With FOC, the effective array aperture mostly of a physical array can be extended, which makes the number of estimated signals greater than or equal to that Belinostat mechanism of sensors possible.But the conventional MUSIC-like algorithms have high computational requirements as a result of the great number of redundant information contained in the FOC matrix as well as the rigorous requirements of sampling snapshots for the FOC matrix estimation. To mitigate Inhibitors,Modulators,Libraries these drawbacks, a fast MUSIC-like algorithm (the MFOC-MUSIC algorithm) is proposed to reduce the computational complexity effectively [7]. On the other hand, the FOC matrix infinitely approaches the theoretical value when the number of the snapshots goes to infinity [8].

However, because of the existence of the estimation error of the FOC matrix, the performance of the MFOC-MUSIC algorithm cannot be asymptotically optimal.

So, the proposed algorithm in [9] successfully applies the Toeplitz approximate method to the cumulants domain, which mainly focuses on the amplitude Inhibitors,Modulators,Libraries and phase error model. In this paper, the MFOC-MUSIC algorithm in conjunction with Toeplitz approximation, which is termed the TFOC-MUSIC algorithm, is proposed. The emphasis of the paper is Inhibitors,Modulators,Libraries on the investigation of how the algorithm is impacted by sampling snapshots. Firstly, in the TFOC-MUSIC algorithm, the reduced-rank FOC matrix is obtained by removing the redundant information encompassed in the primary FOC matrix. Meanwhile, the effective aperture of the virtual array remains unchanged.

Then, with applying the Toeplitz approximation, Inhibitors,Modulators,Libraries the Toeplitz structure of the reduced-rank FOC matrix is recovered.

And finally, Inhibitors,Modulators,Libraries by using the MUSIC algorithm, the direction of arrival signals can be estimated.The rest of this paper Inhibitors,Modulators,Libraries is organized as follows. Section Dacomitinib 2 introduces the system model and the MUSIC-like algorithm. In Section Inhibitors,Modulators,Libraries Inhibitors,Modulators,Libraries 3, the TFOC-MUSIC algorithm is described in detail. Section 4 presents comparative simulation results that show the effectiveness of the proposed algorithm. Finally, we conclude this paper in Section 5.Throughout the paper, lower-case boldface italic letters denote vectors, upper-case boldface italic letters represent matrices, and lower and upper-case italic letters stand for scalars.

The symbol * is used nevertheless for conjugation operation, and the notations (x)T and (x)H represent transpose and conjugate transpose, respectively.

We use E(x), cum(x) and to indicate the expectation operator, the cumulants, and the Kronecker product, separately.2.?System Anacetrapib Model and the MUSIC-Like Algorithm2.1. System ModelAssume that M far-field narrowband plane wave signals sl(t), (l = 1, ��, M) impinging on a uniform linear array (ULA) of N inhibitor Tofacitinib identical omni-directional sensors with ��/2 inter-element spacing, where �� is the wavelength of the carrier.