Underdetermined DOA Estimation of Wideband LFM Signals Based on Gridless Sparse Reconstruction in the FRF Domain

. 2019 May 24;19(10):2383. doi: 10.3390/s19102383

Algorithm 1 Underdetermined DOA Estimation of Wideband LFM Signals Based on Gridless Sparse Reconstruction in FRF Domain.

Input: the received signals based on the coprime array

x (t)

;
Output:

{\hat{θ}}_{k}

;

1:
Initialize: $M, N, L = M (N - 1) + 1$ ;
2:
Derive the peaks model $X_{F}$ of received signals in FRF domain based on coprime array by Equation (15);
3:
Derive the virtual received signals $Y_{v}$ of difference co-array by Equation (21);
4:
Construct the virtual received signals $Y_{U}$ of virtual ULA according to Equation (22) by interpolating virtual sensors into difference co-array;
5:
Construct the covariance matrix of virtual ULA $\tilde{R}$ according to Equation (38);
6:
Defined a binary vector $h$ to respectively represent the interpolated and derived virtual sensors, and construct $H$ to distinguish the zero and non-zero elements in covariance matrix $\tilde{R}$ ;
7:
Solve the atomic norm minimization in Equation (39), and use the equivalent version Equation (43) to get $z$ and $T (z)$ ;
8:
Substitute $T (z)$ as the recovered covariance matrix of reference virtual array into MUSIC algorithm to estimate the DOAs ${\hat{θ}}_{k}$ .