## 5 Simulation Results  
In this section, using the ESPRIT-like [14] algorithm, the \(l_{1}\)-SVD [15] algorithm and the \(l_{1}\)-SRDML [16] algorithm for comparison, some simulation experiments are implemented to demonstrate the efficiency and the advantages of the proposed algorithm. The signal-to-noise ratio (SNR) is defined as \(\text{SNR}=10\text{log}_{10}(||\mathbf{CAS}||_{F}^{2}/||\mathbf{N}||_{F}^{2})\). Let \(\hat{\theta}_{p}^{i}\) be the estimation of the true DOA \(\theta_{p}\) for the \(i\)-th Monte Carlo trial; the root mean square error (RMSE) of angle estimation is defined as:  
\[(1/P)\sum_{p=1}^{P}\sqrt{(1/Q)\sum_{i=1}^{Q}(\hat{\theta}_{p}^{i}-\theta_{p})^ {2}} \tag{26}\]  
where \(Q\) is the total number of the Monte Carlo trials, which is \(Q=200\) in the simulations. Consider a narrowband monostatic MIMO radar system, whose arrays are both half-wavelength spaced ULAs with the effects of mutual coupling, and the numbers of transmit and receive antennas are \(M\) and \(N\), respectively. Let \(K=k+1\) be the nonzero mutual coupling coefficient number; two different mutual coupling cases of the transmitter and the receiver are considered in the following simulations: (1) \(K=2\) with the nonzero mutual coupling coefficients being \([c_{t0},c_{t1}]=[1,0.1844+j0.0427]\) and \([c_{t0},c_{r1}]=[1,0.0522-j0.1049]\); (2) \(K=3\) with \([c_{t0},c_{t1},c_{t2}]=[1,0.6+j0.2,0.02+j0.13]\) and \([c_{t0},c_{r1},c_{r2}]=[1,0.5+j0.1,0.01+j0.05]\). The number of uncorrelated targets \(P\) is assumed to be known. Besides, the confidence interval is set to 0.99, and the discretized grids are uniform with \(0.1^{\circ}\) sampling from \(-90^{\circ}\) to \(90^{\circ}\), for the proposed method, as well as \(l_{1}\)-SVD and \(l_{1}\)-SRDML algorithms. When performing the experiments, we solve the signal reconstruction problem of the noncircular source-based joint reweighted sparse representation framework in Equation (25). The sparse solution vector \(\hat{\mathbf{r}}\) is obtained by using the SOC programming software packages. When there are true DOAs of targets located at certain points of the complete dictionary, the corresponding elements in \(\hat{\mathbf{r}}\) are non-zero, and the rest are zero. Therefore, the true DOA locations in dictionary correspond to the largest \(P\) values of \(|\hat{\mathbf{r}}|\). In the simulations, the functional form \(10\text{log}_{10}[|\hat{\mathbf{r}}|/\text{max}(|\hat{\mathbf{r}}|)]\) is used to plot the spatial spectrum of angle estimation. Then, by finding \(P\) peaks in the spectrum, DOA estimation is achieved. Figure 3 depicts the spatial spectrum of the proposed method for the number of targets being \(P=3\) and \(P=5\), respectively, where \(M=N=6\), \(J=200\), SNR is fixed at SNR = 0 dB and mutual coupling Case (1) is considered. For \(P=3\), the DOAs of the uncorrelated targets are \(\theta_{1}=-10^{\circ}\), \(\theta_{2}=0^{\circ}\), \(\theta_{3}=10^{\circ}\). For \(P=5\), they are \(\theta_{1}=-20^{\circ}\), \(\theta_{1}=-10^{\circ}\), \(\theta_{1}=0^{\circ}\), \(\theta_{2}=10^{\circ}\) and \(\theta_{3}=20^{\circ}\), respectively. From Figure 3, it can be observed that the spatial spectrum peaks of the proposed method are sharp, and the sidelobe suppression is low. In addition, for different target numbers \(P\), the spectrum maintains the accuracy of DOA estimation. This indicates that the proposed method is effective to perform DOA estimation accurately. Figure 4 shows the RMSE of DOA estimation versus SNR in different methods with mutual coupling Case (1), where \(M=N=6\), \(J=200\) and three targets with \(\theta_{1}=-10^{\circ}\), \(\theta_{2}=0^{\circ}\), \(\theta_{3}=10^{\circ}\) are considered. Additionally, the values of RMSE are computed by Equation (26) with \(Q\) trials. As can be seen in Figure 4, \(l_{1}\)-SRDML owns a lower RMSE than the ESPRIT-like and \(l_{1}\)-SVD algorithms, because the deterministic maximum likelihood procedure improves the estimation accuracy.