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Optimal designs for minimising the combination of symbol estimation errors subject to lp-norm constraint are investigated. Instead of considering each constraint in a separate way, the authors develop a unifying framework to obtain the optimal solution by employing a directional derivative method. The sum or peak power constraint turns out to be the case of p=1 or prarrrarr. Simulation results demonstrate the effectiveness of the proposed algorithm. Moreover, based on directional derivative, the authors show that the minimisation of the determinant of the minimum mean-square error (MMSE) matrix and the maximisation of mutual information are equivalent criteria.