JP2023047697A - spectrum estimation system - Google Patents

Abstract

To provide a spectrum estimation system that can estimate a frequency spectrum and an angular spectrum of received signals in a short time.SOLUTION: A spectrum estimation system estimates a frequency spectrum of received signals received by an array antenna and an angular spectrum of an arrival angle of the received signals, and the spectrum estimation system comprises: the array antenna that consists of a plurality of antennas receiving the received signals; a calculation unit that performs discrete Fourier transformation on the received signals received by the antennas and calculates a tensor consisting of a matrix based on the received signals on which the discrete Fourier transformation is performed; and an estimation unit that, on the basis of a dictionary based on compressed signals corresponding to sub-bands of the frequency and steering vectors for respective arrival angles and the tensor calculated by the calculation unit, estimates the frequency spectrum and the angular spectrum by using compressed sensing.SELECTED DRAWING: Figure 1

Description

Patent Law Article 30, Paragraph 2 application filed (Publisher) The Institute of Electronics, Information and Communication Engineers (Publication name) Angular-Frequency Wideband Spectrum Sensing based on Multi-Coset Sampling (Publication date) July 7, 2021 (Meeting Name) Presentation by the Institute of Electronics, Information and Communication Engineers Smart Radio Study Group (Date) July 14, 2021

The present invention relates to spectral estimation systems for the frequency spectrum and angular spectrum of a signal.

With the popularization of 5G mobile communication systems, it is expected that base stations using the millimeter wave band will be densely deployed by multiple operators. Along with this, it is important to know the center frequencies of signals transmitted from multiple base stations in order to prevent interference between operators and base stations and to improve spectrum utilization efficiency. For this reason, attention is being paid to techniques for grasping the center frequencies of signals transmitted from a plurality of base stations, which are disclosed in Non-Patent Documents 1 and 2 and the like.

Non-Patent Document 1 discloses a frequency sweeping technique for sweeping the center frequency using a low-speed ADC (Analog-to-Digital Converter). In addition, Non-Patent Document 2 discloses MCS (multi-coset sampling) that performs sampling at unequal intervals in order to reduce the ADC conversion speed required for estimation.

H. Sun, A. Nallanathan, C. Wang, and Y. Chen, “Wideband Spectrum Sensing for Cognitive Radio Networks: A Survey,” IEEE Wirel. Commun., no. April, pp. 74-81, 2013. C. P. Yen, Y. Tsai, and X. Wang, “Wideband spectrum sensing based on sub-Nyquist sampling,” IEEE Trans. Signal Process., vol. 61, no.12, pp. 3028-3040, 2013.

However, the frequency sweep method disclosed in Non-Patent Document 1 requires a long time for measurement because it uses a low-speed ADC. Therefore, there is a problem that the cost required for the measurement becomes enormous.

In addition, when developing a CPS (cyber physical system) emulator that requires an accurate model of the radio wave propagation channel including angular characteristics, not only the center frequency but also the angular characteristics such as the angular spectrum of the arrival angle of the received signal can be used. Included information is requested.

However, Non-Patent Document 1 does not assume that information including angular characteristics is swept. For this reason, the technology disclosed in Non-Patent Document 1 has a problem that information including angle characteristics cannot be swept.

Also, the MCS algorithm described in Non-Patent Document 2 only supports the case of a single antenna and does not assume the use of multiple antennas. Therefore, the technique disclosed in Non-Patent Document 2 has a problem that the angle spectrum cannot be estimated.

SUMMARY OF THE INVENTION An object of the present invention is to provide a spectrum estimation system capable of estimating the frequency spectrum and angle spectrum of a received signal in a short period of time.

2. The spectrum estimation system according to claim 1, wherein the spectrum estimation system estimates a frequency spectrum of a received signal received by an array antenna and an angle spectrum of an arrival angle of the received signal, from a plurality of antennas receiving the received signal. a calculation unit for performing a discrete Fourier transform on the received signal received by each of the antennas, calculating a tensor consisting of a matrix based on each received signal subjected to the discrete Fourier transform, and a compression unit corresponding to each frequency subband an estimating unit that estimates the frequency spectrum and the angular spectrum using compressed sensing based on a dictionary based on the obtained signal and the steering vector for each angle of arrival, and the tensor calculated by the calculating unit. It is characterized by having

The spectrum estimation system according to claim 2 is the spectrum estimation system according to claim 1, wherein the estimating unit includes a matrix with different components depending on the number of subbands and a matrix with different components depending on the angle of arrival. is characterized by using the dictionary consisting of the Hadamard product of .

The spectrum estimation system according to claim 3 is the spectrum estimation system according to claim 1 or 2, wherein the calculation unit is based on received signals received by two or more antennas selected from among the antennas. The tensor is calculated.

The spectrum estimation system according to claim 4 is the spectrum estimation system according to any one of claims 1 to 3, wherein the calculating unit calculates the three-dimensional tensor composed of a plurality of matrices. Characterized by

The spectrum estimation system according to claim 5 is the spectrum estimation system according to any one of claims 1 to 4, wherein the estimating unit includes a tensor calculated by the calculating unit and a pseudo-generated tensor. calculating the difference value of the received signal, calculating the correlation between the calculated difference value and the dictionary, and based on the subband and angle of arrival of the frequency spectrum with the largest calculated correlation, the frequency spectrum and angle spectrum of the received signal is characterized by repeating estimating a plurality of times.

ここで、ｙ_ｐ［ｎ］は、ｐ番目の前記アンテナにより受信された前記受信信号を示し、Ｙ_ｐ［ｋ］は、ｙ_ｐ［ｎ］を離散フーリエ変換した前記受信信号を示し、ｎは、サンプリングした前記受信信号の標本点を示し、ｋは、離散フーリエ変換したｙ_ｐ［ｎ］の標本点を示し、Ｎ_ｂは、Ｙ_ｐ［ｋ］の標本点の数を示し、Ｌは、前記周波数スペクトルのサブバンドの数を示し、ｃ_ｐは集合｛０・・・Ｌ－１｝から選択される整数を示し、Ｎ_ｓは、行列のスナップショットの数を示す。

ここで、ｆ_ｋは、ｋ番目の標本点の周波数ビンの周波数を示し、ｃは、光速を示し、φ_ｇは、ｇ番目の到来角度候補値を示し、Ｃ_ｐは集合｛０・・・Ｎ_ｅｌ－１｝から選択される整数を示し、ｄはアレイアンテナの間隔を示す。

ここで、×_ｎは、ｎ番目のモードのテンソル・行列の積を示し、Ｓは、下記の［数４］で示される。

ここで、｜｜・｜｜_Ｆは、フロベニウスノルムを示し、Ｓ（ｉ，：，：）は、任意の３次元テンソルＳの１次元目の軸の方向に切り分け、ｉ番目の切り分けを行列として取り出したものを示し、Ｓ_ｌ，ｇ［ｋ］は、ｌ番目の前記サブバンド及び前記到来角度φ_ｇにおけるスペクトルを示す。 7. The spectrum estimation system according to claim 6 is a spectrum estimation system for estimating a frequency spectrum of a received signal received _by an array antenna and an angle spectrum of an arrival angle of the received signal. an array antenna composed of antennas, and a calculation unit for calculating a three-dimensional tensor represented by the following [Equation 1] based on each received signal received by P antennas selected from the array antenna; Using the three-dimensional tensor calculated by the calculation unit and the two-dimensional tensor shown in [Formula 2] below, the sparse solution of [Formula 3] below is obtained, thereby obtaining the angular spectrum of the received signal and and an estimator for estimating the frequency spectrum.

Here, y _p [n] indicates the received signal received by the p-th antenna, Y _p [k] indicates the received signal obtained by discrete Fourier transform of y _p [n], and n is , represents the sample points of the sampled received signal, k represents the sample points of y _p [n] subjected to the discrete Fourier transform, N _b represents the number of sample points of Y _p [k], and L is Denote the number of subbands of said frequency spectrum, c _p denotes an integer selected from the set {0...L-1}, and N _s denotes the number of matrix snapshots.

where f _k denotes the frequency of the k-th sample point frequency bin, c denotes the speed of light, φ _g denotes the g-th angle of arrival candidate value, and C _p denotes the set {0 . N _el −1}, and d indicates the interval of the array antenna.

Here, x _n indicates the tensor-matrix product of the n-th mode, and S is given by [Formula 4] below.

where ||·|| _F indicates the Frobenius norm, S (i, :, :) cuts an arbitrary three-dimensional tensor S in the direction of the first dimension axis, and the i-th cut is taken as a matrix Denoting the extraction, S _l,g [k] denotes the spectrum at the l th subband and the angle of arrival φ _g .

According to the first to fifth inventions, the frequency spectrum and the angle spectrum are estimated using compressed sensing based on the dictionary and the tensor. This makes it possible to reduce the ADC sampling frequency required for wideband frequency spectrum estimation, thereby reducing the cost and the amount of calculation. Furthermore, it becomes possible to estimate the angular spectrum, and more spectral information can be grasped.

In particular, according to the second invention, the estimator uses a dictionary consisting of a Hadamard product of a matrix whose elements differ according to the number of subbands and a matrix whose elements differ according to the angle of arrival. As a result, it becomes possible to reduce the ADC sampling frequency required for wideband frequency spectrum estimation, and it is possible to reduce the cost and the amount of calculation.

In particular, according to the third invention, the calculator calculates a tensor based on received signals received by two or more antennas randomly selected from among the antennas. As a result, the ambiguity of the peak search of the spectrum can be reduced, and the spectrum can be estimated with high accuracy.

In particular, according to the fourth invention, the calculator calculates a three-dimensional tensor consisting of a plurality of matrices. This makes it possible to estimate a spectrum based on a three-dimensional tensor consisting of a plurality of snapshots, thereby estimating the spectrum with high accuracy.

In particular, according to the fifth invention, the estimating section repeats a plurality of times of estimating the frequency spectrum and angle spectrum of the received signal according to the calculated complex amplitude. Thereby, the spectrum can be estimated with high accuracy using compressed sensing.

According to the sixth invention, the estimator estimates the angle spectrum and frequency spectrum of the received signal by using the two-dimensional tensor shown in [Equation 2]. This makes it possible to reduce the ADC sampling frequency required for wideband frequency spectrum estimation, thereby reducing the cost and the amount of calculation. Furthermore, it becomes possible to estimate the angular spectrum, and more spectral information can be grasped. Also, by finding the sparse solution of [Equation 3], it is possible to reduce the cost and the amount of calculation.

FIG. 1 is an overall schematic diagram of a spectrum estimation system to which the present invention is applied. FIG. 2 is a diagram showing arrival angles of received signals. FIG. 3 is a diagram showing a schematic diagram of a three-dimensional tensor S (i,:,:). FIG. 4 is a diagram showing a flow chart of the restoration algorithm.

A spectrum estimation system to which the present invention is applied will be described in detail below with reference to the drawings.

FIG. 1 is an overall schematic diagram of a spectrum estimation system 100 to which the present invention is applied. A spectrum estimation system 100 includes a base station 20 and a spectrum estimation device 1 that receives a signal transmitted from the base station 20 .

The base station 20 serves as a wireless access point between communication devices and serves as an interface with public communication networks such as the Internet. That is, the base station 20 serves as relay means for enabling communication devices to transmit and receive data to and from public communication networks such as the Internet. Base station 20 transmits a signal to spectrum estimation device 1 .

A spectrum estimation device 1 receives a signal transmitted from a base station 20 and estimates the frequency spectrum and angle spectrum of the received signal. The spectrum estimation apparatus 1 includes an array antenna 10 provided with a plurality of antenna elements, a plurality of delay elements 11 respectively connected to the respective antenna elements of the array antenna 10, and a plurality of ADCs 12 respectively connected to the respective delay elements 11. , a processing unit 14 connected to the selection unit 13 , an estimation unit 15 connected to the processing unit 14 , and a storage unit 16 connected to the estimation unit 15 .

The array antenna 10 is composed of a plurality of arrayed element antennas for receiving signals transmitted from the base station 20 . The array antenna 10 is provided with _Nel antenna elements such that the interval between the antenna elements is d. Array antenna 10 outputs the received signal to delay element 11 .

The delay element 11 is configured by a delay circuit that delays the signal output from the array antenna 10 . In the delay element 11, each antenna element included in the array antenna 10 is connected to a delay circuit having a different signal delay time. The delay element 11 outputs the delayed signal to the ADC 12 .

The ADC 12 samples the signal output from the delay element 11 and digitally converts it. The ADC 12 is connected to each delay circuit of the delay element 11 one by one. A converter with a conversion speed of 50 MHz, for example, is used as the ADC 12 . The ADC 12 outputs the digitally converted signal to the selector 13 .

The selection unit 13 selects a predetermined number of digital signals from among the plurality of digital signals output from the ADC 12 and outputs the selected digital signals to the processing unit 14 .

The processing unit 14 performs a discrete Fourier transform on each digital signal output from the selecting unit 13, and calculates a tensor composed of a matrix based on each signal subjected to the discrete Fourier transform. The processing unit 14 outputs the calculated tensor to the estimation unit 15 .

The storage unit 16 stores various information including dictionaries of frequencies and angles of arrival for estimating frequency spectra and angle spectra. The storage unit 16 outputs a pre-stored dictionary of frequencies and angles of arrival to the estimation unit 15 as necessary.

Based on the tensor output from the processing unit 14 and the dictionary output from the storage unit 16, the estimation unit 15 uses compressed sensing to estimate the frequency spectrum and angle spectrum of the received signal. Compressed Sensing (CS) is a method of recovering a signal from fewer observations than originally required. Using an observation matrix Φ of size m×n (m<n), where the original signal is a vector xεR _n , the observed (compressed) signal vector is y=Φ _x εR _m . At this time, if the dimension of the observed signal vector y is lower than the dimension of the original signal vector x, it becomes an ill-posed problem in which a unique solution cannot be obtained, and the original signal vector x cannot be obtained from the observed signal vector y. However, if the original signal vector x can be converted to a sparse signal vector by using a dictionary matrix, the signal vector can be solved to include many zeros, spaces, or sparseness, that is, a sparse solution can be obtained by solving the original signal vector x. signal can be restored.

Next, the operation of estimating the frequency spectrum and the angle spectrum using spectrum estimation system 100 will be described.

A frequency spectrum is a spectrum that indicates the intensity of each frequency of a signal. The frequency spectrum is divided into, for example, L subbands. In such a case, if the spectral bandwidth is B, then the bandwidth of one subband is B/L. The frequency spectrum may be a spectrum indicating the intensity of frequencies contained in the bandwidth of each subband.

The angle spectrum is a spectrum that indicates the intensity of each arrival angle of the reception signal received by the array antenna 10 . The arrival angle is the angle φ of a direction γ perpendicular to the direction β in which the antennas 10a to 10c are arranged with respect to a straight line α connecting the base station 20 and the array antenna 10, as shown in FIG. Also, the arrival angle is AOA (Angle of Arrival).

First, in spectrum estimation system 100 , array antenna 10 receives signals transmitted from base station 20 . In such a case, each of the _Nel antenna elements provided in the array antenna 10 receives the signal. Also, the antenna elements provided in the array antenna 10 are assigned numbers sequentially selected from the set {0 . . . N _el −1}. This number may be selected by, for example, the order in which the antennas are arranged, but is not limited to this and may be selected by any method. The array antenna 10 outputs received signals to the delay elements 11 respectively.

ここでｃ_ｐは集合｛０・・・Ｌ－１｝から選択される整数を示す。また、ｃ_ｐは集合｛０・・・Ｌ－１｝から任意の乱数を用いてランダムに選択された整数を用いてもよい。遅延素子１１は、遅延させた受信信号をＡＤＣ１２に出力する。 Next, the delay element 11 delays the output received signal. The delay time of each element provided in the delay element 11 is indicated by τ ₀ to τ _Nel-1 according to the number of each connected antenna element. Also, τ _p is represented by [Equation 5].

where c _p denotes an integer selected from the set {0 . . . L−1}. Also, c _p may be an integer randomly selected from the set {0 . . . L−1} using an arbitrary random number. The delay element 11 outputs the delayed received signal to the ADC 12 .

Next, the ADC 12 converts the output reception signal into a digital signal. The ADC 12 may sample such that the sampling frequency is B/L, for example. The ADC 12 outputs the converted digital signal to the selector 13 .

Next, the selector 13 selects a predetermined number of digital signals from among the plurality of digital signals output from the ADC 12 . For example, the selection unit 13 may select P antenna elements from _Nel antenna elements provided in the array antenna 10 and select a digital signal based on the received signal received by the selected antenna elements. good. In such a case, the selection unit 13 may randomly select P antenna elements using arbitrary random numbers. This can reduce the peak search ambiguity of the restoration algorithm described below. The selection unit 13 outputs the selected signal to the processing unit 14 .

Next, the processing unit 14 performs a discrete Fourier transform on the signal output from the selecting unit 13, and calculates a tensor composed of a matrix based on each signal subjected to the discrete Fourier transform. The processing unit 14 processes the signal, for example, and calculates a three-dimensional tensor Y as shown in [Formula 1]. where Y _p [k] denotes the received signal that is the discrete Fourier transform of y _p [n], y _p [n] denotes the received signal received by the p-th antenna, and n is the sampled represents the sample points of the received signal, k represents the sample points of y _p [n] subjected to the discrete Fourier transform, N _b represents the number of sample points of Y _p [k], and L represents the sub-range of the frequency spectrum. Denote the number of bands, c _p denotes an integer selected from the set {0...L-1}, and N _s denotes the number of snapshots of the matrix. The three-dimensional tensor Y is obtained by performing a discrete Fourier transform on the output signal y _p [n] of the ADC 12, phase-rotating the samples of N _b frequency bins and P antenna elements into a matrix, and then summarizing It summarizes the matrix into N _s snapshots. This makes it possible to perform processing without using correlation calculations, thereby estimating the complex amplitudes of the frequency spectrum and angle spectrum.

In such a case, the processing unit 14 first uses the discrete Fourier transform to calculate frequency bins based on the received signal y _p [n]. After that, the processing unit 14 generates rows based on frequency bins with different sample points based on the received signals received by the same antenna, and rows based on the same frequency bins with sample points based on the received signals received by different antennas. Operates on a matrix consisting of columns. Further, the processing unit 14 generates a three-dimensional tensor Y based on the calculated N _s matrices. In such a case, the N _s matrices may be snapshots of the same matrix, or a three-dimensional representation of different matrices generated based on different received signals received by the array antenna 10 at different times. It may be a tensor Y. Also, N _s is an integer of 1 or more, and N _s may be 1. In such a case, the tensor represented by [Formula 1] may be a two-dimensional tensor. The processing unit 14 outputs the calculated tensor to the estimation unit 15 .

ここで、｜｜・｜｜_Ｆは、フロベニウスノルムを示し、Ｓ（ｉ，：，：）は、任意の３次元テンソルＳの１次元目の軸の方向に切り分け、ｉ番目の切り分けを行列として取り出したものを示し、Ｓ_ｌ，ｇ［ｋ］は、ｌ番目のサブバンド及び到来角度φ_ｇにおけるスペクトルを示す。 Next, the estimation unit 15 estimates the frequency spectrum and angle spectrum using compressed sensing based on the tensor output from the processing unit 14 and the dictionary of frequencies and angles of arrival output from the storage unit 16. . For example, the estimating unit 15 converts the spectrum compressed by the processing unit 14 into a three-dimensional tensor represented by [Formula 1] output from the processing unit 14 using a dictionary of frequencies and angles of arrival. Alternatively, the frequency spectrum and angle spectrum of the received signal are estimated based on the 3rd order tensor and the dictionary shown by [Equation 2] output from the storage unit 16 . In such a case, the estimating unit 15 uses the three-dimensional tensor shown in [Formula 1] and the dictionary of the two-dimensional tensor shown in [Formula 2] to obtain the sparse solution of [Formula 3]. Estimate the angular and frequency spectra of the signal. where f _k denotes the frequency of the k-th sample point frequency bin, c denotes the speed of light, φ _g denotes the candidate value for the g-th angle of arrival, and C _p denotes the set {0 . N _el −1}, d denotes the spacing of the array antenna, and l denotes the l-th subband. x _n indicates the n-th mode tensor-by-matrix product (Mode-n tensor-by-matrix product), and S is indicated by [Math. 4] below. For φ _g , N _φ candidate values of arrival angles from φ ₀ to φ _Nφ−1 may be prepared.

where ||·|| _F indicates the Frobenius norm, S (i, :, :) cuts an arbitrary three-dimensional tensor S in the direction of the first dimension axis, and the i-th cut is taken as a matrix Denoting the pick, S _l,g [k] denotes the spectrum at the l th subband and angle of arrival φ _g .

FIG. 3 is a diagram showing a schematic diagram of a three-dimensional tensor S (i,:,:). S (1, :, :) denotes a two-dimensional tensor on the first xz plane obtained by cutting the three-dimensional tensor S in the vertical direction y. S (2, :, :) denotes a two-dimensional tensor on the second xz plane obtained by cutting the three-dimensional tensor S in the vertical direction y.

The two-dimensional tensor dictionary shown in [Equation 2] is a dictionary of frequencies and angles of arrival. The frequency and angle of arrival dictionaries are based on the compressed signal corresponding to each subband of frequency and the steering vector for each angle of arrival. A steering vector is a vector that indicates the phase relationship between the antenna elements of the array antenna 10 . The dictionary of frequencies and angles of arrival may be, for example, a matrix consisting of the Hadamard product of a matrix whose components differ according to the number of subbands of the frequency spectrum and a matrix whose components differ according to the angle of arrival. By using this dictionary, it becomes possible to reduce the ADC sampling frequency required for wideband frequency spectrum estimation, and it is possible to reduce the cost and the amount of calculation. Furthermore, it becomes possible to estimate the angle spectrum, and more spectrum information can be grasped.

The estimating unit 15 may estimate the sparse solution of the expression given by [Math. 3] using, for example, the compressed sensing iterative algorithm shown in FIG. The estimation unit 15 calculates the difference value between the tensor output from the processing unit 14 and the pseudo-generated tensor, calculates the correlation between the calculated difference value and the dictionary described above, and the calculated correlation is Multiple iterations of estimating the angular and frequency spectra of the received signal based on the subband and angle of arrival of the largest frequency spectrum. Detailed processing in each step in FIG. 4 will be described below.

First, in S10, a difference value R between the three-dimensional tensor shown in [Formula 1] and the pseudo-generated three-dimensional tensor is calculated. At this time, the three-dimensional tensor shown in [Formula 1] may be used as it is without calculating the difference value.

ここで、１_Ｎｂは、すべての要素が１に等しい長さＮ_ｂのベクトルを示し、ｉとｊとは、それぞれサブバンドと到来角度との番号を示し、Ｔは行列の転置を示す記号であり、Ｈは行列のエルミート転置を示す記号である。また、は、Ｎ_ｂ個の周波数ビンを合計して周波数帯域を形成することによって計算される。 Next, in step S11, the correlation C represented by [Equation 6] between the difference value R and the dictionary represented by [Equation 2] is obtained.

where 1 _Nb denotes a vector of length _Nb with all elements equal to 1, i and j denote the subband and angle of arrival numbers respectively, and T is the symbol denoting the transpose of the matrix. , and H is a symbol indicating the Hermitian transpose of the matrix. Also, is computed by summing _Nb frequency bins to form a frequency band.

Next, in step S12, it is determined whether the stop condition is satisfied. If the estimated spectrum contains an error, it will cause a continuous error when generating a pseudo tensor, which will be described later. Therefore, when the difference value R is calculated in step S10, the detected signal is completely removed. part of the signal remains. This remainder may be detected as a false signal in later iterations. Therefore, a stopping condition is determined to reduce the false alarm rate. In step S12, the loop of the algorithm is interrupted if the stopping condition is met.

ここで、Γ_ｃｄｆ（x）は、それぞれ形状とスケールのパラメーターｋとφを持つガンマ分布の累積分布関数を示し、σ^２ｎは、ガウス分布の分散を示す。 The stopping condition is determined by the magnitude of the frequency bin of the correlation C and the threshold value γ shown in [Formula 7].

where Γ _cdf (x) denotes the cumulative distribution function of the gamma distribution with shape and scale parameters k and φ, respectively, and σ ²ⁿ denotes the variance of the Gaussian distribution.

ここで、κは設定された閾値を示す。 It is also determined whether the stop condition satisfies the expression shown in [Equation 8].

where κ indicates a set threshold.

ここで、１_Ｎｂは、すべての要素が１に等しい長さＮ_ｂのベクトルを示す。 Next, in step S13, the subband and angle with the largest correlation are searched. In such a case, the subband and angle with the largest correlation are searched for, for example, using the formula shown in [Equation 9].

where 1 _Nb denotes a vector of length _Nb with all elements equal to one.

ここでＶ_ｑは、一時的に生成される辞書を示し、（・）^＋は、逆行列を示す。 Next, in step S14, the complex amplitude _Wq of the spectrum is estimated. In such a case, the complex amplitude W _q of the spectrum is estimated using, for example, the formula shown in [Equation 10].

where V _q denotes a temporarily generated dictionary and (·) ⁺ denotes an inverse matrix.

Next, in step S15, it is determined whether the number of iterations exceeds the maximum number of iterations. Break the loop of the algorithm if the maximum number of iterations is exceeded. If the maximum number of iterations is not exceeded, the process proceeds to step S16, which will be described later.

Next, in step S16, a pseudo three-dimensional tensor is generated. After that, the process moves to step S10 again, and the difference value R is calculated using the formula shown in [Equation 11].

This iterative algorithm is an algorithm that repeats steps S10 to S16 a plurality of times while increasing the value of k by one to estimate the frequency spectrum and angle spectrum that satisfy the conditions. Thereby, the spectrum can be estimated with high accuracy using compressed sensing. Also, the estimation unit 15 may estimate the frequency spectrum and the angle spectrum using any method other than the compressed sensing using this iterative algorithm.

By performing the operations described above, the operations of the spectrum estimation system 100 in this embodiment are completed. This makes it possible to reduce the ADC sampling frequency required for wideband frequency spectrum estimation, thereby reducing the cost and the amount of calculation. Furthermore, it becomes possible to estimate the angular spectrum, and more spectral information can be grasped.

While embodiments of the invention have been described, the embodiments have been presented by way of example and are not intended to limit the scope of the invention. Such novel embodiments can be implemented in various other forms, and various omissions, replacements, and modifications can be made without departing from the scope of the invention. This embodiment and its modifications are included in the scope and gist of the invention, and are included in the scope of the invention described in the claims and its equivalents.

1 spectrum estimation device 10 array antenna 11 delay element 12 ADC
13 selection unit 14 processing unit 15 estimation unit 16 storage unit 20 base station 100 spectrum estimation system

Claims (6)

A spectrum estimation system for estimating the frequency spectrum of a received signal received by an array antenna and the angle spectrum of the angle of arrival of the received signal,
an array antenna comprising a plurality of antennas for receiving the received signal;
a calculation unit that performs a discrete Fourier transform on the received signal received by each of the antennas and calculates a tensor composed of a matrix based on each received signal that has undergone the discrete Fourier transform;
Using compressed sensing, the frequency spectrum and the and an estimator for estimating an angular spectrum. 2. The spectrum estimation according to claim 1, wherein the estimation unit uses the dictionary consisting of a Hadamard product of a matrix having different components depending on the number of subbands and a matrix having different components depending on the angle of arrival. system. 3. The spectrum estimation system according to claim 1, wherein the calculator calculates the tensor based on each reception signal received by two or more antennas selected from among the antennas. The spectrum estimation system according to any one of claims 1 to 3, wherein the calculator calculates the three-dimensional tensor composed of a plurality of matrices. The estimating unit calculates a difference value between the tensor calculated by the calculating unit and a pseudo-generated tensor, calculates a correlation between the calculated difference value and the dictionary, and calculates the largest correlation. The spectrum estimation method according to any one of claims 1 to 4, wherein the estimation of the frequency spectrum and angle spectrum of the received signal is repeated a plurality of times based on the subbands and angles of arrival of the frequency spectrum. . A spectrum estimation system for estimating the frequency spectrum of a received signal received by an array antenna and the angle spectrum of the angle of arrival of the received signal,
an array antenna consisting of N _el antennas for receiving the received signal;
a calculation unit that calculates a three-dimensional tensor represented by the following [Equation 1] based on each reception signal received by P antennas selected from the array antenna;
Using the three-dimensional tensor calculated by the calculation unit and the two-dimensional tensor shown in [Formula 2] below, the sparse solution of [Formula 3] below is obtained, thereby obtaining the angular spectrum of the received signal and and an estimator for estimating a frequency spectrum.

Here, y _p [n] indicates the received signal received by the p-th antenna, Y _p [k] indicates the received signal obtained by discrete Fourier transform of y _p [n], and n is , represents the sample points of the sampled received signal, k represents the sample points of y _p [n] subjected to the discrete Fourier transform, N _b represents the number of sample points of Y _p [k], and L is Denote the number of subbands of said frequency spectrum, c _p denotes an integer selected from the set {0...L-1}, and N _s denotes the number of matrix snapshots.

where f _k denotes the frequency of the k-th sample point frequency bin, c denotes the speed of light, φ _g denotes the g-th angle of arrival candidate value, and C _p denotes the set {0 . N _el −1}, and d indicates the interval of the array antenna.

Here, x _n indicates the tensor-matrix product of the n-th mode, and S is given by [Formula 4] below.

where ||·|| _F indicates the Frobenius norm, S (i, :, :) cuts an arbitrary three-dimensional tensor S in the direction of the first dimension axis, and the i-th cut is taken as a matrix Denoting the extraction, S _l,g [k] denotes the spectrum at the l th subband and the angle of arrival φ _g .

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