How the Framework of Expectation Propagation Yields an Iterative IC-LMMSE MIMO Receiver

Based on the Expectation Propagation framework, we derive a MIMO detector that consists of an interference cancellation (IC) step, followed by linear minimum mean square error (LMMSE) filtering. The distinguishing feature of our algorithm, compared to conventional IC-LMMSE detectors for iterative MIMO receivers, is the way how we compute the symbol statistics that are used in the IC and LMMSE steps. In an earlier publication, it has been shown empirically that full posterior feedback from the decoder to the IC-LMMSE detector can outperform the usual choice of extrinsic feedback, which seems to contradict the Turbo principle. The systematic derivation in the present paper provides an explanation of this phenomenon, and results in a further improved algorithm that outperforms the conventional IC-LMMSE detector with either extrinsic or posterior feedback. While we consider only multi-antenna systems, we note that the same principle can be applied to similar problems in signal processing, such as Turbo equalization for frequency-selective channels, or multi-user detection in CDMA systems.