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This key observation allows us to apply tensor decomposition methods to jointly retrieve the estimates of CFO and the MUI-free received training symbol corresponding to each user.
Apart from CFO estimates obtained through A ˆ and B ˆ, the PARAFAC model also provides the estimate of C, whose columns contain MUI-free received signals corresponding to each user.
The CIR information is hidden in the CFO-free, noise-free received signal vector y such that ( mathbf{y}=frac{1}{sqrt{N}}{mathbf{F}}_N^H{mathbf{U}}_X{mathbf{F}}_vmathbf{h} ).
In our case, the criterion includes a weighted difference between target and noise-free received signals, ϵ = 1 c HR - D s (describing the remaining intracluster interference) and a weighted transmit power term.
However, the received data symbols still satisfy Equation 10 with C replaced by a symbol-dependent matrix C q) whose columns contain the MUI-free received data symbols of the users.
Thus, the PARAFAC model is still applicable to the multi-antenna BS reception, and tensor decomposition can still be applied to jointly estimate the CFOs and MUI-free received signal corresponding to different users and receive antennas.
The CFO estimate and the MUI-free received signal estimate corresponding to each user can then be extracted from A ˆ, B ˆ, and C ˆ as shown in the following sections.
These simulation results show that the proposed CFO estimation and compensation schemes offer significant performance improvements in both CFO estimation accuracy and estimation of MUI-free received signals corresponding to different users.
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