Application of MUSIC super-resolution technique in the phased antenna array for directions of arrival estimation of random signals

The article is dedicated to the angle position estimation of multiple signal sources. One of the most effective technique in this field is Multiple Signal Classification that is widely known as MUSIC. However, this technique cannot be applied directly to hybrid analog-digital antenna arrays (including the phased antenna arrays) that have been actively developing recently and widely using in the fifth-generation wireless communication systems and radars. Meanwhile, the existing approaches to MUSIC application in such systems either demand ideal periodic signal or have excessively high computational complexity. The goal of this work is the development of the effective and computational simple approach to the application of MUSIC technique in the phased antenna array for direction of arrival estimation of the random signals. The keystone of the MUSIC algorithm is the antenna array covariance matrix that allows one to single out complimentary signal and noise vector subspaces. However, this matrix cannot be estimated directly in the phased antenna array. The proposed method is based on the Toeplitz form of the antenna array covariance matrix in the case of incoherent (uncorrelated) sources. In this case the whole covariance matrix is determined by its first row (covariance vector). It is proved that covariance vector can be calculated from the discrete spatial power spectrum via discrete Fourier transform. Meanwhile, the discrete spatial power spectrum is estimated via power measurements for the finite number of antenna array beams. Thus, this spectrum is evaluated via conventional beam scanning procedure. It is showed that the covariance matrix can be recovered accurately if the number of the discrete spectrum points (the number of used beams) at least twice more than the number of antenna elements. The performance of the proposed technique is investigated via numerical simulations in comparison with competitors. The results shows that the proposed approach provides super resolution and allows one to effectively estimate angular positions of multiple signal sources. The estimate accuracy provided by the proposed technique is similar to the one of the more complex alternative approach that also does not depend on the waveform. Meanwhile, there is some accuracy loss relatively a periodic-signal-based technique and the digital-array MUSIC that is treated as the cost of waveform independency and phased array application. The devised technique can be applied in radar and fifth-generation wireless communication system to estimate channel state in the millimeter wave band.