1. Envelope and phase distribution of two correlated Gaussian variables
- Author
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Dharmawansa, Prathapasinghe, Rajatheva, Nandana, and Tellambura, Chinthananda
- Subjects
Gaussian processes -- Analysis - Abstract
Probability density functions (pdf's) are derived for the phase and amplitude (envelope) of the complex gain X + jY (j = [square root of -1]), where X and Y are two correlated non zero-mean Gaussian random variables. The pdf of the amplitude is derived as an infinite series, but reduces to a closed-form expression when the means are zero. The classical Rayleigh and Rician pdf's turn out to be special cases of the derived pdf. This pdf is used to analyze the error performance of non-coherent binary frequency shift keying (BFSK) with in-phase/quadrature(I/Q) imbalance over an additive white Gaussian noise (AWGN) channel The resulting bit error rate (BER) expression is derived as an infinite series. The analytical expressions are validated by simulation, and the I/Q imbalance related performance degradation is quantified. Convergence of the PDF series and the BER series is established. Index Terms--Characteristic function (chf), correlated Gaussian, frequency shift keying, in-phase/quadrature imbalance, probability density function (pdf), Rayleigh density.
- Published
- 2009