MIMO中的precoding和beamforming.有什麼區別？

01-29

網上有人說，前者更關注於分集增益後者注重array gain.不太明白。另外對於array gain該怎麼理解

答案來至Massive MIMO 大牛Emil Bj?rnson的博文，我個人是贊成他的答案的。

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.

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).

MIMO是一種用來描述多天線無線通信系統的抽象數學模型，能利用發射端的多個天線各自獨立發送信號，同時在接收端用多個天線接收並恢復原信息。

狹義上來講，Precoding 是多流的beamforming, 但是一般意義上，發射機上所有的空間處理都會使用Precoding, 包括空間復用（Spatial multiplexing ），即Precoding只是MIMO方案中的一個步驟，一個過程。

參見wiki百科MIMO
Precoding is multi-stream beamforming, in the narrowest definition. In more general terms, it is considered to be all spatial processing that occurs at the transmitter.

LTE 下行物理層處理過程，如下，其中MIMO主要涉及到層映射（layer mapping）和預編碼（Precoding）兩部分處理過程。

Array gain即陣列增益

陣列增益即發射的信號的功率增益，是通過發送機和/或接收機的多個天線而實現功率增益的，一般在LTE中，增加一個天線會有3db的增益。

precoding的範圍更大些，beamforming可以理解為linear precoding。至於陣列增益和分集增益都是有的，這個看信道的空間相關性了。

precoding和beamforming（BF）有所區別，但在使用上卻沒有明確的分野，要結合具體語境。一般來講，precoding側重於用多天線的自由度來進行多流傳輸的干擾抑制，而BF側重於獲取分集增益。

從術語的來源講，早期precoding大多稱為pre-equalizer，來源於SISO信道中的碼間干擾預抵消。在mimo-bc信道中由於DPC編碼能夠進行連續的干擾預抵消達到信道容量，而用於MIMO的T-H pre-equalizer作為DPC的一種簡化方法，逐漸被稱為THP。precoding逐漸被廣泛使用，作為發端與equalizer對稱的方法使用。而BF是從陣列天線的術語繼承而來，主要是使用權值網路讓天線形成定向波束。但是在MIMO數字信號處理中，利用信道信息來獲取發端分集增益的方法沿用了這個術語，如MRT BF（最大比傳輸）和DET BF(主特徵傳輸）。

至於array gain，主要是利用相干合併獲得，信噪比的提升，但無法對抗深衰落。當然，等增益合併和最大比合併在獲得分集增益的同時，也能獲得array gain.

關於beamforming我多說一句，這個實際上在設計通信演算法方面有非常重要的意義，可以吧原本是非線性的系統轉換為線性系統，因為MIMO系統往往要考慮時延和多普勒頻移，利用beamspace處理的話，可以把這兩個非線性量轉換為線性量，相當於做了一個二維 DFT，那麼實際應用中我們就可以用FFT來進行處理，寫在工業設計上是非常重要的。

簡單說precoding是設計一個matrix，beamforming是設計一個vector. 就這個區別

不是通信專業人士，看了一些介紹，似乎 beamforming 是用於單流的情況,而precoding用於多流的情況(MIMO。這樣說precoding就是基於MIMO的beamforming了。