1. Introduction

Transmission of microwave signals via analog photonic links (APLs) has been brought into even sharper focus in quest for applications with higher carrier frequency and larger bandwidths, ranging from high-capacity communications systems [1], electronic countermeasures [2], distributed antenna systems [3] to antenna beam forming and steering for phased array radar [4]. Compared with traditional high loss, low bandwidth and cumbersome coaxial cables, photonic technologies possess salient advantages in terms of low transmission attenuation, broad bandwidth, flexible scalability and immunity to electromagnetic interference, which have emerged as an ideal and efficient solution to replace existing coaxial cable links [5,6].

In APLs, linearity is a paramount important parameter, which is defined as the ratio of input signal power to output signal power. The linearity is generally evaluated by the SFDR due to the fact that the SFDR indicates the ability of a system to work between noise and distortion limits, i.e., the difference of minimum detectable signal above noise floor and maximum input signal without distortion. Nevertheless, the SFDR is restricted by the nonlinear electronic-to-optical (E/O) conversion process of the Mach-Zehnder modulator (MZM) [7], which is the dominant contributor of nonlinear distortion in APLs. The nonlinearities inherent in the MZM will generate the intermodulation distortion (IMD) and harmonic distortion (HD) when mixing at the photodiode (PD), thereby resulting in severe spectral overlap phenomenon. Consequently, the system linearity is dramatically degraded, and in turn fails to satisfy the stringent requirement of high dynamic range [8]. Furthermore, for advanced high-speed optical communication systems, such as multi-carrier systems, adjacent channel power ratio (ACPR) is another significant figure of merit. The ACPR represents the ratio of the RF output power at the main channel versus the RF output power of the adjacent channel, which characterizes the amount of the transmitted power leaked from the main channel to the adjacent channel due to nonlinearities. Thus far the nonlinear behavior of the MZM has been considered as a tremendous challenge faced by researchers and engineers in the realm of microwave photonics.

In recent years, a large variety of linearization techniques have been proposed to eliminate nonlinear impairments. In general, these techniques can be roughly divided into two broad categories: electronics-based approaches and photonics-based approaches. The electronics-based approaches, such as digital post-processing [9–11], digital pre-distortion [12–14] and feedforward linearization techniques [15], have been reported for suppression of the IMD3 and HD2. Although high dynamic range and bandwidth can be enhanced by taking advantage of these techniques, this comes at the expense of increased architecture complexity, power consumption, cost and reduced operating frequency.

In order to overcome these limitations, a better alternative approach is to use photonic technologies. Currently, much research work has been mainly focused on linearizing the MZM transfer function due to the widespread use of MZM in APLs. A comparatively prevailing architecture is known as the distortion matching cancellation, of which the underlying principle can be described in the following. The matched optical path or polarization axis is constructed to generate the desired distortion components, which have equal amplitude and opposite polarity with respect to original distortion of the MZM. Then, the two distortion signals can be exactly counteracted during photodetection process. For instance, using this technique, researchers have proposed several effective methods based on a dual-parallel MZM [16,17]. To further reduce the optical or electrical power penalty, a static feedback approach based on an integrated-optical modulator [18] and an approach to jointly using dual-parallel MZM and polarization beam combiner (PBC) [19] are proposed. In addition, an approach based on polarization mixing technique is published in [20], which exploits an optical single sideband (OSSB) dual-electrode MZM with z-cut lithium niobate substrates, and the SFDR can be improved by around 15 dB. Similar approaches can also be reported in [21–23]. The IMD3 can also be suppressed by using electrical phase control technique [24,25], but the system bandwidth and frequency are constricted owing to the frequency-dependent electrical devices involved in these schemes. All the above-mentioned approaches were merely concerned with the third-order products, and the second-order products are neglected. However, with the advent of multi-octave applications, the elimination of the second-order products is becoming increasing important. To achieve such a broadband link, various linearization schemes have been presented in [26–28], aiming to mitigate the IMD3 and HD2 terms simultaneously. In [26], a broadband link based on a polarization division multiplexing dual-parallel Mach-Zehnder modulator (PDM-DPMZM) is implemented by bias point control and RF power distribution techniques. In this scheme, however, the suppression of the IMD3 and HD2 terms require a pair of optical paths, respectively. Recently, a similar linearization photonic link that can be flexibly configured for the sub-octave and multi-octave mode is also reported in [27], but the extra polarization controller and polarizer are required. For both schemes, the distortion matching of optical paths required high precision, which is difficult to realize in practice. Moreover, the photonic-assisted optical sideband filtering scheme has been developed in [28], which is mainly composed of a tunable laser, a polarization modulator, an optical bandpass filter and a balanced photodetector. Nevertheless, the system complexity is increased due to the use of excessive optical devices. Overall, the above-mentioned research work indicates that a simple and feasible multi-octave linearization approach is highly desired currently.

In this paper, we theoretically analyze and experimentally validate a multi-octave linearity optimization analog photonic link with simple and compact architecture, which primarily consists of a polarization division multiplexing Mach-Zehnder modulator (PDM-MZM) and a linear polarizer. The proposed scheme merges power weighting with polarization multiplexing and bias control techniques to achieve the suppression of IMD3 and HD2 simultaneously. The IMD3 is cancelled by adjusting the power weighting factor $\kappa$ and polarization incident angle $\alpha$ instead of the widely used low-biased methods. Consequently, the suppression of HD2 can be achieved by simply biasing the modulators at the quadrature point. Finally, a proof-of-principle experiment is performed and experimental results demonstrate that our scheme is very effective in enhancing the SFDR and ACPR performance.

2. Principe and Optimization Model

The schematic diagram of the multi-octave linearity optimization APLs that can implement both IMD3 and HD2 suppression simultaneously, is sketched in Fig. 1(a). It is primarily built with an integrated PDM-MZM, a polarization controller (PC), a linear polarizer, and a photodiode (PD). A linearly polarized light wave emitted by a laser diode (LD) is injected into the PDM-MZM and then divided into two branches with equal power by a built-in optical coupler (OC). The incident light of each branch is coupled into two sub-MZMs (sub-MZMX and sub-MZMY) connected in parallel, and then is intensity-modulated by two RF signals with different powers, respectively. The modulated optical signals are combined with two orthogonal polarization states (i.e., TE- and TM-modes) using a polarization rotator (PR) and a polarization beam combiner (PBC). To project two orthogonal polarization states of the input optical signal to one polarization direction, a PC and a linear polarizer are placed in the optical path before the PD. By adjusting the polarization incident angle, the signal from the polarizer can be sent to a high-speed PD on only one polarization state.

 

Fig. 1. (a) Schematic diagram of the multi-octave linearity optimization APLs. (b) and (d) the sub-MZMX and sub-MZMY operating point bias conditions. (c) and (e) a pair of complementary RF signals after photodetection. LD: laser diode; PS: power splitter; VEA: variable electrical attenuator; PDM-MZM: polarization division multiplexing Mach-Zehnder modulator; OC: optical coupler; PR: polarization rotator; PBC: polarization beam combiner; PC: polarization controller; Pol.: polarizer, PD: photodiode.

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To evaluate the nonlinear behavior induced by the modulator, a typical method is to use the two-tone sinusoidal test. In the sub-MZMX, a two-tone signal is sent into the RF electrodes of the sub-MZMX via a variable electrical attenuator (VEA). Mathematically, the two-tone signal is expressed as

In the sub-MZMY, the other two-tone signal with same frequencies and initial phases is directly sent into the RF electrodes of the sub-MZMY without power attenuation and expressed as

In the case of push-pull configuration, both the sub-MZMX and sub-MZMY are biased at the quadrature point with opposite slope, as depicted in Fig. 1(b) and (d). Note that when the sub-MZMs operate in the vicinity of the linear region, the fundamental signal power has a maximum value and the modulation efficiency is improved [29]. In the detected photocurrent, the HD2 is eliminated, while a couple of complementary IMD3 products are generated. Assuming the sub-MZMX and sub-MZMY are identical and have the same half-wave voltage. The linearly polarized light generated from the LD is denoted as ${E_c}(t ){e^{j{\omega _c}t}}$, where ${E_c}$ and ${\omega _c}$ are the amplitude and the angular frequency of the linearly polarized light, respectively. The polarization-multiplexed signal at the output of the PDM-MZM are given by

The polarization-multiplexed signal is then injected into a polarizer via a PC. At the input of the polarizer, the polarization incident angle $\alpha$ can be changed by rotating the paddles of the PC to twist the optical fiber. Then, the optical signal is projected to a single polarization direction through the use of a PC in conjunction with a polarizer. Note that the optical power ratio between the two polarization states depends solely on the angle $\alpha$. The optical signal at the output of the polarizer is given by

Then, the nonlinear behavior of the MZM is modelled through Taylor series expansion. Calculating Taylor series expansion of $\sin [{2\beta {S_{upper}}(t )} ]$ and $\sin [{2\beta {S_{lower}}(t )} ]$ in Eq. (6), and neglecting the higher non-dominant terms, the detected optical photocurrent can be simplified in a third-order polynomial form as

After Taylor series expansion, we can clearly see that the photocurrents generated by TE-and TM-polarized optical signals have opposite signs and different amplitudes, which coincide with the curves shown in the Fig. 1(c) and (e). Therefore, the third-order products can be mitigated through the photocurrents subtraction in the PD when satisfying certain conditions. Combining like terms, and neglecting constant terms that is independent of the desired RF signal, Eq. (7) is rearranged as follows

As can be observed from (8), the first term is the fundamental signal, which is proportional to the amplitude of the RF signal. The second term is the third-order products, which will generate the fundamental signal, third-order harmonic and intermodulation distortion. Explicitly, the even-order harmonic distortions have been cancelled by taking advantage of the feature of the quadrature-biased push-pull MZM. This implies that the system bandwidth is no longer limited by the HD2, so that the second-order linearity is significantly enhanced. Nevertheless, the third-order products become the dominant contribution to the system nonlinearity in this situation. Substituting (1) and (2) into $S_{upper}^3(t )$ and $S_{lower}^3(t )$, respectively, and the third-order products is given by

Then, substitution of Eqs. (1), (2) and (9) into Eq. (8) leads to the following photocurrent

This equation suggests that the output power of the fundamental signal and the IMD3 are exactly and uniquely determined by $\kappa$ and $\alpha$, which can be varied by appropriately tuning the VEA and PC. In order to extinguish the IMD3 while maintain a lower loss of the fundamental signal, the following constraint relationships must be satisfied

By performing a mathematical derivation for Eq. (12), the correlations of the parameters of $\kappa$ and $\alpha$ can be given as follows

Therefore, a rather simple and exciting result is obtained. It should be noted that the $\kappa$ could be directly determined by the $\alpha$, and vice versa. The simulated results on the basis of Eq. (13) are illustrated in Fig. 2. We can observe that the worst case occurs at the intersection point of the two curves (magenta circle), the coordinates of which are (${\pi / 4}$, $1$). At this point, the output photocurrents of the fundamental signal and IMD3 decrease to zero (and at this point only) simultaneously. Apparently, this situation must be avoided during experimental operation process. Fortunately, it hardly occurs in practical due to $\kappa$ is always not equal to one.

 

Fig. 2. Simulated power weighting factor $\kappa$ as a function of polarization incident angle $\alpha$ based-on Eq. (13).

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To maximize RF output power, we put forward an optimization model based on two-dimensional programing theory. Inspection of Eq. (11), we can find that the amplitude of fundamental signal is the difference between the TE- and TM-modes photocurrents. Thus, the third-order products can be well suppressed when the constraint conditions Eq. (13) holds true, but only at the expense of sacrificing the fundamental signal power. According to the optimization theory, there exists an extremum value for the coefficient ${C_1}$, which is associated with the parameters of $\kappa$ and $\alpha$. Thus, both $\kappa$ and $\alpha$ should be optimized to maximize the ${C_1}$ and minimize the ${C_2}$. Otherwise, the fundamental signal will be attenuated to a large extent. In previous work [21], [30,31], however, the ${C_1}$ and ${C_2}$ are confirmed by experimental tests, rather than modelling for the optimization problem. In reality, it is very difficult to attain the precise optimal values through experimental tests. Since researchers must control two or more components concurrently. Thus, these methods are only limited to laboratory research. Our proposed optimization model is composed of an objective function and a constraint condition, which can be formulated as

Substituting Eq. (15) into Eq. (14), then the two-dimensional objective function can be transformed into a one-dimensional objective function. Taking the first-order derivative of $C_1$ with respect to $\alpha$, the ultimate result can be approximately written as

According to one-dimensional optimization theory, the maximum point occurs at where the slope is zero, i.e., ${C_1}^\prime \textrm{ = }0$. By solving Eq. (15), we can obtain the maximum point of ${C_1}$ is

Then, substituting Eq. (17) into Eq. (14), we can obtain ${C_1}\textrm{ = }0.33$ when neglecting constant term ${{\Re \beta VE_c^2(t )} / 4}$. Furthermore, $\kappa \textrm{ = 0}\textrm{.5}$ means that the input power ratio is 6 dB, which is easy to achieve by a VEA. Figure 3 shows the simulated results that the coefficients of ${C_1}^\prime$ and ${C_1}$ with respect to the $\alpha$, respectively. We can observe that the ${C_1}$ reaches the maximum value when $\alpha \textrm{ = 0}\textrm{.34}$radians. This point is known as critical point in mathematics. Thus, when the $\kappa$ is set to be 6 dB, the maximum RF output power can be obtained by only adjusting the PC in the experiment.

 

Fig. 3. Simulated first-order derivative of ${C_1}$ with respect to $\alpha$ and ${C_1}$ as a function of polarization incident angle $\alpha$.

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3. Experiment and Analysis

The feasibility of the proposed multi-octave bandwidth APLs is demonstrated by a proof-of-principle experimental setup, which is constructed based on the schematic diagram in Fig. 1. In the scheme, the core component is an integrated PDM-MZM, which is composed of a 3 dB optical coupler (OC), two sub-MZMs (MZMX and MZMY) in parallel and a polarization rotator (PR) embedded in the lower arm followed by a polarization beam coupler (PBC). A continuous-wave light at 1550.12 nm central wavelength with an output power of 16 dBm generated by a LD (KG-DFB-40) is injected into the off-the-shelf PDM-MZM (Fujitsu FTM7980EDA), of which the 3 dB bandwidth and the half-wave voltage are 40 GHz and 3.5 V at 22 GHz, respectively. In order to suppress the HD2 products, two sub-MZMs are both configured for the quadrature-biased mode. The two-tone signals generated from the microwave signal generators (MSG, Agilent E8257D and HP 83640A) are firstly combined with a 3 dB power combiner and then divided into two parts with equal power by a broadband electrical power splitter. Then, one part is fed into the RF electrodes of the sub-MZMX via a VEA, while another part is directly fed to the RF electrodes of the sub-MZMY. To reduce the relative phase difference between RF signals, the total length of coaxial cable connecting the sub-MZMX is approximately equal to that connecting the sub-MZMY in experiments. The VEA is used to control the power levels of the two-tone signal driving the sub-MZMY, thereby varying the power weighting factor $\kappa$. After optical intensity modulation, a polarization-multiplexed signal is generated. The output of the PDM-MZM, which has a polarization-maintaining fiber (PMF) pigtail, is connected to a PC, and then the polarization-multiplexed signal is projected to one polarization direction by using a polarizer placed prior to the PD. In principle, the state of polarization can be altered based on stress-induced birefringence phenomenon in the optical fiber [32]. Then, the optical signal with only one polarization state is detected by a high-speed balanced photodetector (Finisar, BPDV2150RM). In our design, we only use an input port of the BPD. Finally, the generated RF signal is measured and recorded with a 40 GHz electrical spectrum analyzer (R&S, FSQ-40).

To make the system work in the optimal conditions, the experiments are performed in two steps. First, the attenuation of the VEA in the upper branch is set equal to 6 dB (equivalent to $\kappa \textrm{ = }0.5$). Then, the $\alpha$ can be readily confirmed by observing the RF signal power from the spectrum analyzer in the experiment. This is due to the fact that the fundamental signal power reaches the maximum value when the $\alpha$ is adjusted to be 0.34 radians with a PC. In this way, we are able to ascertain the $\kappa$ and $\alpha$ quickly, and the accuracy is also guaranteed to be at high level. Therefore, the linearity enhancement can be achieved by only controlling the polarization incident angle $\alpha$ in our scheme. This draws a sharp distinction from other methods without optimization, in which the maximum RF power is hard to attained when simultaneously adjusting the $\kappa$ and $\alpha$. For comparison purposes, the performance of a typical quadrature-biased link, which only consists of a sub-MZMX based on the PDM-MZM, is also measured.

In the experiment, the two-tone signals with identical power level at frequencies 19 and 19.1 GHz are coupled into the RF electrodes of the PDM-MZM. Shown in Fig. 4(a) and (b) are the measured electrical spectrum of the fundamental signal and the IMD3 products for the quadrature-biased link and the proposed linearity optimization link, respectively. For comparison under identical experimental conditions, the fundamental signal powers are both set equal to around -30 dBm through varying the injection optical power to the PD. It can be observed that a considerable improvement in IMD3 suppression over 25 dB is achieved. Moreover, the HD2 suppression is also measured over a 24 GHz span with 1 MHz resolution bandwidth (RBW), as depicted in Fig. 4(c). It can be shown that by biasing the two sub-MZMs at quadrature point, the HD2 is suppressed more than 55 dB. This reveals that the proposed linearity optimization link can operate over a multi-octave bandwidth. It should be noted, however, a small residue of the HD2 still remains. This is due primarily to the path mismatch, finite extinction ratio (ER) and the bias voltage drift of two sub-MZMs, which are sensitive to mechanical vibrations and environmental temperature perturbations.

 

Fig. 4. Comparison of the electrical spectra for two-tone test at 19 and 19.1 GHz. (a) quadrature-biased link. (b) the proposed linearity optimization link; (c) multi-octave bandwidth span electrical spectrum

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The SFDR performance is measured using a two-tone signal with the same frequency as employed in Fig. 4. The input power of the two-tone signals is varied with a step size of 1 and 2 dBm, and the resultant different components powers are also recorded at the same time. The noise floor is calculated to be -163.1 dBm/Hz at 1 Hz bandwidth. At the input of the PD, the injection optical power remains constant at 14 dBm by using an erbium-doped fiber amplifier (EDFA). This is because the high injection optical power is beneficial to improve the link gain. Figure 5 illustrates the second-order and third-order SFDR for the links with and without linearity optimization. The IMD3 power has a slope of 3, while the slope of the IMD3 power approaches 5 in Fig. 5(b). This implies the IMD3 products have been substantially suppressed with the proposed linearity optimization technique, and the fifth-order products have been the dominant contribution to the link nonlinear distortion. Thus, the link can still maintain a better linear performance, even though the modulators are driven by the RF signal with a large power level. We can observe the third-order SFDR is enhanced from 95.4 dB·Hz^2/3 to 112.3 dB·Hz^2/3, corresponding to an appreciable improvement of 16.9 dB. The second-order SFDR is 94.2 dB·Hz^1/2 and 94.6 dB·Hz^1/2, respectively. It can be seen that the second-order SFDR difference between the two links is small when the bias conditions are the same.

 

Fig. 5. RF output power of the fundamental signal, the IMD3 and HD2 products versus RF input power. (a) quadrature-biased link and (b) the proposed linearity optimization link.

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To further validate the linearity performance of the proposed approach for broadband operation, the ACPR is measured using a 16-ary quadrature amplitude modulation (16QAM) digital modulation signal centered at 19GHz with a symbol rate up to 40 Mbaud driving the PDM-MZM. Figure 6 shows the measured ACPR versus RF input power with and without linearity optimization cases, respectively. As can be seen, initially the ACPRs gradually rise with the increase of the RF input power. This indicates that nonlinear distortions are quite small at lower signal levels and do not lead to detrimental effect on the adjacent channel. Nevertheless, when the RF input power exceeds a certain threshold, the ACPRs begin to drop sharply. This drop in ACPRs can be attributed to the increase of the adjacent power from the main channel power leaking. The peak ACPR of 54.6 dBc is obtained (red line) when RF input power is 12 dBm, while the peak ACPR is 49.2 dBc (blue line) in the quadrature-biased link. It is seen that an improvement of 5.4 dB is achieved. Again, these experimental results demonstrate that the proposed approach is effective for broadband operation.

 

Fig. 6. Measured the ACPR versus RF input power for quadrature-biased link (blue line) and the proposed linearity optimization link (red line).

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Figure 7(a) and (b) depict the electrical spectrum of the recovered 16-QAM digital modulated signal, which is measured and recorded for the links with and without linearity optimization. The input RF powers are 10 dBm and 12 dBm. As shown in Fig. 7(a), the leaked power to the adjacent channel is very evident at high input power and impossible to be ignored. Hence, the large leakage power seriously degrades the link ACPR performance. However, in Fig. 7(b), there is a subtle leakage power observed when the link is linearized, in sharp contrast to the case of the quadrature-biased link. Notably, the plots in Fig. 7(a) and (b) are measured under equal RF input power. This suggests that the adjacent channel power has been reduced to around zero power with linearity optimization technique. The ACPR is naturally enhanced. These results are consistent with the results of Fig. 6.

 

Fig. 7. Measured spectra of a 40 MBaud 16-QAM signal at different RF input power levels. (a) quadrature-biased link and (b) the proposed linearity optimization link

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The eye and constellation diagram as an important indicator of the quality of signal transmission are also investigated in this paper. The plots in Fig. 8 illustrate the measured eye diagrams and constellation diagrams for 16-QAM signal for the links with and without linearity optimization. The input RF powers are set to be 12 dBm. At the top of Fig. 8(a), we can observe that the vertical eye opening is constricted to be small due to the nonlinear distortion and timing jitter, and the corresponding constellation diagram shown at the bottom left of Fig. 8(a) also become blurred. The error vector magnitude (EVM) is 6.4% without optimization. However, from the eye diagram shown in Fig. 8(b), we can see that the vertical eye opening is maximum and four coding levels (00, 01, 10 and 11) can be easily distinguished. At the bottom of Fig. 8(b), we observe these dots in the constellation diagram is evenly spaced and symmetrical distribution, indicating a good signal transmission performance is achieved. The EVM is decreased to 3.1% and shows a considerable improvement of 3.3%.

 

Fig. 8. Measured eye diagrams and constellation diagrams of a 16-QAM digital modulation signal. (a) quadrature-biased link and (b) the proposed linearity optimization link.

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Finally, an investigation on the tolerances for RF and optical input power is performed. The relation between EVM and RF input power is shown in Fig. 9(a). It can be seen the EVM increases gradually when the RF input power varies from -10 dBm to 20 dBm. However, in the range of 0 dBm to 10 dBm, we can observe that the EVM curve has a smooth region with a threshold of about 3%. The peak-to-peak fluctuation of the EVM is below 0.3%. Similar EVM curve can be obtained for the quadrature-biased link, which has a threshold of about 5% in the smooth region. Thus, the EVM is decreased by 2% with the use of the proposed approach. Figure 9(b) illustrates the EVM versus the optical input power of the PD for links with and without linearity optimization, respectively. We can see that the EVM is beyond 5% when the optical power is below 8 dBm. Then, the EVM decreases to around 2.5% as the optical power increases. For the optimized link, the EVM (red line) is approximately 3% in the range of 10 dBm to 18 dBm, with a small fluctuation of below 0.4 dB. As expected, the higher optical power can improve the link gain, resulting in the reduction of EVM. Nevertheless, the EVM will rise rapidly if the optical power is greater than 18 dBm. This is caused by the shot noise generated from the PD, which dominates the link nonlinear performance at high optical power.

 

Fig. 9. (a) Measured EVM curves versus RF input power, and (b) measured EVM curves versus optical input power for the quadrature-biased link and the proposed linearity optimization link.

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4. Conclusion

In conclusion, a novel approach to concurrent suppression of IMD3 and HD2 is thoroughly analyzed and demonstrated based on power weighting, polarization multiplexing and bias control techniques. By modelling and simulating for the optimization problem, we can find that the optimal value for the objective function occurs at $\kappa=0.5$ (equivalent to 6 dB in power) and $\alpha=0.34$ radians. The quantitative results not only assist in maximizing the link linearity, but also simplify experimental operation. In the previous work, however, these parameters were ascertained either by experiment tests or by a random value, leading to the lower accuracy and dynamic range. Therefore, our proposed approach provides an important advancement in the enhancement of system performance. On this basis, a proof-of-principle experiment was performed. Experimental results show that the third-order SFDR and second-order SFDR can achieve up to 112.3 dB·Hz^2/3 and 94.6 dB·Hz^1/2, respectively. Furthermore, the broadband transmission performance and the system tolerances for RF and optical input power are also demonstrated using 16-QAM signal. Despite the evident advantages of photonic technologies in the implementation of multi-octave analog photonic link, there is still a limitation caused by the frequency-dependent VEA involved in our approach. Thus, the frequency tuning range is relatively small. Fortunately, the power weighting factor is kept fixed when operating in the optimal case, so that the VEA could be removed by using hybrid integrated photonic technologies in the future. The approach presented in this paper can find applications in multi-static radar signal transmission and broadband communications systems.