MIMO block-fading channels with mismatched CSIR

This paper presents the outage analysis of multiple-input multiple-output (MIMO) block-fading channels with nearest neighbour decoding and mismatched channel state information at the receiver (CSIR). Based on mismatched decoding arguments, we demonstrate the achievability of the generalised outage probability, the probability that the generalised mutual information (GMI) is less than the target data rate, and show that this probability is the fundamental limit for independent and identically distributed (i.i.d.) codebooks. We then analyse the behaviour of the generalised outage probability at high signal-to-noise ratio (SNR) regime. For both Gaussian and discrete signal codebooks, we provide a simple characterisation of the mismatched CSIR SNR exponents and derive the necessary condition on the block length to achieve those SNR exponents.