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In our method, we utilize a set of d chains to sample inversion paths in parallel.
One possible extension of our method would allow sampling suboptimal sorting paths and their prefixes, and the prescribed sampling distribution would be similar to those of programs like BADGER (Larget et al. 2005) or ParIS Genome Rearrangement (Miklós et al. 2005), which implements a method to sample inversion and transposition histories.
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If the sampled inversion is indeed a sorting inversion (decided by Bader's algorithm in linear time), the change is accepted with the probability in equation (8).
Even better, the proposed scheme has lower computation complexity than the traditional sample matrix inversion algorithm.
The literature commonly refers to the implementation in (3) as sample matrix inversion (SMI).
We apply the Sample Matrix Inversion (SMI) algorithm [23] in the temporal domain, directly after downconversion on an elements array.
Then, the adaptive beamformer ( {mathbf{w}}_{mathrm{SMI}}=frac{{widehat{mathbf{R}}}^{-1}mathbf{a}left {theta}_0right)}{mathbf{a}{left({theta}_0right)}^{-1}mathbf{a}left {theta}_0right{a}{mathbf{ata}{left {theta}_0rightample matrix inversion (SMI) beamformer.
The performance of the proposed algorithm is compared with the sample matrix inversion (SMI) beamformer, the eigenspace-based beamformer (ESB), the reconstruction-estimation (Rec-est).
The most popular approximated method is the sample matrix inversion (SMI) method which consists in inverting the covariance matrix estimated by an average of the sample matrix over the secondary range cells.
The minimum mean square error estimation (MMSE) criterion can be used to estimate the desired user propagation channel, while the covariance matrix can be estimated by the sample matrix inversion (SMI) approach [7 9].
The main difference between the CSB method and the traditional loading sample matrix inversion (LSMI) method lies in that, it's not clear how to choose the diagonal loading factor of the LSMI method, but the loading factor of our CSB method can be decided by the constraint factor δ 0 via Eq. (15).
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