Performance of DQPSK communication systems impaired by mixer imbalance, timing error, and Rayleigh fading

The current North America Digital Cellular (NADC) standards suggest π/4-shifted-DQPSK as the modulation for the current digital mobile communications systems. The performance of differential quaternary-phase-shift-keying (DQPSK) receivers impaired by mixer imbalance and timing error is investigated. Expressions for the system bit error rate (BER) are obtained for channels free of fading and for frequency non-selective slow Rayleigh fading channels in the face of additive white Gaussian noise. To arrive at the desired expressions for the system BER, the conditional probability density function (PDF) of the phase angle between a pair of Gaussian random vectors is averaged over timing error and channel fading effects