Some new twists to problems involving the Gaussian probability integral

• Published in: IEEE transactions on communications 1998-02, Vol.46 (2), p.200-210
• Main Authors: Simon, M.K., Divsalar, D.
• Format: Article
• Language: English
• Subjects: Additive white noise; AWGN; Error probability; Fading; Integral equations; Intersymbol interference; Modulation coding; Phase modulation; Phase shift keying; Tracking loops
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/26.659479

Using an alternate form of the Gaussian probability integral discovered a number of years ago, it is shown that the solution to a number of previously considered communication problems can be simplified and, in some cases, made more accurate (i.e. exact rather than bounded). These problems include the evaluation of: (1) the bit-error probability of uncoded phase shift keying (PSK) with Costas loop tracking; (2) word-error probability of antipodal modulation in the presence of fading; (3) bit-error probability of coded M-ary PSK (MPSK) over the memoryless fading channel with given channel-state information; (4) conditional symbol-error probability of MPSK in the presence of carrier synchronization error; and (5) the average error probability for the binary additive white Gaussian noise (AWGN) intersymbol interference channel. Also obtained is a generalization of this new alternate form to the case of a two-dimensional Gaussian probability integral with arbitrary correlation which can be used to evaluate the symbol-error probability of MPSK with I-Q unbalance.