Research Article  Open Access
Zhongbao Wang, Junhao Xie, Zilong Ma, Taifan Quan, "A Modified STAP Estimator for Superresolution of Multiple Signals", International Journal of Antennas and Propagation, vol. 2013, Article ID 837639, 7 pages, 2013. https://doi.org/10.1155/2013/837639
A Modified STAP Estimator for Superresolution of Multiple Signals
Abstract
A modified spacetime adaptive processing (STAP) estimator is described in this paper. The estimator combines the incremental multiparameter (IMP) algorithm and the existing beamspace preprocessing techniques yielding a computationally cheap algorithm for the superresolution of multiple signals. It is a potential technique for the remote sensing of the ocean currents from the broadened firstorder Bragg sea echo spectrum of shipborne highfrequency surface wave radar (HFSWR). Some simulation results and realdata analysis are shown to validate the proposed algorithm.
1. Introduction
The measurement of the nearsurface currents is a very difficult task by using conventional methods, especially under some harsh sea conditions. Many advanced marine measurement instruments, such as drifting buoys [1] and acoustic current meters [2], have been used to collect sea state information. However, it would be very expensive to collect and interpret data from these devices for the sparse spatial sampling provided. Therefore, it is virtually impossible to form the current maps over a widespread ocean surface timely and accurately with these conventional meters.
In recent years, HFSWR has already become a powerful remotesensing tool which receives increasing attention from oceanographers and research groups for its good ability to determine the largescale sea state under all weather conditions [3, 4]. The measurement principle of HFSWR mainly depends on the Bragg resonant scattering theory and Doppler frequency effect theory in the sea echo spectrum of HFSWR. In the absence of ocean currents, the firstorder Bragg lines would appear symmetrically above and below the zero Doppler frequency, which are caused by the ocean waves with precisely onehalf wavelength of the radar moving towards and away from the radar. In practical application, some displacements will happen in the firstorder Bragg lines since the nearsurface currents always exist on the ocean [5].
As an extension of shorebased HFSWR, shipborne HFSWR not only inherits all the advantages of shorebased HFSWR but also shows some outstanding features, such as flexibility and mobility. However, some new problems emerge as the radar on board is a moving ship. One of the worst problems is that the firstorder Bragg lines have been broadened into two pass bands (when the speed of ship is slow) or one low pass band (when the ship is sailing at a high speed) in the firstorder Bragg sea echo spectrum of shipborne HFSWR [6]. For these cases, it will be hard to determine the ocean currents from the broadened sea echo spectrum. Furthermore, the moving ship yields different Doppler shifts to the different azimuth sea echoes. Thus, there exists a certain spacetime coupling relation in the received sea echo spectrum of shipborne HFSWR.
The novel spacetime IMP algorithm was proposed by Clarke and Spence [7] which was based on onedimensional IMP algorithm and modified to detect and estimate multiple signals from the conventional beamwidth and (or) Doppler resolution bin. Although spacetime IMP estimator effectively improves the robustness of the detection and estimation of multiple signals, the computational load of twodimensional search process is too heavy for realtime application. Lately, Chadwick [8] used the eigendecomposition method instead of the fullsearch process to reduce the heavy computational burden in his proposed polarisationsensitive IMP algorithm. However, for surface wave radar, this method becomes invalid since the returns of HFSWR are mostly vertical polarization sensitive components.
Many researchers, such as Shaw and Wilkins [9], used beamspace preprocessing technique to reduce the computational load and improve robust performance of highresolution DOA (directionofarrival) estimation algorithms. Recently, Hassanien et al. [10, 11], proposed a new concept about beamspace preprocessing algorithm which was able to suppress the outofsector interferences accompanied with the updated array data. This technique was proven to be more robust than the aforementioned beamspace methods.
In this paper, we combine the spacetime IMP algorithm and the adaptive beamspace preprocessing technique yielding a computationally cheap spacetime adaptive estimator for detection, estimation and superresolution of multiple signals. The proposed algorithm is validated by simulation results as well as experimental examples.
This paper is organized as follows. First we introduce the signal model. In the following section, the proposed algorithm and some simulation results are presented. The measurement of the nearsurface currents of the ocean by shipborne HFSWR and some realdata analysis are presented in Section 4. The final part is the study conclusion.
2. Signal Model
Consider a uniform linear array (ULA) with omnidirectional antennas and the antenna spacing . If there are sources that have been received from a far field with different relative delays and attenuations. The received data is then given by [7] as follows: where denotes the data received from the th sensor at th sampling time, denotes the transpose operation, is the array manifold matrix, is the steering vector points to the direction , denotes wavelength of the radar, is a () diagonal matrix containing the signal magnitudes, is a () matrix comprising the normalized source waveforms, is the normalized source waveform, is the frequency of th source, denotes the Hermitian transpose operation, and is the () matrix comprising the zero mean and variance Gaussian noise.
The () covariance matrix of the received data is given by where is the statistical expectation operator, is the () source covariance matrix, and is the identity matrix.
3. Modified STAP Estimator
3.1. SpaceTime IMP
Spacetime IMP is a twodimensional maximum likelihood method which uses a set of spacetime calibration response vectors to match with the received data. Thus, the primary objective of spacetime IMP is to maximize the “signal plus noise” to “expected noise” power ratio (SNR). If the maximum output power is over the threshold, then a target is detected and the corresponding spacetime calibration response vector is recorded. In order to reduce the sidelobe leakage of the detected targets and improve the detection and estimation of the potential signals in the residual data, the detected targets are removed from the original data through an orthogonal subspace projection matrix before each iterative stage.
According to the definition of SNR in spacetime IMP, we have the following [7]: where is the () spacetime calibration response matrix, is the vectorization operation, and is an () orthogonal projection matrix, which is given by where denotes a sum of spacetime calibration response vectors corresponding to the detected signals; that is, projects the received data into a subspace orthogonal to the detected signals.
3.2. Adaptive BeamSpace Preprocessing
The adaptive beamspace preprocessing technique was first mentioned in [10] which used the updated data for adaptive suppression of outofsector interferences. This technique had been shown to be more robust than the aforementioned beamspace methods.
The primary objective of the dataadaptive beamspace preprocessing is to solve the optimal beamspace matrix design problem through minimizing the output power of the transformed data, which can be expressed as follows [12]: where is the trace of a matrix, is the () beamspace matrix, is the beamspace dimension, is the vector 2norm, denotes all outofsector directions which are divided into angular grids, and are the angles corresponding to the inofsector and outofsector directions, and is the stopband attenuation parameter which should meet the requirement [12]
After the beamspace transformation, the array steering vector matrix and manifold matrix have already transformed into
Then, the () covariance matrix in beamspace should be rewritten as
Obviously, the dimension of the matrix is lower than that of . This fact is exploited in all beamspacebased methods to reduce computational load compared with the elementspace algorithms [10].
3.3. SpaceTime Adaptive BeamSpace IMP
In this section, we show how the conventional spacetime estimator combines with the adaptive beamspace preprocessing technique to present a computationally cheap spacetime adaptive beamspace IMP estimator.
Following the discussion above, the twodimensional discriminants shown in (5) should be modified as where and has been reduced to a matrix in beamspace domain, which is given by where denotes a sum of spacetime calibration response vectors corresponding to the detected signals in beamspace domain.
3.4. Threshold Setting
How to select an appropriate threshold to terminate the iterative process in IMP algorithm is very important. Theoretically, when all “significant peaks” have been detected and cleared out from the received data, there is only a completely flat plane in the residual scan [13]. However, it is impossible to accurately estimate the noise statistics from the limited received data. Furthermore, the definition of “significant peak” in IMP algorithm has not been clearly reported.
In the paper, we use a doublethreshold setting method to ensure that the iterative process is halted timely. First, we check two successive scans before the next iteration. If the difference between the two scans is comparable to that of the “expected noise” level, that is, no “significant peak” appears during the last scan, then the iterative process should be halted. Besides, if the difference between two successive estimations has reached the preset threshold, which suggests that the iterations are estimating the same target, then the iterative process should be halted as well.
3.5. Simulation Results
Several simulation results are shown in this section to test the performance of the modified algorithm through comparing it with several conventional algorithms.
During the simulations, we assume that the radar works at , which contains an ULA with omnidirectional sensors and the elements are spaced onehalf wavelength apart. The half power beamwidth is approximately . The number of snapshots and the beamspace dimension are chosen for our simulations. The adaptive beamspace matrix has been solved using the cvx optimization MATLAB toolbox. Since the minimum value in (9) is , we take the parameter for (8). Furthermore, the two simulation targets and are also selected in the simulations.
To define a successful experiment, we use the criterion mentioned in [14] if where and () are, respectively, the estimated and truth values, then the two signals are successfully resolved.
Figures 1 and 2 illustrate the probability of source resolution and their root mean square error (RMSE) versus SNR in Doppler domain, respectively. The conventional spacetime IMP, spacetime beamspace IMP which combines spacetime IMP with discrete fourier transform (DFT) matrix beamspace processing technique [15], and 64 points and 256 points FFT results are used for the comparison in the figures. We find that the beamspacebased algorithms show better resolution and smaller RMSE than the other algorithms in resolving the two simulation targets. Thus, it is reasonable to conclude that the beamspacebased methods require less observation time but maintain high Doppler accuracy compared with the conventional algorithms. By the way, all the simulation results shown in this section have averaged over 1000 independent Monte Carlo experiments.
Figures 3 and 4 are the probability of source resolution and their RMSE versus SNR in azimuth domain, respectively. According to these figures, the beamspacebased algorithms show better performance than the other algorithms. Comparing these methods, the spacetime adaptive beamspace IMP algorithm shows the highest robust and lowest RMSE in resolving the two simulation targets. Thus, it is reasonable to conclude that the proposed algorithm requires smaller antenna array and lower SNR threshold for detection and estimation of multiple signals when compared with the conventional DOA algorithms.
4. Shipborne HFSWR
4.1. SpaceTime Coupling Relation
In [6], Xie et al. had proven that the firstorder Bragg spectrums were broadened along the azimuthal directions from the realdata analysis. The authors concluded that there was a spacetime coupling relation existed in the firstorder Bragg sea echo spectrum of shipborne HFSWR.
Assuming that both the transmitting and the receiving antennas of HFSWR are mounted on a ship which is moving in the positive direction of the xaxis at a constant speed , as shown in Figure 5.
In the absence of ocean current, the spacetime coupling relation in the firstorder Bragg sea echo spectrum of shipborne HFSWR can be expressed as follows [16]: where is the azimuth direction, are the firstorder Bragg frequencies, the positive and negative signs are, respectively, the Bragg waves moving towards and away from the radar.
4.2. Current Measurement
In the presence of ocean currents, the firstorder Bragg lines in (16) are shifted from the theoretical positions. The displacements are proportional to the radial current velocities. Thus, (16) should be rewritten as [17]
As shown in (17), the firstorder Bragg lines are related to the azimuth directions as well as the speed of ship and currents. Therefore, the firstorder Bragg peaks are not only displaced, but also broadened into two pass bands (for slow ship speed case) in the firstorder Bragg sea echo spectrum of shipborne HFSWR.
4.3. RealData Analysis
The real data used in this paper was received from the shipborne HFSWR experiments conducted on the Yellow Sea of China on September 8, 1998 [6]. Figures 6 and 7 show the spacetime coupling relation in the sixth range bin of the realdata file 1128 (containing 7 channels 256 samples 32 range bins and the ship speed was about 4.8 m/s), which is processed through the DFT plus DBF (Digital Beamforming) cascade processing and the proposed algorithm. As shown in the figures, the firstorder Bragg lines are broadened along the azimuth directions, which tally well with the theoretical lines in (16). The displacements may be caused by ocean currents or interferences.
Table 1 is an example of the DOA and Doppler estimations. The modified STAP estimator is used to process the abovementioned real data within the section between the azimuth and . Since there was no information about the sea state recorded during the experiment, we here assume that the detected targets near the theoretical firstorder Bragg lines are considered as ocean currents and their displacements are proportional to their radial velocities. Based on this assumption, five currents have been detected and estimated. All of them are very close to the theoretical firstorder Bragg frequencies and their corresponding radial velocities are calculated in the table.

Table 2 is another example for better understanding the robustness of the proposed algorithm, where we add a simulation target to the real data used previously, as shown in Figure 8. The added simulation target is detected correctly and the estimations of DOA and Doppler frequency are within and of the true signal position.

5. Conclusion
In this paper, we have introduced a modified spacetime adaptive processing estimator that can be used for the detection, estimation, and superresolution of multiple signals. The method combines the conventional IMP method and the existing adaptive beamspace preprocessing techniques yielding a computationally cheap algorithm for estimating the nearsurface currents of the ocean from the broadening of the firstorder Bragg sea echo spectrum of shipborne HFSWR. The proposed algorithm is validated by simulation results as well as experimental examples.
Acknowledgment
This work is supported by the State Key Program of National Natural Science of China (Grant no. 61132005).
References
 S. Tyrberg, O. Svensson, V. Kurupath, J. Engström, E. Strömstedt, and M. Leijon, “Wave buoy and translator motionsonsite measurements and simulations,” IEEE Journal of Oceanic Engineering, vol. 36, no. 3, pp. 377–385, 2011. View at: Publisher Site  Google Scholar
 F. J. Bugnon and I. A. Whitehouse, “Acoustic doppler current meter,” IEEE Journal of Oceanic Engineering, vol. 16, no. 3, pp. 420–426, 1991. View at: Publisher Site  Google Scholar
 L. Wyatt, “Wave mapping with HF radar,” in Proceedings of the 10th IEEE/OES Working Conference on Current, Waves and Turbulence Measurement (CWTM '11), pp. 25–30, Monterey, Calif, USA, March 2011. View at: Publisher Site  Google Scholar
 J. S. Bathgate, M. L. Heron, and A. Prytz, “A method of swellwave parameter extraction from HF ocean surface radar spectra,” IEEE Journal of Oceanic Engineering, vol. 31, no. 4, pp. 812–818, 2006. View at: Publisher Site  Google Scholar
 B. J. Lipa and D. E. Barrick, “Leastsquares methods for the extraction of surface currents from CODAR crossedloop data: application at ARSLOE,” IEEE Journal of Oceanic Engineering, vol. 8, no. 4, pp. 226–253, 1983. View at: Google Scholar
 J. Xie, Y. Yuan, and Y. Liu, “Experimental analysis of sea clutter in shipborne HFSWR,” IEE Proceedings: Radar, Sonar and Navigation, vol. 148, no. 2, pp. 67–71, 2001. View at: Publisher Site  Google Scholar
 I. J. Clarke and G. Spence, “A spacetime estimator for the detection and estimation of multiple sinusoidal signals,” in Proceedings of the IEE Colloquium High Resolution Radar and Sonar (Ref. No. 1999/051), pp. 9/1–9/6, London, UK, 1999. View at: Publisher Site  Google Scholar
 A. Chadwick, “Superresolution for highfrequency radar,” IET Radar, Sonar and Navigation, vol. 1, no. 6, pp. 431–436, 2007. View at: Publisher Site  Google Scholar
 A. Shaw and N. Wilkins, “Frequency invariant electromagnetic source location using true time delay beam space processing,” in Proceedings of the 4th IEEE International Symposium on Phased Array Systems and Technology (Array '10), pp. 998–1003, Boston, Mass, USA, October 2010. View at: Publisher Site  Google Scholar
 A. Hassanien, S. A. Elkader, A. B. Gershman, and K. M. Wong, “Convex optimization based beamspace preprocessing with improved robustness against outofsector sources,” IEEE Transactions on Signal Processing, vol. 54, no. 5, pp. 1587–1595, 2006. View at: Publisher Site  Google Scholar
 A. Hassanien and S. A. Vorobyov, “A robust adaptive dimension reduction technique with application to array processing,” IEEE Signal Processing Letters, vol. 16, no. 1, pp. 22–25, 2009. View at: Publisher Site  Google Scholar
 A. Hassanien and S. A. Vorobyov, “New results on robust adaptive beamspace preprocessing,” in Proceedings of the 5th IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM '08), pp. 315–319, July 2008. View at: Publisher Site  Google Scholar
 J. Mather, “The incremental multiparameter algorithm,” in Proceedings of the 24th Asilomar Conference on Signals, Systems & Computers, vol. 1, pp. 368–372, 1990. View at: Google Scholar
 A. B. Gershman, “Direction finding using beamspace root estimator banks,” IEEE Transactions on Signal Processing, vol. 46, no. 11, pp. 3131–3135, 1998. View at: Publisher Site  Google Scholar
 M. D. Zoltowski, G. M. Kautz, and S. D. Silverstein, “Beamspace rootMUSIC,” IEEE Transactions on Signal Processing, vol. 41, no. 1, pp. 344–364, 1993. View at: Google Scholar
 L. R. Wyatt, “Progress in the interpretation of HF sea echo: HF radar as a remote sensing tool,” IEE Proceedings F, vol. 137, no. 2, pp. 139–147, 1990. View at: Google Scholar
 K. W. Gurgel and H. H. Essen, “On the performance of a shipborne current mapping HF radar,” IEEE Journal of Oceanic Engineering, vol. 25, no. 1, pp. 183–191, 2000. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2013 Zhongbao Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.