denotes the expectation operator. Vectors and matrices are denoted by boldface low- ercase and uppercase characters, receptively. The operators (.)*, (.)T, and (.)H represent complex conjugate, transpose, and conjugate transpose, respectively. The M X M identity matrix is denoted by IM diag(x) is a function returning a square diagonal matrix with the elements of vector X on the main diagonal, while diag(A) returns a column vector of the main diagonal elements of matrix A. I I denotes the magnitude of a complex number, while Il is the Frobenius norm of a matrix. * denotes the circular convolution, and R and C represent real and complex space, respectively. 2.2 System Model for f-OFDM SISO System In this section, we describe a system model for single band f-OFDM systems in which the interference (including ICI, f-ISI, and b-ISI) induced by filtering operations are investigated. 2.2 System Model for f-OFDM SISO System Subband N-point Filter Wireless channel mapper N-point Remove Matched Equalization filter demapping Figure 2.1 Block diagram of the f-OFDM transceiver. These interference components are referred as in-band interference. The interference from the other subbands in the system (inter-subband interference) is out of the scope of our work.¹ Assume M consecutive subcarriers in the range of M = {M, M + 1, M + M - 1) are assigned to the subband with a corresponding waveform shaping filter denoted as vector p in the time domain and p in the frequency domain. Considering the block diagram depicted in Figure 2.1, a sequence of information bits b is fed into a quadrature amplitude modulation (QAM) mapper to obtain symbols from a 2 - valued complex constellation, where is the modulation order. Representing the com- plex symbols in K consecutive OFDM symbols in a sub-frame as a length MK vector gives (2.1) where ECMX1 with the individual element dk.m corresponding to the data symbol transmitted on the m-th subcarrier in the k-th OFDM symbol. The data symbols contained in dk are assumed to be independent and identica