  In the intelligent communication field, deep learning (DL) has attracted much
attention due to its strong fitting ability and data-driven learning
capability. Compared with the typical DL feedforward network structures, an
enhancement structure with direct data feedback have been studied and proved to
have better performance than the feedfoward networks. However, due to the above
simple feedback methods lack sufficient analysis and learning ability on the
feedback data, it is inadequate to deal with more complicated nonlinear systems
and therefore the performance is limited for further improvement. In this
paper, a novel multi-agent feedback enabled neural network (MAFENN) framework
is proposed, which make the framework have stronger feedback learning
capabilities and more intelligence on feature abstraction, denoising or
generation, etc. Furthermore, the MAFENN framework is theoretically formulated
into a three-player Feedback Stackelberg game, and the game is proved to
converge to the Feedback Stackelberg equilibrium. The design of MAFENN
framework and algorithm are dedicated to enhance the learning capability of the
feedfoward DL networks or their variations with the simple data feedback. To
verify the MAFENN framework's feasibility in wireless communications, a
multi-agent MAFENN based equalizer (MAFENN-E) is developed for wireless fading
channels with inter-symbol interference (ISI). Experimental results show that
when the quadrature phase-shift keying (QPSK) modulation scheme is adopted, the
SER performance of our proposed method outperforms that of the traditional
equalizers by about 2 dB in linear channels. When in nonlinear channels, the
SER performance of our proposed method outperforms that of either traditional
or DL based equalizers more significantly, which shows the effectiveness and
robustness of our proposal in the complex channel environment.
