2.18) are met, the adding CR converts the linear convolution * p * into a circular convolution q * h * p * X. From the definition of convolution theorem, circular convolution in the time domain leads to multiplication in the frequency domain. Denote p, h, q as DFT of p, h, q in the subband; the received data symbol vector Yk in (2.14) can be reformed as (2.19) where the M X M diagonal matrix A = QHP with Q = diag(q), H = diag(h), P = diag(p). The Eq. (2.19) implies that Y = L'A = A and the ICI generating matrix Ye = 0. Thus, zero in-band ICI is guaranteed. With the discussion above, we form the following Proposition: Proposition 2.1 Consider a single-band f-OFDM system depicted in Figure 2.1 with the transmitter, the channel, and the receiver filter being defined in (2.4),(2.8),(2.11). It is an in-band interference-free system under the condition of perfect synchronization at the receiver and Ncs Nq, (2.20) and the received data symbol can be expressed as in (2.19). 2.3.2 In-Band Interference Power When the interference-free condition in (2.20) is violated, i.e. Ncp < Np + Nch or Ncs < Nq, the system will not be strictly orthogonal. In the time domain, the signal from adjacent OFDM symbols spreads into the core window of the OFDM symbol of interest, which pro- duces the f- and b-ISI. In the frequency domain, the extended part of the interested OFDM symbol falls out of the range of CP/CS and leads to the energy loss. As a result, the matrix Y is no longer diagonal, causing ICI. The average power of the desired signal and interfer- ence signal including f-ISI, b-ISI, and ICI on all subcarriers in one transmission block can be grouped as an N x 1 vector, obtained as (2.21) Forcing the channel matrix to be an identity = 1, Hu = 0), SO that the interference induced by the channel can be avoided, and the interference signal from filter- ing itself can be studied. The average power of the aforementioned signal can be rearranged (2.22) 2 Filtered OFDM: An Insight into Intrinsic In-Band Interference The system signal to i