2nd term is moved to an IF band with additional loss. Both the two terms are digitally received. In order to establish the XMD compensation signal, two numerical filters are introduced to divide the recovered signal into the low-pass band, *S*_{0}, and the fundamental band around *ω _{k}*,

*S*

_{1}.

*S*

_{0}due to the out of band interferer carriers. So we propose that the XMD distortion can be eliminated by the following algorithm

The above expression illustrates that the XMD introduced by the interferer carriers is corrected. Note that now the signal still suffers from the inter-modulation from the carrier itself, i.e. the IMD3, from Eq. (6). Since *A*2 *k*(*t*) can be approached by *S*2 1(*t*) for the first order approximation, we propose that the IMD3 compensation signal can be built as [15]

*λ*is a matching coefficient related to

*a*.

_{i}*S*

_{IMD3c}is the well-designed IMD3 compensate signal which can be obtained by extracting

*A2 k*(

*t*) out of

*S*2 1(

*t*) through a digital low-pass filter. The filter bandwidth should match the existing distortion. When multiply theafter-XMD-compensation signal, Eq. (6), by the IMD3 compensation signal, the linearized output signal can be finally calculated as

*λ*is constant, and can be evaluated in advance. Both XMD and IMD3 can be compensated simultaneously by means of Eq. (6) and Eq. (9). The general formula for the linearization algorithm based on DSP can be expressed aswhere

*F*{

*·*} means a low-pass filtering whose bandwidth is corresponding to

*A2 k*(

*t*). The above theoretical derivation can be applied to any specific link such as the incoherent IMDD link with down-conversion one, since the MZM-based down-conversion shows no additional nonlinearities in both

*S*

_{0}and

*S*

_{1}[15,16]. After optical down-conversion, the baseband,

*S*

_{0}, is still there, while the target signal,

*S*

_{1}, is moved to IF band with additional insertion loss. Despite the loss, the ratios of

*a*

_{0}/

*a*

_{2}and

*a*

_{3}/

*a*

_{1}are kept unchanged. Hence, the distortion information acquisition and the post-compensation algorithm are compatible to the system with down-conversion. It is well known that OIP3 = −2

*a*3 1/3

*a*

_{3}

*R*

_{50Ω}for an IMDD link, where

*R*

_{50Ω}is the output impedance, generally 50Ω. Finally, the corresponding compensate coefficients can be expressed as Note that the negative sign results from the negative

*a*

_{3}. We must make it very clear that the IMD3 compensation coefficient is different from that in [15], because the IMD3 here has been over compensated due to Eq. (6).

It indicates that the compensation factors in Eq. (11) and Eq. (12), *γ* and *λ*, depend on the bias angle of the MZM_{1} and OIP3, which are constant for a given APL. The linearization is achieved through simply multiplying the distorted signal by the extracted compensation bands. Such property shows a robust signal reconstruction and releases the demand of link parameter estimations. Meanwhile, the nonlinear distortions can be mitigated when the baseband signal *S*_{0} and the target signal *S*_{1} are extracted. The XMD compensation information is acquired directly from the co-transmitted baseband signal *S*_{0}, without calculating from all of the *S*_{k}(*t*) [13], and avoiding an extra nonlinear path in hardware as well the synchronization error between the distorted signal and compensation path. The data volume that the algorithm has to deal with is greatly compressed. Note that the bias angle can be easily achieved by the commercial available bias control circuit [17], while OIP3 can be estimated by a dual-tone training signal in advance: the RF spectrum is captured and the corresponding powers of fundamental and IMD3 tons, *P*_{1} and *P*_{3}, can be calculated, through which we can figure out OIP3 as $OI{P}_{3}\approx \sqrt{{P}_{1}^{3}/{P}_{3}}$.

In the proposed model, the effect of the dispersion is not being considered in Eq. (3). Actually, after the long-distance transmission, the link will be further distorted by dispersion-induced nonlinearity [18]. Our simulation result shows that the proposed nonlinear distortion compensation algorithm will not work under large dispersion.

## 3. Experiment

A proof of concept experiment based on the proposed linearization algorithm is illustrated in Fig. 1(a). In our experiment, the input multi-carrier RF signal is emulated by two dual tones. The target RF signal consists of two tones at frequencies of 15 GHz and 14.993 GHz, spaced by 2*δ*_{2} = 7 MHz, while the interferer tones are selected at 2.5 GHz and 2.496 GHz spaced by 2*δ*_{1} = 4 MHz. The four tones, power coupled by three RF combiners, are applying to MZM_{1}. The down-converted target IF signal should then be distorted by both the IMD3 and XMD nonlinearities, which offset from *f _{IF}* by ± 3

*δ*

_{2}and ± 2

*δ*

_{1}, respectively. The continuous wave laser source (Koheras AdjustiK Benchtop Fiber Laser, with linewidth<1 KHz and power of 16 dBm), operating at a wavelength of 1550 nm, is applied as the optical carrier. By adjusting the polarization controller (PC), the principal axis of the output light beam is aligned with the following standard MZM

_{1}. A bias controller (Pharad MBC-DF-UC) is adopted to stably lock the working point. Then, the target RF and interferer signal tones are directly up-converted on the optical carrier. The cascading MZM

_{2}, which is driven by a 14.9365 GHz LO, is employed to down-convert the target RF signal to IF. The modulated optical signal is received by a PD with responsivity of 0.92 A/W (EM4). The detected electrical signal is digitized by a digitizer (ADlink PCIE-9842) with 14-bit and 200 Mbit/s sampling rate, the output of which then undergoes the offline DSP processing as shown in Fig. 1(b). The nonlinearities are finally corrected by the flow chart. The bias angle of MZM

_{1}is fixed below the quadrature point 30°throughout the whole experiment, and the received optical power by PD is 0 dBm.

The input target and interferer signal powers are scanned respectively while the down- converted target IF, XMD, and IMD3 sidebands are monitored. Firstly, the input interferer signal with fixed power level of 6.5 dBm, and the target signal with the varying powers (from −3.5 dBm to 6.5 dBm) are applied on MZM_{1}. The powers of the down-converted target IF and XMD sidebands are measured, and the suppression ratios are plotted in Fig. 2(a). As expected from our theoretical prediction, the XDM sidebands are suppressed about 33 dB by an offline MATLAB program. Similarly, the target signal power is fixed at level of 6.5 dBm and the powers of interferer two tones signal are variable. The suppression ratios are showed in Fig. 2(b). By the proposed compensation technique, we experimentally obtain about 30 dB reductions in the XMD, which is helpful to improve the dynamic range of the wideband, multi-carrier APL.

As a particular example, when the powers of the input target and interferer signals are 6.5 dBm and 5.5 dBm, respectively, the spectrums of the down-converted target IF as well as the nonlinear distortion sidebands before and after XMD compensation are plotted in Fig. 3. From Fig. 3(a), severe nonlinear distortion components can be observed around the target IF signal before linearization. The calculated suppression ratio of the down-converted target IF to XMD sidebands before compensation is 27.8 dB, which reaches 54.6 dB after compensation as shown in Fig. 3(b). Experiment results proved that the proposed algorithm is highly effective in suppressing the XMD sidebands to a power level well below the IMD3.

After XMD sidebands are compensated, IMD3 becomes the main factor that limits thedynamic range. The residual IMD3 can be corrected by Eq. (9). Compared with Fig. 3(a), as expected, the ratio of down-converted target IF to IMD3 sidebands is improved by 25 dB, which is shown in Fig. 4. Benefiting from the effective XMD and IMD3 correction in DSP module, the down- converted target signal is recovered cleanly.

By varying the input RF powers, both the powers of down-converted target IF and IMD3 sidebands are monitored. Figure 5 shows the measured powers of target IF and IMD3 sidebands as a function of the input RF powers for both cases with and without IMD3 linearization. The slope for the inter-modulation component is 3, which is 5 after linearization, indicating that the fifth order inter-modulation dominates and IMD3 is completely suppressed by the proposed algorithm. The measured noise floor after the PD is −164.2 dBm/Hz, which shows a SFDR enhancement as large as 22 dB. However, the current design is still limited by the quantization noise of the analog to digital converter (ADC), as shown in Fig. 5. Such limitation can be removed by a low-noise electronic amplifier before the ADC [15].

The experimental bandwidth is limited by the bandwidth of the ADC. In the experiment, we use one single ADC (200 Mbit/s, with an analog band with less than 100 MHz) to gather both the baseband signal *S*_{0} and the down-converted IF. Actually, the treatable bandwidth can be enlarged if a separated ADC is used for *S*_{0}. With a cost of further down-conversion of the target IF signal in the electronic domain, the treatable bandwidth may approach that of the ADC.

## 4. Conclusion

In summary, we have theoretically analyzed and experimentally demonstrated a novel linearization scheme for the multi-carrier incoherent IMDD APL. In combination with down- conversion, the nonlinear compensation information can be extracted from the co-received signal to linearize the distorted signal in the DSP module. Experiment results showed that the proposed linearization technology was effective in correcting the two types of nonlinear distortions. Large suppression of XMD and IMD3 were demonstrated by 33 dB and 25 dB, respectively. Improved dynamic range is expected by the simple hardware implementation and digital post-processing, which shows great promise for high fidelity RF link.

## Acknowledgments

This work was supported in part by National 973 Program (2012CB315705), NSFC Program (61107058, 61302016, and 61471065), and NCET-13-0682.

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