A method for reducing a peak-to-rms ratio in a transmitted radio signal while placing a limit on the peak composite symbol amplitude when utilizing multi-dimensional modulation, said method comprising the steps of: encoding information into a stream of binary bits; forming a plurality of groups of bits from the stream of binary bits, wherein each one of the plurality of groups of bits represents a corresponding data symbol, comprising dividing groups of data bits into a first subgroup and a second subgroup; representing each data symbol by a set of coordinates in a multidimensional space; using the first subgroup of bits to select one of a number of constellation points that are distributed within a first multi-dimensional space, where a location of the constellation points have been determined such that a sum of their coordinates is less than a desired maximum value, and the coordinates of the selected constellation point are used to set values of real parts of corresponding complex numbers; using the second subgroup of bits to select another one of a number of constellation points that are distributed within a second multidimensional space, where a location of the constellation points have been determined such that a sum of their coordinates is less than a desired maximum value, and the coordinates of the selected constellation point are then used to set values of imaginary parts of corresponding complex numbers; wherein each multidimensional space is defined by a diamond-shaped constellation; and wherein the diamond-shaped constellation is defined in a three-dimensional space with coordinate axes X, Y and Z, and an outer surface of said diamond-shaped constellation being defined by the boundary equation |X|+|Y|+|Z| = 1. encoding information into a stream of binary bits; forming a plurality of groups of bits from the stream of binary bits, wherein each one of the plurality of groups of bits represents a corresponding data symbol, comprising dividing groups of data bits into a first subgroup and a second subgroup; representing each data symbol by a set of coordinates in a multidimensional space; using the first subgroup of bits to select one of a number of constellation points that are distributed within a first multi-dimensional space, where a location of the constellation points have been determined such that a sum of their coordinates is less than a desired maximum value, and the coordinates of the selected constellation point are used to set values of real parts of corresponding complex numbers; using the second subgroup of bits to select another one of a number of constellation points that are distributed within a second multidimensional space, where a location of the constellation points have been determined such that a sum of their coordinates is less than a desired maximum value, and the coordinates of the selected constellation point are then used to set values of imaginary parts of corresponding complex numbers; wherein each multidimensional space is defined by a diamond-shaped constellation; and wherein the diamond-shaped constellation is defined in a three-dimensional space with coordinate axes X, Y and Z, and an outer surface of said diamond-shaped constellation being defined by the boundary equation |X|+|Y|+|Z| = 1.