the observation matrix Ym = [ym,0, and the noise = of the CFR matrix Hm obey CN(0, o2). The th component of the pilot vector bm,i(1+z) E CN,x1 is obtained as b'm,i(1+z) = d,((1+z) jlm,i(1+z)' where the interference I'm,i(1+z) is obtained as (3.36) The MIMO-FBMC channel matrix Hm of size Nr X N with Nr > N can be decomposed as Hm=WmQH (3.37) 3 FBMC: A Waveform Candidate for Beyond 5G where Qm E CNt x N, and Wm E CNrxNt. and for <m<N- 1, are referred to as unitary (complex rotation) and the whitening (decorrelating) matrices, respectively. 1 Being a unitary matrix, Qm satisfies the constraint QmQH=QHQm = INt. Thus, it follows from (3.37) that (3.38) The semi-blind CSI estimation scheme works on the principle that the whitening matrix Wm can be estimated by exploiting the second-order statistical character- istics of Nd = Lo - M(1+z) data symbols in Fig. 3.3, and the unitary matrix Qm can be estimated using the M pilot symbols in the frame. The matrix Qm is parameterized by a few parameters. It can therefore be estimated accurately with a limited pilot overhead. On the other side, estimation of Wm blindly using statistical properties of data symbols significantly enhances accuracy of the CSI estimation. The covariance matrix Rymym E CNrxNr of the observation vectors , in (3.33) is calculated as (3.39) The above results follow from the identities E[bm,nb 2PdIN and Elm, One can rewrite (3.39) as (3.40) The whitening matrix Wm can now be estimated blindly as (3.41) The matrices m and Um are calculated using SVD as given below: (3.42) The matrix Rymym above, which represents the estimate of Rymym' is obtained by using the observation vectors , for M(1 + z) < < Lo as Rymym () ym,nym.n. Note that the estimate Rymym Rymym with probability as Nd increases [48]. After obtaining the estimate of Wm, the estimate 1 Let the singular value decomposition (SVD) of Hm be expressed as SVD(Hm) = SmImQH.I It is clear that one possible choice for Wm = SmIm and the unitary matrix can be set as Qm. It implies that the whitening unitary de