Range Spread Target Detection For Wideband Radar Based On Compressed Sensing

The wideband radar transmits wideband signals to acquire the more information of range spread targets, which plays the more and more important role in the civil and military applications. As increasing the bandwidth of transmitted signals, however, the wideband radar signal processing subsystem based on the traditional Nyquist sampling theory will meet with a big amount of data, which brings some new problems and challenges for the real-time & low-cost signal processing subsystem of wideband radar.Recently, from the information theory, the matrix theory, the optimization theory and the linear programming, etc., the new compressed sensing(CS) theory based on the sparsity of the signal breaches the limit of signal Nyquist sampling rate. The new CS theory points out that the sparse signal can be sampled at the very low sampling rate and reconstructed from its nonlinear measurements by the recovery algorithms but without losing the information. Note that until now, CS has been found more and more applications in the fields of the communication, radar and image processing, etc., but some problems need to be researched deeply. After analyzing the sparsity of the received echoes of the wideband radar, this dissertation is concerned on the range spread target detection based on CS in the presence of the Gaussian noise. The problems such as the L-1, 2 norm recovery algorithms, the range spread target detection based on CS measurements, based on the cross quasi-ambiguty function(CQAF) and based on the Sinc basis are considered in the dissertation, respectively. Here, the analysis of recovery algorithms based on L-1, 2 norm is proved that CS can be used in the range spread target detection. The main works and contributions can be as follows:In the first part, a new recovery algorithm based on basis pursuit—Moore-Penrose inverse matrix is proposed in this dissertation to reduce the recovery errors of the sparse signal recovery via L-1 norm minimization. The new method includes two steps: first, the support set, locations of non-zero elements in the sparse signal(corresponding with columns of the measurement matrix), is determined by basis pursuit; second, the sparse signal is recovered by solving the super-determined system of the linear equations which are composed of the CS measurements and a sub-matrix of the measurement matrix corresponding with the support set; meanwhile, it is proved that the recovery is its one and only minimize L-2 norm. Finally, both the simulation results and experimental results based on raw data recorded by the wideband radar show that the new method can recover the sparse signal effectively at different kinds of measurement matrices and that the recovery errors are smallest and just located in the support set.In the second part, for compressed sampling matching pursuit(Co Sa MP), twice times elements of the sparse level are simply chosen from the signal proxy in the ascending order as new atoms at each iterative time. However, there is no a quality criterion for choosing the support set at the iterative time. In this dissertation, the stepwise compressed sampling matching pursuit(SWCo Sa MP) is proposed to solve the problem. Based on the definition and characteristics of block matrices, we derive the closed L-2 norm form of recovery errors corresponding to the support set at each iterative time. Meanwhile, both the greedy-add and greedy-remove algorithm is brought into choosing new atoms at each iterative time, hence, reducing the measurement dimensions. Finally, the simulation results and experimental results based on raw data from the wideband radar show that for different kinds of measurement matrices, the new robust method can recover the sparse signal effectively and reduce the measure- ment dimensions successfully.In the third part, for wideband radar, the problem of detecting the range spread target embedded in the Gaussian noise is considered in this dissertation. A new method based on the CS measurements is proposed to solve this problem. Here, the Sinc basis is introduced to sparsely represent the high resolution range profile(HRRP). The coefficient vector is solved by the complex approximate massage passing(CAMP) from its noisy CS measurements; then the L-0 detector is used to realize the range spread target detection. Meanwhile, the probabilities of false alarm and detection are derived. At last, the experimental results based on raw data from wideband radar show that HRRPs are sparser in the Sinc basis than in the time domain and that compared with the traditional detectors, the new method not only can realize the detection using less CS measurements but also has a better detection performance.In the fourth part, transmitting the wideband linear frequency modulated signal, the wideband radar often down-convert its returned echoes by a mixer. The received echos is the sum of some sinusoidal signals and the complex sinusoidal basis including different frequencies is introduced to sparsely represent the received echo. In the Gaussian noise, meanwhile, both the math model of the CS wideband radar receiver and the constant false alarm rate(CFAR) detector based on CQAF is proposed in this dissertation. Then, the HRRP can be directly acquired from the noisy CS measurements via L-1 norm-minimization. In the new detector, the CQAF of the received echo and the dominate scatterer is used to acquire the range spread target feature in order to distinguish the range spread target from the Gaussian noise, thus realizing the target detection. Finally, the experimental results based on raw data of wideband radar show that the proposed basis can sparsely represent the received echo very well and that compared with the traditional detectors, the new detector has a better detection performance but dose not rely on one special recovery algorithm.In the fifth part, the keystone transform can’t correct the range migration which is caused by the moving range spread target containing the complicated motion. In this dissertation, a new coherent integration method based on the sparse representation is proposed to improve the detection performance of the target containing the complicated motion. Of course, the Sinc basis is also used to sparsely represent the HRRPs. First, basis pursuit is adopted to estimate the noise power; then the HRRPs at different step times are recovered from its noisy measurements by basis pursuit de-noising in order to align the range bins via the minimized 1-D entropy of adjacent HRRPs; meanwhile, the recursive multi-scatterer algorithm(RMSA) is used to correct the phase errors between different pulses; finally, the adaptive subspace detector based on Sinc basis with a low complexity is adopted to realize the range spread target detection. The experimental results based on raw data from the wideband radar show that the new method can eliminate the range migration resulting from the complicated motion at low SNRs and improve the detection performance successfully.