CN114221839B - Large-scale MIMO downlink channel estimation method based on reconstructed Hank matrix - Google Patents
Large-scale MIMO downlink channel estimation method based on reconstructed Hank matrix Download PDFInfo
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Abstract
The invention discloses a large-scale MIMO downlink channel estimation method based on a reconstructed Hank matrix. The method comprises the following implementation steps: firstly, modeling a channel; the base station end sends a plurality of pilot signals and the user end receives data; the base station end does not send pilot signals and the user end receives data; designing an optimization problem based on a reconstructed Hank matrix; and solving an optimization problem and channel estimation. The method belongs to a gridless method, and can avoid the problem of base mismatch of the traditional compressed sensing method; secondly, compared with the traditional method, the method can obviously reduce pilot frequency overhead; finally, when the method of the invention receives data at the user end, the noise parameters of the base station receiver are obtained, so that the model has denoising capability, and the accuracy of channel estimation is improved.
Description
Technical Field
The invention belongs to the technical field of wireless communication, in particular to the field of channel estimation of a large-scale MIMO (Massive MIMO) structure communication system, and particularly relates to a large-scale MIMO downlink channel estimation method based on a reconstructed Hank matrix.
Background
Large-scale multiple-input multiple-output (Massive MIMO) is one of the key technologies of the 5G mobile communication system, and has the advantages of high spectral efficiency and high energy efficiency. While the above advantage is obtained on the premise that accurate Channel State Information (CSI) is obtained.
In modern wireless communication systems, CSI acquisition in massive MIMO has been a hotspot in industry research. Since the uplink and downlink channels in a Time Division Duplex (TDD) system use the same frequency point, the uplink and downlink channel state information has reciprocity, i.e., the downlink channel state information is generally considered to be the same as the uplink channel state information, so that huge downlink channel training and feedback overhead can be omitted in the TDD system. However, there is a serious pilot pollution problem in a TDD mode multi-cell scenario of massive MIMO, and when only half of the effective operating time of the TDD system is available in the same time resource, the Frequency Division Duplex (FDD) mode still occupies a dominant position in the current wireless communication system.
In FDD systems, the uplink and downlink are in different frequency bands, so that the uplink and downlink CSI is no longer reciprocal, and the base station needs to estimate the downlink CSI uniquely. While estimating the downlink CSI requires two phases: firstly, a base station transmits pilot signals to all users, and then all users receive the pilot signals to estimate downlink CSI and feed the downlink CSI backAnd (5) a base station. The cost caused by downlink channel estimation of a large-scale MIMO system in the FDD mode is proportional to the number of antennas at a base station end, and a large amount of cost seriously affects the performance of the system, so that the research on how to reduce or remove the cost of downlink CSI measurement in the FDD large-scale MIMO system is very significant. Currently, methods based on compressed sensing (CS, compressed Sensing) are mostly used. Researchers have proposed that the angular domain sparsity of FDD Massive MIMO system channels can be exploited while combining the angular domain reciprocity of the uplink and downlink to obtain effective information of the channel, reducing training and feedback overhead (see documents M.Wang, F.Gao, S.Jin and h.lin, "An Overview of Enhanced Massive MIMO With Array Signal Processing Techniques," in IEEE Journal of Selected Topics in Signal Processing, vol.13, no.5, pp.886-901, sept.2019.). Typical downlink channel estimation methods are DFT-based downlink channel estimation methods (see literature: E.J.Candi, J.Romberg, and T.Tao, "Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol.52, no.2, pp.489-509, feb.2006.), which first construct a discrete Fourier transform basis, represent channel matrix vectors with the Fourier transform basis, and then construct l by constructing l 0 The problem of norm minimization restores the channel matrix vector, typically l 0 The norm problem cannot get an accurate solution, so will l under certain conditions 0 Conversion of the norm problem to l 1 The norm problem is solved, but the method is only applicable to uniform linear arrays, grid points are required to be preset, and the problem of base mismatch is caused. In order to solve the above problems, researchers have proposed a gridless Bayesian method (see document: J.Dai, A.Liu and V.K.N.Lau, "FDD Massive MIMO Channel Estimation With Arbitrary D-Array Geometry," in IEEE Transactions on Signal Processing, vol.66, no.10, pp.2584-2599,15 May15,2018.) which is an improvement of the DFT-based downlink channel estimation method described above, and further reduces the occurrence of the problem of basis mismatch by superimposing grid spacing points such that the preset grid point angle approaches to the true angle of arrival or departure. However, the above methods all require presettingThe grid point angle, while the angle may be an arbitrary value in reality, is unavoidable, and thus a problem of base mismatch occurs.
Disclosure of Invention
The invention aims to provide a large-scale MIMO downlink channel estimation method based on a reconstructed Hank matrix aiming at the defects of the existing compressed sensing method.
The method of the invention is as follows:
step (1) channel modeling;
in the FDD system, a uniform linear array is adopted by a base station antenna, the number of array elements is N, each user only comprises one antenna and is a flat fading channel, and a downlink channel vector from a base station to a kth user is expressed as follows by referring to an SCM channel model proposed by 3GPP general standard organization:wherein N is c Indicating the number of scattering clusters, N s Representing the number of sub-paths per scattering cluster, < >>Complex gain of the s-th sub-path representing the c-th scattering cluster,/for>An exit angle of an s-th sub-path representing a c-th scattering cluster; when the base station antenna array is a uniform linear array, then the array response vector a (θ) is expressed as: />Wherein λ represents wavelength, d represents interval between any two adjacent array elements, +.>Is the imaginary unit, [] T Representing the transpose operation.
Step (2), the base station end transmits a plurality of pilot signals and the user end receives data;
base station end sends pilot signalAnd the user knows the pilot signal, L represents the number of beats, < >>Representing a complex set; the received signal at the user terminal is: y=sh+n; wherein n represents additive white gaussian noise with a mean of 0 and a variance of sigma 2 H represents a channel.
Step (3), the base station end does not send pilot signals and the user end receives data;
the base station end does not send pilot signals, and then the receiving signals of the user end are: epsilon=n'; n and n' are independently co-distributed.
Step (4) designing an optimization problem based on a reconstructed Hank matrix;
when N is odd number, hanker matrixH is a function of H, and the optimization problem based on the reconstruction of the hank matrix is as follows:
wherein I * Representing the core norms 2 Representing the binary norm. H1, H1:]represents the first line of H, H [:, end]Represents the last column of H, H1 (N+1)/2]Represents a vector constituted by 1 st to (n+1)/2 nd elements of h.
When N is an even number, the number,the optimization problem based on the reconstructed Hank matrix is as follows:
step (5) solving an optimization problem and channel estimation;
solving an optimization problem based on a reconstructed Hank matrix to obtain an estimated value of h, namely an estimated value of a channel.
The optimization problem of reconstructing the hank matrix belongs to a convex optimization problem, the solution is performed by a cvx solver, and the downloading and the use of the cvx solver can be referred to as follows: http:// cvxr.com/cvx/download/.
Compared with the prior art, the invention has the following beneficial effects:
the method of the invention utilizes the signal to be estimated to reconstruct the Hank matrix, receives the data construction constraint condition through the user terminal, and minimizes the nuclear norm of the Hank matrix after reconstruction. Firstly, the method belongs to a gridless method, and can avoid the problem of base mismatch of the traditional compressed sensing method; secondly, compared with the traditional method, the method can obviously reduce pilot frequency overhead; finally, when the method of the invention receives data at the user end, the noise parameters of the base station receiver are obtained, so that the model has denoising capability, and the accuracy of channel estimation is improved.
Drawings
FIG. 1 is a block diagram of the overall flow of the method of the present invention;
FIG. 2 is a schematic view of line-of-sight transmission;
fig. 3 is a schematic diagram showing the channel estimation accuracy of the method of the present invention compared with the prior other methods at different grid points;
FIG. 4 is a schematic diagram showing the channel estimation accuracy of the method of the present invention compared with other methods in the prior art at different signal to noise ratios;
fig. 5 is a schematic diagram showing the channel estimation accuracy of the method of the present invention compared with that of other methods in the prior art under different pilot numbers.
Detailed Description
The technical scheme and effect of the invention are further described in detail below with reference to the accompanying drawings.
Referring to fig. 1, the implementation steps of the present invention are as follows.
Step one: and (5) modeling a channel. Considering an FDD system, a base station antenna adopts a uniform linear array, the number of array elements is N, each user only comprises one antenna and is a flat fading channel, and a downlink channel vector from a base station to a kth user is expressed as follows by referring to an SCM channel model proposed by 3GPP general standard organization:wherein N is c Indicating the number of scattering clusters, N s Representing the number of sub-paths per scattering cluster, < >>Complex gain of the s-th sub-path representing the c-th scattering cluster,/for>An exit angle of an s-th sub-path representing a c-th scattering cluster; when the base station antenna array is a uniform linear array, then the array response vector a (θ) is expressed as: />Wherein λ represents wavelength, d represents interval between any two adjacent array elements, +.>Is the imaginary unit, [] T Representing the transpose operation.
The invention sets the interval of adjacent antennas to be less than or equal to half wavelength of the received signal to ensure that the array does not generate grating lobes within the range of the angle of view of-90 degrees and 90 degrees. If the angle of view is less than [ -90 deg., 90 deg. ], then adjacent antenna spacing greater than half wavelength of the received signal can be obtained on the principle that grating lobes are not generated within the corresponding range. And attenuation of signal quality caused by a long transmission distance of a transmitting end and shadow shielding of a large obstacle in a transmission environment is called large-scale fading. Path loss and shadowing fading are used to describe the characteristics of large-scale fading. The path loss is attenuation at the receiving end caused by long-distance propagation of power of a transmitted signal, and is an energy diffusion loss. Depending on whether there is a direct path between the transmitting and receiving ends, the method is divided into line-of-sight propagation (LineofSight, LOS) and non-line-of-sight propagation (Non Line of Sight, NLOS). With particular reference to fig. 2. The method considers LOS situations, namely paths in corresponding direct path clusters are direct paths, the number of channel path clusters is usually less than or equal to 3, and corresponding parameter fluctuation is small.
Step two: base station end sends pilot signalAnd the user knows the pilot signal, L represents the number of beats, < >>Representing a complex set; the received signal at the user terminal is: y=sh+n; wherein n represents additive white gaussian noise with a mean of 0 and a variance of sigma 2 H represents a channel.
Step three: the base station end does not transmit pilot signals and the user end receives data. The base station end does not send pilot signals, and then the receiving signals of the user end are: epsilon=n'; n and n' are independently co-distributed.
The method comprises the step of obtaining noise parameters of a base station receiver, and providing information for denoising for a later model based on the reconstruction Hank matrix optimization problem, namely providing support for model denoising.
Step four: the optimization problem based on the reconstruction of the hanker matrix is designed. Let H be the Hanker matrix and H be a function of H. When N is an odd number, the number of the N,the optimization problem based on the reconstructed hanker matrix is as follows:
wherein I * Representing the core norms 2 Representing the binary norm. H1, H1:]represents the first line of H, H [:, end]Represents the last column of H, H1 (N+1)/2]Represents a vector constituted by 1 st to (n+1)/2 nd elements of h, and the rest are similar. When N is an even number, the number,the optimization problem based on the reconstructed hanker matrix is as follows:
the hank's matrix is characterized by elements that lie on the same diagonal that are all identical. The kernel norm of the matrix is equal to the momentAll singular values of the array are summed. The model built in this step is y-Sh 2 ≤||ε|| 2 I.e. comprising a denoising operation, wherein epsilon is exactly the base station noise parameter obtained in step three. In addition, in this step, when N is an even number, the optimization problem may also take the form of:
step five: and solving an optimization problem and channel estimation. Solving an optimization problem based on a reconstructed Hank matrix to obtain an estimated value of h, wherein the estimated value is the estimated value of the channel.
The optimization problem based on the reconstructed hank matrix in this step belongs to a convex optimization problem, and the solution is performed by a published cvx solver, and the downloading and the use of the cvx solver can be referred to as follows: http:// cvxr.com/cvx/download/.
The effects of the present invention are further explained below in conjunction with three simulation examples.
Simulation example 1: selecting the number of base station antennas N=123, the snapshot number T=120, the antenna interval d=lambda/2, and using LOS channel and scattering cluster N c =3, sub-path N of each scattering cluster s =10, then the total number of channels paths l=n c N s =30, angular spread Δ θ Number of monte carlo experiments M =1° c =500. The channel path gain is set as a random complex gain, and the arrival angles AOD of the centers of three channel paths are [ -pi/3, pi/3]The inner parts are uniformly distributed. The antennas at the base station adopt uniform linear arrays, and the number of grid points ranges from 120 to 200. The algorithm provided by the invention is compared with a channel estimation algorithm based on a compressed sensing algorithm OMP and an offgrid-Bayesian algorithm.
Simulation example 2: selecting the number of base station antennas N=123, the snapshot number T=120, the antenna interval d=lambda/2, and using LOS channel and scattering cluster N c =3, sub-path N of each scattering cluster s =10, then the total number of channels paths l=n c N s =30, angular spread Δ θ Number of monte carlo experiments M =1° c =500. The channel path gains are set to be random complex gains, threeThe channel path center arrival angle AOD is [ -pi/3, pi/3]The inner parts are uniformly distributed. The antenna at the base station adopts a uniform linear array, and the signal to noise ratio variation range is-10 dB to 10dB. The algorithm provided by the invention is compared with a channel estimation algorithm based on a compressed sensing algorithm OMP and an offgrid-Bayesian algorithm.
Simulation example 3: selecting the number of base station antennas N=123, SNR= -5dB, antenna interval d=lambda/2, adopting LOS channel, scattering cluster N c =3, sub-path N of each scattering cluster s =10, then the total number of channels paths l=n c N s =30, angular spread Δ θ Number of monte carlo experiments M =1° c =500. The channel path gain is set as a random complex gain, and the arrival angles AOD of the centers of three channel paths are [ -pi/3, pi/3]The inner parts are uniformly distributed. The antennas at the base station are in a uniform linear array, and the pilot frequency number ranges from 60 to 110. The algorithm provided by the invention is compared with a channel estimation algorithm based on a compressed sensing algorithm OMP and an offgrid-Bayesian algorithm.
As can be seen from the comparison of the normalized mean square error performance of fig. 3, the method based on the reconstructed hank is significantly better than the other two methods, because the downlink channel estimation method based on the hank matrix is a gridless method, and the other two algorithms are gridless methods, the method based on the reconstructed hank matrix does not have the problem of base mismatch, the estimation precision is increased, and the estimation performance of the two methods is unstable along with the change of grid points, because the change of the correlation of the sensing matrix in the compressed sensing method is caused along with the change of the grid points, thereby affecting the estimation precision.
As can be seen from the normalized root mean square error performance comparison diagram of fig. 4, the method based on the reconstruction hank is obviously superior to the other two methods, and the estimation accuracy of the three methods is gradually increased along with the increase of the signal to noise ratio, because the influence of noise on the signal is smaller and smaller along with the increase of the signal to noise ratio, but the range of the channel estimation accuracy change of the two methods along with the increase of the signal to noise ratio is smaller, and the estimation accuracy of the method based on the reconstruction hank matrix is gradually increased along with the change of the signal to noise ratio, and the change is obvious.
As can be seen from the comparison of the normalized root mean square error performance of FIG. 5, the method based on the reconstruction of the Hank matrix has significantly better estimation accuracy than the other two methods under the same pilot overhead, and the advantages of the method are reflected.
The foregoing description is only exemplary of the invention and is not intended to limit the invention to the particular embodiments disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.
Claims (2)
1. The large-scale MIMO downlink channel estimation method based on the reconstructed Hank matrix is characterized by comprising the following steps of:
step (1) channel modeling;
in the FDD system, a uniform linear array is adopted by a base station antenna, the number of array elements is N, each user only comprises one antenna and is a flat fading channel, and a downlink channel vector from a base station to a kth user is expressed as follows by referring to an SCM channel model proposed by 3GPP general standard organization:wherein N is c Indicating the number of scattering clusters, N s Representing the number of sub-paths per scattering cluster, < >>Complex gain of the s-th sub-path representing the c-th scattering cluster,/for>An exit angle of an s-th sub-path representing a c-th scattering cluster; when the base station antenna array is a uniform linear array, then the array response vector a (θ) is expressed as: />Wherein λ represents wavelength, d represents interval between any two adjacent array elements, +.>Is the imaginary unit, [] T Representing a transpose operation;
step (2), the base station end transmits a plurality of pilot signals and the user end receives data;
base station end sends pilot signalAnd the user knows the pilot signal, L represents the number of beats, < >>Representing a complex set; the received signal at the user terminal is: y=sh+n; wherein n represents additive white gaussian noise with a mean of 0 and a variance of sigma 2 H represents a channel;
step (3), the base station end does not send pilot signals and the user end receives data;
the base station end does not send pilot signals, and then the receiving signals of the user end are: epsilon=n'; n and n' are independently and identically distributed;
step (4) designing an optimization problem based on a reconstructed Hank matrix;
when N is odd number, hanker matrixH is a function of H, and the optimization problem based on the reconstruction of the hank matrix is as follows:
wherein I * Representing the core norms 2 Representing the binary norms; h1, H1:]represents the first line of H, H [:, end]Represents the last column of H, H1 (N+1)/2]Represents a vector constituted by 1 st to (n+1)/2 nd elements of h;
when N is an even number, the number,the optimization problem based on the reconstructed Hank matrix is as follows:
or (I)>
Step (5) solving an optimization problem and channel estimation;
solving an optimization problem based on a reconstructed Hank matrix to obtain an estimated value of h, namely an estimated value of a channel.
2. The large-scale MIMO downlink channel estimation method based on the reconstructed hanke matrix of claim 1, wherein: the optimization problem of reconstructing the hank matrix belongs to a convex optimization problem, and the solution is performed by a cvx solver.
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