Bit error rate performance of pi/4-DQPSK in a frequency-selective fast Rayleigh fading channel

The bit error rate (BER) performance of pi/4-differential quadrature phase shift keying (DQPSK) modems in cellular mobile communication systems is derived and analyzed. The system is modeled as a frequency-selective fast Rayleigh fading channel corrupted by additive white Gaussian noise (AWGN) and co-channel interference (CCI). The probability density function of the phase difference between two consecutive symbols of M-ary differential phase shift keying (DPSK) signals is first derived. In M-ary DPSK systems, the information is completely contained in this phase difference. For pi/4-DQPSK, the BER is derived in a closed form and calculated directly. Numerical results show that for the 24 kBd (48 kb/s) pi/4-DQPSK operated at a carrier frequency of 850 MHz and C/I less than 20 dB, the BER will be dominated by CCI if the vehicular speed is below 100 mi/h. In this derivation, frequency-selective fading is modeled by two independent Rayleigh signal paths. Only one co-channel is assumed in this derivation. The results obtained are also shown to be valid for discriminator detection of M-ary DPSK signals.