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Register a new userInferring Remote Channel State Information: Cramer-Rao Lower Bound and Deep Learning Implementation
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Zhiyuan Jiang
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Channel state information (CSI) is of vital importance in wireless communication systems. Existing CSI acquisition methods usually rely on pilot transmissions, and geographically separated base stations (BSs) with non-correlated CSI need to be assigned with orthogonal pilots which occupy excessive system resources. Our previous work adopts a data-driven deep learning based approach which leverages the CSI at a local BS to infer the CSI remotely, however the relevance of CSI between separated BSs is not specified explicitly. In this paper, we exploit a model-based methodology to derive the Cramer-Rao lower bound (CRLB) of remote CSI inference given the local CSI. Although the model is simplified, the derived CRLB explicitly illustrates the relationship between the inference performance and several key system parameters, e.g., terminal distance and antenna array size. In particular, it shows that by leveraging multiple local BSs, the inference error exhibits a larger power-law decay rate (w.r.t. number of antennas), compared with a single local BS; this explains and validates our findings in evaluating the deep-neural-network-based (DNN-based) CSI inference. We further improve on the DNN-based method by employing dropout and deeper networks, and show an inference performance of approximately $90%$ accuracy in a realistic scenario with CSI generated by a ray-tracing simulator.
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To achieve the joint active and passive beamforming gains in the reconfigurable intelligent surface assisted millimeter wave system, the reflected cascade channel needs to be accurately estimated. Many strategies have been proposed in the literature to solve this issue. However, whether the Cramer-Rao lower bound (CRLB) of such estimation is achievable still remains uncertain. To fill this gap, we first convert the channel estimation problem into a sparse signal recovery problem by utilizing the properties of discrete Fourier transform matrix and Kronecker product. Then, a joint typicality based estimator is utilized to carry out the signal recovery task. We show that, through both mathematical proofs and numerical simulations, the solution proposed in this letter can in fact asymptotically achieve the CRLB.
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In this paper we explore the maximum precision attainable in the location of a point source imaged by a pixel array detector in the presence of a background, as a function of the detector properties. For this we use a well-known result from parametric estimation theory, the so-called Cramer-Rao lower bound. We develop the expressions in the 1-dimensional case of a linear array detector in which the only unknown parameter is the source position. If the object is oversampled by the detector, analytical expressions can be obtained for the Cramer-Rao limit that can be readily used to estimate the limiting precision of an imaging system, and which are very useful for experimental (detector) design, observational planning, or performance estimation of data analysis software: In particular, we demonstrate that for background-dominated sources, the maximum astrometric precision goes as $B/F^2$, where $B$ is the background in one pixel, and $F$ is the total flux of the source, while when the background is negligible, this precision goes as $F^{-1}$. We also explore the dependency of the astrometric precision on: (1) the size of the source (as imaged by the detector), (2) the pixel detector size, and (3) the effect of source de-centering. Putting these results into context, the theoretical Cramer-Rao lower bound is compared to both ground- as well as spaced-based astrometric results, indicating that current techniques approach this limit very closely. Our results indicate that we have found in the Cramer-Rao lower variance bound a very powerful astrometric benchmark estimator concerning the maximum expected positional precision for a point source, given a prescription for the source, the background, the detector characteristics, and the detection process.
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