KR100681393B1 - Multipath estimation using channel parameters matrix extension with virtual sensors - Google Patents

Abstract

A method for detecting multiple paths by using virtual sensors is provided to shorten measurement time and to reduce the manufacturing cost of a measurement system by speedily measuring signals through a smaller number of antenna sensors in a mobile communication environment having a complicated channel pattern. An algorithm for executing a method for detecting multiple paths by using virtual sensors first estimates the number of multiple paths by using received signals(Y) and a rank-expanded parameter matrix(S10). Then, the algorithm checks whether the estimated value(LE) gets equal to "M^tot-1"(S20). Until the estimated value(LE) gets equal to "M^tot-1", the algorithm repeats rank expansion of the received signals(S30). Finally, the algorithm calculates "Y^tot", a sample value of the total received signals including virtual sensors, "A^tot" and "N^tot", sample values of parameter matrixes including virtual sensors and noises, and "sigma^2", a reception noise distribution value, and then creates Rx signals of virtual sensors(S40).

Description

Multipath Estimation Using Channel Parameters Matrix Extension with Virtual Sensors

1 is a view for explaining a multipath model used in the present invention.

2 shows a conceptual layout of a virtual sensor with respect to the measured sensor.

3 is a flowchart of the multipath detection method of the present invention.

4 shows a graph of RMSE expressed as a function of SNR for the same power as a result of multipath number estimation.

5 shows a graph of RMSE with respect to different numbers of actual sensors as a result of multipath number estimation.

The present invention relates to multipath detection, and more particularly, to estimating the number of multipaths exceeding the actual number of sensors by constructing a received signal of a virtual sensor using a signal received in a multipath environment.

Research on channel parameter estimation in the mobile communication environment has been extensively conducted for the last decade. Recently, high-resolution channel parameter estimation techniques for received signals in wireless communication environments, particularly mobile communication environments, have been proposed. .

In general, the techniques used for channel parameter estimation include music (MUltiple SIgnal Classification technique, MUSIC) and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT), among which space alternating Generalized EM (SAGE) shows the best performance in terms of algorithm convergence speed and accuracy.

When the SAGE algorithm is applied to channel parameter estimation, the most important factor in determining the estimation time or convergence speed of the algorithm is prior information on the number of multipaths. That is, in order to estimate the channel parameter, it is necessary to know the number of multipaths. Akaike's Information Theoretical Criterion (AIC) or Minimum Description Length (MDL) standard techniques are generally used to estimate the number of multipaths. These methods set the threshold value according to the user's intuition by using the eigenvalue obtained from the sample covariance matrix of the received signal and estimate the number of multipaths. There was a different problem.

To remedy this problem, Mati Wax and Thomas Kailath's paper, "Detection of Signals by Information Theoretic Criteria" (IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-33, no. 2, pp 387-392, Apr. 1985) proposed a method for determining the number of multipaths with values that minimize the AIC or MDL criteria. However, this method is limited to the maximum value of the estimate by the number of antenna sensors (hereafter simply referred to as 'sensors') (ie the number of multipaths that can be estimated is 'number of sensors-1'). However, when the number of multipaths is equal to or greater than the number of sensors, there is a limit that it is impossible to accurately estimate the number of multipaths. This method has no problem in a communication environment in which the channel state is not complicated, but in the recent mobile communication environment, the multipath of the received signal generally has a larger value than the actual number of sensors. As described above, channel parameter estimation using the Information Theoretic Criteria technique and the SAGE algorithm in an environment where multiple paths exist beyond the number of sensors results in incomplete results.

As a way to overcome the limitation of multipath number estimation with limited performance, when estimating channel parameters in a real environment, it is generally assumed that the number L of multipaths is a very large value. However, uncertainty about the number of multipaths (L) leads to several unreasonable results. For example, if the number of multipaths L is set to a value larger than necessary, the algorithm's computation time is unnecessarily increased or the possibility of generating phantom paths that do not actually exist is increased. On the contrary, when the number L of multipaths is smaller than the actual number, some channel information cannot be reflected in channel modeling. As a result, the estimation of the number of multipaths needs to be made more accurately based on more valid evidence.

An object of the present invention is to provide a multi-path estimation method using a virtual sensor that can estimate the multi-path beyond the number of the antenna sensor using a limited number of actual antenna sensors in a wireless communication environment with a complex channel condition. It is done. In other words, it is possible to efficiently measure channel parameters even in a complex channel state environment by realizing an environment in which there are more antenna sensors than the actual number of antenna sensors by software manipulation without physically increasing the number of antenna sensors. To provide.

In order to achieve the above object, the present invention provides a virtual antenna sensor using a limited number of real antenna sensors in an environment in which multiple multipaths and additive white gaussian noise (AWGN) exist. It is a multipath detection method that can estimate the number of multipaths larger than the actual number of antenna sensors by implementing software that can be viewed as more present.

)과 이의 고유값(

)을 계산하여 다중경로의 개수를 추정하는 제2 단계; 추정된 다중경로의 개수(

)가 상기 '실제 안테나 센서 개수(M)-1' 과 같을 때, 상기 수신측에 상기 실제 안테나 센서 외에 가상 센서가 더 존재하는 것으로 가정하고 수신신호의 반복적 인 랭크 확장을 하여 그 가상센서의 수신 신호를 구성하는 제3 단계; 및 상기 실제 안테나 센서에 의한 수신신호 외에 상기 가상 센서에 의한 수신신호까지를 포함하여 상기 제2 단계 및 제3 단계를 반복적으로 수행하는 제4 단계를 구비하는 것을 특징으로 한다. In the multipath detection method using the virtual sensor, specifically, the signals radiated from at least one transmitting antenna and propagated through the multipath L are measured by M real antenna sensors on the receiving side. Sampling a received signal; From the sampled values, a sample covariance matrix (

) And its eigenvalues (

A second step of estimating the number of multipaths by calculating Estimated number of multipaths (

) Is equal to the number of actual antenna sensors (M) -1, assuming that there are more virtual sensors besides the actual antenna sensors on the receiving side, iteratively expanding the received signal and receiving the virtual sensors. A third step of constructing a signal; And a fourth step of repeatedly performing the second and third steps including the received signal by the virtual sensor in addition to the received signal by the actual antenna sensor.

In the multipath detection method, the number of the virtual sensors added in the third step may be equal to the number of the multipaths obtained in the second step.

)값이 상기 가상센서의 개수를 포함한 총 안테나 센서 개수 M^tot-1보다 작게 될 때까지 이루어지고, 그 때의 추정 다중경로의 개수(

)의 값이 얻고자 하는 다중경로의 개수 (L)의 값으로 정하는 것이 바람직하다. In the multipath detection method, iteratively performing the second and third steps may include the estimated number of multipaths (

) Value is made until the total number of antenna sensors including the number of virtual sensors is less than M ^tot -1, and the number of estimated multipaths at that time (

) Is preferably set to the value L of the number of multipaths to be obtained.

에 의해 산출된다. 여기서 N은 수신신호의 샘플 개수이고, y(t_i)는 상기 가상센서의 수신신호이며, H는 허미션 연산자(Hermition Operator)이다. 나아가, 상기 제2 단계에서의 상기 다중경로의 개수의 추정은, 맨 처음에는 상기 실제 안테나 센서의 수신신호만을 이용하며, 그 다음부터는 상기 실제 안테나 센서와 상기 가상 센서에 의한 수신신호를 모두 이용하여 아래 식 (A)를 이용하여 k값을 변경시켜가면서 AIC, MDL 판단기준(criteria)을 계산한 다음, 그 계산된 AIC(k)와 MDL(k) 값들을 아래 식 (B)에 적용하여 이전의 반복 계산 단계에서 다중 경로의 개수

를 추정하는 방식으로 이루어진다. 여기서, M^tot는 실제 센서의 개수와 가상 센서의 개수를 합한 총 안테나 센서의 개수를 의미하며, k는 변수로서

의 값을 가지며, N은 수신 샘플의 개수,

는 내림차순으로 정렬된 샘플 공분산 행렬

의 고유값(eigenvalue)인 것을 특징으로 하는 가상 센서를 이용한 다중경로 검출방법.In such a multipath detection method, the sample covariance matrix is

Calculated by Where N is the number of samples of the received signal, y (t _i ) is the received signal of the virtual sensor, and H is a Hermition Operator. Further, the estimation of the number of the multipaths in the second step may be performed by first using only the received signals of the real antenna sensor, and then using both the received signals of the real antenna sensor and the virtual sensor. Calculate the AIC and MDL criteria by changing the k value using Equation (A) below, and then apply the calculated AIC (k) and MDL (k) values to Equation (B) below. Number of multipaths in the iterative calculation phase of

Is made in the manner of estimating. Here, M ^tot means the total number of antenna sensors, which is the sum of the number of real sensors and the number of virtual sensors, and k is a variable.

Where N is the number of received samples,

Is a sample covariance matrix sorted in descending order

Multipath detection method using a virtual sensor, characterized in that the (eigenvalue) of.

... (A)

... (A)

... (B)

... (B)

The third step of the multipath detection method as described above comprises: an angle of arrival (AoA) representing a phase difference between the respective paths of the received signal by the virtual sensor for repetitive rank expansion of the received signal; Determining parameters constituting a received signal by the virtual sensor, such as channel gain, distribution of received noise, and relative propagation time delay for each propagation path. In this case, the variance ( σ ² ) of the received noise of the received signal by the virtual sensor is determined by Equation (C) below, and y _m ^dif ( t ) in Equation (C) below is applied to the m th actual antenna sensor. Is a difference signal of a sampling value at a specific time point t and a T + T _s after one transmission period thereof, and E denotes an expected value obtained by averaging the duration of a PN sequence of one period.

...(C)

... (C)

)은 아래 식 (D)를 이용하여 경로 인덱스

값을 1부터 1씩 M-1까지 증가시키면서, y _i ^Ts (t)와 송신신호의 버스트신호 a(t-τ)간의 상관도(correlation)를 계산하고 그 계산된 값들 중 최대값(peak)이 전파지연시간

의 값으로 정하되, 경로 인덱스

의 범위는 각 반복단계마다 그 이전의 반복단계에서 추정된 다중경로 개수 L _E 를 가지고

로 새롭게 정의하는 방식으로 계산되며, 아래 식 (D)에서,

은 k 번째 가상 센서에 대한 처음 M-1개의 다중경로의 상대적 전파지연시간

이며, 인덱스 i는 모듈러 연산 i=mod(k-1, M)+1 로 정해지는 값이고, y _i ^Ts (t)는 y _i (t)에 대한 한 주기 동안의 수신신호의 데이터이며, a(·)는 송신신호 x(t)의 버스트신호, <A, B>는 신호 A와 신호 B 간의 상관도(correlation)이다.Furthermore, the relative propagation time delay for each propagation path (

) Is the path index using the following equation (D)

Calculate the correlation between y _i ^Ts ( t ) and the burst signal a (t-τ) of the transmitted signal, increasing the value from 1 to 1 by M-1, and peak among the calculated values. The propagation delay time

Set to, but path index

For each iteration, we have a multipath number L _E estimated at the previous iteration.

Is calculated in a newly defined manner, and in equation (D) below,

Is the relative propagation delay time of the first M-1 multipaths for the k th virtual sensor.

Index i is a value determined by the modular operation i = mod (k-1, M) +1, y _i ^Ts ( t ) is the data of the received signal for one period for y _i ( t ), and a (*) Is a burst signal of transmission signal x (t), and <A, B> is a correlation between signal A and signal B.

...(D)

... (D)

)은 아래 식 (E)에 의해 계산하되 경로 인덱스

의 범위는 각 반복단계마다 그 이전의 반복단계에서 추정된 다중경로 개수 L _E 를 가지고

로 새롭게 정의하는 방식으로 계산하며, 아래 식(E)에서 i=mod(k-1,M)+1이고,

,

이고,

는 한 송신주기 동안의 수신신호,

는 신호 A, B 사이의 상관도를 나타낸다. Furthermore, the complex channel gain (

) Is calculated by the following formula (E)

For each iteration, we have a multipath number L _E estimated at the previous iteration.

Calculate in a newly defined manner, i = mod (k-1, M) + 1 in the formula (E),

,

ego,

Is a received signal for one transmission period,

Denotes a correlation between signals A and B.

...(E)

... (E)

With respect to the rank expansion in the third step of such a multipath detection method, the rank of the channel parameter vector that can be incremented by the virtual sensor at once is &quot; antenna sensor present in the previous iteration step. It is characterized by the number of '1'.

Hereinafter, with reference to the accompanying drawings will be described the present invention in more detail.

(1) theoretical model of multipath channel

1 is a view for explaining a multipath model used in the present invention. On the receiving side Rx, a plurality of receiving antenna sensors are arranged at arbitrary positions, and the transmitting side Tx includes one or a plurality of transmitting units. The transmission signal x (t) is a signal transmitted from at least one signal source Tx, and is composed of a burst signal a (t) of a periodically repeated period T _s and is expressed as follows.

(1)

(One)

의 형태로 나타내진다. 송신측(Tx)에서는 이러한 송신신호 x(t)가 주기 T_s마다 반복적으로 송신된다.In Equation (1), the burst signal is applied to a shaping pulse whose PN (PseudoNoise) sequence [a ₀ , ..., a _s-1 ] and duration T _p (i.e. T _s = ST _p ). About

It is represented in the form of. The transmitting side (Tx) in such a transmission signal x (t) is transmitted repeatedly every period T _s.

번째 경로의 기여는 다음과 같은 벡터로 표현될 수 있다.Suppose that there is an array of M antenna sensors receiving a signal generated by L far-field scattering sources, that is, multipath signals, on the receiving side Rx of FIG. For the M baseband signals at the output of these receiving antenna sensors Rx,

The contribution of the first path can be expressed by the following vector.

(2)

(2)

는

번째 전파를 구성하는 모든 파라미터를 나타내는 벡터이다. 이 벡터에서 파라미 터

는 도래각(AoA),

는 경로이득과 각 전파경로의 상대적인 위상차를 나타내는 복소채널이득,

는 도플러 주파수, 그리고

는 각 전파경로별 상대 전파지연시간을 나타낸다.

은

번째 전파경로에 관한 지연신호를 나타낸다.

으로 정의되는 Mxl 벡터는 수신측의 안테나 센서 어레이의 스티어링 벡터(steering vector)로서 이는 그 안테나 센서 어레이의 각 원소 센서의 안테나 이득과 상대적인 위치정보를 포함하고 있다. Here, if the parameters constituting the formula (2) are defined,

Is

Vector representing all the parameters constituting the first propagation. Parameter in this vector

Is the angle of arrival (AoA),

Is a complex channel gain representing the path gain and the relative phase difference between each propagation path,

Is the Doppler frequency, and

Represents the relative propagation delay time for each propagation path.

silver

The delay signal related to the first propagation path is shown.

The Mxl vector defined as is a steering vector of the antenna sensor array on the receiving side, which includes antenna gain and relative position information of each element sensor of the antenna sensor array.

1 is a general definition of a multipath model, and an object of the present invention is to find a method for finding the number L of multipaths from a received signal in such a multipath model. For simplicity of representation, the channel parameter vector is defined as follows.

(3)

(3)

은 시간지연성분

을 제외한 나머지 모든 요소들로 구성된 새로운 명목 파라미터이다. 시간지연성분을 제외한 나머지 요소들을 모두 합쳐 파라미터 벡터

로 표현할 수 있다.here,

Silver time delay component

New nominal parameter consisting of all elements except for. Parameter vector that combines all elements except time delay

Can be expressed as

The receiver Rx receives a signal sent from the transmitter Tx, and since an obstacle generally exists between the transmitter Tx and the receiver Rx, a signal in which the signals propagated through various paths are combined is received. Therefore, the signal measured at the receiving antenna sensor array (that is, the received signal) y (t) includes a signal input through L multipaths, and when the number of sensors in the receiver is M, It can be expressed in the form of an observation vector y (t) of magnitude.

(4)

(4)

은 해당 다중 경로의 시간지연을 포함한 송신 신호이고, n(t)는 M개의 센서 어레이에 수신되는 신호의 부가잡음성분과 관련되는 Mㅧ 1 크기의 가우시안 벡터 프로세스(Gaussian vector process)이다. 다중 경로의 개수 L은 센서 개수 M보다 큰 값을 가질 수 있으며, 수신신호의 부가 잡음 n(t)는 신호와 관계없이 평균이 0이고 공분산 행렬(covariance matrix)이

이며 (따라서, 각 채널의 잡음 간의 자기 상관도(auto-correlation)는 존재하지만 상호 상관도(cross-correlation)는 존재하지 않는다) 정적인 복소수의 에르고드적인 가우시안 벡터 프로세서로 가정한다. 여기서

는 잡음의 파워를 나타내는 미지의 상수이고,

는 단위행렬이다. 이 때 송신신호는 반복적으로 송출되는 PN시퀀스로 구성되며 한 시퀀스는 T_s (송신신호의 송신주기)의 길이를 갖는다. In equation (4)

Is a transmission signal including the time delay of the corresponding multipath, and n (t) is a Gaussian vector process of size M ㅧ 1 related to the additive noise component of the signal received at the M sensor arrays. The number L of multipaths may have a value greater than the number M of sensors. The additional noise n (t) of a received signal has an average of 0 and a covariance matrix is independent of the signal.

(Hence, there is auto-correlation between each channel's noise but no cross-correlation). It is assumed to be a static, complex, ergand Gaussian vector processor. here

Is an unknown constant that represents the power of the noise,

Is the unit matrix. At this time, the transmission signal is composed of PN sequences that are repeatedly transmitted, and one sequence has a length of T _s (transmission cycle of the transmission signal).

(2) Information theoretic criteria using virtual sensors

FIG. 2 illustrates a method of estimating the number L of multiple paths having a value larger than the number M of receiving antenna sensors, and illustrates a conceptual layout diagram of a virtual sensor for an actual antenna sensor.

To introduce the virtual sensor concept, we first rewrite equation (4) as

(5)

(5)

Where A is an MxL channel parameter matrix defined as follows.

(6)

(6)

을 갖는 Lxl의 전송된 신호 벡터로서 다음과 같이 주어진다.x (t) is the time delay between the elements

The transmitted signal vector of Lxl having is given by

(7)

(7)

를 이용하여 다시 쓰면 다음과 같다.Then, N sampling of the received signal vector y (t) is a received signal matrix.

Rewrite using

(8)

(8)

In this case, X and N are as follows.

(9)

(9)

(10)

10

Assuming that the number of multipaths L is greater than or equal to the number of sensors M, the channel parameter matrix A has the full row rank of M. Assuming that the sample number N of the received signal is sufficiently large, the rank of Y becomes M, and as a result, the number of multipaths estimated by conventional conventional information theoretic criteria is always M-1. Becomes This is because the maximum value of the path detected by the usual criteria is limited by the number of sensors.

는 k번째 가상센서의 수신신호를 나타낸다. 이 때 가상센서의 수신신호는 다중경로의 개수를 결정하는 데 있어 필드 패턴에 아무런 제약도 필요하지 않다. 따라서 식 (3)에서 각 가상센서에 해당하는 스티어링(steering) 벡터

의 원소들에 관해 임의의 값을 선택할 수 있고(즉, 채널에 관계없이 사용자가 조정 가능한 값이고), 이러한 사실은 가상 센서의 복소채널이득에 해당하는

의 선택에 대한 제약조건도 없음을 의미한다. 또한, 일반적인 이동통신 환경에서 도래파의 도플러 주파수의 크기는 1/T_s에 비해 매우 작다. 그러므로 식 (2)의 위상에 해당하는

는 PN 시퀀스의 지속시간과 같은 각 측정시간 동안은 상수로 볼 수 있다. 이러한 가정으로부터 가상센서에 해당하는 파라미터 벡터

의 원소들을 시간에 관계없는 값들로 구할 수 있다.To overcome this limitation, as shown in FIG. 2, a virtual sensor method is proposed that assumes that K virtual sensors are placed in the receiving antenna sensor array so that the total number of antenna sensors M + K is greater than L. In Figure 2,

Denotes the received signal of the k-th virtual sensor. At this time, the received signal of the virtual sensor does not need any restriction on the field pattern in determining the number of multipaths. Therefore, steering vector corresponding to each virtual sensor in equation (3)

You can select any value for the elements of (i.e. user-adjustable value regardless of channel), and this fact corresponds to the complex channel gain of the virtual sensor.

There is no constraint on the choice of. In addition, the magnitude of the Doppler frequency of the arrival wave in a typical mobile communication environment is very small compared to 1 / T _s . Therefore, corresponding to the phase of equation (2)

Can be seen as a constant for each measurement time, such as the duration of a PN sequence. From these assumptions, the parameter vector corresponding to the virtual sensor

The elements of can be found as time-independent values.

The entire channel parameter vector including the elements of the virtual sensor as well as the actual antenna sensor is defined as follows.

(11)

(11)

Meanwhile, the steering vector may be written in a form including a steering vector element of the virtual sensor as follows.

(12)

(12)

The problem is to estimate the number of paths L (≥M) with respect to the set y (t ₁ ), ..., y (t _N ) of a myriad of received signals whose rank is less than L. A possible approach to this problem is to extend the rank of the channel parameter vector with the help of virtual sensors. According to a general information theoretic criterion, if the number M + K, which is the sum of the number of real sensors and the number of virtual sensors, is greater than the number L of multipaths, the value of L can be estimated accurately. The virtual sensor method looks at the received signals measured by the M real antenna sensors, and if there is an M + 1 antenna, estimates what value the antenna sensor received. Extends the rank of the channel parameter vector by estimating the received signal measured by this antenna sensor if present, and by considering how the received signal would be different if K virtual sensors were placed in M real antenna sensors. do. That is, in order to estimate the number of multipaths using AIC and MDL criteria without the condition of the individual propagation type and each position of the virtual sensor, the rank expansion of the received signal matrix is necessary. For this, Equation (4) may be represented by a matrix representation including the received signal by the virtual sensor as in Equation (5) below.

(13)

(13)

로 표현되는 전체 수신신호의 샘플 값으로서 여기에는 실제 안테나 센서에 의한 수신신호와 가상센서에 의한 수신신호가 모두 포함되며,

과

은 각각 실제 안테나 센서와 가상센서에 의한 채널 파라미터 행렬과 노이즈의 샘플 값으로서, 각각 아래와 같이 쓸 수 있다.Where Y ^tot is

Sample values of all the received signals, which are expressed as, include both the received signal by the actual antenna sensor and the received signal by the virtual sensor.

and

Are the sample values of the channel parameter matrix and the noise by the real antenna sensor and the virtual sensor, respectively.

(14)

(14)

(15)

(15)

(3) Estimation of the number of multipaths using the virtual sensor technique

In order to complete the configuration of equation (13), the virtual sensor such as the angle of arrival (AoA) representing the phase difference between each path of the received signal by the virtual sensor, the complex channel gain, the noise dispersion, and the relative propagation time delay for each propagation path are used. The parameters constituting the received signal must be determined.

1) Estimation of Noise Dispersion

In order to apply the virtual sensor technique to determine the number of multipaths, it is necessary to ^first estimate the noise variance σ ² from the actual received signal.

Defining the difference vector y ^dif ( t ) between two consecutive received signal vectors y ( t ) and y ( t + T _s ) with a deviation of one PN sequence period is the signal portion Ax of these two received signal vectors. Since the same with each other as defining a (t), and Ax (t + t _s), you can write the Mx1 vector ^dif y (t) as follows:

(16)

(16)

Further, for y ^dif ( t ) , the covariance of each row is given by the following equation.

(17)

(17)

Where y _m ^dif ( t ) and n _m (??) are the values associated with the m th row of y ^dif ( t ) and n _m (??) . That is, since y _m ( t ) is the sampling value by the m th actual antenna sensor, y _m ^dif ( t ) is the sampling at a point in time t by the m th real antenna sensor and t + T _s after one transmission period thereof. Value difference signal. In addition, n _m (t) is added noise of the received signal by the m th actual antenna sensor. σ _m ² is the noise variance of the m th sensor, and the expected value E in Eq. (17) means to take the average over the duration of one period of PN sequence. At this time, one period corresponds to one period of the transmission signal with T _s .

Using equation (17), the variance σ ² of the received noise can be estimated as follows.

(18)

(18)

Ideally, all noise variances for each sensor are the same. However, the expected value for the finite window causes some difference between the noise variances of the receiving sensors. Therefore, the noise variance is estimated as the ensemble mean of all the calculated values of the noise variance in equation (17). By using Equation (18), it is possible to generate a noise value by the virtual sensor.

2) Rank expansion

Now, to increase the rank of the parameter matrix using the calculated noise variance and the determined transmission sequence, the following process is performed.

은 다음과 같다. As already known by the AIC / MDL technique, assuming that the number L of multipaths is greater than the number M of antenna sensors, in this case, the number of multipaths estimated by the AIC / MDL criterion is 'M-1'. 'Becomes. The propagation time delay must be known to determine when the M-1 multipath signals are received. To this end, first, the propagation time delay of each M-1 multipaths is calculated from the received signal using the correlation characteristics of the PN sequence. The time delay signal has the PN correlation characteristics of the M-1 multipath estimates and the received signal (i.e., the received data), so that the relative propagation time delays of the first M-1 multipaths are obtained from the signals related to the virtual sensors. It can be estimated in the order of intensity. Propagation time delay of the first M-1 multipaths for the kth virtual sensor

Is as follows.

(19)

(19)

값을 1부터 1씩 M-1까지 증가시키면서, y _i ^Ts (t)와 송신신호의 버스트신호 a(t-τ)간의 상관도를 계산하고 그 계산된 값들 중 최대값(peak)이 전파시간지연

의 값으로 정하게 된다. 식 (19)의 두 번째 식에서

를 빼주는 것은,

이 2 이상인 경우에는 그 전까지(즉,

이 1부터

-1인 경우까지)의 상관도의 효과를 빼준 나머지 값들 중에서 최대값을 찾기 위함이다.In equation (19), index i is a value determined by the modular operation i = mod (k-1, M) +1, and y _i ^Ts ( t ) is the value of the received signal for one period for y _i ( t ). Data, and <A, B> means correlation between signal A and signal B. FIG. According to equation (19), path index

Calculate the correlation between y _i ^Ts ( t ) and the burst signal a (t-τ) of the transmitted signal, increasing the value from 1 to 1 by M-1, and the peak value among these calculated values is the propagation time. delay

It is determined by the value of. In the second expression of equation (19)

Subtracting,

Is greater than or equal to 2

From this 1

This is to find the maximum value among the remaining values, which has the effect of the correlation).

은

로 나타낼 수 있다. 또한, 스티어링 벡터 원소

는 임의로 생성된

번째 도래각(AoA)

과 실제 센서들의 패턴을 이용하여 구할 수 있다. 이들 복소채널이득

와 스티어링 벡터 원소

는 각각 다음과 같이 계산될 수 있다. 복소채널이득

의 계산에는 위 식 (19)를 이용하여 구한 상대적 전파시간지연

의 값이 이용된다.The next parameter needed to construct the received signal by the virtual sensor is the complex channel gain. Complex Channel Gain for Virtual Sensors in Equation (11)

silver

It can be represented as. Steering vector elements

Is randomly generated

Second advent angle (AoA)

And the actual sensor pattern. These complex channel gains

Steering vector elements

Can be calculated as follows. Complex Channel Gain

The relative propagation time delay obtained using equation (19)

Is used.

(20)

20

,

이고,

는 한 송신주기 동안의 수신신호, a(·)는 송신신호 x(t)의 버스트신호,

는 신호 A, B 사이의 상관도를 각각 나타낸다. 위 식(20)에서 복소채널이득의 위상은 고려되지 않았는데, 가상 센서의 경우

은 사용자 편의대로 임의적인 값을 부여할 수 있는 것이어서 그러한 고려를 불필요하게 만들기 때문이다.Where i = mod (k-1, M) +1,

,

ego,

Denotes a received signal during one transmission period, a (·) denotes a burst signal of the transmitted signal x (t),

Denotes the correlation between the signals A and B, respectively. In Equation (20), the phase of the complex channel gain is not considered.

This is because an arbitrary value can be assigned at the user's convenience, making such consideration unnecessary.

In Eqs. (19) and (20), the sensor index i is taken into account to reflect the different channel gains between the multipaths of the different sensors into the channel parameters of the virtual sensors, and the steering vector of the virtual sensors is the actual antenna sensor for convenience of calculation. Calculate with their steering vectors.

의 부족한 정보 때문이다. 이를 식으로 표현하면, rank( A ^tot )는 다음과 같이 쉽게 유도될 수 있으며, 식 (21)에서 min(??)는 괄호안의 값들 중 최소값을 의미한다.Equation (18) to (20) can be used to generate the elements of the virtual sensor. That is, the sensor gain due to the angle of arrival of the multipath can be calculated using the propagation pattern of the actual antenna sensor obtained by generating an arbitrary value by using the feature that there is no constraint on the propagation characteristics of the sensor. Can be. However, the rank (rank) of the channel parameter vector to increase at a time by a virtual sensor can be estimated from the number of rank (A ^tot), that is, stage of the multi-path as determined by the AIC, MDL criterion (criteria) Maximum number of antenna sensors present, which is 'number of antenna sensors present in the previous iteration step-1'. This is relative propagation time delay

Because of the lack of information. Expressed in this equation, rank ( A ^tot ) can be easily derived as follows. In equation (21), min (??) means the minimum value among the values in parentheses.

(21)

(21)

rank ( A ^tot ) indicates that the maximum size of the rank extension is M-1 or LM. Since the number of virtual sensor parameters that can be calculated by equations (19) and (20) is limited, that is, due to insufficient rank expansion, the number of virtual sensors is continuously increased by iterative calculation.

If L _E is an estimated number of multipaths in the previous iteration calculation step, with some mathematical manipulation, the rank of the channel parameter matrix after rank expansion can be written as follows.

(22)

(22)

의 범위는 각 반복단계마다 그 이전의 반복 단계에서 추정된 개수 L _E 를 가지고 다시 정의해야 한다. 여기서 경로 인덱스

은 다음과 같고, 가상 센서의 개수 K는 항상 L _E 이다.Here, the rank of the channel parameter matrix may be extended up to L _E. In the last iteration, L _E is greater than LM. In that case, the rank of the entire parameter matrix is L, and L _E- (LM) redundancies are generated in the channel parameter matrix by the L _E virtual sensors. Then the path index in equations (19) and (20)

The range of must be redefined for each iteration with the number L _E estimated at the previous iteration. Where path index

Is as follows, and the number K of virtual sensors is always L _E.

(23)

(23)

(4) Execution Algorithm of Multi-Path Detection Method by Virtual Sensor

3 is a signal flow diagram of a multi-path detection method by a virtual sensor based on the concept described above. First, the number L _E of the multipaths is estimated by using the received signal Y and the parameter matrix whose rank is expanded in the process illustrated in FIG. 3 (S10). First of all for this In this step, first, in order to detect the virtual sensor multipath by iterative calculation, AIC and MDL criteria are calculated according to the existing method using Equation (24). In this case, since the received signal Y is a signal obtained by receiving antennas of M received through N multi-path signals, it is represented by a matrix of M × N. By the way, since at first the signal received by the virtual sensor is generated, only the signal Y received by the actual sensor AIC and MDL criteria are calculated. After the loops S10, S20, S30, and S40 of FIG. 3 are performed once, the reception signal generated by the virtual sensor is generated. Thus, the AIC and MDL judgment criteria are performed using both the actual sensor and the received signal generated by the virtual sensor. Calculate the criteria

(24)

(24)

(25)

(25)

의 값을 가지며, N은 수신 샘플의 개수,

는 내림차순으로 정렬된 샘플 공분산 행렬

의 고유값(eigenvalue)이다. 그리고 위 식을 이용하여 k값을 증가시키면서 계산된 값들을 아래 식 (26)에 적용하여 이전의 반복 계산 단계에서 다중 경로의 개수

를 추정한다. In this case, M ^tot means the total number of antenna sensors, which is the sum of the number of real sensors and the number of virtual sensors, and k is a variable.

Where N is the number of received samples,

Is a sample covariance matrix sorted in descending order

Is the eigenvalue of. The number of multipaths in the previous iteration calculation step is applied by applying the values calculated by increasing the value of k using the equation above to equation (26) below.

Estimate

(26)

(26)

가 얻어지면, 그 추정 개수

이 M^tot-1과 같게 되는 지를 체크한다(S20). 양자가 같다면 구하려는 다중 경로의 개수 L가 현재의 추정 개수

일 수도 있지만 그 이상일 가능성도 내포하는 것이므로, 수신신호의 랭크 확장을 할 필요가 있다. The estimated value of the number of multipaths in step S10

If is obtained, the estimated number

It is checked whether or not it becomes equal to M ^tot -1 (S20). If both are equal, the number L of multipaths to be found is the current estimated number.

It may be possible, but it may also be more than that, so it is necessary to extend the rank of the received signal.

이 M^tot-1과 같게 되는 동안은, 그 추정된 다중경로 개수

에 대하여 위에서 설명한 바와 같이 식 (19), (20) 및 (23)을 이용하여 수신신호의 랭크 확장을 반복한다(S30). 즉, 다중경로 인덱스

를 증가시키면서 다중경로의 전파시간지연

, 경로 이득과 각 경로의 상대적 위상차를 나타내는 복소채널이득

, 도플러 주파수에 관한 정보

와 도래각

정보를 이용하여 계산되는 스티어링 벡터 원소

를 구함으로써, 수신신호의 랭크를 확장한다. Estimated number at step S20

While this is equal to M ^tot -1, the estimated number of multipaths

As described above, rank expansion of the received signal is repeated using equations (19), (20) and (23) (S30). That is, multipath indexes

Multipath propagation time delay

, The channel gain representing the path gain and the relative phase difference between each path

Doppler frequency information

And advent angle

Steering vector element computed using information

By obtaining, the rank of the received signal is expanded.

와

, 그리고 수신잡음의 분산 σ ² 의 값을 산출하여 가상센서의 수신신호를 생성한다(S40). 이렇게 구한 가상센서의 수신신호는 S10 단계에서 다시 기존의 AIC, MDL 판단기준(criteria)을 이용하여 가상센서 다중경로의 추정 값

를 구하는 데 이용된다. Then, using equations (13) to (15) and (18), the sample value Y ^tot of the entire received signal including the virtual sensor, the parameter matrix including the virtual sensor, and the sample value of noise

Wow

Then, a value of the variance σ ² of the received noise is calculated to generate a received signal of the virtual sensor (S40). The received signal of the virtual sensor thus obtained is estimated in the multi-path of the virtual sensor by using the existing AIC and MDL criterion again in step S10.

It is used to find.

값이 가상센서의 개수를 포함한 총 센서 개수 즉, M^tot-1보다 작아질 때까지 이루어진다. 상기 루프의 첫 번째 실행단계에서는 추정된 다중경로

의 값이 M이 될 것이고, 두 번째 실행에서는

는 2M-1이 될 것이다. 이렇게 루프를 반복적으로 실행해나가면, 추정 개수

이 M^tot-1과 같지 않게 되는 경우 즉, 전자가 후자보다 작게 되는 경우를 만나게 되는데, 그 때가 바로 필요한 랭크 확장이 완료된 상태이다. 그리고 그 때의 추정 개수

의 값이 얻고자 하는 다중경로의 개수 L의 값이 된다. The repetition of the loop from step S10 to step S40 is estimated number of multipaths.

The value is set until the total number of sensors including the number of virtual sensors is smaller than M ^tot −1. In the first execution phase of the loop, the estimated multipath

Will be M, and in the second run

Will be 2M-1. If you run this loop repeatedly, the estimated number

When this is not equal to M ^tot -1, that is, the former becomes smaller than the latter, a rank expansion is necessary. And the estimated number at that time

Is the value L of the number of multipaths to be obtained.

(5) simulation result

4 shows simulation results for estimating the number of multipaths using the virtual sensor technique. The simulation relates to a 511 length PN sequence with the same power and with the number of generated multipaths being 10, 15, 20, 25. In this simulation, the SNR defined by 10 log (1 / σ ² ) is from -20 dB to 30 dB, and the number of samples used is equal to that length of the PN sequence. The graph of FIG. 4 shows the root mean squared error (RMS) value of the estimated number for the same power. In FIG. 4, the representation of the 'PNaMb' format indicates that the length of the PN sequence is 2 ^a -1 and the number L of generated multipaths is b. All generated multipaths have different time delays, but may have the same angle of arrival.

This result shows that longer PN sequences have better performance. This is because there is more gain in terms of SNR by the characteristics of the PN sequence when the sample covariance matrix is calculated from finite received signals. For the same power, there is approximately 6 dB SNR gain difference in the sample covariance matrix between PN7 and PN9. Moreover, the likelihood of occurrence of estimation error accumulates at every iteration step, and this error becomes larger as the generated multipath increases. For PN sequences with the same energy, the performance difference between PN7 and PN9 is reduced compared to FIG. All graphs corresponding to PN7 in FIG. 4 will move approximately 6 dB horizontally to the left due to an increase in SNR to equalize the two PN sequences. However, PN7 still suffers from poor performance. This was caused by incorrectly calculated noise power due to the statistical uncertainty of noise due to the use of a small number of samples. The final result relates to the relationship between the number of actual sensors and the estimated performance by the virtual sensors.

FIG. 5 shows the RMSE of the simulation using PN9 for the case where the number of multipaths is 10, 15, 20 and the number of actual sensors is 4, 6, and 8. FIG. The legend 'SaMb' of FIG. 5 indicates that the number a of actual sensors and the generated multipath L are b. The difference in performance in FIG. 5 derives from the difference in the number of iteration steps required to estimate the number of multipaths leading to a cumulative probability of error occurrence. Previous studies have shown that 95% of the average PDP (APDP) for the -20dB threshold in flat rural, hilly rural, and urban high-rise cells environments, respectively. %, 89% and 22% have a maximum of up to 10 paths. In addition, for a threshold of -10dB, the APDP has a maximum of 10 multipaths of nearly 100% in non-urban cells and 79% in urban high-rise cells. This means that for 10 dB or more SNR, only 10 multipaths can represent the appropriate APDP for all cells. From this point of view, according to the simulation results of the present invention, when the PN length is 511 and 8 actual sensors and SNR of 10 dB, the RMSE showed 0.16, 0.67 and 1.67 for the multipath 10, 15 and 20, respectively. . In addition, the RMSE is 0.71, 1.49, 4.00 for four real sensors and 0.37, 0.96, 2.64 for six real sensors. These simulation results can be seen as indicating that the VSC scheme of the present invention is very reasonable and valid.

As described above, the present invention, unlike the conventional information theory criterion, allows to overcome the limitation of the number of antenna sensors. Numerical experiments show that the VSC method is very sophisticated for SNR above 5 dB and 511 PN lengths when the number of multipaths is less than 20. It should be noted that for most environments, the number of multipaths is less than 20. Moreover, all estimation errors are the result of underestimation, indicating that there was no occurrence of false paths due to rank expansion. As described above, the present invention uses a signal measured with a limited number of actual antenna sensors, and transmits a multi-path radio signal more than the number of the antenna sensors, in software without physically increasing the antenna sensor. It is possible to measure by implementing the same conditions (that is, virtual sensors) in which many are present. Therefore, even in a recent mobile communication environment with a complicated channel pattern, it is possible to measure a signal quickly with fewer antenna sensors, thereby greatly reducing the measurement time and the cost of manufacturing the measurement system.

Claims (10)

In measuring the signals radiated from at least one transmitting antenna and propagated through the multipath L with M actual antenna sensors on the receiving side, Sampling a received signal of the actual antenna sensor; From the sampled values, a sample covariance matrix (

) And its eigenvalues (

A second step of estimating the number of multipaths by calculating Estimated number of multipaths (

) Is greater than or equal to the number of the actual antenna sensors (M), assuming that there are more virtual sensors on the receiving side in addition to the actual antenna sensors, and performing repeated rank expansion of the received signals to construct the received signals of the virtual sensors. Three steps; And And a fourth step of repeatedly performing the second and third steps, including the received signal by the virtual sensor, in addition to the received signal by the actual antenna sensor. Way. The method of claim 1, wherein the number of the virtual sensors added in the third step is equal to the number of the multipaths obtained in the second step. The method of claim 1, wherein the iterative performance of the second and third steps is performed based on the estimated number of multipaths (

) Value is made until the total number of antenna sensors including the number of virtual sensors is less than M ^tot -1, and the number of estimated multipaths at that time (

) Is determined by the value of the number of multipaths (L) to be obtained. The method of claim 1, wherein the sample covariance matrix is

Where n is the number of samples of the received signal, y (t _i ) is the received signal of the virtual sensor, and H is a Hermition Operator. Way. 5. The method of claim 4, wherein the estimation of the number of the multipaths in the second step uses only the received signals of the real antenna sensor at first, and then receives the signals received by the real antenna sensor and the virtual sensor. Calculate the AIC and MDL criteria by changing the k value using Equation (A) below, and then calculate the calculated AIC (k) and MDL (k) values using Equation (B) The number of multipaths in the previous iteration calculation step by applying to

Where M ^tot is the total number of antenna sensors that are the sum of the number of real sensors and the number of virtual sensors, and k is a variable.

Where N is the number of received samples,

Is a sample covariance matrix sorted in descending order

Multipath detection method using a virtual sensor, characterized in that the (eigenvalue) of.

... (A)

... (B) The method of any one of claims 1 to 3, wherein the third step comprises: an angle of arrival (AoA) representing a phase difference between the respective paths of the received signal by the virtual sensor for repetitive rank expansion of the received signal. And determining a parameter constituting a received signal by the virtual sensor, such as channel gain, distribution of received noise, and relative propagation time delay for each propagation path. 8. The method of claim 6, wherein the variance of the received noise ( σ ² ) of the received signal by the virtual sensor is determined by the following equation, and in the following equation (C), y _m ^dif ( t ) is determined by the m th actual antenna sensor. Multipath using a virtual sensor characterized in that it is the difference signal of the sampling value at t + T _s after a specific time t and one transmission period thereof, and E means an expected value obtained by averaging the duration of the PN sequence of one period. Detection method.

... (C) The method of claim 6, wherein the relative propagation time delay of each propagation path (

) Is the path index using the following equation (D)

Calculate the correlation between y _i ^Ts ( t ) and the burst signal a (t-τ) of the transmitted signal, increasing the value from 1 to 1 by M-1, and the peak among these calculated values is the propagation delay. time

Set to, but path index

For each iteration, we have a multipath number L _E estimated at the previous iteration.

It is calculated by newly defining with

Is the relative propagation delay time of the first M-1 multipaths for the k th virtual sensor. Index i is a value determined by the modular operation i = mod (k-1, M) +1, y _i ^Ts ( t ) is the data of the received signal for one period for y _i ( t ), and a (·) Is a burst signal of the transmission signal x (t), and <A, B> is a correlation between signal A and signal B.

... (D) 9. The method of claim 8, wherein the complex channel gain

) Is calculated by the following formula (E)

For each iteration, we have a multipath number L _E estimated at the previous iteration.

Calculate in a newly defined manner, i = mod (k-1, M) + 1 in the formula (E),

,

ego,

Is a received signal for one transmission period,

Is a multipath detection method using a virtual sensor, characterized in that it represents a correlation between the signals A, B.

... (E) 4. A method according to any one of the preceding claims, wherein the rank of the channel parameter vector that can be incremented at one time by the virtual sensor in relation to the rank expansion in the third step is &quot; previous iteration. The multi-path detection method using a virtual sensor, characterized in that the number of antenna sensors present '-1' in step.

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