Statistical Description of Channel Estimation Error in Massive MIMO Systems With Ricean Fading

This paper studies the channel estimation performance in massive multiple-input multiple-output (MIMO) systems with Ricean fading through considering the relative channel estimation error (RCEE) metric. The closed-form expressions of the probability distribution function (PDF) and cumulative distribution function of RCEE are derived, according to which the PDFs of RCEE with Rayleigh fading and pure line-of-sight (LoS) propagation are obtained as special cases. Through analyzing RCEE, it notes that as the number of base-station antennas $M$ becomes unbounded, RCEE approaches a given constant. Moreover, the asymptotic analysis proves that, in high $M$ -regime, the increasing rate of the RCEE scales in the order of $\sqrt{M}$ for Rayleigh fading and pure LoS propagation, while the scaling order with general Ricean fading is capped by $\sqrt{M}$ . All the above mentioned results are verified through Monte-Carlo simulations.