Bit-error probability of QPSK with noisy phase reference

An approximate result is obtained for the bit-error probability of quadriphase shift keying in the presence of additive white Gaussian noise and a Tikhonov distributed-phase-reference error. The accuracy of the approximation is verified via actual numerical integration of the bit-error-probability formula. The approximation is easy to compute, and shows correctly the behaviour of the bit-error probability as a function of the signal-to-noise ratio. In particular, it shows that, for high signal-to-noise ratios, the bit-error probability behaves as the reciprocal of the square root of the former.