On the performance of DQPSK communication systems impaired by timing error, mixer imbalance, and frequency nonselective slow Rayleigh fading

In this paper, the error performance of the differential detection scheme is assessed for differentially encoded quaternary-phase-shift-keying (DQPSK) and π/4-shifted-DQPSK signals, It is assumed that the receiver suffers from mixer imbalance and timing error impairments. Expressions for the system bit-error rate (BER) are obtained when the channel is free of fading and when the channel suffers from frequency nonselective (flat) slow Rayleigh fading in the face of additive white Gaussian noise. To arrive at the desired expressions, the probability density function (pdf) of the phase angle between a pair of Gaussian random vectors is used to obtain the probability of bit error conditioned on the channel fading and timing error. The resulting expressions are then averaged over the nonnegligible timing error and the channel fading to arrive at the desired expressions for the system BER. Finally, with the aid of numerical analysis and in the presence of the aforementioned impairments, a number of conclusions are drawn and the performance of differential receivers for DQPSK and π/4-shifted-DQPSK modulation schemes are compared. It is shown here that the performance of a DQPSK receiver in the absence of fading and timing error is substantially impaired by mixer imbalance for BERs less than 10^-4. In the presence of fading, the performance is noticeably degraded due to mixer imbalance when a nonzero timing error is present