In our book, we assume that R is perfectly known since it is a statistical parameter, which means that it is fixed forever so one can easily learn it. This is the standard approach in communication theory; statistics are known, realizations of random variables are unknown.

However, in practice, it is more of a challenge to acquire R using limited resources. There are several different ways to do it. We provide an overview of such algorithms in this paper: https://arxiv.org/pdf/1904.03406

]]>I have a doubt about the estimation of the channel correlation matrix R.

In your book (Massive MIMO Networks) the expression for MMSE is provided in equation (3.9), where the estimation of the channel h depends on the knowledge of the matrix R.

However, in order to obtain R, it is said in Section 3.3.3 that the equipment has to perform N observations of h. This, in my understanding, leads to a cyclic problem, i.e., in order to obtain R we need h, but to get h we need R.

My question is: How can the equipment observe h without knowing R in advance?

]]>Sure, one should always make use of all the priors that are available. I’m quite sure that the vendors of Massive MIMO arrays are already trying to do this.

The practical problems are: 1) Which priors are general enough to cover all users in the cell? One can probably utilize the geometry of the array and some general aspects of the propagation environment, but we cannot expect all users to have the same sparsity pattern. Some users might be subject to rich scattering, while other might have very sparse LOS channels. 2) Algorithms that exploit sparsity are inherently unstable. The conditions for when the algorithms are guaranteed to converge to the right sparse solution are strict and likely not satisfied in practice. As a result, the algorithms will sometimes work very well and some time don’t work at all. This why it is hard to perform reliable interference mitigation with these techniques, if the algorithms should simultaneously exploit sparsity for 8 users.

]]>My question is: Is it practical that I use these prior pieces of information for random access protocols such as SUCR? ]]>

It depends on the number of antennas and propagation environment. It is common that people assume a spatially low-rank channel but (as discussed in this blog post) it does not always appear.

]]>A preprint that describes the algorithm we call BEACHES can be found here: https://arxiv.org/abs/1908.02884

]]>If you know the properties of the channel sparsity, you can use it as a prior in the channel estimation. For example, spatially sparse Rayleigh fading channels will have correlation matrices with many zero-valued eigenvalues. If you know the correlation matrix, you can improve the channel estimation by using an MMSE estimator. If you know that sparsity exists but not exactly where the zeros appear, there is a large theory on sparse estimation that can be utilized to find the zeros. There is plenty of work on both cases, particularly focused on FDD massive MIMO.

It is not possible to do perfect channel estimation in reality, but if sparsity exists and you utilize this information correctly, the estimation errors till reduce.

]]>There are other scenarios in which maybe 64×1 can not resolve the channel sparsity and then 1×64 or 8×8 array can resolve it better. So it can vary from case to case and there is not always different array geometries available for different cases. So if we can utilise channel sparsity with the available array geometry then it is better but it is not necessary and always possible to utilise channel sparsity for channel estimation.

My question is: How can channel sparsity be utilized in channel estimation? Without channel sparsity utilisation, will it be possible to do perfect channel estimation?

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