The paper introduces a novel approach to enhance the diversity order of signal sets, particularly in fading channels, by employing multidimensional rotated QAM constellations. The authors aim to achieve high spectral efficiency and system complexity trade-offs without increasing power or bandwidth requirements. The key idea is to apply rotations to classical signal constellations to maximize the number of distinct components between any two constellation points, thereby increasing the diversity order. This method is demonstrated to provide significant gains over traditional QAM schemes, especially in Rayleigh fading channels, where the performance approaches that of an AWGN channel for large diversity orders. The paper also discusses the construction of rotated lattices from algebraic number fields and the optimization of the minimum product distance between constellation points. Simulation results show that the proposed rotated constellations outperform traditional 16-QAM in terms of bit-error rate, with the gap to the Gaussian curve being minimal for high diversity orders.The paper introduces a novel approach to enhance the diversity order of signal sets, particularly in fading channels, by employing multidimensional rotated QAM constellations. The authors aim to achieve high spectral efficiency and system complexity trade-offs without increasing power or bandwidth requirements. The key idea is to apply rotations to classical signal constellations to maximize the number of distinct components between any two constellation points, thereby increasing the diversity order. This method is demonstrated to provide significant gains over traditional QAM schemes, especially in Rayleigh fading channels, where the performance approaches that of an AWGN channel for large diversity orders. The paper also discusses the construction of rotated lattices from algebraic number fields and the optimization of the minimum product distance between constellation points. Simulation results show that the proposed rotated constellations outperform traditional 16-QAM in terms of bit-error rate, with the gap to the Gaussian curve being minimal for high diversity orders.