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I have the following problem regarding the iterative channel estimation employing LMMSE.

The channel estimation formula is:

H_lmmse,nt,nr,ns=Rhh*Xnt,ns'(sum(Xnt,ns*Rhh*Xnt,ns ')+sigma^2)^-1*Ynr,ns.

Explonation:

Rhh - channel autocorrelation matrix of size KxK (K number of subcarriers)

Xnt,ns - diagonal matrix size Kx, kontaining in its diagonal: pilot symbols, data symbols and zero symbols. nt-Tx antenna index. ns - OFDM symbol index.

sigma-noise variance

sum - goes from 1 to Ntx(for the number of Tx antennas)

Ynr,ns - Rx signal. nr - Rx antenna index.

Is there any posibility to apply the WOODBURY identity to the H_lmmse,nt,nr,ns, and how can this be done?

Thanks in advance

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# WOODBURY identity - Iterative LMMSE channel estimation for LTE

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