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Moreover, by multiplexing the training sequence before precoder, training symbols can be exploited in both the initialization and iteration phases of the iterative channel estimation process.
Therefore, optimal training sequence should be designed carefully that considers both initialization and iteration phases.
In order to design the optimal training symbols and their positions, the CRB on the channel estimations at the initialization and at the iteration phases are minimized.
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By replacing θ in (6) for h and after some manipulations, the FIM for channel estimation in the iteration phase is given by FI M iter ( n p, x p, I p ) = N 0 - 1 I n r ⊗ ( N s ′ - n p N σ x 2 I n t + ∑ τ ∈ I p ∑ τ ′ ∈ I p ( x p ) H x p ⊗ ∑ i = 1 s ′ ( Φ p [ i ] ) H Φ p [ i ] ) + s ′ σ h - 2 I n t n r. (12).
FastWISE continues with the iteration phase.
(b) After iteration phase (COV cur =99.02%, p blck ≈0).
Now consider the training design for the iteration phase.
For the iteration phase, the expression in (12) means that the CRB in the iteration phase always increases by increasing np.
Therefore, the training sequence designed for the initialization is also optimal for the iteration phase.
One step of the iteration phase can certainly be done in time O(n).
The optimum numbers of the training symbols in the initialization phase and iteration phase are not the same.
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Justyna Jupowicz-Kozak
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