Su frequency samples that keeps the signal within the allocated band also preserves the spectral properties. Therefore, x E CNx1,whre , has similar spectral properties of Xu. All these linear steps can be expressed in the form x = 1 (4.25) where E NxNu the allocation matrix, which maps the N FD samples of the FD block Audu to the N points seen as the input of the DFT matrix. Based on that, GFDM can be inte- grated in OFDM by inserting a flexible small-size FD-GFDM modulator to precode the input data of certain subcarriers. At the receiver side, channel equalization is required in addition to the FD-GFDM demodulator, as illustrated in Figure 4.12. One application of this model is to improve the spectral usage of OFDM. Instead of disabling large number of OFDM 4.3 GFDM for OFDM Enhancement GFDM modulation GFDM demodulation OFDM system Inverse Precoding precoding modulator FD Xu yu Channel Yeq, u GFDM FD equalizer demodulator Figure 4.12 Precoded OFDM system model. subcarriers to produce low OOB, GFDM can be used on the edge subcarriers with proper configurations to provide low side lobes. On the other hand, to preserve low complexity, the middle subcarriers can keep using plain OFDM via bypassing of the GFDM precoding. This feature can also be used to support asynchronous multiple access, which allows using fewer guard subcarriers between adjacent users. This model can also be used to introduce differ- ent type of orthogonal precoding, using the extended flexibility of GFDM. The precoding can be used, e.g. to spread the data over larger bandwidth to harvest frequency diversity. 4.3.2 Receiver The receiver first performs the conventional OFDM processing, i.e. removing the CP fol- lowed by N-DFT, and then the deallocation. Therefore, we get the received FD-GFDM symbol (4.26) where 1(hu) is the equivalent FD diagonal channel matrix and vi is the additive white Gaussian noise (AWGN). In several theoretical works, the equivalent demodulation and channel equalization matrix Hu A is considered as a large-scale multiple-in