在里面以前的发布我们在高水平上讨论了MIMO可以用11AC解决方案表现出来的方式。
一个案例是：
- 在单用户MIMO的室外情况下，我们可以引入2nddegree of freedom by using antenna polarization. Polarization is the direction of the electric field. Horizontally and vertically polarized waves are physically and mathematically distinct and so can be used to send 2 streams of independent data. Thus, polarization can be used to create a 2nd在这种环境中的自由程度。注意：只有两个分开的极化。其他任何东西都是两个独立国家的组合。
首先：什么是极化？
When dealing with electric and magnetic field these are vectors which means they have an amplitude and a direction.
在自由空间中，唯一可能的波模式是横向电磁或TEM波。这意味着向Z方向传播的波的方向在垂直于传播方向的平面中描述了电（E）和磁场（H）场。在笛卡尔坐标系（X，Y，Z）中，这意味着E和H场的方向在XY平面中。
Cartesian Coordinates
So if we imagine an electric field in the x direction the magnetic field will be in the y direction. If we lay a wire in the direction of the x axis the E field will excite the electrons on the wire and current will flow proportional to the strength of the field from the bottom to the top of the wire. That same wire laid across the y or z axis will not see the E field so no current will flow.
x方向的e字段
想象一下，现在我们将整个系统转移了90度。现在E场位于Y方向，H场位于X方向
E field in the y direction
As before a wire in the y direction will now be excited by the y directed E field and currents will flow.
要查看两极分化的其他方面，请查看：
http://en.wikipedia.org/wiki/polarization_(Waves）
在坐标系中，X和Y方向相互90度，它们被认为是正交的。（即它们以直角相遇）。
Since we can physically isolate signals in the x and y directions a communications system can take advantage of this to send independent information on the orthogonal branches. Or putting it in 11ac speak; we can send two streams over dual polarized antenna systems.
第二：极化历史
Since the vector nature of fields was fully described by Maxwell when he set down his equations for electromagnetic fieldshttp://en.wikipedia.org/wiki/maxwell's_equations，无线电系统工程师从广播的最早日子就利用了这一点。
具有极化多样性的系统是早期的例子。在这种情况下，在两个流上发送相同的信号。这增加了无线电链路的鲁棒性，因为不同的极化反应不同，例如，对两端之间可能存在的弹跳路径的反应不同。在早期，系统将检测到哪种路径最强，并且简单地切换。因此，这是一个开关/极化多样的系统。
后来利用此功能增加容量的示例是诸如长途微波系统的越野电话。这些需要精确的天线设计和进料的精确对齐，以确保它们真正是正交的，并且两端还必须具有垂直和水平平面的精确比对。即使是1度旋转误差或从一个极化到另一个极化的泄漏也可能导致退化，因为远端无法从所需信号中去除损坏的能量。
随着MIMO处理高精度和高成本安装的日子的出现，后视镜是在后视镜中。MIMO操作允许使用具有不完美极化隔离的较简单天线，并且不再需要安装时的精度天线对准。
第三：实际考虑
在里面previous blog the argument was made that polarization diversity has limited benefits indoor since in most practical environment the bounces that occur between the AP and client randomize the polarization of the signals and the simple antenna structures used in client and APs also tend to provide a mix of polarizations. Measurements with discrete antennas show that aside from particular corner cases the use of polarization diverse antenna subsystems indoors provides limited or no benefit and can degrade in other corner cases.
户外是不同的。在许多室外情况下，很少有或没有显着的反射路径来分布极化，并且缺乏反射往往会降低系统支持多个流的能力。户外偏振天线的使用对系统吞吐量有重大影响。
There is a tradeoff with polarization diversity. Antennas that are cross polarized cannot be combined with beamforming techniques as E fields that are orthogonal cannot be added together. The system designer needs to tradeoff the benefit of the link robustness due to the polarization and the extra signal strength available from beamforming. For access it can be a coin toss. For backhaul it is link distance versus throughput.
For most backhaul solutions and certainly for unlicensed band where the EIRP is regulated the decision is almost always to use polarization diversity and take the benefit of the extra throughput from the additional stream.
第四：交叉极化和MIMO
案例1：对齐天线
As mentioned earlier, MIMO makes the use of cross polarization fairly simple. In this section we will look at how MIMO processing can address this.
首先，让我们看一下源端。在这里，我们有一个双偏振天线在水平和垂直方向上发送信号。
带有水平和垂直极化信号的源天线
最简单和理想的案例是接收天线完全排列
完美对齐的接收天线
从某种意义上说，该系统类似于在镜子里看着自己。向上和向下的方向保留了
在接收天线上，田地看起来像
Fields at the receiver
数学上表示的方式是：
传输和接收信号的数学描述
Break this down and you get that VR = 1*VT + 0 *HT and HR = 0 *VT +(-1)*HT
The 2x2 matrix is a description of the propagation channel that exists between the sending and receiving antennas. The receiver in a Wi-Fi radio estimates the channels from the information encoded in pilot tones in the Wi-Fi signal. From that estimate it calculates the inverse of the channel and using that it can calculate what was originally sent.
让我们拿我们的方程式并将其放在标准的MIMO表格中
y=Hx
y是接收器的信号，
Xis the signal at the transmitter,
H是频道
Using some simple algebra we can multiply both sides of the equation by the inverse of the channel matrix
H-1y= H-1H x
一个矩阵乘以其反向给出的矩阵等同于1，因此它变为
H-1y = x
换句话说，如果您可以测量频道并得出逆向，则可以返回发送的原始信息。
因此，让我们进行简单的频道估算
在这种情况下，逆向完全相同（您可以检查自己h-1H）。
因此，要获取发送的原始数据
情况2：接收天线旋转
Let's make this a bit more difficult. If the receive antenna is rotated,for example, by 45 degrees relative to the transmitter a traditional non-MIMO system would see this as complete corruption of the original signals as the two polarization would appear to have the same amplitude and give a net signal to interference level of 0 dB.
Again let's look at the source end. Here we have a dual polarized antenna sending signals in the horizontal and vertical directions.
带有水平和垂直极化信号的源天线
Here is a diagram with the receive antenna rotated to by some angle
旋转接收天线
在接收天线上，传输的字段看起来像
Fields at the receiver
在接收器上，原始的垂直和水平信号在两个端口上均匀地显示。
To understand what is happening we need to decompose the transmitted signals onto the local coordinates. Will use PR and MR which correspond to the rotated axes on the receive antenna.
本地接收坐标
If we overlay the transmitted signals onto this:
数学上表示的方式是：
传输和接收信号的数学描述
从中可以看出，随着旋转角度接近0，方程将恢复回到我们先前看的东西
因此，现在使用MIMO处理，我们可以提取VT和HT的原始信号。
让我们拿我们的方程式并将其放在标准的MIMO表格中
y=Hx
y是接收器的信号，
Xis the signal at the transmitter,
H是频道
回想一下，我们可以将方程的两侧乘以通道矩阵的倒数
H-1y= H-1H x
一个矩阵乘以其反向给出的矩阵等同于1，因此它变为
H-1y = x
换句话说，如果您可以测量频道并得出逆向，则可以返回发送的原始信息。
因此，让我们进行简单的频道估算：
The inverse is in this case is:
因此，要获取发送的原始数据
如果您想自己进行计算，请记住
概括
因此，我们可以看到如何与偏振系统一起使用MIMO。它使它们更容易部署，并且系统可以最大程度地利用链接的操作。
尽管上面的示例似乎很简单，但它说明了如何使用MIMO处理来解决实际部署问题。在未来的文章中，我们将研究如何适用于室内环境，在室内环境中，反射创造了MIMO的自由度，而不一定是两极分化。
埃里克·约翰逊（Eric Johnson）is director of product management at Aruba, a Hewlett Packard Enterprise company.
