WHAT IS THE DIFFERENCE BETWEEN BEAMFORMING AND PRECODING?

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OCTOBER 3, 2017 EMIL BJÖRNSON        57 COMMENTS
I’ve got an email with this question last week. There is not one but many possible answers to this question, so I figured that I write a blog post about it.

One answer is that beamforming and precoding are two words for exactly the same thing, namely to use an antenna array to transmit one or multiple spatially directive signals.

Another answer is that beamforming can be divided into two categories: analog and digital beamforming. In the former category, the same signal is fed to each antenna and then analog phase-shifters are used to steer the signal emitted by the array. This is what a phased array would do. In the latter category, different signals are designed for each antenna in the digital domain. This allows for greater flexibility since one can assign different powers and phases to different antennas and also to different parts of the frequency bands (e.g., subcarriers). This makes digital beamforming particularly desirable for spatial multiplexing, where we want to transmit a superposition of signals, each with a separate directivity. It is also beneficial when having a wide bandwidth because with fixed phases the signal will get a different directivity in different parts of the band. The second answer to the question is that precoding is equivalent to digital beamforming. Some people only mean analog beamforming when they say beamforming, while others use the terminology for both categories.


Analog beamforming uses phase-shifters to send the same signal from multiple antennas but with different phases. Digital beamforming designs different signals for each antennas in the digital baseband. Precoding is sometimes said to be equivalent to digital beamforming.
A third answer is that beamforming refers to a single-user transmission with one data stream, such that the transmitted signal consists of one main-lobe and some undesired side-lobes. In contrast, precoding refers to the superposition of multiple beams for spatial multiplexing of several data streams.

A fourth answer is that beamforming refers to the formation of a beam in a particular angular direction, while precoding refers to any type of transmission from an antenna array. This definition essentially limits the use of beamforming to line-of-sight (LoS) communications, because when transmitting to a non-line-of-sight (NLoS) user, the transmitted signal might not have a clear angular directivity. The emitted signal is instead matched to the multipath propagation so that the multipath components that reach the user add constructively.

A fifth answer is that precoding consists of two parts: choosing the directivity (beamforming) and choosing the transmit power (power allocation).

I used to use the word beamforming in its widest meaning (i.e., the first answer), as can be seen in my first book on the topic. However, I have since noticed that some people have a more narrow or specific interpretation of beamforming. Therefore, I nowadays prefer only talking about precoding. In Massive MIMO, I think that precoding is the right word to use since what I advocate is a fully digital implementation, where the phases and powers can be jointly designed to achieve high capacity through spatial multiplexing of many users, in both NLoS and LOS scenarios.

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57 THOUGHTS ON “WHAT IS THE DIFFERENCE BETWEEN BEAMFORMING AND PRECODING?”
Ryan Feng
OCTOBER 4, 2017 AT 11:39 AM
The last sentence + “in both NLOS and LOS channel.”

REPLY
Emil Björnson
OCTOBER 4, 2017 AT 11:50 AM
Yes, that is what I meant. You are right that it is important to say this explicitly when dealing with multi-antenna communications. I have updated the text. Thank you!

REPLY
Ali Jemmali
OCTOBER 6, 2017 AT 1:56 AM
I think “Massive Precoding” would make more sense as “Precoding” is well known already in classical MIMO. By classical MIMO I mean non-massive MIMO.

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Rubayet Shafin
OCTOBER 7, 2017 AT 1:15 AM
Maybe a pseudo sixth answer is that precoding can be viewed as beamforming in the eigen direction of the channel rather than in any physical angular direction! However, in the TDD based massive MIMO with fewer resolvable paths (say mmWave) is it possible to set the downlink precoder as the steering matrix containing the angles of arrival estimated in the uplink? In that case, I think, the precoder maximizing the achievable rate and ‘conventional’ beamformer become similar!

REPLY
Emil Björnson
OCTOBER 7, 2017 AT 11:30 AM
You are right, eigenbeamforming is a terminology that is being used even when the eigenvector does not correspond to correspond to a physical direction.

If there is only a small number of resolvable paths, I think that the optimal precoder will be a linear combination of the steering vectors for the angles of arrivals of these paths. If the angles are all similar, the resulting beam will be almost as the steering vector of one of the angles. If the angles are very different, none of the steering vectors will be a good match.

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Anvar
JUNE 20, 2018 AT 11:29 PM
Just curious if there is a physical description of ‘eigen-direction of the channel’? Assuming an N-by-K complex channel matrix H contains gains and phase shifts per transmit-receive antenna, how the ‘channel direction’ information is embedded in H and what it actually means.

REPLY
Emil Björnson
JUNE 21, 2018 AT 10:25 PM
I discourage from talking about eigen-directions of multiuser MIMO channels. It will just lead to confusion. (The terminology is more appropriate for point-to-point MIMO channels.)

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Hiep
DECEMBER 26, 2017 AT 9:16 AM
With analog beamforming, changing the phase of each antenna will create a specific antenna pattern pointing to a certain direction. I am wondering if the same happens with digital beamforming?

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Emil Björnson
JANUARY 1, 2018 AT 10:23 PM
Any analog beamforming can be implemented by digital beamforming, but the opposite is not true.

With digital beamforming you can create antenna patterns that are not achievable with analog beamforming. It will basically be a superposition of any number of analog beams, resulting in an antenna pattern that might not have a distinct direction. For example, it can be tailored to a user channel to provide a strong signal in a non-line-of-sight situation (with many multipath components in different directions). In addition to that, you can assign different antenna patterns to different parts of the frequency spectrum, while analog beamforming must assign the same phases to the entire frequency band.

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