CN101039290B - MIMO Correlation Channel Estimation Method Based on Adaptive Training Sequence - Google Patents

Abstract

This invention discloses a relative channel estimation method of MIMO based on self-adaptive training sequence. The process is that, the receptor determines the best length of the training sequence according to relative known information of the channel and transfers the value of the length and relative information of the channel through feedback link to the transmitter. The transmitter uses this feedback information to compute the optimal training sequence correspondent to current state of the channel according to the training sequence expression St=UD1/2tU*t designed by this model and transfers this optimal training sequence to the receptor through the forward link. Then the training cycle begins and the transmitter launches the training sequence to wireless channel. The receptor estimates the channel parameters of current time according to the known training sequence and the receipted signal in the training cycle and by using the minimum mean square error estimation criteria. The training sequence designed by this invention can make self-adaptive adjustment according to the needs of the actual system and the change of relative information of the channel. The invention has advantages of high estimation performance and strong robustness, thus can be used in wireless communication system with muti-antenna MIMO.

Description

MIMO Correlation Channel Estimation Method Based on Adaptive Training Sequence

technical field

The invention belongs to the field of communication signal processing, and relates to a channel estimation method, which can be used in a multi-antenna MIMO wireless communication system.

Background technique

In the past ten years, information and communication technology and its application systems have developed rapidly, showing unprecedented prosperity. The development and maturity of mobile communication, wireless communication, multimedia information service and the Internet have shown a bright prospect for anyone to perform any kind of information interaction at any time and any place. At the end of the 20th century, the wide application of Internet technology and people's increasing dependence and demand on data transmission services have impacted and promoted the continuous upgrading of mobile communication technology. The existing third-generation mobile communication system has been difficult to meet the high-speed, multi-service, high-quality communication and data transmission requirements of future mobile communication, so people put forward the concept of super 3G or 4G, and many international standardization organizations and forums are also Actively carry out research on future mobile communications. For example, the International Telecommunication Union-Radiocommunication Department ITU-R pointed out in the document on the future development of the third-generation wireless communication global standard IMT-2000 and the system beyond IMT-2000: the capability of the IMT-2000 terrestrial wireless interface will be around 2005 It will be extended to nearly 30Mbps; the new system envisioned to surpass IMT-2000 around 2010 will support a peak rate of about 100Mbps under high-speed mobile conditions, and a peak rate of about 1Gbps under low-speed mobile conditions.

One of the key technologies widely recognized to support the high-speed requirements of future mobile communications is the multiple-input multiple-output MIMO system. MIMO technology can double the channel capacity of wireless channels without increasing the system bandwidth and transmission power. According to the research results of information theory, if the channel fading between different transmit-receive antenna pairs is independent of each other, under the same transmit power and bandwidth, a MIMO system with N _t transmit antennas and N _r receive antennas can achieve the channel The capacity is min(N _t , N _r ) times that of the existing single-antenna system, thus providing an unmatched capacity improvement potential for other current technologies. Therefore, the MIMO system is considered to be one of the key technologies to realize future mobile communication.

However, the prerequisite for the MIMO system to double channel capacity is that the receiver can obtain as accurate channel fading status information as possible, so as to effectively demodulate and decode the received signal. Therefore, channel estimation technology is the key to realize effective transmission of wireless communication, and it is also a technical problem that must be solved first in the practical process of MIMO system.

At present, MIMO channel estimation methods mainly include three types: training sequence/pilot-based channel estimation algorithms, blind channel estimation algorithms and semi-blind channel estimation algorithms. Considering the maturity, robustness, and complexity of the algorithm, combined with various standard specifications, the estimation method based on the training sequence is generally used. The method is fast, simple and effective, and it is beneficial to separate the process of channel estimation and signal detection, which can greatly simplify the design of the receiver.

A large number of existing literatures have done in-depth research on the design of the training sequence, and it is generally believed that the estimated mean square error of the orthogonal training sequence is the smallest. These studies usually assume that the channel fading coefficients between the transceiver antenna pairs are independent and identically distributed, or use suboptimal estimation criteria that do not need to consider channel related information. However, it is well known that in wireless mobile channels, due to the insufficient expansion of the incoming wave angle and the small spacing between antenna elements, the signal space fading correlation is caused by the inter-multipath correlation determined by the pulse-forming filters at both ends of the transceiver and the physical channel response. The characteristics of the MIMO system will be seriously affected by the time correlation introduced by the Doppler frequency shift and the existence of the direct path. These factors must be taken into consideration.

Channel related information belongs to the second-order statistical characteristics of the channel state, and its time-varying rate is much slower than the channel fading coefficient itself. Even in the case of short channel coherence time, it is possible to obtain and track channel related information. Knowing the correlation information of channel fading, the receiving end can use this relevant information to assist channel parameter estimation, and the transmitting end can use the relevant information to design an optimal training sequence, thereby effectively improving the accuracy of channel estimation. In addition, the correlation of channel fading will reduce the number of independent coefficients in the channel matrix and reduce the dimensionality of the channel coefficient space. For the channel estimation mechanism based on the training sequence, the number of parameters to be estimated directly determines the length of the training period, thus limiting the transmission performance of the system. Therefore, under the channel estimation mechanism, the correlation will reduce the number of independent parameters to be estimated, and will also reduce the estimation workload and shorten the length of the training sequence, thus theoretically improving the system capacity.

In recent years, there are also a few papers considering the problem of training sequence design under correlated MIMO channels on the basis of orthogonal training sequences and combined with channel-related information. However, the training sequences designed in these few literatures only blindly pursue the minimization of the mean square error of channel estimation. Obviously, the longer the training sequence is, the better the estimation performance is, without considering the length of the training sequence and data transmission. The compromise of length does not consider the problem from the perspective of the effective transmission rate of the system under the training mechanism. Apparently, the function of the training sequence is only to estimate the channel, but not to transmit any information. The amount of channel transmission time it occupies/consumes will directly affect the actual usability of the system. Moreover, since the structure of the existing training sequence is fixed and immutable, it is impossible to adaptively adjust the length of the training sequence according to the spatial domain related information of the current channel, and it is also impossible to use the known channel related information more effectively, resulting in Estimate performance issues with low robustness.

content of the invention

The purpose of the present invention is to overcome the defects of fixed training sequence structure and poor adaptive adjustment performance of training length in the prior art, and provide an adaptive estimation method of MIMO correlation channel based on training sequence.

The technical idea of realizing the object of the present invention is: aiming at the MIMO flat block fading channel with spatial domain fading correlation, on the basis of assuming that the channel spatial domain correlation obeys the Kronecker separation correlation model, design a channel correlation information that can effectively use and whose length is controllable The training sequence generation method, combined with channel coherence time, comprehensively considers the compromise between estimation accuracy and system transmission capacity, through the minimum mean square error MMSE estimation criterion, and uses the optimization principle to realize adaptive channel estimation of MIMO related channels. The specific process is as follows :

表示矩阵间的直积，该信道相关矩阵R_h的秩K，记作K＝rank(R_h)；(1) The receiver performs a matrix direct product operation on the known spatial correlation matrix R _t at the transmitting end and R _r at the receiving end to obtain the second-order statistical correlation information R _h of the current channel, that is, R _h =R _r R _t ,

Indicates the direct product between matrices, and the rank K of the channel correlation matrix R _h is denoted as K=rank(R _h );

其中N_r表示接收天线数目，

表示向上取整；(2) Determine the length of the training sequence used for channel estimation according to the K value, namely

where N _r represents the number of receiving antennas,

Indicates rounding up;

(3) The receiver feeds back the determined training sequence length T _τ and channel related information R _h to the transmitter through the feedback link between the receiver and the transmitter;

(4) The transmitter determines the diagonal matrix D _τ in the training sequence structure according to the feedback information,

When T _τ ≥ N _t , take ${\mathrm{D.}}_{\mathrm{\τ}}^{1/2}=\left[\begin{array}{c}{\mathrm{D.}}^{1/2}\\ 0_{(T_{\mathrm{\τ}}-N_t)\×N_t}\end{array}\right],$

When T _τ <N _t , take ${\mathrm{D.}}_{\mathrm{\&tau;}}^{1/2}={\mathrm{D.}}_{[1:T_{\mathrm{\&tau;},}:]}^{1/2},$

Among them, N _t represents the number of transmitting antennas, 0 _(Tτ-Nt)×Nt represents a (T _τ -N _t )×N _t dimensional all-0 matrix, superscript ^1/2 represents the square root of the matrix, D _{[1:Tτ ,:]} ^1/2 means to take the first T _τ rows of D ^1/2 , and the matrix D is a N _t ×N _t dimensional diagonal matrix;

(5) Generate the training sequence S _τ from the above matrix D _τ , namely

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; u</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; *</span>}$

Among them, U is an arbitrary T _τ × T _τ dimensional unitary matrix; U _t is the N _t × N _t dimensional eigenvector unitary matrix in the eigenvalue decomposition of the transmitter correlation matrix R _t , and the superscript ^* represents the conjugate of the matrix Transpose operation;

(6) The transmitter notifies the receiver of the specific value of the currently used training sequence S _τ through the forward link from the transmitter to the receiver;

(7) Start the training period, the transmitter transmits the training sequence S _τ to the wireless channel H through the transmitting antenna, and the signal received by the receiver within T _τ symbol periods can be expressed as a T _τ × N _t -dimensional matrix X _τ ;

(8) According to the above-mentioned received signal X _τ and the notified training sequence S _τ , the receiver adopts the minimum mean square error MMSE estimation criterion, and obtains the estimated value of the current channel coefficient by the following formula

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; *</span>}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; *</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}$

接收信号矩阵X_τ和信道矩阵H的列堆积向量，ρ_τ表示训练周期内的平均发射功率， ${\tilde{S}}_{\mathrm{\&tau;}}=(I_{N_r}\&CircleTimes;S_{\mathrm{\&tau;}}),I_{N_r}$ 表示N_r维单位阵，上标^-1表示矩阵求逆运算；in, $\hat{h}=\mathrm{vec}\left(\hat{h}\right),$ x _τ ＝vec(X _τ ), h＝vec(H) represent the channel estimation matrix respectively

The column stacked vector of the received signal matrix X _τ and the channel matrix H, ρ _τ represents the average transmit power in the training period, ${\tilde{S}}_{\mathrm{\&tau;}}=(I_{N_r}\&CircleTimes;S_{\mathrm{\&tau;}}),I_{N_r}$ Represents an N _r- dimensional unit matrix, and the superscript ^-1 represents the matrix inversion operation;

(9) After the training is over, start the transmission of real useful data. After one frame of transmission ends, if the value of channel-related information R _h changes, return to the first step to re-determine a new training sequence for channel estimation and data transmission in the next frame; if the value of channel-related information R _h If the value does not change, return to step (7) to start the channel estimation and data transmission of the next frame.

In the above channel estimation method, the N _t ×N _t dimensional diagonal matrix D can be obtained by minimizing the following formula under the condition that the trace of the matrix D is normalized to N _t T _τ :

$\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; \{</span>{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \}</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}$

Among them, d _i is the i-th diagonal element of D, λ _i (R _t ) represents the i-th eigenvalue of the spatial correlation matrix R _t at the transmitting end, and λ _j (R _r ) represents the spatial correlation matrix R _r at the receiving end The jth eigenvalue of .

Compared with the prior art, the present invention has the following advantages:

(1) The training sequence structure used in the channel estimation is universal and generalized, and can include specific training sequences under the same existing channel conditions and models, such as traditional orthogonal training sequences;

(2) The length of the training sequence generated by the training sequence structure in the channel estimation has adaptive characteristics, and the training time can be adjusted according to different channel spatial domain related conditions and different channel estimation error requirements;

(3) Under the premise of the same training length, the estimation error of channel estimation via the training sequence is significantly smaller than that of using the orthogonal training sequence;

(4) Under the premise of the same channel estimation error, the length of the training sequence should be smaller than the length of the orthogonal training sequence, thereby reducing training overhead and improving system bandwidth utilization;

(5) The training sequence design idea is universal and can be effectively combined with MIMO precoding technology and adaptive transmission technology.

Description of drawings

Fig. 1 is the functional block diagram of the MIMO channel estimation/data detection system based on the training sequence of the present invention

Fig. 2 is a schematic diagram of the training sequence design idea of the present invention

Fig. 3 is the flow chart of adaptive channel estimation of the present invention

Fig. 4 is a comparison diagram of the training sequence of the present invention and the traditional orthogonal training sequence estimation performance

Fig. 5 is the relationship diagram of the length adaptation and estimation accuracy of the training sequence of the present invention

Detailed ways

The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings.

收发两端通过一条独立于数据传输的无差错的双向链路即前向链路和反馈链路来实现信息共享和参数控制之间的交互，从而建立自适应信道估计机制。With reference to Fig. 1, the principle of the MIMO channel estimation/data detection system based on the training sequence of the present invention is that at the beginning of each data frame/grouping, at first transmit a certain number of training symbols known at both ends of the transceiver, called the training sequence S _τ . According to the received signal X _τ and training sequence S _τ in the training period, the receiver uses the minimum mean square error MMSE estimation criterion to estimate the channel parameter matrix in the frame After the training period, the real information data symbol S _d starts to be transmitted, and the receiver uses the estimated channel parameters Demodulate/decode the original data information from the received signal X _d in the data transmission stage

The two ends of the transceiver realize the interaction between information sharing and parameter control through an error-free bidirectional link independent of data transmission, that is, the forward link and the feedback link, so as to establish an adaptive channel estimation mechanism.

Referring to FIG. 2 , the starting point of the training sequence design of the present invention is to fully and effectively utilize known channel related information to improve the performance and robustness of channel estimation. The focus of its consideration is the spatial domain fading correlation of the channel, and the Kronecker correlation model is used to model the spatial domain fading correlation. The main factor reflecting the adaptive principle in the training sequence structure is the controllability of the training length. The evaluation standard adopted in the training sequence design is the minimum mean square error MMSE estimation criterion. In the calculation of deriving the minimum mean square error, the matrix theory is used The derivation of the optimal training sequence is carried out with the optimization principle.

Referring to Fig. 3, the channel estimation system of the present invention is a MIMO system, which has N _t transmitting antennas and N _r receiving antennas, the current N _t ×N _r dimensional channel state matrix is H, and the training sequence length is T _τ , The T _τ × N _t- dimensional training sequence matrix in the entire training period is written as S _τ , the T _τ × N _r- dimensional received signal matrix is X _τ , and the T _τ × N _r- dimensional received complex Gaussian white noise matrix is N _τ . There is a two-way link between the transmitter and receiver in this system, that is, the forward link from the transmitter to the receiver and the feedback link from the receiver to the transmitter. The wireless link between the two-way link and the transceiver antenna The communication link is independent and is only used to transmit a small amount of interactive control information. The communication frequency band is independent from the service data transmission frequency band, and the transmission rate is low, which can be considered as error-free transmission. The receiver in this system can obtain the second-order statistical correlation information of the channel, that is, the spatial correlation matrix R _t of the transmitting end of the channel and the spatial correlation matrix R _r of the receiving end of the channel, and can better track the changes of the channel related information. The specific channel estimation process is as follows:

1. Obtain the second-order statistical related information R _h of the current channel

R_t，

表示矩阵间的直积；该信道相关矩阵R_h的秩为K，记作K＝rank(R_h)；The receiver performs a matrix direct product operation on the known spatial correlation matrix R _t at the transmitting end and the spatial correlation matrix R _r at the receiving end to obtain the second-order statistical correlation information R _h of the current channel, that is, R _h =R _r

R _t ,

Indicates the direct product between matrices; the rank of the channel correlation matrix R _h is K, recorded as K=rank(R _h );

2. Select the training sequence length T _τ ′ for channel estimation

表示向上取整，即可保证估计的可靠性和数据传输速率最大化之间的最优折中；The length of the training sequence T _τ ′ is selected by using the theory of non-coherent capacity and the requirement of the receiver for estimation error performance, that is, according to the principle that the number of independent parameters in the N _t ×N _r dimensional channel matrix H is equal to the rank K of _Rh , According to the maximization criterion of system capacity, choose

Indicates that rounding up can guarantee the optimal compromise between the estimated reliability and the maximum data transmission rate;

3. Determine the final training sequence length T _τ for channel estimation

above threshold It is optimal in theory, but in specific applications, it is necessary to adjust the length of the training sequence according to the limitation of the actual system on the training time and the receiver's requirements on the performance of the mean square error of the current channel estimation. The basic principle of adjustment is to reduce the training overhead as much as possible under the premise of ensuring the performance requirements of the estimation error and the data transmission rate required by the business.

4. The receiver feeds back the final determined training sequence length T _τ and channel related information R _h to the transmitter through the feedback link between the receiver and the transmitter;

5. Determine the diagonal matrix D _τ in the training sequence structure

According to the feedback information, the transmitter determines the specific structure of the matrix D _τ according to the following two situations:

When T _τ ≥ N _t , take ${\mathrm{D.}}_{\mathrm{\&tau;}}^{1/2}=\left[\begin{array}{c}{\mathrm{D.}}^{1/2}\\ 0_{(T_{\mathrm{\&tau;}}-N_t)\&times;N_t}\end{array}\right],$

When T _τ <N _t , take ${\mathrm{D.}}_{\mathrm{\&tau;}}^{1/2}={\mathrm{D.}}_{[1:T_{\mathrm{\&tau;}},:]}^{1/2},$ That is, take the first T _τ rows of D ^1/2 ,

Wherein, the matrix D is an N _t ×N _t dimensional diagonal square matrix. This matrix D can be obtained by minimizing the following formula, namely

$\mathrm{<span\; class="notranslate">\; tr</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}<span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}$

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; tr</span>}{<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; \&CircleTimes;</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}<span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}$

$<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; \{</span>{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \}</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}$

where tr represents the trace of the matrix, d _i is the i-th diagonal element of D, λ _i (R _t ) represents the i-th eigenvalue of the spatial correlation matrix R _t at the transmitting end, and λ _j (R _r ) represents the receiving The jth eigenvalue of the terminal spatial domain correlation matrix R _r , ρ _τ represents the average transmit power in the training period.

The above formula can be solved iteratively through optimization theory, and the optimization constraint is that the trace of matrix D is normalized to N _t T _τ . For the four different cases of high SNR and low SNR, only the spatial correlation at the receiving end and only the spatial correlation at the transmitting end, the above formula can be obtained by Lagrange number multiplication and limit approximation method to obtain a closed-form solution;

6. Generate the training sequence S _τ from the above diagonal matrix D _τ , namely

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; u</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{<span\; class="notranslate">\; *</span>}$

The training sequence structure consists of three parts. Among them, U is an arbitrary T _τ × T _τ dimensional unitary matrix, such as a Fourier matrix, and the word "arbitrary" ensures the generality and wide inclusiveness of the structure; U _t is the eigenvalue decomposition of the correlation matrix R _t at the transmitter The N _t ×N _t -dimensional eigenvector unitary matrix in ; the number of rows of the matrix D _τ is equal to the length of the training sequence, so the training sequence structure can generate training sequences of any length and is adaptive.

It can be proved that when there is no spatial domain correlation in the channel, S _τ is an orthogonal matrix, that is to say, the traditional orthogonal training sequence is an application of a specific case in this invention;

7. The transmitter notifies the receiver of the specific value of the currently used training sequence S _τ through the forward link from the transmitter to the receiver;

8. Start the training period, the transmitter transmits the training sequence S _τ to the wireless channel H through the transmitting antenna, and the signal received by the receiver within T _τ symbol periods can be expressed as a T _τ ×N _t -dimensional matrix X _τ . The mathematical description of the sending and receiving signals in the training phase is as follows:

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}$

$<span\; class="notranslate">\; \&DoubleRightArrow;</span>\mathrm{<span\; class="notranslate">\; vec</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}<span\; class="notranslate">\; \&CircleTimes;</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; vec</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; vec</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; \&DoubleRightArrow;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; tr</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; *</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}$

where x _τ = vec(X _τ ), h=vec(H) represent the column accumulation vectors of the received signal matrix X _τ and channel matrix H respectively, ρ _τ represents the average transmit power in the training period, ${\tilde{S}}_{\mathrm{\&tau;}}=(I_{N_r}\&CircleTimes;S_{\mathrm{\&tau;}}),$ I _Nr represents the N _r- dimensional unit matrix;

9. According to the above-mentioned received signal X _τ and the notified training sequence S _τ , the receiver adopts the minimum mean square error MMSE estimation criterion, and obtains the estimated value of the current channel coefficient by the following formula

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; *</span>}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; *</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}$

的列堆积向量，相应的估计均方误差MSE为：In the formula $\hat{h}=\mathrm{vec}\left(\hat{h}\right)$ Represents the channel estimation matrix

The column-stacked vector of , the corresponding estimated mean square error MSE is:

$\mathrm{<span\; class="notranslate">\; MSE</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; tr</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}^{<span\; class="notranslate">\; *</span>}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}}_{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ;</span>$

10. After the training is over, start the transmission of real useful data

After one frame of transmission ends, if the value of channel-related information R _h changes, return to the first step to re-determine a new training sequence for channel estimation and data transmission in the next frame; if the value of channel-related information R _h If the value does not change, return to step 8 to start the channel estimation and data transmission of the next frame.

The technical effects of the present invention will be further described in detail below with reference to the accompanying drawings.

Referring to Figure 4, assuming a MIMO system with 4 transmissions and 4 receptions, the spatial correlation coefficients at both ends of the transmission and reception are the same, and the exponential correlation coefficient generation model is used, and R _r (i, j) = R _t (i, j) = r ^|ij| , i, j=1, 2, 3, 4, |r|≤1, the larger the value of r, the stronger the spatial correlation. The training length is 4 symbol periods. In FIG. 4, 'ort' represents a traditional orthogonal training sequence, and 'opt' represents a training sequence used in the present invention. It is not difficult to see that although the mean square error of the channel estimation corresponding to the two training sequences will gradually decrease with the increase of the signal-to-noise ratio. However, the estimation performance of the training sequence of the present invention is better than that of the traditional orthogonal training sequence, and with the enhancement of channel spatial domain correlation, the performance improvement is more significant.

Referring to Figure 5, it is still assumed that a 4-transmission and 4-reception MIMO system is used, taking the comparison of the following three situations as an example:

(1) Assuming no spatial correlation, take T _τ = 4;

(2) Assume that there is no receiving correlation, but there is spatial correlation at the transmitting end, and its correlation matrix has three eigenvalues of 2, 1.5, and 0.5, satisfying tr(R _t )=4, at this time, K=12, take $T_{\mathrm{\&tau;}}=\frac{K}{N_r}=3;$

(3) further ignore the 4 smaller positive eigenvalues in _Rh , that is, take K=8, at this time $T_{\mathrm{\&tau;}}=\frac{K}{N_r}=2.$

From the relationship curves of the estimated mean square error with the change of SNR in the three cases given in Figure 5, it can be seen that although the case (2) reduces the training overhead by 25% compared with the case (1), its estimated variance is still smaller than the case ( 1); case (3) uses 50% less training overhead than case (1), and its estimated variance is also better than case (1) at low SNR. This shows that using less training symbols under the correlated channel can still obtain the estimation performance not worse than that under the independent channel condition. At the same time, it is explained that the training sequence of the present invention can make adaptive adjustments to the length of the training sequence in response to changes in the strength of channel correlation and the level of receiver estimation performance, so as to minimize the training overhead on the basis of meeting the estimation performance requirements. Maximize the data transmission rate and improve the frequency band utilization.

Claims (2)

1. A MIMO correlation channel estimation method based on adaptive training sequence, comprising the steps: (1) The receiver performs a matrix direct product operation on the known spatial correlation matrix R _t at the transmitter and R _r at the receiving end to obtain the second-order statistical correlation information R _h of the current channel, namely

Indicates the direct product between matrices, and the rank K of the channel correlation matrix R _h is denoted as K=rank(R _h ); (2) Determine the length of the training sequence used for channel estimation according to the K value, namely where N _r represents the number of receiving antennas,

Indicates rounding up; (3) The receiver feeds back the determined training sequence length T _τ and channel related information R _h to the transmitter through the feedback link between the receiver and the transmitter; (4) The transmitter determines the diagonal matrix D _τ in the training sequence structure according to the feedback information, When T _τ ≥ N _t , take

When T _τ ≥ N _t , take where N _t represents the number of transmit antennas,

Represents a (T _τ -N _t )×N _t -dimensional matrix of all zeros, and the superscript ^1/2 represents the square root of the matrix,

Indicates that the first T _τ rows of D ^1/2 are taken, and the matrix D is a N _t ×N _t dimensional diagonal matrix; (5) Generate the training sequence S _τ from the above matrix D _τ , namely

Among them, U is an arbitrary T _τ × T _τ dimensional unitary matrix; U _t is the N _t × N _t dimensional eigenvector unitary matrix in the eigenvalue decomposition of the transmitter correlation matrix R _t , and the superscript ^* represents the conjugate of the matrix Transpose operation; (6) The transmitter notifies the receiver of the specific value of the currently used training sequence S _τ through the forward link from the transmitter to the receiver; (7) Start the training period, the transmitter transmits the training symbol S _τ to the wireless channel H through the transmitting antenna, and the signal received by the receiver within T _τ symbol periods can be expressed as a T _τ ×N _t -dimensional matrix X _τ ; (8) According to the above-mentioned received signal X _τ and the notified training sequence S _τ , the receiver adopts the minimum mean square error MMSE estimation criterion, and obtains the estimated value of the current channel coefficient by the following formula

in,

x _τ ＝vec(X _τ ), denote the channel estimation matrix respectively

and the column stacked vector of the received signal matrix X _τ , ρ _τ represents the average transmit power in the training period,

Represents an N _r- dimensional unit matrix, and the superscript ^-1 represents the matrix inversion operation; (9) After the training is over, start the transmission of real useful data. After the transmission of one frame, if the value of the channel-related information R _h changes, return to the first step to re-determine a new training sequence, and proceed to the next frame. Channel estimation and data transmission; if the value of the channel-related information R _h does not change, return to step (7) to start the channel estimation and data transmission of the next frame. 2. The channel estimation method according to claim 1, wherein the N _t ×N _t dimensional diagonal matrix D can be obtained by minimizing the following formula under the condition that the normalization of the matrix D is satisfied as N _t T _τ : Among them, d _i is the i-th diagonal element of D, λ _i (R _t ) represents the i-th eigenvalue of the spatial correlation matrix R _t at the transmitting end, and λ _j (R _r ) represents the spatial correlation matrix R _r at the receiving end The jth eigenvalue of .

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