资料翻译之一-CSI from Wikipedia

最近在学习中可能会自己翻译些东西，权当是顺便学英语了。

我的翻译水平十分有限，只能保证写出来我自己能看懂，如果有不通顺的地方也属正常，但是有理解上的错误还望指正，欢迎讨论。

第一篇是来自Wikipedia上关于CSI的内容，公式部分较为复杂我偷懒省去，各位有需要可以去网站上查看。

 

Channel state information

From Wikipedia, the free encyclopedia

Jump to navigationJump to search

In wireless communications, channel state information (CSI) refers to known channel properties of a communication link. This information describes how a signal propagates from the transmitter to the receiver and represents the combined effect of, for example, scattering, fading, and power decay with distance. The method is called Channel estimation. The CSI makes it possible to adapt transmissions to current channel conditions, which is crucial for achieving reliable communication with high data rates in multiantenna systems.

在无线通信中，信道状态信息（CSI）表示一个通信线路的已知信道属性。它描述信号从发送端到接收端的传播情况，以及无线信号受到信号散射、信号衰退、功率衰减及距离的整体影响。用来估计CSI的方法被称为信道估计。CSI使得根据无线信道传输状态实时调整传输成为可能，这对在多天线系统中实现高传输率的可靠通信至关重要。

CSI needs to be estimated at the receiver and usually quantized and fed back to the transmitter (although reverse-link estimation is possible in TDD systems). Therefore, the transmitter and receiver can have different CSI. The CSI at the transmitter and the CSI at the receiver are sometimes referred to as CSIT and CSIR, respectively.

CSI估计应在接收端接收端进行，并且一般会被量化并反馈会发送端(尽管在时分双工系统(Time-division duplex system, TDD)中可以实现反向估计)。因而发送端与接收端往往会有不同的CSI。发送端和接收端的CSI一般会被分别表示为CSIT和CSIR。

 

########################################################################################

Contents

 

########################################################################################

 

Different kinds of channel state information[edit]

There are basically two levels of CSI, namely instantaneous CSI and statistical CSI.

一般会有两种CSI，瞬时CSI和统计CSI。

Instantaneous CSI (or short-term CSI) means that the current channel conditions are known, which can be viewed as knowing the impulse response of a digital filter. This gives an opportunity to adapt the transmitted signal to the impulse response and thereby optimize the received signal for spatial multiplexing or to achieve low bit error rates.

瞬时CSI（或短时CSI）表示实时信道情况是已知的，可以类比的理解为已知一个数字滤波器的脉冲响应。这让发送端可以根据脉冲响应来调整发送信号，从而优化信号的空间复用或实现第错位率。

Statistical CSI (or long-term CSI) means that a statistical characterization of the channel is known. This description can include, for example, the type of fading distribution, the average channel gain, the line-of-sight component, and the spatial correlation. As with instantaneous CSI, this information can be used for transmission optimization.

统计CSI（或长时CSI）表示信道的统计特征是已知的。它可以包括很多信息，比如衰减分布的类型、平均信道增益、直射路径分量以及空间相关性等。与瞬时CSI相同，统计CSI可以用来优化信号传输。

The CSI acquisition is practically limited by how fast the channel conditions are changing. In fast fading systemswhere channel conditions vary rapidly under the transmission of a single information symbol, only statistical CSI is reasonable. On the other hand, in slow fading systems instantaneous CSI can be estimated with reasonable accuracy and used for transmission adaptation for some time before being outdated.

CSI的采集取决于信道状态变化的快慢。在快速衰落系统中，在单个信息符号传输的情况下，信道状态的变化非常快，此时只有统计CSI是有效的。而在慢衰落系统中，可以在有效的精确率范围内估计瞬时CSI，从而在其失去时效前用来调整传输。

In practical systems, the available CSI often lies in between these two levels; instantaneous CSI with some estimation/quantization error is combined with statistical information.

在实际应用中，有效的CSI往往是介于两者之间；经过调整优化后的瞬时CSI会与统计CSI结合起来使用。

 

########################################################################################

 

Mathematical description[edit]

In a narrowband flat-fading channel with multiple transmit and receive antennas (MIMO), the system is modeled as[1]

?=??+?                                      （1）

Where y and x are the receive and transmit vectors, respectively, and H and n are the channel matrix and the noise vector, respectively. The noise is often modeled as circular symmetric complex normal with

? ~ ??0,?                                   （2）

where the mean value is zero and the noise covariance matrix S is known.

在具有多条发送和接收天线(MIMO)的窄带平坦衰落信道中，系统的模型可以表示为(1),其中，y与x分别表示接收信号与发送信号向量，H与n分别表示信道矩阵和噪声向量。系统中的噪声一般会被表示为(2)中的圆对称高斯复合分布，其中分布的均值为0，噪声相关性矩阵S是未知的。

 

Instantaneous CSI[edit]

Ideally, the channel matrix H is known perfectly. Due to channel estimation errors, the channel information can be represented as[2]

???(?????????) ~ ?????(?),??????                                   （3）

where ????????? is the channel estimate and ?????? is the estimation error covariance matrix. The vectorization 

???() was used to achieve the column stacking of H , as multivariate random variables are usually defined as vectors.

理想情况下，信道矩阵H是完全已知的。由于信道估计误差，信道信息可以被表示为公式(3)，其中是?????????信道估计，??????是误差相关矩阵。向量化符号???()是用来整合H的列，以使其变成多变量随机变量常用的向量形式。

Statistical CSI[edit]

In this case, the statistics of H are known. In a Rayleigh fading channel, this corresponds to knowing that[3]

???(?) ~ ??0,?                                   （4）

for some known channel covariance matrix R.

在这种情况下，H的统计信息已知。在一个存在瑞丽衰减的信道里，这相当于知道公式(4),其中，R是已知的信道相关矩阵。

 

 

########################################################################################

 

Estimation of CSI[edit]

Since the channel conditions vary, instantaneous CSI needs to be estimated on a short-term basis. A popular approach is so-called training sequence (or pilot sequence), where a known signal is transmitted and the channel matrix H is estimated using the combined knowledge of the transmitted and received signal.

由于信道状况是变化的，瞬时CSI必须在短时间的情况下估计。一种常用的方法是训练序列法（或者导频序列法），这种方法联合发送信号和接收信号，在发送信号已知的情况下估计信道矩阵H。

Let the training sequence be denoted ?1,?2…??, where the vector ?? is transmitted over the channel as

??=???+??                                      （5）

By combining the received training signals ?? for i=1,…,N, the total training signalling becomes

?=?1,…,??=??+?                                      （6）

with the training matrix P = [?1,…,??] and the noise matrix N = [?1,…,??] .

With this notation, channel estimation means that H should be recovered from the knowledge of P and Y.

使训练序列为?1,?2…??，其中向量经过公式5传输。通过联合起所有收到的训练信号，总的训练序列变为公式6，其中P与N分别为训练矩阵和噪声矩阵。

通过这种表示方法，可以发现信道估计意味着H应该是由P与Y推断而来的。

 

Least-square estimation[edit]

If the channel and noise distributions are unknown, then the least-square estimator (also known as the minimum-variance unbiased estimator) is[4]

???−????????=???(???)−1                                  （7）

where ()? denotes the conjugate transpose. The estimation Mean Square Error (MSE) is proportional to

??(???)−1                                  （8）

where tr denotes the trace. The error is minimized when ??? is a scaled identity matrix. This can only be achieved when N is equal to (or larger than) the number of transmit antennas. The simplest example of an optimal training matrix is to select P as a (scaled) identity matrix of the same size that the number of transmit antennas.

如果信道及噪声分布式未知的，则最小二乘估计器(也被称为最小方差非偏估计器)如公式(7)所示，其中()?是共轭转置符号。估计的均方误差表示为公式(8)，其中tr表示矩阵的迹。当 ???是单位矩阵时误差最小。这一条件仅当N大于或等于传送天线数量是才会达成。最佳训练矩阵的最简单的例子是讲P选择为和传送天线相同大小的单位矩阵。

 

MMSE estimation[edit]

If the channel and noise distributions are known, then this a priori information can be exploited to decrease the estimation error. This approach is known as Bayesian estimation and for Rayleigh fading channels it exploits that

????????−????????~ ??0,?,  ????~ ??0,?                                   （9）

The MMSE estimator is the Bayesian counterpart to the least-square estimator and becomes[2]

????????−????????=?−1+??⊗???−1??⊗?−1??⊗?−1???(?)                                   （10）

where ⊗ denotes the Kronecker product and the identity matrix I has the dimension of the number of receive antennas. The estimation Mean Square Error (MSE) is

???−1+??⊗???−1??⊗?−1                                   （11）

and is minimized by a training matrix P that in general can only be derived through numerical optimization. But there exist heuristic solutions with good performance based on waterfilling. As opposed to least-square estimation, the estimation error for spatially correlated channels can be minimized even if N  is smaller than the number of transmit antennas.[2] Thus, MMSE estimation can both decrease the estimation error and shorten the required training sequence. It needs however additionally the knowledge of the channel correlation matrix R and noise correlation matrix S. In absence of an accurate knowledge of these correlation matrices, robust choices need to be made to avoid MSE degradation.[5][6]

如果信道噪声分布式已知的，则这些先验知识可以用来减少估计误差。这种方式被称为贝叶斯估计。对于瑞丽衰减的信道，如公式(9)所示，则MMSE估计量是最小二乘估计量的贝叶斯形式，被表示为公式(10),其中 是克罗内克积，并且I和接收天线的维数相同。估计的MSE是公式(11),它由一个通常只能通过数值优化得到的训练矩阵P最小化。但是，它存在性能良好的基于水流法的启发式算法解。与最小二乘法不同的是，它在N比传送天线数量小的情况下依然可以最小化。因此，MMSE可以同时减少估计误差和减小所需的训练序列。但是它需要额外的信道相关性矩阵和噪声相关性矩阵。在没有这些矩阵的精确值的情况下，需要做出强力的选择以避免MSE的退化。

 

########################################################################################

 

Data-aided versus blind estimation[edit]

数据辅助与盲估计

In a data-aided approach, the channel estimation is based on some known data, which is known both at the transmitter and at the receiver, such as training sequences or pilot data.[7] In a blind approach, the estimation is based only on the received data, without any known transmitted sequence. The tradeoff is the accuracy versus the overhead. A data-aided approach requires more bandwidth or it has a higher overhead than a blind approach, but it can achieve a better channel estimation accuracy than a blind estimator.

在数据辅助的情况下，信道估计是基于已知的数据，比如来自发送端和接收端的训练序列和前期数据。在盲估计里，估计仅基于接收到的数据，没有任何已知的传送数据。这里需要权衡的是准确率和开销之间的关系。数据辅助的方式需要更大的带宽或者更多的开销，但是可以获得更高的准确率。

 

References[edit]

来自

• ^ J. Kermoal, L. Schumacher, K.I. Pedersen, P. Mogensen, F. Frederiksen, A Stochastic MIMO Radio Channel Model With Experimental Validation Archived 2009-12-29 at the Wayback Machine., IEEE Journal on Selected Areas Communications, vol 20, pp. 1211-1226, 2002.
• ^ M. Biguesh and A. Gershman, Training-based MIMO channel estimation: a study of estimator tradeoffs and optimal training signals Archived March 6, 2009, at the Wayback Machine., IEEE Transactions on Signal Processing, vol 54, pp. 884-893, 2006.
• ^ Y. Li, L.J. Cimini, and N.R. Sollenberger, Robust channel estimation for OFDM systems with rapid dispersive fading channels, IEEE Transactions on Communications, vol 46, pp. 902-915, July 1998.
• ^ M. D. Nisar, W. Utschick and T. Hindelang, Maximally Robust 2-D Channel Estimation for OFDM Systems, IEEE Transactions on Signal Processing, vol 58, pp. 3163-3172, June 2010.
• ^ A. Zhuang, E.S. Lohan, and M. Renfors, "Comparison of decision-directed and pilot-aided algorithms for complex channel tap estimation in downlink WCDMA systems", in Proc. of 11th IEEE Personal and Indoor Mobile Radio Communications (PIMRC), vol. 2, Sept. 2000, p. 1121-1125.
• ^ Jump up to:a b c E. Björnson, B. Ottersten, A Framework for Training-Based Estimation in Arbitrarily Correlated Rician MIMO Channels with Rician Disturbance, IEEE Transactions on Signal Processing, vol 58, pp. 1807-1820, 2010.
• ^ A. Tulino, A. Lozano, S. Verdú, Impact of antenna correlation on the capacity of multiantenna channels, IEEE Transactions on Information Theory, vol 51, pp. 2491-2509, 2005.
• 1Different kinds of channel state information
• 2Mathematical description
• 2.1Instantaneous CSI
• 2.2Statistical CSI
• 3Estimation of CSI
• 3.1Least-square estimation
• 3.2MMSE estimation
• 4Data-aided versus blind estimation
• 5References