AU2004295764B2

AU2004295764B2 - Method for emitting and receiving wave energy

Info

Publication number: AU2004295764B2
Application number: AU2004295764A
Authority: AU
Inventors: Dirk Neumeister
Original assignee: Atlas Elektronik GmbH
Current assignee: Atlas Elektronik GmbH
Priority date: 2003-12-04
Filing date: 2004-11-27
Publication date: 2009-12-03
Anticipated expiration: 2024-11-27
Also published as: KR20060130044A; IL175532A; DE10356577B4; KR101103229B1; DE10356577A1; EP1690110A1; WO2005054897A1; DE502004010366D1; NO20063116L; AU2004295764A1; ATE448492T1; EP1690110B1; IL175532A0; SG124421A1; ZA200604539B

Abstract

The invention relates to a method for emitting and receiving wave energy serving, in particular, for actively locating targets, during which, on the transmitting side, a transmitting antenna is supplied with an electrical signal and, on the receiving side, the signal emitted by the transmitting antenna is detected in the electrical received signal of a receiving antenna. In order to conceal the transmitted signal in the background noise thereby drastically reducing the probability of the locator revealing itself, the electrical signal is generated with a temporal course having a deterministic-chaotic structure. A structural measure characterizing the deterministic-chaotic structure of the generated electrical signal is used on the receiving side for detecting the signal in the received signal of the receiving antenna.

Description

202.03WO 23.11.2004 ATLAS ELEKTRONIK GmbH Bremen 5 METHOD FOR EMITTING AND RECEIVING WAVE ENERGY The invention relates to a method for emitting and receiving wave energy of the generic type defined in the preamble of Claim 1. 10 Such a method is used for locating targets, that is to say for determining the position of targets in a surveillance area or for transmitting identification signals for the identification friend/foe, in which 15 identification signals with predefinable coding are radiated, the coding of which is known only to authorized parties. In a known method for the identification friend/foe 20 (US 3 733 552), noise which can be interpreted as thermal noise by unauthorized parties is continuously transmitted on a transmission channel. In the spectrum of this noise, part-spectra, which can be correlated with one another, are fitted for information 25 transmission in that part-spectra are notched out and from these part-spectra, part-spectra which can be correlated with one another by means of frequency shifting are inserted into the gaps produced. This ensures that the message is transmitted well 30 camouflaged in the noise. However, the difficulty of detection by an unauthorized party is only very large if the bandwidth of the transmission channel is very large since only this ensures that the unauthorized party cannot perform the signal processing necessary 35 for detection within the time available to. him. In addition, the further disadvantage is that when a message is transmitted from ship to ship, unknown Doppler shifts occur due to the water as a consequence 2 of relative movement between transmitter and receiver, which require considerable effort at the receiving end for detecting and decoding the identification signal in order to achieve unambiguous information about the degree of correspondence of the received signal with the transmitter signal. 5 In a known method for locating targets (EP 0 631 153 BI), a transmitter radiates a carrier signal onto which a chaotic code is impressed. The code does not have a fixed sequence length but an arbitrarily selected one. As a result, the individual pulsewidth of the transmitted pulses can be made very narrow in order to obtain good distance 10 resolution and, at the same time, the number of pulses in each sequence can be made very large in order to achieve maximum range which is not limited by the coding. The coding is resistant against monitoring and analyzing by receivers which do not have the coding sequence. In the authorized receiver, which is placed at the location of the transmitter itself for the purpose of locating targets, the transmitted signal emitted and 15 reflected at the target is received and the received signal is correlated with the transmitted signal. The indication of correlation is used as indication of the position of the target. Even if the unauthorized receiver cannot decode the transmitted signal coded in this way, he can still detect it and conclude from the fact of the reception of the signal that there are actively locating opponents in the environment and initiate 20 corresponding counter measures. Any discussion of documents, acts, materials, devices, articles or the like which has been included in the present specification is solely for the purpose of providing a context for the present invention. It is not to be taken as an admission that any or all of 25 these matters form part of the prior art base or were common general knowledge in the field relevant to the present invention as it existed before the priority date of each claim of this application. Throughout this specification the word "comprise", or variations such as "comprises" or 30 "comprising", will be understood to imply the inclusion of a stated element, integer or step, or group of elements, integers or steps, but not the exclusion of any other element, integer or step, or group of elements, integers or steps. The invention is based on the object of specifying a method of the type initially 35 mentioned, in which the transmitted signals radiated by the transmitting antenna are concealed in the background noise and can only be detected by authorized receivers. WQAA i rArr 3 According to the present invention there is provided a method for emitting and receiving wave energy, in which a transmitting antenna is fed with an electrical signal having a deterministic-chaotic structure at the transmitting end and the signal radiated by the transmitting antenna is detected in the received electrical signal picked up from a 5 receiving antenna at the receiving end, characterized in that the deterministic-chaotic structure of the electrical signal is characterized by a structural measure which is determined as a dimension of the structure of the map of the temporal course of the signal in a multi-dimensional phase space, and that the signal is detected in the received signal using the structural measure. 10 The method according to the invention has the advantage that the radiated signals are distinguished by a large bandwidth without characteristic lines in the spectrum so that the auditory impression is noise-like and the transmitted signals are camouflaged well in the ambient noise of the background. At the same time, their energy is distributed 15 over a wide frequency range so that narrow-band Fourier transformation cannot be used for achieving an improvement in the detection performance. Detection of the transmitted signals generated according to the invention is only possible by means of a structural analysis according to chaos theory by means of which the deterministic structure of the transmitted signals , which cannot be detected in the transmitted 20 signals, which cannot be detected in the temporal course of the transmitted signal itself, can be extracted. By comparing the structural measure, obtained by this analysis, of the received electrical signal picked up at the receiving antenna, with the structural measure of the transmitted electrical signal, the transmitted signal can be reliably detected in the output signal at the receiving end. 25 The method according to the invention can be used both to detect targets by means of so-called active location, and to determine their position, and to carry out communication between transmitter and receiver which can be used, e.g. for the so called identification friend/foe. In both cases, the probability of the transmitting party 30 revealing himself is vey low-due to the camouflaging of the transmitted signals in the ambient noise, since neither the target located by means of the transmitted signals nor third parties monitoring the transmitting area can detect the radiation of the transmitted signals. QOAAC 1 A 202.03WO - 4 23.11.2004 The method according to the invention is preferably used in underwater sound technology or underwater acoustics, but can also be applied in the medium of air, e.g. for radar location of targets or for the 5 identification friend/foe in fighting aerial targets. Suitable embodiments of the method according to the invention, with advantageous developments and embodiments of the invention, are obtained from the 10 further claims. According to an advantageous embodiment of the invention, the temporal course of the electrical signal is derived from the chaotic-deterministic oscillation 15 characteristic of a model, the oscillation characteristic of which can be varied by means of at least one parameter. An example of such a model is a pendulum of revolution, known as Pohl pendulum, with unbalance, the oscillation characteristic of which can 20 be described by a differential equation. The variable parameters are the spring constant of a restoring spring, the amplitude and frequency of an external excitation, the damping constant of an abrasive friction, the mass and the lever arm of the unbalance 25 and the damping constant of an eddy current brake. The solution of this differential equation is a chaotic deterministic time series which provides the temporal course of the electrical signal. At least one of the variable parameters of the differential equation is 30 utilized as control parameter for the iterative variation of the differential equation. In the example of the Pohl pendulum, for example, the current through the eddy-current brake can be used as control parameter. 35 To be able to characterize the structure of the electrical signal generated, which cannot be detected in the temporal course itself, by means of a structural 202.03WO - 5 23.11.2004 measure which is required at the receiving end for detecting the transmitted signal, a characteristic of the signal, namely the dimension of the structure of its mapping in an at least two-dimensional space is, 5 according to a preferred embodiment of the invertion, predetermined and the at least one variable control parameter is varied iteratively until the desired dimension has been achieved. This dimension is characteristic of the electrical signal which is 10 radiated via the transmitting antenna and is used for detecting the radiated signal in the received signal at the receiving end. According to a preferred embodiment of the invention, 15 the fractal dimension of the two-dimensional mapping of the electrical signal is calculated as dimension. In the text which follows, the invention is described in greater detail by means of an exemplary embodiment 20 illustrated in the drawing, of a method for the active location of a target. In the drawing: Figure 1 shows a block diagram for illustrating the part of the method at the 25 transmitting end, Figure 2 shows a block diagram for illustrating the part of the method at the receiving end, 30 Figure 3 shows an angular variation a(t) of a chaotic-deterministic oscillation of a model for generating the temporal course of an electrical signal with 35 deterministic-chaotic structure, 202.03WO - 6 23.11.2004 Figure 4 shows a diagram for explaining the function block return map in the block diagram of Figure 1 and 2, 5 Figures 5 and 6 show two diagrams for explaining the function block "fractal dimension" in Figures 1 and 2. In the method described in the text which follows, for 10 the active location of targets located in the water, by means of which both the targets can be acquired, i.e. detected and the position (distance and bearing) of the individual targets can be determined, sound energy is radiated into the medium of water at the transmitting 15 end and wave energy backscattered from the medium is received at the receiving end. For this purpose, a transmitting antenna 11 which radiates the sound energy within a wide sector of space or all around, is used at the transmitting end and a receiving antenna with 20 directional characteristic is used at the receiving end, by means of which the peak of the received wave energy and its direction of incidence is determined. For this purpose, the transmitting antenna 11 is supplied with a wide band electrical signal at the 25 transmitting end and the signal radiated at the transmitting end is detected in the received signal picked up at the receiving antenna 12 at the receiving end. The time between the emission of the transmitted signal by the transmitting antenna 11 and the reception 30 of the radiated signal by the receiving antenna 12 is measured and the measured time is used for calculating the distance between the transmitting antenna 11 and the target. 35 So that the locating of the target by the transmitting signal radiated once or several times with a particular period is not noticed by the target itself, the transmitted signal is concealed in the ambient noise of 202.03WO - 7 23.11.2004 the target by a corresponding formation of the electrical signal feeding the transmitting antenna 11. At the receiving end, in contrast, the transmitted signal reflected from the target can be eliminated from 5 the ambient noise of the receiving antenna 12 in the received signal of the receiving antenna 12. For this purpose, in principle, the electrical signal for feeding the transmitting antenna 11 is generated 10 with a temporal course which has a deterministic chaotic structure, and for the detection at the receiving end, a structural measure is used which characterizes the deterministic-chaotic structure of the electrical signal. As is shown in detail in the 15 block diagram of Figure 1, first the temporal course of the electrical signal is derived from the chaotic deterministic oscillation characteristic of a model, the oscillation characteristic of which can be varied by means of a selected parameter, called control 20 parameter in the text which follows. For example, in the first method step 11 "differential equation model", the differential equation of a pendulum of revolution with unbalance, of a so-called Pohl pendulum, is used as model, the variable parameters of which are the 25 spring constant of a restoring spring, the amplitude and frequency of an external excitation, the damping constant of an abrasive friction, the mass and the lever arm of the unbalance and the damping constant of an eddy-current brake. 30 The complete differential equation of such a Pohl pendulum is: O).aa=D.[a-a,-sincet|+m.g.rosina-k-"--k 2 -va- J2 IVal 35 where the restoring moment is MRuck= D[a - a,. sineet , 202.03WO - 8 23.11.2004 the moment of unbalance is M,,=m-g-rsin, 5 the moment of abrasive friction is 4chleif = kd a and 10 the moment of the eddy-current brake is M.,irbe = -kd 2 Va where: 15 a = instantaneous angle variable v, angular velocity aa= angular acceleration t = time 20 D = spring constant of the restoring spring m = mass of unbalance ro = distance of the unbalance from the axis of rotation g = acceleration due to gravity 25 8 = total moment of inertia a,= amplitude of the excitation We = angular frequency of the excitation kdl = damping constant of the constant abrasive friction 30 kd2 = damping constant of the eddy-current damping I = current through the eddy-current-generating coil. If all parameters are permanently predetermined and 35 only one parameter, in this case the current I through the eddy-current-generating coil, is left as variable control parameter, the following function is obtained.

202.03WO - 9 23.11.2004 = f(t,I), which is used for simulating the temporal course of the 5 electrical signal, where a is the signal amplitude. The solution of this differential equation with permanently predetermined parameters and the assumed input or control parameter I leads to a time series of the signal which is created from the differential equation 10 with method step 14 "calculating of the time series of the signal". Figure 3 diagrammatically shows the chaotic oscillation of the Pohl pendulum for a time segment. The simulated electrical signal has the same temporal course, where a is the instantaneous amplitude 15 variable of the signal. The time series of the electrical signal is mapped in a multi-dimensional space in which its deterministic structure can be recognized, and a dimension of the 20 structure of the map is determined. In the exemplary embodiment, the time series is mapped in a two dimensional phase space by means of a so-called return map in method step 15. As is shown in Figure 3, the lower crest points are used as the selected 25 characteristic of electrical signal for this purpose. Optionally, however, the upper crest points or the time intervals between the crest points or instantaneous values of the electrical signal occurring in the same time intervals can be used. It is also possible to use 30 as selected characteristic the time segments of the penetration points of a Poincar6 section. With respect to the Poincar6 section, reference is made to Crighton Dowling "Modern Methods in Analytical Acoustics", Springer-Verlag London Ltd., 1992, page 698 ff.. The 35 result of the return map thus produced of the electrical signal in the two-dimensional phase space is illustrated in the diagram of Figure 4. The return map is produced in such a manner that the lower crest 202.03WO - 10 23.11.2004 values answ of the electrical signal are plotted along the ordinate of a two-dimensional coordinate system and its previous values aoid are plotted along the abscissa. It can be seen clearly that a considerable data 5 reduction has occurred due to the return map. The mapping in two-dimensional space reveals a structure. This structure, which in this case is derived from the chaotic oscillation of the Pohl pendulum according to Figure 3, only for reasons of simplified 10 representation, also reproduces the structure, obtained by return map from the time series, of the electrical signal with the amplitude variable a. To be able to characterize this deterministic-chaotic 15 structure of the signal, a dimension is calculated for the structure of the map. In the exemplary embodiment, the so-called fractal dimension dF is selected as dimension for the structure. With respect to the term and to the calculation of the fractal dimension, 20 reference is made to Edward Ott, "Chaos in Dynamical Systems", Cambridge University Press 1993, page 69 ff, or Dr. Roman Worg "Deterministisches Chaos" (Deterministic chaos), Bibliographisches Institut & F.A. Brockhaus AG, 1993, page 125 ff. Calculation 25 methods for the fractal dimension dF are, for example, the grating method (GV) , the distance analysis method (AV) and the magnification-multiplication method (VV) . In the exemplary embodiment of Figure 1, the grating method (GV) is used for calculating the fractal 30 dimension dF in method step 16. In this grating method, the map is systematically covered with a grating in two-dimensional space by squares with a side length c. In this process, the side length c is increasingly reduced and in each case the number N of squares is 35 determined which are encountered by the map. Such a coverage of the map with a grating is shown in Figure 5. If c is systematically reduced in size starting from a relatively large value, a relationship 202.03WO - 11 23.11.2004 N(E) is obtained between a number N of the squares affected and the side lengths E. If N(,) is log-log plotted over 1/c, a straight line is obtained, the slope of which is an approximation of the fractal 5 dimension dF Such a straight line which, for example, has a slope of 1.36, is shown in Figure 6. Since a return map of a stochastic signal without any deterministic structure 10 results in a fractal dimension dF = 2, a slope of less than 2 is an index of a deterministic structure in the temporal course of the signal. The magnitude of the slope, i.e. the fractal dimension dF1 is a dimension of this structure. 15 To obtain in the temporal course of the electrical signal a desired deterministic structure which is required for detecting the signal in the ambient noise received via the receiving antenna, a value of the 20 fractal dimension dF is predetermined as default dimension dFV with a permissible tolerance range + s, for example 1.1 + 0.1 in block 19. In method step 17, the dimension for the deterministic structure of the electrical signal generated, calculated via the fractal 25 dimension dFV, is compared with the default dimension. If the comparison shows that the fractal dimension dF calculated in method step 16 as dimension for the deterministic structure of the electrical signal is not within the tolerance range + s, i.e. the calculated 30 fractal dimension dF is greater than dv + s or less than dF - s, the variable parameter of the model, the current I through the eddy-current-generating coil in the exemplary embodiment, is changed with the method step 18 "input of control parameter". Method steps 14 35 17 with generation of the electrical signal by calculating the time series from the modified differential equation, the mapping into the two dimensional phase space by return map, the 202.03WO - 12 23.11.2004 determination of the dimension of the structure of the map by calculating the fractal dimension dF are repeated and the dimension is again compared with the default dimension. As long as no match of default 5 dimension dFv and dimension dF which is within the tolerance range + s is found during the comparison, method steps 14, 15 and 16 are continuously repeated by again changing the control parameter in method step 18, until a match is achieved. 10 If a match is found in the tolerance range, the electrical signal generated last, that is to say the electrical signal which has been generated with the value of the at least one variable parameter of the 15 model leading to the match, is released for feeding the transmitting antenna 11. For this purpose, a gate 20 is opened and the electrical signal is applied to the electrical transformers of the transmitting antenna 11 after filtering, determination of the bandwidth and the 20 transmitting period and after amplification in Block 21. The electrical signal is radiated as sound signal into the water by the transmitting antenna 11, backscattered 25 from a target located in the area of the sea within range of the transmitting antenna 11 and received via the receiving antenna 12 placed at the location of the transmitting antenna 11. Due to the chaotic deterministic structure of the transmitted signal, the 30 latter is concealed in the ambient noise of the target so that the target cannot detect the transmitted signal and thus cannot draw conclusions with respect to an opponent located in the. area of the sea and which is actively locating. At the location of the receiving 35 antenna 12, the backscattered transmitted signal is also concealed in the ambient noise of the receiving antenna 12, but can be detected with the aid of the knowledge of the structural measure, that is to say the 202.03WO - 13 23.11.2004 dimension of the deterministic structure of the transmitted signal. Figure 2 shows the method steps for receiving the 5 transmitted sound signal, performed at the receiver end, in a block diagram. The sound energy incident at the receiving location is received by means of the receiving antenna 12. The receiving antenna 12, used as so-called linear antenna in the exemplary embodiment, 10 has a multiplicity of hydrophones 22 arranged equidistantly in a row. Such a linear antenna is known as towed array or as a flank array attached to the hull of the boat, sometimes also called side streamer. All hydrophones 22 are operated together and by appropriate 15 signal processing of all electrical output signals of the hydrophones 22 in a so-called beam former 23, a directional pattern of the receiving antenna 12 is formed, the axis of greatest acoustic sensitivity of which is at right angles to the receiving antenna 12 or 20 can be tilted at an acute angle -90* > e < + 90* to the normal of the receiving antenna 12. Structure and operation of the beam former 23 is known and described, for example, in US 4 060 792 or DE 21 14 373 Al or in DE 100 27 538. 25 The electrical output signal at the output of the beam former 23, called the received signal picked up at the receiving antenna 12 in the text which follows, is again mapped in the same multi-dimensional phase space 30 by means of the same method as the electrical signal during the generation of the transmitted signal. Since the return map has been selected there, the mapping into the two-dimensional phase space is performed here, too, by means of return map (method step 25) and the 35 fractal dimension dF is calculated as dimension for the structure of the map (method step 26). In method step 27, it is determined whether the dimension dF corresponds to the known default dimension dv within 202.03WO - 14 23.11.2004 the tolerance range ± s. The default dimension dv and the permissible tolerance range + s are known at the receiving end and are input via an input block 29. If a match within the tolerance range + s is given, it is 5 determined by this means that the transmitted signal radiated by the transmitting antenna 11 has also been received at the receiver end. The received signal is now released for evaluation. For example, in the case of a match of the dimension for the deterministic 10 structure of the output signal with the default dimension within the tolerance range + s, a gate 30 is opened at which the tilt angle e of the receiving antenna 12, instantaneously set in each case by the beam former 23, is present. The tilt angle e is shown 15 as bearing of the target in a display unit 31. The time from emission of the transmitted signal by the transmitting antenna 11 to the reception of the transmitted signal reflected or backscattered from the target by the receiving antenna 12 is measured by means 20 of a timer, not shown here, and from this the range r between the locating system and the target is calculated. The range r is also indicated in the display unit 31. With bearing e and range r, the position of the target is acquired. 25 Apart from target detection, the method according to the invention can also be used for identification friend/foe. Since the default dimension for the transmitted signals emitted for identification 30 friend/foe is known to all friendly vehicles, only the friendly vehicles can detect the identification signals which are concealed in the ambient noise. The hostile vehicles, which do not have this information, are not able to detect these transmitted signals in the 35 received ambient noise. As a result, the probability of revealing the group of vehicles operating with identification friend/foe is greatly reduced, on the one hand, and, on the other hand, it is ensured that 202.03Wo - 15 23.11.2004 hostile vehicles cannot simulate the identification signals and thus cannot camouflage themselves by an imitated identification friend/foe. 5 The method according to the invention is not restricted to its application in underwater technology by means of sonar systems. It can also be used for emitting and receiving electromagnetic wave energy by means of radar systems in the medium of air. 10 Instead of a return map, the signal can also be mapped into a multi-dimensional phase space by Poincar6 plotting, attractor plotting or Lorentz plotting or by a phase space representation. With respect to these 15 terms, the literature reference specified above is referred to.

Claims

1. A method for emitting and receiving wave energy, in which a transmitting antenna is fed with an electrical signal having a deterministic-chaotic structure at the 5 transmitting end and the signal radiated by the transmitting antenna is detected in the received electrical signal picked up from a receiving antenna at the receiving end, characterized in that the deterministic-chaotic structure of the electrical signal is characterized by a structural measure which is determined as a dimension of the structure of the map of the temporal course of the signal in a multi-dimensional phase 10 space, and that the signal is detected in the received signal using the structural measure.

2. The method according to claim 1, characterized in that the temporal course of the electrical signal is derived from the chaotic-deterministic oscillation characteristic of a model, the oscillation characteristic of which can be varied by changing at least 15 one parameter in that the electrical signal, generated with an assumed value of the at least one variable parameter of the model, is mapped into a multi-dimensional phase space, that as structural measure a dimension of the structure of the map is determined and compared with a default dimension, that the generation of the electrical signal, its mapping into a multi-dimensional phase space and the determination of the dimension 20 of the structure of the map are repeated with in each case an altered value of the at least one variable parameter of the model, until a match, located within a tolerance range, of the dimension with the default dimension has been reached, that the transmitting antenna is fed with the electrical signal which has been generated with the value of the at least one variable parameter of the model leading to the match, and that the default 25 dimension is utilized as structural measure for the detection at the receiving end.

3. Method according to Claim 2, characterized in that, as a model, the differential equation of a pendulum of revolution with unbalance (Pohl pendulum) is used, the variable parameters of which are the spring constant of a restoring spring, the 30 amplitude and the frequency of an external excitation, the damping constant of an abrasive friction, the mass and the lever arm of the unbalance and the damping constant and the current of an eddy-current brake, and that the at least one parameter which varies the oscillation characteristic is selected from these variable parameters. 35

4. Method according to Claim 2 or 3, characterized in that the received electrical signal of the receiving antenna is mapped into a multi-dimensional phase space at the 17 receiving end, a dimension of the structure of the map is determined and compared with the default dimension, and that, when dimension and default dimension match within the tolerance range, detection of the signal is recognized.

5 5. Method according to any one of Claims 2 to 4, characterized in that a characteristic quantity of electrical signal is used for mapping the electrical signal into the multi-dimensional phase space and the same quantity is used for mapping the received signal into the multi-dimensional phase space. 10

6. Method according to Claim 5, characterized in that as characteristic quantity, - the peaks of the amplitude or - the troughs of the amplitude or - the space between the amplitude peaks or - the space between the amplitude troughs or 15 - the space between the transition points of the amplitude through an arbitrarily selected amplitude threshold or - amplitude samples taken in identical time intervals or - intersections of Poincar6 sections are detected. 20

7. Method according to any one of claims 2 to 6, characterized in that the mapping into a two-dimensional phase space is performed by means of a return map in which the values of the characteristic quantity in a predetermined signal segment are picked up successively in time from the electrical signal or received signal and are allocated to one and the other coordinate in the two-dimensional coordinate system of the phase 25 space.

8.. Method according to any one of Claims 2 to 6, characterized in that the mapping into the multi-dimensional phase space is performed by means of a Poincar6 plot or an attractor plot or a Lorentz plot or a phase-space representation. 30

9. Method according to any one of Claims 2 to 7,, characterized in that a fractal dimension of the two-dimensional map is calculated as dimension of the structure of the map. 890446 1.doc 18

10. Method according to Claim 9, characterized in that the fractal dimension is calculated in accordance with the magnification - multiplication method or in accordance with the grating method or in accordance with the distance analysis method. 5

1 1. Method according to Claim 9 or 10,, characterized in that a value of the fractal dimension between 0 and 2 is selected as default dimension.

12. A method for emitting and receiving wave energy substantially as hereinbefore described with reference to the accompanying drawings. 10 RQAAA 1 rin-