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We consider communication over a multiple-input single-output (MISO) blockfading channel in the presence of an independent noiseless feedback link. Weassume that the transmitter and receiver have no prior knowledge of the channelstate realizations, but the transmitter and receiver can acquire the channelstate information (CSIT/CSIR) via downlink training and feedback. For thischannel, we show that increasing the number of transmit antennas to infinitywill not achieve an infinite capacity, for a finite channel coherence lengthand a finite input constraint on the second or fourth moment. This insightfollows from our new capacity bounds that hold for any linear and nonlinearcoding strategies, and any channel training schemes. In addition to the channelcapacity bounds, we also provide a characterization on the beamforming gainthat is also known as array gain or power gain, at the regime with a largenumber of antennas.

On the MISO Channel with Feedback: Can Infinitely Massive Antennas Achieve Infinite Capacity?