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.

中文翻译：

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一种新型低复杂度 GFDM 中继通信系统：中继选择和滤波转发

在本文中，我们开发了一种基于广义频分复用 (GFDM) 系统的低复杂度协作中继网络。在该网络中，多个中继节点 (RN) 用于从源节点 (SN) 向目标节点 (DN) 中继 GFDM 符号。我们提出了三种方法来设计基于 DN 符号估计后噪声总功率最小化的 RN。在第一种方法中，在所有RN中只选择一个节点将信号从SN转发到DN。在第二种和第三种方法中，使用了滤波转发 (FF) 方案，这样在每个 RN，从 SN 接收到的 GFDM 信号与有限脉冲响应 (FIR) 滤波器循环卷积，然后转发到DN。FIR 滤波器的系数表示为循环矩阵。由于循环矩阵的特征在于其特征值，因此我们获得了所有 RN 的 FIR 系数矩阵的特征值。第二种方法和第三种方法的区别在于前者将滤波器矩阵的特征值限制为1或0，而后者则没有限制地确定特征值。提供了仿真结果以证明所提出的方法在误码率（BER）方面的性能。此外，我们表明，由于使用循环卷积，所提出的方法可以以低复杂度实现。之后，特征值的确定没有任何限制。提供了仿真结果以证明所提出的方法在误码率（BER）方面的性能。此外，我们表明，由于使用循环卷积，所提出的方法可以以低复杂度实现。之后，特征值的确定没有任何限制。提供了仿真结果以证明所提出的方法在误码率（BER）方面的性能。此外，我们表明，由于使用循环卷积，所提出的方法可以以低复杂度实现。