scholarly journals Doppler Ambiguity Resolution Based on Random Sparse Probing Pulses

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yunjian Zhang ◽  
Zhenmiao Deng ◽  
Jianghong Shi ◽  
Linmei Ye ◽  
Maozhong Fu ◽  
...  
Keyword(s):  
Message Passing ◽  
Pulse Train ◽  
Pulse Repetition Frequency ◽  
Doppler Frequency ◽  
Sparse Sampling ◽  
Sampling Frequency ◽  
Sensing Matrix ◽  
Approximate Message Passing ◽  
Target Characteristic ◽  
Novel Method

A novel method for solving Doppler ambiguous problem based on compressed sensing (CS) theory is proposed in this paper. A pulse train with the random and sparse transmitting time is transmitted. The received signals after matched filtering can be viewed as randomly sparse sampling from the traditional fixed-pulse repetition frequency (PRF) echo signals. The whole target echo could be reconstructed via CS recovery algorithms. Through refining the sensing matrix, which is equivalent to increase the sampling frequency of target characteristic, the Doppler unambiguous range is enlarged. In particular, Complex Approximate Message Passing (CAMP) algorithm is developed to estimate the unambiguity Doppler frequency. Cramer-Rao lower bound expressions are derived for the frequency. Numerical simulations validate the effectiveness of the proposed method. Finally, compared with traditional methods, the proposed method only requires transmitting a few sparse probing pulses to achieve a larger Doppler frequency unambiguous range and can also reduce the consumption of the radar time resources.

scholarly journals Optimal Combination of Linear and Spectral Estimators for Generalized Linear Models

2021 ◽  
Author(s):  
Marco Mondelli ◽  
Christos Thrampoulidis ◽  
Ramji Venkataramanan
Keyword(s):  
Message Passing ◽  
Linear Models ◽  
Optimal Combination ◽  
Limiting Distribution ◽  
Linear Estimator ◽  
Sensing Matrix ◽  
Approximate Message Passing ◽  
Message Passing Algorithm ◽  
Spectral Estimators

AbstractWe study the problem of recovering an unknown signal $${\varvec{x}}$$ x given measurements obtained from a generalized linear model with a Gaussian sensing matrix. Two popular solutions are based on a linear estimator $$\hat{\varvec{x}}^\mathrm{L}$$ x ^ L and a spectral estimator $$\hat{\varvec{x}}^\mathrm{s}$$ x ^ s . The former is a data-dependent linear combination of the columns of the measurement matrix, and its analysis is quite simple. The latter is the principal eigenvector of a data-dependent matrix, and a recent line of work has studied its performance. In this paper, we show how to optimally combine $$\hat{\varvec{x}}^\mathrm{L}$$ x ^ L and $$\hat{\varvec{x}}^\mathrm{s}$$ x ^ s . At the heart of our analysis is the exact characterization of the empirical joint distribution of $$({\varvec{x}}, \hat{\varvec{x}}^\mathrm{L}, \hat{\varvec{x}}^\mathrm{s})$$ ( x , x ^ L , x ^ s ) in the high-dimensional limit. This allows us to compute the Bayes-optimal combination of $$\hat{\varvec{x}}^\mathrm{L}$$ x ^ L and $$\hat{\varvec{x}}^\mathrm{s}$$ x ^ s , given the limiting distribution of the signal $${\varvec{x}}$$ x . When the distribution of the signal is Gaussian, then the Bayes-optimal combination has the form $$\theta \hat{\varvec{x}}^\mathrm{L}+\hat{\varvec{x}}^\mathrm{s}$$ θ x ^ L + x ^ s and we derive the optimal combination coefficient. In order to establish the limiting distribution of $$({\varvec{x}}, \hat{\varvec{x}}^\mathrm{L}, \hat{\varvec{x}}^\mathrm{s})$$ ( x , x ^ L , x ^ s ) , we design and analyze an approximate message passing algorithm whose iterates give $$\hat{\varvec{x}}^\mathrm{L}$$ x ^ L and approach $$\hat{\varvec{x}}^\mathrm{s}$$ x ^ s . Numerical simulations demonstrate the improvement of the proposed combination with respect to the two methods considered separately.

A FrFT Based Algorithm for Doppler Frequency Rate Estimation from LFM Coherent Pulse Train

2010 ◽  
Vol 32 (11) ◽  
pp. 2718-2723 ◽  
Author(s):  
Hong Li ◽  
Yu-liang Qin ◽  
Yan-peng Li ◽  
Hong-qiang Wang ◽  
Xiang Li
Keyword(s):  
Pulse Train ◽  
Doppler Frequency ◽  
Rate Estimation ◽  
Frequency Rate ◽  
Coherent Pulse

Speech enhancement based on approximate message passing

2020 ◽  
Vol 17 (8) ◽  
pp. 187-198
Author(s):  
Chao Li ◽  
Ting Jiang ◽  
Sheng Wu
Keyword(s):  
Speech Enhancement ◽  
Message Passing ◽  
Approximate Message Passing

scholarly journals Bilinear Adaptive Generalized Vector Approximate Message Passing

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 4807-4815 ◽  
Author(s):  
Xiangming Meng ◽  
Jiang Zhu
Keyword(s):  
Message Passing ◽  
Approximate Message Passing

scholarly journals A Novel Coherence Reduction Method in Compressed Sensing for DOA Estimation

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Jing Liu ◽  
ChongZhao Han ◽  
XiangHua Yao ◽  
Feng Lian
Keyword(s):  
Compressed Sensing ◽  
Phased Array ◽  
Reduction Method ◽  
Doa Estimation ◽  
Estimation Methods ◽  
Sensing Matrix ◽  
Replacement Method ◽  
Precise Estimation ◽  
Novel Method ◽  
Measurement Vector

A novel method named as coherent column replacement method is proposed to reduce the coherence of a partially deterministic sensing matrix, which is comprised of highly coherent columns and random Gaussian columns. The proposed method is to replace the highly coherent columns with random Gaussian columns to obtain a new sensing matrix. The measurement vector is changed accordingly. It is proved that the original sparse signal could be reconstructed well from the newly changed measurement vector based on the new sensing matrix with large probability. This method is then extended to a more practical condition when highly coherent columns and incoherent columns are considered, for example, the direction of arrival (DOA) estimation problem in phased array radar system using compressed sensing. Numerical simulations show that the proposed method succeeds in identifying multiple targets in a sparse radar scene, where the compressed sensing method based on the original sensing matrix fails. The proposed method also obtains more precise estimation of DOA using one snapshot compared with the traditional estimation methods such as Capon, APES, and GLRT, based on hundreds of snapshots.

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