本文關鍵詞： MIMO雷達 稀疏成像 正交匹配追蹤算法 觀測矩陣失配 擾動矩陣 相位誤差 載頻偏差 網(wǎng)格失配　出處：《中國科學技術大學》2014年博士論文　論文類型：學位論文

【摘要】：MIMO(Multiple input Multiple output,MIMO)雷達是指利用多個發(fā)射和接收天線同時對目標進行觀測的一種新構型的雷達系統(tǒng)。陣列構型設計和波形分集技術使MIMO雷達能夠獲得遠多于實際物理陣元數(shù)目的觀測通道和空間自由度。通過對觀測通道回波的聯(lián)合處理,相比于傳統(tǒng)成像雷達,MIMO雷達在成像的方位向分辨率、實時性和運動補償?shù)确矫嬗忻黠@的性能優(yōu)勢。進一步的,為克服信號帶寬和系統(tǒng)采樣頻率在實現(xiàn)高分辨率成像時對雷達系統(tǒng)設計和實現(xiàn)的困難和限制,基于壓縮感知(Compressed Sensing, CS)的MIMO雷達稀疏成像開始受到廣泛的關注,是當前的一個研究熱點。由CS理論可知,MIMO雷達的稀疏重構(即,反演)性能依賴于觀測矩陣的性質,因此一個精確已知的觀測矩陣是獲得好的反演結果的前提條件。眾所周知,MIMO雷達的觀測矩陣由雷達系統(tǒng)參數(shù)和成像場景的網(wǎng)格點共同決定,如果其中任一的一個因素存在不確定性都將導致實際觀測矩陣不再與默認的觀測矩陣一致,這種觀測矩陣的失配必然對成像算法的有效性、可靠性和穩(wěn)健性提出了挑戰(zhàn)。因此,研究觀測矩陣失配對MIMO雷達稀疏成像的影響是有實際應用意義的。 本文采用正交匹配追蹤算法(Orthogonal Matching Pursuit,OMP)作為反演算法的比較基準,圍繞系統(tǒng)參數(shù)和成像場景網(wǎng)格點這兩類因素的不確定性,重點研究和分析觀測矩陣失配的產(chǎn)生機理、OMP算法在實現(xiàn)有效反演時對這些不確定性的承受能力、以及高效重構算法等問題,主要的研究內容如下： 1、針對相位分集和頻率分集兩種波形分集方式,建立了對應緊湊式MIMO雷達系統(tǒng)的回波模型,分別從點擴散函數(shù)和空間譜的角度推導了成像分辨率和無模糊距離的解析表達式,重點分析了兩種角度下對成像分辨率描述的差異。詳細介紹了OMP算法的算法流程和基于互相關系數(shù)的重構性能推導過程。同時,根據(jù)互相關系數(shù)和點擴散函數(shù)之間的緊密聯(lián)系,確定了通過點擴散函數(shù)來分析觀測矩陣失配和稀疏反演性能的可行性。 2、對于系統(tǒng)可能存在的發(fā)射-接收通道隨機相位誤差,基于其在回波相位中不與散射點坐標信息耦合的先驗假設,在MIMO雷達系統(tǒng)中建立了含有相位不確定性的回波模型,分析了這一類隨機相位誤差對觀測矩陣的作用形式,表現(xiàn)為一左乘對角擾動矩陣。進一步的,利用受擾動的點擴散函數(shù)和相位誤差的隨機特性,分析了左乘擾動矩陣對OMP算法成像的影響,主要表現(xiàn)為幅度衰減且衰減程度由相位的波動范圍決定。特別地,根據(jù)推導的OMP算法重構性能,分別在支撐集恢復和幅值估計兩方面推導了OMP算法對相位誤差的容限。考慮到回波中隨機相位誤差是一隱含變量的事實,引入期望最大化(Expectation Maximization, EM)方法,根據(jù)最大后驗概率準則,提出了期望最大化的稀疏成像算法(Sparse Imaging via EM, SIEM),仿真結果顯示在存在相位誤差時SIEM比OMP具有更穩(wěn)定的反演性能。 3、對于系統(tǒng)可能存在的發(fā)射一接收通道載頻偏差,在相位分集MIMO雷達系統(tǒng)中建立了含有發(fā)射、接收載頻不確定性的解析回波模型,回波表達式表明載頻偏差不僅在回波相位中與散射點位置信息強耦合,而且會影響通道分離的性能,導致通道分離殘差的出現(xiàn)。相比隨機相位誤差,載頻偏差引起更加復雜、嚴重的觀測矩陣失配。根據(jù)受擾動點擴散函數(shù)的峰值變化,分析得到了載頻偏差對OMP算法成像的影響集中表現(xiàn)為對點擴散函數(shù)峰值的衰減,然后進一步推導了存在載頻偏差時OMP算法的反演性能變化以及OMP算法支撐集恢復和幅值估計對載頻偏差的容限。通過將載頻偏差引起的觀測矩陣失配表示為一個具有有界Frobenius范數(shù)約束的加性擾動矩陣,提出了基于有界擾動的稀疏成像算法(Sparse Imaging based on Frobenius-nrom-bounded Perturbation, SIFrobP)。根據(jù)有界擾動的一般性假設,SIFrobP算法的適用范圍廣泛,可適用于實際觀測矩陣中存在任意未知不確定性的場景。 4、研究了連續(xù)成像場景的離散化網(wǎng)格與真實目標散射點之間存在不確定性時的網(wǎng)格失配問題。從細化網(wǎng)格提高散射點位置估計精度的角度,將基于Band-exclusion技術的改進型OMP算法(Band-excluded OMP,BOMP)引入MIMO雷達稀疏成像,利用點擴散函數(shù)指導相關帶門限值的設置使BOMP算法成像的低分辨率得到了有效地改善。同時,從摒棄對連續(xù)成像場景網(wǎng)格化的角度出發(fā),提出了基于連續(xù)參數(shù)估計的MIMO雷達稀疏成像方法(Sparse Imaging via Continuous Parameter Estimate,SICPE),推導了算法的性能條件。該算法不僅避免了經(jīng)典稀疏重構算法對網(wǎng)格的依賴性,而且可以在發(fā)射／接收端稀疏布陣或非均勻采樣時均獲得較好的稀疏成像結果。
[Abstract]:MIMO (Multiple input Multiple output, MIMO) radar refers to a new type of radar system using multiple transmit and receive antennas at the same time to observe the target. The array configuration design and waveform diversity MIMO radar can obtain much more than the actual number of the array observation channel and spatial degrees of freedom. The combined treatment of the observation channel echo, compared to the traditional imaging radar, MIMO radar resolution in the azimuth, has obvious advantages in real-time and motion compensation. Further, in order to overcome the bandwidth of the signal and system sampling frequency in the realization of high resolution imaging radar system to design and realize the difficulties and limitations, based on compression perception (Compressed Sensing, CS) MIMO radar sparse imaging began to receive widespread concern. It is a research hotspot. According to the CS theory, the sparse MIMO radar Structure (i.e., inversion) performance depends on the nature of the observation matrix, so a precisely known observation matrix is a prerequisite for a good inversion result. As everyone knows, the observation matrix of MIMO radar is determined by the radar system parameters and imaging scene of grid points, if a factor in the existence of any uncertainty will cause the actual observation matrix and observation matrix is no longer consistent by default, this observation matrix mismatch and necessity of imaging algorithm, challenges the reliability and robustness. Therefore, research on the observation matrix is has practical significance of the effect of mismatch between MIMO radar sparse imaging.
This paper uses orthogonal matching pursuit algorithm (Orthogonal Matching Pursuit, OMP) as the benchmark inversion algorithm, surrounding the two kinds of factors of system parameters and the imaging scene grid point uncertainty, focuses on the research and analysis of the observation matrix mismatch mechanism, OMP algorithm to achieve effective inversion on these uncertainty capacity problems and efficient reconstruction algorithm, the main research contents are as follows:
1, considering the phase and frequency diversity of two kinds of waveform diversity, established the corresponding echo model of compact MIMO radar system, which spread function and spatial spectrum angle is deduced analytic expressions of imaging resolution and unambiguous distance from the point, the paper introduced two kinds of description on the imaging resolution angle of the differences in detail. Introduces the OMP algorithm and the reconstruction performance based on derivation of correlation coefficient. At the same time, according to the cross-correlation coefficient and point spread function between close contact, determine the feasibility analysis to the observation matrix mismatch and sparse inversion performance by point spread function.
2, the system may exist for transmitting and receiving channel random phase error, based on the echo phase in scattering and coordinate information coupling hypothesis in MIMO radar system, established a model containing echo phase uncertainty, analyzed this kind of random phase error function to form the observation matrix, performance as a left multiplication diagonal perturbation matrix. Further, based on the characteristics of random disturbance point spread function and phase error, analyzes the impact of the matrix on the left by the disturbance OMP imaging algorithm, mainly for the amplitude attenuation and the attenuation degree is determined by the phase fluctuation. Especially, according to the OMP algorithm performance is. Set recovery and amplitude estimation two derived tolerance OMP algorithm for phase error in support. Considering the random phase error is a latent variable echo in fact, into the expectation maximization (Ex Pectation Maximization (EM) method, according to the maximum a posteriori criterion, proposes the expectation maximization sparse imaging algorithm (Sparse Imaging via EM, SIEM). The simulation results show that SIEM has more stable performance than OMP in the presence of phase error.
3, the system may exist for the launch of a receiving channel in the carrier frequency offset, phase diversity MIMO radar system is established with transmitting, receiving and parsing the echo model of uncertainty of carrier frequency, carrier frequency offset echo expression shows that not only in the echo phase and scattering point position information and strong coupling, and will affect the performance of channel separation, resulting in channel the separation of residuals. Compared with the random phase error, carrier frequency deviation caused by the more complex, the observation matrix serious mismatch. According to the peak point spread function disturbance changes, analysis of the performance effect of carrier frequency offset on OMP algorithm for imaging attenuation of the PSF peak, then the carrier frequency offset are deduced when the change of inversion the performance of the OMP algorithm and OMP algorithm support recovery and amplitude estimation of carrier frequency deviation tolerance. The observation matrix caused by carrier frequency offset The mismatch is expressed as a perturbation matrix with additive bounded Frobenius norm constraint, is proposed based on sparse imaging algorithm of bounded disturbances (Sparse Imaging based on Frobenius-nrom-bounded Perturbation, SIFrobP). According to the general assumption of bounded disturbances, the scope of SIFrobP algorithm is widely applicable to the actual observation matrix in the presence of arbitrary the uncertainty in the scene.
4, there is mismatch between grid uncertainty on continuous imaging scene discretization grid and real target scattering points. From the angle of grid refinement to improve the estimation accuracy of scattering points, based on improved OMP algorithm based on Band-exclusion Technology (Band-excluded OMP BOMP) into MIMO radar imaging using sparse, point spread function guide with threshold value setting to effectively improve the low resolution BOMP imaging algorithm. At the same time, starting from the abandon of continuous imaging scene grid point of view, put forward the MIMO radar imaging method for the sparse parameter estimation based on (Sparse Imaging via Continuous Parameter Estimate, SICPE), derived the performance conditions of the algorithm. This method not only avoids the dependence on the grid of the classic sparse reconstruction algorithm, but also in the transmitting and receiving end or sparse array non uniform sampling are Better sparse imaging results were obtained.

【學位授予單位】：中國科學技術大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TN958

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