Capacity of fading channels with imperfect CSI and mismatched decoding at the receiver

In this paper, we consider a real single-input single-output (SISO) channel undergoing i.i.d fading and with the constraint that the transmitter (Tx) has no knowledge of the channel state information (CSI). Without any assumptions on the fading distribution, we prove a lower bound on the capacity when the receiver (Rx) does not have access to perfect CSI and does not have knowledge of the channel distribution. Denoting the average per symbol signal to noise ratio as SNR, we deduce that if the channel estimation error power is O (1/SNR) then the ½ log SNR growth in capacity is maintained. The key advantage of our approach is that the decoding scheme assumes no knowledge of the channel distribution, i.e. p(y|x), at the Rx. As an example, we consider a block fading model where the channel is constant for a block of T time slots and varies in an i.i.d manner from block to block. By allowing for training symbols in n of the T slots in each block, we show that the capacity is at least (1 - n/T)1/2 log SN R - O(1)/n.