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

## TL;DR

This paper investigates whether infinitely many antennas can achieve infinite capacity in a MISO channel with feedback, concluding that finite capacity limits persist due to practical constraints, supported by new capacity bounds and beamforming analysis.

## Contribution

It introduces new capacity bounds for MISO channels with feedback that hold for all coding and training schemes, showing infinite antennas do not yield infinite capacity under realistic conditions.

## Key findings

- Infinite antennas do not achieve infinite capacity with finite coherence length.
- New capacity bounds applicable to all coding strategies.
- Characterization of beamforming gain with large antenna arrays.

## Abstract

We consider communication over a multiple-input single-output (MISO) block fading channel in the presence of an independent noiseless feedback link. We assume that the transmitter and receiver have no prior knowledge of the channel state realizations, but the transmitter and receiver can acquire the channel state information (CSIT/CSIR) via downlink training and feedback. For this channel, we show that increasing the number of transmit antennas to infinity will not achieve an infinite capacity, for a finite channel coherence length and a finite input constraint on the second or fourth moment. This insight follows from our new capacity bounds that hold for any linear and nonlinear coding strategies, and any channel training schemes. In addition to the channel capacity bounds, we also provide a characterization on the beamforming gain that is also known as array gain or power gain, at the regime with a large number of antennas.