1) This is the classical noisy-channel coding theorem, which is the foundation of everything that has to do with channel capacities: https://en.wikipedia.org/wiki/Noisy-channel_coding_theorem

2) Ergodicity and stationarity are concepts in statistics, see for example https://en.wikipedia.org/wiki/Ergodic_process

The random description of channels is just a model, but a good one.

Thank you for your answer.

1) Can you explain why it requires that N tends to infinity to have the decoding with arbitrary low error probability?

2) Also can you explain how the ergodicity of the channel define? And the assumption that the channel is stationary and ergodic to some extent is practical? Especially when the channel is fast fading. ]]>

1) This is explained in the sentence before that statement: “If the scalar input has an SE smaller or equal to the capacity, the information sequence can be encoded such that the receiver can decode it with arbitrarily low error probability as N → ∞.” In practice, it is enough to transmit a few thousand bits to operate close to the capacity (i.e., obtain a small but non-zero error probability). Section 1 in Fundamentals of Massive MIMO provides a plot about this.

2) If the channel is non-ergodic, then you cannot predict which ensemble of channel realizations that you will get during the transmission so you cannot encode that data under the assumption that you know the channel statistics. I don’t know how to define the capacity in this case.

]]>I have two questions related to Section 1 of your book.

1) As you say in the section one of the book, an infinite decoding delay is required to achieve the channel capacity in practice.

Can you explain why it should be satisfied this condition to achieve the capacity in practice?

2) Other question is that as you mentioned in the book, to have ergodic capacity, we should have the stationary ergodic fading channel.

What problem is caused if the channel is not ergodic?

Especially, can we define the capacity for a random channel that is not ergodic? ]]>

The paper is considering the ergodic spectral efficiency as the performance metric, which means that the same APs and users are active for many coherence blocks. We are providing an algorithm for determining which APs to activate. This can be done in practice and probably implemented on top of 5G.

5G systems have a feature called Cell discontinuous transmission (DTX) where the cell is put into sleep mode part of the time to save energy. When its service is not needed it only wakes up to transmit control signals, so that new users can connect to the cell.

]]>I have a question related to one of your recent paper where you turn off some APs in a cell-free system to have an energy efficient system.

A question that arise to my mind is that Is and how such a scenario implemented in practice?

Is there an intelligent algorithm that turn off some of the APs in each coherence block? ]]>

It all depends on how many antennas you want to deploy, at what frequency, and what the maximum form factor is. But Massive MIMO is certainly feasible at cellular frequencies, such as 1-5 GHz. You can read more about this in “Myth 1” in the paper:

Emil Björnson, Erik G. Larsson, Thomas L. Marzetta, “Massive MIMO: Ten Myths and One Critical Question,” IEEE Communications Magazine, vol. 54, no. 2, pp. 114-123, February 2016.

]]>