A common problem that arises in radar imaging systems, especially those mounted on mobile platforms, is antenna position ambiguity. Approaches to resolve this ambiguity and correct position errors are generally known as radar autofocus. Common techniques that attempt to resolve the antenna ambiguity generally assume an unknown gain and phase error afflicting the radar measurements. However, ensuring identifiability and tractability of the unknown error imposes strict restrictions on the allowable antenna perturbations. Furthermore, these techniques are often not applicable in near-field imaging, where mapping the position ambiguity to phase errors breaks down. In this paper, we propose an alternate formulation where the position error of each antenna is mapped to a spatial shift operator in the image-domain. Thus, the radar autofocus problem becomes a multichannel blind deconvolution problem, in which the radar measurements correspond to observations of a static radar image that is convolved with the spatial shift kernel associated with each antenna. To solve the reformulated problem, we also develop a block coordinate descent framework that leverages the sparsity and piecewise smoothness of the radar scene, as well as the one-sparse property of the two-dimensional shift kernels. We evaluate the performance of our approach using both simulated and experimental radar measurements and demonstrate its superior performance compared with state-of-the-art methods.
More generally, the radar autofocus problem can be viewed as a multichannel blind deconvolution problem, where the distortions due to position errors can be considered as unknown channels acting on the signals that are received in each antenna. Blind deconvolution attempts to separate a signal and a channel from their convolved mixture, i.e., their product in the frequency domain, using assumptions on each of the two. The multi-channel version considers multiple channels affecting the same signal. Solutions to the general multichannel blind deconvolution problem have existed in the literature since the 1990s @cite_24 @cite_36 @cite_0 @cite_43 @cite_18 .
@cite_18 @cite_36 @cite_24 @cite_43 @cite_0
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A review of blind channel estimation algorithms is presented. From the (second-order) moment-based methods to the maximum likelihood approaches, under both statistical and deterministic signal models. We outline basic ideas behind several new developments, the assumptions and identifiability conditions required by these approaches, and the algorithm characteristics and their performance. This review serves as an introductory reference for this currently active research area. This paper addresses a problem arising in a context of digital communications. A digital source is transmitted through a continuous channel (the propagation medium), and several measurements are performed at the receiver, either by means of several sensors, or by oversampling the received signal compared to the emission rate. Given only these observations, the baseband equivalents of the corresponding channels have to be recovered. An orthogonality property between "signal" and "noise" subspaces is exploited to build some quadratic form whose minimization yields the desired estimates up to a scale factor. This is in the same spirit as recent works by (see Proc. 25th Asilomar Conf., p.856-860, 1991) but requires fewer computations. Numerical simulations demonstrate the performance of the proposed methods in a channel identification context. > Conventional blind channel identification algorithms are based on channel outputs and knowledge of the probabilistic model of channel input. In some practical applications, however, the input statistical model may not be known, or there may not be sufficient data to obtain accurate enough estimates of certain statistics. In this paper, we consider the system input to be an unknown deterministic signal and study the problem of blind identification of multichannel FIR systems without requiring the knowledge of the input statistical model. A new blind identification algorithm based solely on the system outputs is proposed. Necessary and sufficient identifiability conditions in terms of the multichannel systems and the deterministic input signal are also presented. A new algorithm is proposed for the deconvolution of an unknown, possibly colored, Gaussian or nonstationary signal that is observed through two or more unknown channels described by rational system transfer functions. More specifically, not only the root (pole and zero) locations but also the orders of the channel transfer functions are unknown. It is assumed that the channel orders may be overestimated. The proposed algorithm estimates the orders and root locations of the channel transfer functions, therefore it can also be used in multichannel system identification problems. The input signal is allowed to be nonstationary and the channel transfer functions may be a nonminimum phase as well as noncausal, hence the proposed algorithm is particularly suitable for applications such as dereverberation of speech signals recorded through multiple microphones. Several experimental results indicate improvement compared to the existing methods in the literature. >