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Optimized self-interference cancellation based on optical dual-parallel MZM for co-frequency and co-time full duplex wireless communication under nonlinear distortion and emulated multipath effect

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Abstract

Co-frequency and co-time full duplex (CCFD) technique has the potential to further improve the capacity of the fifth-generation (5G) system. However, in a CCFD-based transceiver, the self-interference-cancellation (SIC) module is essential because the transmitted signal is also captured by the receiving antenna. In this paper, an optimized SIC technique is proposed based on a dual-parallel Mach-Zehnder modulator (DP-MZM). In addition to the multipath effect between the transmitting and receiving antennas, the nonlinear distortion induced by the used optical and electrical components is considered and analyzed for the first time. In this scheme, one of the children MZMs is biased at 90°. The bias points of the other child MZM and the parent MZM are swept for SIC optimization. Compared to the traditional SIC scheme using DP-MZM, the power of the received signal is increased by 6 dB and the robustness to the bias point drift is improved. In our experiment, over 35 dB cancellation ratio is achieved for 200 MHz filtered orthogonal frequency division multiplexing (F-OFDM) interference signal with carrier frequency from 2.5 GHz to 6 GHz. To mitigate the influence of multipath effect and nonlinear distortion, the recursive least squared (RLS) linear equalizer and the RLS Volterra equalizer are designed and compared. Finally, 42 dB cancellation ratio is achieved for 200 MHz F-OFDM signal with carrier frequency of 4.5 GHz in the presence of nonlinear distortion and emulated multipath effect.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The fifth-generation (5G) mobile communication has attracted significant interest, and it promises much larger capacity than current 4G system. However, the conventional duplex methods including time-division duplex (TDD) and frequency-division duplex (FDD) [1] cannot make full use of electrical spectrum resources. As a result, the insufficient spectral efficiency will limit the further increase in capacity. To improve the spectrum usage, a novel full-duplex method called co-frequency and co-time full duplex (CCFD) is reported [2], and the transmitting and receiving can take place at the same time and at the same frequency band. However, for a CCFD-based transceiver, the transmitted signal is also captured by the receiving antenna, which will cause strong interference (>100 dB) over the signal of interest [3]. Therefore, an effective self-interference-cancellation (SIC) technique is essential for the CCFD-based transceiver. Generally, the conventional SIC modules can be divided into three stages: the air interface cancellation module, the analog cancellation module, and the digital cancellation module [4]. The analog cancellation module is expected to provide over 30 dB cancellation ratio for the CCFD-based transceiver [4]. To be specific, the self-interference signal is very similar to the known transmitted signal, and thus the digital method and the analog method can use the transmitted signal to eliminate the self-interference in digital and analog domain, respectively. In practice, the commercial electrical analog cancellation chips (QHx220) can provide about 20-25 dB cancellation ratio by using automatic gain controller (AGC), electrical delayer, and electrical analog subtractor [5]. The electrical analog cancellation method can achieve higher cancellation ratio by using parallel AGC-delayer-subtractor structures to compose an analog finite-impulse-response filter [6,7]. However, the operating carrier frequency and bandwidth of electrical analog cancellation methods are always limited by the well-known electronic bottleneck [8].

Fortunately, the shortcomings of electrical analog cancellation methods can be well-solved by microwave-photonics techniques [913]. In [9], an optical analog SIC scheme is proposed by using two externally modulated lasers, variable optical attenuator and delay line, and 30 dB cancellation ratio over an enormously wide bandwidth of 5.5 GHz are achieved. In this scheme, two optical sources and two optical paths with different fiber length are required, thus the robustness to the optical phase variation and the polarization state instability induced by thermal and mechanical fluctuations is limited. To solve this problem, all optical components including two directly modulated lasers, three semiconductor optical amplifiers, and a pair of balanced photo-diodes are integrated onto a single substrate in [10]. Obviously, it is inspiring that the integrated optical analog SIC chip is realized in this work, and the power consumption of this chip will be decreased if the SOAs could be replaced by the passive components for realizing AGC and subtractor. Another solution is to use only one optical source and the integrated Mach-Zehnder modulator (MZM) for SIC. For example, a dual-drive MZM (DD-MZM) is used as a subtractor to cancel the self-interference signal in [11]. In this scheme, an extra variable electrical attenuator is necessary for the amplitude matching, and the output optical power will be decreased because the DD-MZM is biased at the destructive-interference point. To increase the output optical power, an integrated dual-parallel MZM (DP-MZM) is used in [12]. No extra variable electrical attenuator is required in this scheme because the amplitude-matching and subtraction are both realized in DP-MZM. In our previous work [13], further increase of the output power is achieved by optimizing the bias point of DP-MZM, and the robustness to the bias point drift could be also improved. In this work, 35 dB cancellation ratio is achieved for orthogonal frequency division multiplexing (OFDM) signal with center frequency of 2.5 GHz and bandwidth of 200 MHz.

Generally, not only the uneven frequency response of the used optical and electrical components but also the multipath effects exist in real scenario. To cope with the uneven frequency response of electrical components, an optical delay line instead of an electrical one is used in [14] to match the time delay between the self-interference and the reference signals. A pair of cascaded MZMs are used, and 32.6 dB cancellation ratio over 100 MHz bandwidth is realized in this work. Moreover, the digital predistortion technology is applied to the reference signal in [15,16] to eliminate the multipath interferences. 30 dB cancellation ratio over 1.22 GHz bandwidth and 25 dB cancellation ratio over 3.2 GHz bandwidth are realized in these two works, respectively. Meanwhile, multi-parallel AGC-delayer-subtractor structures are constituted with optical components to realize the optical analog multipath equalizers in [17,18]. 44 dB cancellation ratio over 50 MHz bandwidth and 40 dB cancellation ratio over 200 MHz are realized in these two works, respectively. Obviously, digital and analog multipath equalizers are useful for coping with the uneven frequency response of optical and electrical components and multipath effects, but the elimination of nonlinear distortions induced by optical and electrical components are not concerned in the above researches.

In our previous work in [13], the components and channel are regarded as ideal and the influences of multipath effect and nonlinear distortion are not considered. In this paper, we extend our previous work and further experimentally demonstrate the proposed SIC module based on a dual-parallel MZM. In our scheme, one of the children MZMs is biased at $90^\circ$ for intensity modulation. The bias points of the other child MZM and the parent MZM are swept for SIC optimization. The theoretical analysis and experimental verification have proved that not only the power of the received signal is increased by using the optimized bias point, but also the robustness to the bias point drift is improved compared to the conventional scheme using DP-MZM in [12]. In our experiment, over 35 dB cancellation ratio is achieved for 200 MHz filtered orthogonal frequency division multiplexing (F-OFDM) interference signal with carrier frequency from 2.5 GHz to 6 GHz. In addition to the multipath effect between the transmitting and receiving antennas, the nonlinear distortion induced by the used optical and electrical components is considered and analyzed in our work for the first time. The recursive least squared (RLS) linear equalizer and the RLS Volterra equalizer in digital domain are both designed and evaluated in our experiment for nonlinear distortion and emulated multipath effect elimination. The experimental results show that 42 dB cancellation ratio could be achieved for 200 MHz F-OFDM interference signal with carrier frequency of 4.5 GHz by using RLS Volterra equalizer, even when the input electrical power is 4 dBm and severe multipath effect exists.

2. Principle

Figure 1 shows the schematic diagram of the proposed SIC module. $Rx(\textrm{t})$ and $Tx(\textrm{t})$ are the received signal and the transmitted signal, respectively. $Rx(\textrm{t})$ is the combination of the interest of the received signal $R(\textrm{t})$ and the self-interference signal $Si(\textrm{t})$. As shown in Fig. 1, a copy of the transmitted signal is delayed by a tunable electrical time delay line $\tau$, and it then acts as the reference signal $Ref(\textrm{t})$. In ideal condition, $Si(\textrm{t})$ is equal to ${A_0} \cdot Tx({\mathop{\textrm t}\nolimits} - {\tau _0})$, where ${A_0}$ and ${\tau _0}$ is the attenuation and time delay of channel, respectively. Thus, $Ref(\textrm{t}) = {{Si(\textrm{t})} \mathord{\left/ {\vphantom {{Si(\textrm{t})} {{A_0}}}} \right.} {{A_0}}}$ when $\tau = {\tau _0}$. After that, $Si(\textrm{t})$ can be removed from $Rx(\textrm{t})$ by using a variable attenuator and a subtractor, i.e., $\hat{R}(\textrm{t}) = Rx(\textrm{t}) - {A_0}Ref(\textrm{t})$. In the proposed scheme, the DP-MZM performs as an electro-optical (E/O) converter, a variable attenuator, and a subtractor simultaneously. For E/O conversion, $Rx(\textrm{t})$ and $Ref(\textrm{t})$ are loaded into two children MZMs (MZM_I and MZM_Q) respectively. Note that MZM_I is biased at the quadrature point for intensity modulation, which means the bias phase ${\varphi _I}$ is equal to 90°. Meanwhile, the bias phase of MZM_Q (${\varphi _Q}$) varies in order to match the amplitudes of $Ref(\textrm{t})$ and $Si(\textrm{t})$. Subsequently, the bias phase of the parent MZM (${\varphi _P}$) varies for the subtraction of two signals on two children MZMs. Finally, the total output of the DP-MZM is detected by a PD, and $\hat{R}(\textrm{t})$ can be acquired after a band-pass filter (BPF).

 figure: Fig. 1.

Fig. 1. Schematic diagram of the proposed SIC module.

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In order to explain the principle of interference cancellation mathematically, we assume that the time delay is already matched, then the output signal of PD ${I_{PD}}$ can be written as:

$${I_{PD}} \propto {|{{E_o}} |^2} \propto {\left|\begin{array}{l} \cos [{{{({\varphi_I} + Rx(\textrm{t}))} \mathord{\left/ {\vphantom {{({\varphi_I} + Rx(\textrm{t}))} 2}} \right.} 2}} ]\\ + \cos [{{{({\varphi_Q} + Ref(\textrm{t}))} \mathord{\left/ {\vphantom {{({\varphi_Q} + Ref(\textrm{t}))} 2}} \right.} 2}} ]\exp (j{\varphi_P}) \end{array} \right|^2},$$
where ${E_o}$ is the electric field of the output optical signal of DP-MZM, and $Rx(\textrm{t}) = R(\textrm{t}) + {A_0}Ref(\textrm{t})$. By using a BPF at the output of PD, the high-order harmonic components of $R(\textrm{t})$ and $Ref(\textrm{t})$ are removed, and only the linear terms and the intermodulation distortion terms are retained. Therefore, the electrical signal after the BPF can be expressed as:
$$\begin{aligned} \hat{R}(\textrm{t}) &= BPF\textrm{[}{I_{PD}}\textrm{]}\\ &= {\Gamma _R} \cdot R(\textrm{t}) + {\Gamma _S} \cdot Ref(\textrm{t}) + {\Gamma _3} \cdot IM{D_3} + \cdots . \end{aligned}$$
Here, IMD3 is the 3rd intermodulation distortion which is the largest nonlinear distortion item in the proposed scheme. ${\Gamma _R}$, ${\Gamma _S}$, and ${\Gamma _3}$ are the coefficients of the recovered signal $\hat{R}(\textrm{t})$, the self-interference signal, and IMD3, respectively. Expanding ${\Gamma _R}$, ${\Gamma _S}$, and ${\Gamma _3}$ in series and taking only the first terms [19], we can get expressions as:
$$\begin{array}{l} {\Gamma _R} = \beta \cdot {m_R} + o({m_R}^3)\\ {\Gamma _S} = \eta \cdot {m_{Ref}} + o({m_{Ref}}^3)\\ {\Gamma _3} = \xi \cdot {m_{Ref}}^3 + o({m_{Ref}}^5)\\ \beta = {{({1 + {b_1}} )} \mathord{\left/ {\vphantom {{({1 + {b_1}} )} 2}} \right.} 2}\\ \eta = {{[{\sin ({\varphi_Q}) + {b_2} + {A_0}{b_1} + {A_0}} ]} \mathord{\left/ {\vphantom {{[{\sin ({\varphi_Q}) + {b_2} + {A_0}{b_1} + {A_0}} ]} 2}} \right.} 2}\\ \xi \approx {{[{4\sin ({\varphi_Q}) + {b_2} + {A_0}^3{b_1} + 4{A_0}^3} ]} \mathord{\left/ {\vphantom {{[{4\sin ({\varphi_Q}) + {b_2} + {A_0}^3{b_1} + 4{A_0}^3} ]} {64}}} \right.} {64}}\\ {b_1} = \sqrt 2 \cos ({{{\varphi _Q}} \mathord{\left/ {\vphantom {{{\varphi_Q}} 2}} \right.} 2})\cos({\varphi _P}),\textrm{ }{b_2} = \sqrt 2 \sin ({{{\varphi _Q}} \mathord{\left/ {\vphantom {{{\varphi_Q}} 2}} \right.} 2})\cos({\varphi _P}). \end{array}$$
Here, ${m_R}$ and ${m_{Ref}}$ are the modulation indexes of $R(\textrm{t})$ and $Ref(\textrm{t})$, respectively. In order to suppress IMD3, the input power of $Ref(\textrm{t})$ and $Rx(\textrm{t})$ should be decreased to make ${m_R} \ll {m_{Ref}}\;<\;1$. In practice, the power of IMD3 is much lower than the power of the self-interference signal, and thus the self-interference elimination is considered in priority. In the proposed scheme, ${\Gamma _R} \approx \beta \cdot {m_R}$, ${\Gamma _S} \approx \eta \cdot {m_{Ref}}$, and ${A_0}$ is fixed. Therefore, $\beta$ and $\eta$ entirely depend on the three bias phases ${\varphi _I},{\varphi _P}$ and ${\varphi _Q}$ of the DP-MZM. Meanwhile, due to the optical power coupling of DP-MZM, these three bias phases can be used to adjust the value of ${\Gamma _R}$, ${\Gamma _S}$ and ${\Gamma _3}$. In this way, the power of the recovered signal $\hat{R}(\textrm{t})$ is proportional to ${\beta ^2}$, and ${\beta ^2}$ is defined as the power ratio of the recovered signal $\hat{R}(\textrm{t})$ to the input signal $R(\textrm{t})$ in our work. Similarly, ${\eta ^2}$ is defined as the power ratio of the estimated interference signal to the input self-interference signal $Ref(\textrm{t})$. Obviously, the signal-to-interference ratio ($SIR$) in dB can be written as $SIR = 10 \cdot {\log _{10}}({{{\beta ^2}} \mathord{\left/ {\vphantom {{{\beta^2}} {{\eta^2}}}} \right.} {{\eta ^2}}})$, and $SIR$ is equivalent to the self-interference cancellation ratio.

Figure 2(a) shows the simulated contour map of $SIR$ in terms of ${\varphi _Q}$ and ${\varphi _P}$ when ${A_0} = 0.5$. It can be clearly observed that there are many pairs of bias phases $({\varphi _Q},{\varphi _P})$ which can maximize the $SIR$ value. However, when the bias phases around the range in the dot box of Fig. 2(a) are used, not only good SIC performance can be achieved but also the measured $SIR$ value is not sensitive to ${\varphi _P}$. It means that the proposed scheme has high tolerance to the bias point drift. In addition to $SIR$, the power of $\hat{R}(\textrm{t})$ is also a primary parameter for SIC module. Obviously, ${\beta ^2}$ is expected to be as large as possible when the $SIR$ value is maximized. Figure 2(b) shows the contour map of ${\beta ^2}$ in terms of ${\varphi _Q}$ and ${\varphi _P}$ under the same simulation condition in Fig. 2(a). Clearly, the measured ${\beta ^2}$ is close to the maximum value when the bias phases $({\varphi _Q},{\varphi _P})$ around the same range in the dot box of Fig. 2(a) are used. Based on the above analysis, ${\varphi _P}$ is fixed at 180° and ${\varphi _Q}$ is scanned for SIC optimization in our scheme. Theoretically, the best SIC performance could be achieved at the bias phases of ${\varphi _Q} = 2\pi - \arcsin ({A_0}\sqrt {2 - {A_0}^2} )$ and ${\varphi _P} = \pi$, and in this case $\beta = \frac{{1 + \sqrt {2 - {A_0}^2} }}{2}$. However, in the conventional scheme reported in [12], MZM_Q is biased at 180°, and ${\varphi _P}$ is scanned for SIC. The optimal bias phases for SIC in this scheme are ${\varphi _Q} = \pi$ and ${\varphi _P} = \pi \pm \arccos (\frac{{\sqrt 2 }}{2}{A_0})$ which is shown in black circle in Fig. 2, and in this case $\beta \equiv \frac{1}{2}$. Obviously, compared to the conventional SIC scheme [12], the power of the recovered signal $\hat{R}(\textrm{t})$ is higher in the proposed scheme. Meanwhile, the proposed scheme has higher tolerance to the bias point drift as shown in Fig. 2(a). Figure 2(c) shows the $SIR$ curve versus ${\varphi _Q}$ when $({\varphi _I},{\varphi _P}) = ({\pi \mathord{\left/ {\vphantom {\pi {2,\pi }}} \right.} {2,\pi }})$, and it could be clearly observed that over 40 dB $SIR$ can be achieved within 1° around the optimized ${\varphi _Q}$ value.

 figure: Fig. 2.

Fig. 2. The contour maps of $SIR$ (a), the power of the recovered signal $\hat{R}(\textrm{t})$ (b), and the $SIR$ curve versus ${\varphi _Q}$ curve when $({\varphi _I},{\varphi _P}) = ({\pi \mathord{\left/ {\vphantom {\pi {2,\pi }}} \right.} {2,\pi }})$ (c).

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3. Experimental setup and results

3.1 The SIC performance of the proposed scheme

To evaluate the SIC performance of the proposed scheme and compare our scheme with the conventional method in [12], an experimental setup is built up as shown in Fig. 3. The interest of the received signal $R(\textrm{t})$ and the self-interference signal $Si(\textrm{t})$ are combined in an arbitrary waveform generator (AWG, Keysight M8195A) to act as $Rx(\textrm{t})$. A digital attenuator ${A_0}$ is applied to the transmitted signal $Tx(\textrm{t})$ to emulate the attenuation from the transmitting antenna to the receiving antenna. $Tx(\textrm{t})$ is delayed by a tunable electrical time delay line (Apitech, 6705K-Q) to act as $Ref(\textrm{t})$. The turning range of this time delay line is from 111 ps to 209 ps, and the tuning precision is 4 ps per shaft turn. Subsequently, $Rx(\textrm{t})$ and $Ref(\textrm{t})$ are loaded into a DP-MZM (Fujitsu FTM7961). The half wave voltages of the used DP-MZM in DC port are about 9 V and the adjusting precision of bias voltages is 1 mV in our experiment. Therefore, the adjusting precision of bias phases is about 0.02° and the maximum attenuation of $Ref(\textrm{t})$ can be written as $20 \cdot {\log _{10}}(\sin(0.02/180 \cdot \pi )) \approx{-} 69dB$ in theory. Finally, the output of the DP-MZM is detected by a PD, and the output signal of PD is observed by an electrical spectrum analyzer (ESA, R&S FSV) and a digital storage oscilloscope (DSO, Tektronix DSA72504D).

 figure: Fig. 3.

Fig. 3. The experimental setup of the proposed SIC method.

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In this experiment, a -1 dBm and 200 MHz 16QAM-F-OFDM signal with carrier frequency of 2.5 GHz is generated as $Tx(\textrm{t})$, and an 100 MHz 16QAM-F-OFDM signal with the same carrier frequency is produced as $R(\textrm{t})$. In our test, ${A_0}$ is 0.5, and thus the power of $Si(\textrm{t})$ is about -7 dBm. All of these F-OFDM signals are generated by filtering the conventional OFDM signals with a Hanning-model low-pass filter. The FFT size of the used F-OFDM signal is 256 and the number of sub-carriers is 128. By adjusting the power of $R(\textrm{t})$ from -7 dBm to -25 dBm, the input power ratio of $R(\textrm{t})$ to $Si(\textrm{t})$ varies from 0 dB to -18 dB. For simplicity, the power ratio of $R(\textrm{t})$ to $Si(\textrm{t})$ is defined as $ESNR$ in our test. The bias phases of DP-MZM are adjusted manually for SIC. The output signal of PD $\hat{R}(\textrm{t})$ is recorded by the DSO and it is then demodulated offline. It should be noted that in our test, the acquired bias points of $({\varphi _Q},{\varphi _P})$ for best $SIR$ are $(1.77\pi ,\pi )$ and $(\pi ,0.615\pi )$ in the proposed scheme and the conventional scheme, respectively. These two pair of bias points are very close to the theoretical optimum bias points shown in Fig. 2. Except for bias points, nothing else has be changed in our comparison. Figure 4(a) shows the measured error vector magnitude (EVM) performance of the recovered 16QAM-F-OFDM signal $\hat{R}(\textrm{t})$ in terms of the input $ESNR$ values in the proposed and conventional schemes. Obviously, the measured EVM performance of the proposed scheme outperforms that of the conventional scheme. The reason could be explained in Figs. 4(b) and 4(c), and these two figures present the electrical spectrum of the received signal with and without SIC when $ESNR ={-} 6dB$ in these two schemes, respectively. Theoretically, these two schemes can achieve the same $SIR$ when no noises are considered. However, the power of the output signal is higher in the proposed scheme as analyzed in Section 2, and about 6 dB power improvement can also be clearly observed in our experiment as shown in Figs. 4(b) and 4(c). In this case, the higher signal to noise ratio contributes to the better EVM performance. The achieved maximum $SIR$ is 32 dB and 36 dB in the conventional scheme and the proposed scheme, respectively.

 figure: Fig. 4.

Fig. 4. The measured EVM performance versus $ESNR$ in the proposed and conventional schemes (a), the SIC performance of the proposed method (b) and the conventional method (c).

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To further investigate the SIC performance of the proposed scheme in different carrier frequencies, $R(\textrm{t}) = 0$, and -8 dBm 200 MHz F-OFDM signals with different carrier frequency are used to act as $Si(\textrm{t})$. Subsequently, the $SIR$ of the proposed and the conventional schemes are both measured and plotted in Fig. 5(a). Obviously, over 35 dB cancellation ratio is achieved in the proposed scheme when the carrier frequency is scanned from 2.5 GHz to 6 GHz. Compared to the conventional scheme, the improved $SIR$ can be attributed to the increased power of the output signal. Figures 5(b) and 5(c) present the electrical spectrum of the received signal with and without SIC in these two schemes, respectively. There are a little residual inference signals over 200 MHz band both in these two schemes. This phenomenon is caused by the uneven frequency response of the used optical or electrical components. In practical application, besides the uneven frequency response of components, the multipath effect from the Tx antenna to the Rx antenna has more serious impact on SIC. Moreover, the nonlinear distortion induced by the electrical or optical components may also be a limiting factor for SIC when the power of the input signal is too large.

 figure: Fig. 5.

Fig. 5. The measured cancellation ratio versus different carrier frequency (a), and the electrical spectrum of the received signal with and without SIC in the conventional scheme (b) and the proposed scheme (c) when the carrier frequency is 5.5 GHz.

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For analog application, the spurious-free dynamic range (SFDR) is a main figure of merit which is limited by the linearity, gain and noise figure of system. In our test, a vector signal generator (R&S SMBV100A) is used to generate a pair of two-tone signals ($f(\textrm{t}) = {V_p} \cdot \{{\sin [{2\pi ({f_c} + \Delta f)\textrm{t}} ]+ \sin [{2\pi ({f_c} - \Delta f)\textrm{t}} ]} \}$), where $\Delta f = 0.5\textrm{ MHz}$, ${f_c} = 2.5\textrm{ GHz}$, and ${V_P}$ can be adjusted within certain range. An electrical spectral analyzer (ESA, R&S FSV) is used to measure the power of the first order harmonic (FOH), IMD3 and noise floor. First, the DP-MZM is biased at the operating point of the proposed scheme. Subsequently, the third-order SFDR of the upper MZM_I is measured by setting $Rx(\textrm{t}) = f(\textrm{t})$ and $Ref(\textrm{t}) = 0$. Similarly, the SFDR of the lower MZM_Q is measured by setting $Rx(\textrm{t}) = 0$ and $Rx(\textrm{t}) = f(\textrm{t})$. The measured SFDR performance of MZM_I and MZM_Q are plotted in Figs. 6(a) and 6(b) respectively. It could be clearly observed that the SFDR of 96.1 dB·Hz2/3 and 96.5 dB·Hz2/3 can be achieved for MZM_I and MZM_Q respectively, when the carrier frequency of the input RF signal is 2.5 GHz. The measured results show that the SFDR value of optical SIC system is not decreased even though the bias point of MZM_Q is far away from the linear bias point.

 figure: Fig. 6.

Fig. 6. The SFDR performance of MZM_I (a) and MZM_Q (b) in the proposed SIC module.

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3.2 The tolerance to the multipath effect and nonlinearity distortion

In order to evaluate the tolerance of the proposed SIC scheme to the multipath effect and nonlinear distortion, another experimental setup is built up as shown in Fig. 7, and digital equalizer is designed and used in this test. In this experiment, the frequency response from a Tx antenna (DF58-60V15M) to a Rx antenna (DF58-60V15M) is measured by a vector network analyzer (VNA, R&S ZVL6), and the space between these two antennas is 15 cm. By this means, we can emulate the multipath effect between two antennas in a relatively realistic scenario. The measured frequency response is then used in AWG to generate the digital multipath filter (DMF). At the output of AWG, an electrical dual-channel amplifier with variable gain is used to amplify the produced $Rx(\textrm{t})$ and $Ref(\textrm{t})$, and thus the nonlinear distortion of system could be enhanced easily by increasing the power of the input signal. Figure 8(a) shows the measured frequency response between these two antennas in a simple environment and a complex environment. Because of the multipath transmission between the two antennas in this test, the magnitude response curve is uneven, which makes $Ref(\textrm{t})$ unequal to $Si(\textrm{t})$ and could introduce significant multipath noise in the proposed SIC application. Therefore, the measured data between 4.3 GHz and 4.7 GHz of the complex multipath response are used to design the DMF in AWG and then $Si(\textrm{t})$ emulates a self-interference signal under the multipath effect in following experiments. The frequency response of the used time delay line is also measured as the comparison as shown in Fig. 8(b).

 figure: Fig. 7.

Fig. 7. The experimental setup of the proposed digital equalizer-added SIC method.

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 figure: Fig. 8.

Fig. 8. The measured transmission response between the transmitting and receiving antennas (a), and the frequency response of the used time delay line (b).

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In this test, the amplifier is turned off and a -7 dBm and 200 MHz F-OFDM signal with carrier frequency of 4.5 GHz is produced as $Si(\textrm{t})$. Figure 9(a) presents the electrical spectra of the received signal with and without the optical SIC (OSIC) in the presence of multipath effect respectively, and no equalization algorithms are used in these two cases. Obviously, $Si(\textrm{t})$ can’t be eliminated due to the multipath effect, and the achieved $SIR$ is only 13 dB. In order to suppress the multipath effect, an RLS linear equalizer (RLS-L) [20] in digital domain is designed and adopted. Moreover, the digital equalizer is applied to the RF signal directly for the purpose of combining the optical SIC module with the radio over fiber (RoF) system. The equalized signal ${\hat{R}_E}(\textrm{n})$ could be expressed as:

$${\hat{R}_E}(\textrm{n}) = \hat{R}(\textrm{n}) - \sum\limits_i {{h_L}(\textrm{i})Ref(\textrm{n} - \textrm{i})} ,$$
where $\hat{R}(\textrm{n})$ and $Ref(\textrm{n})$ is the recorded sample of $\hat{R}(\textrm{t})$ and $Ref(\textrm{t})$ respectively, and ${h_L}(\textrm{i})$ is tap coefficient of this RLS-linear equalizer. The tap coefficients of this equalizer are calculated by the RLS algorithm. Figure 9(b) shows the electrical spectra of the received signal without OSIC, and with the combination of OSIC and RLS-L with 61 taps, respectively. It could be clearly observed that about 39 dB cancellation ratio can be easily achieved. The further improvement of $SIR$ is limited by the noise in PD.

 figure: Fig. 9.

Fig. 9. The electrical spectrum of the received signal when the power of the input signal is -7 dBm with and without OSIC (a). The electrical spectrum of the received signal when the power of the input signal is -7 dBm without OSIC, and with the combination of OSIC and RLS-L (b).

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Furthermore, the nonlinear distortion induced by optical or electrical components can also be eliminated by introducing an RLS Volterra equalizer (RLS-V) [21], and the equalized signal ${\hat{R}_E}(\textrm{n})$ could be modified by:

$$\begin{aligned} {{\hat{R}}_E}(\textrm{n}) &= \hat{R}(\textrm{n}) - \\ &\left[ \begin{array}{l} \sum\limits_{i} {{h_L}(\textrm{i})Ref(\textrm{n} - \textrm{i})} + \\ \sum\limits_{{{m}_1}} {\sum\limits_{{m_2}} {{h_2}({\textrm{m}_1},{\textrm{m}_2})Ref(\textrm{n} - {m_1})Ref(\textrm{n} - {m_2})} } + \\ \sum\limits_{{k_1}} {\sum\limits_{{k_2}} {\sum\limits_{{k_3}} {{h_3}({k_1},{k_2},{k_3})Ref(\textrm{n} - {k_1})Ref(\textrm{n} - {k_2})Ref(\textrm{n} - {k_3})} } } + \cdots \end{array} \right]\\ &\approx \hat{R}(\textrm{n}) - \sum\limits_i {{h_L}(\textrm{i})Ref(\textrm{n} - \textrm{i})} \\ & - \sum\limits_{{k_1}} {\sum\limits_{{k_2}} {\sum\limits_{{k_3}} {{h_3}({k_1},{k_2},{k_3})Ref(\textrm{n} - {k_1})Ref(\textrm{n} - {k_2})Ref(\textrm{n} - {k_3})} } } , \end{aligned}$$
where ${h_2}({\textrm{m}_1},{\textrm{m}_2})$ and ${h_3}({k_1},{k_2},{k_3})$ are the 2nd and 3rd tap coefficients, respectively. The 2nd harmonic signal in Eq. (5) can be totally removed by a BPF, and the higher-order nonlinear distortion terms are too small. Therefore, ${h_2}({\textrm{m}_1},{\textrm{m}_2}) = 0$, and this equalizer can be further simplified by only considering the linear tap coefficients and the 3rd tap coefficient. It should be noted that this simplification is only true when the 2nd distortion can be removed by the BPF. Assuming that ${f_c}$ and $BW$ are the central frequency and bandwidth of the equalized signal respectively, the condition of the proposed simplification can be written as $2({{f_c} - {{BW} \mathord{\left/ {\vphantom {{BW} 2}} \right.} 2}} )\;>\;{f_c} + {{BW} \mathord{\left/ {\vphantom {{BW} 2}} \right.} 2}$, i.e., ${f_c}\;>\;\frac{3}{2}BW$. Therefore, this simplified equalizer can be only used to RF or IF (intermediate frequency) signals instead of the baseband signal. Although the sample frequency may be increased, this simplified Volterra equalizer is suitable for optical SIC module especially in RoF application.

In the last experiment, the nonlinear distortion of system is enhanced by using the dual-channel electrical amplifier to increase the power of the F-OFDM signal at the input of DP-MZM from -7 dBm to 4 dBm. In this test, the tap coefficients of the Volterra equalizer are also calculated by the RLS algorithm. Figure 10(a) shows the electrical spectra of the received signal with and without OSIC when the power of the input signal is 4 dBm, and no equalization algorithms are used in these two cases. The multipath effect and the nonlinear distortion could be clearly observed. Figure 10(b) presents the electrical spectra of the received signal when the power of the input signal is 4 dBm without OSIC, with the combination of OSIC and RLS-L, and with the combination of OSIC and RLS-V, respectively. Compared to the OSIC module using the RLS-L, 5 dB $SIR$ gain could be attached with the help of the RLS-V. In this Volterra equalizer, the memory length of the linear item is 61 and the memory length of the 3rd term is 5. Thus, the total tap number of this Volterra equalizer is 96. By using this equalizer, 42 dB cancellation ratio is achieved for 200 MHz band signal with carrier frequency of 4.5 GHz. Moreover, the SIC performance can be further promoted by increasing the memory length of the used equalizer, but the algorithm complexity will be significantly increased.

 figure: Fig. 10.

Fig. 10. The electrical spectrum of the received signal when the power of the input signal is 4 dBm with and without OSIC (a). The electrical spectra of the received signal when the power of the input signal is 4 dBm without OSIC, with the combination of OSIC and RLS-L, and with the combination of OSIC and RLS-V (b).

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4. Conclusion

We have experimentally demonstrated an optimized self-interference cancellation technique by using a dual-parallel MZM. Not only the multipath effect between the transmitting and receiving antennas, but also the nonlinear distortion induced by the used optical and electrical components are considered and analyzed for the first time. Different from the conventional SIC scheme using DP-MZM, the optimum bias points can be acquired by scanning the bias phases of MZM_Q and the parent MZM. In this way, not only the power of the recovered interest of signal is increased by 6 dB, but also the robustness to the bias point drift is improved. In our experiment, over 35 dB cancellation ratio is achieved for 200 MHz F-OFDM interference signal with carrier frequency from 2.5 GHz to 6 GHz. To mitigate the influence of multipath effect and nonlinear distortion, the RLS linear equalizer and the RLS Volterra equalizer are designed and compared. 42 dB cancellation ratio is achieved for 200 MHz F-OFDM signal with carrier frequency of 4.5 GHz. The proposed method provides a high cancellation ratio, high stability, and large bandwidth structure for optical self-interference cancellation, and it can be used in CCFD application for 5G and B5G system.

Funding

National Natural Science Foundation of China (61675083); Fundamental Research Funds for the Central Universities (2019kfyXMBZ033); State Key Laboratory of Advanced Optical Communication Systems and Networks. (2019GZKF7); National Key Research and Development Program of China (2018YFB1800903).

Disclosures

The authors declare no conflicts of interest.

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Figures (10)

Fig. 1.
Fig. 1. Schematic diagram of the proposed SIC module.
Fig. 2.
Fig. 2. The contour maps of $SIR$ (a), the power of the recovered signal $\hat{R}(\textrm{t})$ (b), and the $SIR$ curve versus ${\varphi _Q}$ curve when $({\varphi _I},{\varphi _P}) = ({\pi \mathord{\left/ {\vphantom {\pi {2,\pi }}} \right.} {2,\pi }})$ (c).
Fig. 3.
Fig. 3. The experimental setup of the proposed SIC method.
Fig. 4.
Fig. 4. The measured EVM performance versus $ESNR$ in the proposed and conventional schemes (a), the SIC performance of the proposed method (b) and the conventional method (c).
Fig. 5.
Fig. 5. The measured cancellation ratio versus different carrier frequency (a), and the electrical spectrum of the received signal with and without SIC in the conventional scheme (b) and the proposed scheme (c) when the carrier frequency is 5.5 GHz.
Fig. 6.
Fig. 6. The SFDR performance of MZM_I (a) and MZM_Q (b) in the proposed SIC module.
Fig. 7.
Fig. 7. The experimental setup of the proposed digital equalizer-added SIC method.
Fig. 8.
Fig. 8. The measured transmission response between the transmitting and receiving antennas (a), and the frequency response of the used time delay line (b).
Fig. 9.
Fig. 9. The electrical spectrum of the received signal when the power of the input signal is -7 dBm with and without OSIC (a). The electrical spectrum of the received signal when the power of the input signal is -7 dBm without OSIC, and with the combination of OSIC and RLS-L (b).
Fig. 10.
Fig. 10. The electrical spectrum of the received signal when the power of the input signal is 4 dBm with and without OSIC (a). The electrical spectra of the received signal when the power of the input signal is 4 dBm without OSIC, with the combination of OSIC and RLS-L, and with the combination of OSIC and RLS-V (b).

Equations (5)

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I P D | E o | 2 | cos [ ( φ I + R x ( t ) ) / ( φ I + R x ( t ) ) 2 2 ] + cos [ ( φ Q + R e f ( t ) ) / ( φ Q + R e f ( t ) ) 2 2 ] exp ( j φ P ) | 2 ,
R ^ ( t ) = B P F [ I P D ] = Γ R R ( t ) + Γ S R e f ( t ) + Γ 3 I M D 3 + .
Γ R = β m R + o ( m R 3 ) Γ S = η m R e f + o ( m R e f 3 ) Γ 3 = ξ m R e f 3 + o ( m R e f 5 ) β = ( 1 + b 1 ) / ( 1 + b 1 ) 2 2 η = [ sin ( φ Q ) + b 2 + A 0 b 1 + A 0 ] / [ sin ( φ Q ) + b 2 + A 0 b 1 + A 0 ] 2 2 ξ [ 4 sin ( φ Q ) + b 2 + A 0 3 b 1 + 4 A 0 3 ] / [ 4 sin ( φ Q ) + b 2 + A 0 3 b 1 + 4 A 0 3 ] 64 64 b 1 = 2 cos ( φ Q / φ Q 2 2 ) cos ( φ P ) ,   b 2 = 2 sin ( φ Q / φ Q 2 2 ) cos ( φ P ) .
R ^ E ( n ) = R ^ ( n ) i h L ( i ) R e f ( n i ) ,
R ^ E ( n ) = R ^ ( n ) [ i h L ( i ) R e f ( n i ) + m 1 m 2 h 2 ( m 1 , m 2 ) R e f ( n m 1 ) R e f ( n m 2 ) + k 1 k 2 k 3 h 3 ( k 1 , k 2 , k 3 ) R e f ( n k 1 ) R e f ( n k 2 ) R e f ( n k 3 ) + ] R ^ ( n ) i h L ( i ) R e f ( n i ) k 1 k 2 k 3 h 3 ( k 1 , k 2 , k 3 ) R e f ( n k 1 ) R e f ( n k 2 ) R e f ( n k 3 ) ,
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