Claims:

1. A method for generating Non-Linear Frequency Modulated (NLFM) waveforms, the method comprising:
receiving, by a random population generator (1042), a plurality of parameter values of a desired NLFM waveform from a user and generating an initial population of Bezier control points based on the received parameter values of the desired NLFM waveform;
generating, by a Bezier curve generator (1044), a plurality of NLFM time frequency curves according to the generated initial population of Bezier control points and by using a sampling frequency (Fs) specified in the parameter values of the desired NLFM waveform;
evaluating, using a plurality of optimization model units (1046, 1048), that the generated NLFM time frequency curves is meeting the parameter values of the desired NLFM waveform, calculating and allotting scores to the generated NLFM time frequency curves based on a fitness of the generated NLFM time frequency curves;
allotting, by a cumulative fitness score unit (10410), a cumulative score to the generated NLFM time frequency curves based on the allotted scores by the plurality of optimization model units (1046, 1048); and
receiving, by a genetic method search unit (10412), the cumulative score allotted to the generated NLFM time frequency curves; determining based on the cumulative score, whether the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user and generating optimum Bezier control points corresponding to the generated NLFM frequency curves, in response to determining that the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user.
2. The method as claimed in claim 1, wherein generating the optimum Bezier control points in response to determining that the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user further comprises:
storing, by a memory unit (106), the generated optimum Bezier control points;
accessing, by a Bezier curve generator (1082) of a synthesizer unit (108), the stored optimum Bezier control points and generating a plurality of NLFM time frequency curves based on the stored optimum Bezier control points; and
generating, by a waveform generator (1084) of the synthesizer unit (108), NLFM waveforms based on the generated NLFM time frequency curves, where the generated NLFM waveforms meets the plurality of parameter values of the desired NLFM waveform.
3. The method as claimed in claim 1, wherein determining based on the cumulative score that the generated NLFM time frequency curves is achieving the fitness is by selecting the generated NLFM time frequency curves with the highest cumulative score.

4. The method as claimed in claim 1, wherein the plurality of parameter values of the desired NLFM waveform received from the user comprise at least one of a Bandwidth (B), a pulse width (T), the sampling frequency (Fs), a Side lobe level (SLL), a main Lobe width (ML) of the desired NLFM waveform.
5. The method as claimed in claim 1, wherein in response to determining that the generated NLFM time frequency curves is not achieving the fitness according to the parameter values of the desired NLFM waveform from the user, the method comprises:
generating, by the Bezier curve generator (1044), the plurality of NLFM time frequency curves according to the generated initial population of Bezier control points and the sampling frequency (Fs)specified in the parameter values of the desired NLFM waveform.
6. The method as claimed in claim 1, wherein after generating by the Bezier curve generator (1044), the NLFM time frequency curves according to the generated initial population of Bezier control points and the sampling frequency (Fs) specified in the parameter values of the desired NLFM waveform, the method comprises:
determining validity of the generated NLFM time frequency curves; and
performing a waveform matched filtering on the generated NLFM time frequency curves in response to determining that the generated NLFM time frequency curves are valid.

7. The method as claimed in claim 6, wherein in response to determining that the generated NLFM time frequency curves are not valid, the method comprises:
checking the validity of the generated NLFM time frequency curves for a one-to-one mapping between time and corresponding frequency values.
8. The method as claimed in claim 6, wherein performing, by the Bezier curve generator (1044), the waveform matched filtering comprises:
obtaining an autocorrelation output of the generated NLFM time frequency curves;
determining a main lobe width and side lobe levels of the autocorrelated output;
determining whether the main lobe width of the autocorrelated output is meeting a main lobe criterion, wherein the main lobe criterion is determining whether 3*(6 dB width of the main lobe) is greater than first null to null width; and
determining whether the side lobe levels of the autocorrelated output is monotonically decreasing in response to determining that the main lobe width of the autocorrelated output is meeting the main lobe criterion.
9. The method as claimed in 8, wherein in response to determining that the main lobe width of the autocorrelated output is not meeting the main lobe criterion and in response to determining that the side lobe levels of autocorrelated output is not monotonically decreasing, the method comprises:
allotting, by the Bezier curve generator (1044), a fitness score of 10-300 to the generated NLFM time frequency curves.

10. The method as claimed in claim 1 and 8, wherein evaluating using the plurality of optimization model units (1046, 1048) comprises: a first optimization model unit (1046) and a second optimization model unit (1048), wherein the first optimization model unit (1046) is for evaluating a side lobe level of the autocorrelated output and is defined by: f1(x) = ,where W is the side lobe level specified in the parameter values of the desired NLFM waveform and the σw affects the rate of change of slope of the score values around the desired parameter value of the side lobe level, and the second optimization model unit (1048) is for evaluating the main lobe width of the autocorrelated output and is defined by: f2(y) = ,where is the main lobe width in number of samples, and are constants and c is the main Lobe width (ML) specified in the parameter values of the desired NLFM waveform.
11. The method as claimed in 10, wherein when the condition in the second optimization model unit (1048), f2(y) is not satisfied, a fitness score of 10-300 is allotted to the generated NLFM time frequency curves and when the condition in the second optimization model (1048) is satisfied, value on left hand side of f2(y) is taken as the fitness score.
12. The method as claimed in claims 1, 10 to 11 wherein the cumulative score allotted to the generated NLFM time frequency curves is defined by: .
13. A system for generating Non-Linear Frequency modulated (NLFM) waveforms, the system comprising:
a random population generator (1042) configured to: receive a plurality of parameter values of a desired NLFM waveform from a user and generate an initial population of Bezier control points based on the received parameter values of the desired NLFM waveform;
a Bezier curve generator (1044) configured to: generate a plurality of NLFM time frequency curves according to the generated initial population of Bezier control points and by using a sampling frequency (Fs) specified in the parameter values of the desired NLFM waveform;
a plurality of optimization model units (1046, 1048) configured to: evaluate that the generated NLFM time frequency curves is meeting the parameter values of the desired NLFM waveform, calculate and allot scores to the generated NLFM time frequency curves based on a fitness of the generated NLFM time frequency curves;
a cumulative fitness score unit (10410) configured to: allot a cumulative score to the generated NLFM time frequency curves based on the allotted scores by the plurality of optimization model units (1046, 1048);
a genetic method search unit (10412) configured to: receive the cumulative score allotted to the generated NLFM time frequency curves, determine based on the cumulative score, whether the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user and generate optimum Bezier control points corresponding to the generated NLFM frequency curves, in response to determining that the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user;
a memory unit (106) configured to: store the generated optimum Bezier control points;
a Bezier curve generator (1082) of a synthesizer unit (108) configured to: access the stored optimum Bezier control points and generate a plurality NLFM time frequency curves based on the stored optimum Bezier control points; and
a waveform generator (1084) of the synthesizer unit (108) configured to: generate NLFM waveforms based on the generated NLFM time frequency curves, where the generated NLFM waveforms meets the plurality of parameter values of the desired NLFM waveform.
14. The system as claimed in claim 13, wherein each member of the generated initial population of Bezier control points is a 12x1 vector array of floating-point values.
, Description:
FORM 2
THE PATENTS ACT, 1970
(39 of 1970)
&
THE PATENTS RULES, 2003
COMPLETE SPECIFICATION
(See section 10, rule 13)

“A METHOD AND SYSTEM FOR GENERATING NON-LINEAR FREQUENCY MODULATED WAVEFORMS”
By
BHARAT ELECTRONICS LIMITED
WITH ADDRESS: OUTER RING ROAD, NAGAVARA, BANGALORE 560045, KARNATAKA, INDIA

The following specification particularly describes the invention and the manner in which it is to be performed.

Field of the Invention
The present invention mainly relates to a field of pulse compression systems and more particularly, the present invention relates to a method and system for generating Non-Linear Frequency Modulated (NLFM) waveforms.

Background of the invention
Pulse compression is a signal processing technique commonly used by Radar (radio detection and ranging) and Sonar (sound navigation and ranging) to increase range resolution as well as the signal to noise ratio (SNR). That is, pulse compression systems are widely used to improve range resolution in Radar systems. But this improved range resolution comes at the cost of high side lobes. Thus, the side-lobes of strong targets will hide the returns of any weak target that is close to the strong target. Therefore, it is necessary to find mechanisms that can suppress side-lobes in pulse compression systems.
Conventionally, Linear Frequency Modulated (LFM) waveforms have been widely used in pulse compression systems due to their ease of generation and good range resolution. However, LFM waveforms suffer from high side-lobe levels (-13.3 dB). Time/range side-lobes in compressed output limits the ability to detect weak targets against strong returns like detecting a small tugboat towing a big cargo ship or detecting a small passenger aircraft moving against a hanger or building. These side-lobes in LFM waveforms can be reduced with amplitude windowing or weighing in the time domain. Windowing of an LFM pulse gives good performance in terms of side-lobe reduction, but at the cost of main lobe broadening and inefficient transmission. Further, mismatched filtering results in significant losses in range resolution and SNR.
An alternate approach in pulse compression systems involves using Non Linear Frequency Modulated waveforms (NLFM). NLFM waveforms have a potential to have a range profile with lower side-lobes without windowing. But due to inherent non-linearity of NLFM waveforms, they are more complex to design and generate compared to an LFM waveform. Conventionally NLFM waveforms have been generated using methods such as stationary phase method and search based methods. Stationary phase methods involve recreating time frequency curve from desired power spectrum by utilizing the stationary phase points in a power spectrum. Numeric methods need to be employed to solve inverse functions to retrieve the time frequency characteristic.
Search based methods use optimization of certain cost functions to converge to a solution. These cost functions may be designed on the basis of parameter values such as side lobe level, integrated side lobe level, compressed pulse width etc and similar work is disclosed in one of the prior arts. The prior art uses a genetic method for finding orthogonal NLFM waveforms using two optimization methods. Further, another prior art discloses scaled multiple function non linear frequency modulated waveform generation. However, conventional systems require complex equations for waveform generation.
Therefore, there is a need in the art with a method and system for generating Non-Linear Frequency Modulated (NLFM) waveforms and to solve the above mentioned limitations.

Objective of the invention
The main objective of the present invention is to provide a method and a system for generating valid and non-redundant Non-Linear Frequency Modulated (NLFM) waveforms with low sidelobe-levels, low mismatch losses and less main lobe degradation.

Summary of the invention
An aspect of the present invention is to address the above-mentioned problems and/or disadvantages and to provide at least the advantages described below.

Accordingly, in one aspect of the present invention relates to a method for generating Non-Linear Frequency Modulated (NLFM) waveforms, the method comprising: receiving, by a random population generator, a plurality of parameter values of a desired NLFM waveform from a user and generating an initial population of Bezier control points based on the received parameter values of the desired NLFM waveform, generating, by a Bezier curve generator, a plurality of NLFM time frequency curves according to the generated initial population of Bezier control points and by using a sampling frequency (Fs) specified in the parameter values of the desired NLFM waveform, evaluating, using a plurality of optimization model units, that the generated NLFM time frequency curves is meeting the parameter values of the desired NLFM waveform, calculating and allotting scores to the generated NLFM time frequency curves based on a fitness of the generated NLFM time frequency curves, allotting, by a cumulative fitness score unit, a cumulative score to the generated NLFM time frequency curves based on the allotted scores by the plurality of optimization model units and receiving, by a genetic method search unit, the cumulative score allotted to the generated NLFM time frequency curves, determining based on the cumulative score, whether the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user and generating optimum Bezier control points corresponding to the generated NLFM frequency curves, in response to determining that the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user.

Accordingly, another aspect of the present invention relates to a system for generating Non-Linear Frequency modulated (NLFM) waveforms, the system comprising: a random population generator configured to: receive a plurality of parameter values of a desired NLFM waveform from a user and generate an initial population of Bezier control points based on the received parameter values of the desired NLFM waveform, a Bezier curve generator configured to: generate a plurality of NLFM time frequency curves according to the generated initial population of Bezier control points and by using a sampling frequency specified in the parameter values of the desired NLFM waveform, a plurality of optimization model units configured to: evaluate that the generated NLFM time frequency curves is meeting the parameter values of the desired NLFM waveform, calculate and allot scores to the generated NLFM time frequency curves based on a fitness of the generated NLFM time frequency curves, a cumulative fitness score unit configured to: allot a cumulative score to the generated NLFM time frequency curves based on the allotted scores by the plurality of optimization model units, a genetic method search unit configured to: receive the cumulative score allotted to the generated NLFM time frequency curves, determine based on the cumulative score, whether the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user and generate optimum Bezier control points corresponding to the generated NLFM frequency curves, in response to determining that the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user, a memory unit configured to: store the generated optimum Bezier control points, a Bezier curve generator of a synthesizer unit configured to: access the stored optimum Bezier control points and generate a plurality NLFM time frequency curves based on the stored optimum Bezier control points and a waveform generator of the synthesizer unit configured to: generate NLFM waveforms based on the generated NLFM time frequency curves, where the generated NLFM waveforms meets the plurality of parameter values of the desired NLFM waveform.

Other aspects, advantages, and salient features of the invention will become apparent to those skilled in the art from the following detailed description, which, taken in conjunction with the annexed drawings, discloses exemplary embodiments of the invention.
Brief description of the drawings
The above and other aspects, features, and advantages of certain exemplary embodiments of the present invention will be more apparent from the following description taken in conjunction with the accompanying drawings in which:
Figures 1(a), 1(b), 1(c) shows a block diagram of a system for generating Non-Linear Frequency Modulated (NLFM) waveforms and subcomponents of the system according to one embodiment of the present/proposed invention.
Figure 2 shows a block diagram illustrating modules in a processor of the system for generating NLFM waveforms, according to one embodiment of the present invention.
Figure 3 shows a block diagram illustrating modules in a synthesizer of the system for generating NLFM waveforms, according to one embodiment of the present invention.
Figure 4 shows a flow diagram of a method for generating NLFM waveforms, according to one embodiment of the present invention.
Figure 5 shows a graph illustrating structure of an input vector array to genetic method, according to one embodiment of the present invention.
Figure 6 shows a flow diagram for NLFM waveform generation, according to one embodiment of the present invention.
Figure 7 shows a main lobe width and side lobe level of matched filter output measured at - 6 dB level and first side lobe peak respectively, according to one embodiment of the present invention.
Figure 8 shows a flow diagram of genetic method fitness function, according to one embodiment of the present invention.
Persons skilled in the art will appreciate that elements in the figures are illustrated for simplicity and clarity and may have not been drawn to scale. For example, the dimensions of some of the elements in the figure may be exaggerated relative to other elements to help to improve understanding of various exemplary embodiments of the present disclosure.
Throughout the drawings, it should be noted that like reference numbers are used to depict the same or similar elements, features, and structures.

Detailed description of the invention

The following description with reference to the accompanying plots/drawings is provided to assist in a comprehensive understanding of exemplary embodiments of the invention as defined by the claims and their equivalents. It includes various specific details to assist in that understanding but these are to be regarded as merely exemplary. Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the invention. In addition, descriptions of well-known functions and constructions are omitted for clarity and conciseness.
The terms and words used in the following description and claims are not limited to the bibliographical meanings but are merely used by the inventor to enable a clear and consistent understanding of the invention. Accordingly, it should be apparent to those skilled in the art that the following description of exemplary embodiments of the present invention are provided for illustration purpose only and not for the purpose of limiting the invention as defined by the appended claims and their equivalents.
It is to be understood that the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a component surface” includes reference to one or more of such surfaces.
By the term “substantially” it is meant that the recited characteristic, parameter, or value need not be achieved exactly, but that deviations or variations, including for example, tolerances, measurement error, measurement accuracy limitations and other factors known to those of skill in the art, may occur in amounts that do not preclude the effect the characteristic was intended to provide.
Figures discussed below, and the various embodiments used to describe the principles of the present disclosure in this patent document are by way of illustration only and should not be construed in any way that would limit the scope of the disclosure. Those skilled in the art will understand that the principles of the present disclosure may be implemented in any suitably arranged system. The terms used to describe various embodiments are exemplary. It should be understood that these are provided to merely aid the understanding of the description, and that their use and definitions in no way limit the scope of the invention. Terms first, second, and the like are used to differentiate between objects having the same terminology and are in no way intended to represent a chronological order, unless where explicitly stated otherwise. A set is defined as a non-empty set including at least one element.
The present invention mainly relates to a field of pulse compression systems. More particularly, the present invention relates to a method and system for generating Non-Linear Frequency Modulated (NLFM) waveforms.
The objective of the present invention is to provide the method and the system for generating valid and non-redundant Non-Linear Frequency Modulated (NLFM) waveforms with low sidelobe-levels, low mismatch losses and less main lobe degradation.
The present invention arose out of a requirement for waveforms with low matched filtering sidelobes and low mismatch losses without the requirement of complex waveform generation equations. The waveforms (NLFM waveforms) generated using the present invention outperform standard Linear Frequency Modulated (LFM) waveform along with standard windowing mechanisms w.r.t the side-lobe and mismatch performance.
The present invention provides a method for generation of (NLFM) waveforms using search optimizations techniques, that is, a search based method for NLFM generation which requires as input only desired parameter values of matched filter response.
The present invention mainly focusses on search based method for generation of Non Linear Frequency Modulated waveforms.
In the present invention, a plurality of optimization models/functions for the search based method is implemented to generate NLFM waveforms with the desired characteristics/ desired parameter values and rejection of invalid and redundant waveforms during search optimization which ensure search is limited to generation of valid and non-redundant NLFM time frequency curves. The generated NLFM waveforms have better target detection range than standard windowed LFM waveform with lesser mismatch loss and main lobe degradation. Further, the present invention provides better matched filtering characteristics as compared to LFM with standard windows.
Figures 1(a), 1(b), 1(c) shows a block diagram of a system for generating Non-Linear Frequency Modulated (NLFM) waveforms and subcomponents of the system according to one embodiment of the present/proposed invention. Figure 1(a) illustrates components/modules/units in the system 100 for generating NLFM waveforms. Figures 1(b) and 1 (c) illustrates modules/units in the subcomponents of the system. User input is taken at an input module/unit 102 which is passed to a processor 104. The processor 104 may be a Central Processing Unit (CPU) connected with an accelerator board through a PCIE slot as shown in Figure 1(b). The user input may be a plurality of parameter values of a desired NLFM waveform. For example, the plurality of parameter values of the desired NLFM waveform received from the user comprise at least one of a Bandwidth (B), a pulse width (T), a sampling frequency (Fs), a Side lobe level (SLL), a main Lobe width (ML) and the like.
Figure 2 shows a block diagram illustrating modules in the processor 104 of the system for generating NLFM waveforms, according to one embodiment of the present invention. Figure 2 shows the modules/units implemented in the processor 104. The modules/units include a random population generator 1042, a Bezier curve generator 1044, a plurality of optimization model units 1046, 1048, a cumulative fitness score unit 10410, a genetic method search unit 10412. The random population generator 1042 generates the initial population of control points/ Bezier control points based on the user input, which is passed on to the Bezier curve generator 1044. For example, the plurality of parameter values of the desired NLFM waveform from the user is received by the random population generator 1042 and the initial population of Bezier control points is generated based on the received parameter values of the desired NLFM waveform.
The Bezier curve generator 1044 generates a plurality of NLFM time frequency curves according to the generated initial population of Bezier control points and by using the sampling frequency (Fs) specified in the parameter values of the desired NLFM waveform. The generated NLFM time frequency curves/waveforms are then evaluated using two optimization models 1046, 1048 and scores are calculated and allotted to the generated NLFM time frequency curves/waveforms based on their fitness. The fitness of the generated NLFM time frequency curves is determined by evaluating whether the generated NLFM time frequency curves are achieving received parameter values of the desired NLFM waveform. The plurality of optimization model units includes two optimization models/optimization model units 1046, 1048.
Further, a cumulative score is then allotted, by the cumulative fitness score unit 10410, to the generated NLFM time frequency curves based on the allotted scores by the plurality of optimization model units 1046, 1048.
These scores are then passed on to the Genetic method search module/unit 10412. The cumulative scores allotted to the generated NLFM time frequency curves are received by the genetic method search unit 10412. Further, based on the cumulative score, whether the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user is determined. Optimum Bezier control points corresponding to the generated NLFM frequency curves is generated by the genetic method search unit 10412, in response to determining that the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user.
Further, in the present invention, the optimum control points/ optimum Bezier control points from the genetic method search unit 10412 are stored in a memory unit 106. The memory unit 106 stores the generated optimum Bezier control points. The stored optimum Bezier control points is accessed by a synthesizer 108. In an embodiment, the memory unit 106 stores multiple versions of Bezier control points, corresponding to different target detection scenario, which can be accessed by the synthesizer 108.
Figure 3 shows a block diagram illustrating modules in the synthesizer 108 of the system for generating NLFM waveforms, according to one embodiment of the present invention. As shown in Figure 1(c), the synthesizer 108 is either a Field Programmable Gate Array (FPGA) with Digital-to-Analog Converter (DAC) or a Radio Frequency System-on-Chip (RF-SOC) to generate the desired waveform which is then sent to a transmitter. The synthesizer 108 consists of a module/unit to generate Bezier curve (Bezier curve generator 1082) from the stored Bezier anchor (control) points and a waveform generator 1084 as shown in Figure 3.
The Bezier curve generator 1082 of the synthesizer unit 108, accesses the stored optimum Bezier control points and generates the plurality of NLFM time frequency curves based on the stored optimum Bezier control points. The waveform generator 1084 of the synthesizer unit 108 generates NLFM waveforms based on the generated NLFM time frequency curves. The generated NLFM waveforms meets the plurality of parameter values of the desired NLFM waveform from the user.
Figure 4 shows a flow diagram of a method for generating NLFM waveforms, according to one embodiment of the present invention. Referring to Figure 4, at step 410, the method comprises receiving the plurality of parameter values of the desired NLFM waveform from the user and generating the initial population of Bezier control points based on the received parameter values of the desired NLFM waveform by the random population generator 1042.
At step 420, the method comprises generating the plurality of NLFM time frequency curves according to the generated initial population of Bezier control points and by using the sampling frequency (Fs) specified in the parameter values of the desired NLFM waveform by the Bezier curve generator 1044. At step 430, the method comprises evaluating that the generated NLFM time frequency curves is meeting the parameter values of the desired NLFM waveform, calculating and allotting scores to the generated NLFM time frequency curves based on the fitness of the generated NLFM time frequency curves using the plurality of optimization model units 1046, 1048.
At step 440, the method comprises allotting, by the cumulative fitness score unit 10410, the cumulative score to the generated NLFM time frequency curves based on the allotted scores by the plurality of optimization model units 1046, 1048.
At step 450, the method comprises receiving the cumulative score allotted to the generated NLFM time frequency curves by the genetic method search unit 10412. The method further comprises determining, by the genetic method search unit 10412, based on the cumulative score, whether the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user and generating optimum Bezier control points corresponding to the generated NLFM frequency curves, in response to determining that the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user.
In an embodiment, the method further comprises generating, by the Bezier curve generator 1044, the plurality of NLFM time frequency curves according to the generated initial population of Bezier control points and the sampling frequency (Fs) specified in the parameter values of the desired NLFM waveform, in response to determining that the generated NLFM time frequency curves is not achieving the fitness according to the parameter values of the desired NLFM waveform from the user.
Figure 5 shows a graph illustrating structure of an input vector array to genetic method, according to one embodiment of the present invention. The structure of the input vector array to the genetic method consisting of two dimensional coordinate points corresponding to the Bezier curve control points is illustrated in Figure 5.
In the present invention, the method aims to find a converging mechanism for multi parameter optimization for search space based optimization method, more specifically genetic method based search. The search space is the set of points in time frequency points bounded by and , where bandwidth of the system is and the pulse width is denoted by .
In the present invention, the random population generator 1042 receives the plurality of parameter values of the desired NLFM waveform from the user and generates the initial population of Bezier control points based on the received parameter values of the desired NLFM waveform. The initial population for the genetic method is randomly generated with number of members in the initial population being P. Each member of the population is 12x1 vector array of floating point values as shown in Figure 5. The first 6 values are generated randomly within the limits 0 and T/2 whereas the next 6 values are generated randomly between 0 and B/2. These are then positional associated among the first 6 and the next 6 values to generate the two dimensional coordinate points in the search space. These two dimensional coordinate points are the control points of a Bezier curve. The Bezier curve is used to generate the time-frequency plot/NLFM time frequency curve. The control points of the Bezier curve form the members of the population in the genetic method. The Bezier curve is created with 8 control points. The first and the last control point are fixed at and . Each member is an array of size 12x1, corresponding to the 6 control points in the two dimensional coordinate system. These 12 genes of every member are used to create time frequency Bezier curve for the corresponding member. The Bezier curve parameter is varied over the interval to generate the two dimensional coordinates of the Bezier curve.
Figure 6 shows a flow diagram for NLFM waveform generation, according to one embodiment of the present invention. At step 602, the plurality of parameter values of the desired NLFM waveform is received from the user. The plurality of parameter values comprises at least one of the Bandwidth (B), the pulse width (T), the sampling frequency (Fs), the Side lobe level (SLL), the main Lobe width (ML) of the desired NLFM waveform.
As shown in step 604, the search based method for NLFM waveform generation starts with the initial population generated with random coordinate values. At step 606, the member of the initial population is used to create the time frequency Bezier curve, which is then fed to a spline interpolation block which generates the time frequency curve/NLFM time frequency curve according to the user specified sampling frequency (Fs). The NLFM time frequency curve is then fed to a system which tests monotonicity of the produced waveform. That is, after generating the NLFM time frequency curves by the Bezier curve generator 1044, at step 608, validity of the generated NLFM time frequency curves (Bezier curve) are determined. At step 610, a waveform matched filtering is performed on the generated NLFM time frequency curves in response to determining that the generated NLFM time frequency curves are valid.
For checking the validity of the generated NLFM time frequency curves, frequency values are stored in an array. The difference between adjacent values of the frequency is computed. These difference values are sent through a comparator block which finds the presence of negative values. If negative values are present, then the corresponding member/NLFM time frequency curve is assigned a score of . If negative values are not present, then the score given is 1. This NLFM time frequency curve is used to generate a complex waveform. This waveform is then used in an autocorrelation block. That is, waveform matched filtering is performed on the generated NLFM time frequency curves in response to determining that the generated NLFM time frequency curves are valid.
In an embodiment, at step 622, the validity of the generated NLFM time frequency curves are checked for a one-to-one mapping between time and corresponding frequency values, in response to determining that the generated NLFM time frequency curves are not valid.
At step 612, side lobe level of the autocorrelated output is evaluated by optimization model unit 1/first optimization model unit 1046. At step 614, main lobe width of the autocorrelated output is evaluated by optimization model unit 2/second optimization model unit 1048.
At step 616, the cumulative score is allotted to the generated NLFM time frequency curves by the cumulative fitness score unit 10410 based on the evaluation and the allotted scores by the first optimization model unit and the second optimization model unit 1046, 1048.
At step 618, the genetic method search unit 10412 determines whether the generated NLFM time frequency curves is achieving the fitness according to the parameter values of the desired NLFM waveform from the user and generates optimum Bezier control points upon determining that the generated NLFM time frequency curves is achieving the fitness. At step 620, the synthesizer unit 108, synthesize NLFM waveforms based on the generated NLFM time frequency curves, where the generated NLFM waveforms meets the plurality of parameter values of the desired NLFM waveform. In an embodiment, the synthesizer unit 108, synthesize NLFM waveforms from the generated NLFM time frequency curves which has the highest fitness score/highest cumulative score.
In an embodiment, at step 618, in response to determining that the generated NLFM time frequency curves is not achieving the fitness according to the parameter values of the desired NLFM waveform from the user, the method comprises generating, by the Bezier curve generator 1044, the plurality of NLFM time frequency curves according to the generated initial population of Bezier control points and the sampling frequency (Fs) specified in the parameter values of the desired NLFM waveform.
Figure 7 shows a main lobe width and side lobe level of matched filter output measured at - 6 dB level and first side lobe peak respectively, according to one embodiment of the present invention. The matched filter output with the measurements of 6dB pulse width and the side-lobe levels is shown in Figure 7. The max of this autocorrelation output/ matched filter output is found out. Then the system searches for the next first -6dB crossing from this peak. The width at the 3dB point from the peak is measured as the 6dB width. Then the first minimum after the maximum peak is found. For measuring the peak side-lobe level, the maximum value found between this minimum value and the end of the autocorrelation sequence is taken as the peak side-lobe level (SLL).
Figure 8 shows a flow diagram of genetic method fitness function, according to one embodiment of the present invention. As shown in Figure 8, the genetic method fitness function provides the cumulative score.
At step 812, during the waveform matched filtering, the autocorrelation output of the generated NLFM time frequency curves are obtained. Further, at step 814, the main lobe width and side lobe levels of the autocorrelated output are determined.
Further, peak of all side lobes throughout a range of interest is measured and stored in an array according to the range. The magnitude difference between successive side lobes is calculated for testing monotonicity of side lobes across range. This difference value is then passed through a comparator block which finds if there are any negative difference values. If negative difference values are present, then the member/ generated NLFM time frequency curves is given a score of , else it is given a score of 1.
As described above, in the present invention, whether the main lobe width of the autocorrelated output is meeting the main lobe criterion is determined at step 816. Further, in the present invention, whether the side lobe levels of the autocorrelated output is monotonically decreasing is determined at step 818, in response to determining that the main lobe width of the autocorrelated output is meeting the main lobe criterion. The main lobe criterion is determining whether 3*(6 dB width of the main lobe) is greater than first null to null width.
In the present invention, in response to determining that the main lobe width of the autocorrelated output is not meeting the main lobe criterion and in response to determining that the side lobe levels of autocorrelated output is not monotonically decreasing, a fitness score of 10-300 is allotted to the generated NLFM time frequency curves as illustrated in step 826.
At steps 820 and 822, if the main lobe width of the autocorrelated output is meeting the main lobe criterion and when the side lobe levels of the autocorrelated output is monotonically decreasing, then the plurality of optimization model units 1046, 1048, evaluate that the generated NLFM time frequency curves is meeting the parameter values of the desired NLFM waveform. Further scores are calculated and allotted to the generated NLFM time frequency curves based on the fitness of the generated NLFM time frequency curves.
In the present invention, the plurality of optimization model units 1046, 1048 use the 6dB pulse width, side-lobe level and monotonicity of side lobes to calculate a score as shown in Figure 8. The 6dB pulse width is measured as the width of the pulse at 3db below the highest peak.
For example, each candidate of a generation/ each generated NLFM time frequency curve is an input to the system of optimization model units 1046, 1048. The system first calculates an array of correlation values from the waveform generated with each candidate. The beam width of the main lobe is calculated as the difference in samples between the maximum value in the array and the first time the value goes below 6db of the maximum value, henceforth referred to as the 6db level. The ratio between the width in samples of 6db level and the first null after the maxima is fixed at 3. Any candidate with a main lobe width more than this ratio is given a lower score by the optimization model unit. The 6 dB level width in samples is fed into the optimization model for the generation of a scoring value for the main lobe width.
In the present invention, the plurality of optimization model units 1046, 1048 comprises: the first optimization model unit 1046 and the second optimization model unit 1048. The first optimization model unit 1046 is for evaluating the side lobe level of the autocorrelated output and is defined by: f1(x) = ,where W is the side lobe level specified in the parameter values of the desired NLFM waveform and the σw affects the rate of change of slope of the score values around the desired parameter value of the side lobe level. The first optimization model unit 1046 is an exponential function of the side lobe level. The first optimization model unit 1046 calculates and allots scores for the side lobe level of the autocorrelated output.
In the present invention, the second optimization model unit 1048 calculates and allots the scoring value for the main lobe width of the autocorrelated output. The second optimization model unit 1048 is for evaluating the main lobe width of the autocorrelated output and is defined by: f2(y) = , where y is the main lobe width in number of samples, a and b are constants and c is the main Lobe width (ML) specified in the parameter values of the desired NLFM waveform.
Further, when the condition in the second optimization model unit 1048, f2(y) is not satisfied, a fitness score of 10-300 is allotted to the generated NLFM time frequency curves and when the condition in the second optimization model 1048 is satisfied, value on left hand side of f2(y) is taken as the fitness score. The second optimization model unit 1048 is a linear function of the main lobe width within the constraints w.r.t the specified maximum main lobe width.
At step 824, the scores from the above two optimization models pass through cumulative fitness score unit 10410 which calculates the cumulative score. The cumulative score is of the form of where is the first optimization model and is the second optimization model. That is, the cumulative scores allotted to the generated NLFM time frequency curves are defined by: . The cumulative score for each member of a generation/ each generated NLFM time frequency curves is used by the Genetic method / Genetic method search unit 10412 to find the fittest member in the generation (fittest among the NLFM time frequency curves). The fittest member/ fittest among the generated NLFM time frequency curves is the member with the highest cumulative score. Further, the best fit members from the previous generation are then used to create a new generation with population size N, using the processes of reproduction, crossover and mutation. Each new subsequent generation will have a best fit member with cumulative score better (higher) or equal to the previous generation. The iteration continues until there is no change in the cumulative score in continuous subsequent set of generations or if the cumulative score has fallen lower than a predefine threshold, .
In the present invention, the Bezier generated time frequency plot/curve is stored in an array and its monotonicity is enforced on the GA generated candidates. These parameters are then fed into the optimization model units 1046, 1048 to get a scoring value. The Genetic method implements three processes to generate the new candidates, namely reproduction, crossover and mutation. The population size for each generation is fixed at N. The number of candidates for reproduction, crossover and mutation is fixed at respectively, where The mutation rate is fixed at .
In an embodiment, the present invention discloses a method to generate smooth NLFM waveforms using multiple optimization models wherein the multiple optimization models generate scores for a scoring mechanism/the cumulative fitness score unit 10410 which provides the cumulative score which is used for a search based optimization of the present invention.
In an embodiment, the present invention discloses a method for restricting the search based optimization for generation of valid time frequency curves.
In an embodiment, the present invention discloses a system for generating NLFM waveforms, where the input is the required/desired side lobe level and the main lobe width of the NLFM waveform, and the output is a waveform with similar matched filtering parameters.
In an embodiment, the present invention discloses a system for generating NLFM waveforms with a plurality of optimization models to restrict waveform search to NLFM waveforms which is achieving parameter values similar to the set parameter values/the plurality of parameter values of the desired NLFM waveform.
In an embodiment, the present invention discloses the optimization model to restrict the search of NLFM waveform by limiting the search to waveforms with monotonic decrease in the side lobe levels across a range and specific time-frequency curves, wherein the specific time frequency curves are the NLFM time frequency curves that follow a monotonic increasing pattern and have a one to one mapping between time and frequency values.
In an embodiment, the present invention discloses the method which accumulates the peak side lobe levels in the array and gives an output or score according to the compressed pulse shape requirements of the desired NLFM waveform.
In an embodiment, the present invention discloses the method which compares the scoring value of side lobe levels with the second optimization model and generates the cumulative score.
In an embodiment, the optimization model of the present invention adaptively suppresses waveform search with respect to the parameters including side lobe level and the main lobe width as the parameter values start reaching pre-defined/desired values.
In an embodiment, the present invention discloses a method to fix the main lobe width at different power levels and first null level as a ratio of the required main lobe width to prevent search of waveforms with excessive main lobe shape distortion. That is, the method fixes the ratio of the main lobe width at different power levels and the first null width as a function of the required main lobe width and required first null width to prevent search of waveforms with excessive main lobe shape distortion.
In an embodiment, the present invention discloses the method to restrict search of waveforms w.r.t to a parameter, such as the Bandwidth (B), the pulse width (T), the sampling frequency (Fs), the Side lobe level (SLL), the main Lobe width (ML), which has attained similar values as the required/desired values and encourage searches with respect to improvement in other parameter values.
Figures are merely representational and are not drawn to scale. Certain portions thereof may be exaggerated, while others may be minimized. Figures illustrate various embodiments of the invention that can be understood and appropriately carried out by those of ordinary skill in the art.
In the foregoing detailed description of embodiments of the invention, various features are grouped together in a single embodiment for the purpose of streamlining the disclosure. This device or unit or arrangement of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments of the invention require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter lies in less than all features of a single disclosed embodiment. Thus, the following claims are hereby incorporated into the detailed description of embodiments of the invention, with each claim standing on its own as a separate embodiment.
It is understood that the above description is intended to be illustrative, and not restrictive. It is intended to cover all alternatives, modifications and equivalents as may be included within the spirit and scope of the invention as defined in the appended claims. Many other embodiments will be apparent to those of skill in the art upon reviewing the above description. The scope of the invention should, therefore, be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled. In the appended claims, the terms “including” and “in which” are used as the plain-English equivalents of the respective terms “comprising” and “wherein,” respectively.