UFMC principles

Universal Filtered Multi-Carrier (UFMC) can be seen as a generalization of OFDM and FBMC. The ultimate goal of UFMC is to combine the advantages of OFDM and FBMC while avoids their main drawbacks. By filtering groups of adjacent subcarriers, the sidelobe levels (compare with OFDM) and the prototype filter length (compare with FBMC) can be simultaneously significantly reduced. Starting from the $k$-th OFDM signal of a considered $i$-th Physical Resource Block (PRB) with $$x_{k,i}(m) = \sum_{n \in S_i} s_{k,n} e^{j\frac{2\pi}{N_{\textrm{sub}}}kn}, m=0,\cdots,N_{\textrm{sub}}-1$$ where $S_i$ is a set which contains consecutive subcarrier indexes that are assigned to the i-th PRB. This signal is then filtered by an FIR-filter $f_i$ with the length of $L_{F}$. Thus, the transmit $k-$th symbol is written as $$\tilde{x}_{k}(m) = \sum_{i}\sum_{l=0}^{L_{F}-1}f_{i}(l)x_{k,i}(m-l), m=0,\cdots,N_{\textrm{sub}}+L_{F}-2.$$ The FIR-filter can be differently designed for each PRB, in this demo we use the same Chebyshev-filter with variable sidelobe attenuation for every PRB except that the filter is shifted to the center frequencies of every PRB.