r, the optimal CP length can be found close to the width of the first main lobe ([N/M]) due to the energy distribution nature of the filter. Therefore, the complexity of the search algorithm is O(N/M). 2.3.4 An Alternative for In-Band Interference Mitigation: Frequency Domain Equalization (FDE) 2.3.4.1 Linear Equalizers Two representative equalizers, i.e. zero-forcing (ZF) and minimum mean squared error (MMSE), apply an equalization matrix to the current symbol to reverse the effective chan- nel effect. Considering that the received signal of the k-th f-OFDM symbol can be expressed = d + interference terms + , (2.27) we define ZF and MMSE equalizers in f-OFDM systems as (2.28) 2 How close the effective channel to a diagonal matrix can be measured quantitatively by Frobenius norm of the matrix . The smaller the ellF is, the closer the effective channel is equivalent to a diagonal matrix. 11YellF = 0 indicates a perfect diagonal matrix. 2 Filtered OFDM: An Insight into Intrinsic In-Band Interference 2.3.4.2 Nonlinear Equalizers A nonlinear equalizer has improved performance relative to linear receivers by employing interference cancellation (IC) techniques. Conventional successive interference cancella- tion (SIC) algorithms come with significantly high computational complexity due to their high cancellation granularity. We propose a novel interference cancellation algorithm customized for f-OFDM systems, namely, block-wise parallel interference cancellation (BwPIC), which only performs cancellation once for all f-OFDM symbols in a data block per iteration. The algorithm comes with lower complexity than SIC because the cancellation is only carried out on a block basis. The algorithm cancels the in-band interference of all f-OFDM symbols in one block in parallel. The detail is shown in Algorithm 2.1. It involves a sequence of interference can- cellation/equalization/slicing operations. At each iteration of the outer loop, a vector d = is updated, and dpre/dnext are derived accordingly. Then the interference correspo