In this paper, a novel intermodulation-compensation optical receiver based on the bias-modulated photo detector (PD) is proposed and demonstrated to eliminate the third-order intermodulation (IMD3) for the intensity-modulation direct-detection (IMDD) analog photonic link. We directly extract the key nonlinear distortion from the distorted optical intensity by a low-pass optical receiver, which is used to modulate the home-made, high-speed PD with bias modulation. Inside the high speed PD, the distorted radio frequency (RF) band is mixed with the above extracted baseband signal, and the IMD3 elimination can be achieved. Our proposal is theoretically analyzed, and the performance of the bias-modulated PD is experimentally demonstrated. Spurious-free dynamic range (SFDR) of 123.4 dB within 1-Hz bandwidth is obtained with 18.1 dB improvement. A low-biased Mach-Zehnder modulator (MZM) is used, keeping a simple transmitter with an improved link gain. The proposed post linearization requires no digital processing, avoiding the high quantization noise.
© 2015 Optical Society of America
Analog photonic link has become extremely attractive in recent years for analog radio-frequency (RF) signal transport and processing, because of its advantages such as broad bandwidth, low insertion loss, and immunity against electromagnetic interference . Significant applications have been demonstrated in the areas of radio over fiber (RoF) system, phased array radar, cable television, and so on [2, 3]. Its frequency capacity, gain, and dynamic range have been considered as the key quality factors . Due to the capacity for high carrier frequency, high power-handling potential, and commercial availability, external intensity modulation by a Mach-Zehnder modulator (MZM) is adopted in most high-frequency links. But the nonlinear transfer function of the MZM decreases the signal fidelity. Even in the sub-octave span applications, the generated third-order intermodulation distortion (IMD3) occupies the same frequency band as the signal, which cannot be removed by simple filtering. The spurious-free dynamic range (SFDR) is then usually used to describe the signal fidelity loss due to IMD3, and its improvement has been especially considered in the relative research areas .
Over the past years, various approaches have been reported to improve the SFDR, which can be classified according to where the IMD3 is eliminated. The pre-distortion, where the linearization is performed at the transmitter, has been demonstrated by electronic and optic ways. The electrical pre-distortion  has limited RF carrier frequency. Optical linearization is usually to employ two MZMs in parallel  or series , one of which builds an additional “nonlinear” link to cancel out exactly the nonlinearity of the other link. The input RF signal has to be power split, which costs additional RF loss (e.g. the loss of a 50:50 broadband RF power splitter can approach 6 dB). Keeping a precise and constant power split ratio under widely changed RF carrier frequency range is also a challenge for current RF devices. Note that the additional RF devices before the electro-optical conversion introduce extra link loss. Though the link loss can be maintained by increasing the optical power, the noise floor at the photo detector (PD) will be enlarged so that the noise figure will be worsened accordingly.
Another optical linearization at the transmitter can solve this problem, where the optical carrier or the band around is manipulated [9,10]. Though additional loss nearly 4.8 dB was also observed meanwhile, the link loss can be compensated optically by increasing the laser power. Since the photo current of the PD is unchanged, the noise performance is maintained . However, the required advanced electro-optical modulator with complicated bias control or specially designed and very narrow optical filter is a challenge now [9, 10].
Without complicating the transmitter, the post linearization at the receiver end can solve the above problem. Lately, the post digital signal processing (DSP) linearization technique [11–18] makes it a promising alternative to exclude IMD3 components for its flexibility and accuracy. Such technology, in the digital domain, either builds a reversed system so that the original signal can be perfectly recovered [11–14], or builds a cascaded nonlinear link so that the newly generated IMD3 can balance out the actual one [15–18]. Digital linearizations, both for phase/polarization-modulation coherent-detection links [11–14] and for intensity-modulation direct-detection (IMDD) links [15–18], have been widely researched. Due to the limited bandwidth of the analog to digital converter (ADC), the down-conversion is essential in order to increase the RF carrier frequency [14–16]. Another limitation on the digital linearization is that currently the broadband ADC (e.g. with analog bandwidth larger than 100 MHz) has limited effective number of bits (ENOB). As a result, its quantization noise (e.g. −137.6 dBm/Hz ) is much larger than the output noise from the PD. The spurious tones power is even higher.
In this paper, we propose and experimentally demonstrate a post but digitalization-free linearization technique based on a novel IMD3-compensation receiver for the IMDD analog photonic link. Our theory shows that when the MZM at the transmitter is low-biased, the IMD3 information is contained within the baseband of the photo current. Therefore, in our IMD3-compenstaion receiver, we firstly extract such distortion information by a low-pass optical receiver, and then the linearization is achieved by mixing the distorted RF band photo current with the above extracted baseband at our home-made high-speed PD under bias modulation [19, 20]. Experimentally, the IMD3 is greatly suppressed, and we demonstrate an IMDD link with SFDR improvement from 105.3 to 123.4 dB in 1-Hz bandwidth around 3 GHz. At the transmitter, neither lossy RF power splitting nor complicated modulator is required. The low-bias angle can increase the link gain. Besides, there is no additional quantization noise, compared to the post digital linearization technology.
2. Operation principle
The schematic diagram of the proposed post linearized IMDD link with an IMD3-compensation optical receiver is shown in Fig. 1. A sub-octave span RF signal, x(t) = A(t)cos[ωRFt + φ(t)], works as the input signal, where ωRF is the RF angle frequency and A(t) and φ(t) are the amplitude and phase modulation, respectively. As the MZM is low-biased, the link involves all orders of harmonics. We assume that the RF voltage to photo current transfer function of the IMDD link can be expressed in terms of the input signal x, as y = a0 + a1x + a2x2 + a3x3, where ai (i = 0, 1, 2, 3) are the coefficients of the power series and are determined by the specific parameters of the link. With small-signal approximation, higher order harmonics than three are ignored because of their minor contributions. For a sub-octave span IMDD link, the received harmonic components can be eliminated by suitable RF filters, so that only the low-pass band, y0, and the fundamental RF band around ωRF, y1, are considered in our design. According to , they are
In this paper, we propose that the linearization can be achieved by directly multiplying the distorted RF band signal y1 with the low-pass band signal y0 as follows,Equation (2) shows that the desired IMD3 nonlinearity compensation will occur whenEq. (2) shows the IMD3 compensation principle mathematically. The low-pass band, which contains a2A2(t)/2, modulates the fundamental band, i.e. a1A(t), to generate a new IMD3, which then eliminates the original IMD3 component.
One can see that the non-zero a2 is essential for successful IMD3 compensation, which means that the MZM in the link should not be biased at its quadrature point. For an IMDD link with external MZM under certain bias angle, all of the ais are shown in , which, together with Eq. (3), determine the proposed IMD3 compensation. Especially, substitute ais to Eq. (3) and we can find that a1a2 and a0a3 have opposite sign when the MZM is low-biased. Besides, the generated photo current at the bias-modulated PD and its bias modulation are in phase (i.e. the PD responsivity increases with its bias voltage; see below in Fig. 3). As a result, the low bias at MZM guarantees that the newly-generated intermodulation has inverse phase with the original one, and the inverse phase requirement is satisfied automatically. However, the low bias angle limits the proposed linearized link within the sub-octave-span applications. Besides, precise bias angle control on the MZM is also demanded. The bias angle stability requirement can be estimated according to , which shares the similar mathematical equation with the proposed one here. The IMD3 can be suppressed larger than 40 dB as long as the bias angle drift away the best value is less than ± 2 degrees. Such stability can be easily achieved by a commercial bias controller .
Different from , here the multiplication in Eq. (2) is obtained by the proposed IMD3 compensation receiver. The receiver consists of a low-pass optical receiver and a high-speed PD with bias voltage modulation, which receive the low-pass band y0 and the RF band y1, respectively. The y0 and y1 must be time synchronized at the bias-modulated PD, which is realized by a matched fiber delay before the PD. The output of the low-pass optical receiver, combined with a fixed direct current (DC) voltage, acts as the bias of the high-speed PD. When the DC voltage is properly set, the output photo current of the PD can be modulated by the output of the low-pass optical receiver [19, 20]. After the modulation at the high-speed PD, new intermodulation will be generated inside the photo current. As long as Eq. (3) is satisfied, the new intermodulation will have the same amplitude, with however opposite phase, as the original one (which has been generated at the MZM), resulting in the IMD3 compensation. Since y1 is modulated by y0 at the PD, the PD acts as a modulator, whose modulation depth is determined by both the input y0 and its modulation efficiency. The modulation efficiency (which is analog to Vπ of an MZM) is constant under a fixed DC bias voltage (further discussion will be in section 3). As a result, the output power of the low-pass optical receiver has to be tuned correctly to achieve the required modulation depth, determined by Eq. (3). Such tuning can be achieved by adjusting the input optical power or adjusting the electronic amplifier in the receiver.
Compared with previous methods, our receiver-end IMD3 compensation technique keeps the transmitter as simple as possible. No additional RF loss is required, so that the noise figure can be kept. The low-biased MZM can increase the link gain performance as well, and there is no digital noise at the receiver end.
3. Experiment and results
Our experimental setup based on the proposed IMD3-compensation receiver as well as the verification IMDD link is shown in Fig. 2. The continuous-wave (CW) laser (NKT Photonics) operates at wavelength of 1550 nm and the output optical power is 16.2 dBm. Two RF sinusoidal wave generators with a power combiner are used to generate a two-tone RF signal around 3.0400 GHz with interval of about 7.7 MHz. Then the two-tone RF signal modulates the optical carrier through an MZM (EOSpace, 20 GHz, Vπ is around 4.5 V at 3 GHz), where an auto bias controller is adopted to stabilize the MZM at a low bias angle of 138°. The lightwave from the MZM is sent to the IMD3-compensation receiver, which consists of a tunable optical coupler, a low-pass optical receiver, a matched delay fiber, a bias-modulated PD, a fixed DC bias voltage, and a bias-tee. The optical coupler splits the lightwave into two parts, one part of which (around 0 dBm) is received by the low-pass optical receiver. In experiment we use a commercial module (New Focus, Model 1611), which has a bandwidth of around 1 GHz and the responsivity of 700 V/W after its inside electronic amplifier. The power of the recovered baseband signal is controlled by slightly adjusting the input optical power of the low-pass optical receiver through the optical coupler. Next, the output of the low-pass receiver and the DC bias voltage are combined by the bias-tee and transmitted to the bias port of the high-speed PD. Our bias-modulated PD has a responsivity of 0.99 A/W, and the bandwidth of the optical port is 3 GHz. The input optical power is also around 0 dBm.
The PD performance related to its DC bias voltage is investigated firstly. When the MZM is low-biased at 138°, the input RF power is 6 dBm, and the input optical power to the PD is 0 dBm, the output RF power from the PD is measured under different DC bias voltages and under different input RF frequencies. The result is shown in Fig. 3. As can be seen, the output power of the PD increases rapidly when the DC bias voltage varies from 0 V to 2 V, whereas it remains almost the same while the DC bias voltage is above 2 V. One can also see that the frequency response of the PD changes only slightly at different bias voltage. The responsivity of our PD drops quickly after 3 GHz, so that the maximum carrier frequency of the RF signal should also be 3 GHz around.
In our home-made bias-modulated PD, the capacitor between the bias port and ground was removed and impedance matched to 50 ohm to ensure wideband signal can be coupled into the PD. Figure 3 illustrates that the PD responsibility changes with the bias voltage. As a result, bias modulation can be realized. The bias modulation performance of the PD is studied. By applying an alternating current (AC) bias with a certain intermediate frequency (IF), the RF photo current will mix with the IF tone, and then at the PD output one can observe the intermodulation component. In our experiment, the input IF AC bias power is kept −12 dBm, which is an estimate of the typical value of the output of the low-pass optical receiver. By scanning the AC bias frequency from 0.5 MHz to 30 MHz under a certain DC bias voltage, the power of the output intermodulation component is recorded and shown in Fig. 4. One can apparently see that the PD output power of the intermodulation component, i.e., the mixing of the AC bias signal and the optically carried RF signal, is basically unchanged, which means that the bias-modulated PD has a flat modulation efficiency within 30 MHz bandwidth. Above30 MHz the modulation efficiency drops, which shows the bandwidth limitation on the input RF signal bandwidth. Note that such modulation bandwidth on PD can be much larger, up to 7 GHz .
Figure 4 also shows the output intermodulation power under different DC bias voltages at 0.5 V, 1.3 V, 2 V and 4 V separately. One can see that the intermodulation gets weaker, i.e. the modulation efficiency decreases when the DC bias voltage gets large. We find that the real PD responsivity and its modulation efficiency is a tradeoff, according to Figs. 3 and 4: low link loss requires a high DC bias voltage, while the high modulation efficiency requires a low DC bias voltage. As a result, the DC bias voltage is finally chosen as 1.3 V.
The IMD3-compensation receiver performance is evaluated by a typical two-tone IMDD link in Fig. 2. We compare the electrical spectra between links without and with the low-pass optical receiver path, and the results are shown in Fig. 5(a) and Fig. 5(b), respectively. The input two-tone RF power is −3.5 dBm per tone. The fundamental RF signal at 3.0400 GHz and 3.0477 GHz as well as the corresponding IMD3 component at 3.0323 GHz and 3.0554 GHz are monitored for both cases. We can clearly observe considerable nonlinear distortions around the fundamental RF band in Fig. 5(a) with a fundamental to IMD3 power ratio of 35.8 dB due to the intrinsic nonlinear characteristic in the MZM. After the proposed post compensation, the ratio approaches 57.9 dB as shown in Fig. 5(b), which indicates that the nonlinearity has been significantly suppressed by as much as 22.1 dB.
When the input RF power is scanned from −3.5 dBm to 2.5 dBm, the powers of both the fundamental and the IMD3 are monitored and recorded. The measurement results versus the input RF power before and after compensation are plotted in Fig. 6(a) and Fig. 6(b), respectively. The measured overall noise floor, which is dominated by the shot noise, is −164.6 dBm/Hz around 3 GHz. As can be seen in Fig. 6(a) and Fig. 6(b), the SFDR increases from 105.3 to 123.4 dB within 1-Hz bandwidth. Compared with the conventional IMDD link, the improvement of SFDR is as large as 18.1 dB by the proposed IMD3-compensation optical receiver. Figure 6(a) and Fig. 6(b) also indicate the well suppression of IMD3: the slope of the fundamental component is 1, while the slopes of the intermodulation components are 3 and 5, respectively, before and after the proposed linearization. The phenomenon suggests that the IMD3 is perfectly cancelled out and the fifth-order intermodulation becomes the dominant nonlinear component after the proposed linearization.
In our experiment, we use a 50:50 optical coupler. It is possible to reduce the amount of optical power sent to the low-pass receiver by using a coupler with different splitting ratio. However, the gain of the low-noise amplifier inside the receiver should be increased accordingly to guarantee the output power and effective modulation on the PD. The nonlinearity of the amplifier is measured. At 0 dBm input optical power and the maximum RF power (2.5 dBm per tone), the second order harmonic (which is at 15.4 MHz, i.e. the double frequency of the dual tone separation) is > 40 dB lower than the fundamental. Much larger power ratio can be found when the RF power is lower. As a result, the nonlinearity of the low-pass receiver can be ignored. The noise floor of the bias-modulated PD dependent on its bias voltage and modulation is also studied. Experimentally, we compare two links with 1.3 V DC bias and with 5 V DC bias, where the two links have the same link loss by changing the laser power. We find that the noise floors are the same. When the AC bias is on the noise floor at the RF band (3 GHz) is also found unchanged. The reason is that the output of the PD is the multiplication of the y1 and y0, and the baseband y0 shows no impact on the RF band when the input RF signal is none.
In conclusion, we have theoretically analyzed and experimentally demonstrated a novel IMD3-compensation optical receiver based on a bias-modulated PD. Our theory showed that by properly mixing the RF-band signal and the baseband signal of an IMDD link with a low-biased MZM, the IMD3 could be well suppressed. Such mixing was demonstrated to be achieved by the bias-modulated PD without significant PD responsivity loss. In an IMDD link, the new IMD3-compensation receiver delivered an enhanced SFDR of 123.4 dB within 1-Hz bandwidth around 3 GHz, which was 18.1 dB more than that without compensation. Our method keeps a simple transmitter with an improved link gain, and the post linearization without digital processing avoids the high quantization noise.
This work was supported in part by NSFC Program (61471065), National 973 Program (2012CB315705), NSFC Program (61271042), and NCET-13-0682.
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