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In this paper, we introduce a neural network (NN)-based symbol detection scheme for Wi-Fi systems and its associated hardware implementation in software radios. To be specific, reservoir computing (RC), a special type of recurrent neural network (RNN), is adopted to conduct the task of symbol detection for Wi-Fi receivers. Instead of introducing extra training overhead/set to facilitate the RC-based symbol detection, a new training framework is introduced to take advantage of the signal structure in existing Wi-Fi protocols (e.g., IEEE 802.11 standards), that is, the introduced RC-based symbol detector will utilize the inherent long/short training sequences and structured pilots sent by the Wi-Fi transmitter to conduct online learning of the transmit symbols. In other words, our introduced NN-based symbol detector does not require any additional training sets compared to existing Wi-Fi systems. The introduced RC-based Wi-Fi symbol detector is implemented on the software-defined radio (SDR) platform to further provide realistic and meaningful performance comparisons against the traditional Wi-Fi receiver. Over the air, experiment results show that the introduced RC based Wi-Fi symbol detector outperforms conventional Wi-Fi symbol detection methods in various environments indicating the significance and the relevance of our work.