Reconfigurable microwave photonic mixer for hybrid macro-micro cellular systems

Yongsheng Gao; Fangjing Shi; Jing Zhang; Biao Cao; Boyuan Ma; Weile Zhai; Yangyu Fan

doi:10.1364/OE.481373

1. Introduction

In the hotspot and high-capacity intensive scenario of the fifth generation (5 G) wireless communication system, the wireless environment is complex and the interference is changeable. The spectral efficiency of the system can be improved to some extent by the ultra-dense networking of base stations [1]. Taking the centralized radio access network (C-RAN) based on enhanced mobile broadband (eMBB) scenarios as an example, dual or multiple connections is an effective network deployment to meet the coverage and capacity requirements of eMBB services [2]. One connection is for coverage and another connection is for capacity enhancement, which can achieve the ideal combination of coverage and data. However, due to the high operating frequency and large bandwidth of 5 G networks, the deployment and operation costs increase hugely when high-power macro base stations are used. Therefore, a hybrid macro-micro cellular network is a potential solution. Macro cells are responsible for wide coverage and support high-priority services, while microcells provide hotspot coverage, eliminating the “blind spots” in macro cells and targeting low-priority, high-speed services [3].

In the hybrid macro-micro cellular system, there are two architectures for macro and micro cellular cells, separated centralized unit (CU) and shared CU. For macro base stations, the distributed unit (DU) and remote radio unit (RRU) are usually separated. While for micro base stations, the DU and RRU can be separated or integrated. The architecture of a 5 G C-RAN with a shared CU is shown in Fig. 1(a).

Fig. 1. (a) The architecture of a 5 G C-RAN with a shared CU; (b) A possible hybrid macro-microcell architecture based on microwave photonic technology.

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With the gradual opening and use of the 5 G mm-Wave band, the common public radio interface (CPRI) is under high pressure for bandwidth and transmission capacity, and the mobile front end of the entire 5 G network will suffer from bandwidth limitations due to electronic bottlenecks. Thanks to the advantages of high operating frequency, large transmission bandwidth, and low fiber loss, microwave photonic technology has received a lot of attention in 5 G C-RAN deployment [4–7]. A possible hybrid macro-microcell architecture based on microwave photonic technology is shown in Fig. 1(b). The use of optical fiber for broadband, efficient analog RF signal transmission, and simple signal processing in the optical domain can greatly alleviate the bandwidth pressure of the system. The performance of the 5 G system can be maximized by reasonably allocating macro base stations and micro base stations. For example, the macro base station is used to achieve wide coverage, while the micro base station is used to cover the blind area, and the corresponding signal processing is carried out according to the demand characteristics of different regions. In addition, enabling macro-cell-assisted management of micro-cells can enhance the coordination and shunt processing of multiple services.

In the above applications, microwave photonic mixers with large bandwidth, reconfiguration, and high compatibility are important components of the RF front-end. For example, in the downlink of a macro base station, mixers with dispersion immunity are required to achieve long-range coverage. In the uplink of a micro base station, a mixer with low spurious is required to eliminate interference introduced by the complex electromagnetic environment in blind areas. In particular, the proposed microwave photonic mixer can also solve the self- interference problem of terminals in the background of 5 G dual-connection applications, that is, the intermodulation interference generated by uplink to downlink reception due to the nonlinear distortion [8].

In recent decades, microwave photonic mixers have been extensively studied [9–14]. Except for the single function of frequency conversion, some multifunction mixers have been widely proposed, such as in-phase and quadrature-phase (I/Q) mixers, image rejection mixers, double-balanced mixers, and dispersion immune mixers. The I/Q mixers can be realized by constructing 90° phase difference between two frequency conversion channels through optical filtering and polarization control [15–18], dc bias control [19–21], optical coupling [22–24], and 90° electric phase shifting [25,26], respectively. Besides, applying a 90° electric hybrid to the output of the I/Q mixers can further obtain the image rejection mixers [15,16,18–20,24]. A notch filter based on nonlinear effects can also filter out the image signals [27,28]. Furthermore, by changing the introduced phase difference from 90° to 180°, a double-balanced mixer can be obtained [29,30], which can find applications in switching, attenuation, and binary phase modulation. Finally, in order to solve the problem of dispersion-induced power fading after fiber transmission, a dispersion immune mixer can be realized by adjusting the dc bias angle of the modulator [31,32], tuning the output phase shift of the spectra [33], and implementing the single-sideband modulation [34].

Reconfigurable multifunctional mixers also have been focused on in recent years. Through dc bias control [29,35], polarization control [36], and optical coupling [22,30] to introduce different phase differences, the multifunctional mixers with single-ended mixing, double-balanced mixing, I/Q mixing, image rejection mixing, and dispersion immune mixing can be obtained simultaneously. However, in the above solutions, nonlinear distortion still exists and is rarely considered for suppression, which thus lead to a low spur-free dynamic range (SFDR).

In this paper, a large SFDR and reconfigurable microwave photonic mixer is proposed for RF front-end applications in hybrid macro-micro cellular systems. This scheme has the following three characteristics:

(1) By tuning the main dc bias angle of the modulator and different DSP processing, the dispersion immune single-ended mixer, I/Q mixer, image rejection mixer, and double-balanced mixer can be realized, respectively.
(2) By constructing two similar optical paths and using convex optimization to select an appropriate electrical attenuation, the third-order intermodulation distortion (IMD3) can be canceled, and the link gain can be optimized thus improving the SFDR of the system.
(3) An I/Q imbalance compensation algorithm is adopted to further compensate the I/Q amplitude imbalance and phase imbalance, thereby improving the image rejection ratio (IRR).

2. Principles

Taking the uplink as an example, the feasibility of the proposed reconfigurable microwave photonic mixer is theoretically verified, and Fig. 2 shows the schematic diagram. The proposed reconfigurable microwave photonic mixing system includes a laser diode (LD), a dual-polarization in-phase and quadrature-phase (DP-IQ) modulator, two 50/50 electric power dividers (EPDs), two electric attenuators (EAs), a dual-channel WDM, two photodetectors (PDs), an analog to digital converter (ADC), and the digital signal processing (DSP) unit. An Erbium-doped fiber amplifier (EDFA) amplifies the modulated signal and provides it to the subsequent photoelectric detection module. When different operations are performed on the DSP, the following functions can be realized:

(1) Basic single-ended mixing can be achieved using only data from a single PD. Dispersive immune mixing can also be achieved by appropriately adjusting the main bias point of the DP-IQ modulator.
(2) An I/Q mixer is implemented when the two main modulators of DP-IQ are adjusted to obtain two quadrature intermediate frequency (IF) signals. The data of the two PDs are coupled at 90° in the digital domain to achieve image rejection. In addition, an I/Q imbalance compensation algorithm is added to further improve the image rejection ratio.
(3) When the two main modulators of DP-IQ are adjusted to obtain two IF signals with a phase difference of 180°, the differential mixing of the received signal can be realized.

Fig. 2. Schematic diagram of the proposed reconfigurable microwave photonic mixer in the uplink.

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The LD generates a continuous laser signal expressed as E_c(t)=E_cexp(jω_ct), where E_c and ω_c represent its amplitude and angular frequency, respectively. The laser signal is modulated by the received RF signal V_RF(t) and the locally generated LO signal V_LO(t) in the integrated DP-IQ. The RF signal is divided into two paths by EPD1, where the upper path directly drives the sub-modulator Xa, and the lower path drives the sub-modulator Ya after being attenuated by EA1. Similarly, the LO signal V_LO(t)=V_LOcos(ω_LOt) is also divided into two paths by EPD2. The upper path drives the sub-modulator Xb after being attenuated by EA2 and the lower path directly drives the sub-modulator Yb. V_LO and ω_LO represent the amplitude and angular frequency of the LO signal, respectively.

2.1 Linearized dispersion immune single-ended mixer

Assuming that the RF signal is V_RF(t)=V_RFcos(ω_RFt), where V_RF and ω_RF are the amplitude and angular frequency, respectively. The output expression of the DP-IQ modulator is:

(1)$${E_{DP - IQ}}(t )= j\frac{{\sqrt \mu }}{{2\sqrt 2 }}{E_c}(t )\left\{ \begin{array}{l} [{{J_1}({{m_{Xa}}} )({{e^{j{\omega_{RF}}t}} - {e^{ - j{\omega_{RF}}t}}} )+ {J_1}({{m_{Xb}}} )({{e^{j{\omega_{LO}}t}} - {e^{ - j{\omega_{LO}}t}}} ){e^{j{\varphi_{Xm}}}}} ]{{\vec{e}}_{TE}}\\ + [{{J_1}({{m_{Ya}}} )({{e^{j{\omega_{RF}}t}} - {e^{ - j{\omega_{RF}}t}}} )+ {J_1}({{m_{Yb}}} )({{e^{j{\omega_{LO}}t}} - {e^{ - j{\omega_{LO}}t}}} ){e^{j{\varphi_{Ym}}}}} ]{{\vec{e}}_{TM}} \end{array} \right\}$$

where µ is the insertion loss of the modulator; ${m_{Xa}} = {{\pi {V_{RF}}} / {\sqrt 2 {V_\pi }}}$, ${m_{Xb}} = {{\sqrt {{\alpha _2}} \pi {V_{LO}}} / {\sqrt 2 {V_\pi }}}$, ${m_{Ya}} = {{\sqrt {{\alpha _1}} \pi {V_{RF}}} / {\sqrt 2 {V_\pi }}}$ and ${m_{Yb}} = {{\pi {V_{LO}}} / {\sqrt 2 {V_\pi }}}$ are the input modulation indices of the sub-modulators Xa, Xb, Ya and Yb, respectively. In order to discard the optical carrier that does not carry signal information, the four sub-modulators all work at the minimum bias point. α₁ and α₂ are the power attenuation coefficients of EA1 and EA2. φ_Xm and φ_Ym are the main bias angles of the X-Pol IQ modulator and Y-Pol IQ modulator. J_n(·) represents the first kind of n-order Bessel function, and high-order sidebands are ignored under small-signal modulation. ${\vec{e}_{TE}}$ and ${\vec{e}_{TM}}$ represent the unit vectors of the TE mode and TM mode of the optical field, respectively.

The use of modulator and attenuators will result in a loss of signal energy, so an optical amplifier is used to compensate for the power before the signal enters PD. After the EDFA, the expression of the optical signal finally entering the PD is as follows:

(2)$${E_{PD}}(t) = \sqrt {{G_{EDFA}}} {E_{DP - IQ}}(t )$$

where G_EDFA is the optical gain of EDFA.

After photoelectric detection, the final photocurrent output from PD is:

(3)$$\begin{aligned} {i_{PD}}(t) &= \eta {G_{EDFA}}{|{{E_{DP - IQ}}(t )} |^2}\\& \approx \frac{{\mu \eta E_c^2{G_{EDFA}}}}{2}\left[ \begin{array}{l} {J_1}({{m_{Xa}}} ){J_1}({{m_{Xb}}} )\cos {\varphi_{Xm}}\\ + {J_1}({{m_{Ya}}} ){J_1}({{m_{Yb}}} )\cos {\varphi_{Ym}} \end{array} \right]\{{\cos [{({{\omega_{RF}} - {\omega_{LO}}} )t} ]- \cos [{({{\omega_{RF}} + {\omega_{LO}}} )t} ]} \}\end{aligned}$$

where η is the responsivity of PD.

It is known that the IMD3 term and the third-order harmonic term have similar coefficients [37,38]. Therefore, assuming φ_Xm=φ_Ym± (2k + 1)π and applying the approximate Bessel function J₁(m)≈m/2-m³/16, the output photocurrent under the two-tone RF signal V_RF[cos(ω_RF1t)+cos(ω_RF2t)] after neglecting the constant term can be expressed as:

(4)$${i_{PD}}(t )\approx {C_1}({{\alpha_1},{\alpha_2}} )[{\cos ({{\omega_{RF1}}t} )+ \cos ({{\omega_{RF2}}t} )} ]+ {C_2}({{\alpha_1},{\alpha_2}} )\left\{ \begin{array}{l} \cos [{({2{\omega_{RF1}} - {\omega_{RF2}}} )t} ]\\ + \cos [{({2{\omega_{RF2}} - {\omega_{RF1}}} )t} ]\end{array} \right\}$$

where C₁(α₁, α₂) and C₂(α₁, α₂) are defined as the objective and constraint functions respectively. And ${C_1}({{\alpha_1},{\alpha_2}} )= \sqrt {{\alpha _\textrm{2}}} - \sqrt {{\alpha _1}} ,{C_2}({{\alpha_1},{\alpha_2}} )= \sqrt {{\alpha _\textrm{2}}} - {\left( {\sqrt {{\alpha_1}} } \right)^3}$.

When C₂(α₁, α₂) = 0 is satisfied, the IMD3 term can be eliminated. Due to the use of the attenuator, the fundamental frequency power is bound to be impaired. In order to maximize the fundamental frequency term while eliminating the IMD3 term, the Lagrange multiplier method can be used to convert the above problem into an optimization problem solving for the equation constraint.

(5)$$\begin{array}{c} \max \{{{C_1}({{\alpha_1},{\alpha_2}} )} \}\\ s.t.{C_2}({{\alpha_1},{\alpha_2}} )= 0 \end{array}$$

For the equation constraint, the above functions can be combined into a new unconstrained function through a Lagrange factor λ.

(6)$$L({{\alpha_1},{\alpha_2},\lambda } )= {C_1}({{\alpha_1},{\alpha_2}} )- \lambda {C_2}({{\alpha_1},{\alpha_2}} )$$

The optimal solutions α₁= 1/3, α₂= 1/27, and λ=1 can be obtained by solving for the extreme values of the above functions. The result shows that when the two electrical attenuation values are 4.77 dB and 14.31 dB respectively, the IMD3 term can be eliminated and the fundamental frequency term power can be maximized. In fact, these two electrical attenuation values are almost non-existent and can be replaced by 5 dB and 15 dB with very little fundamental frequency power impairment. A detailed description of the choice of electrical attenuation is given in the discussion section.

In the case of long-distance fiber transmission, the periodic power fading introduced by fiber dispersion deserves consideration. As we know, the transmission function of fiber can be expressed as:

(7)$$H(\omega )= \exp \{{{{ - \alpha L} / {2 + j[{{{{\beta_0} + {\beta_1}L({\omega - {\omega_c}} )+ {\beta_2}L{{({\omega - {\omega_c}} )}^2}} / 2} + \cdots } ]}}} \}$$

where α is the attenuation factor, β₀ is the propagation constant of the medium at the central frequency ω_c, β₁ is the reciprocal of the group velocity, and β₂ is the group velocity dispersion. In fact, the periodic power fading is only related to β₂, while β₀ and β₁ will only introduce a fixed phase shift [39,40]. Therefore, to simplify the subsequent derivation process, the β₀ and β₁ terms are ignored and only the β₂ term is considered. The output expression of the fiber can be written as:

(8)$${E_{SMF}}(t )= \frac{{\sqrt \mu }}{{2\sqrt 2 }}\sqrt {{G_{EDFA}}} {E_c}(t ){e^{{{ - \alpha L} / 2}}}\left[ {\begin{array}{{c}} {j\left\{ \begin{array}{l} {J_1}({{m_{Xa}}} )[{{e^{j({{\omega_{RF}}t + {\theta_{RF}}} )}} - {e^{ - j({{\omega_{RF}}t - {\theta_{RF}}} )}}} ]\\ + {J_1}({{m_{Xb}}} )[{{e^{j({{\omega_{LO}}t + {\theta_{LO}}} )}} - {e^{ - j({{\omega_{LO}}t - {\theta_{LO}}} )}}} ]{e^{j{\varphi_{Xm}}}} \end{array} \right\}{{\vec{e}}_{TE}}}\\ {j\left\{ \begin{array}{l} {J_1}({{m_{Ya}}} )[{{e^{j({{\omega_{RF}}t + {\theta_{RF}}} )}} - {e^{ - j({{\omega_{RF}}t - {\theta_{RF}}} )}}} ]\\ + {J_1}({{m_{Yb}}} )[{{e^{j({{\omega_{LO}}t + {\theta_{LO}}} )}} - {e^{ - j({{\omega_{LO}}t - {\theta_{LO}}} )}}} ]{e^{j{\varphi_{Ym}}}} \end{array} \right\}{{\vec{e}}_{TM}}} \end{array}} \right]$$

where θ_RF=β₂Lω²_RF/2 and θ_LO=β₂Lω²_LO/2.

When the conditions φ_Xm=φ_Ym± (2k + 1)π and α₁= 1/3 are satisfied, the linearity optimization is realized. The photocurrent output from the PD is expressed as:

(9)$$\begin{aligned} {i_{PD}}(t) &\approx \frac{{\eta \mu {G_{EDFA}}{e^{ - \alpha L}}}}{2}{\left( {\frac{{\pi {E_c}}}{{\textrm{4}{V_\pi }}}} \right)^2}\left\{ {\left[ {{{\left( {\sqrt {{\alpha_1}} } \right)}^3} - \sqrt {{\alpha_1}} } \right]{V_{RF}}{V_{LO}}} \right\}\cos ({{\theta_{RF}} - {\theta_{LO}} - {\varphi_{Ym}}} )\\& \times \{{\cos [{({{\omega_{RF}} - {\omega_{LO}}} )t} ]- \cos [{({{\omega_{RF}} + {\omega_{LO}}} )t} ]} \}\end{aligned}$$

It can be found that when the condition θ_RF-θ_LO-φ_Ym=±kπ is satisfied, the power fading compensation can be achieved by adjusting the main bias angle φ_Ym, and finally a dispersion immune mixer can be obtained.

2.2 Linearized I/Q mixer and image rejection mixer

Assuming that the image signal is V_IM(t)=V_IMcos(ω_IMt), then the signal received by the receiving antenna can be written as V_RF(t)+V_IM(t)=V_RFcos(ω_RFt)+V_IMcos(ω_IMt). The output signal of the DP-IQ modulator can be expressed as:

(10)$${E_{DP - IQ}}(t )= \frac{{\sqrt \mu }}{{2\sqrt 2 }}{E_c}(t )\left[ {\begin{array}{{c}} {j\left\{ \begin{array}{l} {J_1}({{m_{Xa}}} )[{{e^{j{\omega_{RF}}t}} - {e^{ - j{\omega_{RF}}t}}} ]+ {J_1}({{m_{Xa}}} )[{{e^{j{\omega_{IM}}t}} - {e^{ - j{\omega_{IM}}t}}} ]\\ + {J_1}({{m_{Xb}}} )[{{e^{j{\omega_{LO}}t}} - {e^{ - j{\omega_{LO}}t}}} ]{e^{j{\varphi_{Xm}}}} \end{array} \right\}{{\vec{e}}_{TE}}}\\ {j\left\{ \begin{array}{l} {J_1}({{m_{Ya}}} )[{{e^{j{\omega_{RF}}t}} - {e^{ - j{\omega_{RF}}t}}} ]+ {J_1}({{m_{Ya}}} )[{{e^{j{\omega_{IM}}t}} - {e^{ - j{\omega_{IM}}t}}} ]\\ + {J_1}({{m_{Yb}}} )[{{e^{j{\omega_{LO}}t}} - {e^{ - j{\omega_{LO}}t}}} ]{e^{j{\varphi_{Ym}}}} \end{array} \right\}{{\vec{e}}_{TM}}} \end{array}} \right]$$

The two main bias angles are set to satisfy the condition φ_Xm=φ_Ym-π. After power compensation, the +1st and -1st order sidebands are separated by a dual-channel WDM. The signals output from two channels are respectively subjected to photoelectric detection, and two photocurrents can be obtained:

(11)$${i_{PD1}}(t )\approx \frac{{\eta \mu E_c^2{G_{EDFA}}}}{4}\left\{ {[{{J_1}({{m_{Ya}}} ){J_1}({{m_{Yb}}} )- {J_1}({{m_{Xa}}} ){J_1}({{m_{Xb}}} )} ]\times \left[ \begin{array}{l} \cos ({{\omega_{RF}}t - {\omega_{LO}}t - {\varphi_{Ym}}} )\\ + \cos ({{\omega_{LO}}t - {\omega_{IM}}t + {\varphi_{Ym}}} )\end{array} \right]} \right\}$$

(12)$${i_{PD2}}(t )\approx \frac{{\eta \mu E_c^2{G_{EDFA}}}}{4}\left\{ {[{{J_1}({{m_{Ya}}} ){J_1}({{m_{Yb}}} )- {J_1}({{m_{Xa}}} ){J_1}({{m_{Xb}}} )} ]\times \left[ \begin{array}{l} \cos ({{\omega_{RF}}t - {\omega_{LO}}t + {\varphi_{Ym}}} )\\ + \cos ({{\omega_{LO}}t - {\omega_{IM}}t - {\varphi_{Ym}}} )\end{array} \right]} \right\}$$

According to Eqs. (11) and (12), when φ_Xm= -135° and φ_Ym= 45° are satisfied, the IF signals with quadrature phases are generated from the two PDs. Therefore, the I/Q frequency conversion can be realized.

When the signals output from the I/Q channels are coupled at 90° in the digital domain, and the nonlinear distortion suppression is considered, the final IF signal output by the mixer is expressed as:

(13)$${i_{IF}}(t )= \eta \mu {G_{EDFA}}{\left( {\frac{{\pi {E_c}}}{{\textrm{4}{V_\pi }}}} \right)^2}\left\{ {\left[ {{{\left( {\sqrt {{\alpha_1}} } \right)}^3} - \sqrt {{\alpha_1}} } \right]{V_{RF}}{V_{LO}}} \right\} \times \cos ({{\omega_{RF}}t - {\omega_{LO}}t - {\pi / 4}} )$$

where α₁= 1/3. It can be found that the image signal is completely canceled, leaving only the desired IF signal. In addition, by adding an I/Q compensation algorithm in the digital domain, the amplitude imbalance and phase imbalance between the I and Q branches can be compensated, thus improving the IRR. The specific compensation method is given in the discussion section.

2.3 Linearized double-balanced mixer

In the case of single-frequency RF signal input, the output of the DP-IQ modulator is shown in Eq. (1). We set φ_Xm= -90°, φ_Ym= 90° and apply the nonlinear distortion suppression condition. After EDFA and dual-channel WDM, the photoelectric detection can be performed to obtain two output photocurrents as follows:

(14)$${i_{PD1}}(t )\approx \eta \mu {\left( {\frac{{\pi {E_c}}}{{4\sqrt 2 {V_\pi }}}} \right)^2}{G_{EDFA}}\left[ {\left( {{{\left( {\sqrt {{\alpha_1}} } \right)}^3} - \sqrt {{\alpha_1}} } \right){V_{RF}}{V_{LO}}} \right] \times \cos [{({{\omega_{RF}} - {\omega_{LO}}} )t - {\pi / 2}} ]$$

(15)$${i_{PD2}}(t )\approx \eta \mu {\left( {\frac{{\pi {E_c}}}{{4\sqrt 2 {V_\pi }}}} \right)^2}{G_{EDFA}}\left[ {\left( {{{\left( {\sqrt {{\alpha_1}} } \right)}^3} - \sqrt {{\alpha_1}} } \right){V_{RF}}{V_{LO}}} \right] \times \cos [{({{\omega_{RF}} - {\omega_{LO}}} )t + {\pi / 2}} ]$$

As can be seen, the photocurrent output from the two PDs is equal in amplitude and opposite in phase. It means that differential mixing of the received signals is realized, and therefore a double-balanced mixer is achieved. Similarly, when α₁= 1/3, the frequency conversion efficiency of the double-balanced mixer reaches the optimal value.

3. Experiment and results

The experimental setup is shown in Fig. 3 (a), and an integrated modulator and receiver assembly (IMRA) evaluation kit from Elenion that includes both a tunable laser (ITLA) and an IMRA is used. The picture of the IMRA evaluation kit is shown in Fig. 3 (b). The IMRA integrates a silicon-based modulator DP-IQ, a coherent receiver, and an RF amplifier driver. Compared with separated devices, the IMRA can reduce the size of the system, improve stability, and make more practical sense. It should be noted that both the DP-IQ modulator and the coherent receiver can be used independently. In the proposed scheme, only the DP-IQ modulator with a bandwidth of 22 GHz is used. The continuous lightwave with a power of 16 dBm from the ITLA is used as the optical carrier, and then the optical carrier is sent directly to the DP-IQ. The modulator is equipped with an insertion loss of 15 dB, and its bias voltages can be manually or automatically adjusted the supporting bias controller and software. The RF and LO signals are generated by two analog signal generators (ASG) (HP, E8257D and 83752A). The EDFA (Keopsys CPB30) with a noise figure (NF) of less than 5 dB is operated in automatic power control (APC) mode to compensate for the optical power. The WDM with a channel interval of 50 GHz is used to separate the +1st and -1st order optical sidebands, and the output signals are sent to two broadband PDs (Finisar, XPRV2150R) with a responsivity of 0.6 A/W for photoelectric detection. The vector signal analyzer (VSA, R&D FSQ40) is used to analyze the obtained frequency conversion signals. Finally, the electrical signals output from the PDs are respectively sent to analog-to-digital conversion and digital signal processing.

Fig. 3. (a) Experimental setup; (b) IMRA evaluation kit. ASG, analog signal generator; SMF, single mode fiber; WDM, Wavelength Division Multiplexing; PD, Photodetector; OSA, optical spectrum analyzer; VSA, vector signal analyzer; EDFA, Erbium doped fiber amplifier; IMRA, integrated modulator and receiver assembly; ADC, analog to digital converter; DSP, digital signal processing.

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First, the half-wave voltages of the sub-modulators Xa, Xb, Ya, and Yb are tested, respectively, as shown in Fig. 4. In the experiment, the dc bias voltage of Xa is changed between 0–2.5 V with a step interval of 0.1 V, the bias voltages of Xb, Ya, and Yb are reset to zero, and the total output power of DP-IQ is measured. The testing procedure for Xb, Ya, and Yb is similar to Xa. It can be found that the half-wave voltage of the sub-modulator is about 0.8 V.

Fig. 4. dc bias curve of the sub-modulators in DP-IQ modulator.

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The resolution bandwidth of the optical spectrum analyzer (Finisar, Waveshaper 100S) is 1.75 GHz. In order to clearly observe the modulated optical spectra, an RF signal with a frequency of 15 GHz and a power of 0 dBm is generated from an ASG, and an LO signal with a frequency of 10 GHz and a power of 5 dBm is generated from another one. The RF and LO signals drive the sub-modulators Xa, Ya, Xb, and Yb simultaneously after passing through the electronic power divider and electronic attenuator (5 and 15 dB). The four sub-modulators are all biased at the minimum point, and the two main modulators are biased at the minimum and maximum points, respectively. A PBS is used to split the output signal of DP-IQ modulator into two orthogonal polarization states, and the output spectra are shown in Fig. 5. It can be found that both RF and LO signals have realized the carrier-suppressed double-sideband modulation. Also, the Y-polarization state has a smaller optical carrier.

Fig. 5. Optical spectra after DP-IQ modulator.

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It is well known that the conversion gain is related to the LO power, so an appropriate LO power needs to be selected to get the best conversion gain [41]. For convenience, the conversion gain and NF at different LO powers are measured in the control group of a single DPMZM, as shown in Fig. 6. When the LO power is 0 dBm, the maximum conversion gain and relative low NF level can be obtained.

Fig. 6. Measured conversion gain and NF as a function of LO power.

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3.1 Linearized dispersion immune single-ended mixer

Two-tone signals with frequencies of 10.5/10.51 GHz are used as the input RF signal of the system, and a single-frequency signal with a frequency of 10 GHz and power of 0 dBm is used as the LO signal. For comparison, a typical microwave photonic mixing link based on a single DPMZM with a minimum bias point is set as the control group (without linearization). When the input RF power is 10 dBm, the fundamental component power of the IF signal is -17.1 dBm, and the IMD3 power is -44.6 dB, as shown in Fig. 7 (a). Due to the RF driving amplifier, in order to observe the IMD3 suppression level under the same fundamental frequency power, the input two-tone RF signal power in the experimental group is changed to 0 dBm, and the IMD3 power is about -64.8 dBm. As shown in Fig. 7 (b), compared with the control group, the proposed scheme has an IMD3 improvement of 19.8 dB.

Fig. 7. The two-tone spectrum output from PD: (a) control group, RF input power is 10 dBm; (b) proposed scheme, RF input power is 0 dBm.

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Next, the SFDR of the proposed scheme and the control group is measured. Tuning the power of the input two-tone signals in turn, the fundamental component, IMD3, and noise floor output from the PD are measured, and the curves are shown in Fig. 8. The SFDRs of the control group and the proposed scheme are 90.6 dB·Hz^2/3 and 111.4 dB·Hz^4/5, respectively. Due to the instrument limitations, the measured noise floor is relatively high. When the theoretical prediction of the noise floor is -155.5 dBm/Hz, the predicted SFDR is 118.3 dB·Hz^4/5. Compared with the control group as shown in Fig. 8 (a), 27.7-dB improvement of the SFDR is achieved in the proposed scheme.

Fig. 8. The fundamental component, IMD3 and noise floor in the output IF signal as functions of the input RF power: in the control group; (b) in the proposed scheme.

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The linearization effect of the proposed scheme in the communication system is further explored by receiving a wideband RF vector signal with 16 quadrature amplitude modulation (QAM). The bandwidth of the vector signal is 50 MHz, and its center frequency is converted from 10.5 GHz to 0.5 GHz using the proposed mixer. The output spectrum, demodulated constellation diagram and calculated error vector magnitude (EVM) in the control group and the proposed scheme are shown in Fig. 9. In the control group, the RF input signal with a power of 10 dBm has caused significant distortion in the frequency down-converted IF signal, and the EVM is 6.3%. For a fair comparison, the RF input power is set to 0 dBm in the proposed scheme to achieve the same IF power in the control group. After adopting the linearization method proposed in this paper, the distortion in the IF signal is significantly suppressed, and the EVM is only 3.4%. To ensure a real-time analysis speed for the EVM, the constellation points per-calculation in the spectrum analyzer is only set to 4000, so the constellation is not an ideal circle.

Fig. 9. The wideband spectrum output by the PD in (a) the control group and (b) the proposed scheme.

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The EVM refers to the ratio of the root mean square (RMS) value of the average power of the error vector signal to the ideal signal, and is one of the important indicators to measure the quality of wireless communication systems. The EVM of the frequency down-converted IF signal with different RF input powers is measured to evaluate the signal quality, as shown in Fig. 10. In the control group, when the RF input power is about 10 dBm, the EVM is 6.3%. While in the proposed scheme, when the input RF power is about 0 dBm, the EVM is only 3.4%.

Fig. 10. In the control group and the proposed scheme, the system EVM varies with the input RF power.

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Finally, a fiber link with a length of 29.706 km is established to verify the effectiveness of the single-ended mixing system in compensating for the periodic power fading. First, the frequency of the RF signal is set to step at 1 GHz within the range of 6–11 GHz, while the LO frequency is fixed at 5 GHz. The frequency down-conversion is carried out, and IF signals with the frequency from 1 to 6 GHz are obtained. Then, the RF frequency is changed step by 1 GHz within the range of 2–15 GHz, and the LO frequency remains unchanged at 5 GHz. The frequency up-conversion is carried out to obtain the IF signals from 7 to 20 GHz. The conversion gain as a function of the converted IF frequency is shown in Fig. 11. In the control group based on double-sideband modulation, the fiber dispersion leads to additional phase mismatching of the two IF components after fiber transmission. Therefore, a fading point at about 15 GHz is observed, which is consistent with theoretical calculations. In the proposed single-ended mixing scheme, by controlling the bias angle of the main modulator, the phase mismatch of the IF components introduced by the fiber dispersion is compensated, so the periodic power fading is avoided.

Fig. 11. In the control group and the proposed scheme, the system conversion gain varies with the converted IF frequency with 29.706-km fiber.

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3.2 Linearized I/Q mixer and image rejection mixer

In this section, a linearized I/Q mixer or image rejection mixer is experimentally demonstrated. Similar to Fig. 5, to facilitate observation of the spectra, the frequency of RF signal is set to 15 GHz. The I-path and Q-path data from the two PDs are coupled by 90° in the digital domain to achieve image rejection. The dual-channel WDM is used as two optical bandpass filters. After the WDM, the +1st and -1st order sidebands of the modulated optical signals (both RF and LO signals) are filtered out, respectively. The optical carrier and other undesired sidebands in each channel are also suppressed. For example, in the output spectra of channel I shown in Fig. 12 (a), the +1st order optical sideband is suppressed by 36 dB compared with the -1st order optical sideband.

Fig. 12. WDM wavelength responses and filtered spectra: (a) CH1; (b) CH2.

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Changing the frequency of the RF signal to 10.5 GHz, and power of the RF and LO signals unchanged, the recovered I/Q IF spectrum are measured. The power of the IF signal output by channel I and channel Q is -18.5 dBm and -18.7 dBm, respectively, as shown in Fig. 13 (a) and Fig. 13 (b). Then the time-domain waveforms of the two IF signals are observed by an oscilloscope (AWG7061B). When the two main bias angles of the DP-IQ modulator are adjusted to -135° and 45°, respectively, two orthogonal time-domain waveforms with equal amplitudes can be obtained, as shown in Fig. 13(c). Then the RF frequency is changed to 10.2 GHz to obtain 0.2-GHz I/Q IF signals, and the time-domain waveforms are shown in Fig. 13 (d). Similarly, two waveforms with equal amplitudes and quadrature phases are observed.

Fig. 13. In the proposed linearized I/Q mixer: (a–b) single-frequency I/Q IF spectrum; (c–d) time-domain waveforms.

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Next, the RF frequency is tuned from 1.5 to 20.5 GHz in steps of 1 GHz, while the LO frequency synchronously changes with the RF frequency to keep the IF frequency at 0.5 GHz. The amplitude imbalance and phase imbalance of the I/Q IF signals are measured and shown in Fig. 14. The 3-dB frequency response of the RF signal is 5–20 GHz. In this frequency range, the phase imbalance and amplitude imbalance are lower than ±0.7° and 0.7 dB, respectively. The phase jitter between the I/Q IF signals may have three reasons. First is the bias drift of the modulator in the IMRA, although modulator bias control is implemented in the experiment. Second, the length of two optical paths may be not exactly matched, and the fibers and RF cables are susceptible to environmental influence. Third, the IF noise will also lead to phase jitter after measurement.

Fig. 14. In the proposed linearized I/Q mixer, the amplitude and phase difference between the I/Q IF signals as functions of RF frequency.

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Keep the frequency and power of the LO signal unchanged. The RF signal and the image signal are set as single-tone signals with frequencies of 10.5 GHz and 9.49 GHz, respectively, and the power is 0 dBm. The signal spectrum output by a single PD is shown in Fig. 15 (a), where the desired IF signal frequency is 0.5 GHz, and the IF signal frequency after the down-conversion of the image signal is 0.51 GHz. After I/Q imbalance compensation and image rejection in the digital domain, the spectrum diagram is shown in Fig. 15 (b), and the IRR is about 60.1 dB.

Fig. 15. The output spectrum. (a) Before image rejection; (b) After image rejection.

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In the following experiment, the SFDR of the proposed linearized image rejection mixer is measured. The frequencies of the two-tone RF signals are set to 10.5/10.51 GHz, and the image frequency is set to 9.4 GHz to facilitate the simultaneous observation of the desired IF signal and the down-converted image signal in the spectrum analyzer. The RF and image signals are both down-converted by a 10-GHz LO signal. The power of two-tone RF and image signals is changed from -7 to 3 dBm, and the power of the output IF fundamental component, IMD3, image products and noise floor are measured, as shown in Fig. 16. It can be seen that the SFDR is 117.5 dB·Hz^4/5, and the average IRR is about 60.6 dB.

Fig. 16. The fundamental component, IMD3, and noise floor power in the output IF signal and the power of the image signal vary with the input RF power.

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Finally, a bandwidth-limited vector signal is used for testing and verification. An I/Q 16QAM baseband signal is used to modulate the RF signal at the carrier frequency of 10.5 GHz, with the bandwidth of 50 MHz. The LO signal has a frequency of 10 GHz and a power of 0 dBm. The image signal is frequency modulated with the same frequency and the same power as the RF signal, and the bandwidth is 10 MHz. The power of both RF and image signals is 0 dBm. First, the same control group as describe in subsection 3.1 is used for testing. The output spectrum without linearization and image rejection is shown in Fig. 17 (a), and the EVM is 29.6%. After adopting the mixing scheme with improved linearity, a single PD output spectrum is shown in Fig. 17 (b). We can see that the IMD3 in the spectrum is significantly suppressed. However, since the image signal still exists, the EVM is 28.9%. Then, the image rejection is adopted and the IF spectrum is shown in Fig. 17 (c). Thanks to the cancellation of the IM interference, the demodulated constellation diagram is clearly distinguished, and the final EVM is 6.4%.

Fig. 17. The IF spectrum output from PD: (a) without linearization and image rejection; (b) with linearization; (c) with linearization and image rejection.

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3.3 Linearized double-balanced mixer

The last section carries out the experimental test for the proposed double-balanced mixer. The two main bias angles of DP-IQ modulator are adjusted to -90° and +90°, respectively. With other parameter settings unchanged, the spectrum and the time-domain waveforms of the 0.5-GHz IF signal down-converted from a 10.5-GHz RF signal is shown in Fig. 18 (a–c). It can be found that there is a 180° phase difference between the two IF signals, indicating that two differentially output IF signals are obtained. The RF frequency is switched to 10.2 GHz, and the two time-domain IF waveforms with the frequency of 0.2 GHz are obtained, as shown in Fig. 18 (d). Similarly, the two IF waveforms feature the same amplitude but opposite phases.

Fig. 18. In the proposed linearized double-balanced mixer: (a–b) single-frequency IF spectrum; (c–d) time-domain waveforms.

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Finally, after frequency down-conversion from 10.5 GHz to 0.5 GHz, the IF fundamental component, IMD3, and noise floor output from the two PDs are measured and shown in Fig. 19. The two differential down-conversion system features a similar performance. The two SFDRs are 117.6 dB·Hz^4/5 and 116.5 dB·Hz^4/5, respectively.

Fig. 19. Measured SFDR of the proposed linearized double-balanced mixer: (a) channel 1; (b) channel 2.

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4. Discussion

4.1 Selection of electrical attenuation α₁ and α₂

As shown in section 2.1 of the Principles, the IMD3 is suppressed properly setting the two electrical attenuators and two main bias angles. The influence of the values of α₁ and α₂ on the fundamental component and IMD3 in the output IF signal is discussed below.

According to the previous derivation, when α₁ and α₂ satisfy the relationship C₂(α₁, α₂) = 0, the IMD3 component is suppressed. When α₁ is between 2.77–6.77 dB at 0.1 dB steps and α₂ is between 12.31–16.31 dB at 0.1 dB steps, the variation trend of the obtained IMD3 power with α₁ and α₂ is shown in Fig. 20. It can be found that when α₂ (dB) = 3α₁ (dB), the power of IMD3 is lower than -100 dBm, which means that it has been entirely suppressed in theory.

Fig. 20. The variation trend of the obtained IMD3 power with α₁ and α₂.

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Similarly, the variation trend of the fundamental frequency power with α₁ and α₂ is shown in Fig. 21 (a), where only the optimal point on the curve of α₂ (dB) = 3α₁ (dB) is the desired optimal value. The curve is individually mapped to the three-dimensional (3D) plane as shown in Fig. 21 (b). It can be found that the optimal fundamental frequency power is obtained at the combination of 4.77 dB and 14.31 dB, which conforms to the theoretical expectation. And at a combination of 5 dB and 15 dB, the reduction in fundamental frequency power is very small, about 0.01 dB. Therefore, it is feasible to replace 4.77 dB and 14.31 dB with 5 dB and 15 dB in practice.

Fig. 21. (a) The variation trend of the obtained fundamental frequency power with α₁ and α₂; (b) Curve α₂ (dB) = 3α₁ (dB) mapped separately to the 3D plane.

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4.2 I/Q amplitude, phase imbalance and compensation algorithm

According to the Eqs. (11) and (12), when φ_Xm= -135°, φ_Ym= 45°, an I/Q mixer can be obtained. The image rejection can be achieved when the image signal is introduced and a 90° electric hybrid is added to the I/Q output terminals. Here, we suppose the amplitude error of the proposed I/Q mixer is u, and the amplitude imbalance in dB is defined as U = 10log(1 + u)². The phase imbalance in radians is φ. The RF and image signals after frequency down-conversion can be expressed as:

(16)$${i_{IF}}(t )= {V_{RF}}({1 + u} )\times \cos ({{\omega_{RF}}t - {\omega_{LO}}t - {\pi / {4 - \varphi }}} )+ {V_{RF}} \times \cos ({{\omega_{RF}}t - {\omega_{LO}}t - {\pi / 4}} )$$

(17)$${i_{IM}}(t )= {V_{IM}}({1 + u} )\times \cos ({{\omega_{LO}}t - {\omega_{IM}}t + {\pi / {4 - \varphi }}} )- {V_{IM}} \times \cos ({{\omega_{LO}}t - {\omega_{IM}}t + {\pi / 4}} )$$

where

(18)$${V_{RF}} = {V_{IM}} = \frac{{\eta \mu E_c^2{G_{EDFA}}}}{4}[{{J_1}({{m_{Ya}}} ){J_1}({{m_{Yb}}} )- {J_1}({{m_{Xa}}} ){J_1}({{m_{Xb}}} )} ]$$

Then the IRR can be calculated as:

(19)$$IRR = \frac{{{P_{IF}}}}{{{P_{IM}}}} = \frac{{V_{RF}^2[{{{({1 + u} )}^2} + 2({1 + u} )\cos \varphi + 1} ]}}{{V_{IM}^2[{{{({1 + u} )}^2} - 2({1 + u} )\cos \varphi + 1} ]}}$$

In order to evaluate the effect of I/Q amplitude imbalance and phase imbalance on IRR, the IRR as a function of amplitude imbalance and phase imbalance is plotted according to the above equation derivation, as shown in Fig. 22. When the phase imbalance is not considered and the amplitude imbalance is lower than 1 dB, the IRR is higher than 34 dB. In addition, when the amplitude imbalance is not considered and the phase imbalance is lower than 2°, the IRR is higher than 18 dB. In the experiments, it’s required to keep the amplitude imbalance within 1 dB and the phase imbalance within 2° as much as possible to achieve an IRR of above 18 dB.

Fig. 22. IRR as a function of I/Q amplitude imbalance and phase imbalance.

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According to Fig. 14 and Fig. 22, the I/Q imbalance exists during the experiments and can seriously deteriorate the IRR. Therefore, a compensation algorithm for I/Q imbalance is added to the proposed scheme.

The ideal I and Q signals are assumed to be I'=Acos(θ) and Q'=Asin(θ), and the actual signal with amplitude imbalance and phase imbalance is written as:

(20)$$\begin{array}{l} I = A\cos (\theta )\\ Q = ({1 + u} )A\sin ({\theta - \varphi } )\end{array}$$

where A is the ideal magnitude of the I and Q paths, θ represents the desired information, and the time variance of θ is not considered here.

The linear relationship between the ideal signal and the actual signal can be expressed as:

(21)$$\left[ {\begin{array}{{c}} I\\ Q \end{array}} \right] = \mathbf{P}\left[ {\begin{array}{{c}} {A\cos (\theta )}\\ {A({1 + u} )\sin ({\theta - \varphi } )} \end{array}} \right] = \left[ {\begin{array}{{c}} {{I^{\prime}}}\\ {{Q^{\prime}}} \end{array}} \right]$$

The conversion matrix P can be calculated as:

(22)$$\mathbf{P} = \left[ {\begin{array}{{cc}} 1&0\\ {\tan \varphi }&{\frac{1}{{({1 + u} )\cos \varphi }}} \end{array}} \right]$$

Therefore, as long as u and φ can be estimated, the ideal I and Q signals can be reconstructed, and then the image signal can be completely eliminated.

According to [42], the estimated u and φ can be expressed as:

(23)$$\begin{array}{l} u = \sqrt {\frac{{E\{{{Q^2}(n )} \}}}{{E\{{{I^2}(n )} \}}}} - 1\\ \varphi ={-} \arcsin \frac{{E\{{I(n )Q(n )} \}}}{{\sqrt {E\{{{I^2}(n )} \}E\{{{Q^2}(n )} \}} }} \end{array}$$

where E{} represents the expectation of a random signal. The compensation algorithm is implemented in MATLAB. Finally, the IIRs are obtained after theory, simulation, and algorithm compensation for different amplitude and phase imbalances, as shown in Table 1. The simulation results are in agreement with the theoretical results. After algorithm compensation, IIR can exceed 61 dB even under the amplitude imbalance and phase imbalance of 2 dB and 2°.

Table 1. Comparison of theory, simulation, and algorithm compensation

View Table

5. Conclusion

In this paper, a large dynamic range and reconfigurable microwave photonic mixer is proposed. By matching the appropriate DSP operation and adjusting the dc biases of the modulator, the single-ended dispersion immune mixer, I/Q mixer, image rejection mixer, and double-balanced mixer can be achieved, respectively. In addition, the IMD3 can be greatly suppressed, and the conversion gain can be optimized by using convex optimization method to select the electronic attenuation values. A series of experiments are conducted to verify the large dynamic range and reconfigurable microwave photonic mixer. In the linearized single-ended dispersion immune mixer, the measured SFDR, constellation diagram and EVM are significantly improved after linearization, and the power fading after 30-km fiber transmission is compensated. In the I/Q mixer, RF signals with the operating frequency from 5 to 20 GHz are frequency down-converted to I/Q IF signals with amplitude imbalance below 0.7 dB and phase imbalance below ±0.7°. Incorporated with the I/Q imbalance compensation and image rejection algorithm in the digital domain, an image reject mixer is implemented with an IIR above 60 dB. Also, frequency down-conversion for the RF vector signals is demonstrated, and the constellation diagram and EVM are tested in detail to verify the linearization and image rejection effect. Thanks to the large operating frequency range, high dynamic range, reconfigurable functions, and simple integrated system structure, the proposed microwave photonic mixer exhibits excellent potential applications in various electronic systems, including wideband wireless communications, high throughput satellites, high- resolution radars, advanced electronic countermeasures, precision microwave measurement and instruments. Like many pre-research schemes, our schemes also have the problem of rising costs. On this issue, we think the breakthrough in the optoelectronic integrated chip may be a solution.

Funding

National Natural Science Foundation of China (62171374); Key Research and Development Program of Shaanxi (2021GY-096); Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (CX2022014); Natural Science Basic Research Plan in Shaanxi Province of China (2023-JC-QN-0732).

Disclosures

The authors declare that there are no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Amplitude imbalance (dB)	Phase imbalance (°)	Theory IIR (dB)	Simulation IIR (dB)	After algorithm compensation IIR (dB)
0	0	+∞	63.08	61.82
0.2	0.2	38.68	38.53	61.81
0.5	0.5	30.72	30.66	61.79
1	1	24.71	24.68	61.77
2	2	18.72	18.7	61.72

Reconfigurable microwave photonic mixer for hybrid macro-micro cellular systems

Abstract

1. Introduction

2. Principles

2.1 Linearized dispersion immune single-ended mixer

2.2 Linearized I/Q mixer and image rejection mixer

2.3 Linearized double-balanced mixer

3. Experiment and results

3.1 Linearized dispersion immune single-ended mixer

3.2 Linearized I/Q mixer and image rejection mixer

3.3 Linearized double-balanced mixer

4. Discussion

4.1 Selection of electrical attenuation α₁ and α₂

4.2 I/Q amplitude, phase imbalance and compensation algorithm

5. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (22)

Tables (1)

Equations (23)

Optics Express

Abstract

1. Introduction

2. Principles

2.1 Linearized dispersion immune single-ended mixer

2.2 Linearized I/Q mixer and image rejection mixer

2.3 Linearized double-balanced mixer

3. Experiment and results

3.1 Linearized dispersion immune single-ended mixer

3.2 Linearized I/Q mixer and image rejection mixer

3.3 Linearized double-balanced mixer

4. Discussion

4.1 Selection of electrical attenuation α1 and α2

4.2 I/Q amplitude, phase imbalance and compensation algorithm

5. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (22)

Tables (1)

Equations (23)

Optics Express

4.1 Selection of electrical attenuation α₁ and α₂