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Based on forward distortion information acquisition and post digital signal processing (DSP), we propose and demonstrate a novel scheme to effectively suppress the third-order intermodulation distortion (IMD3) and cross-modulation distortion (XMD) in a channelized RF photonic link. The simultaneous distortion compensation capacity is studied numerically, and suppression of XMD and IMD3 by about 28 dB and 25 dB, respectively, is achieved experimentally. The scheme principle and the digital compensation procedure are discussed, which shows a simple hardware implementation and algorithm.
©2012 Optical Society of America
1. Introduction
The frequency channelization of broadband radio-frequency (RF) signals relieves the bandwidth limitation of high-resolution analog-to-digital converters (ADCs) and the data volume challenge of downstream digital signal process (DSP), which is a key functionality in both commercial and military microwave applications. Recently the RF photonics has made enormous strides since it owns the advantages such as large RF bandwidths, continuous spectral coverage, enhanced signal processing capabilities, and size, weight, and power (SWaP) benefits. Several innovative photonic-assisted RF channelization schemes have been demonstrated [1–5]. In an optical channelized receiver, the wideband RF signal is up-converted to an optical signal, divided into multiple frequency bands, and then extracted individually. The down-conversion into intermediate frequency (IF) or baseband is required for digitalization and further processing.
The link linearity or dynamic range is a key to achieve high fidelity analog link in each channel, which challenges on the design of the whole channelized receiver. Linearity in RF photonic links is frequently limited by the modulator response. In a conventional narrow-band link where the third-order inter modulation distortion (IMD3) dominates, the linearization has been demonstrated by several designs, such as electronic pre-distortion [6, 7] or feed-forward compensation [8], cascaded or parallel electro-optic modulators [9, 10], and post digital signal compensation [11, 12], etc. However, in a channelized RF photonic link where the input RF signal is broadband with multiple frequency components, a component in one channel is not only distorted by IMD3, but also impacted by all other frequency components of the input RF signal, which is referred as cross-modulation distortion (XMD) and has been demonstrated the same order as IMD3 in a multi-component RF photonic link. Obviously both nonlinearities are demanded to be minimized in a high-quality optical channelized receiver, which however has been achieved in few reports. In [13] XMD is suppressed by predistortion, where the dynamic range is still limited by IMD3. In [14], IMD3 and XMD are mitigated through post digital distortion compensation. 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 this paper, we propose a novel linearization scheme to suppress both XMD and IMD3 in a coherent optical channelized receiver. The distortions information is firstly acquired by hardware, and then fed forward to a DSP unit where the XMD and IMD3 are extracted to linearize the received signal. The nonlinear transfer function of the broadband channelized RF photonic link, as well as the XMD and IMD3 compensation functions, is presented. The proposed scheme is studied numerically, where the important practical concerns, as well as the multi-component capacity, are discussed. Experimentally, simultaneous suppression of XMD and IMD3 by about 28 dB and 25 dB, respectively, is achieved.
2. Operation principle
The proposed linearization technique for the general optical channelization is shown in Fig. 1 . The output of a continuous wave (CW) laser is modulated by a wideband RF signal consisting of multiple frequency components centered at ωk with amplitude of vk(t) and phase of φk(t):
The 1 × 2 Mach-Zehnder modulator (MZM) is biased so that its lower branch works under the carrier-suppression condition, and the optical carrier and all even order sidebands are suppressed. The optical-carried broadband RF signal is then optically channelized. In each channel, the corresponding portion of the first-order upper (or lower) sideband of the optical-carried RF signal is coherently down-converted to IF by a proper local oscillator (LO). The coherent detection has the advantage of coherent gain, simultaneous recovery of both RF amplitude and phase information, as well as the improved link performance due to the balanced photodetector (BPD). It should be noted that a narrow filter is required in each channel to reject the out-of-channel components as well as the higher order harmonics, which can be done either optically during the optical channelization, or electronically in each channel after the coherent detection [5]. Because of the coherent detection, both implementations are equivalent. In either case, the entire optical signal spectrum does not reach the detector due to the after-modulation filtering, and the single channel transfer function is different from that of the traditional link. It has been demonstrated that the kth RF component after coherent detection is received as [13].
where β = π/Vπ (Vπ is the half-wave voltage of the MZM), Jn(x) is the nth order Bessel function of the first kind, and ωIF is the IF carrier. Obviously nonlinearities from both XMD (the first term on the right side that does not depend on vk) and IMD3 (the second term that depends on vk) are reflected.In order to minimize the XMD, the first term in Eq. (2) is acquired by directly detecting the output of the upper branch of the 1 × 2 MZM through a photo detector (PD). Under the designed bias condition (the lower branch is carrier-suppressed), all the even order sidebands are present at the upper output port, and the received signal after narrow-baseband filtering (the bandwidth is less than the minimum beating frequency of all RF components), IXMDC(t), has been proved [13] to reflect the XMD information since
The above XMD information signal has no RF carrier, so it can be digitalized by a low speed ADC with high resolution. In our design, both the channelized IF signal [Sk(t)] and the XMD information signal are digitalized, and the XMD is easily removed numerically after the two signals are correctly synchronized:
Note that in the last term the following approximations are considered: J0(x)≈1-0.25x2 and J1(x)≈0.5(x-0.125x3). From Eq. (4) one can get the inter-channel distortion signal aswhere means x(t) is narrow-band filtered, and κ is a constant related to β, the optical powers of CW source and LO, response coefficients of the BPD and PD, insertion losses of modulators and other passive components in the links, etc. In practice, the value of κ is kept unchanged, and can be evaluated in advance. Based on Eqs. (4) and (5), the linearized output IF signal can be finally calculated asIn the proposed linearization design, Sk(t) and IXMDC(t) are measured individually, while other processes are performed in the numerical domain. The whole linearization process is plotted in Fig. 1. Both XMD and IMD3 can be compensated simultaneously. In the proposed scheme, the XMD information is digitalized and processed in the DSP unit, avoiding the previous analog processing (including inverse, etc.), while the digital processing allows the simultaneous suppression of both distortions [13]. Different from [14], we acquire the XMD information by hardware, which is then used for all channels. Such scheme avoids heavy computation. It should be noted that the XMD information signal, IXMDC(t), has larger bandwidth than the maximum of the individual RF components, and the DSP with corresponding processing speed is required.
3. Simulation and experiment
As a proof of concept, one channel of an optical channelized receiver is tested. The experiment setup is illustrated in Fig. 2 . A CW light (Koheras AdjustiK Benchtop Fiber Laser) with wavelength of 1550 nm, linewidth <1 kHz, and power of 17 dBm is divided into two paths through an optical coupler. In the lower path (the LO path), a microwave tone with frequency of 15.05 GHz and power of 18 dBm is fed into an MZM that is biased under carrier suppression condition. By a WaveShaper (Finisar 4000S; the bandwidth is 15 GHz), the + 1st order sideband is filtered out as the LO. In the upper path (the signal path), the CW light is modulated through a polarization modulator (PolM). The PolM is a special phase modulator where transverse electric (TE) mode and transverse magnetic (TM) mode get the opposite but equal-depth phase modulation [15]. The polarization state of the incident CW light is rotated at 45° to one principal axis of the PolM using a polarization controller (PC). Following the PolM, a second PC and a polarization beam splitter (PBS) are used to convert the polarization modulation to two intensity modulation outputs. When the second PC is adjusted so that the principal axis of the PBS is at 45° to that of the PolM, the PolM followed by PBS is equivalent to a 1 × 2 MZM (Vπ is about 8.8V). Both the PolM and the MZM could be stabilized by proper bias controls. The multi-component RF signal is emulated by two dual-tone RF signals:
where f1 / f2, α1 / α2, and 2δ1 / 2δ2 are the center frequencies, amplitudes, and frequency intervals of the two dual-tone RF signals, respectively. The dual-tone RF signal centered at f1 is the fundamental signal that will be received in the tested channel, while the other one (centered at f2) is the out-of-channel signal. The carrier-suppressed output is filtered by a second WaveShaper (with bandwidth of 15 GHz), and the + 1st order sideband is mixed with the LO and received by a BPD, as the coherently-down-converted RF component [Sk(t)]. The other output of the PBS is received directly by a PD, as the XMD information signal [IXMDC(t)]. Outputs from both BPD and PD are sent to a real-time sampling oscilloscope (LeCroy WavePro 7400A with 8-bit resolution). An offline MATLAB program is used to achieve the numerical linearization. Polarization controllers are used in order to optimize the polarization states within each fiber link, which could be stabilized by polarization-maintaining devices. Note that though the coherent down-conversion is used, both the signal and the LO path use the same CW light source, and the impact of the laser phase noise could be voided by matching the lengths of the signal and LO fibers. Meanwhile, no transmission is involved, and the chromatic dispersion and the polarization mode dispersion are ignored in our scheme.The setup is studied numerically. The fundamental dual-tone signal is at 14.999 GHz and 15.001 GHz, spaced by 2δ1 = 2 MHz, while the out-of-channel dual-tone signal is at 11.000 GHz and 11.005 GHz, spaced by 2δ2 = 5 MHz. When α1 and α2 are both 0.15Vπ, the time-domain waveform and spectrum of the coherent downconverted electric signal without any compensation are shown in Fig. 3(a) and 3(b), respectively. One can observe that the fundamental signal is distorted by both IMD3 and XMD which offset from fIF by ± 3δ1 and ± 2δ2, respectively [13]. Figure 3(c) shows the signal when only the XMD is compensated [i.e. by Eq. (4)], which is stilled distorted by IMD3. However, both XMD and IMD3 are minimized by Eq. (6), and the original fundamental signal is recovered effectively as shown in Fig. 3(d).
Fig. 3 A numerical example for the proposed digital distortions compensation. (a) The time domain waveform and (b) the spectrum of the coherently-down-converted electrical signal without distortion compensation; (c) the spectrum of the down-converted signal with only XMD compensation and (d) XMD + IMD3 compensation.
The maximum distortion suppression ratio in practice is mainly impacted by three factors. Firstly, if the output IF signal power is quite low, the finite digital resolution of the ADC will show limit on the distortion compensation capacity. In our simulation, we assume that the output range of both PD and BPD in Fig. 2 are digitalized under different resolutions, and the corresponding XMD and IMD3 distortion suppression ratios are shown in Fig. 4(a) , in terms of ENOB (Effective Number Of Bits). Clearly the ratio under low ADC resolution is much lower than that in the ideal case [Fig. 3(d)]. Increasing the CW light power can increase the received down-converted IF signal power as well as the XMD information signal power. One can also see the saturation as the digital resolution increases.
Fig. 4 The XMD and IMD3 suppression related to (a) the ADC resolution, (b) the power of fundamental signal, and (c) the power of interfering signal. (d) The XMD suppression ratio related to the time synchronization error and bandwidth of RF component (the out-of-channel signal)
Secondly, since Eq. (2) stands under small-signal approximation, the suppression ratio would decrease when the input RF power is increased. The compensation capacity for both distortions related to the input RF powers (the fundamental signal and the out-of-channel one, respectively) is shown in Fig. 4(b) and 4(c). Simulation shows that within an acceptable suppression ratio, the proposed scheme can support a wide input power range.
Thirdly, the XMD compensation by Eq. (4) requires the synchronization between the downconversion and the XMD information path. Profile rather than the phase synchronization is demanded. Obviously the timing error would result in a less XMD suppression, which is shown in Fig. 4(d). The simulation shows that a larger individual RF component bandwidth requires a more precise timing. In our experiment, a piece of optical fiber is used to match the time delay difference of the two paths, and the time delay difference is less than 0.1 ns, which is sufficient for our case [the bandwidths of the two dual-tone RF signals (i.e., their frequency internals) are 2 MHz and 5 MHz, respectively]. Note that the required precision could always be obtained by soft-synchronization in DSP, since the XMD is suppressed digitally in our scheme, which is especially useful when the channel number is increased.
The theory from Eq. (2) shows no limit on the channel number. The simultaneous distortions suppression for more RF components is also tested by simulation. Figure 5 shows the compensation capacity when the input broadband RF signal contains ten components, each of which is a dual-tone signal. The RF carriers range randomly from 5 GHz to 15 GHz, and the bandwidth of each component (i.e. the frequency interval of each dual-tone signal) is from 1 MHz to 10 MHz. The 1-MHz component is received and distortion compensated. The simulation shows good XMD and IMD3 suppression under multi-component input.
Fig. 5 The simulated simultaneous XMD and IMD3 compensation for ten-component broadband RF signal. (a) without compensation; (b) with compensation
The above compensation scheme is demonstrated experimentally. The frequencies of the tones are the same as those in the simulation. Firstly, the power of the fundamental dual-tone signal is fixed at 15 dBm, while the power of the out-of-channel dual-tone signal is variable. The powers of the received fundamental signal, IMD3 sidebands and XMD sidebands are plotted in Fig. 6(a) . One can observe that as the power of the out-of-channel signal increases, the power (in dBm) of the XMD sidebands increases with the slope of two, while the powers of the fundamental signal and IMD3 do not change almost, which agrees with the analysis [14]. Under each out-of-channel signal power, the XMD and IMD3 are compensated based on Eq. (6), and the measured residual distortions are plotted in Fig. 6(a). The XMD and IMD3 are suppressed by about 28 dB and 25 dB, respectively.
Fig. 6 The powers of the received fundamental signal, XMD sidebands and IMD3 sidebands with increased power of (a) the input out-of-channel signal and (b) the input fundamental signal, before and after the distortions compensation.
Secondly, when the power of the out-of-channel signal is fixed at 15 dBm, and that of the fundamental signal is variable, the powers of the received signal and both distortions are also measured and shown in Fig. 6(b). As expected, with increase of the fundamental signal power, the powers of the XMD sidebands and IMD3 sidebands increase with the slope of one and three, respectively. By the proposed compensation technique, the XMD and IMD3 are suppressed by about 30 dB and 27 dB, respectively, as shown in Fig. 6(b).
As a particular example, when the powers of the fundamental and out-of-channel dual-tone signals are 15 and 16 dBm, respectively, the spectrum of the measured signal as well as both distortions is plotted in Fig. 7 , before and after compensation.
Fig. 7 The received spectrum of fundamental signal before (the blue line) and after (the red line) the simultaneous distortions compensation.
4. Conclusion
In conclusion, based on forward distortion information acquisition and post digital distortion compensation, we have theoretically analyzed and experimentally demonstrated a novel linearization scheme for a coherent channelized RF photonic link. Important practical factors that would show impact on the capacity were discussed numerically. Greatly suppressed traditional IMD3 and XMD from all other channels were demonstrated. Improved dynamic range is expected by the simple hardware implementation and digital processing.
Acknowledgments
This work was supported in part by 863 Program (2011AA010306, 2011AA010305), National 973 Program (2012CB315705) NSFC Program (61107058, 61120106001, and 61271042) and Beijing Excellent Doctoral Thesis Project under Grant YB20101001301.
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