Enhancing Calibration Precision in MIMO Radar with Initial Parameter Optimization

Abstract

For Advanced Driver Assistance Systems (ADASs), lots of researchers have been constantly researching various devices that can become the eyes of a vehicle. Currently represented devices are LiDAR, camera, and radar. This paper suggests one of the operation processes to study radar, which can be used regardless of climate change or weather, day or night. Thus, we propose a simple and easy calibration method for Multi-Input Multi-Output (MIMO) radar to guarantee performance with initial calibration parameters. Based on a covariance matrix, the modified signals of all channels improve performance, reducing unexpected interferences. Therefore, using the proposed coupling matrix, we can reduce unexpected interference and generate accurately calibrated results. To prove and verify the improvement in our method, a practical experiment is conducted with Frequency-Modulated Continuous-Wave (FMCW) MIMO radar, mounted on an automotive.

1. Introduction

In the area of radar, a lot of researchers have studied to develop various applications to more accurately detect interest targets. Especially in the field of autonomous driving, radar is one of the most powerful technologies for recognizing various targets. The other technologies, which compete with radar, are cameras and LiDAR. In an ideal case, camera and LiDAR show strong performance in detecting multiple targets and the surrounding environment. However, the most fatal weakness is that detection performance rapidly decreases depending on unexpected environmental factors. In other words, since camera and LiDAR are based on ‘light’, it becomes difficult to distinguish and recognize the interested targets during snow/rain, night/day, unexpected weather conditions, and various blockages. It has been previously studied that adverse weather conditions, such as rain and fog, significantly increase light attenuation [1]. This phenomenon critically affects the performance degradation of camera and LiDAR, particularly for Lane Departure Warning Systems, which are designed to prevent accidents caused by driver carelessness [2]. Consequently, many automotive manufacturers are actively striving to enhance sensing accuracy by integrating the advantages of multiple sensors, ensuring reliable performance even under adverse weather conditions. Due to the characteristics of electromagnetic waves, radar can have stronger detection performance even under the interference of these unexpected environmental factors. Nevertheless, the target resolution of radar is still insufficient compared with the performance of camera and LiDAR. Thus, various technologies have been researched to improve the performance of detection and classification using radar.

In this paper, we introduce an improved calibration technique, used to increase the accuracy of radar detection. Not only in the automotive field but also in the small radar system field, radar calibration is an essential process to generate a high performance in not only target detection but also target classification for MIMO radar [3,4,5,6,7,8]. Signals received across multiple channels must preserve accurate phase information to enable precise target localization. This approach underpins high-precision target detection. In the conventional calibration method for MIMO-type radar, the phase and magnitude of the echo signal are measured and calculated to be a fractional form. One of the channels should be chosen for the standard. The first channel is selected as the standard point in a normal MIMO-type radar system. After an accurate calibration process, we can expect the direction and angle of each target in the received signals due to the difference of each phase and magnitude of the MIMO channel [9]. Therefore, using a specific form on a standard signal, the calibration process needs to erase and compensate for the unexpected signals, which interfere with the estimated angle at each channel. In other words, in certain calibration environmental conditions, all signals are compensated as the same phase and magnitude on the standard channel. Depending on calibration performance, it can lead to detection of the accurate location and make it easy to classify the specific shape of the interested target.

In mass production in the small radar industry (automotive, UAV/UAM, cube-SAT, etc.), cost competitiveness necessitates achieving optimal performance at minimal expense. Consequently, RF chips and memory capacity are often limited, making it challenging to execute the calibration process for every chirp signal. Additionally, due to memory constraints, the calibration parameters calculated during initial manufacturing at the factory are conventionally stored in EEPROM. These initial parameters are then used to compensate all MIMO signals for radar detection throughout the radar’s lifespan. In as close to an ideal environment with low interference, we can compensate for the unexpected phase and magnitude difference between each MIMO channel using the initial parameters. However, we cannot always measure the expected reference signal with a stable and low-noise environment. And also, the reference signal can be changed according to various environmental conditions. In a situation with unexpected interference during the operation of radar, it becomes difficult to secure the reliability of the calibration and causes inaccurate results such as errors in target detection and target classification, etc. In recent research, there are various calibration methods to compensate for the unexpected interference [3,4,5,6,7,8] using saved parameters. A method of obtaining high-resolution-quality radar images by adjusting the calibration values of the received MIMO structure has also been studied [10,11]. However, it is optimized for Synthetic Aperture Radar (SAR) image extraction, and research on applying it to real-time vehicle radar has not yet been conducted.

In this paper, comparing other calibration studies, we propose an easy and simple calibration method with a covariance matrix of MIMO channels and design to preserve accurate phase information, specifically targeting real-time MIMO FMCW radar systems such as automotive applications. The proposed technique can compensate for every signal with initial calibration parameters, even though the received signal is not matched with initial calibration parameters due to unexpected environmental conditions. It leads to the least disturbance and derives accurate calibration results even in adverse conditions outside the radar. In other words, the proposed process diversifies the matching point of calibration for the MIMO radar based on the coupling matrix method.

2. Improved Calibration Method

For the proposed process, we need to introduce the conventional calibration method. In this paper, we utilize MIMO FMCW radar, which is designed with four channels for receiving (Rx) and three channels for transmitting (Tx), respectively, as shown in Figure 1. A total of 12 channels can be used to detect the interested target with the beamforming signal processing. In addition, 12 channels are commonly used in radar mass production in the automotive market.

2.1. Conventional Calibration Method for MIMO Radar

In an un-echoic chamber, we can generate the reference signals for the calibration method and assume that the reference signal is measured with a corner reflector, which is located at 0-degrees (calibration point) of the radar. The reason is that the main beam of the antenna is assumed to be in the ideal center. According to the beam pattern of an antenna, the location of the calibration point can be changed. From the received signals at the 0-degree point, we can calculate the calibration parameters and operate an accurate compensation process for each channel. Based on the calibration data, every transmitted signal in MIMO radar is able to estimate the accurate location of each target in the received signals. It leads to increasing the overall performance of MIMO radar. However, when we receive the reference signal in unexpected conditions, it is hard to analyze the received signals as accurate targets. Thus, it is an important task before radar signal processing. The conventional calibration procedure for MIMO channels is as follows:

(1)

Measurement for ideal signals: measuring each signal of each channel in an un-echoic chamber.

(2)

Averaging: applying the averaging technique with all the stacked data.

(3)

Estimating fractional term: estimating the fractional term of magnitude and phase to compensate for the raw data.

(4)

Extracting final calibration function: define the final calibration function of each channel with the estimated magnitude and phase results.

Based on the measured signal in an un-echoic chamber, we arrange all the data of each channel according to the available angle of the MIMO radar. The reflected signal can be analyzed with a virtual array MIMO system. Nth Tx and Mth Rx antennas generate a total $N\times M$ channels, and it can be the same as the extended Rx multiple channels. Therefore, we can define the mathematical signal model for the received signals with a range-compressed signal [9] (in FMCW) as shown below:

$$\begin{gathered} S_{r,id}=\left[s_{r1}{s}_{r2}{s}_{r3}\cdots s_{r\left(k-2\right)}{s}_{r\left(k-1\right)}{s}_{r\left(k\right)}\right] \\ \mathrm{with}{S}_{r,id}\left(R,m\right)=aW(R-R_t)e^{j2\pi {\displaystyle \frac{f_0}{c_0}}{y}_{RX}(m)\mathrm{s}\mathrm{i}\mathrm{n}({\theta }_t)} \end{gathered}$$

(1)

where subscript r means the received signal; a indicates the amplitude of the received signal; W indicates the window function; f₀ is the center frequency of the chirp pulse signal; and c₀ is the speed of light. As described in the above equation, it is necessary to select one channel, which can be used as a reference among the signals received in all channels. Based on the signal information of the selected reference channel, we start to calculate the calibration parameters. The calibration process aims to have the same phase and magnitude of all signals in MIMO channels when the radar receives the reflected signals from the same target. Before the calibration process, even if a signal is received from the same target, the signals of each channel can have a different phase and magnitude depending on unexpected conditions, such as MIMO antenna position error, circuit length error, etc. Thus, these phase and magnitude errors cause deterioration of the target resolution even though the signal is reflected and received from the same target. In general, the conventional calibration sets the first channel for standard reference with the phase and magnitude terms. The phase and magnitude of each channel are normalized to be shown as the first channel. Equations (2) and (3) indicate the compensation factor, arranged as a first channel signal.

$$\angle S_{cal}=[1{\displaystyle \frac{\angle s_{r1}}{\angle s_{r2}}}{\displaystyle \frac{\angle s_{r1}}{\angle s_{r3}}}\cdots {\displaystyle \frac{\angle s_{r1}}{\angle s_{r(k-2)}}}{\displaystyle \frac{\angle s_{r1}}{\angle s_{r(k-1)}}}{\displaystyle \frac{\angle s_{r1}}{\angle s_{r\left(k\right)}}}]$$

(2)

$$\left|S_{cal}\right|=[1{\displaystyle \frac{\left|s_{r1}\right|}{\left|s_{r2}\right|}}{\displaystyle \frac{\left|s_{r1}\right|}{\left|s_{r3}\right|}}\cdots {\displaystyle \frac{\left|s_{r1}\right|}{\left|s_{r(k-2)}\right|}}{\displaystyle \frac{\left|s_{r1}\right|}{\left|s_{r(k-1)}\right|}}{\displaystyle \frac{\left|s_{r1}\right|}{\left|s_{r\left(k\right)}\right|}}]$$

(3)

In all channels of MIMO, Equation (2) represents the compensation matrix matching with the phase of the first channel, and Equation (3) represents the compensation matrix matching with the magnitude of the first channel. To increase the accuracy of the above compensation matrices, several chirp pulses are collected from FMCW Rx signals, and the average values thereof are defined as expected calibration factors.

$$\begin{gathered} \angle s_{r\left(m\right)}={\displaystyle \frac{1}{l}}\sum _{n=1}\angle s_r(m,n) \\ \left|s_{r\left(m\right)}\right|={\displaystyle \frac{1}{l}}\sum _{n=1}\left|s_r(m,n)\right| \end{gathered}$$

(4)

where m is channel number; k is the maximum channel number ($N\times M$); and l is the overall number of accumulated signals for averaging. The calibration factors of the phase and magnitude, estimated as the fractional form, can be synthesized and extracted in the form of a complex signal. Therefore, the following equation is finally defined as a general calibration parameter.

By using the extracted calibration parameter, we can receive and calculate the signals of all channels with the expected phase and magnitude when detecting the interested target in MIMO radar.

$$S_{cal}=\left|S_{cal}\right|e^{1i(\angle S_{cal})}$$

(5)

In order to not only match the target into the expected location but also secure the expected resolution of the target, the calibration process is essential for MIMO channel radar. However, as mentioned before, when the intensity of the unexpected interference increases, it is hard to expect the desired result with the initial calibration parameters measured in an ideal environment. Therefore, this paper introduces a method of estimating calibration parameters with a simplified process, using a coupling matrix, rather than adding a complex process to derive a more accurate calibration factor.

2.2. Calibration Method with Proposed Coupling Matrix

As mentioned in the previous Section 2.1, we try to improve the conventional calibration process based on the initial calibration parameters. It has the advantage of being applicable to existing processes. In other words, it is simple to upgrade the previous calibration method with low cost and low complexity. Based on the calibration parameters estimated in the existing method, a coupling matrix for every chirp can be derived, and we can generate more accurate calibration parameters. Thus, we introduce the overall proposed algorithm as shown in Figure 2b.

(1)

Measurement for ideal signals: measuring each signal of each channel in an un-echoic chamber.

(2)

Averaging: applying the averaging technique with all the stacked data.

(3)

Estimating fractional term: estimating the fractional term of magnitude and phase to compensate for the raw data.

(4)

Extracting final calibration function: define the final calibration function of each channel with the estimated magnitude and phase results.

(5)

Applying the coupling matrix with the loop-back process: extracting the coupling matrix from the conventional calibration model and finding an adequate final model.

As the unexpected signal becomes stronger, the accuracy of calibration parameters can be decreased. Figure 1 illustrates various interference in MIMO radar. In the case of high interference, the standard signal (first channel) can be contaminated before proceeding with the existing calibration process. It causes unexpected errors in all radar signals. Therefore, to increase the accuracy of the calibration results, it is important to modify the calibration parameters according to the various conditions. For example, the radar detection process generates the wrong Direction of Angle (DOA) of each target because the initial signal, calibrated by the inaccurate reference, indicates the wrong direction. Moreover, in Synthetic Aperture Radar (SAR) processing, the interested targets can be blurred and focused on an unwanted area. It leads to reducing the overall quality of the final image. Therefore, in this chapter, we use the covariance matrix and re-calibrated process with a simple and easy method considering the practical situation. The proposed covariance matrix between the received signal and the previously calibrated signal calculates the modified calibration function. And we define its meaning. The proposed matrix is estimated from each mutual signal between each channel. In the previous section, the conventional calibrated signal can be defined as follows:

$$S_{r,cal}=S_{cal}{S}_{r,id}$$

(6)

Based on the above equation, all signals of the MIMO channel are unified as the first channel, considering the phase and magnitude difference. In the existing calibration method, the desired final signal $S_{r,cal}\left(r\right)$ is extracted by multiplying with Equation (5). For explaining the method, Equation (5) is defined as matrix ‘C’. The signal model, defined in (1), shows the standard form, which indicates the received signal model in each channel. The standard form does not consider the interference, using a covariance matrix between channels. Therefore, we can introduce a complex-valued $NM\times NM$ coupling matrix (NM is the total channel number and equal to ‘k’ in Equation (6)) with an angle-independent and linear model:

$$\begin{gathered} S_{r,cal}\left(r\right)=C{S}_r\left(r\right) \\ C=\left[c_1{c}_2{c}_3\cdots c_{k-2}{c}_{k-1}{c}_k\right]=[s_{cal1}{s}_{cal2}{s}_{cal3}\cdots s_{cal(k-2)}{s}_{cal(k-1)}{s}_{cal\left(k\right)}] \end{gathered}$$

(7)

Based on the initial calibration parameters, the covariance matrix model can be re-generated for the received MIMO signals, received every time. To analyze the proposed coupling matrix, we use the originally defined signal, which is calibrated into the standard channel. As shown below, the calibrated signals detect the target (CR, Corner Reflector) with the same phase and amplitude in the initial case:

$$S_{r,cal}\left(r\right)=\left(\begin{array}{c}{s}_{cal1}\\ s_{cal2}\\ \begin{array}{c}{s}_{cal3}\\ ⋮\\ \begin{array}{c}{s}_{cal\left(k-2\right)}\\ s_{cal\left(k-1\right)}\\ s_{cal\left(k\right)}\end{array}\end{array}\end{array}\right)\times \left(\begin{array}{c}{S}_r\left(1\right)\\ S_r\left(2\right)\\ \begin{array}{c}{S}_r\left(3\right)\\ ⋮\\ \begin{array}{c}{S}_r\left(k-2\right)\\ S_r\left(k-1\right)\\ S_r\left(k\right)\end{array}\end{array}\end{array}\right)=\left(\begin{array}{c}{s_{cal1}S}_r\left(1\right)\\ s_{cal2}{S}_r\left(2\right)\\ \begin{array}{c}{s_{cal3}S}_r\left(3\right)\\ ⋮\\ \begin{array}{c}{s}_{cal\left(k-2\right)}{S}_r(k-2)\\ {s_{cal\left(k-1\right)}S}_r(k-1)\\ {s_{cal\left(k\right)}S}_r\left(k\right)\end{array}\end{array}\end{array}\right)$$

(8)

$$\begin{array}{l}CovarianceMatrix={cov\left(T_{ij}\right)}_{k\times k}=cov\left[S_{r,cal}\left(r_i\right),S_{r,cal}\left(r_j\right)\right]\\ =\left(\begin{array}{c}{c}_1{S}_{\mathrm{1,1}}\\ c_2{S}_{\mathrm{1,2}}\\ \begin{array}{c}\begin{array}{c}{c}_3{S}_{\mathrm{1,3}}\\ ⋮\end{array}\\ \begin{array}{c}{c}_{k-2}{S}_{1,k-2}\\ c_{k-1}{S}_{1,k-1}\\ c_k{S}_{1,k}\end{array}\end{array}\end{array}\right)\times {\left(\begin{array}{cc}{c}_1{S}_{\mathrm{2,1}}& \begin{array}{ccc}{c}_2{S}_{\mathrm{2,2}}& \cdots & \begin{array}{cc}{c}_{k-1}{S}_{2,k-1}& c_k{S}_{2,k}\end{array}\end{array}\end{array}\right)}^T\\ =\left(\begin{array}{ccc}\begin{array}{cc}{\left|c_1\right|}^2{S}_{\mathrm{1,1}}{S}_{\mathrm{2,1}}^{\ast }& c_1{c}_2^{\ast }{S}_{\mathrm{1,1}}{S}_{\mathrm{2,2}}^{\ast }\\ c_2{c}_1^{\ast }{S}_{\mathrm{1,2}}{S}_{\mathrm{2,1}}^{\ast }& {\left|c_2\right|}^2{S}_{\mathrm{1,2}}{S}_{\mathrm{2,2}}^{\ast }\end{array}& \cdots & \begin{array}{cc}{c}_1{c}_{k-1}^{\ast }{S}_{\mathrm{1,1}}{S}_{2,k-1}^{\ast }& c_1{c}_k^{\ast }{S}_{\mathrm{1,1}}{S}_{2,k}^{\ast }\\ c_2{c}_{k-1}^{\ast }{S}_{\mathrm{1,2}}{S}_{2,k-1}^{\ast }& c_2{c}_k^{\ast }{S}_{\mathrm{1,2}}{S}_{2,k}^{\ast }\end{array}\\ ⋮& \ddots & ⋮\\ \begin{array}{cc}{c}_{k-1}{c}_1^{\ast }{S}_{1,k-1}{S}_{\mathrm{2,1}}^{\ast }& c_{k-1}{c}_2^{\ast }{S}_{1,k-1}{S}_{\mathrm{2,2}}^{\ast }\\ c_k{c}_1^{\ast }{S}_{1,k}{S}_{\mathrm{2,1}}^{\ast }& c_k{c}_2^{\ast }{S}_{1,k}{S}_{\mathrm{2,2}}^{\ast }\end{array}& \cdots & \begin{array}{cc}{\left|c_{k-1}\right|}^2{S}_{1,k-1}{S}_{2,k-1}^{\ast }& c_{k-1}{c}_k^{\ast }{S}_{1,k-1}{S}_{2,k}^{\ast }\\ c_k{c}_{k-1}^{\ast }{S}_{1,k}{S}_{2,k-1}^{\ast }& {\left|c_k\right|}^2{S}_{1,k}{S}_{2,k}^{\ast }\end{array}\end{array}\right)\end{array}$$

(9)

When the calibrated signal is interfered with by an increase in the unexpected signals, the direction points of each channel also deviate in unexpected directions. To accurately analyze this phenomenon, we first apply the covariance matrix to our proposed process. The covariance matrix generates a square matrix and informs the covariance values between the pairs of each element. Using the calculated matrix, we can find the related tendency between each element, which can be seen as random variance. And also, it indicates the dispersion value and is easy to analyze more accurately. In other words, it helps to understand the interaction parameters between each channel. Therefore, for the first step, the covariance matrix is calculated with the received signal and initial calibrated parameters as shown in Equation (9). It is composed of a k $\times$ k square matrix and shows the correlation of each channel that has been compensated by the initial values. In the next step, the initial calibrated signal can be analyzed with vector matching, and it leads to concentrating the interest on the expected signals even in the interference situation. The accuracy of calibration can be further improved by applying the vector product between the proposed covariance matrix and the initial calibrated signals of all channels. The vector product amplifies two signals with the same tendency, and simultaneously, weakens two signals, which have a different tendency, compared to the previous value. Based on the initial calibration parameters, the calculation results of the covariance matrix and the received signals are as follows:

$$cov{\left(T_{ij}\right)}_{k\times k}\times \left(\begin{array}{c}{c_{1}S}_{\mathrm{2,1}}\\ c_2{S}_{\mathrm{2,2}}\\ \begin{array}{c}{c_{3}S}_{\mathrm{2,3}}\\ ⋮\\ \begin{array}{c}{c}_{k-2}{S}_{2,k-2}\\ {c_{k-1}S}_{2,k-1}\\ {c_{k}S}_{2,k}\end{array}\end{array}\end{array}\right)=\left(\begin{array}{c}\begin{array}{c}{\mathit{c}}_1{\mathit{S}}_{1,1}\left({\left|{\mathit{c}}_1\right|}^2{\left|{\mathit{S}}_{\mathrm{2,1}}\right|}^2+{\left|{\mathit{c}}_2\right|}^2{\left|{\mathit{S}}_{\mathrm{2,2}}\right|}^2+\cdots +{\left|{\mathit{c}}_{11}\right|}^2{\left|{\mathit{S}}_{\mathrm{2,11}}\right|}^2+{\left|{\mathit{c}}_{12}\right|}^2{\left|{\mathit{S}}_{\mathrm{2,12}}\right|}^2\right)\\ {\mathit{c}}_2{\mathit{S}}_{1,2}\left({\left|{\mathit{c}}_1\right|}^2{\left|{\mathit{S}}_{\mathrm{2,1}}\right|}^2+{\left|{\mathit{c}}_2\right|}^2{\left|{\mathit{S}}_{\mathrm{2,2}}\right|}^2+\cdots +{\left|{\mathit{c}}_{11}\right|}^2{\left|{\mathit{S}}_{\mathrm{2,11}}\right|}^2+{\left|{\mathit{c}}_{12}\right|}^2{\left|{\mathit{S}}_{\mathrm{2,12}}\right|}^2\right)\\ ⋮\end{array}\\ ⋮\\ \begin{array}{c}{\mathit{c}}_{11}{\mathit{S}}_{1,11}\left({\left|{\mathit{c}}_1\right|}^2{\left|{\mathit{S}}_{\mathrm{2,1}}\right|}^2+{\left|{\mathit{c}}_2\right|}^2{\left|{\mathit{S}}_{\mathrm{2,2}}\right|}^2+\cdots +{\left|{\mathit{c}}_{11}\right|}^2{\left|{\mathit{S}}_{\mathrm{2,11}}\right|}^2+{\left|{\mathit{c}}_{12}\right|}^2{\left|{\mathit{S}}_{\mathrm{2,12}}\right|}^2\right)\\ {\mathit{c}}_{12}{\mathit{S}}_{1,12}\left({\left|{\mathit{c}}_1\right|}^2{\left|{\mathit{S}}_{\mathrm{2,1}}\right|}^2+{\left|{\mathit{c}}_2\right|}^2{\left|{\mathit{S}}_{\mathrm{2,2}}\right|}^2+\cdots +{\left|{\mathit{c}}_{11}\right|}^2{\left|{\mathit{S}}_{\mathrm{2,11}}\right|}^2+{\left|{\mathit{c}}_{12}\right|}^2{\left|{\mathit{S}}_{\mathrm{2,12}}\right|}^2\right)\end{array}\end{array}\right)$$

(10)

Based on the above results, it can be confirmed that the calculated matrix is constructed as the form, which is combined with the compensation values for each channel and the initial calibration signals. Moreover, it can be simplified as shown below:

$$S_{r,final\_cal}=\left(\begin{array}{c}{c}_1{S}_{1,1}{\displaystyle \sum _{m=1}}{A}_1{A}_n{e}^{j\left({\theta }_n-{\theta }_0\right)}\\ \begin{array}{c}{c}_2{S}_{1,2}{\displaystyle \sum _{m=1}}{A}_1{A}_n{e}^{j\left({\theta }_n-{\theta }_0\right)}\\ ⋮\\ c_{11}{S}_{1,11}{\displaystyle \sum _{m=1}}{A}_1{A}_n{e}^{j\left({\theta }_n-{\theta }_0\right)}\end{array}\\ c_{11}{S}_{1,12}{\displaystyle \sum _{m=1}}{A}_1{A}_n{e}^{j\left({\theta }_n-{\theta }_0\right)}\end{array}\right)=A_1{e}^{-j{\theta }_0}\sum _{n=1}^{12}{\displaystyle \frac{B_n^2}{A_n}}{e}^{j{\theta }_n}\left(\begin{array}{c}\begin{array}{c}{c}_1{S}_{1,1}\\ c_2{S}_{1,2}\\ ⋮\end{array}\\ ⋮\\ \begin{array}{c}{c}_{11}{S}_{1,11}\\ c_{12}{S}_{1,12}\end{array}\end{array}\right)$$

(11)

where B_n is the amplitude and ${\theta }_n$ is phase of the received signal. $S_{r,final\_cal}$ indicates the calibrated results by the proposed technique. In Equation (11), the phases that affect each channel are grouped into a common variable, and only the existing initial calibration phase remains. As shown in Figure 3, in this proposed method, the modified calibration point can be changed to the same form as the initial calibration point. The final magnitude must be cubed because the signal is multiplied three times by our proposed calculation. For each channel, the magnitude is amplified to a calibrated signal. And the magnitude deviation of each channel signal is minimized.

$$\left|S_{r,result}\right|=\sqrt[3]{\left|S_{r,final\_cal}\right|}$$

(12)

That is, when calibrating with the standard channel at a specific angle, it means the reference point can be changed slightly depending on the environment in which signals are transmitted and received. As an aspect of the calibrated phase, it indicates the received signals of all channels can be arranged in the calibration standard point (0-degree). The proposed technique re-generates calibration parameters to improve detection performance, using the covariance matrix of the received signals and the initial calibration parameters stored in the memory. Thus, our technique can reduce the effect of the current unexpected conditions in the signal processing of radar detection. Through the proposed method, MIMO radars can use existing calibration values without having to calibrate for every transmitted pulse. It is simple and useful for solving environmental conditions because we cannot expect the phase direction of the interference. As mentioned in the previous section, the only saved calibration parameters cannot be adequate to compensate for each signal of all channels, according to various environmental conditions. The results of the proposed technique are better than those of conventional calibration signal processing. In the next section, to verify the performance of the proposed method, we introduce a calibration experiment and show the improved results.

3. Experiment and Results

To verify the proposed calibration method, we designed the FMCW MIMO radar system, which is conventionally used for the front radar and corner radar of automobiles. The experiment was performed with a corner reflector in an anechoic chamber. And also, we operated the designed radar, combined with a 360-degree rotator to monitor the signals in all angle directions. In

Table 1. FMCW MIMO radar system specification.

System Parameter	Value
Center Frequency Range	70–80 GHz
Chirp Signal Bandwidth	200–500 MHz
PRF	3000–10,000 Hz
Chirp Duration	100 us–0.5 ms
Sampling Rate	<10 Mbps
Total Channel	3 Tx/4 Rx (12 channels)

, the specifications of the FMCW MIMO radar system are introduced within the following system specification range. In other words, our proposed method is applicable to various radars with multi-channels.

The radar for the test was mounted on a stable motor, which can rotate from −180° to 180°. In this experiment, we rotated the radar from −70° to 70° according to two types of beam patterns. The first type has one peak point, and the second type has two peak points for the main beam. Figure 4 shows an illustration of the experiment environment condition for verifying calibration performance. The received data in 12 MIMO channels were processed through the conventional and proposed calibration algorithms in Figure 2a,b, respectively. Based on experiment conditions in Figure 4a,b shows the results, which indicate the phase difference along the antenna direction from −70° to 70°. By using a phase-monopulse method [12], the phase error of the MIMO channel should appear linearly depending on the measurement angle. As can be seen in Figure 4a, the existing calibration method shows the phase errors. On the other hand, as shown in Figure 4b, the proposed method shows results in which the error was properly compensated. Moreover, we measured the beam pattern of each channel and the received magnitude and phase of signals at each angle. We found an improvement in the processed results in Figure 5 and Figure 6. In Figure 5a, it shows the noise level from −70° to 70° of the antenna when the target is located at around edge in the field of view (FOV). In the measured range of angle, we found the noise level is decreased compared to the conventional method. Because the gain at around edge of the antenna can be low, the detection probability of the expected target can be increased. Decreasing the unexpected noise interference is one of the important issues. In Figure 5b, when the target is located at the center of the FOV of the antenna, the side lobe level can be reduced by 2 dB more than the conventional method. The power decrease of the second lobe is important to detect the expected target because some of the side lobe, which has a magnitude high enough to interfere with the main beam, can be detected as a ghost target. As shown in Figure 6, there are the results of analyzing the two types of antenna beam patterns. The channel difference of each pattern is noticeably reduced compared to the conventional correction method. It means that the probability of information error can be reduced between channels for targets detected by all channels.

In summary,

Table 2. Processing performance comparison.

	Noise Level		Channel Difference		Processing Complexity
	Front Radar	Corner Radar	Front Radar	Corner Radar
The conventional method	-	-	≥1 dB	≥1 dB	Low
The proposed method	−6 dB	−2 dB	≥0.3 dB	≥1 dB	Low

defines the performance of each method. The proposed method has a lower noise level not only at the edge of the antenna but also in the center of the antenna. Furthermore, we can reduce the difference between each channel compared to the conventional method. The proposed method is a simple and easy-to-handle calibration process, and we can reduce the signal processing complexity for MIMO radar.

4. Conclusions

In this paper, we propose an easy and simple method for how to calibrate the received signals in MIMO channel radar. In the small radar (automotive, UAV/UAM, cube-SAT, etc.) industry, using a limited memory and an RF chip with limited performance, the proposed calibration method can be important. In a situation where calibration values cannot be extracted in real-time, this method is one of the ideas that can improve detection performance. Based on the proposed signal processing, it can generate an improved calibration result compared to the conventional method, and it can be applied for real-time processing. To introduce the proposed method, we extract the fractional terms of each channel from the received data and apply them to the covariance matrix with a loop-back process. Thus, it is easy to handle the calibration process and generate only a slight difference in the magnitude and phase of each signal in MIMO channels. In addition, our proposed method secures low complexity in terms of computational amount and accurate calibration results with a low noise level. Furthermore, we can verify our method using a real experiment with main coverage of the antenna. In future work, the proposed calibration method can be applied to an outdoor automobile platform because it has low complexity and improved performance compared to the conventional method. It can be operated for real-time processing in an autonomous driving assistant system (ADAS).