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This study considers the joint transmission precoding design for downlink multicell multiuser multiple-input single-output systems where imperfect channel variances are available at the base stations. The authors aim to tackle the robust signal-to-interference-plus-noise ratio (SINR) balancing problem to maximise the minimum worst-case user rate. To solve the non-convex problem, a duality relationship between the downlink max-min worst-case SINR optimisation problem and the virtual uplink min-max worst-case SINR optimisation problem is first revealed. Based on this, a new algorithm is developed to solve the virtual problem by using jointly the sub-gradient method and the geometric programming methods, whose achieved solution is finally converted to the downlink. Their analysis shows that the proposed algorithm is guaranteed to converge and has lower computational complexity than conventional approaches. Moreover, computer simulations validate the effectiveness of the proposed method and show that the proposed algorithm has fast convergence and achieves a performance close to that of the brute search method.