CN116224249B - Doppler frequency width acquisition method for main lobe clutter region of airborne radar - Google Patents
Doppler frequency width acquisition method for main lobe clutter region of airborne radar Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/86—Combinations of radar systems with non-radar systems, e.g. sonar, direction finder
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Abstract
The application discloses a Doppler frequency width acquisition method of an airborne radar main lobe clutter zone, which comprises the following steps: s1, acquiring a velocity vector V= (V) under a plane coordinate system of the machine body x ，V y ，V z ) The method comprises the steps of carrying out a first treatment on the surface of the S2, acquiring an antenna main lobe beam center vector b under a plane coordinate system of the machine body; s3, acquiring Doppler frequency f corresponding to the antenna main lobe beam center according to the speed vector V and the antenna main lobe beam center vector b under the plane coordinate system of the machine body d0 The method comprises the steps of carrying out a first treatment on the surface of the S4, acquiring Doppler frequency f of point K in antenna main lobe clutter region where antenna main lobe beam strikes the ground under machine body coordinate system dk The Doppler frequency width of the main lobe clutter zone is f dkmax ‑f dkmin ，f dkmax And f dkmin Respectively f dk Maximum and minimum of (2). According to the application, by utilizing the IMU information of the carrier, the Doppler frequency corresponding to the main lobe beam center of the antenna and the Doppler frequency width of the main lobe clutter region under different postures can be obtained in real time, so that the main lobe clutter region can be avoided or the main lobe clutter can be processed during target detection.
Description
Technical Field
The application belongs to the technical field of radar target detection and signal processing, and particularly relates to a Doppler frequency width acquisition method of an airborne radar main lobe clutter zone.
Background
When the airborne radar looks down to detect, target echo and ground clutter will enter the radar receiver together, will cause adverse effect to the radar reception in the low altitude, especially the Doppler frequency of target and clutter is close when the tail is chased, seriously influences the detection performance of the radar. Although the prior art researches the target detection under the ground clutter background, the main lobe clutter is generally far stronger than the target echo, and the speeds of scatterers in different directions relative to a carrier are different, so that clutter spectrum is widened, and the detection performance of a moving target is seriously affected.
When the airborne radar detects and tracks the target, the Doppler frequency width range of the main lobe clutter region can be determined in real time, so that the main lobe clutter is restrained by adopting an adaptive algorithm or the main lobe clutter region is avoided as much as possible when the target is detected. In the prior art, the attitude of a carrier is not considered when the Doppler frequency range of a ground main lobe clutter region is acquired, and the Doppler frequency positioning accuracy of the main clutter center is not enough and the subsequent detection and tracking performances are affected due to the influence of the specific working environment of a radar.
Therefore, in order to solve the above-mentioned technical problems, it is necessary to provide a doppler frequency width acquisition method for the main lobe clutter region of the airborne radar.
Disclosure of Invention
Accordingly, an object of the present application is to provide a method for obtaining a doppler frequency width of a main lobe clutter region of an airborne radar, so as to obtain a doppler frequency of a main lobe beam center of an antenna and a doppler frequency width of the main lobe clutter region.
In order to achieve the above object, an embodiment of the present application provides the following technical solution:
a method for obtaining doppler frequency width of main lobe clutter region of airborne radar, the method comprising the steps of:
s1, acquiring a velocity vector V= (V) under a plane coordinate system of the machine body x ，V y ，V z )；
S2, acquiring an antenna main lobe beam center vector b under a plane coordinate system of the machine body;
s3, acquiring Doppler frequency f corresponding to the antenna main lobe beam center according to the speed vector V and the antenna main lobe beam center vector b under the plane coordinate system of the machine body d0 ；
S4, acquiring Doppler frequency f of point K in antenna main lobe clutter region where antenna main lobe beam strikes the ground under machine body coordinate system dk The Doppler frequency width of the main lobe clutter zone is f dkmax -f dkmin ，f dkmax And f dkmin Respectively f dk Maximum and minimum of (2).
In one embodiment, the step S1 specifically includes:
according to the velocity vector V in the northeast coordinate system 0 ＝(V x0 ，V y0 ，V z0 ) Obtaining the velocity vector V= (V) under the plane coordinate system of the machine body x ，V y ，V z ) The method comprises the following steps:
wherein alpha is the course angle of the carrier.
In one embodiment, the step S2 specifically includes:
vector b pointing to the ground according to the center of the main lobe beam of the antenna under the machine body coordinate system 0 ＝(x b0 ，y b0 ，z b0 ) Acquiring the central vector of the main lobe beam of the antenna under the plane coordinate system of the machine body as b= (x) b ′，y b ′，z b ' s), satisfy:
wherein θ 0 Andthe pitch angle and the azimuth angle of the antenna under the machine body coordinate system are respectively shown, wherein beta is the pitch angle of the carrier, Y is the roll angle of the carrier, and H is the flying height of the carrier.
In an embodiment, in the step S2, the antenna main lobe beam center vector in the body plane coordinate system is b= (x) b ，y b ，z b )＝(x b ′，y b ′，z b ' s), satisfy:
wherein H is the flying height of the carrier.
In one embodiment, the Doppler frequency f corresponding to the center of the antenna main lobe beam in the step S3 d0 The method comprises the following steps:
wherein,sigma is O' M and the plane coordinate system X of the machine body h The included angle of the axes, M is the intersection point of the main lobe beam center of the antenna on the ground, O' is the plane coordinate system Y of the machine body h Intersection of axes on the ground, +.>θ is the included angle between the central vector b of the main lobe beam of the antenna and O' M, andlambda is the signal wavelength.
In one embodiment, the step S4 includes:
acquiring an elliptic equation of an antenna main lobe clutter region of an antenna main lobe beam on the ground under a plane coordinate system of the machine body;
judging whether the point K is positioned in the antenna main lobe clutter zone according to the coordinate of the point K and an elliptic equation, and obtaining the Doppler frequency f of the point K in the antenna main lobe clutter zone dk 。
In one embodiment, the ellipse equation of the antenna main lobe clutter region in the step S4 is:
wherein m and n are the major and minor axes of the ellipse, θ EL Is half of the antenna elevation beam width, θ AZ X is half of the beam width of the azimuth direction of the antenna b 、y b 、z b The three-axis coordinates of the main lobe beam center vector to the point M on the ground are respectively given.
In one embodiment, the X-axis coordinate X of the coordinate of the point K in the step S4 k And Z-axis coordinate Z k The method comprises the following steps of:
z k ＝x k tanσ。
in one embodiment, the step S4 further includes:
when meeting the requirementsAnd when the antenna is in the main lobe clutter region, the judging point K is positioned in the main lobe clutter region of the antenna.
In one embodiment, the step S4 further includes:
traversing the values of sigma and theta according toAndObtaining Doppler frequency f of point K in main lobe clutter zone of all antennas dk ；
Wherein, sigma epsilon [ -pi, pi),
the application has the following beneficial effects:
according to the application, by utilizing the IMU information of the carrier, the Doppler frequency corresponding to the main lobe beam center of the antenna and the Doppler frequency width of the main lobe clutter region under different postures can be obtained in real time, so that the main lobe clutter region can be avoided or the main lobe clutter can be processed during target detection.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings may be obtained according to the drawings without inventive effort to those skilled in the art.
FIG. 1 is a flow chart of a Doppler frequency width acquisition method of a main lobe clutter zone of an airborne radar in the application;
FIG. 2 shows the northeast and north coordinate system (X) 0 Y 0 Z 0 ) Schematic of (2);
FIG. 3 shows the body coordinate system (X) t Y t Z t ) Schematic of (2);
FIG. 4 shows the plane coordinate system (X) h Y h Z h ) Schematic of (2);
fig. 5 is a schematic diagram of a central vector of a main lobe beam of an antenna under a body coordinate system according to an embodiment of the present application;
FIG. 6 is an exploded view of velocity vectors in a plane coordinate system of a machine body according to an embodiment of the present application;
FIG. 7 shows an embodiment of the present application X h OZ h A schematic decomposition diagram of the plane velocity vector;
FIG. 8 is an exploded view of the OM 'MO' plane velocity vector in accordance with an embodiment of the present application;
FIG. 9 is a schematic diagram illustrating a solution of the major axis m of an ellipse in an embodiment of the present application;
fig. 10 is a schematic diagram illustrating a solution of the minor axis n of the ellipse in an embodiment of the present application.
Detailed Description
In order to make the technical solution of the present application better understood by those skilled in the art, the technical solution of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are only some embodiments of the present application, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present application without making any inventive effort, shall fall within the scope of the present application.
According to the embodiment, the Inertial Measurement Unit (IMU) on the airborne radar is utilized to acquire the attitude information of the airborne machine in real time, wherein the attitude information comprises a course angle, a pitch angle and a roll angle, and the triaxial speed of the airborne machine under the northeast day coordinate system (ENU), so that the Doppler frequency of the beam center of the main lobe of the antenna and the Doppler frequency width of the clutter region of the main lobe of the antenna are acquired, and the Doppler frequency width is avoided during target detection.
In order to facilitate understanding of the embodiments of the present application, several elements that may be introduced in the description of the embodiments of the present application are first described herein.
IMU: the inertial measurement unit is a module composed of a plurality of sensors such as a triaxial accelerometer, a triaxial gyroscope and a triaxial magnetometer, and can be used for measuring parameters such as speed, course angle, pitch angle, roll angle and triaxial speed of a carrier.
Northeast day coordinate system (X) 0 Y 0 Z 0 ) The three-axis coordinates of which are shown with reference to figure 2.
Organism coordinate system (X) t Y t Z t ) The three-axis coordinates of which are shown in figure 3.
Plane coordinate system of machine body (X) h Y h Z h ) The three-axis coordinates of which are shown in fig. 4.
Referring to fig. 1, the application discloses a Doppler frequency width acquisition method of an airborne radar main lobe clutter zone, which comprises the following steps:
s1, acquiring a speed direction under a plane coordinate system of a machine bodyThe quantity is V= (V) x ，V y ，V z )；
S2, acquiring an antenna main lobe beam center vector b under a plane coordinate system of the machine body;
s3, acquiring Doppler frequency f corresponding to the antenna main lobe beam center according to the speed vector V and the antenna main lobe beam center vector b under the plane coordinate system of the machine body d0 ；
S4, acquiring Doppler frequency f of point K in antenna main lobe clutter region where antenna main lobe beam strikes the ground under machine body coordinate system dk The Doppler frequency width of the main lobe clutter zone is f dkmax -f dkmin ，f dkmax And f dkmin Respectively f dk Maximum and minimum of (2).
The following describes each step in the method for acquiring the doppler frequency width of the main lobe clutter region of the airborne radar in this embodiment in detail.
S1, acquiring a plane coordinate system (X) h Y h Z h ) The velocity vector at v= (V) x ，V y ，V z )。
Calculation of the Main lobe clutter region in the plane coordinate System (X) h Y h Z h ) The speed given by the IMU is the northeast-north day coordinate system (X 0 Y 0 Z 0 ) The speed vector is converted into a plane coordinate system of the machine body, specifically:
the velocity vector given by the IMU is recorded as V 0 ＝(V x0 ，V y0 ，V z0 ) The velocity vector in the plane coordinate system of the machine body is V= (V) x ，V y ，V z ) Then:
wherein alpha is the course angle of the carrier, and is defined as the included angle between the longitudinal axis (the machine head direction) of the machine body and the north direction, and north is positive in the east direction.
S2, acquiring the central vector of the antenna main lobe beam under the plane coordinate system of the machine body as b.
Referring to FIG. 5, the pitch angle and azimuth angle of the antenna in the machine body coordinate system are respectively θ 0 Andfirstly, solving a vector of the center of the main lobe beam of the antenna pointing to the ground under a machine body coordinate system, and marking as b 0 ＝(x b0 ，y bo ，z b0 ) Then:
the central vector of the main lobe beam of the antenna under the plane coordinate system of the organism is recorded as b= (x) b ′，y b ′，z b '), then:
wherein beta is the pitch angle of the carrier and is defined as the body X 0 The included angle between the shaft and the horizontal plane is positive when the aircraft is lifted; y is the roll angle of the carrier, and is defined as the included angle between the plane where the two wings of the airplane are positioned and the horizontal line, and the left wing is positive when inclining upwards.
Y taking into account the vector of the beam centre to ground in the plane coordinate system of the machine body h The axis size should be the flying height H of the carrier, so the coordinate value in the formula (3) is changed to obtain:
then b= (x b ，y b ，z b ) Is the central vector of the main lobe beam of the antenna under the plane coordinate system of the final body.
S3, acquiring Doppler frequency f corresponding to the antenna main lobe beam center according to the speed vector V and the antenna main lobe beam center vector b under the plane coordinate system of the machine body d0 。
Converting both the velocity vector V and the antenna main lobe beam center vector b to body planeAfter the plane coordinate system, the Doppler frequency f corresponding to the main lobe beam center of the antenna can be calculated under the coordinate system d0 。
S31, solving radial velocity V of the beam center relative to the carrier by utilizing a geometric decomposition method b 。
Referring to FIG. 6, the velocity vector in the plane coordinate system of the machine body is shown as X h OZ h The component of the plane being V xz Easily-knownLet the vector V xz And X is h The included angle of the axes is delta, then->In FIG. 6M is the intersection of the antenna main lobe beam center on the ground, OM' is X h OZ h Plane and parallel to O' M on the ground.
Referring to FIG. 7, at X h OZ h Will V on plane xz Decomposed into the OM' direction radial velocity component V xz1 And V perpendicular to OM xz2 。V xz2 T Y axis, V xz2 T OM', so V xz2 Perpendicular to the OM 'MO' plane, so V xz2 T b, i.e. V xz2 Is the tangential velocity of vector b and the corresponding doppler frequency is 0.
So at X h OZ h The plane only needs to take into account the velocity component V xz1 It can be seen that |V xz1 |＝|V xz The expression of |cos (sigma-delta) |represents modulo arithmetic, and sigma is O' M and X h And an included angle of the axes.
Referring to FIG. 8, V is shown xz1 The radial velocity component V being decomposed into vectors b xz11 And a tangential velocity component V perpendicular to vector b xz12 ，|V xz11 |＝|V xz1 And cos theta, theta is the angle between the antenna beam vector b and O' M,
considering the velocity component V in the OM 'MO' plane y V is set up y Decomposing into radial velocity components of vector bV y1 And a tangential velocity component V perpendicular to vector b y2 ，|V y1 |＝|V y |sinθ。
Synthesizing the radial velocity components:
V b ＝V xz11 +V y1 (5)
the radial speed is as follows:
V y for the velocity vector in the plane coordinate system of the machine body at Y h The magnitude of the axis is obtained by the formula (1), and the vector V y When the direction is upward, V y ＞0；V y When the direction is downward, V y ＜0。
S32, acquiring Doppler frequency f corresponding to the center of the main lobe beam of the antenna according to the radial speed in the step 3.1 d0 The method comprises the following steps:
where λ is the signal (radar-transmitted signal) wavelength.
S4, acquiring Doppler frequency width of the main lobe clutter region, comprising the following steps:
s41, an ellipse is formed when the main lobe beam of the antenna is hit on the ground, and an ellipse equation of the antenna beam hit on the ground is obtained according to the current main lobe beam scanning area.
First, the major axis m and the minor axis n of the ellipse are obtained.
As shown in reference to figure 9 of the drawings,the major axis m of the ellipse is:
wherein θ EL Pitching a beam for an antennaHalf of the width (x) b ，y b ，z b ) The tri-axial coordinates of the point M on the ground are struck for the main lobe beam center vector b.
Referring to fig. 10, the minor axis n of the ellipse is:
wherein θ AZ Is half the beamwidth of the antenna azimuth.
Then the elliptic equation is:
s42, judging whether the point K is positioned in the antenna main lobe clutter region according to the coordinate and the elliptic equation of the point K, and obtaining the Doppler frequency f of the point K in the antenna main lobe clutter region dk 。
Traversing all possible value ranges of sigma and theta, sigma epsilon, -pi, pi in this embodiment,according to the current angles sigma and theta, the X-axis coordinate X of the corresponding ground current point K is obtained k And Z-axis coordinate Z k The specific solving method is as follows:
x k the sign of (c) is determined by the following formula,
obtaining x k Then, z can be obtained according to the following formula k ，
z k ＝x k tanσ (13)
Substituting the elliptic equation of formula (10), if satisfied:
the decision point K is located within the antenna mainlobe clutter region.
Substituting sigma and theta into the above formulas (6) and (7) to obtain Doppler frequency f corresponding to point K dk 。
In this embodiment, the matlab software is used to perform the traversal of σ and θ, and in other embodiments, other software may be used, which will not be described herein.
S43, after traversing, obtaining the Doppler frequency width f of the main lobe clutter region dkmax -f dkmin ，f dkmax And f dkmin Respectively f dk Maximum and minimum of (2).
Compared with the prior art, the application has the beneficial effects that:
according to the application, by utilizing the IMU information of the carrier, the Doppler frequency corresponding to the main lobe beam center of the antenna and the Doppler frequency width of the main lobe clutter region under different postures can be obtained in real time, so that the main lobe clutter region can be avoided or the main lobe clutter can be processed during target detection.
The detailed description set forth above in connection with the appended drawings describes exemplary embodiments, but does not represent all embodiments that may be implemented or fall within the scope of the claims. The term "exemplary" used throughout this specification means "serving as an example, instance, or illustration," and does not mean "preferred" or "advantageous over other embodiments. The detailed description includes specific details for the purpose of providing an understanding of the described technology. However, the techniques may be practiced without these specific details. In some instances, well-known structures and devices are shown in block diagram form in order to avoid obscuring the concepts of the described embodiments.
The previous description of the disclosure is provided to enable any person skilled in the art to make or use the disclosure. Various modifications to the disclosure will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other variations without departing from the scope of the disclosure. Thus, the disclosure is not limited to the examples and designs described herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (5)
1. The Doppler frequency width acquisition method of the main lobe clutter zone of the airborne radar is characterized by comprising the following steps of:
s1, acquiring a velocity vector V= (V) under a plane coordinate system of the machine body x ，V y ，V z )；
S2, acquiring an antenna main lobe beam center vector b under a plane coordinate system of the machine body;
s3, acquiring Doppler frequency f corresponding to the antenna main lobe beam center according to the speed vector V and the antenna main lobe beam center vector b under the plane coordinate system of the machine body d0 ；
S4, acquiring Doppler frequency f of point K in antenna main lobe clutter region where antenna main lobe beam strikes the ground under machine body coordinate system dk The Doppler frequency width of the main lobe clutter zone is f dkmax -f dkmin ，f dkmax And f dkmin Respectively f dk Maximum and minimum of (2);
the step S4 includes:
acquiring an elliptic equation of an antenna main lobe clutter region of an antenna main lobe beam on the ground under a plane coordinate system of the machine body;
judging whether the point K is positioned in the antenna main lobe clutter zone according to the coordinate of the point K and an elliptic equation, and obtaining the Doppler frequency f of the point K in the antenna main lobe clutter zone dk ；
The elliptic equation of the antenna main lobe clutter region in the step S4 is as follows:
wherein m and n are the major and minor axes of the ellipse, θ EL Is half of the antenna elevation beam width, θ AZ X is half of the beam width of the azimuth direction of the antenna b 、y b 、z b Respectively the triaxial coordinates of the main lobe beam center vector to the point M on the ground;
the X-axis coordinate X of the coordinate of the point K in the step S4 k And Z-axis coordinate Z k The method comprises the following steps of:
z k ＝x k tanσ；
the step S4 further includes:
when meeting the requirementsWhen the antenna is in the main lobe clutter region, the judging point K is positioned in the main lobe clutter region of the antenna;
the step S4 further includes:
traversing the values of sigma and theta according toIs->Obtaining Doppler frequency f of point K in main lobe clutter zone of all antennas dk ；
Wherein, sigma epsilon [ -pi, pi),
2. the method for obtaining the doppler frequency width of the main lobe clutter region of the airborne radar according to claim 1, wherein the step S1 specifically comprises:
according to the velocity vector V in the northeast coordinate system 0 ＝(V x0 ，V y0 ，V z0 ) Obtaining the velocity vector V= (V) under the plane coordinate system of the machine body x ，V y ，V z ) The method comprises the following steps:
wherein alpha is the course angle of the carrier.
3. The method for obtaining the doppler frequency width of the main lobe clutter region of the airborne radar according to claim 1, wherein the step S2 specifically comprises:
vector b pointing to the ground according to the center of the main lobe beam of the antenna under the machine body coordinate system 0 ＝(x b0 ，y b0 ，z b0 ) Acquiring the central vector of the main lobe beam of the antenna under the plane coordinate system of the machine body as b= (x) b ′，y b ′，z b ' s), satisfy:
wherein θ 0 Andthe pitch angle and the azimuth angle of the antenna under the machine body coordinate system are respectively shown, beta is the pitch angle of the carrier, gamma is the roll angle of the carrier, and H is the flying height of the carrier.
4. An airborne radar according to claim 3The method for obtaining the doppler frequency width of the main lobe clutter region is characterized in that the antenna main lobe beam center vector under the plane coordinate system of the machine body in the step S2 is b= (x) b ，y b ，z b )＝(x b ′，y b ′，z b ' s), satisfy:
wherein H is the flying height of the carrier.
5. The method for obtaining doppler frequency width in main lobe clutter region of airborne radar according to claim 4, wherein in step S3, the doppler frequency f corresponding to the antenna main lobe beam center is d0 The method comprises the following steps:
wherein,sigma is O' M and the plane coordinate system X of the machine body h The included angle of the axes, M is the intersection point of the main lobe beam center of the antenna on the ground, O' is the plane coordinate system Y of the machine body h The intersection of the axes at the surface,θ is the included angle between the central vector b of the main lobe beam of the antenna and O' M, andlambda is the signal wavelength.
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