The paper investigates the problem of a distributed robust relay beamforming in one-way relay networks with imperfect channel state information. The aim is to maximize the SNR (signal-to-noise ratio) of the receiver with the constraint of the total transmits power of relays is less than a certain predefined threshold. Because the channel is imperfect and the objective function is fractional quadratic form, the optimal problem is a non-convex problem which is hard to be solved. We first change the fractional problem into a non-fractional one. Second, we consider the semi-definite programming (SDP) method efficiently by exploiting S-procedure theorem and relaxing the rank-one constrain to obtain the robust beamforming vector. The paper gives the schematic total algorithm too. Numerical results show that the proposed algorithm can solve the maximum problem with robust features efficiently and obtain satisfactory results.
