Cross Beam STAP for Nonstationary Clutter Suppression in Airborne Radar

Abstract

A novel space-time adaptive processing (STAP) method for nonstationary clutter suppression is proposed. The developed method forms a multibeam along the cross line to participate in adaptive processing, which sufficiently utilizes the spatial information both in azimuth and elevation and guarantees the least system degrees of freedom (DOFs). The characteristics of this structure help to suppress the short-range clutter which is the primary component of nonstationary clutter. Therefore, this method provides favorable clutter suppression performance when clutter range dependence exists. Approach analysis and simulation results are given to demonstrate the effectiveness of the method.

1. Introduction

Space-time adaptive processing (STAP) can achieve perfect clutter suppression performance in stationary clutter circumstance [1]. However, for non-side looking airborne radar (non-SLAR) (i.e., the radar with inclined side looking array and forward looking array), the clutter is range dependent or nonstationary, especially at short range [2]. In other words, the clutter is mostly nonstationary in practice because of detecting in all directions. Nonstationary clutter can result in the degraded performance of the adaptive processor compared to theoretical predictions.

So far, much effort has been put into this problem. The multiple-PRFs STAP scheme can relieve the blind regions induced by non-side looking and range ambiguity [3]. The main contribution of this attempt is just for solving the range ambiguity problem and not resolving the short-range clutter problem in essence. Compensation methods [4–6] work well when range ambiguity does not exist. Once the radar works at the medium or high pulse repletion frequency (PRF), it cannot identically compensate the ambiguity clutter. In fact, the short-range clutter, induced from the array elevation sidelobe, is the dominant reason for the clutter nonstationarity. The 3D STAP [7] with elevation elements or subarrays can cancel the short-range clutter effectively in theory. Unfortunately, it is hard to get enough independent identically distributed (IID) sample data and requires more computation load because of its large system DOFs. Subarray synthesis algorithm with prefiltering in elevation [8] can effectively suppress the short-range clutter when the element errors do not exist. However, the array antenna errors are inevitable in practice, thereby significantly degrading the performance. In this paper, a STAP method based on cross beam forming is presented in which the auxiliary beams are reasonably chosen in elevation and azimuth to cancel the clutter induced by elevation and azimuth sidelobes.

This paper is organized as follows. In Section 2, the principle of the cross beam STAP method is introduced. Section 3 shows the approach analysis. Simulation results are shown in Section 4, and Section 5 gives the conclusions.

2. Clutter Characteristics for Non-SLAR

In this section, the clutter math model is described and the clutter characteristics for non-SLAR are analyzed. Note that range ambiguity is considered in this model. As shown in Figure 1, the airplane flies along 𝑋-axis with velocity 𝑉, the 𝜃_𝑝 is the angle between the array axes and flying direction, 𝜃_𝑎 and 𝜑 are the azimuth angle and elevation angle of the clutter patch, respectively, and Ψ denotes the cone angle.

Figure 1 

Geometry of non-SLAR.

The normalized Doppler frequency of the clutter patch can be described as follows: 𝑓_𝑑=2𝑓_𝑑𝑓_𝑟=4𝑉𝜆𝑓_𝑟cos𝜃_𝑎+𝜃_𝑝𝜑=cos4𝑉𝜆𝑓_𝑟cos𝜓cos𝜃_𝑝−sin𝜃_𝑝cos²𝜑−cos²𝜓, (1) where 𝜆 is the wavelength, 𝑓_𝑑 and 𝑓_𝑟 denote the Doppler frequency and the PRF, respectively. From (1) we see that the Doppler frequency of the clutter patch varies with the cone cosine when 𝜃_𝑝 is nonzero (i.e., the situation of non-SLAR). In other words, the distribution of clutter spectrum varies with range.

The clutter spectrum characteristic of a forward-looking planar array in azimuth-Doppler plane and range-Doppler plane is shown in Figures 2 and 3, respectively. The scenario parameters are given in Section 5. In Figure 2, we see that the clutter is comprised of three parts which are named 𝑋₁, 𝑋₂, and 𝑋₃. According to the conventional planar array pattern, we can conclude that 𝑋₁, 𝑋₂, and 𝑋₃ are, respectively, induced from elevation sidelobe, azimuth main lobe, and azimuth sidelobe. From Figure 3, we can see that the Doppler frequency of short-range clutter 𝑋₁ severely varies with range.

Figure 2 

Clutter spectrum distribution of forward-looking planar array in azimuth-Doppler plane.

Figure 3 

Clutter spectrum distribution of forward-looking planar array in range-Doppler plane.

3. Principle of the Cross Beam STAP

A schematic of the proposed STAP architecture is shown in Figure 4. An 𝑀 row by 𝑁 column vertical rectangular array is considered. The first stage is beam forming involving MN digitized spatial elements or subarray channels. This results in a total of 𝑃+𝑄−1 beams which include main beam, 𝑄−1 auxiliary beams along elevation with the azimuth main lobe, and 𝑃−1 auxiliary beams along azimuth with the elevation main lobe. One thing to be noted is that 𝑃 or 𝑄 is always an odd number. After Digital Fourier Transform (DFT) for the data received from each beam, adaptive processing is applied for clutter suppression.

Figure 4 

Schematic of the cross beam STAP method.

The received data can be reshaped into an 𝑀𝑁×𝐾 data cube 𝐗. Let 𝐗_𝑀𝑁∈𝐶^1×𝐾 denote the echo signals received by the 𝑚th element or subarray channel in elevation and the nth element or subarray channel in azimuth, and let 𝐾 be the pulse number in one coherent pulse interval. The multiple beams can be obtained by 𝐀=𝐓^𝐻_𝑎𝐗,𝐄=𝐓^𝐻_𝑒𝐗, (2) where (⋅)^𝐻 denotes the conjugate transpose, 𝐓_𝑎∈𝐶^{𝑀𝑁×𝑃} and 𝐓_𝑒∈𝐶^{𝑀𝑁×𝑄} are the azimuth and elevation beam transformation matrix, respectively. The 𝑝th column of 𝐓_𝑎 and the 𝑞th column of 𝐓_𝑒 have the following forms: 𝐓_𝑎𝑝=𝐒_𝑠𝑒0,𝐒_𝑠𝑒0𝑒^{𝑗𝜋cos𝜃𝑝cos𝜑0}𝐒,…,_𝑠𝑒0𝑒^{𝑗𝜋(𝑁−1)cos𝜃𝑝cos𝜑0𝑇}𝐓,𝑝=1,2,…,𝑃,_𝑒𝑞=𝐒_𝑠𝑒𝑞,𝐒_𝑠𝑒𝑞𝑒^{𝑗𝜋cos𝜃0cos𝜑𝑞}𝐒,…,_𝑠𝑒𝑞𝑒^{𝑗𝜋(𝑁−1)cos𝜃0cos𝜑𝑞𝑇},𝑞=1,2,…,𝑄, (3) where (⋅)^𝑇 denotes the transpose, 𝜃_𝑝 (𝑝=1,2,…,𝑃) and 𝜑_𝑞 (𝑞=1,2,…,𝑄) are the angle of beams in azimuth and the angle of beams in elevation, respectively, and 𝜃₀=𝜃_(𝑝+1)/2 and 𝜑₀=𝜑_(𝑞+1)/2 are the azimuth angle and elevation angle of the main lobe. 𝐒_𝑠𝑒0 and 𝐒_𝑠𝑒𝑞 are defined as follows: 𝐒_𝑠𝑒0=1,𝑒^{𝑗𝜋sin𝜑0},…,𝑒^{𝑗𝜋(𝑀−1)sin𝜑0},𝐒_𝑠𝑒𝑞=1,𝑒^{𝑗𝜋sin𝜑𝑞},…,𝑒^{𝑗𝜋(𝑀−1)sin𝜑𝑞}. (4) Then the transformation matrix for cross beams can be written as 𝐓_𝑠=𝐓_𝑎,𝐓_𝑒1,2,…,𝑄−12,𝑄+32,…,𝑄. (5)

Let 𝐓∈𝐶^{𝑀𝑁𝐾×(𝑃+𝑄−1)𝐿} be the transformation matrix in space and time domain. Then it has the following form: 𝐓=𝐓_𝑡⊗𝐓_𝑠, (6) where 𝐿 is the dimension after dimension reducing in time domain, ⊗ denotes the Kronecker product, and 𝐓_𝑡∈𝐶^𝐾×𝐿 is the dimension-reduced matrix in time domain and often transforms the pulse data to several adjacent Doppler bins in most conventional STAP algorithms.

After transforming the received data 𝐗 to beam-Doppler domain, we can get the optimum weight by solve the following optimization problem: min𝐖^𝐻𝐓^𝐻𝐑𝐓𝐖,s.t.𝐖^𝐻𝐓^𝐻𝐒_𝑡⊗𝐒_𝑠=1, (7) where 𝐑=𝐸[Vec(𝐗)Vec(𝐗)^𝐻], Vec(⋅) denotes the matrices operation that stacks the matrix under each other to form a column vector, and 𝐒_𝑡 and 𝐒_𝑠 are the time domain and space domain steering vectors which can be represented by 𝐒_𝑡=1,𝑒^{𝑗2𝜋𝑓𝑑/𝑓𝑟},…,𝑒^{𝑗2𝜋(𝐾−1)𝑓𝑑/𝑓𝑟𝑇},𝐒_𝑠=𝐒_𝑠𝑒0,𝐒_𝑠𝑒0𝑒^{𝑗𝜋cos𝜃0cos𝜑0},…,𝐒_𝑠𝑒0𝑒^{𝑗𝜋(𝑁−1)cos𝜃0cos𝜑0𝑇}. (8)

4. Approach Analysis

For STAP in non-SLAR, the more system degrees of freedom (DOFs) in elevation, the better the nonstationary clutter suppression performance can be achieved [7, 8]. However, the added elements or subarrays in elevation lead to the huge requirements for IID samples and computation load. The 3D STAP [7] is a typical example for that. Fortunately, it can be more flexible and effective to utilize the information in elevation if the data are transformed into beam domain. Figure 5 shows the normalized amplitude of the adaptive weight in space domain at the 28th Doppler bin when all the received data are transformed to multibeams. The clutter at the 28th Doppler bin is comprised of short-range clutter and azimuth sidelobe clutter. It can be seen from Figure 5 that the adaptive weight amplitude is large in the cross lines aiming at the elevation and azimuth main beam region, and small in the other position. It further demonstrates that the selection strategy of the cross beams is reasonable for nonstationary clutter suppression.

Figure 5 

Adaptive weight normalized amplitude of the multibeams at the 28th Doppler bin.

Figure 6 shows the eigenspectrum of the clutter at the 28th Doppler bin. The scenario parameters are described in the next part. From Figure 6 we can see that the eigenvalue number of cross beams is the least and the eigenvalue number of synthesized channels is the most. This result indicates that there are more redundant system DOFs to suppress clutter [9] for the new method compared with conventional 2D and 3D STAP method.

Figure 6 

Eigenspectrum of clutter at the 28th Doppler bin.

5. Simulation Results

A 220-element forward-looking planar array steered to 0^∘ in azimuth and 3^∘ in elevation is used, in which 22 elements are in azimuth and 10 elements are in elevation. Three correlative STAP methods are considered in this simulation for comparison. The typical 2D STAP with synthesized 22 spatial channels in azimuth is firstly considered. The second is the 3D STAP method with synthesized 11×2 spatial channels in azimuth and elevation. The recent STAP method based on elevation spatial prefiltering is also investigated in ideal and error conditions, respectively. The platform height is 8000 m. The platform velocity is chosen so that there are no Doppler ambiguities. The pulse number and Doppler bins are both 32 and the short-range clutter distributed at the 24th to 30th Doppler bins. The number of Doppler bins for STAP is selected as 3. The range cell under test is chosen as 50. The numbers of formed beams are 21 and 9 in azimuth and elevation, and 𝑃 and 𝑄 are, respectively, chosen as 15 and 7.

Figure 7 shows the signal-to-clutter-plus-noise ratio (SCNR) loss (i.e., loss relative to the clutter-free case) against Doppler frequency for a target located at the look direction when there are no errors in array. From Figure 7 we can see that the short-range clutter suppression performance of 3D STAP is better than that of the 2D STAP and worse than elevation prefiltering and cross beam STAP method when array errors are ignored. In this condition, the performance of cross beam STAP is close to the elevation prefiltering STAP method.

Figure 7 

SCNR loss comparison of 2D STAP, 3D STAP, elevation prefiltering STAP, and cross beam STAP (no errors).

Figure 8 shows the SCNR loss of the elevation prefiltering STAP method and cross beam STAP method when element errors exist. From Figure 8 we can see that the clutter suppression performance in short-range region of elevation prefiltering STAP method evidently degrades than the no error situation. However, the proposed cross beam STAP method’s performance only slightly degrades and is significantly superior to the elevation prefiltering STAP method. Therefore, the cross beam STAP method has better robustness than the elevation prefiltering STAP method.

Figure 8 

SCNR loss comparison of elevation prefiltering STAP and cross beam STAP with different errors.

6. Conclusions

A new postbeam STAP method for nonstationary clutter suppression in airborne radar has been presented. Simulation results show that the short-range clutter suppression performance of cross beam STAP is superior to the existing 2D STAP, 3D STAP, and elevation prefiltering STAP methods. The computation load of the new method is close to the 2D and 3D STAP when the system DOF is chosen to be the same, and is larger than the elevation prefiltering STAP.

Acknowledgment

This work was supported in part by the National Nature Science Foundation of China under contract 60925005 and 61102169.