Original link: https: //blog.csdn.net/weixin_39274659/article/details/89810132
In the hot research into the 5G technology: Before mixing beamforming introduction, I would like first to intuitively understand the concept of this article describes in simple terms 5G, large-scale MIMO and beamforming and so on. Aims to use the most simple language, as far as possible zero-based readers can easily grasp its essence, so as to lay a solid foundation for discussion of the latest hybrid beamforming algorithm for follow-up.
Article Contents Preface 5G and millimeter wave and millimeter wave Massive MIMOMIMO beamforming (beamforming, beamforming) mathematical modeling 5G beamforming: Mixed beamforming opportunities and challenges
5G and Millimeter
compared to 4G, 5G on a higher communication quality requirements: a faster rate, lower latency and higher efficiency. Although the development of 5G looks birth contains many new technologies, but in essence, all gains are derived from the use of millimeter waves. Communication Nyquist first criterion tells us that the communication speed and bandwidth is proportional relationship (first Nyquist criterion). With the rapid development of the times, people's increasing demand for communication, due to the 4G used primarily bands below 6GHz bandwidth is already stretched. To speed up the communication speed, to solve the bandwidth shortage, most straightforward way is to higher frequencies open up , so the use of millimeter wave emerged.
As we all know, the frequency and wavelength of electromagnetic waves with the following formula:
That inverse relationship, which means that the shorter the wavelength , the higher the frequency .
Obviously, this formula can be obtained in different frequency bands in the figure above. Millimeter wave, by definition refers to the wavelength of 1mm - between the electromagnetic wave 10mm, its frequency is also interposed between 30-300GHz (particularly on the range of millimeter wave band remains to be discussed, but we talk about the content and unrelated).
By using millimeter waves (shorter wavelength), the communication carrier frequency is significantly improved, far more than can be obtained than the conventional LTE 4G broad frequency band several times, the origin is the fundamental gain 5G.
Massive MIMO millimeter wave and
other hand, however, the millimeter wave has significant disadvantages. The Friis transmission formula communication:
(Gt, Gr, Pt, Pr representing send, receive antenna gain power.) Can be seen, the received power is proportional to the wavelength . While the shorter wavelength millimeter wave, but also means a higher transmission loss (reception power is small). More than that, such as millimeter wave penetration ability is also greatly reduced, even the rain droplets can interfere with the transmission. Transmission loss introduced in this regard in a number of papers everywhere, not given here in detail. We only need to remember that, compared to the current 4G LTE transmission carrier, using millimeter waves though bring a broader bandwidth, but also suffered the loss of transmission, how to solve the increased without significantly enhance the transmission power receiving the signal to noise ratio , it has become a priority.
It is often said God gave you close one door, it often opens a window for you. For the millimeter-wave terms, Massive MIMO is this window. Some people say, millimeter wave and large-scale antenna array (massive MIMO) is a natural fit.
MIMO
Speaking before the massive MIMO, the first thing to say is the classic MIMO (multi-input-multi- output, multiple-input multiple-output), which was first proposed by Marconi in 1908. That is, by all transmitted using a plurality of antennas in the transmitting side and the receiving / receive, acquire diversity gain, spatial multiplexing, to thereby obtain a higher transmission rate. (A special case, such as a base station including multiple antennas and the UE is subject to hardware constraints using a single antenna system is called MISO (multi-input-single- output))
MIMO transmission of personal gain considered to be very easy to understand. Two office (Common Communication System 1 × 11 × 1 1 \ times11 × 1) is definitely smaller than the speed of four office (2 × 22 × 2 2 \ times MIMO system of 22 × 2) efficiency. Though all four may be lost due to (interference between different antenna data stream information) fit, but a little training (pre-send and receive equalization) two people did not want rolling pressure. And more, as we have known it, strength in numbers, antenna (MIMO large scale such as 100 × 100100 × 100 100 \ times 100100 × 100), the gain will be greater. This is the original intention Massive MIMO raised.
Closer to home, why millimeter wave and Massive MIMO is a natural fit it? We consider some physical limitations to implement MIMO, such as the arrangement of the antenna array spacing. In order to allow the receiving end to distinguish the information from different antennas, the antenna can not be so close. (Imagine the most extreme case, all of the antennas coincident with all, is that the information receiving side is emitted by an antenna, not resolved, the MIMO gain freedom is not obtained.) Taking into account the long-distance transmission, If you only have a small spacing distance, it seems that you and the receiving end of a coincidence also lacks distinction. In a wireless communication infrastructure David Tse book mentions, for uniform one-dimensional antenna array is arranged (see below), the antenna separation should be satisfied:
L≥0.5λL≥0.5λ 
For a two-dimensional array antenna even in terms of the three-dimensional arrangement of derivation may slightly change (no in-depth study of the author), but there was no doubt that the antenna interval is positively correlated with the wavelength. Here in the one-dimensional antenna array as an example, i.e., L = 0.5λL = 0.5λ L = 0.5 \ lambdaL = 0.5λ (theoretical minimum antenna spacing, the small can not get the full gain). If we want to use the antennas 101 do massive MIMO, then the total length of the antenna array must be 100 × L = 50λ100 × L = 50λ 100 \ times L = 50 \ lambda100 × L = 50λ, we are now commonly used to 2.4GHz as an example, λ = c / f = 0.125 yards λ = c / f = 0.125 yards \ lambda = {c} / {f} = 0.125 yards λ = c / f = 0.125 meters, this is to say the total length will reach 6.25 Meter. This obviously can not be done in the length of the phone, even using the base station side is feeling the pressure.
At this time mm wave length advantage is reflected out again, if the wavelength of a millimeter, even if the order of hundreds of antenna arrays, nor to the total length of 1 m. In other words, the inner space of the same size, the conventional LTE system may be placed only one antenna, but can be integrated, several tens of millimeter-wave systems.
Beamforming (beamforming, Beamforming)
accompanied by the introduction Massive MIMO, another important issue is inevitable: beamforming. The concept of MIMO appear almost immediately been made, but also because of massive MIMO plays a more important role in the 5G. All hybrid beamformer algorithms to be discussed in this column, which is a specific implementation in hardware limitations 5G. I very much stronger push here earlier seen a science, its easy to understand the style of writing called us the model, the ease and far better than the public fiddle formula unintelligible articles. Although previous bead front, in order to ensure the full wording, I would also like to write their own understanding.
First, we must clear the need for beam shaping, which is directly derived from two questions MIMO systems:
一般的天线发送信号，没有指定的角度，而是以一种比较无脑的方式，几乎是360度往空间各个方向发送信号。干扰了别人要接收的信号不说，哪怕从一个自私的角度出发，也浪费了大量的发送功率。就好像以前自习课你和同桌聊天，非要喊得全班都听见，既让自己消耗了更多的卡路里，也吵到其他人学习。
前面说到，MIMO的增益本质上就是人多力量大，然而人与人之间的配合不默契会导致一定的损耗，难以达到1+1=21+1=2 1 + 1 =21+1=2的效果。比如空间中其实有多条独立的路径可以到达接收端，明明大家可以各走一条，但如果挤在一起，反而会互相造成干扰。
盗用下前辈的这张图，上图就是不经处理的MIMO，效率感人。下图则是我们期望的结果，按部就班。 而要想达到这样的效果，就需要这一节的主角出场：波束赋形。
一句话来说的话就是：
一根天线是360度地发送信号，但一列天线不是。
我们初中高中的时候学过波的干涉与衍射，不同相位的波在叠加之后，在某些方向上增强，在某些方向上减弱。 电磁波亦如是。波束成形的根本就在于，改变每根发送天线信号的幅度与相位，使得最后一列天线的叠加效果，在空间上看就是对准了个别方向的波束。即能量集中于少数几个方向，而在绝大部分空间中都是0，如同手电筒对准了一般。 这也就是波束成形一名的由来。
具体的实现如下图：
即每根天线的传输信号，会根据一些先验信息（如信道信息等），进行幅度和相位的调整，从而使得最后形成的发送信号对准某个角度。
波束成形的数学建模
近十几年有无数波束成形算法的研究文章。对于波束成形的研究，笔者认为尽管上述的物理背景介绍以及极其深入浅出，仍不足以直观地想象其算法原理。因此在这一节，笔者给出了自己觉得最为简洁的波束成形数学建模。
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