  In this paper, we introduce a new neural network (NN) structure, multi-mode
reservoir computing (Multi-Mode RC). It inherits the dynamic mechanism of RC
and processes the forward path and loss optimization of the NN using tensor as
the underlying data format. Multi-Mode RC exhibits less complexity compared
with conventional RC structures (e.g. single-mode RC) with comparable
generalization performance. Furthermore, we introduce an alternating least
square-based learning algorithm for Multi-Mode RC as well as conduct the
associated theoretical analysis. The result can be utilized to guide the
configuration of NN parameters to sufficiently circumvent over-fitting issues.
As a key application, we consider the symbol detection task in
multiple-input-multiple-output (MIMO)
orthogonal-frequency-division-multiplexing (OFDM) systems with massive MIMO
employed at the base stations (BSs). Thanks to the tensor structure of massive
MIMO-OFDM signals, our online learning-based symbol detection method
generalizes well in terms of bit error rate even using a limited online
training set. Evaluation results suggest that the Multi-Mode RC-based learning
framework can efficiently and effectively combat practical constraints of
wireless systems (i.e. channel state information (CSI) errors and hardware
non-linearity) to enable robust and adaptive learning-based communications over
the air.
