On physical limits of massive MISO systems

We analyze the performance of a fixed-size uniform circular array which is used to transmit information to a single antenna receiver as a function of the number of transmit side antennas. We find that the minimum necessary energy to transfer one information bit stops decreasing once the number of antennas grows over a certain bound. We relate this bound to the diameter of the array and show that there is an optimum and finite number of antennas for every such array. For large array diameters this optimum number grows linearly with the diameter, the factor of proportionality primarily depending on whether the receiver is inside or outside of the transmit uniform circular array.