A nakagami fading phase difference distribution and its impact on BER performance

We propose a new model for investigating the impact of complex imperfect channel state information (CSI) over Nakagami-m fading channels. The phase difference between two correlated complex Nakagami random variables (RVs) is proposed and its statistical properties are investigated. A closed-form expression for the distribution is obtained using an approach from [1] and depends on the Nakagami-m parameter and the power correlation coefficient (p) between two correlated complex RVs. A simple approximation is given when p is close to unity. The proposed phase difference is shown to accurately approximate that of the Ricean. We derive the joint density function of this phase difference and its associated correlated envelopes. This is given in a closed form in terms of a generalized hypergeometric function, but the RVs can be easily generated for simulation. We analyze the impact of imperfect CSI on the bit error rate (BER) of uncoded and coded modulation. For uncoded modulation, the average BER and a closed-form expression of the asymptotic BER or error floor are obtained. For coded modulation, we determine the error free feedback bound of bit-interleaved coded modulation with iterative decoding for both perfect and imperfect CSI. We show that imperfect phase estimation is the major cause of the error floor.