Double Khatri–Rao Space-Time-Frequency Coding Using Semi-Blind PARAFAC Based Receiver

We first introduce a new class of tensor models for fourth-order tensors, referred to as “nested PARAFAC models.” Then, we present a space-time-frequency (STF) coding scheme for multiple antenna orthogonal frequency division multiplexing systems. This scheme, called double Khatri-Rao STF (D-KRSTF) coding, combines time-domain spreading with space-frequency precoding and provides an extension of Khatri-Rao space-time (KRST) coding . We show that the received signals define a fourth-order tensor satisfying two nested PARAFAC models, and a semi-blind receiver is then derived using a two-step alternating least squares algorithm for joint channel and symbol estimation. Simulation results show that our receiver offers superior performance compared with previously proposed tensor-based solutions and operates close to the zero forcing receiver with perfect channel state information.