1. Introduction

Earliest possible warning of weapon radar is significantly required for military applications [1]. Angles-of-arrival (AOA) estimation is an efficient way to confirm the direction of the incoming radar beam, so as to achieve the position of target weapon radar [2]. It is usually employed in an intercept warning receiver (INR) to directly receive the enemy’s radar beam and provide real-time warning. The early radar warning system should first determine the approximate location of the target as quickly as possible. Therefore, a very accurate AOA estimation is not necessary at this time. Moreover, when the main radar beam straightly points to the receiver, the AOA estimation result is the most reliable. It means the intercept received signal power of the INR is stronger than that of the echo wave, which thus only requires moderate sensitivity [3].

In recent years, to expand the operation bandwidth, decrease the power consumption, be immune to electromagnetic interference, and compress the system volume, microwave photonics (MWP) technology has been widely developed to realize the AOA estimation. Up to now, many kinds of photonic-based AOA estimation structures have been reported [4–15]. A direct way is to down-convert the received RF signal into an IF signal, and extract the phase information [4] or monitor the signal amplitude [5] through a digital processor. However, extra frequency conversion would increase the complexity of the system. To simplify the system configuration, parameters mapping for AOA is a good choice. For example, AOA can be mapped to time delay [6–7], phase shift [8], optical power [9], electrical power [10–12], power notch location [13], or DC voltages [14]. These above literatures all reveal very efficient AOA estimation ability and very simple configurations. In particular, a linear antenna array (LAA) with only two antennas is required in these methods. However, they can only distinguish the AOA in a single dimension (1-D), because two antennas can only extract 1-D AOA. In fact, the direction of incoming RF-beam is three-dimension (3-D) information. As for this, 2-D AOA should be firstly estimated, so as to define the third angle by the two estimated AOAs [15]. To realize 2-D AOA estimation, large antenna arrays should be constructed, which requires more antennas [16]. For a photonics link, a large antenna array means a large electro-optic (E/O) conversion array. It may increase the complexity of the system and distort the performance. To be honest, when considering the microwave signal detection, AOA estimation is the hardest one [3]. Because the measurement for other parameters (such as frequency, amplitude, or phase) requires only one antenna, but the AOA estimation needs at least two. To achieve 2-D AOA of the incoming signal, the number of antennas is inevitably increased. It also means, if needed, properly increasing the number of antennas is acceptable. Our target is to design a stable, efficient, and moderate sensitivity 2-D AOA estimation method with simplest photonic structure and minimum antenna number. Then construct the 3-D location of the target through the estimated 2-D AOA.

In this paper, we design a very simple photonic structure and effective antenna layout to realize 2-D AOA estimation. Only one dual-polarization binary phase shift keying modulator (DP-BPSKM) and an L-shaped antenna array (L-sAA) are required. Comparing with the aforementioned methods, four advantages can be listed as follow:

The detailed comparison results with other reported AOA measurement methods are given in the final section of this paper.

2. Principle

2.1 Geometrical models

Figure 1(a) shows the traditional coordinate system. The position of the signal source in this coordinate system is described as S(x, y, z), and the direction of arrival is defined by the elevation-elevation system, which is expressed as (α, β, γ). Here, α, β, and γ are the elevation angles relative to the three axes, respectively. Assuming that the distance between the original point O(0, 0, 0) and target S is R. In this coordinate system, an L-shaped antenna array (L-sAA) with three antennas (A₁, A₂, and A₃) can be designed. As Fig. 1(b) shows, the three antennas are located on the origin, x-axis, and y-axis, respectively. Especially, the spacing of the two adjacent antennas is d, which means the locations of these three antennas can be expressed as A₁(0, 0, 0), A₂(d, 0, 0), and A₃(0, d, 0). It should be emphasized that when the signal source S is very far away from the L-sAA, this means that R>>d, thus the signal paths from the signal source S to each sub-antennas in the L-sAA can be approximately regarded as parallel to each other. As shown in Fig. 1(c), SA₁//SA₂//SA₃.

 

Fig. 1. (a) Elevation-Elevation coordinates, (b) the scenario of the L-shaped antenna array, and (c) the equivalent schematic diagram when R>>d.

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According to the geometrical principle, the coordinates of the signal source is expressed as (x = Rcosα, y = Rcosβ, z = Rcosγ). In fact, the L-sAA can be regarded as two uniformly distributed linear antenna arrays (A₁A₂, and A₁A₃) that settled are in orthogonal. The shape looks like an “L”. One line with one point can form a unique plane. Line A₁A₂ and point S define a unique plane A₁SA₂, Line A₁A₃ and point S define another sole plane A₁SA₃. Thus, line SA₁ is given by the intersection of the plane A₁SA₂ and plane A₁SA₃.

It is very familiar to us that two antennas can realize excellent 1-D AOA estimation. For the linear antenna array A₁A₂, it works in plane A₁SA₂, and the 1-D AOA is α. Similar, the linear antenna array A₁A₃ works in plane A₁SA₃, and the related 1-D AOA is β. It is obvious that through the L-sAA, a 2-D AOA (α and β) can be achieved. However, another dimension with the AOA of γ should be known to confirm the exact 3-D direction of the signal source. Fortunately, based on the geometrical principle, in the elevation-elevation coordinates, only two angles are needed to define the third elevation angle [15]. Thus, based on the relationship in Eq. (1), we can calculate the numerical value of the third AOA from the measured α and β.

2.2 Photonic 2-D AOA estimation principle

The schematic diagram of the proposed 2-D AOA estimation system is shown in Fig. 2(a). It mainly consists of a dual-polarization binary phase shift keying modulator (DP-BPSKM) and L-sAA. A laser diode (LD) emits a lightwave with the amplitude of E_c, and the angular frequency of ω_c. It is simply expressed as ${E_c}(t )= {E_c}{e^{j{\omega _c}t}}$. After being controlled by the polarization controller (PC1), the lightwave is injected into the modulator. This modulator is an integrated one, which parallelly embeds two dual-driven Mach-Zehnders (DMZM1 and DMZM2) in two arms. A 90° polarization rotator (90° PR) is followed in one arm and makes this modulator polarization-multiplexed. Then, the polarization-multiplexed signals from the two arms are recombined by a polarization beam combiner (PBC) in the modulator. The detailed structure of the integrated modulator is shown in Fig. 2(b), there are four microwave ports (x_u, x_d, y_u, and y_d) in it and connect to the L-sAA. The L-sAA is composed of three antennas and its shape looks like an “L”. As is shown in Fig. 2(c), the antenna-1 (A₁) is settled at the origin point of the coordinate system. Antenna-2 (A₂) and antenna-3 (A₃) are located (d, 0, 0) and (0, d, 0), respectively. Where, d is the distance between each two antennas and is normally designed to be d=λ/2 (λ is the incoming RF signal wavelength) to avoid the grating lobes in the radiation pattern. A₂ and A₃ pick up the RF signals and directly send them to microwave ports y_d and x_u, respectively. Meanwhile, A₁ also captures the RF signal. It should be strengthened that the RF signal that received by A₁ is firstly amplified by an electrical amplifier (EA) and then power divided by an electrical splitter (ES). Under this process, the power of the two signals from the ES is equal to that from A₂ and A₃. Then, they are sent to microwave ports x_d and y_u, respectively. It should be emphasized that the three signal paths from the three sub-antennas to the modulator should be equal to each other. Two DC bias voltages (V_D1, V_D2) are all set to quadrature transmission point (QTP) to make the modulator perform dual-sideband (DSB) modulation.

 

Fig. 2. (a) Schematic diagram of the proposed 3-D AOA estimation method. (b) Detail structure of the DP-BPSKM and the connection of the L-sAA. (c) Geometrical locations of the L-sAA and the target. LD: laser diode, PC: polarization controller, DP-BPSKM: dual polarization binary phase shift keying modulator, EDFA: erbium-doped fiber amplifier, PBS/C: polarization beam splitter/combiner, PD, photo-diode, DMZM: dual-driven Mach-Zehnder modulator, 90 PR: 90 degree polarization rotator, EA: electrical amplifier, ES: electrical splitter, L-sAA: L-shaped antenna array.

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Regarding the signal that received by A₁ as the reference signal, which can be expressed as V₁(t)=V_RFsinω_RFt. According to the geometrical model in Section 2.1, A₂ and A₃ work in different planes. Therefore, we can separately process the received signals from these two antennas. Firstly, consider the incoming radar beam received by A₁ and A₂. As Fig. 2(b) shows, due to the incoming direction relatives to the x-axis, time delay τ_x=dcosα/c will be caused in the two antennas and thus introduces a phase difference of φ_x=ω_RFτ_x=πcosα. In this way, the signal received by A₂ can be expressed as V₂(t)=V_RFsin(ω_RFt+φ_x). Similarly, because of the arriving angle in plane A₁SA₃, the time delay τ_y=dcosβ/c would also be introduced. Then the signal received by A₃ can be written as V₃(t)=V_RFsin(ω_RFt+φ_y), where φ_y=ω_RFτ_y=πcosβ is the phase difference between A₁ and A₃ that is caused by the time delay. Thus, under the small signal condition, the Jacobi-anger expanded output signal from the DP-BPSKM can be expressed as

As can be seen in Eq. (4), the final result is the vector sum between two same-frequency signals with different phases. Therefore, the related power responses can be expressed as

It can be seen in Eq. (5), the power responses of the two outputs are related to the φ_x and φ_y, respectively. In order to extract out the phase information, an electrical power meter (EPM) can be adopted to measure the output electrical power. However, these two responses are also influenced by the input RF signal power. The fluctuation of the received power would distort the system performance, which is not desired. Therefore, the amplitude comparison function (ACF) should be introduced.

In general, when detecting the AOA of the incoming signal, the received power is low-level. It means that the small signal condition can be satisfied, and thus J₀(m)≈1, J₁(m)≈m/2 [17]. In this way, Eq. (5) can be written as

3. Experimental results

To demonstrate the proposed 2-D AOA estimation method, experimental work is conducted. A distributed feedback laser (DFB) launches a lightwave with a wavelength of 1550.12 nm and a power of 10 dBm. Before injecting it into a DP-BPSKM (FTM Fujitsu7980/EDA), the polarization state of the lightwave is adjusted by the PC1. An EDFA with the gain of 20 dB is followed to amplify the modulated lightwave. Then the amplified signal is controlled by the PC2 to align the polarization states to the two principal axes of the PBS. After passing through the PBS, the lightwave is polarized, de-multiplexed into two paths and sent to the two PDs, respectively. Two microwave sources (Agilent E8257D) are employed to function as the signals that are received by the antennas. It should be emphasized that these two microwave sources have been previously synchronized. One of them generates a RF signal with a frequency of 5 GHz and a power of 0 dBm. It is split by an ES (Marki PD0140), and then led to the two microwave ports (X_d and Y_u) of the DP-BPSKM. Another one also emits a RF signal with a frequency of 5 GHz and a power of 0 dBm. Use another ES to separate the microwave signal into two. Differently, two electrical phase shifters are followed here to imitate the time delays caused by the AOAs when the antennas 2 and 3 are receiving signals. After that, they are led to microwave ports X_u and Y_d, respectively. Most importantly, the equal signal path lengths from the microwave sources to the modulator are guaranteed by choosing probable cables. Due to the limited experimental condition, the EPM is not available in our lab. Therefore, we try to capture the output signal from the PDs through an electrical spectrum analyzer (ESA) and observe the power variation of the fundamental signal ω_RF.

It should be emphasized that our scheme is to perform 2-D AOA estimation for α and β in two polarization states, respectively. Thus, the quality of polarization multiplexing/de-multiplexing is very important. The result of the polarization de-multiplexing is observed by the optical spectrum analyzer (OSA, FINISAR). In this work, the RF signal is only introduced to the DMZMx, while the DMZMy not. The DC bias voltages are set to QTP. Therefore, it can be predicted that the carrier in the x-polarization is driven by the RF signal and will stimulate certain sidebands. In contrast, the optical signal from y-polarization can only be observed with a single carrier. As shown in Figs. 3(a) and 3(b) show, the spectrum in Fig. 3(a) agrees well to the predicted results that the DSB modulation is well performed in the x-polarization. Moreover, the un-modulated carrier from the y-polarization is also observed in Fig. 3(b). The results imply that this link has good polarization de-multiplexing quality. In particular, it can be seen that the total power (including the carrier and the noise figure) from the y-polarization is lower than that from x-polarization. The reason is the non-ideal fabrication art and the inaccurate polarization alignment that cause unequal polarization-dependent loss.

 

Fig. 3. Polarization de-multiplexing results in (a) x-polarization, (b) y-polarization.

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Next, the experimental work is continued to verify the 2-D AOA estimation ability. It includes the AOAs related to the x-axis and y-axis. Here, the AOA on the x-axis is firstly considered. Figure 4(a) shows the ACF response between the output signal from the PDx and the input RF signal. The measurement data is in good agreement with the theoretically predicted curve. Based on the measured data, the phase of the signal can be recovered. The result shown in Fig. 4(b) implies the possibility of signal phase measurement through this structure. Assume that the frequency of the incoming RF signal is known and the antenna spacing is equal to λ/2, where λ is the wavelength of the received RF signal. Therefore, the AOA information α relates to the x-axis direction can be obtained from the measured phase information through the relationship of φ_x=πcosα, and the results are shown in Fig. 4(c). In addition, the corresponding measurement error is also calculated in Fig. 4(g), which describes that the measurement error on the x-axis can be less than 1°. The same processing is also conducted for the output from PDy. As the measured result shown in Fig. 4(d), the monotonous ACF response makes the phase measurement available. The recovered phase is shown in Fig. 4(e). Similarly, using the relationship of φ_y=πcosβ, we can achieve the AOA information β that relates to y-axis. The results are shown in Fig. 4(f). Finally, the measurement error for β is also obtained in Fig. 4(h), which is better than 0.5°.

 

Fig. 4. (a) Measured ACF response for α, (b) the recovered signal phase caused by α, (c), the recovered α, (d) the measured ACF response for β, (e) the recovered signal phase caused by β, (f) the recovered β, (g) the measurement error for α, and (h) the measurement error for β.

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Then, an important process is to employ the 2-D AOA (α and β) estimation results to calculate the third AOA information γ. Different from α and β, γ is a numerical result that comes from mathematical calculation. According to the geometrical conclusion in Eq. (1), the γ calculation can be achieved from the measured α and β. The result is shown in Fig. 5(a), as α and β vary from 18.22° to 90° and satisfy the condition of cos²α+ cos²β<1, there is always a unique γ value. In addition, the measurement error of γ is also calculated. As is shown in Fig. 5(b), it is about 2°. In comparison with the estimation results of α and β, the calculated γ is not very accurate. It is because of the error propagation law during the calculation [18]. The numerical error of γ is determined by the measurement error from α and β.

 

Fig. 5. (a) AOA recovery of γ, and (b) the measurement error of γ

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For a RF intercept receiver, the received signal power is generally in a low-level. Therefore, the sensitivity is a significant factor in evaluating the performance of the receiver. In this work, we decrease the RF signal power of the input RF signal from 0 dBm in step of 5 dB to investigate the sensitivity. Figures 6(a)–6(c) emerge the measured results and the theoretical curves under the input RF power of -20 dBm, -40 dBm, and -50 dBm, respectively. It can be seen that the measured results still match well with the theoretical curves. However, as Fig. 6(c) shows, when the received RF power is too low, the ACF responses in the low phase range deviate from the standard values seriously. The reason why the measurement error deteriorates greatly is the undesirable power response from the PD. Note that the ACF curves shown in Figs. 6(a)–6(c) are all monotonically strict increasing responses, which means that the signal with smaller phase will be mapped to lower output power by this link. Moreover, as Fig. 6(d) shows, if the input RF power decreases, the related output power from the PD is also weakened. Particularly, the noise floor of this link is measured about -80 dBm. It implies that the output signal from the PD will be buried into the noise floor when the driven power is too low. Undesirable fluctuations caused by noise can lead to inaccurate data reading, thereby distorting the measurement error.

 

Fig. 6. The measured ACF responses under the RF power of (a) -20 dBm, (b) -40 dBm, (c) -50 dBm, respectively, (d) the power response based on different input RF power, and (e) the measurement error for different input RF power

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To better observe the deviation, the measurement errors under different RF powers are calculated. The results are shown in Fig. 6(e), it can be seen that the measurement error gets worse as the RF power is decreased. When the input RF power is near -55 dBm, the measurement error is about 10°. As for the received signal power lower than -55 dBm, a low noise amplifier can be employed to pre-amplify the signal to a desired level. Or, improve the noise source. For example, adopt a laser with narrow linewidth (<10 kHz) to reduce the relative intensity noise (RIN). Consider an arrayed waveguide grating (AWG) to suppress amplified spontaneous emission (ASE) from the amplifier [19]. Design a shot-noise-limited link to achieve high quality detection results from the PD [20].

Next, whether this link is applicable for a bandwidth signal is also investigated. In this work, a bandwidth signal with the central frequency of 5 GHz, the bandwidth of 1 MHz, and the power of 0 dBm is generated by a vector signal generator (VSG, Agilent E8267C). Its spectrum is shown in Fig. 7(d). Unfortunately, due to the limited experimental condition in our laboratory, only one VSG is available. Thus, we just led the bandwidth signal to DMZMx in the DP-BPSKM to verify the feasibility of AOA measurement in one direction. The link configuration is unchanged. As the measured result shown in Fig. 7(a), the measured data match well with the theoretical curve. Then, the related signal phase is recovered and shown in Fig. 7(b). Interpret it into AOA information through φ_x=πcosα and show the results in Fig. 7(c), good AOA estimation still realized. The measurement error is also calculated. As Fig. 7(e) shows, the measurement error is better than 2.5°. According to the results, we can easily predict that if the bandwidth signal is led to DMZMy, the AOA of bandwidth signal can also be measured. Therefore, it can be concluded that the 2-D AOA estimation for a bandwidth signal is available, which also implies that the third AOA (γ) can be calculated later.

 

Fig. 7. (a) The measured ACF response of a bandwidth signal, (b) the recovered signal phase caused by AOA, (c) the recovered AOA, (d) the spectrum of the bandwidth signal, and (e) the measurement error for the bandwidth signal

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Fig. 8. Power response versus (a) different signal bandwidths and (b) different signal frequencies.

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Noteworthy, power response stability is a key to achieve high quality AOA estimation under different signal frequencies or signal bandwidths. Therefore, we continue the experiment by changing the signal bandwidth and monitoring the power response. It should be mentioned that due to the limited experimental condition, the signal bandwidth of our VSG can only generate a signal with the bandwidth up to 20 MHz. Thus, we fix the signal frequency at 5 GHz, and change the signal bandwidth from 1 MHz to 18 MHz. As shown in Fig. 8(a), under different signal bandwidths, the power response fluctuates. Fortunately, the variation range is lower than 1 dB. Then, focus on the system tunability. In our lab, the operation range of the VSG is DC∼20 GHz. Thus, we try to fix the signal bandwidth at 10 MHz, and change the signal frequency from 1 GHz∼18 GHz. The results are shown in Fig. 1(b). It can be seen that although the power response still changed with the frequency variation, the deviation range is better than 1.5 dB.

4. Discussion

In this section, the comparison results between this work and the state-of-art AOA estimation techniques are given. As is shown in Table 1, to make a single modulator can realize 2-D AOA estimation, an L-sAA is designed, which is unique when comparing with all the mentioned literatures. Based on the 2-D measurement results, the third azimuthal angle γ can be numerically achieved. Thus, we can declare that our method is able to evaluate the 3-D positioning information of the target. Noteworthy, it is the first time to realize the 2-D AOA estimation based on a photonic link. Moreover, when considering Refs. [7], [9–10], [12] and [14], our structure works in QTP, which does not need a high extinction ratio or an optical filter to suppress the unwanted sidebands. Thanks to the DSB modulation, a better sensitivity about -55 dBm can be achieved when comparing with the mentioned literatures. Especially, most of the AOA measurement methods only concentrate on how to map the AOA information to other measurable parameters, but neglect whether the power variation of the received RF signal power may influence the measurement results. In our work, the ACF is introduced to get rid of the received RF signal power (P_in).

Table 1. Comparison with other state-of-art AOA estimation techniques (NA = Not Available) ^a

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In fact, as the theoretical analysis shown in Eq. (3), DC component, fundamental, and second order harmonics are all phase-related items. However, to realize the properties of better sensitivity and signal power irrelevant, a special component should be chosen. When considering the second-order harmonics, the intensity is 2J₁²(m_RF), and that of the fundamental component is 4J₀(m_RF)J₁(m_RF). Their power is calculated and shown in Fig. 9, it can be seen that when the modulation index is very low, the fundamental power is much higher than that of harmonics. It means that under the condition of a low modulation index, the fundamental component can be easier to be detected. This also implies that the fundamental can map a much lower received signal power, which improves the system sensitivity. For the DC component, it consists of two items: 2J₀²(m_RF) and 4J₁²(m_RF)(1+cosφ). Although the DC power can also be detected in a low signal power, it can hardly escape the influence from the signal power variation and therefore distorts the measurement quality. Then, consider the fundamental. Its amplitude is 4J₀(m_RF)J₁(m_RF), it not only occupies the majority power of the carrier, but also easy to construct ACF to make the AOA estimation is amplitude irrelevant. Therefore, the fundamental component is a good choice to reflect the AOA information.

 

Fig. 9. Power responses of the fundamental and second order harmonics.

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Finally, whether the fabrication tolerance of this method will influence the AOA estimation is considered. Usually, as for a modulator, the most important standards for scaling the fabrication process quality are extinction ratio, half-wave voltage, and polarization dependent loss. Firstly, let us consider the extinction ratio. The extinction ratios of the two sub-modulators are measured to be 22 dB and 25 dB, respectively. Even though the extinction ratios are different, it influences little to the system performance. The reason is that the two sub-modulators are biased to work at quadrature transmission point (QTP) in our structure. Therefore, the extinction ratio is not very important, because there is no need to suppress any sidebands. Secondly, focus on the half-wave voltage. According to the measurement results, the half-wave voltages of the two sub-modulators are 3.75 V and 3.53 V respectively. According to the theoretical analysis in Eq. (7), it can be seen that the ACF is related to the half-wave voltages. The ACF responses from the two polarization states will be influenced by the half-wave voltages. Fortunately, the monotonicity of the ACF response is not affected by half-wave voltage. Therefore, the AOA estimation can still be realized in the two polarization states. Thirdly, the polarization-dependent loss is considered. In this case, Eq. (1) can be rewritten as

5. Conclusion

In conclusion, a photonic-based 2-D AOA estimation method is proposed and experimentally demonstrated. Only one modulator and an L-sAA are required in this system, which makes it very simple and meets the potential to be integrated on a mobile platform. The AOA is mapped to the electrical power response. It means we can capture the AOA through an EPM, which simplifies the operation processing. Moreover, the introduction of ACF makes the system able to get rid of received signal power variation. Based on the theoretical analysis and the experimental results, the 2-D AOA is estimated with the range from 18.22° to 90° and the accuracy lower than 1°. Then, the third AOA (γ) is achieved through numerical calculation, and the numerical error is about 2°. The sensitivity is measured to be -55 dBm. This structure can also handle the bandwidth signal, and the related AOA measurement error is about 2.5°. To our knowledge, this is the first time to experimentally verify the possibility of 2-D AOA estimation based on a photonics link.