What is channel hardening in Massive MIMO?. Please explain in details?
I need to understand why it is called hardening. Also why does this phenomenon happen. what effect does it have on system.
http://www.ece.iisc.ernet.in/~achockal/pdf_files/wcnc2014_chemp_rx.pdf
This article covers the topic in great detail. It's a phenomenon that happens in MIMO, as the number of antennas increases. Or in massive MIMO, as the number of base station antennas increases, and the number on single-antenna user terminals increases. Same basic effect. The correlation matrix becomes increasingly a diagonal matrix. Take a look at Figure 2 in the linked article.
They even have a name for the effect: Marcenko-Pastur law. Cool!
The effect on the MIMO system should be, if I understand this correctly, as follows:
In MIMO systems where the base station and the user terminals both have large number of antennas, the MIMO capacity should become close to n * the capacity of a SISO system, where n is the least of the base station or user terminal antenna quantities.
In massive MIMO, where the user equipment only has one antenna, then I would expect that the number of base station antennas will closely match the number of user terminals the system can support simultaneously.
Perfect example of why downvoting should mandate an explanation. Otherwise, no one learns.
What Albert describes is the initial channel hardening concept for point-to-point MIMO channels, while the details are a bit different in Massive MIMO.
As answer to your questions, I have written as blog post that explains the channel hardening in detail:
http://ma-mimo.ellintech.se/2017/01/25/channel-hardening-makes-fading-channels-behave-as-deterministic/
A more technical definition and discussion is found in the paper "No Downlink Pilots are Needed in TDD Massive MIMO": https://arxiv.org/abs/1606.02348
Hi Emil and Albert, Channel hardening definition in Emil's blog i.e. "fading becomes deterministic" can also be applied for large bandwidth systems. Different from Massive MIMO concept i.e. large number of antennas reduce the small scale fading provided we have large number of multipath components (MPCs). I am wondering if we can use the definition of channel hardening for large bandwidth systems as well, even if the channel is spatially sparse in terms of number of MPCs?...What do you think?
Channel hardening is a phenomenon where the norms of the channel vectors {g_k} k = 1, . . . ,K, fluctuate only little. We say that the propagation offers channel hardening if
〖〖||h〗_k ||〗^2/(〖〖E{||h〗_k ||〗^2})→0 as M→∞, k= 1,……. K
I think the easy way to understand is to watch Emil's video starting from minute 24 till it ends.
Thanks Emil for the video.
https://www.youtube.com/watch?time_continue=1498&v=qjqYRHYLoWo
Channel hardening is an important phenomena in massive MIMO where a randomly fluctuating or a fading channel (h) behaves like a deterministic channel whose channel gain doesn't vary much and in fact is same as its average channel gain i.e., ratio of instantaneous channel gain and its average gain tends to unity as base station antennas (M) becomes very large.
||h||2/E{||h||2} tends to 1 as M tends to infinity,
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