Some new twists to problems involving the Gaussian probability integral

Author

Simon, Marvin K. ; Divsalar, Dariush

Author_Institution

Jet Propulsion Lab., California Inst. of Technol., Pasadena, CA, USA

Volume

46

Issue

2

fYear

1998

fDate

2/1/1998 12:00:00 AM

Firstpage

200

Lastpage

210

Abstract

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

Keywords

Gaussian channels; coding errors; correlation methods; error statistics; fading; integral equations; intersymbol interference; memoryless systems; phase locked loops; phase shift keying; probability; tracking; AWGN channel; Costas loop tracking; Gaussian probability integral; I-Q unbalance; MPSK; PSK; antipodal modulation; average error probability; binary additive white Gaussian noise channel; bit-error probability; carrier synchronization error; channel-state information; coded M-ary PSK; communication problems solution; correlation; fading; generalised 2D Gaussian probability integral; intersymbol interference channel; memoryless fading channel; onditional symbol-error probability; uncoded phase-shift keying; word-error probability; AWGN; Additive white noise; Error probability; Fading; Integral equations; Intersymbol interference; Modulation coding; Phase modulation; Phase shift keying; Tracking loops;

fLanguage

English

Journal_Title

Communications, IEEE Transactions on

Publisher

ieee

ISSN

0090-6778

Type

jour

DOI

10.1109/26.659479

Filename

659479