This letter considers a multiuser peer-to-peer communication network using a number of shared relays for collaborative beamforming and aims to minimize the total transmitted power of the relays whilst satisfying the targets of the signal-to-interference and noise ratios (SINRs) at the destination nodes by optimizing the relaying coefficients with imperfect channel state information (CSI). By deriving an equivalent form for the SINR constraints and an upper bound for the relay power, the problem can be tackled by solving a semi-definite program (SDP). Results reveal that the proposed technique outperforms significantly a conventional robust approach in terms of the transmitted power, and has only a mild increase in power if compared to the non-robust optimum which fails to meet the SINR targets.
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