CN113938360B - Distributed MIMO system covariance matrix estimation method based on fingerprint positioning - Google Patents
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Abstract
The invention discloses a distributed MIMO system covariance matrix estimation method based on fingerprint positioning, which aims at the situation that a covariance matrix changes along with time due to rapid environmental change, eliminates interference and noise by introducing random phase shift, and obtains more accurate covariance matrix estimation by changing a pilot frequency distribution mode by using fingerprint positioning so as to solve the problems that the covariance matrix is not known in most of the prior art, the covariance matrix estimation is inaccurate and the calculation complexity is high. Compared with the prior art, the method does not additionally increase pilot frequency, has low calculation complexity on the basis of high estimation accuracy, can further effectively improve the accuracy of covariance matrix estimation by the pilot frequency allocation updating algorithm based on fingerprint positioning, is suitable for various wireless communication systems, and has very important significance for researching non-ideal factors of mobile scenes, so that the method has a certain practical value.
Description
Technical Field
The invention relates to the technical field of distributed MIMO systems, in particular to a distributed MIMO system covariance matrix estimation method based on fingerprint positioning.
Background
Distributed MIMO systems are a practical, scalable network MIMO scenario in which a large number of access points are geographically distributed and connected to one central processing unit to serve all users with the same time-frequency resources. In addition to the advantages of good propagation and channel reinforcement, distributed MIMO also has the characteristics of a distributed architecture, such as macro diversity, no handoff and higher coverage benefits. Therefore, research on channel estimation techniques based on the case where covariance matrix is unknown is becoming more and more important.
However, all of these desirable advantages are largely dependent on accurate channel state information. The covariance matrix of the channel vectors characterizes the spatial correlation and is generally considered to be well known in most techniques. But the covariance matrix is not known in practical situations due to the mobility of the user and the linear relationship between the covariance matrix dimension and the number of antennas. In particular, in the scene of fast channel variation such as high-speed movement, the estimation of covariance matrix to accurately estimate the channel has great benefit for analyzing and optimizing the system performance. Thus, research into covariance matrix estimation techniques with high accuracy and low complexity is becoming increasingly important.
Currently, wireless positioning is receiving increasing attention, especially in next generation communication systems, because location information can provide context-aware communication services. Fingerprint positioning is a fingerprint map based on channel state statistics, and has been widely developed due to higher positioning accuracy in a rich scattering environment. Due to the limitation of the coherence interval length of the channel and the access of a large number of users, the users cannot be guaranteed to be distributed as mutually orthogonal pilots, which leads to pilot pollution and seriously reduces the system performance. Pilot pollution is related to the user location of the shared pilot, and thus pilot pollution can be mitigated by optimizing pilot allocation based on location information. Thus, the estimation accuracy of the covariance matrix can be improved by using the position information, which has an important role in dealing with non-ideal factors in the communication system, however, a solution for fusing the covariance matrix estimation with the positioning information has not yet emerged in the prior art.
Disclosure of Invention
In view of the above, the present invention is directed to providing a distributed MIMO system covariance matrix estimation method based on fingerprint positioning, which is used to solve the problem that the accuracy of channel estimation is not high in the actual situation because the covariance matrix is not considered in the prior art. The invention takes the estimated covariance matrix as the fingerprint to locate, clusters according to the locating information, and further changes the pilot frequency distribution to obtain more accurate covariance matrix estimation, thereby improving the accuracy of covariance matrix estimation.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a distributed MIMO system covariance matrix estimation method based on fingerprint positioning, in the distributed MIMO system, M access points are connected to a central processing unit, each access point has N antennas, K single-antenna users in an area are jointly served, and reference points of Z single antennas are uniformly distributed in a coverage area, the method specifically comprises the following steps:
step S1, establishing an uplink signal transmission model of a distributed MIMO system to obtain a channel estimation expression of a covariance matrix under an unknown condition;
s2, firstly, adopting a channel block fading model, introducing random phase shift, alternately using allocated pilot frequency and the random phase shift of the pilot frequency in adjacent coherent blocks to obtain a received signal expression of the adjacent coherent blocks, then estimating a sample covariance matrix by using the spaced pilot frequency, and finally, receiving a signal observation value by using the adjacent staggered pilot frequency and considering Hermite symmetry to obtain user initial covariance matrix estimation;
step S3, firstly taking a user initial covariance matrix as a user fingerprint, taking covariance matrix estimation of reference points as a fingerprint database, comparing the user fingerprint with the fingerprint database by utilizing Euclidean distance, taking a reference point corresponding to the minimum Euclidean distance as an initial position of the user, then clustering the user by utilizing a K-means algorithm according to the position of the user, and finally adopting orthogonal pilot frequency in the cluster according to a clustering result, and further carrying out pilot frequency redistribution to obtain the accurate covariance matrix estimation of the user.
Further, the step S1 specifically includes:
step S101, consider a block fading channel, and model the channel vector from user k to all access points as:
in the formula (1),λ k,m indicating large scale fading from the mth access point to the kth user, I N Represents an N-dimensional identity matrix, h k Representing a small scale fading, whose elements obey the standard rayleigh distribution +.>
Step S102, assume that there is orthogonal pilot frequency number P with length sigma in the uplink channel estimation<K, use ofRepresenting a subset of users using pilot p, after correlating the received training signal with the conjugate of the pilot sequence, the base station estimates the channel:
in the formula (2), y p The received signals, p being the transmit power,representing noise, sigma, of the transmitted pilot p 2 Representing noise power;
due to g k Satisfy the following requirementsThen for->Channel g k The expression of the minimum mean square error MMSE estimate is:
in the formula (3), I MN Represents an M x N-dimensional identity matrix, and is sigma p For covariance matrix of received signal, Λ i Channel g representing user i i Is a covariance matrix of (a).
Step S103, because of Λ k Sum sigma p Are unknowns and therefore translate equation (3) into:
in the formula (4) of the present invention,and->Respectively represent lambda k Sum sigma p Is a function of the estimate of (2).
Further, the step S2 specifically includes:
step S201, firstly, assume that the channel is a block fading model, specifically, that the channel is in sigma c ＝B c T c Unchanged in each symbol, wherein B c Expressed as coherence bandwidth, T c Expressed as time, then assume the covariance matrix at σ s Constant within each coherent block and finally using the uncorrelation of random phase shift to eliminate interference and noise, so each user alternates transmission of assigned pilot X in adjacent coherent blocks p And phase shift pilot Φ k The method comprises the following steps:
in the formula (5), Φ k [2n]Representing the phase shift pilot frequency transmitted by the 2 n-th coherent block user k, X p [2n-1]Pilot p, n=1, 2, representing pilot allocation of the 2n-1 th coherent block to user k k,2n Random phase shift for the 2 n-th coherent block of k users, which is independent of channel vector and noise and satisfies
Step S202, selecting N ∑ ≤σ s Covariance matrix sigma of 2 interval coherent block estimated received signal p The expression is:
in the formula (6), y p [2n-1]Received signal representing the 2N-1 th coherent block, N ∑ Representation for estimating sigma p Is marked with a superscript (·) for the number of coherent blocks H Represents the conjugate transpose of the object,sample covariance matrix sigma expressed as received signal p Is determined by the estimation of (a);
step S203, in order to estimate Λ k Adjacent coherent blocks are required for decorrelation, and therefore pilots are sent to adjacent coherent blocks, and the received signal observations are:
in the formula (7) and the formula (8),representing the observation of the received signal when user k transmits the 2n-1 st coherent block pilot signal, for>Representing the received signal observations, θ, when user k transmits the 2 n-th coherent block pilot signal i,2n Representing the random phase generated by the pilot sequence generator at the 2 n-th coherent block for user i.
Taking into account that the signal is free from noise and random phase shift θ k,2n To cancel interference by observation of adjacent coherent blocks, forThe covariance matrix of the estimated channel can be obtained according to the correlation of the observed values of the adjacent staggered pilot frequency receiving signals is:
user initial covariance matrix considering hermite symmetryThe expression of (2) is:
in the formula (10), N Λ Representation for estimating Λ k The number of coherent block pairs required.
Further, the step S3 specifically includes:
step S301, respectively calculating covariance matrix estimation of the reference point and the user, wherein the covariance matrix estimation of the reference point approximately adopts orthogonal pilot frequency, and the orthogonal pilot frequency is used as a fingerprint databaseWherein (1)>Representing a covariance matrix estimated from the reference point 1 to the reference point Z as a fingerprint in a fingerprint database; estimating a user initial covariance matrix of user k>As a user fingerprint, the user fingerprint is compared with a fingerprint database, the Euclidean distance is used for measuring the correlation degree between two different fingerprints, and the expression is as follows:
in the formula (11), the color of the sample is,the ith row and jth column of the user initial covariance matrix denoted as user k>An ith row and a jth column of a covariance matrix estimated by a reference point z in the fingerprint database are represented;
selecting a reference point with the minimum Euclidean distance as an initial position of a user k;
step S302, dividing K users into K users by adopting a K-means clustering algorithm according to the user positioning resultA disjoint cluster, where P represents the number of orthogonal pilots and the set of users in cluster t is denoted Γ, results in a center of gravity t ；
Step S303, for |Γ t |>P clusters, sorting the distances from each user to the corresponding center of gravity, and determining that the P users with the smallest distances directly become one cluster, and the rest |Γ t -P users are saved in set D; for |Γ t |<Clusters of P, additionally randomly selecting P- Γ in set D t The i users form a cluster;
step S304, distributing orthogonal pilot frequency in the cluster, and estimating the accurate covariance matrix of the user k again
The beneficial effects of the invention are as follows:
the method provided by the invention is used for estimating the covariance matrix by considering the problem that the covariance matrix in the actual channel is unknown, and the method provided by the invention does not additionally increase pilot frequency, but only utilizes the special structure of the transmitted pilot frequency to effectively eliminate interference and noise, further relieves pilot frequency pollution by utilizing a fingerprint positioning mode, improves the estimation precision of the covariance matrix, has low calculation complexity and is suitable for various wireless communication systems.
Drawings
Fig. 1 is a schematic diagram of a cellular-free distributed massive MIMO system provided in example 1;
fig. 2 is a flow chart of a distributed MIMO system covariance matrix estimation method based on fingerprint positioning according to embodiment 1;
FIG. 3 is a simulation diagram of a relationship between the number of coherent block pairs of an individual covariance matrix and a normalized mean square error NMSE for channel estimation using different covariance matrix estimation methods, wherein random pilots represent an initial allocation of a random pilot estimation covariance matrix, fingerprint positioning represents a reassignment of a pilot estimation covariance matrix after fingerprint positioning, and via-Q is a covariance matrix estimation using a classical via-Q method;
fig. 4 is a simulation diagram of the correlation block logarithm and the total spectral efficiency for calculating the individual covariance matrix in different covariance matrix estimation methods under MRC and ZF receivers.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
Referring to fig. 1-4, the present embodiment provides a distributed MIMO system covariance matrix estimation method based on fingerprint positioning, which is implemented based on the following massive MIMO system and its uplink received signal model, and specifically includes:
as shown in fig. 1, assuming that a cellular-free distributed massive MIMO system employs a Time Division Duplex (TDD) mode, there are m=5 APs, each AP having n=50 antennas. The reference points are uniformly distributed in the area with r=2km as intervals, the area has k=12 users, and the users are assumed to be equipped with single antennas and are independently distributed to share p=4 pilots, so as to improve the utilization rate of pilot resources.
The channel model consists of three parts: path loss, shadowing and small scale fading, which can be expressed asWherein (1)>Let the path fading factor a=3.7, the reference distance is 1, s m,k To satisfy the shadow fading variable of exponential normal distribution, h m,k Representing a small scale fading, whose elements obey the standard rayleigh distribution +.>Thus user k's uplink channel g to all access points k Satisfy->I.e. < ->The transmission power of each user is ρ=1w, and the noise is related to σ 2 = -63dBm. K users send information at the same time, so that the uplink receiving signal model of the system is that
In formula (1), y represents that the AP receives information from all users, x k Is the information that is to be transmitted and,represent noise, let g k Independent of n.
Based on the above-mentioned non-cellular distributed massive MIMO system and the constructed uplink received signal model, the covariance matrix estimation method provided in this embodiment specifically includes the following steps:
step S1, an uplink signal transmission model of a distributed MIMO system is established, and a channel estimation expression under the condition that a covariance matrix is unknown is obtained:
in this embodiment, step S1 specifically includes:
step S11, assuming the channel is a block fading model, and the channel is set to be a certain phase bandwidth B c And a certain coherence time T c In which the channel remains unchanged, i.e. the channel is at sigma c ＝B c T c Hold constant for 200 symbols. The covariance matrix is constant over the transmission bandwidth and varies slowly over time compared to the rapid variation of the channel vector, so it can be reasonably assumed that it is at σ s Hold constant within 20000 coherent blocks.
Step S12, useRepresenting a subset of users using pilot p, after correlating the received training signal with the conjugate of the pilot sequence, the observations of the base station are:
in the formula (2), y p Representing the received signals of all users transmitting pilot p,representing noise of transmitted pilot p due to g k Satisfy->Then for->Channel g k The minimum mean square error MMSE estimate of (2) should be:
in the formula (3), I MN Represents an M x N-dimensional identity matrix, and is sigma p For covariance matrix of received signal, Λ i Channel g representing user i i Is a covariance matrix of (a).
Step S13, in practical applications, the covariance matrix is usually imperfect, meaning Λ k Sum sigma p Are unknowns and thus convert the channel estimation expression into
In the formula (4) of the present invention,and->Respectively represent lambda k Sum sigma p Is a function of the estimate of (2).
And S2, adopting a channel block fading model, introducing random phase shift, and alternately using the distributed pilot frequency and the random phase shift of the pilot frequency in the adjacent coherent blocks to obtain a received signal expression of the adjacent coherent blocks. Estimating a sample covariance matrix by using the spaced pilot frequency; the alternating received signals are utilized and the Hermite symmetry is considered, so that individual covariance matrix estimation is obtained.
In this embodiment, step S2 specifically includes:
step S21, using the uncorrelation of random phase shift to eliminate interference and noise, so each user alternately transmits the assigned pilot X in the adjacent coherent block p And phase shift pilot Φ k The expression is:
in the formula (5), Φ k [2n]Pilot frequency, X, representing user k of the 2 n-th coherent block p [2n-1]Pilot p, n=1, 2, representing pilot allocation of the 2n-1 th coherent block to user k k,2n 2 n-th coherent block for k usersRandom phase shift, which is independent of channel vector and noise and satisfies
Step S22, selecting N ∑ ＝5000<σ s Coherent block estimation sigma for 2 coherent block intervals p The expression is:
in the formula (6), y p [2n-1]The received signal representing the 2n-1 st coherent block, superscript (·) H Represents conjugate transpose, when N ∑ In the case of a larger number of the pieces,is more accurate.
Step S23, in order to estimate the individual covariance matrix Λ k Adjacent coherent blocks are required for decorrelating, pilot frequencies are transmitted to the adjacent coherent blocks, and the received signal observations are
In the formula (7) and the formula (8),representing the observation of the received signal when user k transmits the 2n-1 st coherent block pilot signal, for>Representing the received signal observations, θ, when user k transmits the 2 n-th coherent block pilot signal i,2n Indicating that user i generates pilot sequence generator at 2 n-th coherent blockIs a random phase of (a) for a random phase of (b).
Taking into account that the signal is free from noise and random phase θ k,2n The present embodiment eliminates interference by observing neighboring coherent blocks, forThe covariance matrix of the channel estimated from the observations of the adjacent interlaced pilot received signals is:
in addition, in view of the hermitian symmetry,should be as follows
In the formula (10), N Λ Representation for estimating Λ k The number of coherent block pairs required.
Step S3, an overall flow chart of the covariance matrix estimation method based on fingerprint positioning is shown in FIG. 2. In the off-line phase, the uplink pilot signal may be transmitted by the single antenna test equipment at each different access point in turn. Thus, there is no mutual interference between the access points. The present embodiment uses estimated reference point covariance matrices as fingerprint databases because they can reflect location information. In the online stage, each user estimates covariance matrix as fingerprint and compares it with fingerprint database. And obtaining an initial position according to the matching result, and clustering the users by using a K-means algorithm. And re-distributing pilot frequency according to the clustering result, re-estimating the covariance matrix, and obtaining more accurate channel estimation. The following specific implementation steps are as follows:
step S31, respectively calculating covariance matrix estimation of the reference point and the user, and taking the covariance matrix estimation of the reference point as a fingerprint databaseWherein (1)>The covariance matrix of the reference point 1 to reference point Z estimate is represented as a fingerprint in the fingerprint database. Estimating a user initial covariance matrix of user k>As a fingerprint, the fingerprint is compared with a fingerprint database, and the Euclidean distance is used for measuring the correlation degree between two different fingerprints
In the formula (11), the color of the sample is,the ith row and jth column of the user initial covariance matrix denoted as user k>An ith row and a jth column of the covariance matrix representing the reference point z estimate in the fingerprint database.
And selecting the reference point with the minimum Euclidean distance as the initial position of the user k.
S32, dividing K users into K groups by adopting a K-means clustering algorithm according to the user positioning resultEach cluster has a center of gravity, and the number of iterations t=20. Where P represents the number of orthogonal pilots and the set of users in cluster t is denoted Γ t 。
Step S33, for |Γ t |>And the P clusters are used for sequencing the distances from each user to the corresponding gravity center, and the P users with the smallest distances are determined to be directly formed into one cluster. The remainder of the L t Keep P users inIn set D; for |Γ t |<Clusters of P, additionally randomly selecting P- Γ in set D t The i users together form a cluster.
Step S34, distributing orthogonal pilot frequency in the cluster, and estimating the accurate covariance matrix of the user k again
The above demonstrates the whole process of performing the covariance matrix estimation of the non-cellular massive MIMO based on fingerprint positioning using the method provided by the present embodiment.
Fig. 3 is a simulation diagram showing the relationship between the number of coherent block pairs used to calculate the individual covariance matrices and the normalized mean square error NMSE of the channel estimate using different covariance matrix estimation methods, wherein the error represents the channel estimation error when the covariance matrices are known and unknown. The random pilot frequency represents an initial allocation random pilot frequency estimation covariance matrix, fingerprint positioning represents a pilot frequency estimation covariance matrix which is reallocated after fingerprint positioning, and via-Q is a classical covariance matrix estimation method which eliminates interference by transmitting pilot frequencies of other users sharing the same pilot frequency. And adopting random pilot frequency allocation in the initial stage, and carrying out covariance matrix re-estimation after fingerprint positioning and pilot frequency re-allocation to obtain a positioning and pilot frequency re-allocation algorithm based on fingerprints. It can be seen that the covariance matrix estimation performance of the method is better than via-Q under the same random pilot allocation, and approaches the case where the covariance matrix is known. Based on fingerprint-based positioning, covariance matrix estimation becomes more accurate due to pilot reassignment.
Fig. 4 is a simulation diagram showing the relationship between the number of coherent block pairs and the total spectral efficiency for calculating the individual covariance matrix in the MRC and ZF receiver using different covariance matrix estimation methods. It can be seen that the covariance matrix estimation method provided in this embodiment has better overall spectrum efficiency than the via-Q method, and further improves system performance after fingerprint positioning and pilot frequency redistribution. At the same time, the total spectral efficiency is related to the number of coherent block pairs N used to calculate the individual covariance matrix estimate Λ Is increased by (a)And increases because the calculated covariance matrix estimate is more accurate. In addition, the system performance of the ZF receiver is better than that of the MRC receiver.
In summary, the invention provides a covariance matrix estimation method of a distributed antenna system for eliminating interference and noise by introducing random phase shift and utilizing cross correlation of allocated pilot frequency and random phase shift pilot frequency, aiming at the covariance matrix estimation problem of the distributed MIMO system, so as to solve the problem that the prior art does not consider that the covariance matrix is unknown, and the accuracy of channel estimation is low in the actual situation. In addition, the estimated covariance matrix is used as a fingerprint for positioning, clustering is carried out according to positioning information, so that pilot frequency allocation is changed to obtain more accurate covariance matrix estimation, the accuracy of covariance matrix estimation is improved, and the method has practical significance.
The present invention is not described in detail in the present application, and is well known to those skilled in the art.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (1)
1. In the distributed MIMO system, a total of M access points are connected to a central processing unit, each access point has N antennas, K single-antenna users in an area are jointly served, and reference points of Z single antennas are uniformly distributed in a coverage area, and the method is characterized by comprising the following steps:
step S1, establishing an uplink signal transmission model of a distributed MIMO system to obtain a channel estimation expression of a covariance matrix under an unknown condition;
s2, firstly, adopting a channel block fading model, introducing random phase shift, alternately using allocated pilot frequency and the random phase shift of the pilot frequency in adjacent coherent blocks to obtain a received signal expression of the adjacent coherent blocks, then estimating a covariance matrix by using the spaced pilot frequency, and finally, receiving a signal observation value by using the adjacent staggered pilot frequency and considering Hermite symmetry to obtain user initial covariance matrix estimation;
step S3, firstly taking a user initial covariance matrix as a user fingerprint, taking covariance matrix estimation of reference points as a fingerprint database, comparing the user fingerprint with the fingerprint database by utilizing Euclidean distance, taking a reference point corresponding to the minimum Euclidean distance as an initial position of the user, then clustering the user by utilizing a K-means algorithm according to the position of the user, and finally adopting orthogonal pilot frequency in the cluster according to a clustering result, and further carrying out pilot frequency redistribution to obtain user accurate covariance matrix estimation;
the step S1 specifically includes:
step S101, consider a block fading channel, and model the channel vector from user k to all access points as:
in the formula (1),λ k,m indicating large scale fading from the mth access point to the kth user, I N Represents an N-dimensional identity matrix, h k Representing a small scale fading, whose elements obey the standard rayleigh distribution +.>
Step S102, assuming that the number P of orthogonal pilots with length tau exists in the uplink channel estimation<K, use ofIndicating that a subset of users using pilot p will receiveAfter correlating with the conjugate of the pilot sequence, the base station estimates the channel:
in the formula (2), y p The received signals, p being the transmit power,representing noise, sigma, of the transmitted pilot p 2 Representing noise power;
due to g k Satisfy the following requirementsThen for->Channel g k The expression of the minimum mean square error MMSE estimate is:
in the formula (3), I MN Represents an M x N-dimensional identity matrix, and is sigma p For covariance matrix of received signal, Λ i Channel g representing user i i Is a covariance matrix of (a);
step S103, because of Λ k Sum sigma p Are unknowns and therefore translate equation (3) into:
in equation (4), the user initial covariance matrixAnd->Respectively represent lambda k Sum sigma p Is determined by the estimation of (a);
the step S2 specifically includes:
step S201, firstly, assume that the channel is a block fading model, specifically, that the channel is at τ c ＝B c T c Unchanged in each symbol, wherein B c Expressed as coherence bandwidth, T c Expressed as time, then assume the covariance matrix is at τ s Constant within each coherent block and finally using the uncorrelation of random phase shift to eliminate interference and noise, so each user alternates transmission of assigned pilot X in adjacent coherent blocks p And phase shift pilot Φ k The method comprises the following steps:
in the formula (5), Φ k [2n]Representing the phase shift pilot frequency transmitted by the 2 n-th coherent block user k, X p [2n-1]Pilot p, n=1, 2, representing pilot allocation of the 2n-1 th coherent block to user k k,2n Random phase shift for the 2 n-th coherent block of k users, which is independent of channel vector and noise and satisfies
Step S202, selecting N ∑ ≤τ s Covariance matrix sigma of 2 interval coherent block estimated received signal p The expression is:
in the formula (6), y p [2n-1]Received signal representing the 2N-1 th coherent block, N ∑ Representation for estimating sigma p Is marked (X) on the coherent block number H Represents the conjugate transpose of the object,represented as covariance matrix sigma of received signal p Is determined by the estimation of (a);
step S203, in order to estimate Λ k Adjacent coherent blocks are required for decorrelation, and therefore pilots are sent to adjacent coherent blocks, and the received signal observations are:
in the formula (7) and the formula (8),representing the observation of the received signal when user k transmits the 2n-1 st coherent block pilot signal, for>Representing the received signal observations, θ, when user k transmits the 2 n-th coherent block pilot signal i,2n Representing the random phase generated by the pilot sequence generator at the 2n coherent block of user i;
taking into account that the signal is free from noise and random phase shift θ k,2n To cancel interference by observation of adjacent coherent blocks, forThe covariance matrix of the channel estimated according to the correlation of the observed values of the adjacent staggered pilot frequency receiving signals is:
considering the hermite symmetry again, the user initial covariance matrixThe expression of (2) is:
in the formula (10), N Λ Representation for estimating Λ k The number of coherent block pairs required;
the step S3 specifically includes:
step S301, approximate adopting orthogonal pilot frequency for covariance matrix estimation of reference point, and using the orthogonal pilot frequency as fingerprint databaseWherein (1)>Representing a covariance matrix estimated from the reference point 1 to the reference point Z as a fingerprint in a fingerprint database; estimating a user initial covariance matrix of user k>As a user fingerprint, the user fingerprint is compared with a fingerprint database, the Euclidean distance is used for measuring the correlation degree between two different fingerprints, and the expression is as follows:
in the formula (11), the color of the sample is,the ith row and jth column of the user initial covariance matrix denoted as user k>An ith row and a jth column of a covariance matrix estimated by a reference point z in the fingerprint database are represented;
selecting a reference point with the minimum Euclidean distance as an initial position of a user k;
step S302, dividing K users into K users by adopting a K-means clustering algorithm according to the user positioning resultA disjoint cluster, where P represents the number of orthogonal pilots and the set of users in cluster t is denoted Γ, results in a center of gravity t ；
Step S303, for |Γ t |>P clusters, sorting the distances from each user to the corresponding center of gravity, and determining that the P users with the smallest distances directly become one cluster, and the rest |Γ t -P users are saved in set D; for |Γ t |<Clusters of P, additionally randomly selecting P- Γ in set D t The i users form a cluster;
step S304, distributing orthogonal pilot frequency in the cluster, and estimating the accurate covariance matrix of the user k again
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