A Novel Low-Complexity GFDM Relay Communication System: Relay Selection and Filter-and-Forward

In this paper, we develop a low-complexity cooperative relay network based on generalized frequency division multiplexing (GFDM) system. In this network, multiple relay nodes (RNs) are used to relay GFDM symbols from a source node (SN) toward a destination node (DN). We propose three methods to design the RNs based on the minimization of the total power of the noise after symbol estimation at the DN. In the first method, only one node is selected among all RNs to forward the signal from the SN to the DN. In the second and third methods, a filter-and-forward (FF) scheme is used, such that at each RN, the received GFDM signal from the SN is circularly convolved with a finite impulse response (FIR) filter and then, forwarded to the DN. The FIR filter's coefficients are represented as a circulant matrix. Since a circulant matrix is characterized by its eigenvalues, we obtain the eigenvalues of the FIR coefficient matrices for all RNs. The difference between the second and third methods is that in the former, the eigenvalues of the filter matrices are restricted to be one or zero, however, in the later, the eigenvalues are determined with no restrictions. Simulation results are provided to demonstrate the performance of the proposed methods in terms of bit error rate (BER). Moreover, we show that because of using circular convolution, the proposed methods can be implemented with a low complexity.