Block-term tensor decomposition (BTD) was recently reconsidered in the context of array signal processing, and shown to be the natural choice in sensor arrays of increased dimensionality and channel multipath. Semi-blind joint channel estimation/data detection (JCD) was addressed in the special but important case of the uniform rectangular array (URA), via efficient algorithms that wed existing JCD schemes with BTD approximation. That work is revisited in this paper from a Bayesian standpoint to address the discrete nature of the input symbol constellation. This offers a new interpretation of the outstanding BTD JCD scheme among those previously developed. Moreover, two probabilistic methodologies are followed, which, when endowed with the BTD structure, result in additional JCD schemes that provide alternatives to our previous work in detection performance and computational complexity. The receivers are evaluated via simulation results at various noise levels, and different array and constellation sizes and favorably compared with the training-only-based solution.

Multiple-input multiple-output (MIMO) systems employing multicarrier modulation (MCM), including flexible MCM that unifies a number of MCM schemes, have been well studied recently also in their tensor-based formulation. The latter naturally allows for (semi-)blind joint channel estimation/data detection (JCD), of particular interest in future generation massive MIMO systems, given the uniqueness properties of the tensor decomposition (TD) models. Of course, in the presence of time-varying channels, adaptive JCD needs to be implemented. However, the rich literature on recursive TD has only very little been considered in this context and only for orthogonal frequency division multiplexing (OFDM). In this paper, online TD is adapted to realize adaptive JCD for time-varying flexible MIMO-MCM systems. The common assumptions underlying online TD schemes are revisited on this occasion and shown to be inadequate to cope with fast-fading channels. This is demonstrated via simulation results on two of the most popular MCM systems. The results of this work can serve to motivate further study of online TD to extend its applicability in this and other demanding application contexts.