MUSIC and ML-based Direction-of-Arrival Estimation for narrowband signals - Acay, Jules T. (2008.)
This project evaluated the performance of eight different direction-of-arrival estimation algorithms for use in multipath environments where coherent signals may occur in practice. The eight programs consist of four MUSIC-based and four ML-based methods. The four MUSIC-based programs include conventional MUSIC, MUSIC with forward spatial smoothing (FSS-MUSIC), and two variants of MUSIC with covariance differencing (CD-MUSIC). The four ML-based programs include Conditional or Deterministic ML (CML), Unconditional or Stochastic ML (UML), UML with CML initialization and global search (CML+UML(G)), and UML with CML initialization and local search (CML+UML(L)). It was shown that the CD-MUSIC1 and CD-MUSIC2 algorithms proposed in this study are viable alternatives to FSS-MUSIC in determining the directions-of-arrival of uncorrelated as well as coherent signals. CD-MUSIC1 and CD-MUSIC2 were shown to be less computationally complex than FSS-MUSIC by a factor of approximately 10/t, where t is the number of samples. CD-MUSIC1 and CD-MUSIC2 were also shown to require only approximately half the number of antenna elements than FSS-MUSIC for two or more incident signals. The CD-MUSIC programs, however have less accurate estimates and lower resolution than FSS-MUSIC. For a 16-element antenna array using 10,000 data samples, an error of less than 1 degree is achieved by CD-MUSIC1 and CD-MUSIC2 for SNRs greater than 5 dB and O dB, respectively, while FSS-MUSIC achieves the same accuracy for SNRs even less than -10 dB. In terms of resolution for a 16-element array at 20 dB SNR using 500 samples, CD-MUSIC1 and CD-MUSIC2 have similar resolution of about 10 degrees while FSS-MUSIC has a resolution of approximately 2 degrees. It was also shown that CML+UML(L) is the best option for direction-of-arrival estimation among the four ML-based methods. For a small sample size of 10 samples and low SNR of 0 dB, it achieves an accuracy of 0.7 degree similar to CML, compared to accuracies of approximately 6.5 degrees for UML and CML+UML(G). For large sample size of 10,000 samples, it achieves a better accuracy of about 0.08 degree similar to CML+UML(G) over an accuracy of 0.1 degree for CML using a 16-element antenna array at -10 db SNR. In addition, for a 16-element antenna array at 20 dB SNR using 500 samples, CML+UML(L) has a high resolution of approximately 0.3 degree at par with CML, and second only to CML+UML(G) with a resolution of 0.2 degree. It is also the second least computationally complex to CML, with 330k more operations of cubic complexity than CML, where k is the number of iterations in the convergence phase. In this study, the relative differences between the MUSIC and ML-based methods were ascertained. It was observed that the ML methods are superior to MUSIC methods in terms of accuracy and resolution. This advantage, however, comes at a much higher computational complexity for the ML-based methods. Whereas the MUSIC-based methods perform only a few operations of cubic complexity, the ML-based methods perform a significant number of operations of cubic complexity.
Undergraduate Student Project (B.S. ECE)--University of the Philippines, Diliman.
Keywords: Signal processing -- Digital techniques; Algorithms -- Data processing; Direction-of-Arrival Estimation; MUSIC algorithm