ep the signal dispersed due to the transmitter and receiver filtering under one f-OFDM symbol duration, such that the f-OFDM symbol of interest only suffers ISI from its direct neighbors. As illustrated in Figure 2.2, the signal spreads bidirectionally and inflicts interference between adjacent OFDM symbols. The forward/backward ISI are generated by the for- ward/backward spreading of the previous/next OFDM symbols to the current symbol window, while the ICI comes from the energy loss of the current OFDM symbol due to its bidirectional spreading. To facilitate the interference analysis caused by filtering, we derive the equivalent matrix form of a linear filtering process. The L received samples relative to the k-th OFDM symbol are grouped in the vector Sk, thus obtaining (2.5) where the L XL matrix Pu spreads the (k - 1)-th OFDM symbol into the core window of the k-th OFDM symbol and causes the f-ISI. It is a strictly upper triangular matrix defined by its (i,j)-th element as (2.6) The matrix Pm is a Toeplitz matrix specified by its first column first row It is a matrix in which all nonzero entries are on the main diagonal and the first diagonals above and below. The matrix Pl extends the (k+1)-th OFDM symbol into the core window of the k-th OFDM symbol and leads to the b-ISI. It is a strictly lower triangular matrix defined by its (i,j)-th element (2.7) 2.2 System Model for f-OFDM SISO System Backward Forward spreading spreading (k - 1)th symbol kth symbol (k+1)th symbol Forward ISI Backward ISI Figure 2.2 f-OFDM filtering illustration. (3) Passing the channel. An (Nch+1)-tap (Nch N Ncp) channel is assumed to have an impulse response (2.8) After passing the above channel followed by an addition of additive white Gaussian noise (AWGN), the L received samples corresponding to the k-th OFDM symbol can be written as (2.9) where Hm is a Toeplitz matrix with [hT, E CLx1 as its first column and [ho,01x(L-1)] ¹ E CLx1 as its first row. Hu is the matrix relative to the channel spreading, and it is a strictly upper trian