Semi-blind channel estimation using the EM algorithm in iterative MIMO APP detectors

We consider channel estimation in multiple-input multiple-output (MIMO) systems using iterative detection at the receiver. Space-time bit-interleaved coded modulation. (BICM) and soft-input soft-output maximum a posteriori (MAP) symbol detection and decoding are considered. Channel coefficients are updated at each iteration of the detector using a semi-blind estimation approach based on the expectation maximization (EM) algorithm. We first show that a "classical" and non-optimized EM implementation, as already proposed in some previous works, gives a biased estimate of the channel coefficients. We then try to optimize the EM implementation and propose a modification to it that provides an unbiased channel estimate and leads to a better convergence of the iterative detector. We show that considerable improvement in the receiver performance can be obtained by using our proposed modified unbiased (MU) FM algorithm, especially for large number of transmit antennas and short training sequences. We also show that when MIMO signal detection is strongly asymmetric in the sense of too few receive antennas, the EM-based channel estimation may be of little interest. Moreover, we consider a simple semi-blind estimation scheme, based on hard decisions on reliable decoded data bits, and compare its performance with the EM based estimation methods.