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The spatial and intertap correlation matrices of fading channels are first estimated for underwater multiple input multiple output (MIMO) systems using real experimental data. We confirm that underwater MIMO channels exhibit strong spatial and temporal correlation. The bit error rate (BER) performance of the MIMO system at different correlation scenarios are also evaluated with computer simulation. At BER=0.01%, the required SNR of highly correlated channel is 5 dB higher than the i.i.d. channel. BER results of the experimental data also quantitatively show the performance degradation caused by the correlation.