基于正交压缩采样系统的脉冲雷达回波信号实时重构方法
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摘要
正交压缩采样是低速获取带通模拟信号同相和正交分量的新型模信转换系统,可广泛应用于雷达、通信等电子系统。但是对于宽带或超宽带脉冲雷达,重构奈奎斯特率的全程回波信号需要大的存储空间和计算量,以致于难以实现实时重构。该文在对正交压缩采样系统特性进行分析的基础上,将测量矩阵近似成一种具有特殊带状结构的矩阵,然后采用分段滑动重构思想实现实时重构。仿真结果表明,在对测量矩阵进行合理近似的基础上,该文提出的重构方法可以极大地节省存储空间和计算时间,实现近似最优的重构性能。
Quadrature Compressive Sampling(Quad CS) is an efficient Analog-to-Information Conversion(AIC) system to sample band-pass analog signals at sub-Nyquist rates. The Quad CS can be widely used in radar and communication systems to acquire sub-Nyquist samples of inphase and quadrature components. However, for wideband or ultra-wideband pulsed radars, it is often impractical to reconstruct Nyquist samples of full-range echoes in real-time because of huge storage and computational loads. Based on the characteristics of Quad CS system, an approximate scheme is proposed to transform the Quad CS measurement matrix into a matrix with a special banded structure. With the banded matrix, a segment-sliding reconstruction method is adopted to perform real-time reconstruction. Simulation results show that with a reasonable approximation of the measurement matrix, the proposed reconstruction scheme achieves nearly optimal reconstruction performance with a significant reduction of data storage and computational time.
Quadrature Compressive Sampling(Quad CS) is an efficient Analog-to-Information Conversion(AIC) system to sample band-pass analog signals at sub-Nyquist rates. The Quad CS can be widely used in radar and communication systems to acquire sub-Nyquist samples of inphase and quadrature components. However, for wideband or ultra-wideband pulsed radars, it is often impractical to reconstruct Nyquist samples of full-range echoes in real-time because of huge storage and computational loads. Based on the characteristics of Quad CS system, an approximate scheme is proposed to transform the Quad CS measurement matrix into a matrix with a special banded structure. With the banded matrix, a segment-sliding reconstruction method is adopted to perform real-time reconstruction. Simulation results show that with a reasonable approximation of the measurement matrix, the proposed reconstruction scheme achieves nearly optimal reconstruction performance with a significant reduction of data storage and computational time.
引文
[1]DONOHO D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.doi:10.1109/TIT.2006.871582.
[2]CANDèS E J and TAO T.Near-optimal signal recovery from random projections:universal encoding strategies?[J].IEEE Transactions on Information Theory,2006,52(12):5406-5425.doi:10.1109/TIT.2006.885507.
[3]CANDèS E J and TAO T.Decoding by linear programming[J].IEEE Transactions on Information Theory,2005,51(12):4203-4215.doi:10.1109/TIT.2005.858979.
[4]YOO J,TURNES C,NAKAMURA E B,et al.A compressed sensing parameter extraction platform for radar pulse signal acquisition[J].IEEE Journal on Emerging and Selected Topics in Circuits and Systems,2012,2(3):626-638.doi:10.1109/JETCAS.2012.2214634.
[5]BARANSKY E,ITZHAK G,WAGNER N,et al.SubNyquist radar prototype:hardware and algorithm[J].IEEE Transactions on Aerospace and Electronic Systems,2014,50(2):809-822.doi:10.1109/TAES.2014.120475.
[6]BAR-ILAN O and ELDAR Y C.Sub-Nyquist radar via Doppler focusing[J].IEEE Transactions on Signal Processing,2014,62(7):1796-1811.doi:10.1109/TSP.2014.2304917.
[7]LIU C,XI F,CHEN S,et al.A pulse-Doppler processing scheme for quadrature compressive sampling radar[C].Proceedings of the 19th International Conference on Digital Signal Processing(DSP),Hong Kong,China,2014:676-681.doi:10.1109/ICDSP.2014.6900750.
[8]LIU C,XI F,CHEN S,et al.Pulse-Doppler signal processing with quadrature compressive sampling[J].IEEE Transactions on Aerospace and Electronic Systems,2015,51(2):1217-1230.doi:10.1109/TAES.2014.130475.
[9]KIROLOS S,LASKA J,WAKIN M,et al.Analog-toinformation conversion via random demodulation[C].Proceedings of the IEEE Dallas/CAS Workshop on Design,Applications,Integration and Software(DCAS),Richardson,TX,USA,2006:71-74.doi:10.1109/DCAS.2006.321036.
[10]TROPP J A,LASKA J N,DUARTE M F,et al.Beyond Nyquist:efficient sampling of sparse bandlimited signals[J].IEEE Transactions on Information Theory,2010,56(1):520-544.doi:10.1109/TIT.2009.2034811.
[11]BECKER S R.Practical compressed sensing:modern data acquisition and signal processing[D].[Ph.D.dissertation],California Institute of Technology,Pasadena,CA,USA,2011.
[12]MISHALI M,ELDAR Y C,and ELRON A J.Xampling:signal acquisition and processing in union of subspaces[J].IEEE Transactions on Signal Processing,2011,59(10):4719-4734.doi:10.1109/TSP.2011.2161472.
[13]XI F,CHEN S,and LIU Z.Quadrature compressive sampling for radar echo signals[C].Proceedings of the International Conference on Wireless Communications and Signal Processing(WCSP),Nanjing,China,2011:1-5.doi:10.1109/WCSP.2011.6096838.
[14]XI F,CHEN S,and LIU Z.Quadrature compressive sampling for radar signals[J].IEEE Transactions on Signal Processing,2014,62(11):2787-2802.doi:10.1109/TSP.2014.2315168.
[15]TROPP J A and GILBERT A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Transactions on Information Theory,2007,53(12):4655-4666.doi:10.1109/TIT.2007.909108.
[16]YIN W,OSHER S,GOLDFARB D,et al.Bregman iterative algorithms for L1-minimization with applications to compressed sensing[J].SIAM Journal on Imaging Sciences,2008,1(1):143-168.doi:10.1137/070703983.
[17]WU Q,ZHANG Y D,AMIN M G,et al.Complex multitask Bayesian compressive sensing[C].Proceedings of the IEEE International Conference on Acoustics,Speech and Signal Processing(ICASSP),Florence,Italy,2014:3375-3379.doi:10.1109/ICASSP.2014.6854226.
[18]TROPP J A and WRIGHT S J.Computational methods for sparse solution of linear inverse problems[J].Proceedings of the IEEE,2010,98(6):948-958.doi:10.1109/JPROC.2010.2044010.
[19]PETROS T B and ASIF M S.Compressive sensing for streaming signals using the streaming greedy pursuit[C].Proceedings of the Military Communications Conference(MILCOM),San Jose,CA,USA,2010:1205-1210.doi:10.1109/MILCOM.2010.5680110.
[20]ASIF M S and ROMBERG J.Sparse recovery of streaming signals using L1 homotopy[J].IEEE Transactions on Signal Processing,2014,62(16):4209-4223.doi:10.1109/TSP.2014.2328981.
[21]QIN S,ZHANG Y D,WU Q,et al.Large-scale sparse reconstruction through partitioned compressive sensing[C].Proceedings of the 19th International Conference on Digital Signal Processing,Hong Kong,China,2014:837-840.doi:10.1109/ICDSP.2014.6900784.
[22]ZHANG S,XI F,CHEN S,et al.Segment-sliding reconstruction of pulsed radar echoes with sub-Nyquist sampling[OL].http://arxiv.org/abs/1503.00434,2015.
[23]HERMAN M A and STROHMER T.General deviants:an analysis of perturbations in compressed sensing[J].IEEE Journal of Selected Topics in Signal Processing,2010,4(2):342-349.doi:10.1109/JSTSP.2009.2039170.
[24]HERMAN M A and NEEDELL D.Mixed operators in compressed sensing[C].Proceedings of the 44th Annual Conference on Information Sciences and Systems(CISS),Princeton,NJ,USA,2010:1-6.doi:10.1109/CISS.2010.5464909.
[25]DING J,CHEN L,and GU Y.Perturbation analysis of orthogonal matching pursuit[J].IEEE Transactions on Signal Processing,2013,61(2):398-410.doi:10.1109/TSP.2012.2222377.
[26]VAUGHAN R G,SCOTT N L,and WHITE D R.The theory of bandpass sampling[J].IEEE Transactions on Signal Processing,1991,39(9):1973-1984.doi:10.1109/78.134430.
1)式(8)在数学上是一个NP问题,在实际中,我们通常将式(8)转化为式(9)的凸优化问题进行求解。
[2]CANDèS E J and TAO T.Near-optimal signal recovery from random projections:universal encoding strategies?[J].IEEE Transactions on Information Theory,2006,52(12):5406-5425.doi:10.1109/TIT.2006.885507.
[3]CANDèS E J and TAO T.Decoding by linear programming[J].IEEE Transactions on Information Theory,2005,51(12):4203-4215.doi:10.1109/TIT.2005.858979.
[4]YOO J,TURNES C,NAKAMURA E B,et al.A compressed sensing parameter extraction platform for radar pulse signal acquisition[J].IEEE Journal on Emerging and Selected Topics in Circuits and Systems,2012,2(3):626-638.doi:10.1109/JETCAS.2012.2214634.
[5]BARANSKY E,ITZHAK G,WAGNER N,et al.SubNyquist radar prototype:hardware and algorithm[J].IEEE Transactions on Aerospace and Electronic Systems,2014,50(2):809-822.doi:10.1109/TAES.2014.120475.
[6]BAR-ILAN O and ELDAR Y C.Sub-Nyquist radar via Doppler focusing[J].IEEE Transactions on Signal Processing,2014,62(7):1796-1811.doi:10.1109/TSP.2014.2304917.
[7]LIU C,XI F,CHEN S,et al.A pulse-Doppler processing scheme for quadrature compressive sampling radar[C].Proceedings of the 19th International Conference on Digital Signal Processing(DSP),Hong Kong,China,2014:676-681.doi:10.1109/ICDSP.2014.6900750.
[8]LIU C,XI F,CHEN S,et al.Pulse-Doppler signal processing with quadrature compressive sampling[J].IEEE Transactions on Aerospace and Electronic Systems,2015,51(2):1217-1230.doi:10.1109/TAES.2014.130475.
[9]KIROLOS S,LASKA J,WAKIN M,et al.Analog-toinformation conversion via random demodulation[C].Proceedings of the IEEE Dallas/CAS Workshop on Design,Applications,Integration and Software(DCAS),Richardson,TX,USA,2006:71-74.doi:10.1109/DCAS.2006.321036.
[10]TROPP J A,LASKA J N,DUARTE M F,et al.Beyond Nyquist:efficient sampling of sparse bandlimited signals[J].IEEE Transactions on Information Theory,2010,56(1):520-544.doi:10.1109/TIT.2009.2034811.
[11]BECKER S R.Practical compressed sensing:modern data acquisition and signal processing[D].[Ph.D.dissertation],California Institute of Technology,Pasadena,CA,USA,2011.
[12]MISHALI M,ELDAR Y C,and ELRON A J.Xampling:signal acquisition and processing in union of subspaces[J].IEEE Transactions on Signal Processing,2011,59(10):4719-4734.doi:10.1109/TSP.2011.2161472.
[13]XI F,CHEN S,and LIU Z.Quadrature compressive sampling for radar echo signals[C].Proceedings of the International Conference on Wireless Communications and Signal Processing(WCSP),Nanjing,China,2011:1-5.doi:10.1109/WCSP.2011.6096838.
[14]XI F,CHEN S,and LIU Z.Quadrature compressive sampling for radar signals[J].IEEE Transactions on Signal Processing,2014,62(11):2787-2802.doi:10.1109/TSP.2014.2315168.
[15]TROPP J A and GILBERT A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Transactions on Information Theory,2007,53(12):4655-4666.doi:10.1109/TIT.2007.909108.
[16]YIN W,OSHER S,GOLDFARB D,et al.Bregman iterative algorithms for L1-minimization with applications to compressed sensing[J].SIAM Journal on Imaging Sciences,2008,1(1):143-168.doi:10.1137/070703983.
[17]WU Q,ZHANG Y D,AMIN M G,et al.Complex multitask Bayesian compressive sensing[C].Proceedings of the IEEE International Conference on Acoustics,Speech and Signal Processing(ICASSP),Florence,Italy,2014:3375-3379.doi:10.1109/ICASSP.2014.6854226.
[18]TROPP J A and WRIGHT S J.Computational methods for sparse solution of linear inverse problems[J].Proceedings of the IEEE,2010,98(6):948-958.doi:10.1109/JPROC.2010.2044010.
[19]PETROS T B and ASIF M S.Compressive sensing for streaming signals using the streaming greedy pursuit[C].Proceedings of the Military Communications Conference(MILCOM),San Jose,CA,USA,2010:1205-1210.doi:10.1109/MILCOM.2010.5680110.
[20]ASIF M S and ROMBERG J.Sparse recovery of streaming signals using L1 homotopy[J].IEEE Transactions on Signal Processing,2014,62(16):4209-4223.doi:10.1109/TSP.2014.2328981.
[21]QIN S,ZHANG Y D,WU Q,et al.Large-scale sparse reconstruction through partitioned compressive sensing[C].Proceedings of the 19th International Conference on Digital Signal Processing,Hong Kong,China,2014:837-840.doi:10.1109/ICDSP.2014.6900784.
[22]ZHANG S,XI F,CHEN S,et al.Segment-sliding reconstruction of pulsed radar echoes with sub-Nyquist sampling[OL].http://arxiv.org/abs/1503.00434,2015.
[23]HERMAN M A and STROHMER T.General deviants:an analysis of perturbations in compressed sensing[J].IEEE Journal of Selected Topics in Signal Processing,2010,4(2):342-349.doi:10.1109/JSTSP.2009.2039170.
[24]HERMAN M A and NEEDELL D.Mixed operators in compressed sensing[C].Proceedings of the 44th Annual Conference on Information Sciences and Systems(CISS),Princeton,NJ,USA,2010:1-6.doi:10.1109/CISS.2010.5464909.
[25]DING J,CHEN L,and GU Y.Perturbation analysis of orthogonal matching pursuit[J].IEEE Transactions on Signal Processing,2013,61(2):398-410.doi:10.1109/TSP.2012.2222377.
[26]VAUGHAN R G,SCOTT N L,and WHITE D R.The theory of bandpass sampling[J].IEEE Transactions on Signal Processing,1991,39(9):1973-1984.doi:10.1109/78.134430.
1)式(8)在数学上是一个NP问题,在实际中,我们通常将式(8)转化为式(9)的凸优化问题进行求解。