Digital antenna array

Digital antenna array (DAA) is a smart antenna with multi channels digital beamforming, usually by using fast Fourier transform (FFT). The development and practical realization of digital antenna arrays theory started in 1962 under the guidance of Vladimir Varyukhin (USSR).

Digital antenna array (DAA) is a smart antenna with multi channels digital beamforming, usually by using fast Fourier transform (FFT). The development and practical realization of digital antenna arrays theory started in 1962 under the guidance of Vladimir Varyukhin (USSR). \hat{P}_{Bartlett}(\theta)=\boldsymbol v^H \boldsymbol R \boldsymbol v \ \ (1) . The angle that maximizes this power is an estimation of the angle of arrival. \hat{P}_{Capon}(\theta)=\frac{1}{\boldsymbol v^H \boldsymbol R^{-1} \boldsymbol v} \ \ (2) . The MVDR/Capon beamformer can achieve better resolution than the conventional (Bartlett) approach, but this algorithm has higher complexity due to the full-rank matrix inversion. Technical advances in GPU computing have begun to narrow this gap and make real-time Capon beamforming possible. \boldsymbol R = \boldsymbol U_s \boldsymbol \Lambda_s \boldsymbol U_s^H + \boldsymbol U_n \boldsymbol \Lambda_n \boldsymbol U_n^H \ \ (3) . MUSIC uses the noise sub-space of the spatial covariance matrix in the denominator of the Capon algorithm \hat{P}_{MUSIC}(\theta)=\frac{1}{\boldsymbol v^H \boldsymbol U_n \boldsymbol U_n^H\boldsymbol v} \ \ (4) . Therefore, MUSIC beamformer is also known as subspace beamformer. Compared to the Capon beamformer, it gives much better DOA estimation. As an alternative approach can be used ESPRIT algorithm as well.

References

Further reading

The estimation and tracking of frequency, Quinn and Hannan, Cambridge University Press 2001.

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