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Table 1 Mathematical notations

From: Joint user clustering and resource allocation for device-to-device communication underlaying MU-MIMO cellular networks

Notation Physical interpretation
K rb Denotes the number of all available time-frequency RBs
K c , K d Denote the number of CUEs or D2D pairs in a cell
N c , N d Denote the number of CUEs in a CUE subcluster and the number of D2D pairs in a DUE subcluster
C i Denotes the label of CUE in a CUE subcluster, where i varies from 1 to N c
D j Denotes the label of D2D pairs in a DUE subcluster, where j varies from 1 to N d , and each D2D pair includes a D j  − T x and D j  − R x
\( {\mathbf{s}}_{C_i}^m,{\mathbf{s}}_{D_j}^m \) Denote the transmitted signal transmitted at the m-th subcarrier, and the subscript indicates the source of the signal
\( {\mathbf{E}}_{C_i},{\mathbf{E}}_{D_j} \) Denote the diagonal matrix of the multiantenna transmit power, where the subscript indicates the source of the signal
\( {\mathbf{H}}_{i,j}^m \) Denotes the Rayleigh channel matrix from node j to node i over the m-th subcarrier, with 0 mean and unit variance
L i,j Denotes the diagonal matrix of the path loss from node j to node i
r i,j Denotes the distance between node j and node i
\( {\mathbf{n}}_{\mathrm{BS}}^m,{\mathbf{n}}_{D_j}^m \) Denote the additive white Gaussian noise (AWGN) on the m-th subcarrier