An Upper Bound on the Capacity Loss Due to Imprecise Channel State Information for General Memoryless Fading Channels

A remarkably simple upper bound on the capacity loss due to imprecise channel state information (CSI) is presented for single-input single-output (SISO) general memoryless fading channels, (Capacity Loss) ≤ log(1+var(h - ĥ)SNR) where var(h - ĥ) represents the variance of channel estimation error, i.e. CSI inaccuracy. The bound extends earlier work on Rayleigh channels to general memoryless channels and confirms that the effect of CSI inaccuracies on the communication capacity is secondary to the receiver noise when the signal-to-noise ratio (SNR) is smaller than the reciprocal of the channel estimation error variance, SNR <; 1/var(h - ĥ). An extension to the single-input multiple-output (SIMO) case is also provided.