Research On Observation Matrix Mismatch For MIMO Radar Sparse Imaging

Multiple-input-multiple-output (MIMO) radar is an emerging technology of radar with multiple transmitters and multiple receivers. Benefit from the flexible configu-ration of transmitter/receiver arrays and the diversity gain of transmitted orthogonal waveforms, MIMO radar enjoys increased degree of freedom and is able to probe tar-gets from more observation channels than that restricted by the real number of physical array elements. The joint signal processing afterwards among the attainable observation channels makes MIMO radar outperform the traditional imaging radar systems in terms of imaging performance, such as azimuth resolution, real time imaging, and the free of motion compensation, etc. Moreover, the arising compressed sensing (CS) paves a new way for MIMO radar imaging to try to solve the problems in increasing both the signal bandwidth and sampling frequency for high resolution requirements. From the compressed sensing view of point, the perfect knowledge of the observation matrix is the absolute prerequisite for the performance guarantee of CS-based sparse recovery algorithms. The observation matrix of a MIMO radar is well-known determined by two kinds of factors, one refers to the accurately known system parameters and the other is a premise requiring completely match between the defined grids over the interested scene and the ready-to-estimate positions of the real scatterers. Any uncertainties of these two factors would lead to observation matrix mismatch and challenge the existed imaging algorithms. Therefore, it is of significant importance to study the impact of observation matrix mismatch on performance of MIMO radar sparse imaging.This dissertation seeks to find the representation of observation matrix mismatch caused by different kinds of uncertainties, and to study the variation in imaging perfor-mance by orthogonal matching pursuit (OMP) algorithm, and surely to propose algo-rithms of more stable imaging performance. Among these, OMP is took as the baseline with which the proposed algorithms can be compared. The main works and contribu-tions are as follows:Firstly, considering the waveform diversity in phase and frequency domain, the echo model is respectively established for the MIMO radar with closely distributed an-tennas. Based on uniformly linear array, the analytical expressions of the resolutions and the unambiguous area of imaging are derived both from the perspective of point spread function (PSF) and from the perspective of spatial spectrum, and the difference therein are then presented. Sepecially, the difference performed by phase diversity and frequency diversity are compared. The flow of OMP algorithm and its mutual-coherence-based performance guarantee are described in detail. The inferred relation- ship between mutual coherence and PSF makes it possible to use PSF instead to analyze the imaging performance by sparse recovery algorithms.Secondly, a non-ideal situation, in which phase errors are existed among transmitter-receiver channels, is considered. Suppose that the potential phase errors are random and decoupling terms with respect to scatterers in the phase of echo. The analytical echo is then obtained, showing that the observation matrix mismatch turns out to be a diagonal multiplicative matrix on the left of the assumed observation matrix. Its main impact is identified to a scale-down factor on the amplitude of MIMO PSF, and thereby the con-dition of performance guarantee by OMP is re-derived for this case. Specifically, two phase-error tolerances are respectively provided for guaranteeing the successful sup-port recovery and amplitude estimation under an acceptable level by OMP. In view of that the phase errors are latent variables, a sparse imaging via expectation maximization (SIEM) algorithm is proposed by exploiting the maximum-a-posterior (MAP) criterion, and simulations verify its effectiveness.Thirdly, considering the carrier offsets across transmitters and receivers, the ana-lytical echo is availably established based on phase-diversity MIMO radar. In contrast to phase errors, carrier offsets are terms strongly coupling with scatterers in the phase of echo, and obviously would lead to the arising of residual after channel separation, such that carrier offsets would cause more complicated and serious observation matrix mis-match. Though difficult to make an analytical MIMO PSF, the impact of carrier offsets is identified in the light of the variation in peak of MIMO PSF. Condition is re-derived for successful support recovery by OMP, and the performance loss is characterized in terms of l2distance. A sparse imaging algorithm with Frobenius-norm-bounded pertur-bation (SIFrobP) due to carrier offsets is also proposed, which improves upon the OMP algorithm. Due to the generalization of the perturbation, SIFrobP can be easily applied into other situations of uncertainties.Fourthly, the basis mismatch problem is studied. This is a conflict between the tacit assumption by CS-based algorithms that scatterers exactly lie on pre-discretized grids and the nature that sactterers are arbitrarily distributed continuously in spatial space. By refining the grids to improve the estimated accuracy, band-excluded OMP (BOMP) algorithm is introduced as well as its performance. In specific, MIMO PSF is utilized to guide the setting of threshold of coherence band, efficiently alleviating the inherent resolution-loss of BOMP. In contrast to BOMP, invoked by the merits of continuous parameter estimation methods, a sparse imaging approach via continuous parameter es-timate (SICPE) is proposed to recovery the positions of arbitrarily distributed scatterers, and the condition of performance guarantee is derived as well. SICPE is not only to-tally getting rid of grid dependence, but also can be available for the sparse arrays and non-uniformly sampling.