**3.6 Conclusion**

An improved version of the Root-MUSIC algorithm, called Root-MUSIC with real-valued eigendecomposition (RVED-Root-MUSIC), has been presented in this chapter. The computational complexity is reduced significantly by exploiting the one-to-one correspondence between centro-Hermitian and real matrices, allowing a transformation to real matrices, which can be maintained for all steps of the algorithm. Due to the inherent forward-backward averaging effect, RVED-Root-MUSIC can separate two completely coherent sources and provide improved estimates for correlated signals.

126 Fourier Transform Applications


Fig. 22. and Fig. 23. depict DOA departure versus snapshot number results of RVED-Root-MUSIC and Root-MUSIC respectively, where the SNR=5dB. In figure 22. and 23., the x-axis denotes the snapshot number, and y-axis denotes the departure of signal

Fig. 24. and Fig. 25. depict DOA departure versus SNR results of RVED-Root-MUSIC and Root-MUSIC respectively, where the snapshot number =1000. In figure 24. and 25., the

From the detecting results and the comparison between RVED-Root-MUSIC and Root-MUSIC, we can conclude that RVED-Root-MUSIC can detect DOA of signal quickly and effectively. At the same time, the results validate the correctness and effective of this

An improved version of the Root-MUSIC algorithm, called Root-MUSIC with real-valued eigendecomposition (RVED-Root-MUSIC), has been presented in this chapter. The computational complexity is reduced significantly by exploiting the one-to-one correspondence between centro-Hermitian and real matrices, allowing a transformation to real matrices, which can be maintained for all steps of the algorithm. Due to the inherent forward-backward averaging effect, RVED-Root-MUSIC can separate two completely

Fig. 25. DOA departure vs SNR. Signal DOA=[-80 -20 40], Snapshot number =1000

x-axis denotes the SNR, and y-axis denotes the departure of signal DOA .

coherent sources and provide improved estimates for correlated signals.


Root MUSIC

0.5

0.4

0.3

DOA Departure

DOA.

algorithm.

**3.6 Conclusion** 

0.2

0.1

0
