# Simultaneous Correlative Interferometer Technique for Direction Finding of Signal Sources
## 5 Comparison of MUSIC and CI-Based DOA Estimation Algorithms  
In this section, the existing MUSIC and CI techniques are compared by using the DOA spectra, which indicate the normalized spatial spectrum for the MUSIC algorithm and the cost function value for the CI technique, respectively. Figure 3 shows the DOA spectra for both MUSIC and CI techniques. In this simulation, we also consider the ULA antenna structure at the receiver for providing clear comparison between MUSIC and CI algorithms. For the ULA-based receiver, we consider two signal sources with different azimuth (horizontal) DOA angles, which are \(-50^{\circ}\) and \(10^{\circ}\). On the other hand, for the UCA receiver, we consider a single signal source with azimuth DOA angle of \(150^{\circ}\) and elevation DOA angle of \(40^{\circ}\), i.e., \(\phi=150^{\circ}\), \(\theta=40^{\circ}\). The number of antennas in both ULA and UCA array structures are assumed to be \(10\), i.e., \(M=10\). For both array structures, the SNR and the number of time samples are assumed to be \(-10\) dB and \(10\), respectively.  
When we use the ULA antenna structure at the receiver, both MUSIC and CI algorithms find two azimuth angles that yield the two largest DOA spectra or DOA cost function values in the range of azimuth angles, respectively, as DOA angles of two signal sources. On the other hand, when we use the UCA antenna structure at the receiver, both MUSIC and CI algorithms find a single tuple, consisting of azimuth and elevation angles, which yields the largest DOA spectrum or DOA cost function value in the two-dimensional DOA (azimuth and elevation angle) range, respectively, as a DOA angle of a single signal source. It is worth noting that the number of time samples may not be sufficiently large and the spatial correlation is not well-captured in the computed covariance matrix for the MUSIC algorithm in Figure 3. Thus, the resultant direction-finding performance of MUSIC algorithm is not very satisfactory. On the other hand, the conventional CI-based direction-finding technique finds the direction of received signals by directly comparing the phases of the received signal with reference dictionaries generated by assuming ideal phases of a certain signal direction. Thus, the CI-based direction-finding technique provides more accurate direction-finding performance compared with MUSIC algorithm for both ULA and UCA antenna structures, as shown in Figure 3. The conventional CI outperforms the conventional MUSIC when the number of time samples is small or the received SNR is large.  
Figure 3: An example of normalized DOA spectra of the conventional MUSIC and CI algorithms. For a ULA receiver, there exist two signal sources with different azimuth DOA angles, which are equal to \(-50^{\circ}\) and \(10^{\circ}\). For a UCA receiver, there exists a single signal source whose azimuth and elevation DOA angles are equal to \(150^{\circ}\) and \(40^{\circ}\), respectively. **(a)** Normalized DOA spectrum of the conventional MUSIC algorithm with a ULA receiver. **(b)** Normalized DOA cost function value of CI algorithm with a ULA receiver. **(c)** Normalized 2D-DOA spectrum of conventional MUSIC algorithm with a UCA receiver. **(d)** Normalized 2D-DOA cost function value of CI algorithm with a UCA receiver.  
low. In fact, obtaining enough time samples to rigorously analyze the spatial correlation characteristics of the received signals may not be _feasible_ in practical dynamic environments, including military communication systems with anti-jamming/anti-spoofing functions, low earth orbit (LEO) satellite communication systems, and 5G/6G mobile communication systems with multiple-input multiple-output (MIMO) DOA beamforming. Hence, the CI technique may be appropriate for such practical dynamic environments due to its simple operation with direct phase comparison.