WO2020232475A1 - Devices, systems, and software including signal power measuring and methods and software for measuring signal power - Google Patents
Devices, systems, and software including signal power measuring and methods and software for measuring signal power Download PDFInfo
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- WO2020232475A1 WO2020232475A1 PCT/US2020/070053 US2020070053W WO2020232475A1 WO 2020232475 A1 WO2020232475 A1 WO 2020232475A1 US 2020070053 W US2020070053 W US 2020070053W WO 2020232475 A1 WO2020232475 A1 WO 2020232475A1
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- 238000001228 spectrum Methods 0.000 claims abstract description 44
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- 238000012806 monitoring device Methods 0.000 claims description 9
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- 238000004364 calculation method Methods 0.000 abstract description 6
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- 230000005540 biological transmission Effects 0.000 description 17
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B17/00—Monitoring; Testing
- H04B17/30—Monitoring; Testing of propagation channels
- H04B17/309—Measuring or estimating channel quality parameters
- H04B17/318—Received signal strength
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/16—Spectrum analysis; Fourier analysis
- G01R23/165—Spectrum analysis; Fourier analysis using filters
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/16—Spectrum analysis; Fourier analysis
- G01R23/18—Spectrum analysis; Fourier analysis with provision for recording frequency spectrum
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R29/00—Arrangements for measuring or indicating electric quantities not covered by groups G01R19/00 - G01R27/00
- G01R29/02—Measuring characteristics of individual pulses, e.g. deviation from pulse flatness, rise time or duration
- G01R29/023—Measuring pulse width
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B17/00—Monitoring; Testing
- H04B17/0082—Monitoring; Testing using service channels; using auxiliary channels
- H04B17/0087—Monitoring; Testing using service channels; using auxiliary channels using auxiliary channels or channel simulators
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
Definitions
- the present invention relates in general to measuring signal power, and, more specifically to systems, devices, software, and methods to perform signal power measurements over a frequency spectrum for use in occupied bandwidth (OBW) and other frequency spectrum analyses.
- OBW occupied bandwidth
- the data transmission capacity of a communication system depends generally on the number of communication channels that the system can support and the data transmission capacity of each communication channel.
- the number of channels that may be used in a given frequency range depends upon the frequency range, or bandwidth, that is occupied by each channel being transmitted by the system, which is known as the occupied bandwidth (OBW) of the channel.
- OBW occupied bandwidth
- System channel layouts are based on a maximum expected OBW for each channel along with an additional guardband to determine the channel spacing as typically defined by the frequency range separating the center frequency of each channel.
- OBW power spectral density
- STFT short-time Fourier Transform
- spectrogram a technique that uses a sliding time-window, with a trade-off between time and frequency resolution.
- Joint time-frequency distributions are an alternative technique, in which a function is derived that is distributed simultaneously in the time and frequency domains.
- all of these techniques are based on the FT, which, despite sophisticated adaptations, is fundamentally not suited to the study of a time-varying spectrum.
- RTSAs Real time spectrum analyzers capture signals over short intervals, which are then stored and analyzed using Fast Fourier Transform (FFT) algorithms. Some RTSAs may sequence the FFT results to show changes in the spectrum over time.
- FFT Fast Fourier Transform
- HSTSA hardware swept-tuned spectrum analyzer
- the HSTSA does not use an FT, it inherently avoids the problems with FT- based OBW measurement described above.
- the HSTSA since the HSTSA sweeps through a frequency range, the assumption of a stationary spectrum remains over the duration of the sweep.
- the HSTSA requires physical signal transmission and is often an expensive piece of equipment that is not easily used outside of the laboratory.
- Systems, devices, software, and methods of the present invention enable frequency-based signal power analyses in software, thereby providing for a software frequency spectrum analyzer (“SSA”) and other power signal analyses.
- SSA software frequency spectrum analyzer
- the present invention solves long standing problems associated with making consistent spectrum measurements and enables spectrum analysis to be performed on both hardware and software generated signals.
- the present invention may be used to enable system design, feedback, and control based on the actual OBW performance of the operational system.
- the SSA may be used in software simulators to evaluate the simulated system performance, such as analyzing the OBW of simulated signals. Because the present invention may be applied to hardware & software generated signals, analyses may be performed consistently across hardware and software platforms.
- the present invention may be employed with signals that have stationary or non stationary spectrums.
- the present invention is particularly useful for signals where the spectrum to be measured is highly time-variant (non- stationary), because of the limitations of FT-based techniques.
- the methods are generally applicable and may be employed in combination with, or in lieu of, FT-based techniques on stationary spectrum signals.
- Systems, devices, and methods of the present invention have an electrical signal input, which may have been generated in hardware by receiving an information carrying signal, such an optical or radio signals, or in software by simulating the preceding reception.
- the analysis of the input signal may be performed pursuant to various analysis inputs provided by the user. For example, prior to analyzing the input signal, the user may specify a frequency spectrum range having a minimum frequency (f_min) and a maximum frequency (f_max) and define at least one frequency bin within the frequency spectrum range and having a frequency bin width, f_width, and a source frequency, f_source, associated with each frequency bin.
- a target intermediate frequency may be specified for each frequency bin.
- the target frequency may be the same for each frequency bin, or may be varied by the skilled artisan. In some applications, it may be desirable to make the target frequency the same for all frequency bins, so the same filter may be used for each bin.
- a software intermediate frequency bandpass filter ifbpf, in terms of Fs, f Jarget, and f_width, may be defined along with an input signal software bandpass filter, INbf, to remove frequencies outside of the passband.
- an input signal SIGin is received, having power distributed over a signal frequency range.
- the input signal software bandpass filter, INbf is applied to the input signal SIGin to produce a filtered input signal, which is normalized to produce a normalized signal power, SIGin_norm, which may be stored for use in various calculations.
- a mixing stream, cos jnix, of length sig en equal to the input signal length may then be calculated by evaluating the cosine function over the range from 0 to rads_per_signal in increments of rads_per_sample, which may be written as:
- rads_per_signal rads_per_sample(sig en-l)
- the corresponding intermediate frequency bandpass filter, ifbpf is applied to each intermediate frequency (IF) signal, sig JF, to generate a filtered IF signal, sig JF iltered.
- a bin power, bin rower, in the filtered IF signal, sig JF Jiltered may be calculated by summing the square of the amplitudes in sig JF Jiltered and dividing this sum by the time interval, and stored.
- the frequency bin having the maximum bin rower, max rower may be identified and used for various purposes.
- the occupied bandwidth of the input signal may be calculated in various ways, such as by summing the frequency widths of frequency bins based on the bin power, bin rower, in each frequency bins proximate to the frequency bin with maximum power.
- the OBW may be calculated as a two-sided occupied bandwidth of the input signal by starting with the frequency width of the maximum power bin, then successively summing the frequency widths of the frequency bins with highest power adjacent on either side to the maximum power bin or to a previously summed frequency bin based until the sum of the power in the frequency power bins is equal to 99% or some desired percentage of the input signal power.
- the single-sided occupied bandwidth may be calculated by dividing the two-sided occupied bandwidth by two to provide an average or by summing the power in frequency bins spanning lower and higher frequencies, respectively, than the frequency bin with the maximum power.
- Systems, devices, software, and methods of the present invention may be applied at many, if not all, of the various design and operational stages.
- the present invention may be implemented in simulation software, as well as in the device and system level design and prototypes.
- the present invention may be implemented transmitters, repeaters, receivers, stand-alone signal monitoring devices and other devices in which in signal power measurements over a frequency spectrum may be of use, such as signal power monitors and control devices.
- the present invention addresses the continuing need for hardware and/or software systems, devices, and methods that measure signal power, such as the OBW of signals, in software simulation or hardware transmission, and may be particularly of importance in the case of a highly non stationary spectrum.
- FIG. 1 illustrates exemplary data transmission systems.
- FIG. 2 illustrates exemplary data transmission systems.
- FIG. 3 illustrates an exemplary initial PSW alphabet.
- FIGS. 4-8 illustrates the exemplary initial PSW alphabet convolved with a polynomial corresponding to a Gaussian with mean zero and sigma values of 0.8, 1.0, 1.2, 1.6, and 2, respectively.
- FIGS. 9-15 show the normalized difference between the SSA and HSTSA OBW calculation as a function of bit stream length, number of frequency bins, and IF filter length using two methods of calculating the OBW based on the calculated power in the frequency bins.
- FIG. 16 shows an eight (8) polynomial symbol waveform (PSW) alphabet corresponding to a Root Raised Cosine (RRC)-filtered 8-PSK symbol waveform alphabet.
- PSW polynomial symbol waveform
- RRC Root Raised Cosine
- sequences of actions are described in terms of sequences of actions to be performed by, for example, elements of a computing device. It will be recognized that various actions described herein can be performed by specific circuits (e.g., application specific integrated circuits (ASICs)), by field programmable gate arrays, by program instructions being executed by one or more processors, or by a combination thereof. Additionally, sequence(s) of actions described herein can be considered to be embodied entirely within any form of computer readable storage medium having stored therein a corresponding set of computer instructions that upon execution would cause an associated processor to perform the functionality described herein. Thus, the various aspects of the invention may be embodied in a number of different forms, all of which have been contemplated to be within the scope of the claimed subject matter.
- ASICs application specific integrated circuits
- transmitter, receivers, management systems, and other devices in systems of the present invention may include one or more processors, memory, storage, input and components, communication interfaces, as well as other components that may be interconnected as desired by the skilled artisan via one or more buses and circuit boards, cards, etc.
- FIG. 1 shows exemplary systems 10 including exemplary transmitter 12 and receiver 14 pairs that may be used in transmission or communication systems, such as further shown in FIG. 2.
- Bits, usually representing data/information, to be transmitted as a signal through the system 10 may be encoded in a channel encoder 16 section of the transmitter 12, as well as have other signal processing performed to prepare a signal for transmission.
- the encoded bits may then be used to modulate a carrier wave having a center frequency provided by a carrier source 20, or frequency source, using an external modulator 22 as shown in FIG. 1 or to directly modulate the carrier/frequency source 20 to produce the transmission signal.
- the signals may be transmitted using one carrier or multiple carriers simultaneously, such as when implemented with Instantaneous Spectral Analysis (“ISA”), see U.S. Patent No. 10,069,664 incorporated above.
- ISA Instantaneous Spectral Analysis
- the encoder 16 and decoder 18 are shown as single blocks in FIG. 1. However, the encoder 16 and decoder 18 may include one or more stages/components that are used to process the information passing through the system 10. The encoding and decoding function may be performed inside and/or outside the transmitter 12 and receiver 14, as desired by the skilled artisan.
- a detector 24 may detect the transmission signal and provide the transmission signal to signal processors, which may include the decoder 18 to perform any decoding necessary to output the bits.
- the bits output from the system 10 may be in the form of data and clock signals, or otherwise.
- the system 10 may be locally and/or remotely monitored and/or controlled by a management system 25 as is known in the art.
- the system 10 may be deployed as part of a local private point-to-point network, as well as part of the global terrestrial and satellite infrastructure and managed accordingly.
- FIG. 2 shows exemplary systems 10 that include a plurality of transmitters 12 and receivers 14 that may be deployed in various transmission and communication systems employing various wired and wireless transmission media 26 and may include PSW technology of the present invention.
- Signal monitoring may be performed at the transmitters, receivers, amplifiers/repeaters, and other devices in the system 10 and/or with stand-alone signal monitoring devices 27 deployed at various locations in the system 10.
- the present invention may be implemented as software, including firmware, embedded logic, etc. that is stored in a computer readable medium, such as memory, drives, and other storage devices and executed by process running proximate (on or near) the devices as is known in the art.
- Systems 10 such as shown in FIG. 1 and FIG. 2 and other systems, may be deployed in various electrical and optical wired transmission and communication networks, as well as satellite and terrestrial wireless networks.
- the transmission signals may be multiplexed in a multiplexer 28 before transmission and may require demultiplexing before detection in a demultiplexer 30 after transmission, as is commonly performed in wired and wireless systems carrying multiple channels.
- Systems, devices, and methods of the present invention have an electrical signal input, which may have been generated in hardware by receiving a data/information carrying signal, such an optical or radio signals, or in software by simulating the preceding reception.
- the analysis of the input signal may be performed pursuant to various analysis inputs provided by the user. For example, prior to analyzing the input signal with a center frequency, f_c, the user may specify a frequency spectrum range (f_range) having a minimum frequency (f_min) and a maximum frequency (f_max). Because the analysis is being performed in software and the input signal may be stored, the user may be able to vary the frequency range (f_range) of interest and re-run the analysis to assess the sensitivity of the analysis to various user inputs.
- f_range frequency spectrum range having a minimum frequency (f_min) and a maximum frequency (f_max).
- the user may define at least one frequency bin within the frequency spectrum range (f_range) and having a frequency width, f_width. This may be done by specifying the number of frequency bins and segmenting the frequency range (f_range) of interest accordingly.
- the width of each frequency bin is termed f_width. It is usually desirable to segment the frequency range evenly from an efficiency and ease of use standpoint, but there may be scenarios that it is preferred to unevenly segment the frequency range, such as in frequency ranges where the signal power is expected to change rapidly (narrow bins) and not change significantly (wide bins).
- a target intermediate frequency (fjarget) and corresponding software intermediate frequency bandpass filter, ifbpf, in terms of fjarget, sampling frequency, Fs, and f_width may be defined.
- Various target intermediate frequencies may be selected by the skilled artisan depending upon the particular application of the present invention. The use of intermediate target frequencies enables the skilled artisan to translate the signal power to a lower frequency. For example, for RF signals in the range of 900 MHz, target intermediate frequencies may be in the range of 100 KHz.
- the intermediate frequency bandpass filter may be implemented using various techniques as known to those of skill in the art. For example, using the MathWorks® MATLAB® filter design tools, which may include the designfilt function.
- the signal length sig_len may be determined from the length of the signal in samples.
- the sample time interval may be varied by the skilled artisan based on preference and the bit rate of the signal as will be discussed further herein.
- an input signal software bandpass filter INbf
- the bandpass filter may be implemented using various techniques as known to those of skill in the art, such as described above.
- an input signal, SIGin having power distributed over a signal frequency range is received.
- the input signal software bandpass filter, INbf may be applied to the input signal, SIGin to produce a filtered input signal, which is normalized to produce a normalized signal power, SIGin_norm, which may be stored for use in various calculations.
- f_mix f_source - fjarget.
- a mixing stream, cos_mix, of length sig_len equal to the input signal length may then be calculated by evaluating the cosine function over the range from 0 to rads_per_signal in increments of rads_per_sample, which may be written as:
- rads_per_signal rads_per_sample(sig_len-l)
- An intermediate frequency (IF) signal, sig_IF may be generated using the formula
- sig_IF SIGin_norm*cos_mix.
- the corresponding bandpass filter, ifbpf is applied to each intermediate frequency (IF) signal, sig_IF, to generate a filtered IF signal, sig_IF_filtered.
- a bin power, bin_power, in the filtered IF signal, sig_IF_filtered may be calculated by summing the square of the amplitudes in sig_IF_filtered and dividing this sum by the time interval, and stored.
- the frequency bin having the maximum bin_power, max_power may be identified and used for various purposes.
- the occupied bandwidth of the input signal may be calculated in various ways, such as by summing the frequency widths of frequency bins based on the bin power, bin_power, in each frequency bin proximate to the frequency bin with maximum power.
- the OBW may be calculated as a two-sided occupied bandwidth of the input signal by starting with the frequency width of the maximum power bin, then successively summing the frequency widths of the frequency bins with highest power adjacent on either side to the maximum power bin or to a previously summed frequency bin based until the sum of the power in the frequency power bins is equal to 99% or some desired percentage of the input signal power.
- the single-sided occupied bandwidth may be calculated by dividing the two-sided occupied bandwidth by two to provide an average or by summing the power in frequency bins spanning lower and higher frequencies, respectively, than the frequency bin with the maximum power.
- the OBW may be calculated by successively summing power from the lowest frequency bin to the highest frequency bin and calculating the 99% OBW as the difference between the frequencies at which the 0.5% power and the 99.5% power is reached.
- This method may be used with the present invention. However, the method described above, which starts from the peak power frequency bin and successively expands to adjacent frequency power bins, may more accurately reflect the desire to define OBW as centered around the peak power. The two methods may be equivalent if the spectrum is symmetric around the peak power, but may diverge if for any reason the spectrum is not symmetric around the peak power.
- Systems 10 and devices of the present invention include software and/or hardware to analyze signal power over a frequency range, which may be useful for OBW and other signal processing and control purposes.
- the signal analysis methods may be implemented at various points in the system 10 including the transmitters, receivers, and locations along a link as desired, for example, for feedback loops and link performance analyses.
- PSWs 8“polynomial symbol waveforms”
- FIG. 3 which may be collectively referred to as a PSW alphabet.
- the initial PSW alphabet was convolved with a polynomial corresponding to a Gaussian with mean zero and sigma values of 0.8, 1.0, 1.2, 1.6, and 2, as shown in FIGS. 4-8, respectively.
- the initial PSW alphabet (which has very high OBW) was not tested, only the convolved PSW alphabets.
- a three-bit sequence was assigned to each of the PSWs in each of the convolved PSW alphabets.
- bit stream length refers to the number of bits transmitted ⁇
- the OBW measurements are based on analyzing time-amplitude sequences generated by converting a random sequence of bits into a corresponding random sequence of PSWs from a particular PSW alphabet.
- all PSW alphabets have 8 symbols, corresponding to bit sequences of length 3, and each polynomial symbol waveform is represented by 25 sample points.
- f_c 922MHz, where f_c is the center frequency of the signal
- the one-sided OBW is reported.
- OBW is measured in terms of the 99% power spectral density (PSD) width. Two approaches to OBW measurement were performed, although a multiple of other approaches may be selected by the skilled artisan.
- Method I Adding frequency power bins. Find the range of frequency power bins containing 99% of the signal power. The results of which are shown in FIGS. 9-12.
- Method II Find the frequency difference between the frequency bin of the maximum power point and the frequency bin of 1 % signal power. The results of which are shown in FIGS. 13-15.
- Method I generally produced better agreement with the HSTSA, and much better test/re- test consistency (lower standard deviation), as further described herein.
- the second approach produced reasonable results and may prove more appropriate for other applications.
- the following data derived from trials reported in more detail below, shows consistency between the SSA and the HSTSA to within less than 10%. A summary of the comparison is provided in Table 1 below.
- FIG. 9 shows several comparisons were made to examine the question of how the SSA performance is affected by the length (in bits) of the input stream (100, 1,000, 10,000).
- the SSA IF filter is of length 500 for the trials reported below.
- the number of frequency bins is
- OBW Diff 0.054167(0.027136)
- OBW Diff 0.051042(0.015317)
- bit stream ten 10000, Norm.
- OBW Diff 0.053125(0.014565)
- OBW Diff 0.05679(0.028744)
- bit stream ten 1000, Norm.
- OBW Diff 0.05679(0.018793)
- bit stream ten 10000, Norm.
- OBW Diff 0.059259(0.018455)
- bit stream ten 100, Norm.
- OBW Diff 0.066667(0.026596)
- bit stream ten 1000, Norm.
- OBW Diff -0.038462(0)
- bit stream len 100, Norm.
- OBW Diff -0.088889(0.1057)
- bit stream len 1000, Norm.
- OBW Diff -0.084848(0.025353)
- bit stream len 10000, Norm.
- the (logarithmic) x-axis provides the number of bits transmitted.
- the y-axis provides the mean normalized difference between the SSA and the HSTSA OBW for matched conditions with the standard deviation over 30 trials per condition provided in parentheses.
- the HSTSA value is provided as the last number of each line.
- the standard deviations are indicated by the error bars.
- the SSA stores the entire input sequence and analyzes it repeatedly for different frequency bins, whereas the HSTSA analyzes different parts of the input signal for each frequency bin. This allows the SSA to be more compact than the HSTSA in terms of required input sequence length.
- FIG. 10 show a comparison of the SSA performance as affected by the number of frequency bins (20, 40, 60, 80, 100, 120, 140).
- the number of bits transmitted is 10,000 and the SSA IF filter length is 500.
- the x-axis provides the number of frequency bins.
- the y-axis provides the mean normalized difference between the SSA and the HSTSA OBW for matched conditions. The standard deviations are indicated by the error bars based on the following data.
- the SS A and the HSTSA show a comparison between the SS A and the HSTSA as a function of the length of the SSA IF filter (50, 100, 250, 500, 1000).
- the bit stream length is 10,000 for the trials reported below.
- the number of frequency bins is 100.
- the x-axis provides the SSA IF filter length.
- the y-axis provides the mean normalized difference between the SSA and the HSTSA OBW for matched conditions. The standard deviations are indicated by the error bars.
- PSW Gaussian Sigma 0.8
- filter len 50
- Normalized OBW Diff 0.084375(0.014565)
- HSTSA OBW 3.2e+06
- PSW Gaussian Sigma 0.8
- filter len 100
- Normalized OBW Diff 0.0625(0)
- HSTSA OBW 3.2e+06
- PSW Gaussian Sigma 0.8
- PSW Gaussian Sigma 1.2
- filter len 100
- Normalized OBW Diff 0.076923(0)
- filter len 250
- Normalized OBW Diff 0.061538(0.019164)
- filter len 500
- Normalized OBW Diff 0.052564(0.018851)
- filter len 1000
- Normalized OBW Diff 0.053846(0.019164)
- filter len 50
- Normalized OBW Diff 0.038462(0)
- filter len 100
- Normalized OBW Diff -0.038462(0)
- FIG. 12 shows the variation as a function of the number of bits transmitted as 100, 1,000, and 10,000.
- FIGS. 13-15 show comparison analogous to the comparisons shown in FIGS. 9- 11 , but using Method II of calculating the OBW instead of Method I.
- Method II of calculating the OBW instead of Method I.
- Table 2 A summary of the comparison is provided in Table 2 below.
- Method II comparison the number of bits transmitted was 1.5 million for both the SSA and the HSTSA.
- the data shows consistency between the SSA and the HSTSA to within about 20%, which is worse than for Method I as documented above. Also, Method II calculation has a standard deviation across trials that is much higher. These results may suggest that for these alphabets, Method I may be preferred based on the HSTSA comparison or the time averaging of the HSTSA does not adequately capture the spectrum, or some combination thereof.
- FIG. 13 shows the Method II SSA performance as a function of the length (in bits) of the input stream.
- the SSA IF filter length is 500 and the number of frequency bins is 100, which yielded the following data with the standard deviation over 30 trials per condition provided in parentheses.
- the HSTSA value is provided as the last number of each line.
- FIG. 14 shows the Method II SSA performance as a function of the number of frequency bins (20, 40, 60, 80, 100, 120, 140).
- the number of bits transmitted is 10000 and the SSA IF filter is of length 500.
- the x-axis provides the number of frequency bins.
- the y-axis provides the mean normalized difference between the SSA and the HSTSA OBW for matched conditions. The standard deviations are indicated by the error bars for the following data.
- OBW Diff -0.23737(0.027663)
- OBW Diff -0.22727(0.10969)
- OBW Diff -0.23906(0.10438)
- OBW Diff -0.25758(0.13552)
- OBW Diff -0.32828(0.15268)
- OBW Diff -0.26178(0.14972)
- OBW Diff -0.26623(0.15725)
- HSTSA OBW 6.6e+06
- FIG. 15 shows the Method II SSA performance as a function of the length of the SSA IF filter (50, 100, 250, 500, 1000).
- the bit stream length is 10000 for the trials reported below.
- the number of frequency bins is 100.
- PSW Gaussian Sigma 0.8
- FIG. 16 shows an eight (8) polynomial symbol waveform (PSW) alphabet corresponding to Root Raised Cosine (RRC)-filtered 8-Phase Shift Keying (PSK) waveforms (8- PSK).
- PSK waveforms are based on sinusoids with constant amplitude, and therefore produce a relatively stationary spectrum, to within filtering and symbol boundary effects.
- FT- based spectrum analysis techniques may be used to accurately analyze the PSK signals.
- MATLAB ® software simulations were ran to evaluate the OBW at 99% power for the 8-PSK waveform shown in FIG. 16 using the SSA of the present invention and the MATLAB ® FT-based OBW function called obw.
- the OBW calculated using the SSA and FT-based techniques were in close agreement to within a few percent. The close agreement between the SSA of the present invention and FT analysis is expected, because 8-PSK waveforms have stationary spectra over time, which is the underlying assumption of FT analysis.
- the SSA may provide a robust alternative to HSTSA for use with hardware system and for the first time enable simulations and spectral analysis of signals with non-stationary spectra.
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Priority Applications (5)
Application Number | Priority Date | Filing Date | Title |
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KR1020217040726A KR20220035330A (en) | 2019-05-15 | 2020-05-15 | Devices, systems and software including signal power measurements and methods and software for signal power measurements |
JP2021567976A JP2022531981A (en) | 2019-05-15 | 2020-05-15 | Devices, systems, and software, including signal power measurements, and methods and software for measuring signal power. |
CA3178386A CA3178386A1 (en) | 2019-05-15 | 2020-05-15 | Devices, systems, and software including signal power measuring and methods and software for measuring signal power |
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US11876569B2 (en) | 2024-01-16 |
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