Different to[10], the precoding matrix at the relay is constructed by projecting each aligned message on a single carefully chosen direction of the null space, respectively, where the inverse of large size matrices can be avoided.
The key idea of OP-SI scheme at the relay is to project the desired message to an orthogonal direction of the null space, i.e., the aligned message for the i th user should be project to a vector which is belongs to the null space generated by h1,…,hi−1hi + 1,…,h M.
Based on a submatrix of H, an orthogonal projection matrix U i ‡ can be generated for the aligned message of s i and x i, U i ‡ = ( I N − W i ( W i H W i ) − 1 W i H ) N × N, i ∈ 1, …, M. (57).
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As given by (1), the aligned messages for all the users are mixed together, which causes strong interference at the user side.
According to the precoding matrix proposed by (4), the relay can obtain the aligned messages, which can be expressed as r = H ( α B s + x ) + n R. (8).
First, we can rewrite (1) as the mixture of the aligned messages for the users, r = ∑ i = 1 M h i ( α B s i + x i ) + n R. (9).
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