Three-dimensional orthogonal vector basis functions for time-domain finite element solution of vector wave equations

It was previously shown that the number of array elements must exceed the number of sources for subspacebased directional-of-arrival (DOA) estimation. This is clearly not practical for a direct-sequence code-division multiple access (DS-CDMA) wireless system since the number of mobile users is very large. To overcome the restriction, a DOAʹs estimator employing the code-matched filters and parallel MUSIC algorithms is proposed. In the asynchronous DS-CDMA system, we show that the multiple access interference (MAI) throughout the codematched filter tends toward the real Gaussian distribution with zero mean. In addition, based on the singular value decomposition (SVD) of a finite amount of data, we achieve a theoretical expression for the mean-squared error (MSE) of the DOAʹs estimation. With the advantage of code-matched filter inherent in the DS-CDMA system, we prove that the proposed technique can obtain an unbiased DOA estimation with low MSE, even in the environment where the number of mobile users far exceeds the number of array elements. Simulation results verify the theoretical derivation.