CN105846879B - A kind of iteration beam-forming method in millimeter wave pre-coding system - Google Patents

Abstract

The invention belongs to wireless communication technology fields, a kind of more particularly to method for the antenna training expense for reducing iteration beam forming using interchannel sparsity in wireless multiple-input and multiple-output (Multiple Input Multiple Output, MIMO) communication system.The present invention proposes a kind of iteration beam-forming method in millimeter wave pre-coding system, for overcoming the defect that dominant eigenvalue antenna training expense is excessive in extensive mimo system, this method utilizes the spatial sparsity of millimeter wave channel, sparse Problems of Reconstruction is converted by the estimation problem of received vector in the training of millimeter wave mimo antenna, to reduce loss using the correlation theory of compressed sensing.

Description

An Iterative Beamforming Method in Millimeter Wave Precoding System

technical field

The invention belongs to the technical field of wireless communication, and in particular relates to a method for reducing antenna training overhead of iterative beamforming by utilizing inter-channel sparsity in a wireless multiple input multiple output (MIMO) communication system.

Background technique

Beamforming technology is an array signal processing technology, which can be regarded as spatial linear filtering. In MIMO systems, it can be used to overcome path loss, improve received signal-to-noise ratio, and increase system capacity. In the beamforming technology, the key is to obtain the optimal array signal weight vector of the transceiver end that satisfies the set criteria under the current channel state. Under the optimal capacity criterion, the beamforming weight vector at the transceiver end is a singular vector obtained by singular value decomposition (SVD) of the channel matrix. The specific principle is described as follows:

Assuming that the number of receive antennas in a MIMO system is _NT , the number of transmit antennas is _NR , and the channel matrix SVD decomposition can be performed, expressed as H=UΛV ^H , where (·) ^H represents the matrix conjugate transpose, and are unitary matrices of size N _R ×N _R and N _T × _NT respectively, and Λ is an N _R × _NT diagonal matrix whose diagonal elements are the singular values of H in descending order (σ ₁ ,σ ₂ , . . . σ _m ), m=min( _NT , _NR ).

For _NS -dimensional beamforming, the beamforming matrices of the transmitting end and the receiving end respectively use the right singular matrix V and the first m columns of the left singular matrix U of the channel matrix H, that is, F=[v ₁ ,v ₂ ,..., v _m ], W=[u ₁ , u ₂ , . . . , _um ], where N _S ≤ m.

Assuming that the transmitted symbol is x=[x ₁ , x ₂ ,...,x _m ] ^T , the received symbol is y=[y ₁ , y ₂ ,..., y _m ] ^T , the noise but

It can be seen that the eigenbeamforming equivalently divides the MIMO channel into m parallel independent sub-channels, each of which achieves a maximized signal-to-noise ratio.

Usually, the receiving end obtains the beamforming matrices of the transmitting and receiving parties by estimating the channel matrix H and performing SVD decomposition, and then the receiving end feeds back the beamforming matrix F of the transmitting end to the transmitting end. This direct estimation and feedback method is suitable for a small number of antennas, but in a MIMO system with a large number of antennas (for example, the number of antennas in a millimeter-wave MIMO system is up to several tens), its computational complexity and training Expenses have become unbearable.

In a Time Division Duplex (TDD) system, an iterative beamforming method that can obtain eigenvectors without estimating channel parameters is proposed by utilizing the reciprocity of the uplink channel and the downlink channel, that is, the power iteration method. Later, this method is further extended to multi-dimensional beamforming, that is, N _S beamforming vectors, that is, beamforming matrices, are obtained by peeling off stage by stage, and each stage has to undergo one round of power iteration. In one-stage iteration of the traditional power iterative method, in order to obtain a complete receiving vector, the receiver assumes that the receiver uses the identity matrix as the receiving beamforming matrix during forward iteration, and the transmitter must send the same training sequence N _T times. Similarly, during reverse iteration, the receiver must send the training sequence _NR times. Assuming that the preset number of iterations is N _ITER , then the number of iterative transceivers in one stage is N _ITER ( _NT + _NR ), and the iterative overhead is proportional to the sum of the number of antennas on both sides of the transceiver.

It can be seen that when the number of antennas on both sides of the transceiver is small, the overhead is not large, but as the number of antennas increases, the overhead in the training phase increases exponentially with the number of antennas.

SUMMARY OF THE INVENTION

In order to overcome the defect that the antenna training overhead of the power iteration method in the massive MIMO system is too large, the present invention proposes an iterative beamforming method in the millimeter wave precoding system. The estimation problem of the received vector in MIMO antenna training is transformed into a sparse reconstruction problem, so that the related theory of compressed sensing can be used to reduce the loss.

In order to conveniently describe the content of the present invention, the concepts and terms used in the present invention are first defined.

Spatial sparsity: Due to the high path loss and extremely poor scattering performance of wireless signals, the transmitter and receiver are only connected by a limited number of electromagnetic wave propagation paths. The signal calculation problem related to the channel can be conveniently expressed as a sparse reconstruction problem.

Sparse multipath channel model: A sparse multipath channel can be modeled as a geometric model with K-path multipath in, represents the complex channel gain of the i-th path, θ _i represents the departure angle of the i-th path, φ _i represents the arrival angle of the i-th path, a _T (φ _i ) is the antenna array response of the transmitter, a _R (θ _i ) is the receiving end The antenna array response at the end, i=1,2,...,K. The antenna array adopts Uniform Linear Arrays (ULAs), then the antenna array response at the transmitting end can be expressed as The antenna array response at the receiver can be expressed as Among them, λ is the signal wavelength, d is the distance between the antenna elements, generally taken as

An iterative beamforming method in a millimeter wave precoding system, the steps are as follows:

S1. Use the geometric model of the sparse multipath channel for sparse modeling, express the estimation problem of the received signal associated with the channel as the recovery problem of the sparse signal, and define the dictionary matrix of the receiving end Define the sender dictionary matrix Among them, N represents the length of the dictionary at the receiving end, and M represents the length of the dictionary at the receiving end;

S2, the establishment of the angle quantization codebook, the receiving end codebook is The transmitter codebook is in, is the codebook size, _NT is the number of transmit antennas, and _NR is the number of receive antennas;

S3, initial stage processing, as follows:

S31. The sender generates an N _T ×1 vector [1,0,0,...,0] ^T and normalizes it as an initial vector, and puts it into a codebook and uses a sparse signal recovery algorithm to estimate the initial vector f;

S32, respectively define the measurement times Nmr ⁰ and Nmt ⁰ of the sender and the receiver in this process;

S33. Select the optimal measurement matrix Φ _T ⁰ of the transmitting end from the O random matrices, and select the optimal measurement matrix Φ _R ⁰ of the receiving end, where O is a non-zero natural number, and select the optimal measurement matrix Φ _T ⁰ of the transmitting end and selecting the optimal measurement matrix Φ _R ⁰ of the receiving end as the empirical judgment process;

S34, receive beamforming vector training, as follows:

S34-1. The transmitting end continuously sends the vector f of Nmt ⁰ times to the receiving end, and the receiving end uses the column of Φ _R ⁰ as the beamforming weighted combining vector in the receiving process, and the receiving end obtains Among them, n _R represents the additive white Gaussian noise vector at the receiver,

S34-2. The receiving end uses a sparse signal recovery algorithm to calculate a sparse vector z _{R representing} the position of the angle of arrival of the received signal in the dictionary matrix A _RD described in S1, where z _R is an N×1 column vector, and N represents The length of the dictionary A _RD , there are K non-zero elements in z _R , K<<N;

S34-3, Hf≈A _RD z _R , the Hf is stored in the _NR ×1 vector g, that is, g=A _RD z _R , where the channel matrix The receiver normalizes the vector g, that is, and will return to the sender;

S35. Send beamforming vector training, as follows:

S35-1, the receiving end continuously sends Nmr ⁰ times the vector described in S34-3 To the transmitting end, the transmitting end uses the column of Φ _T ⁰ as the beamforming weighted combining vector in the receiving process, and the transmitting end obtains Among them, n _T represents the additive white Gaussian noise vector at the sender of the k-th iteration,

S35-2. The transmitting end uses a sparse signal recovery algorithm to calculate a sparse vector z _T representing the position of the angle of arrival of the received signal in the dictionary matrix A _TD described in S1, where z _T is an M×1 column vector, and M represents The length of the dictionary A _TD , there are K non-zero elements in z _T , K<<M;

S35-3, said Stored in the N _T ×1 vector f, that is, f=A _TD z _T , and the sender normalizes the vector f, that is, and will return to the receiver;

S4, the iterative process, as follows:

S41, respectively define the measurement times Nmr and Nmt of the sender and the receiver in this process;

S42. Find the angles corresponding to the positions of the K non-zero elements in S24-2 and S25-2, and put the K angles into Find the closest phase among the phases, and finally get the phase Transposing it is the measurement matrix of the sender and receiver, where, A phase is the process of -π～π quantification;

S43. Receive beamforming vector training, as follows: the transmitting end continuously sends Nmt times vector f to the receiving end, and the receiving end uses the column of Φ _R as the beamforming weighted combining vector in the receiving process, and the receiving end obtains r=Φ _R ^H (Hf +n _R ), the receiver uses the least squares method to calculate the coefficient h _R =(Φ _R A _R ) ^-1 r, and obtains v=A _R h _R , and puts v into the codebook and uses the sparse signal recovery algorithm To estimate, the receiver normalizes the estimated vector v, that is, and will return to the sender;

S44. Sending beamforming vector training, the details are as follows: the receiving end continuously sends Nmr vectors To the transmitting end, the column of Φ _T is used as the beamforming weighted combining vector in the receiving process of the transmitting end, and the transmitting end obtains The transmitting end uses the least squares method to calculate the coefficient h _T =(Φ _T A _T ) ^-1 t, and obtains f=A _T h _T , and puts f into the codebook and uses the sparse signal recovery algorithm for estimation. The transmitting end Normalize the estimated vector f, i.e. and will Return to the receiving end, that is, return to S43 for iteration;

S5. Finally, output v _and f obtained after iteration.

Further, O=10000 in S33.

The beneficial effects of the present invention are:

The present invention retains the advantages of the power iteration method, that is, the channel state information need not be estimated, and the convergence is better. At the same time, using the spatial sparsity of the millimeter-wave MIMO channel, when obtaining the received signal vector, it is not necessary to send the same training sequence as many times as the number of antennas, but only the number of times far less than the number of antennas needs to be sent, and the array system adjusts the signal phase of each antenna.

Similar to the power iteration method, the present invention adopts a multi-stage projection iteration method, which can be easily extended to the antenna training of the multi-stream MIMO system.

Description of drawings

Figure 1 Diagram of a mmWave MIMO beamforming system.

Fig. 2 is a flow chart of the simulation program of the present invention.

FIG. 3 is a comparison diagram of capacity performance curves when the present invention is applied to two-stream beamforming.

FIG. 4 is a comparison diagram of capacity performance curves in the case where the present invention is applied to four-stream beamforming.

Detailed ways

The technical solutions of the present invention will be described in detail below with reference to the embodiments and the accompanying drawings.

As shown in Figure 1, the millimeter-wave MIMO beamforming system diagram shows a MIMO system with N _S data streams. Using eigenbeamforming, the beamforming matrix at the transmitting end Receiver Beamforming Matrix

FIG. 3 is a capacity performance curve in the case where the present invention is applied to two-stream beamforming, from top to bottom are the curves under SVD conditions and the curves of the present invention. FIG. 4 is a capacity performance curve for the case where the present invention is applied to four-stream beamforming.

example,

S1. Use the geometric model of the sparse multipath channel for sparse modeling, express the estimation problem of the received signal associated with the channel as the recovery problem of the sparse signal, and define the dictionary matrix of the receiving end Define the sender dictionary matrix Among them, N represents the length of the dictionary at the receiving end, M represents the length of the dictionary at the receiving end, the larger the N, the finer the quantization, and the smaller the quantization error, the larger the M, the finer the quantization, and the smaller the quantization error;

S2, the establishment of the angle quantization codebook, the receiving end codebook is The transmitter codebook is in, is the codebook size, _NT is the number of transmit antennas, and _NR is the number of receive antennas;

S3, initial stage processing, as follows:

S31. The sender generates an N _T ×1 vector [1,0,0,...,0] ^T and normalizes it as an initial vector, and puts it into a codebook and uses a sparse signal recovery algorithm to estimate the initial vector f;

S32, respectively define the measurement times Nmr ⁰ and Nmt ⁰ of the sender and the receiver in this process;

S33, find the optimal measurement matrix Φ _T ⁰ , Φ _R ⁰ representing the sender and the receiver among the 10,000 random matrices;

S34, receive beamforming vector training, as follows:

S34-1. The transmitting end continuously sends the vector f of Nmt ⁰ times to the receiving end, and the receiving end uses the column of Φ _R ⁰ as the beamforming weighted combining vector in the receiving process, and the receiving end obtains Among them, n _R represents the additive white Gaussian noise vector at the receiver,

S34-2. The receiving end uses a sparse signal recovery algorithm to calculate a sparse vector z _{R representing} the position of the angle of arrival of the received signal in the dictionary matrix A _RD described in S1, where z _R is an N×1 column vector, and N represents The length of the dictionary A _RD , there are K non-zero elements in z _R , K<<N;

S34-3, Hf≈A _RD z _R , the Hf is stored in the _NR ×1 vector g, that is, g=A _RD z _R , where the channel matrix The receiver normalizes the vector g, that is, and will return to the sender;

S35. Send beamforming vector training, as follows:

S35-1, the receiving end continuously sends Nmr ⁰ times the vector described in S34-3 To the transmitting end, the transmitting end uses the column of Φ _T ⁰ as the beamforming weighted combining vector in the receiving process, and the transmitting end obtains Among them, n _T represents the additive white Gaussian noise vector at the sender of the k-th iteration,

S35-2. The transmitting end uses a sparse signal recovery algorithm to calculate a sparse vector z _T representing the position of the angle of arrival of the received signal in the dictionary matrix A _TD described in S1, where z _T is an M×1 column vector, and M represents The length of the dictionary A _TD , there are K non-zero elements in z _T , K<<M;

S35-3, said Stored in the N _T ×1 vector f, that is, f=A _TD z _T , and the sender normalizes the vector f, that is, and will Return to the sender and receiver;

S4, the iterative process, as follows:

S41, respectively define the measurement times Nmr and Nmt of the sender and the receiver in this process;

S42. Find the angles corresponding to the positions of the K non-zero elements in S24-2 and S25-2, and put the K angles into Find the closest phase among the phases, and finally get the phase Transposing it is the measurement matrix of the sender and receiver, where, A phase is the process of -π～π quantification;

S43. Receive beamforming vector training, the details are as follows: the transmitting end continuously sends the Nmt times vector f to the receiving end, and the receiving end uses the column of Φ _R as the beamforming weighted combining vector in the receiving process, and the receiving end obtains r=Φ _R ^H (Hf +n _R ), the receiver uses the least squares method to calculate the coefficient h _R =(Φ _R A _R ) ^-1 r, and obtains v=A _R h _R , and puts v into the codebook and uses the sparse signal recovery algorithm To estimate, the receiver normalizes the estimated vector v, that is, and will return to the sender;

S44. Sending beamforming vector training, the details are as follows: the receiving end continuously sends Nmr vectors To the transmitting end, the column of Φ _T is used as the beamforming weighted combining vector in the receiving process of the transmitting end, and the transmitting end obtains The sender uses the least squares method to calculate the coefficient h _T =(Φ _T A _T ) ^-1 t, and obtains f=A _T h _T , and puts f into the codebook and uses the sparse signal recovery algorithm for estimation. Normalize the estimated vector f, i.e. and will Return to the receiving end, that is, return to S43 for iteration;

S5. Finally, output v _and f obtained after iteration.

Claims (2)

1. An iterative beamforming method in a millimeter wave precoding system, comprising the steps of:

s1, sparse modeling is carried out by utilizing a geometric model of a sparse multipath channel, the estimation problem of the received signal related to the channel is expressed as the recovery problem of the sparse signal, and a receiving end dictionary matrix is definedWherein d is the antenna array element spacing, and λ is the signal wavelength, defining the transmitting end dictionary momentMatrix ofWherein, N represents the length of the receiving end dictionary, and M represents the length of the sending end dictionary;

s2, establishing an angle quantization codebook, wherein the codebook at the receiving end isThe transmitting end codebook isWherein, is the codebook size, N_TFor the number of transmitting antennas, N_RIs the number of receive antennas;

s3, initial stage processing, specifically including:

s31, the sending end generates an N_TX 1 vector [1,0,0, …,0]^TNormalizing the vector to be used as an initial vector, and putting the initial vector into a codebook to obtain an initial vector f by using a sparse signal recovery algorithm for estimation;

s32, defining the measuring times Nmr of the transmitting end and the receiving end in the process respectively⁰,Nmt⁰；

S33, selecting optimal measurement matrix phi of sending end from O random matrices_T ⁰Selecting the optimal measurement matrix phi of the receiving end_R ⁰Wherein O is a natural number not equal to zero, and selecting the optimal measurement matrix phi of the transmitting end_T ⁰And selecting the optimal measurement matrix phi of the receiving end_R ⁰Is an experience judging process;

s34, training a receiving beam forming vector, specifically as follows:

s34-1, sending end continuously sends Nmt⁰The sub-vector f reaches the receiving end, and phi is used in the receiving process of the receiving end_R ⁰The column of (a) is used as a beam forming weighting merging vector, and the receiving end obtainsWherein n is_RRepresenting an additive white gaussian noise vector at the receiving end,σ²is the variance;

s34-2, the receiving end uses sparse signal recovery algorithm to calculate dictionary matrix A representing the arrival angle of the received signal in S1_RDSparse vector z of a position in (1)_RWherein z is_RIs an N x 1 column vector, N representing the dictionary A_RDLength of (1), z_RK nonzero elements exist in the alloy, and K is less than N;

S34-3、Hf≈A_RDz_Rsaid Hf is stored in N_RX 1 vector g, i.e. g ═ a_RDz_RWherein the channel matrixThe receiving end normalizes the vector g, i.e.And will beReturning to the sending end;

s35, training a transmitting beamforming vector, specifically as follows:

s35-1, receiving end continuously sends Nmr⁰Vector of sub S34-3To the transmitting end, the transmitting end uses phi in the receiving process_T ⁰As a beamforming weighted combining vector, transmitEnd to obtainWherein n is_TRepresenting an additive white gaussian noise vector at the sender for the kth iteration,

s35-2, the transmitting end uses sparse signal recovery algorithm to calculate dictionary matrix A representing the arrival angle of the received signal in S1_TDSparse vector z of a position in (1)_TWherein z is_TIs an M x 1 column vector, M representing the dictionary A_TDLength of (1), z_TK nonzero elements exist in the alloy, and K is less than M;

S35-3、the above-mentionedIs stored in N_TX 1 vector f, i.e. f ═ A_TDz_TThe transmitting end normalizes the vector f, i.e.And will beReturning to the receiving end;

s4, an iteration process is specifically as follows:

s41, respectively defining the measuring times Nmr and Nmt of the transmitting end and the receiving end in the process;

s42, finding the corresponding angles of the positions of K nonzero elements in S34-2 and S35-2, and putting the K angles intoFinding the nearest phase from the phases to obtain the phase And transposing the obtained matrix to obtain a measurement matrix of a transmitting end and a receiving end, wherein,a phase is to carry out-piQuantizing;

s43, training a receiving beam forming vector, specifically as follows: the transmitting end continuously transmits the Nmt subvectors f to the receiving end, and the receiving end uses phi in the receiving process_RThe column of (b) is used as a beam forming weighting merging vector, and the receiving end obtains r ═ phi_R ^H(Hf+n_R) The receiving end calculates the coefficient h by using a least square method_R＝(Φ_RA_R)^-1r, and find v ═ A_Rh_RAnd v is put into a codebook and is estimated by using a sparse signal recovery algorithm, and the receiving end normalizes the estimated vector v, namelyAnd will beReturning to the sending end;

s44, training a transmitting beamforming vector, specifically as follows: the receiving end continuously sends Nmr times of vectorsTo the transmitting end, phi is used in the receiving process of the transmitting end_TThe column of (a) is taken as a beam forming weighting merging vector, and the sending end obtainsTransmitting end using least squaresCalculating coefficient h by the method_T＝(Φ_TA_T)^-1t, and find f ═ A_Th_TAnd f is put into a codebook and is estimated by using a sparse signal recovery algorithm, and the transmitting end normalizes the estimated vector f, namelyAnd will beReturning to the receiving end, namely returning to S43 for iteration;

and S5, finally outputting the v and f obtained after iteration.

2. The iterative beamforming method in a millimeter wave precoding system according to claim 1, wherein: s33 where O is 10000.