Approximate Sum Rate for Integer-Forcing Receiver With Imperfect Channel Estimation

We analyze the performance of integer-forcing and compute and forward transform receivers in the presence of channel estimation errors. We derive an approximation for the mean achievable sum rate for both the receivers. For the integer-forcing receivers, we use a known approximation for its sum rate probability density function (PDF) to derive the PDF of the mean achievable sum rate with respect to the channel realizations, considering both correlated and uncorrelated scenarios. Numerical simulations highlight the tightness of all approximations and the sensitivity of these receivers to imperfect channel state information.