Reweighted smoothed l 0 -norm based DOA estimation for MIMO radar

Joint Smoothed l0-Norm DOA Estimation Algorithm for Multiple Measurement Vectors in MIMO Radar

“…The simulation results of the proposed method are compared with those of the $l_1$-SVD [7], RV $l_1$-SVD [16], RV $l_1$-SRACV [14] and reweighted smoothed $l_0$-norm (RSL0) [22] algorithms. In all of the simulations, a narrowband monostatic MIMO radar system with ULAs is considered.…”

“…For the white noise in Figure 6a, the RSL0 algorithm in [22] performs the best, and the proposed algorithm provides better estimation performance than the $l_1$-SVD, RV $l_1$-SVD and RV $l_1$-SRACV methods. For the colored noise in Figure 6b, the performance of the proposed algorithm stands out among the analyzed methods, while the performance of the RV $l_1$-SRACV is severely degraded.…”

“…In the far field, there are P uncorrelated targets regarded as point scatterers at the same range. In addition, it is assumed that $P\le M+N-2$ [22,25,26]. Thus, at the receive array, the N antennas are impinged by the echo signals reflected by the P targets.…”

“…However, large $\sigma$ causes the deviation of the approximation in Equation (25), and it will further decrease the precision of the signal reconstruction. To guarantee both of the speed and the accuracy, a decreasing sequence for $\sigma$, i.e., $[{\sigma }_1,{\sigma }_2,\dots ,{\sigma }_K]$ with ${\sigma }_1\ge {\sigma }_2\ge \dots \ge {\sigma }_K$, which is known as the graduated non-convexity (GNC) approach [18,22], can be exploited. Even though large $\sigma$ is desired to avoid a lot of local maxima and improve the speed, the value of ${\sigma }_1$ in the decreasing $\sigma$ sequence may be set as one to four times of the maximum absolute value of ${\mathbf{U}}_0^{\hat{\theta }}$.…”

“…When recovering the sparse signal matrix ${\mathrm{bold-italicT}}_{\hat{\theta }}$, the main computational burden is caused by the $QK$ iterations, which require about $O[PLQK+(M+N-1\left)PLQK\right]$, where L is the number of the sample grid cells in the complete dictionary ${\mathrm{boldB}}_{\hat{\theta }}$. For the SMV based reweighted smoothed $l_0$-norm algorithm in [22], recovering the sparse signal vector requires about $Ofalse[{(M+N-1)}^{2}LQKfalse]$. However, $l_1$-norm minimization based DOA estimation methods, such as $l_1$-SVD and RV $l_1$-SVD, require $Ofalse[{\left(PL\right)}^{3}false]$ and $Ofalse[\frac{1}{4}{\left(PL\right)}^{3}false]$, respectively.…”