#### Abstract

Radio and clutter that cover a certain number of range-Doppler-angle cells have a major impact on the detection performance of a high-frequency surface wave radar (HFSWR) system. Especially for a small-aperture array, the angle spectrums of radio and clutter suffer from severe broadening, so the targets that are more easily submerged in the broadened radio and clutter can be hardly detected. To tackle this issue, this paper proposes an algorithm for radio decontamination and clutter suppression to enable detection of the submerged targets. First, the spatial correlation of the array is derived, and the characteristics of radio and clutter are analyzed based on angle-Doppler joint eigenvector. Then owing to the analysis, the information of radio and clutter in the main beam can be accurately estimated from that in the auxiliary beams and eliminated by subtracting it. The results of simulations and measured data indicate that the proposed method offers a significant performance improvement and has a strong robustness against the array amplitude-phase errors.

#### 1. Introduction

HFSWR has gained much attention in recent years due to its remarkable capabilities in target monitoring and remote sensing over the horizon [1–3]. However, the HF band is a heavily congested part of radio and clutter spectrum, which makes the desired signals easily submerged and difficult to detect. What is worse, among the HFSWR operated worldwide, large portion small-aperture array systems are utilized, such as WERA [4] (four-element configuration), OSMAR [5] (eight-element configuration), and CODAR [6]. Radio and clutter have much more serious effects on these radars than on those with large-aperture arrays. Because the broadened space beams owing to a small-aperture array will make the echo energy of radio and clutter from any observation direction overall exist in the main beam, few array degrees of freedom (DOF) can be used to cancel radio and clutter. Hence, how to overcome these problems in a practical radar system has been a key topic.

Radio, which works on HF band, can be received by an HFSWR receiver. It is a kind of strong direction interference and occupies a large number of range cells [7, 8]. The clutter is composed of sea clutter and ionospheric clutter: Sea clutter is the collection of several spectrum lines in a narrow Doppler band, which is a part of the common area that we are concerned with for detecting moving vessels [9, 10]; ionospheric clutter comes from the nonideality of the antenna in the zenith direction and possibility contaminates all the range cells, Doppler cells, and angle cells above 100 km [11, 12].

In [13], an adaptive interference cancellation algorithm adding four auxiliary horizontal dipoles configured as two separate crosses to the HFSWR system is proposed. The interference component received by the vertically polarized antennas (main antennas) can be estimated from the auxiliary horizontal antennas. By subtracting this estimate, the interference is suppressed while this method is completely ineffective for a small-aperture array. Xianrong et al. proposed a scheme just using vertical antennas based on subarray technology to suppress the ionospheric clutter, instead of implementing any auxiliary facilities [14]. But its blocking module is only designed to protect two Bragg lines rather than the desired targets with unknown distribution characteristics, which will cause the target self-cancellation. Another adaptive array processing with a 2D-array configuration has been proposed to restrain ionospheric clutter in [15] and reported to work well. However, this method increases the system complexity and degrades practicability when the antenna field is limited. Based on a single-notch filter, a main-lobe canceller of space spread clutter [16] is developed. Though the excellent suppression performance for sea clutter and ionospheric clutter can be achieved by an effective clutter estimation method, it needs a large-aperture array to ensure nulling depth of the filter and sufficient clutter sample statistics. To overcome the array aperture limit, many temporal and time-frequency approaches [17, 18] are also investigated to remove radio interference from HFSWR systems, but these methods are merely based on chirp signals.

In the small-aperture HFSWR system, considering the weak targets submerged by radio and clutter more easily and possessing a strong correlation between the beams, this paper proposes a novel radio and clutter suppression algorithm. Instead of exploiting the auxiliary array, subarray, and specific signal form, our presented method focuses on the space characteristics of the small-aperture array. Firstly, the conclusion that there is a strong correlation between the beams is deduced. Then, during the process of the proposed canceller, the radio and clutter in the main beam can be estimated and suppressed through the data set collected from the auxiliary beams. Finally, an important factor, namely, the robustness versus array amplitude-phase errors, is detailedly analyzed.

This paper is organized as follows. Section 2 introduces the system structure and spatial distribution characteristics of the small-aperture array. The proposed radio and clutter suppression algorithm is presented in Section 3. The radio and clutter with four typical distributions are simulated to demonstrate the effectiveness in theory in Section 4. The experiments, comparison, and analysis are provided in Section 5. Section 6 concludes this paper.

#### 2. Space Distribution of Array, Radio, and Clutter in Small-Aperture HFSWR

In contrast to the large-aperture array, the spatial distribution of radio and clutter in the small-aperture array will change significantly since a smaller array aperture can cause the beams to widen severely. In addition, the study of radio and clutter suppression method is mostly conducted based on the comprehension of their properties; thus we need to do an accurate analysis of the correlation characteristics of radio and clutter in this section.

##### 2.1. Small-Aperture HFSWR System

The small-aperture HFSWR system presented in this paper was developed by Harbin Institute of Technology in Weihai, whose receiving array composed of 8 vertically polarized elements is shown in Figure 1. The facility can transmit the phase-modulated signals or the frequency-modulated interrupting continuous wave at an operating frequency range from 4 to 10 MHz. System bandwidth and range resolution are 60 kHz and 2.5 km, respectively. In order to have abilities to detect fast-moving and slow-moving targets, the coherent integration time will be set to 10~30 s (Doppler resolution is 0.1~0.033 Hz) and 120~393 s (Doppler resolution is 0.0083~0.0025 Hz) typically.

##### 2.2. Space Characteristics of Array

The array steering vector is determined by the operating wavelength, the array geometry, and the array aperture. That is, the spatial distribution characteristics produced by the array itself can be acquired through solving the correlation coefficient between the array steering vectors with two different directions. Here, considering a uniform linear array, two array steering vectors with arbitrary directions are shown below: where is the element spacing, indicates operating wavelength, and is the total element number. The correlation coefficient of both the above vectors can be calculated by the following equation: where is the complex conjugation. Let ; it is a variable that has no relation with array aperture as element spacing and wavelength are fixed. The expression of the correlation coefficient can be rewritten as

As shown above, it can be concluded that the array elements are fewer (i.e., the array aperture is smaller) and the correlation between two steering vectors is stronger. The correlation results are shown in Figure 2. Suppose that 0° is a reference direction to calculate the correlation coefficients with all the other directions, element spacing is 10 m, and operating frequency is 5 MHz. Moreover, in the practical system, the window function usually is needed to limit side-lobe level when doing the digital beam forming (DBF). In this paper, the 25 dB Chebyshev coefficients are multiplied by the array steering vector to analyze the correlation.

According to the previous studies in [19], the correlation coefficient is larger than 0.7, which can be treated as homogeneity. And the homogeneity becomes stronger as the coefficient becomes larger. In order to avoid generating target self-cancellation in the proposed algorithm, the deviation angle between auxiliary beams and the desired direction of the main beam must be larger than 10°, at least based on experience. But as shown in Figure 2, the number of homogeneous beam bins is smaller than 13 when the number of array elements is larger than or equal to 16, which greatly reduces the number of clutter samples obtained by secondary beams. Hence, the proposed algorithm can be considered to be effective from 4 to 14 array elements concerning both beam width and sample number.

##### 2.3. Investigation on Space Characteristics of Radio and Clutter

This section shows the spatial distribution characteristics of radio and clutter analyzed in the practical small-aperture HFSWR system. The measured data set comes from radar experiment conducted in Weihai, China, on May 12, 2016, using an eight-element configuration. It is processed in turn by pulse compression, Doppler, and DBF. The range-Doppler maps of radio, sea clutter, and ionospheric clutter in 0° beam (the normal direction is 0°) are successively shown in Figure 3. The working frequencies are 4.47 MHz, 4.47 MHz, and 5.6 MHz, respectively.

**(a) Range-Doppler map of radio**

**(b) Range-Doppler map of sea clutter**

**(c) Range-Doppler map of ionospheric clutter**

A correlation analysis method whose correctness has been proved in [19] based on angle-Doppler joint eigenvector is used to effectively study the space property of radio and clutter with the real data. The detailed procedures are as follows: (1)Select a range-Doppler local region that consists of three adjacent range cells and Doppler cells contaminated by radio and clutter to construct a test matrix .(2)Stack the columns of the test matrix under each other to form a new column vector .(3)Calculate the self-correlation matrix by ; then eigen-decompose to acquire 9 eigenvalues and corresponding 9 eigenvectors ; finally normalize the eigenvectors by .(4)Determine their contributions with , and choose the eigenvector , which has the maximal contribution.(5)According to steps (1) to (4), the eigenvectors , can be obtained by making the same processing, where is the number of total angle cells.(6)Calculate the correlation coefficients employing , from step (5) by

The spatial scanning area is from −30° to 30°, angle interval of the digital beam forming is 1°, and the reference direction is 0°. We choose continuous radio and clutter region in the range-Doppler spectrum as the processing region to make the contained components as simple as possible. All the correlation coefficients are averaged over 50 independent trials with different processing regions for radio, sea clutter, and ionospheric clutter severally, and approximately equal to 1. As shown in Figure 4, radio and clutter both indicate the extreme strong space correlation in the practical small-aperture HFSWR system.

#### 3. Radio and Clutter Decontamination Algorithm Utilizing Multiple Beam Method

##### 3.1. Problem Formulation

Assume the considered small-aperture HFSWR consists of an array with *N* elements, and it transmits a burst of *K* pulses (Doppler cell numbers) in a coherent processing interval; the sampling points in each transmitted signal pulse (range cell numbers) are *L*. The echo data of one range cell and Doppler cell can be expressed as
where and , respectively, represent the number of the desired signal and radio and clutter; and are the complex envelopes of the *i*th desired signal and the *j*th radio and clutter; and indicate manifold vectors corresponding to the *i*th desired signal and the *j*th radio and clutter, which are the array response at the directions and ; denotes additive white Gaussian noise.

Signal-to-interference ratio (SIR) and signal-to-clutter ratio (SCR) are negative as the target energy is weak to interference and clutter; thus, the targets submerged in both cannot be detected. Minimum variance distortionless response (MVDR) is a classical space filter keeping the response to the expected direction distortionless and output power minimum. In the ideal condition, the signal to interference/clutter and noise ratio (SINR/SCNR) can be maximum by MVDR. The correlated matrix of the echo can be indicated as where is the covariance matrix of interference, clutter, and noise, which can be indicated as ; is the power of noise; denotes the dimensions identity matrix. Suppose is the expected direction, and the optimal adaptive beamforming vector can be indicated as

##### 3.2. Proposed Algorithm

In the practical radar system, the signals’ directions of arrival (DOA) and covariance matrix cannot be known in advance. The proposed algorithm is an effective way to solve these problems, and the framework is shown in Figure 5. This algorithm does not require prior access to the targets’ DOA and covariance matrix . Firstly, the secondary samples that have similar distribution characteristics as the radio and clutter of the main beam can be obtained via auxiliary beams; then implement the information statistics in the range domain and Doppler domain to calculate matrix , which guarantees that the component of radio and clutter is greatly superior to that of the targets; finally, the optimal weight vector for suppressing radio and clutter and meanwhile protecting target nature can be achieved. This algorithm is applied in a uniform linear array but is not restricted to this array.

The echo in which the signals are blocked by a block matrix is used to deduce the adaptive weights for the canceller. The output of the method can be expressed as

The output power is defined by

The output power is minimized to make radio and clutter suppression performance be optimal [14]. At this point, calculating the adaptive weight vector is equivalent to solving the following optimization problem:

From this minimization, we obtain a steady-state optimal weight vector in the form of the Wiener solution where is a coefficient matrix of auxiliary beams, and let be the auxiliary beams’ directions. The starting direction of this area is equal to the corresponding angle of −3 dB attenuation of the main beam, and other directions of auxiliary beams can be successively obtained in the direction away from the main beam with 1° angle interval. The beam structure is shown in Figure 6.

The black solid line displays the spatial response of the main beam, which consists of radio, clutter, noise, and targets. The dotted line is the spatial response of auxiliary beams to estimate radio and clutter information. Matrix is written as

In (12), is a self-correlation matrix of radio and clutter counted via the auxiliary beams, and is the cross-correlation matrix between the outputs of the auxiliary beams and those of the main beam, expressed as follows:

Suppose that the main beam direction is (it can be an interesting arbitrary direction), so its output is given by

##### 3.3. Robustness Analysis for Amplitude-Phase Errors

In this section, we describe a metric called cancellation ratio (CR) [20, 21] to measure radio and clutter suppression performance. It is defined as the ratio of the output power of the main beam to the output power of the difference of output signals (residue). Mathematically, the CR is defined as where is the estimated radio and clutter information from auxiliary beams. In addition, (17) can be simplified as where is the correlation coefficient of radio and clutter between the main beam and auxiliary beams, which has a crucial effect on the output CR of the proposed algorithm. Note that by this definition, a good CR will be close to infinity (i.e., if expressed in decibels, it would have a large positive value). Combining the conclusion drawn in Section 2.2, this paper can receive the outstanding radio and clutter suppression performance by the derived space distribution and the presented new method to achieve training data set. Whereas amplitude-phase errors universally exist in the actual radar systems, the error robustness has been an important indicator to judge if the algorithm has practicability or not. Next, robustness analysis is provided, and then (1) and (2) can be rewritten, respectively, as where are amplitude errors and are phase errors; amplitude errors and phase errors are independent of each other. The error means indicate and ; variances denote and . Right now, the correlation coefficient of the array steering vectors taking into account the above amplitude-phase errors is expressed as

The correlation coefficient is not affected by the amplitude-phase errors as the means equal to zero and variances are nonnegative. In other words, the radio and clutter correlation between the main beam and auxiliary beams is not degraded. As a result, this algorithm that has a strong robustness against the errors mainly benefits from sampling format of second training data of radio and clutter based on auxiliary beams.

#### 4. Simulation Trails

In the practical small-aperture radar system, the echo signals are usually polluted by the radio, sea clutter, and ionospheric clutter. The energy distributions of radio and clutter will be very different. In theory, the algorithm will have remarkable effects on any distribution characters based on a framework of statistical estimation. For the distribution characteristics of angle dimension, Gaussian distribution, uniformed distribution, Poisson distribution, and Rayleigh distribution are the four most typical distributions.

In this section, to verify radio and clutter suppression performance, a weaker signal than the radio and clutter has been injected in the 0°, with 8 array elements, 20 auxiliary beams, and 25 dB Chebyshev coefficient. Simulation results averaged over 500 Monte Carlo trials are shown in Figure 7, which obviously demonstrates that the radio and clutter can be accurately estimated by the auxiliary beams and that the injected signal is visible for all the distribution characters.

**(a) Gaussian distribution**

**(b) Uniformed distribution**

**(c) Rayleigh distribution**

**(d) Poisson distribution**

#### 5. Measured Data Verification

In this part, the measured data are applied to illustrate the advancement and validity of the proposed algorithm, compared to DBF, coherent side-lobe cancellation (CSLC), and spread clutter estimated canceller (SCEC). The measured data of small-aperture HFSWR as introduced in Section 2 are used. The main beam and auxiliary beams, respectively, are formed for target detection and radio and clutter estimation using 25 dB Chebyshev weighting. The whole detection space (from −30° to 30°) is divided into 7 beam areas whose desired directions are as follows: −30°, −20°, −10°, 0°, 10°, 20°, and 30°. The starting direction of auxiliary beams equals the corresponding angle of −3 dB attenuation of the main beam, and 20 auxiliary beams can be successively selected in the direction away from the starting direction with 1° angle interval.

##### 5.1. Radio Result with Ideal Target

As depicted in Figure 3(a), there are two strong energy radios covering all the range units above the 30th range unit in the range-Doppler spectrum. A simulation target with the same azimuth as radio is injected into the real radio data; the detailed target information is shown in Table 1. In order to facilitate observation, an enlarged spectrum of the target’s position is shown in Figure 8(a); the result after mitigating radio in the corresponding area is provided in Figure 8(b); to underline the advantage gained, Figure 8(c) shows a Doppler frequency profile at the range of the 147th range bin when the beam bin is set to the 7th. From Figure 8, it is obvious that the performance of the proposed algorithm is superior to that of the others and that it obtains the optimal output SIR.

**(a) Range-Doppler map before suppression**

**(b) Range-Doppler map after suppression**

**(c) Doppler profile**

##### 5.2. Sea Clutter Result with Ideal Target

The range-Doppler spectrum of the actual sea clutter is shown in Figure 3(b), and its theoretical first-order Bragg frequencies generated from working frequency are ±0.215 Hz. Owing to current, the real Bragg frequencies are shifted to −0.215 Hz and 0.219 Hz. The echo of sea clutter will be received in all front directions because of the geographical environment that the receiving array faced. Therefore, the azimuth of the added target is in the normal direction, and the detailed information is in Table 2. Figures 9(a) and 9(b) depict the target range-Doppler maps before and after the proposed method processing after injecting a simulation target. Figure 9(c) illustrates that the proposed algorithm can effectively suppress the sea clutter and detect the target submerged by sea clutter.

**(a) Range-Doppler map before suppression**

**(b) Range-Doppler map after suppression**

**(c) Doppler profile**

##### 5.3. Ionospheric Clutter Result with Ideal Target

Three pieces of strong ionospheric clutter exist in Figure 3(c), which makes the target in this area difficulty to be detected if the target echo is weaker than the echo of ionospheric clutter. The distribution characteristics of the target are introduced in Table 3. Figure 10(a) presents an original range-Doppler map that is contaminated by ionospheric clutter from Doppler frequency −0.4 Hz to 0.5 Hz, whereas Figure 10(b) illustrates the map after suppressing the clutter by the proposed method. To show the benefits more clearly, Figure 10(c) shows the Doppler profile with the 2nd beam bin and the 141st range bin, which have the same direction and range with the injected target. It is noticed that the clutter energy has been suppressed by the proposed method, even as the target energy has persevered. The output SCR has improved over 28 dB by the proposed algorithm, which is 5 dB higher than that of SCEC and 12 dB higher than that of CSLC.

**(a) Range-Doppler map before suppression**

**(b) Range-Doppler map after suppression**

**(c) Doppler profile**

##### 5.4. Robustness Result

For the realistic situation as in the discussion in Section 3.3, the amplitude-phase errors generally exist between array elements of the small-aperture HFSWR system. In this section, to evaluate the robustness of the proposed algorithm, a set of the real array errors is first extracted by using 500 measured data files and then calculating statistical mean and variance based on the above files. At last, the statistical result is applied to the injected target, and the mitigating performance comparison of radio and clutter between errors and ideal cases is given in Figure 11. The amplitude-phase error parameters are shown in Table 4. As can be seen from Figure 11 and Table 4, the proposed algorithm has the same radio and clutter suppression ability and approximately optimal output SIR/SCR. The thinned performance loss is mainly derived from the nonzero mean of the errors in the practical system.

**(a) Radio Doppler profile**

**(b) Sea clutter Doppler profile**

**(c) Ionospheric clutter Doppler profile**

##### 5.5. Suppression Results with Simulated Real Targets

Here, the capability of the proposed algorithm for suppressing radio and clutter in the case of the real target is studied. The real targets can be simulated by broadening Doppler bin and range bin of the ideal targets; that is, the number of covering bin changes from one to three. Compared to the above trials, a marked target that has the same signal power as the submerged target is added in the noise area to contrast the attenuation of the signal before and after processing. The two target parameters used in this experiment are listed in Tables 5 and 6. Figures 12(a), 12(c), and 12(e) reveal that the radio and clutter are significantly suppressed while two injected targets are well preserved and clearly visible. Figures 12(b), 12(d), and 12(f) indicate that the marked targets almost do not suffer any attenuation of output SNR and that the submerged targets can also acquire 20–25 dB performance improvement of output SIR and SCR.

**(a) Range-Doppler map after radio suppression**

**(b) Doppler profile of radio suppression**

**(c) Range-Doppler map after sea clutter suppression**

**(d) Doppler profile of sea clutter suppression**

**(e) Range-Doppler map after ionospheric suppression**

**(f) Doppler profile of ionospheric suppression**

##### 5.6. The Analysis of Beam Deviation

Two simulated real targets that have the same parameters as in Section 5.5 except azimuth are injected into the radio and clutter to quantize the performance degradation while the target directions are different from the desired directions of the main beam. The angular deviation between targets and the associated main beam varies from −5° to 5° considering that the angle interval of the main beam is 10°, and the detailed information is illustrated in Table 7. As shown in Figure 13 and Table 7, the proposed algorithm only suffers a small performance loss, not more than 1 dB, regardless of the kind of experimental situation.

**(a) Radio Doppler profile**

**(b) Sea clutter Doppler profile**

**(c) Ionospheric clutter Doppler profile**

##### 5.7. Performance Analysis

The worst scenarios are considered in the above trials, that is, the target absolutely submerged by radio, sea clutter, and ionospheric clutter in range-Doppler-angle domains. From the comparison results in range-Doppler spectrum and Doppler profile, the proposed algorithm can absolutely restrain radio and clutter while introducing no false target outside the injected target position. Besides, our algorithm can obtain 26 dB output SIR/SCR improvement averaged from situation a to situation c, but only 0.55 dB and 0.6 dB performance loss for the real amplitude-phase errors and beam deviation severally. Hence, it is concluded that compared to the other methods, in the cases of ideal and real target characteristics, the proposed algorithm can have better radio and clutter restraint performance, higher output SIR/SCR, and stronger amplitude-phase error robustness.

#### 6. Conclusion

In this paper, the spatial distribution characteristics of radio and clutter in the small-aperture HFSWR system are first derived. It is a theoretical basis of our proposed algorithm, which presents a cascaded method for radio decontamination and clutter suppression to enable detection of the submerged targets. Simulations and measured data have demonstrated that the radio and clutter in the main beam can be estimated by auxiliary beams and effectively cancelled by this algorithm while preserving almost all the target echo energy. Another contribution of the method is the robustness against amplitude-phase errors, which makes great sense for improving algorithm stability and reliability of a radar system. Compared with DBF, CSLC, and SCEC methods, the proposed algorithm has been shown to have better radio and clutter suppression results and higher output SIR/SCR. The theory about how to choose auxiliary beams to achieve the optimal output performance will be studied in a future paper.

#### Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

#### Acknowledgments

The authors would like to thank the associate editor and the anonymous reviewers for their helpful comments and suggestions. This work is supported by the National Science Find Committer (NSFC) of China (61701140, 61032011, and 61171182).