Comment on "Direction and polarization estimation using arrays with small loops and short dipoles" [with reply]

The authors comments that Li (see ibid., vol.41, p.379-87, 1993) proposed an algorithm for the estimation of the two-dimensional (2-D) direction and polarization of incoming waves using loops and dipoles. The algorithm does not require sensors to be uniformly spaced. However, if sin/spl theta//sub i/=0, tan/spl gamma//sub i/=e/sup -i/spl eta/i/, or tan/spl gamma//sub i/=-e/sup -j/spl eta/i/, the algorithm does not necessarily provide correct estimates, even when the exact data covariance matrix is available. The reason is shown. Li replies that the special cases pointed out by Cheng and Hua (see ibid., vol.46, no.3, p.461, 1998) occur with zero probability. They correspond to /spl theta//sub k/=0 or /spl pi/ or (/spl gamma//sub k/,/spl eta/k)=(/spl pi//4,0) or (/spl pi//4,-/spl pi/). It can be easily checked to see if these rare cases have indeed occurred. Hence, one could avoid using the proposed approach of by simply checking to see if these matrices are ill conditioned.