Echo state network (ESN) is a specific neural network structure composed of high dimensional nonlinear dynamics and learned readout weights. This thesis considers applying ESN for symbol detection in multiple-input, multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems. A new ESN structure, namely, windowed echo state networks (WESN) is introduced to further improve the symbol detection performance. Theoretical analysis justifies WESN has an enhanced short-term memory (STM) compared with the standard ESN such that WESN can offer better computing ability. Additionally, the bandwidth spent as the training set is the same as the demodulation reference signals defined in 3GPP LTE/LTE-Advanced systems for the ESN/WESN based symbol detection. Meanwhile, a unified training framework is developed for both comb and scattered pilot patterns. Complexity analysis demonstrates the advantages of ESN/WESN based symbol detector compared to conventional symbol detectors such as linear minimum mean square error (LMMSE) and sphere decoder when the system is employed with a large number of OFDM sub-carriers. Numerical evaluations show that ESN/WESN has an improvement of symbol detection performance as opposed to conventional methods in both low SNR regime and power amplifier (PA) nonlinear regime. Finally, it demonstrates that WESN can generate a better symbol detection result over ESN.