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The Reservoir Computing, a neural computing framework suited for temporal information processing, utilizes a dynamic reservoir layer for high-dimensional encoding, enhancing the separability of the network. In this paper, we exploit a Deep Learning (DL)-based detection strategy for Multiple-input, Multiple-output Orthogonal Frequency-Division Multiplexing (MIMO-OFDM) symbol detection. To be specific, we introduce a Deep Echo State Network (DESN), a unique hierarchical processing structure with multiple time intervals, to enhance the memory capacity and accelerate the detection efficiency. The resulting hardware prototype with the hybrid memristor-CMOS co-design provides in-memory computing and parallel processing capabilities, significantly reducing the hardware and power overhead. With the standard 180nm CMOS process and memristive synapses, the introduced DESN consumes merely 105mW of power consumption, exhibiting 16.7% power reduction compared to shallow ESN designs even with more dynamic layers and associated neurons. Furthermore, numerical evaluations demonstrate the advantages of the DESN over state-of-the-art detection techniques in the literate for MIMO-OFDM systems even with a very limited training set, yielding a 47.8% improvement against conventional symbol detection techniques.