Multi-carrier signal angle and time delay estimation method based on nested array

Abstract

A multi-carrier signal angle and time delay estimation method based on a nested array belongs to the field of wireless communication, and comprises the following steps: firstly, designing a nested array set according to the number of radio frequency links and the number of pilot frequency carriers, and designing a beam forming matrix into a random banded Toeplitz matrix; meanwhile, selection of pilot frequency carriers is determined according to the nested array of the pilot frequency carriers. At a transmitting end, each pilot carrier transmits a unit matrix signal in each pilot block period time, at a receiving end, the signal received by each pilot carrier is vectorized, and all pilot carrier vectors are gathered to form a new pilot vector. The method comprises the following steps of: calculating a covariance of a new pilot frequency vector, selecting a maximum continuous holeless vector, improving a rank of the holeless vector by using a smoothing technology, finally solving a time delay, a departure angle and an arrival angle of each path by using a 3-D ESPRIT algorithm, and pairing all the time delays, departure angles and arrival angles through a MUSIC algorithm. After the method is used for processing data, a super-resolution method 3-D ESPRIT can be used for time delay and angle estimation, and the angle and time delay estimation precision is effectively improved.

Description

Technical Field

[0001] The invention belongs to the technical field of mobile communications, and in particular refers to an angle and time delay estimation method for multi-carrier signals based on a nested array. Background Art

[0002] With the development of the times and the advancement of science and technology, people have higher and higher requirements for mobile communications. The millimeter wave (30-300GHz) frequency band has rich spectrum resources and available bandwidth, which is the guarantee for 5G networks to provide gigabit connectivity. According to the characteristics of millimeter waves, large-scale MIMO-OFDM technology has been widely studied. However, due to the high frequency of millimeter waves, their transmission loss is large. In order to overcome this problem, signals are sent in the form of beams. In order to form beams, it is necessary to know the location information of the transmitter when receiving the signal, that is, to obtain the direction and delay information of the transmitter during the beam training phase.

[0003] However, in order to save costs, when deploying large-scale MIMO systems, one antenna is usually not equipped with one RF link. Hybrid beamforming is usually used. In the process of mapping from the spatial domain to the beam domain, the signal is compressed, making it impossible to directly use the super-resolution estimation method and obtain accurate angle and delay information. In addition, if the number of subcarriers for transmitting pilot signals is too large, the efficiency of the entire communication system will be low. Summary of the invention

[0004] In view of the existing technical problems, the present invention provides a multi-carrier signal angle and delay estimation method based on nested arrays. The hybrid beamforming matrix is ​​designed as a banded Toeplitz matrix, and the composition of the matrix is ​​determined by the nested array, so that each pilot carrier signal can be guaranteed to be sparse in the departure angle (DOD) and arrival angle (DOA) dimensions, and the nested array is applied to the selection of pilot carriers, so that virtual data with a larger aperture can be generated in the space-frequency domain, and then the maximum continuous non-aperture vector is selected, and then the space-frequency smoothed signal is obtained by smoothing technology. The space-frequency smoothed signal has rotation invariance, so the 3-D ESPRIT algorithm can be used to estimate the delay, DOD and DOA, and finally the MUSIC algorithm is used to pair the delay, DOD and DOA, thereby improving the performance of the system.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A method for estimating signal angle and delay of multiple carriers based on nested arrays, the method comprising two parts: generation of virtual data and parameter estimation:

[0007] (1) According to the number of RF links at both ends of the transmission and reception, the corresponding nested array is designed, and the nested array is applied to the matrix design of the transmission and reception hybrid beamforming, that is, the above matrix is ​​designed as a random band Toeplitz matrix, the composition of the matrix is ​​determined by the nested array, and the prototype vector of the random band Toeplitz matrix is ​​a random vector. Similarly, the nested array is applied to the selection of the pilot carrier, that is, the pilot carrier is selected according to the nested array.

[0008] (2) The received signal on the selected carrier is vectorized to form a pilot data vector in order. Then, the effective virtual data is obtained by calculating the covariance matrix of the vector. Since the virtual data has duplicate items (same phase offset), the virtual data with the same phase offset need to be averaged. The maximum continuous non-hole vector is selected from the virtual data, and the rank of the vector is improved using smoothing technology, and then the space-frequency smoothing matrix is ​​obtained. Finally, the subspace 3-DESPRIT method is used to solve the values ​​of delay, DOD and DOA, and the MUSIC algorithm is used to pair the delay, DOD and DOA.

[0009] For the convenience of expression, some symbols are explained here:

[0010] (·) T 、(·) * and(·) H and The inverse symbol represents the transpose, conjugate, conjugate transpose and pseudo-inverse operations of a vector or matrix respectively; [·] i,j represents the element in the i-th row and j-th column of the matrix, [·] i,: represents the row vector of the i-th row, [·] :,j represents the column vector of the jth column of the matrix, [·] i Represents the i-th element of a vector; 0 m×n represents a zero matrix with m rows and n columns, I N represents the N×N dimensional identity matrix, vec(·) represents the vectorization of the matrix by column; ⊙ represents the Khatri–Rao product, Represents the Kronecker product; if x is a diagonal matrix, diag{x} means extracting the diagonal elements of x to form a new vector; if x is a vector, diag{x} means constructing a diagonal matrix using the vector x.

[0011] Assume that in a large-scale millimeter-wave MIMO-OFDM system, the number of antennas at the transmitting and receiving ends is N r and N t , and are evenly distributed on a straight line. The number of RF links is M r and M t Due to the hybrid beamforming method, the number of RF links is much smaller than the number of antennas, that is, Mr <<N r , M t <<N t The number of OFDM symbol subcarriers is K, of which the number of carriers transmitting pilot signals is M. c For the convenience of representation, the subcarrier index is defined as m, m∈{0,1,…,K-1}, and the subcarrier frequency with index g is gΔf, where Δf represents the carrier spacing. Assume that the index of the kth pilot carrier is n k ,k=1,2,…,M c ,n k ∈{0,1,…,K-1}.

[0012] During the beam training phase, Q block pilot signals are sent, each containing M t OFDM symbols, each OFDM symbol is transmitted after adding a cyclic prefix and IFFT filtering. After removing the cyclic prefix and FFT at the receiving end, the kth pilot carrier receives the qth block pilot signal as

[0013]

[0014] Among them, W q and F q They represent the hybrid beamforming matrices at both ends of the transmitter and receiver during the qth block signal cycle time, W q The conjugate transpose of . represents the qth block pilot signal sent by the kth pilot carrier, represents white noise that follows Gaussian distribution, A r and A t represents the steering matrix of the antennas at both ends of the transmission and reception, represents the channel complex gain. And

[0015] A r =[a r (θ 1 ),a r (θ 2 ),…,a r (θ L ] (2)

[0016]

[0017] Among them, L represents the number of paths, a r (θ l )and Respectively represent the steering vectors of the transmitting array antenna and the receiving array antenna in the lth path, and are determined by the array structure of the antenna. The present invention considers that both the transmitting / receiving array antennas are linear uniform arrays, and considers the narrowband signal model, then

[0018]

[0019]

[0020] where u l =2πdsin(θ l ) / λ, where θ l ∈[-π / 2,π / 2], represents the DOA and DOD of the lth path, d represents the antenna spacing, and λ represents the signal wavelength.

[0021]

[0022] in, α q,l represents the path loss coefficient of the lth path, T s Denoted as the sampling period, τ l represents the propagation time of the lth path.

[0023] The specific steps of the present invention are as follows:

[0024] Step 1: Design the corresponding nested array according to the number of RF links and the number of pilot carriers. Design the transmit and receive beamforming matrix as a random band Toeplitz matrix according to the nested array of the transmit and receive ends. The composition of the random band Toeplitz matrix is ​​determined by the nested arrays at both ends of the transmit and receive ends, and its matrix prototype vector is a random vector. Select the pilot carrier according to the nested array of the pilot carrier. Vectorize the data received by each pilot carrier and aggregate them in the index order of the pilot carrier to form a new pilot data vector. The specific processing is as follows:

[0025] Step 1.1: Design corresponding nested arrays according to the number of RF chains and the number of pilot carriers.

[0026] The design principles of nested arrays are as follows:

[0027] Assume that the number of elements in the nested array is N and the number of elements in the outer array is N 1 , the number of inner arrays is N 2 , satisfying N 1 +N 2 =N, then the nested array position NA can be represented as [0,1,…,N 1 ,2N 1 +1,3N 1+2,…,N 1 +(N 2 -1)(N 1 +1)]. Then the differential common matrix generated by NA is CA NA =[-(N 2 N 1 +N 2 -1),…,0,…,N 2 N 1 +N 2 -1]. In order to obtain more degrees of freedom, when N is an even number, N 1 =N 2 =N / 2, when N is an odd number,

[0028] According to the above design principles, in this step, according to the number M of radio frequency links at both ends of the transmission and reception, r and M t and the number of pilot carriers M c Get its corresponding nested array

[0029]

[0030] where x∈{r,t,c}. For convenience of representation, let the nested arrays corresponding to the sender and receiver be and The nested array corresponding to the pilot carrier is x i Represents NA x The i-th element of x , x∈{r,t,c}. It should be noted that NA c When determining the number of pilot carriers, Cannot be greater than K-1.

[0031] Step 1.2: Design the transmit and receive beamforming matrix W based on the nested transmit and receive array obtained in step 1.1 q and F q .

[0032] In order to make the data received by the pilot carrier sparse, W q and F q The banded Toeplitz matrix is ​​set. The banded Toeplitz matrix shape consists of a nested array of NA r and NA t control.

[0033] Step 1.3: W q and F q The prototype vector w q and f q Designed as random vectors.

[0034] In a millimeter wave communication system, different paths are not necessarily independent of each other. q and f q is a random vector to remove the correlation between paths, that is, w q Elements f q Elements where λ q,i and x q,i represents an independent random variable, that is, the probability of taking 1 and -1 is 1 / 2. w and L f Indicates w q and f q The length of the RF link is much smaller than the number of antennas. and Less than N r and N t , so let

[0035] After processing in steps 1.1, 1.2 and 1.3, W q and F q becomes a random banded Toeplitz matrix, W q The j-th column vector of can be written as

[0036]

[0037] r j for NA r The jth element of F q The j-th column vector of can be written as

[0038]

[0039] t j for NA t The j-th element of .

[0040] but:

[0041]

[0042]

[0043] where Λ q is a diagonal matrix whose lth diagonal element u l =2πdsin(θ l ) / λ, d represents the distance between antennas, λ represents the wavelength of the transmission carrier; qis a diagonal matrix whose lth diagonal element represents the transposed conjugate of the beamforming matrix at the receiving end within the qth pilot block time; F q represents the beamforming matrix of the transmitter in the qth pilot block time; from (2), we know that A r represents the steering matrix of the receiving antenna; from (3) we know Represents the conjugate transpose of the steering matrix for the transmit antenna.

[0044] and

[0045]

[0046] Indicates a nested array corresponding to the receiving end NA r The steering matrix of which the lth column vector

[0047]

[0048] Indicates the receiving end nested array NA r The guiding vector of the lth path, θ l represents the arrival angle of the lth path.

[0049]

[0050] Indicates that the corresponding transmitter is nested NA t The steering matrix of which the lth column vector

[0051]

[0052] Indicates the nested array NA on the transmitter side t The guiding vector of the lth path, represents the departure angle of the lth path.

[0053] Step 1.4: Determine the index of the pilot carrier according to the nested array corresponding to the pilot carrier.

[0054] Determine the index of the pilot carrier as That is, the index of the kth pilot carrier is c k .

[0055] After processing in step 1.4, the kth pilot carrier index is c k , c k ∈NA c represents the index of the kth pilot carrier. The signal sent by each pilot carrier at the transmitting end is Substituting equations (10) and (11) into equation (1), we can get the signal received by the kth pilot carrier: for:

[0056]

[0057] in, is a diagonal matrix, consider equation (6), and replace the subscript n k Replace with c k have to represents the channel complex gain of the kth carrier, then The lth diagonal element α q,l represents the loss coefficient of the lth path; The noise matrix of the received signal of the kth pilot carrier is represented by a matrix whose mean is 0 and variance is Gaussian distribution.

[0058] Step 1.5: Vectorization is performed column by column, and all vectors are arranged in index order to form a new pilot signal vector.

[0059] After step 1.1, step 1.2, step 1.3 and step 1.4, different pilot carrier signals have sparse properties in the frequency domain, and each pilot carrier signal also has sparse properties in the spatial domain. Vectorization is performed, and all pilot vectors are aggregated to form a new pilot vector:

[0060]

[0061] in, Represents the vector form of the kth pilot carrier signal, k = 1, 2…, M c ;d q represents an L×1 column vector, whose lth element [d q ] l =[Λ q ] l,l α q,l [Π q ] l,l ; z q represents the set of all pilot carrier noise vectors; Represents nested array NA c The steering matrix, whose lth column Represents nested array NA c The steering vector of the lth path, and

[0062] Step 2: Calculate y qThe covariance matrix of is vectorized to obtain virtual data, and the virtual data of repeated positions are averaged. Then the largest continuous vector without holes is selected from the virtual data of all positions, and its rank is improved using smoothing technology. The details are as follows:

[0063] Step 2.1: Calculate y in step 1 q The covariance of is as follows:

[0064] Calculate y q The covariance of and cumulative average is obtained:

[0065]

[0066] in, is a diagonal matrix; Q represents the total number of pilot blocks transmitted during the training phase; d q is an L×1 column vector, representing the complex gain vector within the qth pilot block time, and its lth element [d q ] l =[Λ q ] l,l α q,l [∏ q ] l,l ,q∈1,2,…,Q; represents the noise variance.

[0067] Step 2.2: R y Vectorized, we get:

[0068]

[0069] Among them, r y Represents R y The vector representation of D; d = vec (D) represents the vector form of D; express in vector form.

[0070] Step 2.3: Through step 2.2, all possible virtual data can be obtained. Since many of the generated virtual data are repeated, it is necessary to average the repeated virtual data to reduce errors. Then, new vectors are arranged from small to large in the order of delay-DOD-DOA to obtain the maximum continuous non-hole vector. The specific steps are:

[0071] Define the function:

[0072]

[0073] Indicates that the coordinates in the three-dimensional space of delay-DOD-AOA are (k 1 ,k 2 ,k 3) data, where k 1 , k 2 and k 3 Respectively represent the position on the delay, DOD, and AOA axes, and and Respectively represent nested arrays NA c ,NA t and NA r The last element of . δ(x) represents the Kronecker function. When x=0, δ(x)=1, and when x≠0, δ(x)=0.

[0074] Definition: Given and if Then it is called and Same location.

[0075] Consider the Khatri-Rao product in (19) The i 1 OK, The i 2 OK, The i 3 OK, The i 4 OK, The i 5 Line and The i 6 OK, we can get:

[0076]

[0077] where z = ((i 1 -1)M t M r +(i 2 -1)M r +i 3 -1)M c M t M r +((i 4 -1)M t M r +(i 5 -1)M r +i 6 ), 1≤z≤(M c M t M r ) 2 , 1≤i 1 ,i 4 ≤M c , and Respectively represent nested arrays NA c i-th 1 and i 4 elements, and Respectively represent nested arrays NA t No. and elements, and Respectively represent nested arrays NA r No. and elements.

[0078] From step 1.2, we can know that the differential common array of the transmitting and receiving ends and the pilot carrier index is The virtual data at the same position are averaged, and then the virtual data at consecutive positions are aggregated together to form the maximum continuous hole-free vector

[0079]

[0080] Step 2.4: After step 2.3, we can get the hole-free vector Can be expressed as equipment The receiving end of the antenna is equipped with The transmitting end of the antenna sends The vector form of the OFDM block signal composed of subcarriers. It can be seen that applying the nested array to the design of the beamforming matrix and the selection of pilot carriers can obtain virtual data with a higher space-frequency aperture, which not only improves the resolution of the system, but also increases the maximum number of sources that can be estimated by the system. However, due to The rank of is 1, and the subspace method cannot be used directly. In this step, a smoothing technique will be used to obtain a space-frequency smoothing matrix with a rank greater than L so that the parameters of all paths can be correctly estimated. The specific steps are as follows:

[0081] First, determine the row selection matrix:

[0082]

[0083] x∈{c,t,r}.

[0084] make

[0085]

[0086] in,

[0087] Arrange the selected vectors in order from left to right to form a space-frequency smoothing matrix R ss :

[0088]

[0089] in, The lth column vector The lth column vector The lth column vector

[0090] Step 3: After step 2, the enhanced covariance matrix R is obtained ss , R ss The rank of is much larger than L, so L paths can be accurately distinguished. ss With rotation invariance, R ss As input data, the 3-D ESPRIT algorithm can be used to estimate the delay, DOD and DOA of all paths. Since the estimated parameters are not one-to-one, the MUSIC algorithm is used to pair all delays, DOD and DOA. The specific steps are:

[0091] Step 3.1: R ss Perform singular value decomposition.

[0092] R ss Perform singular value decomposition to obtain:

[0093] R ss =[U s U n ]Λ[V s V n ] H (26)

[0094] Where Λ represents the eigenvalue diagonal matrix, U s is the signal subspace, which is composed of the left eigenvectors corresponding to the first L largest eigenvalues. n is the noise subspace, The left eigenvector corresponding to the smallest eigenvalue is composed of V s It is composed of the right eigenvectors corresponding to the first L largest eigenvalues, V n Depend on The right eigenvector corresponding to the smallest eigenvalue is formed.

[0095] Step 3.2: Delay estimation.

[0096] make

[0097]

[0098] in, and Represented as a selection matrix. express forward OK, express back OK.

[0099] Yes c Diagonalize and we get:

[0100]

[0101] Then the delay of all paths can be obtained, that is, Where angle(x) represents the phase of vector x, K represents the number of subcarriers in OFDM symbol, and T s is the sampling period.

[0102] Step 3.3: DOD estimation.

[0103] Similar to delay estimation, that is:

[0104]

[0105] in and Represented as a selection matrix. Depend on forward OK, express back OK.

[0106] Yes t Diagonalize and we get:

[0107]

[0108] Then the DOD of all paths can be obtained, that is, λ represents the transmission carrier wavelength and d represents the antenna spacing.

[0109] Step 3.4: DOA estimation.

[0110] This step is similar to step 3.2 and step 3.3, where express forward OK, express back OK, then r Diagonalize to get Φ r Then we can get the DOA of all paths, that is,

[0111] Step 3.5: Pair the delay, DOD and DOA.

[0112] Since the obtained delay, DOD and DOA are not necessarily in the order in their vectors, it is necessary to perform a pairing operation on each delay, DOD and DOA.

[0113] Define the null-spectrum as:

[0114]

[0115] By traversing all the delays, DODs and DOAs on the space-frequency spectrum, the parameters corresponding to the L maximum values ​​obtained are for the same path, and the delay, DOD and DOA of each path can be obtained.

[0116] The beneficial effects of the present invention are:

[0117] The present invention applies nested arrays to the design of beamforming matrices at both ends of the transmitter and receiver and the selection of pilot carriers, thereby generating continuous virtual data with a larger aperture in the space-frequency domain. In this way, the super-resolution method 3-D ESPRIT can be used to estimate the delay and angle, and the accuracy of angle and delay estimation is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] Figure 1 It is a system flow chart of the present invention. DETAILED DESCRIPTION

[0119] The present invention is further described below in conjunction with specific embodiments.

[0120] The present invention is applied in a large-scale millimeter wave MIMO-OFDM communication system, and its purpose is to accurately estimate the time delay, DOA (angle of arrival) and DOD (angle of departure) of a multi-carrier signal.

[0121] Parameter setting: In the system, the number of antennas at the transceiver end is N r =64 and N t =64, the number of RF links is M r =6 and M t =6, the number of OFDM subcarriers K = 64, the frequency interval is 125kHz. The number of pilot carriers M c =6. The number of pilot blocks in the training phase is Q = 100. The transmission carrier frequency is 100 GHZ. The number of paths is L = 3.

[0122] A method for estimating signal angles and delays of multiple carriers based on nested arrays. First, a nested array set is designed according to the number of RF links and the number of pilot carriers, and the beamforming matrix is ​​designed as a random banded Toeplize matrix. At the same time, the selection of pilot carriers is determined according to the nested array of pilot carriers. At the transmitting end, each pilot carrier transmits a unit matrix signal within each pilot block period. At the receiving end, the signal received by each pilot carrier is vectorized, and all pilot carrier vectors are gathered to form a new pilot vector. The covariance of the new pilot vector is calculated, the maximum continuous non-aperture vector is selected, and the smoothing technique is used to improve the rank of the non-aperture vector. Finally, the 3-D ESPRIT algorithm is used to calculate the delay, departure angle, and arrival angle of each path, and all delays, departure angles, and arrival angles are paired using the MUSIC algorithm. The specific steps are as follows:

[0123] Step 1: Design the corresponding nested array according to the number of RF links and the number of pilot carriers. Design the transmit and receive beamforming matrix as a random band Toeplitz matrix according to the nested array of the transmit and receive ends. The composition of the random band Toeplitz matrix is ​​determined by the nested arrays at both ends of the transmit and receive ends, and its matrix prototype vector is a random vector. Select the pilot carrier according to the nested array of the pilot carrier. Vectorize the data received by each pilot carrier and aggregate them in the index order of the pilot carrier to form a new pilot data vector. The specific processing is as follows:

[0124] Step 1.1: Design corresponding nested arrays according to the number of RF chains and the number of pilot carriers.

[0125] In this step, according to the number M of radio frequency links at both ends of the transmission and reception, r =6 and M t =6 and the number of pilot carriers M c =6 to get its corresponding nested array

[0126] NA c =[0,1,2,3,7,11]

[0127] NA t =[0,1,2,3,7,11]

[0128] NA r =[0,1,2,3,7,11]

[0129] where x∈{r,t,c}. For convenience of representation, let the nested array NA corresponding to the sender and receiver be r =[r 1 ,r 2 ,…,r 6 ] and NA t =[t 1 ,t2 ,…,t 6 ], the nested array corresponding to the pilot carrier is NA c =[c 1 ,…,c 6 ].

[0130] Step 1.2: Design the transmit and receive beamforming matrix W based on the nested transmit and receive array obtained in step 1.1 q and F q .

[0131] In order to make the data received by the pilot carrier sparse, W q and F q The banded Toeplitz matrix is ​​set. The banded Toeplitz matrix shape consists of a nested array of NA r and NA t control.

[0132] Step 1.3: W q and F q The prototype vector w q and f q Designed as random vectors.

[0133] In a millimeter wave communication system, different paths are not necessarily independent of each other. q and f q is a random vector, that is, w q Elements f q Elements where λ q,i and χ q,i represents an independent random variable, and the probability of taking 1 and -1 is 1 / 2. 6 =11<64, t 6 =16<64, so let L w =53,L f =53. Then

[0134] After steps 1.1, 1.2 and 1.3, W q and F q becomes a random banded Toeplitz matrix. q The j-th column vector of can be written as

[0135]

[0136] r j for NA r The jth element of F q The j-th column vector of can be written as

[0137]

[0138] t j for NA t The j-th element of .

[0139] but:

[0140]

[0141]

[0142] Among them, Λ q is a diagonal matrix whose lth diagonal element u l =2πdsin(θ l ) / λ, d represents the distance between antennas, and λ represents the wavelength of the transmission carrier. q is a diagonal matrix whose lth diagonal element represents the transposed conjugate of the beamforming matrix at the receiving end within the qth pilot block time, F q represents the beamforming matrix of the transmitter in the qth pilot block time. From (2), we can know that A r represents the steering matrix of the receiving antenna. From (3), we know Represents the conjugate transpose of the steering matrix for the transmit antenna.

[0143] and

[0144]

[0145] Indicates a nested array corresponding to the receiving end NA r The steering matrix of which the lth column vector

[0146]

[0147] Indicates the receiving end nested array NA r The guiding vector of the lth path, θ l represents the arrival angle of the lth path.

[0148]

[0149] Indicates that the corresponding transmitter is nested NA t The steering matrix of which the lth column vector

[0150]

[0151] Indicates the nested array NA on the transmitter side t The guiding vector of the lth path, represents the departure angle of the lth path.

[0152] Step 1.4: Determine the index of the pilot carrier according to the nested array corresponding to the pilot carrier.

[0153] Determine the index of the pilot carrier as NA c =[c 1 ,…,c 6 ], that is, the index of the kth pilot carrier is c k That is, the frequency of the pilot carrier is [0,1,2,3,7,11]*125k.

[0154] After processing in step 1.4, the kth pilot carrier index is c k , c k ∈NA c represents the index of the kth pilot carrier. The signal sent by each pilot carrier at the transmitting end is Then the signal received by the kth pilot carrier is for

[0155]

[0156] in, is a diagonal matrix, consider equation (6), and replace the subscript n k Replace with c k have to represents the channel complex gain of the kth carrier, which The lth diagonal element α q,l represents the loss coefficient of the lth path; The noise matrix of the received signal of the kth pilot carrier is represented by a matrix whose mean is 0 and variance is Gaussian distribution.

[0157] Step 1.4: Vectorization is performed column by column, and all vectors are arranged in index order to form a new pilot signal vector.

[0158] After steps 1.1, 1.2, 1.3 and 1.4, different pilot carrier signals have sparse properties in the frequency domain, and each pilot carrier signal also has sparse properties in the spatial domain. Vectorization is performed, and all pilot vectors are aggregated to form a new pilot vector

[0159]

[0160] in Represents the vector form of the kth pilot carrier signal, k = 1, 2…, 6; d q represents a 3×1 column vector, whose lth element [d q ]l =[Λ q ] l,l α q,l [∏ q ] l,l ; represents the set of all pilot carrier noise vectors; Represents nested array NA c The steering matrix, whose lth column Represents nested array NA c The steering vector of the lth path, and K represents the number of subcarriers, T s represents the sampling period.

[0161] Step 2: Calculate y q The covariance matrix of is vectorized to obtain virtual data, and the virtual data of repeated positions are averaged. Then the largest continuous vector without holes is selected from the virtual data of all positions, and its rank is improved using smoothing technology. The details are as follows:

[0162] Step 2.1: Calculate y in step 1 q The covariance of is as follows:

[0163] Calculate y q The covariance of and cumulative average is obtained:

[0164]

[0165] in, is a diagonal matrix; Q represents the total number of pilot blocks transmitted during the training phase; d q is a 3×1 column vector, representing the complex gain vector within the qth pilot block time, and its lth element [d q ] l =[Λ q ] l,l α q,l [Π q ] l,l ,q∈1,2,…,100; represents the noise variance.

[0166] Step 2.2: R y Vectorized, we get:

[0167]

[0168] Among them, r y Represents R y The vector representation of D; d = vec (D) represents the vector form of D; Indicates I 216 in vector form.

[0169] Step 2.3: Through step 2.2, all possible virtual data can be obtained. Since many of the generated virtual data are repeated, it is necessary to average the repeated virtual data to reduce errors. Then, new vectors are arranged from small to large in the order of delay-DOD-DOA to obtain the maximum continuous non-hole vector. The specific steps are:

[0170] Define the function:

[0171]

[0172] Indicates that the coordinates in the three-dimensional space of delay-DOD-AOA are (k 1 ,k 2 ,k 3 ) data, where k 1 , k 2 and k 3 Respectively represent the position on the delay, DOD, and AOA coordinate axes, and -c 6 ≤k 1 ≤c 6 , -t 6 ≤k 2 ≤t 6 , -r 6 ≤k 3 ≤r 6 .c 6 ,t 6 and r 6 Respectively represent nested arrays NA c ,NA t and NA r The last element of . δ(x) represents the Kronecker function. When x=0, δ(x)=1, and when x≠0, δ(x)=0.

[0173] Definition: Given and if Then it is called and Same location.

[0174] Consider the Khatri-Rao product in (19) The i 1 OK, The i 2 OK, The i 3 OK, The i 4 OK, The i 5 Line and The i 6OK, we can get:

[0175]

[0176] where z = ((i 1 -1)*36+(i 2 -1)*6+i 3 -1)*216+((i 4 -1)*36+(i 5 -1)*6+i 6 ), 1≤z≤216 2 , 1≤i 1 ,i 4 ≤6, 1≤i 2 ,i 5 ≤6, 1≤i 3 ,i 6 ≤6. and Respectively represent nested arrays NA c i-th 1 and i 4 elements, and Respectively represent nested arrays NA t The tth i2 and t i5 elements, and Respectively represent nested arrays NA r No. and elements.

[0177] From step 1.2, we can know that the differential common array of the transmitting and receiving ends and the pilot carrier index is The virtual data at the same position are averaged, and then the virtual data at consecutive positions are aggregated together to form the maximum continuous hole-free vector

[0178]

[0179] Step 2.4: After step 2.3, we can get the hole-free vector It can be expressed as a vector form of an OFDM block signal composed of 23 subcarriers sent by a transmitter equipped with 23 antennas and received by a receiver equipped with 23 antennas. It can be seen that applying nested arrays to the design of beamforming matrices and the selection of pilot carriers can obtain virtual data with a higher space-frequency aperture, which not only improves the resolution of the system, but also increases the maximum number of sources that can be estimated by the system. However, due to The rank of is 1, and the subspace method cannot be used directly. In this step, a smoothing technique will be used to obtain a space-frequency smoothing matrix with a rank greater than 3 so that the parameters of all paths can be correctly estimated. The specific steps are as follows:

[0180] First, determine the row selection matrix:

[0181]

[0182] x∈{c,t,r}.

[0183] make

[0184]

[0185] in,

[0186] Arrange the selected vectors in order from left to right to form a space-frequency smoothing matrix R ss :

[0187]

[0188] in, The lth column vector The lth column vector The lth column vector

[0189] Step 3: After step 2, the enhanced covariance matrix R is obtained ss , R ss The rank of is much larger than 3, so the three paths can be accurately distinguished. ss With rotation invariance, R ss As input data, the 3-D ESPRIT algorithm can be used to estimate the delay, DOD and DOA of all paths. Since the estimated parameters are not one-to-one, the MUSIC algorithm is used to pair all delays, DOD and DOA. The specific steps are:

[0190] Step 3.1: R ss Perform singular value decomposition.

[0191] R ss Perform singular value decomposition to obtain:

[0192] R ss =[U s U n ]Λ[V s V n ] H

[0193] Where Λ represents the eigenvalue diagonal matrix, U s is the signal subspace, which is composed of the left eigenvectors corresponding to the first three largest eigenvalues. n is the noise subspace, which is composed of the left eigenvectors corresponding to the 1725 smallest eigenvalues, V s It is composed of the right eigenvectors corresponding to the first three largest eigenvalues, V n It consists of the right eigenvectors corresponding to the 1725 smallest eigenvalues.

[0194] Step 3.2: Delay estimation.

[0195] make

[0196]

[0197] in, and Represented as a selection matrix. Indicates I 12 The first 11 lines, Indicates I 12 Last 11 lines.

[0198] Yes c Diagonalize and we get:

[0199]

[0200] Then the delay of all paths can be obtained, that is, Where angle(x) represents the phase of vector x, K represents the number of subcarriers in OFDM symbol, and T s is the sampling period. That is, we can get the delay estimation value τ=[τ 1 ,τ 2 ,τ 3 ].

[0201] Step 3.3: DOD estimation.

[0202] Similar to delay estimation, that is:

[0203]

[0204] in and It is represented as a selection matrix. t + byI 12 First 11 rows, P t - Indicates I 12 Last 11 lines.

[0205] Yes t Diagonalize and we get:

[0206]

[0207] Then the DOD of all paths can be obtained, that is, λ represents the transmission carrier wavelength, and d represents the antenna spacing. That is, the estimated value of DOD can be obtained

[0208] Step 3.4: DOA estimation.

[0209] This step is similar to step 3.2 and step 3.3, where Indicates I 12 The first 11 lines, Indicates I 12 After 11 lines, then r Diagonalize to get Φ r Then we can get the DOA of all paths, that is, That is, the estimated value of DOA is θ = [θ 1 ,θ 2 ,θ 3 ].

[0210] Step 3.5: Pair the delay, DOD and DOA.

[0211] Since the obtained delay, DOD and DOA are not necessarily in the order in their vectors, it is necessary to perform a pairing operation on each delay, DOD and DOA.

[0212] Define the null-spectrum as:

[0213]

[0214] By traversing all the delays, DODs and DOAs on the space-frequency spectrum, the parameters corresponding to the L maximum values ​​obtained are for the same path, and the delay, DOD and DOA of each path can be obtained.

[0215] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for estimating signal angle and delay of multiple carriers based on nested arrays, characterized in that: The method described includes two parts: generating virtual data and parameter estimation: (1) Design a corresponding nested array according to the number of RF links at both ends of the transmission and reception, and apply the nested array to the matrix design of the transmission and reception hybrid beamforming, that is, design the above matrix as a random band Toeplitz matrix, the composition of the matrix is ​​determined by the nested array, and the prototype vector of the random band Toeplitz matrix is ​​a random vector; similarly, apply the nested array to the selection of pilot carriers, that is, select the pilot carrier according to the nested array; (2) The received signal on the selected carrier is vectorized to form a pilot data vector in sequence. Then, the effective virtual data is obtained by calculating the covariance matrix of the vector. Since the virtual data has duplicate items, the virtual data with the same phase offset are averaged. The maximum continuous non-hole vector is selected from the virtual data, and the rank of the vector is improved using a smoothing method to obtain a space-frequency smoothing matrix. Finally, the subspace 3-DESPRIT method is used to solve the values ​​of the time delay, departure angle DOD, and arrival angle DOA, and the MUSIC algorithm is used to pair the time delay, DOD, and DOA.

2. The method for estimating signal angle and delay of multiple carriers based on nested arrays according to claim 1, characterized in that: The angle and delay estimation method specifically comprises the following steps: First, let's explain the symbols: (·) T 、(·) * and(·) H and The inverse symbol represents the transpose, conjugate, conjugate transpose and pseudo-inverse operations of a vector or matrix respectively; [·] i,j represents the element in the i-th row and j-th column of the matrix, [·] i,: represents the row vector of the i-th row, [·] :,j represents the column vector of the jth column of the matrix, [·] i Represents the i-th element of a vector; 0 m×n represents a zero matrix with m rows and n columns, I N represents the N×N dimensional identity matrix, vec(·) represents the vectorization of the matrix by column; ⊙ represents the Khatri–Rao product, represents the Kronecker product; if x is a diagonal matrix, diag{x} means extracting the diagonal elements of x to form a new vector; if x is a vector, diag{c} means constructing a diagonal matrix with vector c; Step 1: Design the corresponding nested array according to the number of RF links and the number of pilot carriers; design the transceiver beamforming matrix as a random band Toeplitz matrix according to the nested array of the transceiver end, the composition of the random band Toeplitz matrix is ​​determined by the nested arrays at both ends of the transceiver, and its matrix prototype vector is a random vector; select the pilot carrier according to the nested array of the pilot carrier; vectorize the data received by each pilot carrier, and aggregate them according to the index order of the pilot carrier to form a new pilot data vector; specifically: Step 1.1: Based on the number of radio frequency links M at both ends of the transmission and reception r and M t and the number of pilot carriers M c Get its corresponding nested array: Where x∈{r,t,c}; for convenience of representation, let the nested array corresponding to the sender and receiver be and The nested array corresponding to the pilot carrier is x i Represents NA x The i-th element of x , x∈{r,t,c}; It should be noted that NA c When determining the number of pilot carriers, Cannot be greater than K-1, where K represents the number of subcarriers; Step 1.2: The nested array NA of the transmitter and receiver obtained in step 1.1 r and NA t Design the transmit and receive beamforming matrix W q and F q ; In the qth pilot period, it is assumed that the beamforming matrices of the transmitting and receiving ends are W q and F q ; W q and F q The banded Toeplitz matrix is ​​set. The banded Toeplitz matrix shape consists of a nested array of NA r and NA t control; Step 1.3: W q and F q The prototype vector w q and f q Design is a random vector; Assume W q and F q The prototype vector is w q and f q ; In the millimeter wave communication system, by setting w q and f q is a random vector, removing the correlation between paths, that is, w q Elements f q Elements where λ q,i and χ q,i represents an independent random variable, that is, the probability of taking 1 and -1 is 1 / 2; L w and L f Indicates w q and f q Length, and Less than N r and N t , so let After processing in steps 1.1, 1.2 and 1.3, W q The j-th column vector of can be written as: r j for NA r The jth element of F q The j-th column vector of can be written as: t j for NA t The jth element of ; but: Among them, Λ q is a diagonal matrix whose lth diagonal element u l =2πdsin(θ l ) / λ, d represents the distance between antennas, λ represents the wavelength of the transmission carrier; π q is a diagonal matrix whose lth diagonal element [π q ] l,l = represents the transposed conjugate of the beamforming matrix at the receiving end within the qth pilot block time, F q A represents the beamforming matrix of the transmitter within the qth pilot block time, r represents the steering matrix of the receiving antenna, represents the conjugate transpose of the steering matrix of the transmit antenna; and Indicates a nested array corresponding to the receiving end NA r The steering matrix of which the lth column vector Indicates the receiving end nested array NA r The guiding vector of the lth path, θ l represents the arrival angle of the lth path; Indicates that the corresponding transmitter is nested NA t The steering matrix of which the lth column vector Indicates the nested array NA on the transmitter side t The guiding vector of the lth path, represents the departure angle of the lth path; Step 1.4: Determine the index of the pilot carrier according to the nested array corresponding to the pilot carrier; Determine the index of the pilot carrier as That is, the index of the kth pilot carrier is c k ; After processing in step 1.4, the kth pilot carrier index is c k , c k ∈NA c represents the index of the kth pilot carrier; the signal sent by each pilot carrier at the transmitting end is Then the signal received by the kth pilot carrier is for in, is a diagonal matrix, is a diagonal matrix representing the complex gain, and its lth diagonal element is expressed as α q,l represents the path loss coefficient of the lth path, T s Denoted as the sampling period, τ l represents the propagation time of the lth path, then The lth diagonal element The noise matrix of the received signal of the kth pilot carrier is represented by a matrix whose mean is 0 and variance is Gaussian distribution of Step 1.5: Vectorize by column, and arrange all vectors in index order to form a new pilot signal vector; After step 1.1, step 1.2, step 1.3 and step 1.4, different pilot carrier signals have sparse properties in the frequency domain, and each pilot carrier signal also has sparse properties in the spatial domain; Vectorization is performed, and all pilot vectors are aggregated to form a new pilot vector: in, Represents the vector form of the kth pilot carrier signal, k = 1, 2…, M c ;d q represents an L×1 column vector, whose lth element [d q ] l =[Λ q ] l,l α q,l [Π q ] l,l ; z q represents the set of all pilot carrier noise vectors; Represents nested array NA c The steering matrix, whose lth column Represents nested array NA c The steering vector of the lth path, and Step 2: Calculate y q The covariance matrix of is vectorized to obtain virtual data, and the virtual data of repeated positions are averaged. Then, the largest continuous vector without holes is selected from the virtual data of all positions, and its rank is improved using smoothing technology; specifically: Step 2.1: Calculate y in step 1 q The covariance of is as follows: Calculate y q The covariance of and cumulative average is obtained: in, is a diagonal matrix; Q represents the total number of pilot blocks transmitted during the training phase; d q is an L×1 column vector, representing the complex gain vector within the qth pilot block time, and its lth element [d q ] l =[Λ q ] l,l α q,l [Π q ] l,l ,q∈1,2,…,Q; represents the noise variance; Step 2.2: R y Vectorized, we get: Among them, r y Represents R y The vector representation of D; d = vec (D) represents the vector form of D; express The vector form of Step 2.3: Obtain all possible virtual data through step 2.2, average the repeated virtual data, and then arrange them in the order of delay-DOD-DOA from small to large to form a new vector, and obtain the maximum continuous hole-free vector; Step 2.4: Get the hole-free vector after step 2.3 The rank of the matrix is ​​1; the smoothing technique is used to obtain a space-frequency smoothing matrix with a rank greater than L, and the parameters of all paths are correctly estimated; Step 3: After step 2, the enhanced covariance matrix R is obtained ss , R ss The rank of is much larger than L, and L paths can be accurately identified; R ss As input data, the delay, DOD and DOA of all paths are estimated using the 3-D ESPRIT algorithm; and all delays, DOD and DOA are paired using the MUSIC algorithm; Step 3.1: R ss Perform singular value decomposition and get: R ss =[U s U n ]Λ[V s V n ] H (20) Where Λ represents the eigenvalue diagonal matrix, U s is the signal subspace, which is composed of the left eigenvectors corresponding to the first L largest eigenvalues; U n is the noise subspace, The left eigenvector corresponding to the smallest eigenvalue is composed of V s It is composed of the right eigenvectors corresponding to the first L largest eigenvalues, V n Depend on The right eigenvector corresponding to the smallest eigenvalue is composed; Step 3.2: Estimating the delay; make in, and Represented as a selection matrix; express forward OK, express back OK; Yes c Diagonalize and we get: Then the delay of all paths can be obtained, that is, Where angle(x) represents the phase of vector x, K represents the number of subcarriers in OFDM symbol, and T s is the sampling period; Step 3.3: DOD estimation; in and Represented as a selection matrix; Depend on forward OK, express back OK; Yes t Diagonalize and we get: Then the DOD of all paths can be obtained, that is, λ represents the transmission carrier wavelength, and d represents the antenna spacing; Step 3.4: DOA estimation; express forward OK, express back OK, then r Diagonalize to get Φ r ; Then we can get the DOA of all paths, that is Step 3.5: Pair the delay, DOD and DOA; Since the obtained delay, DOD and DOA are not necessarily in the order in their vectors, a pairing operation is performed on each delay, DOD and DOA; Define the null-spectrum as: All delays, DODs and DOAs are traversed on the space-frequency spectrum. The parameters corresponding to the L maximum values ​​obtained are for the same path, and the delay, DOD and DOA of each path can be obtained.

3. The method for estimating signal angle and delay of multiple carriers based on nested arrays according to claim 2, characterized in that: The step 2.3 is specifically as follows: Define the function: represents data with coordinates (k1, k2, k3) in the three-dimensional space of delay-DOD-AOA, where k1, k2 and k3 represent the positions on the delay, DOD and AOA axes respectively, and and Respectively represent nested arrays NA c ,NA c and NA r The last element of ; δ(x) represents the Kronecker function, when x = 0, δ(x) = 1, when x ≠ 0, δ(x) = 0; Definition: Given dummy data and if Then it is called and Same location; Consider the Khatri-Rao product in step 2.2 The i1th row of The i2th row of The i3th row of The i4th row of The i5th row and The i6th row of r y The zth element is: where z = ((i1 - 1)M t M r +(i2 - 1)M r +i3 - 1)M c M t M r +((i4 - 1)M t M r +(i5 - 1)M r +i6), 1 ≤ z ≤ (M c M t M r ) 2 , 1 ≤ i1, i4 ≤ M c , 1 ≤ i2, i5 ≤ M t , 1 ≤ i3, i6 ≤ M r ; From step 1.2, we can know that the differential common array of the transmitting and receiving ends and the pilot carrier index is The virtual data at the same position are averaged, and then the virtual data at consecutive positions are aggregated together to form the maximum continuous vector without holes:

4. The method for estimating signal angle and delay of multiple carriers based on nested arrays according to claim 2, characterized in that: The step 2.4 is specifically as follows: First, determine the row selection matrix: make in, Arrange the selected vectors in order from left to right to form a space-frequency smoothing matrix R ss : in, The lth column vector The lth column vector The lth column vector

Images