Generalized Tensor Contraction with Application to Khatri-Rao Coded MIMO OFDM Systems

In this work, we present a multilinear algebra operator referred to as generalized tensor contraction. This operator defines an inner product between two higher-order tensors over a set of modes of compatible dimensions. We show that this tensor operator is useful to model Multiple-Input Multiple-Output - Orthogonal Frequency Division Multiplexing (MIMO-OFDM) communication systems. In our application, the transmit signal tensor contains Khatri-Rao coded symbols that can be modeled via a Canonical Polyadic (CP) decomposition. This new tensor based model facilitates the design of a receiver based on the least squares Khatri-Rao factorization (LS-KRF) that jointly estimates the channel and the data symbols. We reduce the number of required pilot symbols compared to other receivers based on the LS-KRF by exploiting the correlation of the channel between adjacent subcarriers. Due to the tensor gain, the proposed receiver significantly outperforms the traditional Zero Forcing - Fast Fourier Transform (ZF-FFT) receiver while using the same amount of pilot symbols.