Читать книгу Multi-Processor System-on-Chip 2 - Liliana Andrade - Страница 24

We consider a GFDM resource grid with K subcarriers and M symbols. In total, N = MK complex data symbols are transmitted within a GFDM block, where dk [m] represents a data symbol to be transmitted on the kth subcarrier and the mth symbol for k = 0, 1, …, K − 1, m = 0, 1, …, M − 1. The signal corresponding to the kth subcarrier is constructed by K-times up-sampling the data vector dk = [dk [0], dk [1], …, dk [M − 1]]^T, followed by pulse shape filtering with g [mK] and subcarrier modulation . The resulting GFDM signal x [n] for n = lK + i; l = 0, 1, …, M − 1; i = 0, 1, …, K − 1 is shown in [1.1]

[1-1]

where l = 0, 1 ,…, M − 1; n = 0, 1,…,K − 1 and g [.]_{mod N} is the impulse response of the K-times over-sampled pulse shaping filter with circular symmetry. Reordering the sums in equation [1.1] leads to a K-point IDFT{d [m]} of the mth data symbol vector d [m] = [d0 [m], d1 [m] ,…, dK−1 [m]]^T and subsequent filtering of IDFT outputs D [m] = [D₀ [m], D₁ [m],…, D_K–1 [m]]^T. IDFT is a well-researched topic, hence the novelty of interest in our work is the filtering of D [m].