Thresholding the ambiguity function

Abstract

In this paper we propose a new method for estimating the Ambiguity Function (AF) of a random process with limited spreading support. The observed process is modelled as the aggregation of a non-stationary signal of interest and noise. As the AF has limited spreading, thresholding is a suitable estimation procedure. Some key stochastic properties of the Empirical Ambiguity Function are derived to obtain a suitable threshold. Based on a median absolute deviation estimator for the variance, we derive a suitable threshold, which forms the basis for our proposed estimator. The estimator is tested on both artificial and real signals, and our results demonstrate a remarkably high resolution and reduced variance.

Detection of sparse targets with structurally perturbed echo dictionaries

“…Specifically, ratio between maximum and median values of |χ (τ , ν)| is computed as: (50) and compared with a properly chosen threshold value, ξ . If the calculated ratio is higher than the determined threshold value then that peak point is considered as the center location of the strongest multipath cluster [50,51]. This detection phase enable us to determine corresponding grid points that will be perturbed to be able to detect multipath components that reside on possible off-grid locations.…”

“…In the following, formulation of the proposed technique for each cluster is presented. Associated with the cth cluster, the following fitness function is optimized: (51) where η represents the iteration index of the algorithm, ϕ ∈ R N 2 is the vector containing all possible discrete delay-Doppler values: ,ŷ c (t, η) is the estimated output signal and Ψ c is the sub-dictionary created using the columns of dictionary matrix Ψ that are in the set Λ c which contains column index of vectors of Ψ , that are in support of cluster c:…”

Multipath channel identification by using global optimization in ambiguity function domain

“…Specifically, ratio between maximum and median values of the jvðt,nÞj is computed and compared with a properly chosen threshold value. If the calculated ratio is higher than the determined threshold value then that peak point is considered as the location of the multipath cluster [42,49,50].Once the peak location of the multipath cluster is detected, a window of size, 1:5Dt  1:5Dn, around the detected peak is determined and PSO optimization is conducted on the extracted data to estimate parameters of each multipath component.…”