A Modified Sequential Multiplexed Method for Detecting Airborne and Sea Targets With Over-the-Horizon Radar

Phased array over-the-horizon (OTH) radar usually needs to detect sea target and airborne target in different directions. Conventionally, the sea target and airborne target are detected sequentially with the coherent integration completely accomplished for each of them. However, the long coherent integration time (CIT) required by the sea target makes the time interval between two airborne target detections too long, which is not conducive to tracking airborne target. To overcome this problem, this paper proposes a new timeframe multiplexing scheme, in which several short-time detections of airborne target are inserted into a long CIT of sea target detection. The proposed scheme seeks to improve the detection frequency of airborne target while ensuring the detection performance of two types of target. However, due to the insertion of airborne target detection, the echo from sea surface is received discontinuously which means that the coherent integration of sea target is incomplete. To tackle it, a recovery algorithm based on the Hankel structured matrix is introduced, which recovers the slow-time domain signal of each range bin and thereby guarantees the detection performance of sea target not damaged. Numerical simulations prove the effectiveness of the proposed algorithm for signal recovery, and also verify that the proposed operating scheme has a shorter time interval for airborne target detection, while the detection performance of two targets are well guaranteed.


I. INTRODUCTION
High-frequency sky-wave over-the-horizon (OTH) radar can monitor a broad area via ionospheric reflection [1]- [3]. It is a very common requirement for OTH radar to monitor the sea surface and airspace simultaneously, and generally the aircraft and ship are most concerned by the radar for early warning. For multi-target detection, one of the methods is to form a multi-beam transmit beam-pattern to achieve concurrent detection [4], [5]. However, to detect aircraft in airspace and to detect ship on sea surface, the pulse repetition interval (PRI) of the transmit waveform and the coherent integration time (CIT) are different, due to the different characteristics of environments and targets [6]- [8]. Therefore, the concurrent detection, which detects different targets using the same configuration of PRI and CIT, is not suitable in The associate editor coordinating the review of this manuscript and approving it for publication was Wei Wang . this scenario. That is to say, the OTH radar has to scan the sea surface and airspace alternatively, and therefore the detections to different targets are processed sequentially.
To perform sequential detection, the radar conventionally finishes a complete coherent integration of sea target detection, before changing the beamforming direction for airborne target detection. Considering that a long CIT of 30sec-100sec is usually required for sea target detection to achieve a high Doppler resolution to separate the sea target from the strong sea clutter, there will be a long time interval between two adjacent detections of airborne target. This is undesirable since the airborne target usually move at high speed and long detection interval can cause trouble for tracking. To overcome this shortage, some works resort to shorten the CIT of sea target detection [9]- [12], with the modern spectrum estimation method [9], [10] or high accuracy parameter estimation method [11] used to compensate the Doppler loss caused by the short CIT. However, due to the short CIT, the information contained in the echo is limited, and the performance of the above estimation methods can be affected by many factors. For example, the time-varying characteristics of the ionosphere.
In this paper, we engage a novel operating scheme for OTH radar simultaneously detecting the sea target and airborne target. To reduce the time interval of airborne target detection, we are not committed to shortening the CIT of sea target detection within the framework of conventional scheme, but attempt to insert several airborne target detections into a long CIT of sea target detection. However, due to the insertion of airborne target detection, the coherent integration of sea target detection is incomplete, i.e., several pulses in sea surface echo are missed. Fortunately, the coherence of sea surface echo can be maintained as long as we can recover the data in those missing pulses.
Assume that M s pulses are received in a CIT of ship detection. After pulse compression, the sea surface echo of M s pulses from a certain range bin is compressed into an M s ×1 vector, which is denoted as r and is referred as slow-time domain signal [13,Section 4.2.1]. Due to the absence of some pulses, the corresponding elements in r are vacant. Hence, in order to maintain the detection performance of ship, the key problem is to recover the missing element in r. Inspired by the matrix recovery techniques [13]- [17], we first organize r into a Hankel matrix, which can be proven to be low rank [18]. Then, a low-rank matrix recovery problem is proposed, which involves Hankel structure constraint to ensure that its solution is also a Hankel matrix. Thereby, a vector can be extracted from the obtained matrix, which is regarded as the recovered signal of r. Also, an iterative algorithm is developed, which extends the Inexact Augmented Lagrange Multiplier (IALM) [19] method and is capable of solving the proposed problem with Hankel structure constraint.
The main contents and contributions of this article are summarized as follows.
(1) A new operating scheme is developed for OTH radar to detect airborne target and sea target in different directions. The proposed schemes can improve the data update rate of airborne target detection, while maintaining the detection performance of two types of target. In addition, it can be implemented on the current hardware equipment, with mature technology, i.e., digital beamforming.
(2) An iterative algorithm is developed to recover the incomplete slow-time domain signal of sea surface echo (i.e., r). The proposed algorithm extends the IALM method to involve Hankel constraint and recovers r based on the basis of Hankel matrix.
(3) Simulation experiments show that the proposed algorithm can effectively recover the incomplete slow-time domain signal of sea surface. Moreover, the sea target detection performance based on the recovered data is evaluated, regarding the main-to-side lobe ratio and peak-to-average ratio after clutter suppression filter.
The remainder of this paper is organized as follows. A brief introduction to the conventional sequential detection scheme is given in Sec.II. The proposed operating scheme is introduced in Sec.III and Sec.IV. Numerical simulations are illustrated in Sec.IV. And the conclusion is drawn in Sec.V.
Notations: Throughout this paper, the italic letters indicate scalars, the bold italic lowercase letters are used to represent vectors, and bold italic uppercase letters signify matrices. N ×N complex space is denoted by C N ×N . {·} H , {·} * and {·} T denote the operations of complex conjugate transpose, conjugate, and transpose, respectively. tr(·) represents the matrix trace and A, B is the inner product of A and B. · F is the Frobenius norm and · * denotes the nuclear norm of a matrix. svd(·) means the singular value decomposition. x[m] denotes the m-th element of the vector x and [X] i,j denotes the (i, j)-th element of the matrix X. I n represents a n×n identity matrix and 0 n 1 ×n 2 represents a n 1 ×n 2 matrix with all elements equal to zero.

II. CONVENTIONAL OPERATING SCHEME AND SIGNAL MODEL
A. CONVENTIONAL OPERATING SCHEME Denoting the PRI as T and the number of pulses within a CIT as M , the transmitted waveform can be expressed as where f 0 is the operating frequency. x 0 (t) is baseband transmitted pulse, which should have good pulse compression property, e.g., the linear frequency modulation (LFM) waveform. However, when the radar detects different types of targets, the settings of M and T are different. To ease the discussion, Table 1 details the definitions of the parameters involved in the following discussion. The conventional operating scheme is illustrated in Fig.1. VOLUME 8, 2020 As shown in the figure, the radar first focuses on the direction θ 1 to detect sea target, consuming CIT (s) = M s T s for the coherent integration. Then, the radar changes the beamforming direction to θ 2 and spends CIT (a) = M a T a for coherent integration.

B. SIGNAL MODEL FOR CONVENTIONAL SCHEME
In this section, we briefly illustrate the formulations of received signal from sea surface for the conventional scheme. For details of related theory and formula derivation, interested readers can refer to [20].
At the receiving end, the carrier frequency of the echo (including M s pulses) is first removed. Then, after beamforming in direction θ 1 , we obtain an M s N ×1 vector, where N is the number of samples in one PRI. The M s N ×1 vector is next processed by matched filter and phase compensation. After that, echoes with different time-delays (or in other word, from different range bins) can be separated and each of them is compressed into an M s ×1 vector. As a consequence, we can arrange a matrix D s = [s 1 , . . . ,s n , . . . ,s N ] ∈C M s ×N . In matrix D s , the n-th column vector (s n ) is called as the slow-time domain signal of the n-th range bin [20,Section 4.2]. More specifically, s n is the pulse compression result of the echo from the n-th range bin, and the m-th element in s n (i.e., s n [m]) represents the data received from n-th range bin in m-th pulse. Further signal processing such as clutter suppression and target detection will be performed on each s n .
In the following, we omit the subscript n of s n , using s to broadly represent the slow-time domain signal of a range bin. Depending on whether the target exists, s can be formulated as follows where u∈C M s ×1 and c∈C M s ×1 are respectively the slow-time domain signals of the target echo and the sea clutter echo. n∈C M s ×1 is the slow-time domain signal of environmental noise. Usually, the noise can be modeled as white Gaussian noise with zero mean. In the following, the formulations of u and c are derived, based on the several general assumptions [21]: (1) In radar illuminating region, there is a sea target moving at a constant speed. That is, its Doppler frequency is a constant and the its Doppler rate is zero. In addition, its speed is relatively slow, so that its movement dose not cross the range bin during a CIT (s) .
(3) The ionospheric phase contamination can be completely corrected by phase compensation.
(4) The sea state is unchanged during a CIT (s) . Generally, for a target moving at a constant speed, its echo (in baseband) can be modeled as follows [22], [23]: where b is a complex coefficient associating with the propagation loss and initial phase. τ is time delay and f d is the Doppler frequency of the target. φ is the phase shift due to ionospheric phase contamination. After pulse compression and phase compensation, the corresponding slow-time domain signal (i.e., u), can be equivalently expressed as: The detailed derivation from (3) to (4) can refer to [20, Equations (4.36)-(4.42)]. Sea clutter is composed of echoes backscattered by a large number of ocean waves. According to Bragg scattering hypothesis [24], [25], there are two ocean waves moving with specific direction and speed can strongly scatter the radar wave, composing the main component of the sea clutter. Based on this, the sea clutter echo can be formulated as: where f B = √ gf 0 /π c is called as Bragg frequency. yc (t) stands for the other components in y c (t). a 1 , a 2 and a 3 are the complex coefficients, with a 3 much smaller than a 1 and a 2 . Based on (5) and following with [26, Equations (6)-(8)], the slow-time domain signal c can be given as follows: wherec ∈ C M s ×1 is the slow-time domain signal of yc (t).

III. PROPOSED OPERATING SCHEME AND SIGNAL MODEL
A. PROPOSED OPERATING SCHEME According to the above discussion, the conventional scheme takes the time of CIT (a) + CIT (s) to sequentially complete a sea target detection and an airborne target detection. In this section, we try to develop a new operation scheme for OTH radar, which has also been illustrated in Fig.1. Three key points of the proposed scheme are concludes as follows.
(1) L detections of airborne target are inserted into a coherent detection of sea target. By doing so, the proposed scheme seeks to complete one detection to sea target and L times of detection to airborne target within the time of CIT (s) .
(2) Comparing with the traditional scheme, the time interval for radar detecting airborne target is significantly reduced. This is very attractive, since the airborne target usually moves fast and a long-time interval between two detections is not suitable for tracking.
(3) In the proposed scheme, each inserted airborne target detection has a complete coherent integration, so there is no impact on the airborne target detection performance. However, the coherent integration of the sea surface echo is interrupted. More specifically, each time the airborne target detection is inserted, the radar will miss the sea surface echo of P pulses, where P = CIT (a) /T s . We denote that M a , T a and T s can be carefully selected to satisfy that P is an integer.
Based on the above discussion, it is necessary to tackle the incomplete coherent integration of the sea surface echo so that the sea target detection performance is not lost. In the following, we first develop the signal model for the case of incomplete coherent integration. Then, we introduce how to complete the missing data.

B. SIGNAL MODEL FOR PROPOSED SCHEME
Now, we consider the received signal from sea surface for the proposed scheme. As we have discussed, the radar dose not have a complete echo signal of M s pulses now. After pulse compression and other necessary operations, the incomplete echo is arranged to a matrix D r ∈C M s ×N , as shown in Fig.2. The grey rows represent to those pulses during which the radar detects airborne target (i.e., the orange pulses in Fig.1). We define a set to index the positions of those pulses employed for airborne target detection, which is given as: where δ i denotes the location of the first pulse of the i-th airborne target detection. Therefore, for a particular range bin, we denote the corresponding slow-time domain signal as r∈C M s ×1 , and the m-th element of r is given as: According to (8), r is an incomplete version of s (the slow-time domain signal obtained in conventional scheme, as shown in (2)). It is unreliable to use r to detect sea target. However, if we can recover the missing data in r, the sea target detection can be accomplished with the performance equal or almost equal to that of the conventional scheme. In the next section, a Hankel structured low-rank matrix completion algorithm is elaborated to address this critical issue.

IV. HANKEL STRUCTURED LOW-RANK MATRIX COMPLETION
In this section, we will demonstrate how to recovery the missing data in r. We first introduce the concept of Hankel matrix. Then, a recovery algorithm is introduced, the schematic diagram of which can refer to Fig.3. Finally, the convergence performance of the proposed algorithm is analyzed.

A. LOW-RANK MATRIX IN HANKEL STRUCTURE
Let us take the vector s in (2) as an example. The Hankel matrix of s with m 1 rows and m 2 columns is constructed as where m 1 + m 2 − 1 = M s . In the following, we use H (·) to represent the operation that constructs a Hankel matrix with a vector. Similarly, for vector r in (8), we can obtain the corresponding Hankel matrix R = H (r).
As we have mentioned before, it is expected to obtain s by recovering r. To achieve this, we resort to an equivalent scheme, i.e., obtaining S by recovering R. For successful recovery, the following two requirements should be satisfied.
(1) The matrix S is low rank. (2) The missing data in matrix R is sparse. As P (the number of pulses employed for airborne target detection) is much smaller than M s , requirement (2) is easily satisfied. In the following, we prove that the requirement (1) is also meet. First, an important property of Hankel matrix is given in Lemma 1 [18].
Lemma 1: Given that the vector s is composed of d sinusoids and d min(m 1 , m 2 ), its Hankel matrix S has rank d if the sinusoidal frequencies are constant or the rank of S is close to d if the frequencies of sinusoids change significantly slow over the period of m 2 .
According to (2), (4) and (6), the dominant components of s is 2 or 3 sinusoids, and the frequencies of them can be considered as time-varying slowly. Therefore, we can infer from Lemma 1 that the rank of S is close to 2 or 3. Moreover, as the number of pulses M s 3, the matrix S is low-rank.
As a conclusion, it is possible to successfully obtain S by recovering R. And the method will be introduced in the following.

B. MATRIX RECOVERY METHOD
We first define an indicator φ∈C M s ×1 for r, which is:  Then, the relationship between S and R can be expressed as follows: In (11), E is an error matrix. ζ (·) is performed as follows: where [·] i,j represents the (i, j)-th element of the corresponding matrix. More intuitively, ζ (E) = 0 m 1 ×m 2 means that the existing entries in R maintain the same as the corresponding entries in S. To obtain S by recovering R, the typical optimization problem formulated with matrix completion theories [13], [17] is given as: However in this work, the solution of (13) is further required to be a Hankel matrix so that a vector can be extracted from it. Therefore, (13) is improved to involve a Hankel structure constraint, resulting in the following optimization problem: where λ = [λ 1 , · · · , λ m ] T , with λ m being the complex weight coefficient, and B m is a m 1 ×m 2 basis matrix with the m-th anti-diagonal element equal to 1 and the others are 0.
To solve the problem in (14), we extend the inexact Augmented Lagrange Multiplier method (IALM) [19] and present a Hankel structure based IALM, which admits closed form updates and guarantees the Hankel constraint. The augmented Lagrange function of (14) is where Y 1 , Y 2 ∈C m 1 ×m 2 are Lagrange multiplier matrices. µ is a penalty parameter. Based on (15), the iteration is processed as follows where ρ>1 and k is the index of iteration. Equations (16d), (16e) and (16f) respectively give the closed-form solutions for updating Y and µ (k+1) . In the following, we will show that the other variables also have closed-form solutions for updating.

2) UPDATE λ
The optimization problem (16b) for updating λ can be expressed as follows: Defining and therefore Equation (21) indicates that problem (20) is quadratic and convex with respect to λ. Therefore, we can update each element of λ (k) by letting ∂ F (k) 2 F /∂λ (k) m = 0, resulting:

3) UPDATE E
According to (16c), we have For problem (23), there is a closed-form solution, given as where Finally, the entire algorithm for recovering the incomplete slow-time domain signal r is described in Algorithm 1.  5: M s ] T , which is the recovered slow-time domain signal.

C. CONVERGENCE PROPERTY
The convergence of standard ILAM for tackling the linearly constrained convex programming has been well studied in [19], [27], where the objective function is assumed to have two blocks. However, problem (14) involves a smooth objective function with three blocks (S, E and λ), therefore, the convergence of proposed Hankel structure based ILAM need a further discussion. According to the sufficient (may not necessary) condition in [28], the algorithm 1 is ensured to converge when the gap of each iteration is monotonically decreasing. That is to say, the error ε (k) in Algorithm 1: should be monotonically decreasing, where ( S, E, λ) is the optimal solution for minimizing the Lagrangian function in (15). As the convexity of the Lagrangian function could guarantee the monotonically decreasing to some extent [29], therefore Algorithm 1 could be well expected to have good convergence properties. There, following with the discussion in [19], the stopping criteria of Algorithm 1 are given as follows: where the thresholds 1 2 and 3 should be sufficient small. With the above stopping criteria, the convergence and complexity of Algorithm 1 will be further evaluated through simulation experiment.

V. EXPERIMENTAL DATA PROCESSING RESULTS
In this section, a series of numerical simulations are conducted based on the experimental data from a sky-wave OTH VOLUME 8, 2020  radar, which transmits the LFM waveform. The carry frequency of the radar is f 0 = 20 MHz and the other parameters are listed in Table 2.
Notice that the coherent integration time actually required by the airborne target detection is 1.536sec, but we set CIT (a) =2sec. There, the additional 0.464 seconds is reserved for array to change the beamforming direction and the parameter settings. We totally insert three airborne target detections, which respectively start at the 100-th, 285-th, and 400-th pulses. Since the performance of airborne target detection is guaranteed, the key for evaluating the proposed scheme is sea target detection performance. The signal recovery results and signal processing results of sea surface echo are given and discussed in the following.
Generally, the sea surface echo successively undergoes carrier frequency removal, beamforming, pulse compression (matched filtering) and phase compensation, after which the slow time-domain signal of each range bin (i.e., r in (8)) is obtained. In each r, there are 60 elements vacant. Then, for the purpose of target detection, r will further undergo a series of signal processing.
As shown in Fig.4, r is firstly recovered by the proposed Algorithm 1, obtaining a recovered slow-time domain signalŝ. Next,ŝ is processed by a clutter filter, with an M s ×1 vector generated as the indicator for detector [20,  In the following experiments, we focus on the 510-th range bin in which a sea target with Doppler frequency f d = 1.445Hz exists. The slow-time domain signals appearing behind are both corresponding to the 510-th range bin. The signal processing results ofŝ are fully analyzed, with the results of r and s also given as references.

A. SIGNAL RECOVERY RESULT
First, we depict in Fig.5 the real parts of s, r andŝ. More specifically, Fig.5(a) shows the real part of r. In r, the elements corresponding to some pulses are zero, since the radar can not receive echo from sea surface during these pulses. In Fig.5(b), the real parts of s andŝ are depicted. It can be seen that the vacant elements in r are restored inŝ, and the recovered signalŝ is highly similar to s, indicating that the effectiveness of Algorithm 1 on recovering the incomplete signal r. (The imaginary parts of s, r andŝ shows similar results and therefore are not displayed to avoid redundancy.) Next, we evaluate the signal recovery performance through Doppler spectrum. The Doppler spectrum of the echo signal in a range bin is obtained by performing FFT on the corresponding slow-time domain signal, which can reflect the power of signal components with different Doppler frequencies.
In Fig.6, totally three Doppler spectra (after normalization) are depicted, which are respectively associated with s, r andŝ. Moreover, the horizontal axis corresponds to the Doppler frequency of the signal component, which is from  − 1 2T s to 1 2T s , and the ordinate axis denotes the power of the corresponding signal component. From Fig.6(a) and Fig.6(b), we can observe that the Doppler spectrum of r is severely damaged, in which the target is totally submerged in the sea clutter. This is because that the r is obtained with the incomplete sea surface echo, in which the power of target is not sufficiently accumulated. On the other hand, Fig.6(c) shows a Doppler spectrum similar to that in Fig.6(a). Importantly, a spike re-appears at the Doppler frequency of the sea target. This result means that the proposed algorithm guarantees the coherence of signal when recovering r.

B. TARGET DETECTION PERFORMANCE
Through the above two experiments, we intuitively show the signal recovery result from time domain and frequency domain. Beside, the Doppler spectra given in Fig.6 reflect that the sea clutter is very strong in the echo which seriously affects the sea target detection. In order to evaluate the sea target detection performance, it is necessary to concern the result after sea clutter suppression. Therefore, the signalŝ is supposed to be processed by a clutter filter [30], [31], through which an M s ×1 vectorŝ sup can be obtained to reflect the power of each signal component after clutter suppression. Following with [20, Equations (4.102)-(4.103)], the m-th element ofŝ sup is calculated aŝ where R c ∈C M s ×M s is the covariance matrix of the clutter signal c, and is the steering vector corresponding to the Doppler frequency f dm . We denote thatŝ sup [m] is a statistic for detection. That is to say, ifŝ sup [m] is higher than a set threshold, the detector considers that a target with Doppler frequency f dm exists. In Fig.7(c), we depictŝ sup , while s sup and r sup are given in Fig.7(a) and Fig.7(b). Both of them are normalized. It can be seen that, after clutter suppression, the power of target component (f d = 1.455Hz) is significantly higher than those of the other signal components. Therefore, with an appropriate threshold, the detector can correctly determine that there is a target with Doppler frequency 1.455Hz exists, and the signal component with other Doppler frequencies does not cause misjudgment.
Based on the above discussion, the key factors that affect the target detection performance are the main-to-side lobe ratio (MSLR) and peak-to-average ratio (PAR) of clutter filter output. Usingŝ sup as an example, its MSLR and PAR are We denote that larger MSLR or PAR results in lower false alarm probability and vice versa. According to Fig.7, the MSLRs of s sup andŝ sup are close (13.2dB and 13.76dB, respectively), while that of r sup is significantly smaller (about 8.56dB). This indicates that the recovered signal can achieve a target detection performance similar to that achieved by the conventional scheme.
Up to now, we follow with the signal processing flew given in Fig.4, comparing the performance of the proposed scheme and conventional scheme step by step. Also, we illustrate that the PAR and MSLR of clutter filter output are the two key indicators to assess the sea target detection performance. In the following, a more comprehensive evaluation to the sea target detection performance is conducted based on these two indicators. We change the power of the target to make the signal to clutter plus noise ratios (SCNR) of received sea surface echo different. Then for different SCNR levels, we obtain s sup , r sup andŝ sup and calculate the corresponding PARs and MSLRs. The results are concluded in Fig.8 and Fig.9.
First, we can observe that the PAR and MSLR obtained byŝ are larger than those obtained by r, regardless of SCNR level in echo signal. This shows that the sea target detection performance can be improved in different SCNRs cases, indicating the reliability of the proposed algorithm. Moreover, by observing the results ofŝ and s, we have the following statements.
(1) When the SCNR of echo signal is small, the PAR and MSLR obtained byŝ are slightly higher than those obtained by s, which indicates thatŝ can achieve a better sea target detection performance thanŝ in this case. This is because  that the Algorithm 1 preferentially recovers the principal components (i.e., target and clutter), and the noise component is not well recovered. As a consequence, the power of the sea target component inŝ is close to that in s, while the power of the noise component is smaller than that in s. Therefore, in the case that SCNR is small (which means that the noise power is relatively strong in s), the proposed scheme can provide a better target detection performance.
(2) When the SCNR is large, the MSLR ofŝ is slightly worse than that of s. In the case of large SCNR, the decisive factor of MSLR is the power of signal component and the effect of noise is relatively weak. Considering that the recovery algorithm can not fully recovery the sea target to bring it to the same level as in s, such result is reasonable.

C. CONVERGENCE PERFORMANCE OF ALGORITHM 1
Finally, we verify the convergence of proposed Algorithm 1. Reviewing the stopping criteria given in (27), Fig.10 exhibits the iteration curves of ξ 1 , ξ 2 and ξ 3 .
With the convergence threshold setting as 1 = 2 = the convergence speed of the proposed algorithm is relatively fast, and therefore it does not consume a large amount of calculation.

VI. CONCLUSION
In this paper, we propose a new timeframe multiplexed scheme for OTH radar detecting sea target and airborne targets in different directions. The scheme inserts several airborne target detections into a CIT of sea target. Compared with the conventional scheme, the frequency of airborne target detection is improved, which facilitates tracking and monitoring of airborne target. Besides, a signal recovery algorithm is proposed to recover incomplete signal received from sea surface, so as to keep the detection performance of sea target the same or close to the conventional scheme. Experimental examples show the signal recovery result, proving the effectiveness of the proposed algorithm. Besides, the sea target detection performance of the proposed scheme is compared with the conventional scheme. The results verify that the proposed scheme can improve the detection frequency of airborne target without losing the detection performance of the sea target. He is currently an Associate Research Fellow with the School of information and Communication Engineering, UESTC. His research interests include array signal processing, MIMO radar waveform design, one-bit signal processing, and optimization theory. He is currently a Professor with the School of Electronic Engineering, UESTC. He has finished more than two hundred articles and has written two books. His current research interests include involved in array signal processing, digital beam forming, the theory on MIMO radar, and adaptive signal processing.