Approximate Message Passing-Aided Iterative Channel Estimation and Data Detection of OFDM-IM in Doubly Selective Channels

The channel estimation and data detection of orthogonal frequency-division multiplexing with index modulation in doubly selective channels is a challenging problem due to the large number of channel parameters and the severe inter-carrier interference. In this paper, an iterative channel estimation and data detection scheme is proposed with the aid of the recent compressed sensing algorithm of approximate message passing (AMP). The time-varying channel is first approximated by basis expansion model (BEM) to reduce the number of channel parameters to be estimated, and AMP is utilized to estimate the BEM coefficients based on the pilot signals and soft information of data from the decoder. The channel is then reconstructed from the estimated BEM coefficients, and AMP is also employed to recover the transmit data based on the estimated channel and soft information of data from the decoder. The soft information of AMP detector is further sent to the decoder, which feeds soft information to both AMP estimator and AMP detector. To address the undesired measurement matrix in both channel estimation and data detection, two variants of AMP, i.e., damped AMP and vector AMP (VAMP), are utilized as practical estimator and/or detector here. Moreover, in both damped AMP/VAMP estimator and detector, the efficient utilization of soft data information is presented. Finally, simulation results are given to verify the performance of the proposed receiver.