A Closed-Form Power Allocation and Signal Alignment for a Diagonalized MIMO Two-Way Relay Channel With Linear Receivers

A novel channel diagonalization scheme for an amplify-and-forward, multiple-input multiple-output (MIMO), two-way relay channel (TWRC) is proposed using generalized singular value decomposition (GSVD). Diagonalization of the MIMO TWRC is a sub-optimal approach that achieves two main purposes: reducing the computational complexity for optimizing the linear precoders at each node; and reducing the detection complexity at the source nodes by separating the multiple data streams. For the given diagonalized structure, we first align the entries of the diagonalized channels using a permutation to maximize a lower bound of average achievable sum rate (ASR), and a joint source-relay power allocation is then performed to maximize the ASR of the aligned TWRC; the overall problem is divided into two convex subproblems, the solutions to which are provided in closed-form. Our analysis for the proposed scheme underlines the benefits of acquiring channel state information. Simulation results demonstrate that the proposed GSVD-based relaying scheme, with the signal alignment and closed-form power allocation, significantly improves the ASR while retaining the diagonalized channel structure. In addition, the proposed scheme achieves the same level of ASR with much less computational complexity as compared to the iterative schemes.