What is Channel Hardening and Favorable Propagation in Massive MIMO?

5G is around the corner and soon will be deployed worldwide. If one has been following the technical community closely, we may know that “Massive MIMO” is one of the key enabling technology in 5G. If someone is not aware what the acronym MIMO stands for, MIMO actually stands for multiple-input-multiple-output. Here, the multiple input corresponds to the multiple-transmit antennas that can send various signals by multiplexing, and multiple-output corresponds to multiple users to which the base station will be serving. The word “Massive” indicates that the base station has very large number of antennas, practically 64 antennas and more. For more information, refer to: https://ma-mimo.ellintech.se/2020/05/13/how-massive-are-the-current-massive-mimo-base-stations/

One may wonder what makes Massive MIMO so special than its pioneering technology MIMO, except that it has a massive number of antennas rather than four to eight antennas. One immediate benefit that one can easily guess is that with a very large number of antennas, the various gains and benefits Massive MIMO networks can provide over standard MIMO networks (4-8 antennas) will be significant. However, two key important features of Massive MIMO that make this technology unique compared to MIMO technology are channel hardening and favourable propagation.

To mathematical understand these concepts, consider the following noiseless signal model where base station has $N$ antennas in downlink where there are $2$ users and user $1$ receives the following signal:

where $n$ is the noise which we will assume for sake of this tutorial zero, $\mathbf{h}_{1} \in \mathbb{C}^{N\times 1}$ is the channel between the base station and user $1$ and $\mathbf{x} \in \mathbb{C}^{N\times 1}$ is the transmitted signal by base station to all users.

As $N \rightarrow \infty$, two remarkable properties emerge: the effective channel becomes constant (channel hardening) and interference terms vanish (favorable propagation). These properties make Massive MIMO unique compared to conventional MIMO with 4-8 antennas.

By using simple precoders like Maximum Ratio Transmission (MRT), Massive MIMO can effectively turn a Rayleigh fading channel into an effective AWGN channel and mitigate interference through favorable propagation. This is what makes Massive MIMO so powerful.

However, some questions for readers to ponder: Why can’t we deploy infinite antennas and get optimal performance? Are there practical limitations? The research community is exploring distributed MIMO approaches (Cell-Free Massive MIMO, Cell-Free Networks, Network MIMO) to overcome such limitations.