The multiple-input multiple-output relay broadcast channel with one source, one relay, and two destinations is studied. It is assumed that the source and the relay cooperatively serve one of two destinations, which may have a weaker channel from the source (due to, for example, being located far from the source), while the source alone serves the other destination that has a stronger channel. Given the asymmetry in the use of the relay as well as in the channel strengths, the performance of the

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... system is evaluated through the minimum of the rates for the two destinations instead of the sum of the rates. A new linear transmit and receive beamforming scheme is proposed for this max-min fairness problem that can be implemented in practical scenarios. Numerical results show that the proposed scheme yields a significant gain over existing schemes. Index Terms-MIMO relay broadcast channel, half-duplex relay, max-min fairness, interference alignment, repetition coding.