Skip to main content
Log in

Measurement matrix design for CS-MIMO radar using multi-objective optimization

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, we design a measurement matrix for a compressive sensing-multiple-input multiple-output radar in the presence of clutter and interference. To optimize the measurement matrix, three main criteria are considered simultaneously to improve detection and sparse recovery performance while suppressing clutter and interference. To this end, we consider three well-known criteria including Bhattacharyya distance, mutual coherency of sensing matrix, and signal-to-clutter-plus-interference ratio. Due to the use of simultaneous multi-objective functions, a multi-objective optimization (MOO) framework is exploited. Some numerical examples are provided to illustrate the achieved improvement of our proposed method in target detection and sparse recovery performance. Simulation results show that the proposed MOO technique for measurement matrix design can achieve superior performance in target detection compared with Gaussian random measurement matrix technique.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Abolghasemi, V., Ferdowsi, S., Makkiabadi, B., & Sanei, S. (2010). On optimization of the measurement matrix for compressive sensing. In Proceedings European signal processing conference (pp. 427–431).

  • Abraham, A., & Jain, L. (2005). Evolutionary multiobjective optimization. Theoretical advances and applications (pp. 105–145). Berlin: Springer.

    Book  MATH  Google Scholar 

  • Aubry, A., Maio, A. D., Farina, A., & Wicks, M. (2013). Knowledge-aided (potentially cognitive) transmit signal and receive filter design in signal-dependent clutter. IEEE Transactions Aerospace Electronic Systems, 49(1), 93–117.

    Article  Google Scholar 

  • Bliss, D. W., & Forsythe, K. W. (2003). Multiple-input multiple-output (MIMO) radar and imaging: Degrees of freedom and resolution. In Proceedings of 37th Asilomar conference on signals, system computer (Vol. 1, pp. 54–59), Pacific Grove, CA.

  • Chen, Ch. Y., & Vaidyanathan, P. P. (2008). Compressed sensing in MIMO radar. In 42nd Asilomar conference on signals, systems and computers (pp. 41–44).

  • Deb, K. (2001). Multi-objective optimization using evolutionary algorithms (1st ed.). New York: Wiley.

    MATH  Google Scholar 

  • Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197.

    Article  Google Scholar 

  • Donoho, D. L., & Huo, X. (2001). Uncertainty principles and ideal atomic decomposition. IEEE Transactions on Information Theory, 47(7), 2845–2862.

    Article  MathSciNet  MATH  Google Scholar 

  • Du, X., & Cheng, L. (2015). Three stochastic measurement schemes for direction-of-arrival estimation using compressed sensing method. Multidimensional Systems and Signal Processing, 25(4), 621–636.

    Article  MATH  Google Scholar 

  • Elad, M. (2007). Optimized projections for compressed sensing. IEEE Transactions on Signal Processing, 55(12), 5695–5702.

    Article  MathSciNet  Google Scholar 

  • Gini, F., & Rangaswamy, M. (2008). Knowledge based radar detection, tracking and classification. New York, NY: Wiley-Interscience.

    Book  Google Scholar 

  • Gureci, J. R. (2010). Cognitive radar: The knowledge-aided fully adaptive approach. Norwood, MA: Artech House.

    Google Scholar 

  • Haimovich, A. M., Blum, R. S., & Cimini, L. J. (2008). MIMO radar with widely separated antennas. IEEE Signal Processing Magazine, 25(1), 116–129.

    Article  Google Scholar 

  • Hassanien, A., & Vorobyov, S. A. (2009). Transmit/receive beamforming for MIMO radar with colocated antennas. In 2009 IEEE international conference on acoustics, speech and signal processing (pp. 2089–2092).

  • Haykin, S. (2006). Cognitive radars. IEEE Signal Processing Magazine, 23(1), 30–40.

    Article  Google Scholar 

  • Hu, Q., Su, H., Zhou, Sh, Liu, Z., & Liu, J. (2016). Target detection in distributed MIMO radar with registration errors. IEEE Transactions on Aerospace and Electronic Systems, 52(1), 438–450.

    Article  Google Scholar 

  • Jabbarian-Jahromi, M., & Bizaki, H. K. (2014). Target tracking in MIMO radar systems using velocity vector. Journal of Information Systems and Telecommunication, 2, 150–158.

    Google Scholar 

  • Jabbarian-Jahromi, M., & Kahaei, M. H. (2014a). Two-dimensional iterative adaptive approach for a sparse matrix solution. IET Electronics Letters, 50(1), 45–47.

    Article  Google Scholar 

  • Jabbarian-Jahromi, M., & Kahaei, M. H. (2014b). Two-dimensional sparse solution for bistatic MIMO radars in presence of jammers. In 22nd Iranian conference on electrical engineering (ICEE) (pp. 1755–1759). IEEE, Tehran.

  • Jabbarian-Jahromi, M., & Kahaei, M. H. (2015). Two-dimensional SLIM with application to pulse Doppler MIMO radars. EURASIP Journal on Advances in Signal Processing, 69(1), 1–12.

    Google Scholar 

  • Jabbarian-Jahromi, M., & Kahaei, M. H. (2016). Complex two-dimensional TNIPM for \(l_1\) norm-based sparse optimization to collocated MIMO radar. IEEJ Transactions on Electrical and Electronic Engineering, 11(2), 228–235.

    Article  Google Scholar 

  • Jabbarian-Jahromi, M., Mohammadpour-Aghdam, K., Foudazi, G., & Mohammad-Salehi, M. (2014). DOA estimation based on sparse covariance vector representation using two-channel receiver. In 11th European radar conference (EuRAD).

  • Jabbarian-Jahromi, M., Shahbazi, N., Kahaei, M. H., & Abbasfar, A. (2016). Fast two-dimensional sparse Bayesian learning with application to pulse Doppler multiple-input multiple-output radars. IET Radar, Sonar & Navigation, 10(5), 966–975.

    Article  Google Scholar 

  • Kailath, T. (1967). The divergence and Bhattacharyya distance measures in signal selection. IEEE Transactions on Communication, 15(2), 52–60.

    Article  Google Scholar 

  • Karbasi, S. M., Aubry, A., Carotenuto, V., Naghsh, M. M., & Bastani, M. H. (2015). Knowledge-based design of space-time transmit code and receive filter for a multiple-input multiple-output radar in signal-dependent interference. IET Radar, Sonar and Navigation, 9, 1124–1135.

    Article  Google Scholar 

  • Knowles, J., & Corne, D. (1999). The Pareto archived evolution strategy: A new baseline algorithm for multiobjective optimization. In Proceedings of the 1999 Congress on Evolutionary Computation (pp. 98–105). Piscataway, NJ: IEEE Press.

  • Kuo, Y., Wu, K., & Chen, J. (2017). A scheme for distributed compressed video sensing based on hypothesis set optimization techniques. Multidimensional Systems and Signal Processing, 28(1), 1–15.

    Article  Google Scholar 

  • Li, B., & Petropulu, A. P. (2015). Distributed MIMO radar based on sparse sensing: Analysis and efficient implementation. IEEE Transactions on Aerospace and Electronic Systems, 51(4), 3055–3070.

    Article  Google Scholar 

  • Li, H., Zhou, M., Guo, Q., Wu, R., & Xi, J. (2016). Compressive sensing-based wind speed estimation for low-altitude wind-shear with airborne phased array radar. Multidimensional Systems and Signal Processing. https://doi.org/10.1007/s11045-016-0448-6.

  • Liao, B., & Chan, Sh. (2015). Direction finding in MIMO radar with unknown transmitter and/or receiver gains and phases. Multidimensional Systems and Signal Processing, 28(2), 691–707.

    Article  MATH  Google Scholar 

  • MacQueen, J. B. (1967). Some methods for classification and analysis of multivariate observations. In Proceedings of 5th Berkeley symposium on mathematical statistics and probability (Vol. 1, pp. 281–297).

  • Naghsh, M. M., & Modarres-Hashemi, M. (2012). Exact theoretical performance analysis of optimum detector for statistical MIMO radars. IET Radar, Sonar and Navigation, 6, 99–111.

    Article  Google Scholar 

  • Niu, M., Salari, S., Kim, I., Chan, F., & Rajan, S. (2015). Recovery probability analysis for sparse signals via OMP. IEEE Transactions on Aerospace and Electronic Systems, 51(4), 3475–3479.

    Article  Google Scholar 

  • Rousseeuw, P. J. (1989). Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20, 53–65.

    Article  MATH  Google Scholar 

  • Sen, S., Tang, G., & Nehorai, A. (2011). Multiobjective optimization of OFDM radar waveform for target detection. IEEE Transactions on Signal Processing, 59(2), 639–652.

    Article  MathSciNet  Google Scholar 

  • Shahbazi, N., Abbasfar, A., & Jabbarian-Jahromi, M. (2017). Efficient two-dimensional compressive sensing in MIMO radar. EURASIP Journal on Advances in Signal Processing, 1(23), 1–15.

    Google Scholar 

  • Stoica, P., He, H., & Li, J. (2009). New algorithms for designing unimodular sequences with good correlation properties. IEEE Transactions on Signal Processing, 57(4), 1415–1425.

    Article  MathSciNet  Google Scholar 

  • Sun, C., Wang, B., Fang, Y., & Song, Z. (2017). Narrow-band radar imaging for off-grid spinning targets via compressed sensing. Multidimensional Systems and Signal Processing, 28(4), 1167–1181.

    Article  MathSciNet  Google Scholar 

  • Taboada, H., & Coit, D. (2005). Post-Pareto optimality analysis to efficiently identify promising solutions for multi-objective problems. Rutgers University ISE Working Paper, 5-15.

  • Tan, X., Roberts, W., Li, J., & Stoica, P. (2011). Sparse learning via iterative minimization with application to MIMO radar imaging. IEEE Transactions on Signal Processing, 59(3), 1088–1101.

    Article  MathSciNet  Google Scholar 

  • Tan, Z., Yang, P., & Nehorai, A. (2014). Joint sparse recovery method for compressed sensing with structured dictionary mismatches. IEEE Transactions on Signal Processing, 62(19), 4997–5008.

    Article  MathSciNet  Google Scholar 

  • Tropp, J. A. (2004). Greed is good: Algorithmic results for sparse approximation. IEEE Transactions on Information Theory, 50(10), 2231–2242.

    Article  MathSciNet  MATH  Google Scholar 

  • Yu, Y., Petropulu, A. P., & Poor, H. V. (2010). MIMO radar using compressive sampling. IEEE Journal of Selected Topics in Signal Processing, 4(1), 146–163.

    Article  Google Scholar 

  • Yu, Y., Petropulu, A. P., & Poor, H. V. (2011). Measurement matrix design for compressive sensing-based MIMO radar. IEEE Transactions on Signal Processing, 59(11), 5338–5352.

    Article  MathSciNet  Google Scholar 

  • Yu, Y., Petropulu, A. P., & Poor, H. V. (2012). CSSF MIMO RADAR: Compressive-sensing and step-frequency based MIMO radar. IEEE Transactions on Aerospace and Electronic Systems, 48(2), 1490–1504.

    Article  Google Scholar 

  • Yu, Y., Sun, Sh, Madan, R. N., & Petropulu, A. P. (2014). Power allocation and waveform design for the compressive sensing based MIMO radar. IEEE Transactions on Aerospace and Electronic Systems, 50(2), 898–909.

    Article  Google Scholar 

  • Zhu, W., & Chen, B. X. (2015). Novel methods of DOA estimation based on compressed sensing. Multidimensional Systems and Signal Processing, 26(1), 113–123.

    Article  MathSciNet  Google Scholar 

  • Zhu, H., Leus, G., & Giannakis, G. B. (2011). Sparsity-cognizant total least-squares for perturbed compressive sampling. IEEE Transactions on Signal Processing, 59(5), 2002–2016.

    Article  MathSciNet  Google Scholar 

  • Zibetti, M. V. W., & De Pierro, A. R. (2017). Improving compressive sensing in MRI with separate magnitude and phase priors. Multidimensional Systems and Signal Processing, 28(4), 1109–1131.

    Article  MathSciNet  Google Scholar 

  • Zitzler, E. (1999). Evolutionary algorithms for multiobjective optimization: Methods and applications. Doctoral dissertation ETH 13398, Swiss Federal Institute of Technology (ETH), Zurich.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Aliazam Abbasfar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shahbazi, N., Abbasfar, A. & Jabbarian-Jahromi, M. Measurement matrix design for CS-MIMO radar using multi-objective optimization. Multidim Syst Sign Process 29, 761–782 (2018). https://doi.org/10.1007/s11045-017-0542-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11045-017-0542-4

Keywords

Navigation