Performance Analysis of OFDM with Wiener Phase Noise and Frequency Selective Fading Channel

We analyze the effect of Wiener phase noise on the capacity and signal-to-interference-plus-noise (SINR) ratio. Our analysis includes phase noise at the transmitter and receiver end of an OFDM communication link. We see that the capacity and SINR are random variables whose distribution depends on the phase noise and the fading channel. Using a Taylor series approximation, we show that the random variable, characterizing the phase noise, in the performance metrics can be expressed as a sum of correlated gamma variables with rank-deficient square-root normalized covariance matrix. The approximation holds well when the ratio between the subcarrier spacing and the 3dB bandwidth of the oscillator power spectral density is at least one order of magnitude, which for most practical oscillators is the case. In earlier literature, the probability density function of a sum of correlated gamma variables with full-rank square-root normalized covariance matrix was derived. We extend these results to the rank-deficient case and apply them to the random variable of our case. With the probability density functions characterizing the phase noise and the fading channel at hand, we proceed to obtain closed-form statistical measures of capacity and SINR. The simulations show the good agreement with our analytical expressions.