KR101887404B1 - Multi-Beam MVDR Technique for Removing Interference Signals in Array Antenna Based GPS Receivers - Google Patents

Abstract

The method for processing an array antenna-based multi-beam MVDR according to the present invention comprises the steps of: a) determining a beamforming vector ( w ) of each of a plurality of antennas, assuming that the power of the jammer is greater than noise, Obtaining a power of a time filter output r (n); b) obtaining a plurality of independent constraints that set the beam in a plurality of directions; c) determining each independent constraint as a beamforming vector and converting into a single constraint, using the (w), d) calculating the beamforming vector (w opt) which minimizes the output power by using a Lagrange multiplier (λ), e) how the functions optimized Time domain filter coefficients; and f) simplifying the algorithm by finding the spatial-time domain filter coefficients by assigning the current sample values to the autocorrelation matrix.

Description

[0001] The present invention relates to an array antenna-based multi-beam MVDR processing method,

The present invention relates to a multi-beam MVDR processing method based on an array antenna, and more particularly, to an array antenna based multi-beam MVDR technique for removing an interference signal in a GPS receiver.

In general, GPS (Global Positioning System) is a system that receives the signals of various GPS satellites orbiting the Earth orbit and finds its absolute position by using difference of reception time of each satellite. It is widely used not only for private purpose but also for military purposes . Reliable GPS reception is even more important in the military, especially since it is used in guided weapons. However, there is a problem that the GPS system can easily disable the GPS system by transmitting an artificial jamming signal because the used frequency band is known and the received signal power is weak.

In consideration of this problem, there are known techniques for forming one or more beams in the satellite direction and forming a null in the jammer direction to remove the jammer.

In the MVDR (Minimum Variance Distortionless Response) method, as a signal processing technique related to the present invention, the satellite signal arrives in the zenith direction but the jammer arrives in the vicinity of the horizon direction, Adjust the position of the null to remove jammers spatially. This method is known to have good GPS reception performance because it simultaneously performs jammer removal and beam forming in the satellite signal direction.

Conventionally, since only one directional beam can be set in one MVDR algorithm, in order to receive a plurality of GPS signals, a plurality of MVDR algorithms are used in parallel and the directions of beams are directed to different GPS signals in each MVDR Should be. However, since much computation is required to implement one space-time adaptive processing (STAP), this method has a disadvantage in that the complexity, size, and power consumption of the receiver increase in proportion to the number of beams .

Open Patent Publication No. 10-2016-0107740 (published on Sep. 19, 2016, device and method for heterogeneously polarized single antenna antenna jamming)

(2), Issue (5), May 2012. 315-324 (Beam forming Algorithms Technique by Using MVDR and LCMV)

SUMMARY OF THE INVENTION The present invention has been made in view of the above problems, and it is an object of the present invention to provide an array antenna based multi-beam MVDR processing method capable of forming a plurality of beams in a desired direction while using one algorithm based on MVDR (Minimum Variance Distortionless Response) .

The present invention also provides an array antenna based multi-beam MVDR processing method capable of eliminating jammers and preventing deterioration of reception performance of GPS signals in response to a jammer direction changing with time.

According to another aspect of the present invention, there is provided a method of processing an array antenna based multi-beam MVDR, the method comprising the steps of: a) determining a beamforming vector w of each of a plurality of antennas, Obtaining a power of a space-time filter output (r (n)) including a vector, b) obtaining a plurality of independent constraints for setting the beam in a plurality of directions, c) Transforming the condition into a single constraint using a beamforming vector w ; d) calculating a beamforming vector w opt that minimizes the output power using a Lagrange multiplier ( lambda ) ) A step of obtaining an algorithm for finding a space-time domain filter coefficient using a function optimization method, and f) a step of simplifying an algorithm for finding the space-time domain filter coefficient by substituting a current sample value for an autocorrelation matrix .

The present invention can form a plurality of beams in a desired direction using one algorithm, simplifying the structure of the receiver, and reducing the size and power consumption.

In addition, since the beam and the null can be formed in various directions, the present invention has the effect of preventing deterioration of the reception performance of the satellite signal while increasing the removal efficiency of the jammer.

1 is a block diagram of a GPS receiver model to which the present invention may be applied.
2 is a conceptual diagram of an azimuth angle and an altitude angle.
3 is a comparative diagram of a conventional multi-beam MVDR structure and a multi-beam MVDR of the present invention.
4 is a layout diagram of an antenna in an experimental example of the present invention.
5 is a graph showing a spectrum of a received signal and a spectrum of a filter output according to the present invention.
FIG. 6 is a graph showing the instantaneous power | r (n) | of the space-time filter output r (n) when the adaptive algorithm of the present invention represented by equation (19) ² in accordance with time.
7 is a beam pattern of a space-time filter after adaptive algorithm convergence of the present invention.

The embodiments of the present invention can make various changes and have various embodiments, and specific embodiments will be described in detail with reference to the drawings. It should be understood, however, that the embodiments of the present invention are not limited to specific embodiments, but include all modifications, equivalents, and alternatives falling within the spirit and scope of embodiments of the present invention.

Terms including ordinals, such as first, second, etc., may be used to describe various elements, but the elements are not limited to these terms. The terms are used only for the purpose of distinguishing one component from another. For example, without departing from the scope of the embodiments of the present invention, the first component may be referred to as a second component, and similarly, the second component may also be referred to as a first component. And / or < / RTI > includes any combination of a plurality of related listed items or any of a plurality of related listed items.

The terminology used in the embodiments of the present invention is used only to describe a specific embodiment and is not intended to limit the embodiments of the present invention. The singular expressions include plural expressions unless the context clearly dictates otherwise. In the embodiments of the present invention, terms such as " comprise " or " comprise ", etc. designate the presence of stated features, integers, steps, operations, elements, parts, or combinations thereof, It should be understood that the foregoing does not preclude the presence or addition of other features, numbers, steps, operations, elements, parts, or combinations thereof.

Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which the embodiments of the present invention belong. Terms such as those defined in commonly used dictionaries are to be interpreted as having a meaning consistent with the meaning of the context in the related art and, unless explicitly defined in the embodiments of the present invention, are intended to mean ideal or overly formal .

The multi-beam MVDR processing method based on an array antenna according to a preferred embodiment of the present invention will be described in detail with reference to the accompanying drawings.

1 is a block diagram of a GPS receiver model to which the processing method of the present invention may be applied.

The receiver model of FIG. 1 is a baseband equivalent model and shows the structure of space-time signal processing in a receiver. Assume that the number of antennas is M and the length of the time domain filter at each antenna is L. There are Q GPS signals, _{q q} (n), and azimuth angle Φq and altitude angle θq in the received direction. The concept of the azimuth angle and elevation angle is shown in Fig.

Assuming that the received signal is a plane wave, the wave vector kq of the q-th GPS received signal can be expressed by Equation 1 below.

Speaking Assuming the M antennas to point the antenna has a beam pattern of forward (Omni), the x, y, z coordinates of the m-th antenna um = [x _m, y _m, z _m] ^T q th gps signal The magnitude Mx1 steering vector for Equation (2) can be expressed by Equation (2) below.

The q-th GPS signal vector received from the M antennas is s _q (n) v (k _q ). If the p jamer signal is _p (n) and the steering vector for the incident angle of the jammer is v (k _p ), then the p-th received jammer signal is ψ _p (n) v (k _p ). As a result, the final received signal in which the satellite signal and the jammer are mixed is expressed by Equation 3 below.

In Equation (3), z (n) denotes an M x 1 noise vector. When the received signal is expressed as Equation (3), the output of FIG. 1 can be expressed as Equation (4) below.

And in the above Equation 4 y (n-1) = [y 1 (n-1), y 2 (n-1), ..., y M (n-1)] T, ~ y (n) is Can be expressed by the following equation (5).

w ₁ and w are the size M x 1, 1 x ML as the beam-forming vector _{w 1 = w 1, l,} w 2, l , _{respectively,} .... w _{M, l]} ^T and, w = w ₁ ^T , w ₂ ^T , .... w _L ^T _] ^T.

The present invention is to design w so that jammer is removed at the space-time filter output r (n) and the GPS signal in the desired direction is not compromised.

First, we define the cost function for the w design, assuming that the magnitude of the GPS signal in the received signal is much smaller than the noise. In fact, it is known that GPS reception signal is 15dB less than thermal noise power. On the other hand, the jammer's power is assumed to be much larger than the noise. Jammers smaller than noise do not have a significant effect on the reception of GPS signals using the spread spectrum approach, so consider jammer removal, which is much larger than noise. If the weak GPS signal is ignored, the received signal can be viewed as jammer + noise. To remove the jammer, the cost function is determined to minimize the power of the space-time filter output. The power of the space-time filter output r (n) can be expressed as Equation (6) below.

In the above Equation (6), Ryy is expressed by Equation (7) below.

Also, the steering vector in the direction in which the beam is desired is defined as v ₁ (k _d ), ..., v _N (k _d ). Defines a steering vector that removes jammers received in the remaining directions without damaging the beam in the N directions. Here, the direction of the beam is a value to be set by the user, and the sum of the direction of the beam and the direction of the null is set to be one less than M-1, that is, the number of antennas.

If you set the beam in multiple directions, the number of jammers that can be removed is reduced.

The characteristics of an ideal time-domain filter through which a signal received in the direction of the beam passes are defined as h _d = [h ₁ , ... h _L ] ^H , and this filter characteristic is user- Pass filter so as not to pass through the remaining band. To create a constraint that does not compromise the beam in the desired direction, it is necessary to set the time domain filter characteristic of the received signal in the direction of v _n (k _d ), n = 1, ..., N to be h _d . An equivalent time domain filter through which a signal received in a desired direction passes is a signal received in the direction of FIG. 1 where [w ₁ ^H v _n (k _d ), w ₂ ^H v _n (k _d ), ... , w _L ^H v _n (k _d )] and this vector should be made to be h _d . Taken together, the constraint can be expressed by Equation 8 below.

Equation (8) is a condition for setting the beam in N directions, and it can be modified as shown in Equation (9) to express it as one constraint instead of N independent constraints.

In order to solve the optimization problem of finding the desired beam forming coefficient, the constraint condition should be expressed by w . To do this, we first define the vector c _l of size MLx1 as:

In Equation (10), O _M is an M x 1 vector and all elements are zero. A matrix C of ML x L size is defined using the c _l vector defined in Equation (10). In this case, the C matrix can be expressed as [c ₁ , c ₂ , ..., c _L ], and the constraint condition of the desired beam can be expressed as C ^w w = N h _d .

Considering the conditional expression of the above beam and Equation (6), w, which minimizes the power of the space-time adaptive signal processing filter output while satisfying the constraint condition for the beam, can be expressed by Equation have.

The solution of the above equation (11) can be obtained by using a lagrange multiplier. Equation (12) can be obtained by solving Equation (11) by introducing a Lagrange multiplier ? Of size L x 1, and Equation (13) can be obtained by differentiating Equation (12) below with respect to w .

Obtaining a w satisfying ▽ H (w) = 0 to obtain the optimal solution can be obtained w _opt = λ C -Ryy ^-1, Substituting this to the constraint λ = - [Ryy ^-1 C] ^-1 Nh _d is obtained.

When λ is substituted into w _opt , the final solution is expressed by the following equation (14).

We derive an adaptive algorithm using the solution given above.

Since Equation (14) requires an inverse matrix, a large amount of computation may be required, and an adaptive algorithm is obtained in order to reduce it. In this case, the adaptive algorithm uses the steepest descent algorithm for latitude and uses the following equation (15).

In Equation (15), μ denotes the step size, and in the adaptive algorithm, the time variable n is added because the coefficient changes with time. The Lagrange multiplier must be selected to satisfy the constraint that w (n + 1) is obtained at each time n, and the filter characteristic h _d including such a condition can be expressed by Equation (16) below.

Equation 17, which is an adaptive algorithm for finding a space-time domain filter coefficient, can be obtained by obtaining λ (n) in Equation 16 and substituting the result into Equation 15.

In Equation 17, since ? And ? Are values that can be obtained in advance before the execution of the algorithm, the amount of calculation can be reduced. However, in Equation (17), the autocorrelation matrix Ryy for the antenna reception signal is required. To obtain the autocorrelation matrix, an average of the long time reception signal vector is required. In this process, the calculation amount is increased, It is difficult to cope with situations where the correlation matrix changes over time. Therefore, it is replaced with the current sample value instead of the autocorrelation matrix. In this case, the autocorrelation matrix can be expressed by the following equation (18), and the final adaptive algorithm (19) can be obtained by substituting the equation (18) into the equation (17).

3 (a) shows a conventional multi-beam MVDR structure, and FIG. 3 (b) shows a multi-beam MVDR structure to which the above adaptive algorithm is applied. As shown, the present invention can implement multi-beam MVDR using one space-time adaptive processing (STAP).

To verify the effectiveness of the adaptive algorithm, a simulation was performed.

<Experimental Example>

In order to verify the performance of the present invention, a computer simulation was performed. The GPS signal uses a L1 band signal with a center frequency of 1.5 GHz, assuming that the number of receiving antennas is 25 and is arranged in a square on the x, y plane as shown in Fig. The distance between adjacent antenna elements is assumed to be 10 cm, which is a half wavelength.

GPS satellite signals are assumed to receive 12 signals from different directions and the reception SNR of each satellite signal is set to 15dB. The satellite azimuths were assumed to be equidistant from 0 to 360 degrees at 30 degree intervals, and altitude was set at 45 degrees for all GPS satellite signals.

The jammer signal, which is an interference signal, generated one narrowband jammer and one broadband jammer. Narrowband jammers were generated as sinusoids with a single frequency and broadband jammers were generated as signals with a bandwidth of 2 MHz.

The jammer to noise ratio (JNR) of each jammer was set to 50 dB. That is, the jammer's power is assumed to be 50 dB higher than the noise. In this case, the power of the jammer is 65 dB higher than the power of the GPS satellite signal. These values are such that GPS signals can not be recognized by GPS receivers.

For the broadband jammers, the azimuth angle was set at 120 degrees and the elevation angle was set at 10 degrees. Narrowband jammers were set at an azimuth angle of 90 degrees and an altitude angle of 10 degrees. Assuming that jammers are transmitted from the ground, they are set at a lower elevation angle than GPS satellite signals.

The operating clock of the signal processing unit in which the space-time signal processing is performed is set to 5 MHz. Given that the spreading code chip rate of the GPS signal is 1 MHz, simulations have been conducted in a situation of about 5 times over. We also set the filter length of the time domain of the space-time filter to L = 3. Therefore, the total coefficient of the space-time filter is 35x5 = 75. The time domain filter coefficients needed to set the constraint were set to h _d = [1,1,1] ^T. This can be seen as the simplest form of a low-pass filter. The user must set the number and direction of beams for multi beam setup and use two beams for experiment. The direction of the first beam was set at an azimuth angle of 0 degrees and an altitude angle of 45 degrees, and a direction of a second beam was set at an azimuth angle of 90 degrees and an altitude angle of 45 degrees.

5 is a graph showing a spectrum of a received signal and a spectrum of a filter output according to the present invention.

The left graph of FIG. 5 shows the spectrum of the received signal. If the GPS signal is normally received, the GPS signal is weaker than the noise, so only noise should be seen. However, it is confirmed that broadband jammer and narrowband jammer are received 50 dB higher than noise by jammer.

The right graph of FIG. 5 shows the spectrum of the space-time filter output after the algorithm converges. The broadband jammer and the narrowband jammer are removed, which shows that the power density is greatly reduced to the noise level. The shape of the final spectrum is also similar to the frequency response of h _d = [1,1,1] ^T. That is, it is preferable to use a longer h _d to remove interference signals in a band other than the GPS signal bandwidth having a bandwidth of about 2 MHz.

FIG. 6 is a graph showing the instantaneous power | r (n) | of the space-time filter output r (n) when the adaptive algorithm of the present invention represented by equation (19) ² in accordance with time. Significantly higher power values begin to shrink rapidly over time and remain stable after about 1,500 samples. Converting this to time, it can be seen that the adaptive algorithm converges after about 300 microseconds.

Figure 7 shows the beam pattern of a space-time filter after adaptive algorithm convergence. Red indicates the area where the beam is formed due to high antenna gain, and blue indicates the area where the antenna is formed due to low antenna gain. It can be seen that a null is formed at an azimuth angle of 90 degrees, a high altitude angle of 10 degrees, and an azimuth angle of 120 degrees and an altitude angle of 10 degrees, at which broadband jammers are received. Also, it can be confirmed that the beam is formed at the azimuth angle of 0 degrees, the altitude angle of 45 degrees, the azimuth angle of 90 degrees, and the altitude angle of 45 degrees which are set as the restriction condition.

As described above, according to the present invention, one space-time filter can be used to maintain a beam in a plurality of directions desired to be received and nulls in a jammer direction received in the remaining direction, thereby effectively removing the jammer.

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit and scope of the invention will be.

Claims (7)

a) obtaining the power of the space-time filter output r (n) including the beamforming vector, assuming that the power of the jammer is greater than the noise to determine the beamforming vector w of each of the plurality of antennas;
b) obtaining a plurality of independent constraints for setting beams in a plurality of directions;
c) transforming each independent constraint to a single constraint using a beamforming vector ( w );
d) calculating a beamforming vector ( w opt) that minimizes output power using a Lagrange multiplier ( ? );
e) obtaining an algorithm for finding a space-time domain filter coefficient using a function optimization method; And
f) simplifying the algorithm for finding the space-time domain filter coefficients by substituting the current sample value for the autocorrelation matrix,
Wherein the constraint of step b) is expressed by the following equation.

Equation

The method according to claim 1,
Wherein the spatial-temporal filter output r (n) of step a) is expressed by the following equation (1).
Equation 1

delete The method according to claim 1,
The single constraint of step c) is C ^w w = N h _d Wherein the multi-beam MVDR method is based on an array antenna.
The method according to claim 1,
Wherein the beamforming vector ( w _opt ) of step (d) is expressed by the following equation (3).
Equation 3
w _opt = -Ryy ^-1 C ?
The method according to claim 1,
Wherein the algorithm of step (e) is expressed by the following equation (4).
Equation 4

The method according to claim 1,
Wherein the final algorithm of step (f) is expressed by the following equation (5).
Equation 5

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