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Both in the signal processing and in the information theory literature, it is common to assume that the array gain of antenna arrays grows linearly with the number of antennas. However, such an assertion is valid only when the antennas are uncoupled. When antenna coupling is present and properly taken into account by the signal processing algorithms, we show that both the transmit and the receive array gain can grow super-linearly with the number of antennas. In special cases, the receive array gain can even grow exponentially with the antenna number. These results are exciting, for they imply that the potential of radio communication systems which use more than one antenna at the receiver or the transmitter, is likely to be much higher than previously reported.