双色散信道估计的超分辨率方法
Super-Resolution for Doubly-Dispersive Channel Estimation
摘要：
在这项工作中，我们考虑的问题的识别和重建的双色散信道运营商，这是由有限的线性组合的时间-频率偏移。这种算子作为时变线性系统出现，例如在雷达和无线通信中。特别地，对于高度非平稳环境中的信息传输，需要利用短持续时间的识别信号快速地估计信道，并且对于车辆应用，也期望同步高分辨率雷达。我们考虑时间连续设置，并证明了一个确切的resternary reformulation的涉及的通道运营商时，应用到一个三角多项式作为标识符的稀疏线性组合的实值原子。受Heckel等人最近工作的启发，我们提出了一种精确的离网超分辨方法，该方法允许使用具有紧凑支持的可实现信号进行识别。然后，我们展示了如何交替下降条件梯度算法可以适应解决重新制定的问题。数值算例表明了该算法的性能，特别是与一个简单的自适应网格加密策略和正交匹配追踪算法的比较。
英文摘要：
In this work we consider the problem of identification and reconstruction of doubly-dispersive channel operators which are given by finite linear combinations of time-frequency shifts. Such operators arise as time-varying linear systems for example in radar and wireless communications. In particular, for information transmission in highly non-stationary environments the channel needs to be estimated quickly with identification signals of short duration and for vehicular application simultaneous high-resolution radar is desired as well. We consider the time-continuous setting and prove an exact resampling reformulation of the involved channel operator when applied to a trigonometric polynomial as identifier in terms of sparse linear combinations of real-valued atoms. Motivated by recent works of Heckel et al. we present an exact approach for off-the-grid superresolution which allows to perform the identification with realizable signals having compact support. Then we show how an alternating descent conditional gradient algorithm can be adapted to solve the reformulated problem. Numerical examples demonstrate the performance of this algorithm, in particular in comparison with a simple adaptive grid refinement strategy and an orthogonal matching pursuit algorithm.
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