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The conventional additive white Gaussian noise (AWGN) model adequately simulates many noisy environments that hamper the performance of practical digital communication systems. However if the channel noise is impulsive, the approximation this model provides reduces significantly. The AWGN channel may then be replaced by the more general additive white symmetric α-stable noise (AWSαSN) model. When converted to its complex baseband form, the resulting noise for the non-Gaussian AWSαSN case is radically different from its Gaussian counterpart. In this paper we investigate the properties of baseband noise for the general AWSαSN case using conventional passband-to-baseband conversion schemes. The converted noise is generally not isotropic and furthermore the real and imaginary components may be dependent. By varying certain physical parameters we may attain different non-isotropic distributions. Using the variable geometry offered by these distributions, efficient placement of signal points on the constellation map for the quadrature phase-shift keying (QPSK) scheme is proposed. It is shown that efficient placement of signal points significantly improve the uncoded error performance of the system. We plot the bit error rate (BER) and symbol error rate (SER) curves against a signal-to-noise ratio (SNR) measure for a few selected rotated versions of the QPSK scheme.