Joint Design of Colocated MIMO Radar Constant Envelope Waveform and Receive Filter to Reduce SINR Loss
Abstract
:1. Introduction
- Beampattern. Compared with the methods proposed in [23,47] and PA, the beampattern by our proposed methods has deeper nulls in the interference direction and good energy accumulation in the target azimuth. Moreover, when the interference number (or power) increases (no more than (DOF-1)), nulls can still be formed in the interference azimuth.
- Waveform properties. The constant envelope waveform designed in this paper meets the actual hardware requirements of the radar transmitter and avoids the distortion of the waveform caused by the nonlinear effect of the amplifier. The good waveform characteristics of LFM are shared with the designed constant envelope waveform.
- The computational complexity of the proposed JD-CD is smaller than that of JD-SFR, and it reflects the process of waveform design concisely and intuitively, which can realize real-time waveform and receive filter design.
2. System Model
3. Problem Formulation
3.1. Maximize Output SINR
3.2. Receive Filter Design
3.3. Constrained Waveform Design
4. Proposed Algorithm
4.1. JD-SFR Algorithm
Algorithm 1. JD-SFR |
Input: Output: and 0: Set , initialize the transmit waveform (use Equation (13) to calculate the reference waveform , ) and the receive filter is calculated by (12). Then, compute by Equation (10). 1: 2: Compute and using the problem in Equation (22), respectively 3: 4: Compute by Gaussian randomization technique 3: 4: Compute by Equation (12) 5: Compute by Equation (10) 6: If , where is a user selected parameter to control convergence, stop iterating the output optimal transmit waveform and receive filter . Otherwise, repeat step 1 until convergence. |
4.2. JD-CD Algorithm
Algorithm 2. JD-CD |
Input: Output: and 0: Set , initialize the transmit waveform (use expression (13) to calculate the reference waveform , ) and the receive filter is calculated by (12). Then, compute by (10). 1: , 2: 3: Compute by (12) 4: Compute and by (24) and (25), respectively 5: 6: Compute and by (28) and (29), respectively 7: Compute and by (31) and (32), respectively 8: Compute using the problem in (33) or (40) 9: Synthesize by (16) and to replace immediately 10: If , and compute by (42), then . Otherwise, return to step 5. 11: If , where is a user selected parameter to control convergence, stop iterating the output optimal transmit waveform and receive filter . Otherwise, repeat step 1 until convergence. |
5. Simulation Results
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
ADMM | Alternating Direction Method of Multipliers |
APSL | Auto-correlation Peak Sidelobe Level |
BSUM | Block Successive Upper-bound Minimization |
CD | Coordinate Descent |
DOF | Degrees Of Freedom |
DOA | Direction Of Arrival |
DRFM | Digital Radio Frequency Memory |
FIR | Finite Impulse Response |
ISL | Integrated Sidelobe Level |
INR | Interference-to-Noise Ratio |
JD-SFR | Joint Design method based on Semidefinite Relaxation, Fractional Programming and Randomization Technique |
JD-CD | Joint Design method based on Coordinate Descent |
JOSA | Joint Optimization of Transmit Waveform and Receive Filter by Sequential Algorithm |
JOAC-MAPP | Joint Optimization Algorithm Case, Majorization-Maximization Algorithm for Parametric Problem |
LFM | Linear Frequency Modulation |
MIMO | Multiple-Input Multiple-Output |
MSE | Mean-Squared Error |
MVDR | Minimum Variance Distortionless Response |
MMSE | Minimum Mean-Square Error |
PA | Phased Array |
PDAM | Phase-only Dual Ascent Method |
PSL | Peak Sidelobe Level |
PAR | Peak-to-Average Ratio |
PCCL | Peak Cross-Correlation Level |
RD-MUSIC | Reduced-Dimension Multiple Signal Classification |
RCS | Radar Cross Section |
SDR | Semidefinite Relaxation |
SINR | Signal-to-Interference-plus-Noise Ratio |
SQP | Sequential Quadratic Programming |
SNR | Signal-to-Noise Ratio |
TR-MUSIC | Time-Reversal Multiple Signal Classification |
ULA | Uniform Linear Array |
Appendix A
Characteristics of References | Category | Subcategory | References Number |
---|---|---|---|
Arrangement of array spacing | Distributed | / | [5] |
Colocated | [6,7,17,18,34,38,39], etc. | ||
Waveform design | Consider only the transmitter | Transmit covariance matrices | [15,17,18,38,39] |
Transmit beampattern | [7,8,9,10,19,20] | ||
Joint transmitter and receiver | / | [14,21,22,23,24,25,26,27,28,29,31,33,34,36,40] | |
Methods | Convex optimization | / | [3,11,14,16,23,31,35,36] |
Other design ideas | / | [17,22,31,33,34,36,38,39,40] | |
Constraints | Constant envelope | / | [3,8,9,10,11,12,16,18,21,27,30,32,34,35,36,38,50] |
PAR | / | [8,9,19,35,47] | |
Similarity | / | [11,16,29,43,50,51] | |
Sidelobe | / | [15,21,22,30,32,33,38,47,50] | |
Expect the parameters | SINR | Parameter estimation | [7,41,42,43,44] |
High-resolution range contour | [21,45] | ||
Target detection | [16,38,40,46,47,48] | ||
Rank | / | [4,15,17,27,38,39] | |
Receive filter design | MVDR | / | [3,4,14,17,18,21,27,34,35,36,38], etc. |
MMSE | [6,37] |
References
- Stoica, P.; Jian, L.; Yao, X. On Probing Signal Design for MIMO Radar. IEEE Trans. Signal Process. 2007, 55, 4151–4161. [Google Scholar] [CrossRef] [Green Version]
- Jian, L.; Stoica, P.; Luzhou, X.; Roberts, W. On Parameter Identifiability of MIMO Radar. IEEE Signal. Process. Lett. 2007, 14, 968–971. [Google Scholar] [CrossRef]
- Feraidooni, M.M.; Gharavian, D.; Imani, S. Signal-dependent interference reduction based on a new transmit covariance matrix and receive filter design for colocated MIMO radar. SignalImage Video Process. 2019, 13, 1275–1282. [Google Scholar] [CrossRef]
- Liu, J.; Li, H.; Himed, B. Joint Optimization of Transmit and Receive Beamforming in Active Arrays. IEEE Signal. Process. Lett. 2014, 21, 39–42. [Google Scholar] [CrossRef]
- Haimovich, A.M.; Blum, S.; Cimini, L.J. MIMO Radar with Widely Separated Antennas. IEEE Signal. Process. Mag. 2008, 25, 116–129. [Google Scholar] [CrossRef]
- Li, J.; Stoica, P. MIMO Radar with Colocated Antennas. IEEE Signal. Process. Mag. 2007, 24, 106–114. [Google Scholar] [CrossRef]
- Xu, L.Z.; Li, J.; Stoica, P. Target Detection and Parameter Estimation for MIMO Radar Systems. IEEE Trans. Aerosp. Electron. Syst. 2008, 44, 927–939. [Google Scholar]
- Fan, W.; Liang, J.; Li, J. Constant Modulus MIMO Radar Waveform Design with Minimum Peak Sidelobe Transmit Beampattern. IEEE Trans. Signal. Process. 2018, 66, 4207–4222. [Google Scholar] [CrossRef]
- Imani, S.; Bolhasani, M.; Ghorashi, S.A.; Rashid, M. Waveform Design in MIMO Radar Using Radial Point Interpolation Method. IEEE Commun. Lett. 2018, 22, 2076–2079. [Google Scholar] [CrossRef]
- Liu, B.; Chen, B.; Yang, M. Constant-Modulus-Waveform Design for Multiple-Target Detection in Colocated MIMO Radar. Sensors 2019, 19, 4040. [Google Scholar] [CrossRef] [Green Version]
- Wang, X.; Zhang, G.; Zhang, Y.; Wang, Q.; Leung, H. Design of spectrally compatible waveform with constant modulus for colocated multiple-input multiple-output radar. IET RadarSonar Navig. 2019, 13, 1373–1388. [Google Scholar] [CrossRef]
- Tang, B.; Tang, J. Joint Design of Transmit Waveforms and Receive Filters for MIMO Radar Space-Time Adaptive Processing. IEEE Trans. Signal. Process. 2016, 64, 4707–4722. [Google Scholar] [CrossRef]
- Yu, X.; Cui, G.; Piezzo, M.; Iommelli, S.; Kong, L. Robust constrained waveform design for MIMO radar with uncertain steering vectors. Eurasip J. Adv. Signal. Process. 2017, 2017, 2. [Google Scholar] [CrossRef] [Green Version]
- Imani, S.; Ghorashi, S.A. Transmit Signal and Receive Filter Design in Co-located MIMO Radar Using a Transmit Weighting Matrix. IEEE Signal. Process. Lett. 2015, 22, 1521–1524. [Google Scholar] [CrossRef]
- Ahmed, S.; Alouini, M.-S. MIMO-Radar Waveform Covariance Matrix for High SINR and Low Side-Lobe Levels. IEEE Trans. Signal. Process. 2014, 62, 2056–2065. [Google Scholar] [CrossRef]
- Yu, X.; Cui, G.; Kong, L.; Li, J.; Gui, G. Constrained Waveform Design for Colocated MIMO Radar with Uncertain Steering Matrices. IEEE Trans. Aerosp. Electron. Syst. 2019, 55, 356–370. [Google Scholar] [CrossRef]
- Imani, S.; Ghorashi, S.A.; Bolhasani, M. SINR maximization in colocated MIMO radars using transmit covariance matrix. Signal. Process. 2016, 119, 128–135. [Google Scholar] [CrossRef]
- Bolhasani, M.; Mehrshahi, E.; Ghorashi, S.A. Waveform covariance matrix design for robust signal-dependent interference suppression in colocated MIMO radars. Signal. Process. 2018, 152, 311–319. [Google Scholar] [CrossRef]
- Fan, W.; Liang, J.; Yu, G.; So, H.C.; Lu, G. MIMO Radar Waveform Design for Quasi-Equiripple Transmit Beampattern Synthesis via Weighted $l_p$-Minimization. IEEE Trans. Signal. Process. 2019, 67, 3397–3411. [Google Scholar] [CrossRef]
- Hua, G.; Abeysekera, S.S. Colocated Mimo Radar Transmit Beamforming Using Orthogonal Waveforms. In Proceedings of the 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Kyoto, Japan, 25–30 March 2012; pp. 2453–2456. [Google Scholar]
- Bolhasani, M.; Mehrshahi, E.; Ghorashi, S.A.; Alijani, M.S. Constant envelope waveform design to increase range resolution and SINR in correlated MIMO radar. Signal. Process. 2019, 163, 59–65. [Google Scholar] [CrossRef]
- Zhou, S.; Lu, J.; Varshney, P.K.; Wang, J.; Ma, H.; Liu, H. Colocated MIMO radar waveform optimization with receive beamforming. Digit. Signal. Process. 2020, 98, 102635. [Google Scholar] [CrossRef]
- Imani, S.; Nayebi, M.M.; Ghorashi, S.A. Transmit Signal Design in Colocated MIMO Radar Without Covariance Matrix Optimization. IEEE Trans. Aerosp. Electron. Syst. 2017, 53, 2178–2186. [Google Scholar] [CrossRef]
- Tong, R.; Zhang, J.; Zhou, Q. Joint Robust Design Method of Transmit Waveform and Receive Filter Bank for Airborne MIMO Radar. J. Detect. Control. 2020, 42, 35–43. [Google Scholar]
- Imani, S.; Nayebi, M.M.; Ghorashi, S.A. Colocated MIMO Radar SINR Maximization Under ISL and PSL Constraints. IEEE Signal. Process. Lett. 2018, 25, 422–426. [Google Scholar] [CrossRef]
- Tong, R.; Zhang, J.; Zhou, Q. Optimization Algorithm of Fast Waveform Design for Airborne MIMO Radar with Constant Modulus and Similarity Constraints. Shipboard Electron. Countermeas. 2019, 42, 45–52. [Google Scholar]
- Imani, S.; Feraidooni, M.M.; Gharavian, D.; Nayebi, M.M. SINR improvement based on joint design of transmit covariance matrix and receive filter design for colocated MIMO radar. IET Commun. 2020, 15, 603–612. [Google Scholar] [CrossRef]
- Zhou, Q.; Li, Z.; Shi, J.; Mao, Y. Robust cognitive transmit waveform and receive filter design for airborne MIMO radar in signal-dependent clutter environment. Digit. Signal. Process. 2020, 101, 102709. [Google Scholar] [CrossRef]
- Cheng, X.; Aubry, A.; Ciuonzo, D.; De Maio, A.; Wang, X. Robust Waveform and Filter Bank Design of Polarimetric Radar. IEEE Trans. Aerosp. Electron. Syst. 2017, 53, 370–384. [Google Scholar] [CrossRef]
- Wang, Y.C.; Wang, J.T. Constant Modulus Probing Waveform Design for Mimo Radar via Admm Algorithm. In Proceedings of the 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, AB, Canada, 15–20 April 2018; pp. 3305–3309. [Google Scholar]
- Feraidooni, M.M.; Gharavian, D.; Imani, S.; Alaee-Kerahroodi, M. Designing M-ary sequences and space-Time receive filter for moving target in cognitive MIMO radar systems. Signal. Process. 2020, 174, 107620. [Google Scholar] [CrossRef]
- Xu, L.; Zhou, S.; Liu, H.; Liu, J. Repeat radar jammer suppression for a colocated MIMO radar. IET RadarSonar Navig. 2019, 13, 1448–1457. [Google Scholar] [CrossRef]
- Feraidooni, M.M.; Gharavian, D.; Alaee-Kerahroodi, M.; Imani, S. A Coordinate Descent Framework for Probing Signal Design in Cognitive MIMO Radars. IEEE Commun. Lett. 2020, 24, 1115–1118. [Google Scholar] [CrossRef]
- Feraidooni, M.M.; Alaee-Kerahroodi, M.; Imani, S.; Gharavian, D. Designing Set of Binary Sequences and Space-Time Receive Filter for Moving Targets in Colocated MIMO Radar Systems. In Proceedings of the 2019 20th International Radar Symposium (IRS), Ulm, Germany, 26–28 June 2019; pp. 1–10. [Google Scholar]
- Wu, L.; Babu, P.; Palomar, D.P. Transmit Waveform/Receive Filter Design for MIMO Radar with Multiple Waveform Constraints. IEEE Trans. Signal. Process. 2018, 66, 1526–1540. [Google Scholar] [CrossRef]
- Alaee-Kerahroodi, M.; Imani, S.; Shankar, M.R.B.; Nayebi, M.M.; Ottersten, B. A Coordinate Descent Framework to Joint Design of MPSK Sequences and Receive Filter Weights in MIMO Radar Systems. In Proceedings of the 2019 IEEE Radar Conference, Boston, MA, USA, 22–26 April 2019. [Google Scholar]
- Herbert, S.; Hopgood, J.R.; Mulgrew, B. MMSE Adaptive Waveform Design for Active Sensing with Applications to MIMO Radar. IEEE Trans. Signal. Process. 2018, 66, 1361–1373. [Google Scholar] [CrossRef] [Green Version]
- Xiong, W.; Greco, M.; Gini, F.; Zhang, G.; Leung, H.; Deng, X. Toeplitz covariance matrix of colocated MIMO radar waveforms for SINR maximization. Signal. Process. 2019, 158, 156–165. [Google Scholar] [CrossRef]
- Xiong, W.; Greco, M.; Gini, F.; Zhang, G.; Peng, Z.N. Toeplitz Matrix-Based Transmit Covariance Matrix of Colocated Mimo Radar Waveforms for Sinr Maximization. In Proceedings of the 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, AB, Canada, 15–20 April 2018; pp. 3295–3299. [Google Scholar]
- Yu, Z.; Wang, S.; Liu, W.; Li, C. Joint Design of Space-Time Transmit and Receive Weights for Colocated MIMO Radar. Sensors 2018, 18, 2722. [Google Scholar] [CrossRef] [Green Version]
- Wen, F.; Xiong, X.; Su, J.; Zhang, Z. Angle estimation for bistatic MIMO radar in the presence of spatial colored noise. Signal. Process. 2017, 134, 261–267. [Google Scholar] [CrossRef]
- Wen, F. Computationally Efficient DOA Estimation Algorithm for MIMO Radar with Imperfect Waveforms. IEEE Commun. Lett. 2019, 23, 1037–1040. [Google Scholar] [CrossRef]
- Cheng, Z.Y.; Liao, B.; He, Z.S.; Li, J.; Xie, J.L. Joint Design for Mimo Radar and Downlink Communication Systems Coexistence. In Proceedings of the 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, UK, 12–17 May 2019; pp. 4270–4274. [Google Scholar]
- Ciuonzo, D.; Romano, G.; Solimene, R. Performance Analysis of Time-Reversal MUSIC. IEEE Trans. Signal. Process. 2015, 63, 2650–2662. [Google Scholar] [CrossRef]
- Wang, X.H.; Zhang, G.; Wen, F.Q.; Ben, D. Schemes for synthesizing high-resolution range profile with extended OFDM-MIMO. J. Syst. Eng. Electron. 2017, 28, 424–434. [Google Scholar]
- Liu, J.; Zhou, S.; Liu, W.; Zheng, J.; Liu, H.; Li, J. Tunable Adaptive Detection in Colocated MIMO Radar. IEEE Trans. Signal. Process. 2018, 66, 1080–1092. [Google Scholar] [CrossRef]
- Zheng, H.; Jiu, B.; Liu, H. Joint Optimization of Transmit Waveform and Receive Filter for Target Detection in MIMO Radar. IEEE Access 2019, 7, 184923–184939. [Google Scholar] [CrossRef]
- Guerci, J.R.; Pillai, S.U. Theory and application of optimum transmit-receive radar. In Record of the IEEE 2000 International Radar Conference; IEEE: Piscataway, NJ, USA, 2000; pp. 705–710. [Google Scholar]
- Gruber, F.K.; Marengo, E.A.; Devaney, A.J. Time-reversal imaging with multiple signal classification considering multiple scattering, between the targets. J. Acoust Soc. Am. 2004, 115, 3042–3047. [Google Scholar] [CrossRef]
- Yu, X.; Cui, G.; Zhang, T.; Kong, L. Constrained transmit beampattern design for colocated MIMO radar. Signal. Process. 2018, 144, 145–154. [Google Scholar] [CrossRef]
- Cui, G.; Li, H.; Rangaswamy, M. MIMO Radar Waveform Design with Constant Modulus and Similarity Constraints. IEEE Trans. Signal. Process. 2014, 62, 343–353. [Google Scholar] [CrossRef]
- Kocjancic, L.; Balleri, A.; Merlet, T. Multibeam radar based on linear frequency modulated waveform diversity. IET RadarSonar Navig. 2018, 12, 1320–1329. [Google Scholar] [CrossRef] [Green Version]
- Yang, D.F.; Zhou, S.H.; Gao, H.Y.; Liang, C.J.; Liu, H.W.; Liang, X.L. MIMO Signal Design for Coexistence with LFM. In Proceedings of the 2018 International Conference on Radar (RADAR), Brisbane, QLD, Australia, 27–31 August 2018; pp. 1–5. [Google Scholar]
- Capon, J. High-resolution frequency-wavenumber spectrum analysis. Proc. IEEE 1969, 57, 1408–1418. [Google Scholar] [CrossRef] [Green Version]
- Cheng, Z.; He, Z.; Liao, B.; Fang, M. MIMO Radar Waveform Design with PAPR and Similarity Constraints. IEEE Trans. Signal. Process. 2018, 66, 968–981. [Google Scholar] [CrossRef]
- Li, H.; Zhao, Y.; Cheng, Z.; Feng, D. Correlated LFM Waveform Set Design for MIMO Radar Transmit Beampattern. IEEE Geosci. Remote Sens. Lett. 2017, 14, 329–333. [Google Scholar] [CrossRef]
- Boyd, S.; Vandenberghe, L. Convex Optimization; Cambridge University Press: Cambridge, UK, 2004. [Google Scholar]
- Charnes, A.; Cooper, W.W. Programming with linear fractional functionals. Nav. Res. Logist. Q. 1962, 9, 181–186. [Google Scholar] [CrossRef]
- De Maio, A.; De Nicola, S.; Huang, Y.; Luo, Z.-Q.; Zhang, S. Design of Phase Codes for Radar Performance Optimization with a Similarity Constraint. IEEE Trans. Signal. Process. 2009, 57, 610–621. [Google Scholar] [CrossRef]
- Grant, M.; Boyd, S. CVX: Matlab Software for Disciplined Convex Programming, version 2.1. 2014. Available online: http://cvxr.com/cvx (accessed on 10 July 2019).
- Hoctor, R.T.; Kassam, S.A. The Unifying Role of the Coarray in Aperture Synthesis for Coherent and Incoherent Imaging. Proc. IEEE 1990, 78, 735–752. [Google Scholar] [CrossRef]
Simulation Parameter | First Simulation | Second Simulation | Third Simulation | Fourth Simulation |
---|---|---|---|---|
Arrangement spacing of ULA: | ||||
4 | 4 | 4 | 4 | |
4 | 4 | 4 | 4 | |
16 | 16 | 16 | 16 | |
300 | 300 | 300 | 300 | |
32 | 32 | 32 | 32 | |
0.5 | 0.5 | 0.5 | [0.1, 0.5, 1.5, 2] | |
3 | 3 | 3 | 3 | |
6 | 6 | |||
20 dB | 20 dB | [−30, 30] dB | 20 dB | |
20 dB | [−10, 40] dB | 20 dB | 20 dB | |
0 dB | 0 dB | 0 dB | 0 dB | |
0.001 | 0.001 | 0.001 | 0.001 |
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Huang, L.; Deng, X.; Zheng, L.; Qin, H.; Qiu, H. Joint Design of Colocated MIMO Radar Constant Envelope Waveform and Receive Filter to Reduce SINR Loss. Sensors 2021, 21, 3887. https://doi.org/10.3390/s21113887
Huang L, Deng X, Zheng L, Qin H, Qiu H. Joint Design of Colocated MIMO Radar Constant Envelope Waveform and Receive Filter to Reduce SINR Loss. Sensors. 2021; 21(11):3887. https://doi.org/10.3390/s21113887
Chicago/Turabian StyleHuang, Liang, Xiaofang Deng, Lin Zheng, Huiping Qin, and Hongbing Qiu. 2021. "Joint Design of Colocated MIMO Radar Constant Envelope Waveform and Receive Filter to Reduce SINR Loss" Sensors 21, no. 11: 3887. https://doi.org/10.3390/s21113887
APA StyleHuang, L., Deng, X., Zheng, L., Qin, H., & Qiu, H. (2021). Joint Design of Colocated MIMO Radar Constant Envelope Waveform and Receive Filter to Reduce SINR Loss. Sensors, 21(11), 3887. https://doi.org/10.3390/s21113887