Interference Subspace Alignment in Multiple-Multicast Networks

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In the traditional interference channel (IC), each transmitter works in the mode of one-to-one. For serving more user terminals (UTs), a multiple-multicast network is proposed, in which there are multiple transmitters, and each transmitter works in the mode of one-to-many. Thus, each UT would suffer from both the intra-transmitter and inter-transmitter interference. Given the transmitting and receiving degrees of freedom, the desired signal would be more difficult to be separated from the numerous interference signals. For managing the interference, an interference subspace alignment (ISA) algorithm is proposed to decrease the dimension of the interference subspace. Different from the traditional iterative interference alignment (IA) algorithms, which iteratively calculate the precoding and receiving combining matrices to minimize the strength of interference, the ISA algorithm directly aligns the interference subspace spanned by the $T-N$ transmitters within that spanned by the residual $N$ transmitters, in which $T$ denotes the number of all the transmitters, and $N$ is the cardinality of the transmitter set used for IA. Now, the dimension of each UT's interference subspace is determined via $N$ transmitters ( $N ). During the subspace alignment, we, respectively, construct the composite IC state matrices for the $T-N$ and $N$ transmitters, and the composite precoding vector, which lies in the null space of the composite IC matrices. Thus, all the precoding matrices can be obtained once. After the subspace alignment, each UT's receiving combining matrix can be designed to lie in the null space of the aligned interference subspace. According to the simulation results, the proposed ISA algorithm can effectively suppress the interference and improve the system sum rate compared with the traditional interference management algorithms.