On the Outage Capacity of a Practical Decoder Accounting for Channel Estimation Inaccuracies

The optimal decoder achieving the outage capacity under imperfect channel estimation is investigated. First, by searching into the family of nearest neighbor decoders, which can be easily implemented on most practical coded modulation systems, we derive a decoding metric that minimizes the average of the transmission error probability over all channel estimation errors. Next, we specialize our general expression to obtain the corresponding decoding metric for fading MIMO channels. According to the notion of Estimation-induced outage (EIO) capacity introduced in our previous work and assuming a block Rayleigh-fading channel, we characterize the maximal achievable information rates using Gaussian codebooks associated to the proposed decoder. These achievable rates are compared to the rates achieved by the classical mismatched maximum likelihood (ML) decoder and the ultimate limits given by the EIO capacity. Numerical results show that the derived metric provides significant gains, in terms of achievable EIO rates and bit error rate (BER), in a bit interleaved coded modulation (BICM) framework, without introducing any additional decoding complexity. However, the achievable rates of such metric are still far from the EIO capacity.