CN110933011B - High-resolution blind scanning method for WFRFT (WFRFT) signals - Google Patents

High-resolution blind scanning method for WFRFT (WFRFT) signals Download PDF

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CN110933011B
CN110933011B CN201911263420.8A CN201911263420A CN110933011B CN 110933011 B CN110933011 B CN 110933011B CN 201911263420 A CN201911263420 A CN 201911263420A CN 110933011 B CN110933011 B CN 110933011B
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刘芳
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    • H04L27/00—Modulated-carrier systems
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    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • H04L27/2647—Arrangements specific to the receiver only
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Abstract

A high resolution blind scanning method of WFRFT signal belongs to the technical field of receiving method of WFRFT communication system, the method comprises establishing rule relation of modulation order error and error rate under theoretical condition, determining minimum main value window; setting a left modulation order and a right modulation order in each channel, further performing WFRFT inverse processing of two branches on a received signal by each channel, calculating a peak-to-average ratio to obtain a theoretical boundary value, calculating a mapping channel, and further calculating a demodulation order corresponding to the channel; calculating an estimated modulation order; and performing WFRFT inverse processing by using the estimated modulation order and the received signal, and obtaining demodulation data. The invention solves the scanning problem under the unknown modulation order condition and the fuzzy modulation order condition in the severe environment and the fuzzy resolution problem of the successful channel in the multi-channel scanning.

Description

High-resolution blind scanning method for WFRFT (WFRFT) signals
Technical Field
The invention belongs to the technical field of receiving methods of WFRFT communication systems, and particularly relates to a blind scanning receiving method under the condition of unknown modulation orders.
Background
Weighted Fractional Fourier Transform (WFRFT) is a Transform domain signal processing means in wireless communication systems. The modulation order (parameter) in the general WFRFT system is known only to own users and is unknown to other users. Therefore, considering the uncertain modulation order under unknown conditions or severe environment conditions, the setting of the demodulation order at the receiving end cannot meet the requirement of correctly recovering the original data, so blind scanning processing is required. The current scanning methods are all scanning in one period of modulation order at intervals of 0.01, so the scanning times are 400 times, obviously, for a high-speed processor, 400 times of WFRFT inverse processing are not a problem, but how to distinguish exact successful channels from the demodulation results of 400 channels becomes a difficult problem. If the successful channel cannot be distinguished, the subsequent analysis, analysis and other processing are required to be carried out on the 400 groups of data all the time, and the channel which is real data cannot be distinguished after the analysis. If 400 channels of data processing are required for each cycle, a great complexity and ambiguity resolution are involved for a continuous multi-cycle or real-time data transmission system. Therefore, the blind scanning method with high resolution capability is researched to become the key of the WFRFT signal processing field.
Disclosure of Invention
The invention provides a high-resolution blind scanning method of a WFRFT signal, which discusses the shunt relevant characteristics of a left modulation order and a right modulation order by establishing a rule between a modulation order error and a theoretical bit error rate, gives a rectangular relevant interval, obtains an estimated modulation order by utilizing a rectangular relevant interval boundary and a relevant mapping channel, and further recovers real data to achieve the aim of high-resolution blind scanning.
The technical scheme is as follows:
in a high-resolution blind scanning method of WFRFT signals, firstly, a modulation order error and bit error rate rule relation under a theoretical condition is established, and a minimum principal value window is determined.
Then, a multi-channel demodulation order is established in a main value window, a left modulation order and a right modulation order are set in each channel, each channel further carries out WFRFT inverse processing of two branches on the received signal, correlation operation is carried out by using the inverse processing results of the two branches in each channel, and the peak-to-average ratio is calculated.
Further, a rectangular correlation interval is established by using the theoretical correlation degree, and a theoretical boundary value is obtained.
Then, a mapping channel is calculated by using the peak-to-average ratios of a plurality of channels, and a demodulation order corresponding to the channel is further calculated.
Secondly, the estimated modulation order is calculated by using the calculation result.
And finally, performing WFRFT inverse processing by using the estimated modulation order and the received signal, and obtaining demodulation data.
Further, a method for high resolution blind scanning of WFRFT signal according to claim 1 is specifically as follows:
establishing a regular relation between modulation order error delta beta and an error rate under a theoretical condition, setting a minimum main value window K to be 2, and setting a stepping amount to be 0.01;
in a minimum principal value period, namely 0-2 intervals, carrying out multichannel scanning by taking lambda as a stepping quantity, wherein the scanning upper limit is N:
Figure BDA0002312203310000031
defining a demodulation order set betaiFormula (7), wherein i ∈ [ 1N ]]，
βi＝i·λ (7)
Assuming the estimated modulation order is α ', the error between the demodulation order of each channel and α' is:
Δβi＝α'-βi (8)
will betaiIs subjected to periodic continuation to obtain
Figure BDA0002312203310000032
Then, the reverse rotation and the translation are carried out to obtain
Figure BDA0002312203310000033
And
Figure BDA0002312203310000034
in each channel betaiOn the basis, the right modulation order beta is carried outiRLeft modulation order betaiLAnd (3) calculating:
Figure BDA0002312203310000035
Figure BDA0002312203310000036
using two branches beta per channeliRAnd betaiLPerforming WFRFT inverse processing on the received signals S (n):
Figure BDA0002312203310000037
Figure BDA0002312203310000038
two-branch inverse processing result S in each channeliR(n) and SiL(n) performing correlation operation to obtain correlation result C of each channeli(n), wherein fft (-), ifft (-) are fast fourier transform and inverse transform processing functions;
Figure BDA0002312203310000041
By Ci(n) calculating the peak-to-average ratioPiWhere max (·) is a maximum computation function;
Figure BDA0002312203310000042
Figure BDA0002312203310000043
Figure BDA0002312203310000044
ΔβRis the right boundary of the rectangular correlation interval, Δ βLIs the left boundary of the rectangular correlation interval;
using peak-to-average ratio P of N channelsiComparing with a threshold G, and further calculating to obtain a continuous sequence R (j), wherein mod (·) is a modular operation function;
Figure BDA0002312203310000045
and (3) performing minimum value calculation on the continuous sequence R (j) by using a minimum value calculation function min (·), and performing minimum periodic processing to obtain a mapping channel H corresponding to a rectangular correlation interval:
H＝mod(min[R(j)],N) (18)
calculating the demodulation order beta corresponding to the channel by using the mapping channel HH：
Figure BDA0002312203310000051
By using betaHAnd the right boundary Δ β of the rectangular intervalRAnd, in conjunction with equation (8), an estimated modulation order α' can be calculated:
Figure BDA0002312203310000052
wherein m is an integer and is more than or equal to 0, and the alpha' is the minimum positive value in the range of [04 ] by selecting m;
using the estimated alpha' and the received signal S (n) to perform WFRFT inverse processing:
Figure BDA0002312203310000053
calculating to obtain data D' (n) after WFRFT inverse processing as a formula (22); if the modulation order alpha of the transmitting end is in a range of 0-2, the demodulation data D '(n) is real data x (n), and if the modulation order alpha of the transmitting end is in a range of 2-4, the demodulation data D' (n) is inverted data x (-n) of the real data;
Figure BDA0002312203310000054
The data D ' (n) and the data D ' (-n) after the data D ' (n) are inverted are output simultaneously.
The invention has the advantages and effects that:
a high-resolution blind scanning method for WFRFT signals aims to solve the problems of scanning under unknown modulation order conditions and fuzzy modulation order conditions in severe environments and the problem of fuzzy resolution of successful channels in the conventional multi-channel scanning. A high-resolution blind scanning method for WFRFT signals not only can not increase the complexity of a system, but also can accurately estimate the modulation order and correctly output the original data, thereby achieving the purpose of high-resolution blind scanning. The blind scanning method is not only suitable for a 4-WFRFT communication system, but also suitable for a multi-item WFRFT communication system, and is compatible with the conditions of fixed single parameters and variable single parameters.
Drawings
Fig. 1 is a diagram of the relationship between modulation order error and bit error rate rule in the high-resolution blind scanning method of WFRFT signal of the present invention.
Fig. 2 is a diagram of an implementation scheme of a high-resolution blind scanning method for a WFRFT signal according to the present invention.
Detailed Description
The invention is further explained below with reference to the figures and the examples.
Let the data information to be transmitted in the digital communication system be x (n), and the length of data transmitted per period be L, for which n belongs to [1L ]. Defining 4 kinds of state functions of X (n), X (-n) and X (-n) as 0, 1, 2 and 3 times Fourier transform results of X (n), respectively. Since all the multiple WFRFT systems can be converted into corresponding 4 WFRFT systems, the implementation of the 4-WFRFT system can be universally applied to the multiple WFRFT systems.
At the communication transmitting end, alpha is defined as the modulation order (parameter) of WFRFT process, and the weighting coefficient omega can be established by utilizing alphal(α) (l is 0,1,2,3), ω is determined as shown in formula (1)lThe modulation order α of (α) is 4-period as in the fourier transform, for which [ 04) is set as a main period, and all modulation orders can be equivalent to one [ 04) period.
Figure BDA0002312203310000061
Using established omegal(alpha) subjecting the data x (n) to be transmitted to alpha-order WFRFT processing, as shown in formula (2), wherein Fα(. cndot.) is a WFRFT processing function of order α.
S(n)＝Fα(x(n))＝ω0(α)x(n)+ω1(α)X(n)+ω2(α)x(-n)+ω3(α)X(-n) (2)
At the receiving end of the communication, the purpose is to recover the data information by performing corresponding processing on the received signal s (n). If the demodulation order of the receiving end is beta, carrying out beta-order WFRFT inverse transformation on the received signal S (n):
Figure BDA0002312203310000071
setting:
Δβ＝α-β (4)
it can be seen that equation (3) can be written as equation (5) only when Δ β → 0, i.e., β ═ α, which indicates that the original data x (n) can be correctly recovered.
SΔ(n)＝FΔβ(x(n))≈x(n) (5)
However, for the communication receiving end, the modulation order α is known only to the own user and is unknown to other users. Therefore, considering the uncertain modulation order under unknown conditions or severe environment conditions, the setting of the receiving end β cannot satisfy the condition of β ═ α, and therefore, the modulation order β needs to be scanned blindly, so that Δ β → 0 can receive data x (n) correctly, thereby providing a high-resolution blind scanning method for WFRFT signals.
In a high-resolution blind scanning method of a WFRFT signal, firstly, a modulation order error delta beta and an error rate rule relation under a theoretical condition are established, as shown in FIG. 1, the error rate does not have a linear ascending trend but has a periodic cyclic change along with the increase of the delta beta, and the cyclic period is also 4. In addition, Δ β ═ 2 is a symmetric axis in one period, and the minimum principal value window K is set to be 2. Then, the step amount is set to λ 0.01.
Based on this, in a minimum principal value period, namely 0-2 intervals, with lambda as the stepping quantity, multi-channel scanning is carried out, the scanning upper limit is N:
Figure BDA0002312203310000081
secondly, define the demodulation order set betaiFormula (7), wherein i ∈ [ 1N ]]There are 201 channels in total.
βi＝i·λ (7)
Further, assuming that the estimated modulation order is α ', the error between the demodulation order of each channel and α' is:
Δβi＝α'-βi (8)
further, beta is adjusted toiIs subjected to periodic continuation to obtain
Figure BDA0002312203310000084
Then, the reverse rotation and the translation are carried out to obtain
Figure BDA0002312203310000085
And
Figure BDA0002312203310000086
as can be seen from FIG. 1, the following steps are carried out
Figure BDA0002312203310000087
And the change in alpha,
Figure BDA0002312203310000088
and
Figure BDA0002312203310000089
has the lowest correlation characteristic, for this reason, the error rate curve of the channel has the beta in each channeliOn the basis, the right modulation order beta is carried outiRLeft modulation order betaiLAnd (3) calculating:
Figure BDA0002312203310000082
Figure BDA0002312203310000083
in channel 201, two branches beta of each channel are used iRAnd betaiLPerforming WFRFT inverse processing on the received signals S (n):
Figure BDA0002312203310000091
Figure BDA0002312203310000092
then, the two-branch inverse processing result S in each channeliR(n) and SiL(n) performing correlation operation to obtain correlation result C of each channeli(n), wherein fft (. cndot.) and ift (. cndot.) are fast Fourier transform and inverseThe processing function is transformed.
Figure BDA0002312203310000093
Further, use of Ci(n) calculating the Peak-to-average ratio PiWhere max (·) is a maximum calculation function.
Figure BDA0002312203310000094
As can be seen in fig. 1, within the main value window of α' ═ 0, with βiWhen scanning to
Figure BDA0002312203310000095
In the interval, two intervals with the maximum shunt correlation degree appear, and the interval presents rectangular distribution and is called as a rectangular correlation interval. The rectangular correlation interval range with respect to Δ β can be obtained by calculation, as shown in equations (15) and (16), Δ βRIs the right boundary of the rectangular correlation interval, Δ βLThe left border of the rectangular correlation interval.
Figure BDA0002312203310000101
Figure BDA0002312203310000102
As can be seen from fig. 1, as the main value window is shifted, the variation of the α 'value is equivalent, and no matter what the α' value is, within each shifted main value window, a rectangular correlation interval between Δ β and the peak value appears, and its right boundary Δ βRAnd left boundary Δ βLThe results of equations (15) and (16) are always satisfied.
Then, the peak-to-average ratio P of N channels is usediAnd comparing with a threshold G, and further calculating to obtain a continuous sequence R (j), wherein mod (-) is a modulus operation function.
Figure BDA0002312203310000103
And then, performing minimum value calculation on the continuous sequence R (j) by using a minimum value calculation function min (-) and performing minimum periodic processing to obtain a mapping channel H corresponding to the rectangular correlation interval:
H＝mod(min[R(j)],N) (18)
calculating the demodulation order beta corresponding to the channel by using the mapping channel HH：
Figure BDA0002312203310000104
By using betaHAnd the right boundary Δ β of the rectangular intervalRAnd, in conjunction with equation (8), an estimated modulation order α' can be calculated:
Figure BDA0002312203310000111
wherein m is an integer, and m is greater than or equal to 0, and is selected so that alpha' is the minimum positive value within [04 ]. Since the real modulation order α is 4 as a period, the value of α is equivalent to be in the range of [04 ].
Then, WFRFT inverse processing is performed using the estimated α' and the received signal s (n):
Figure BDA0002312203310000112
finally, the WFRFT inverse data D' (n) is calculated as formula (22). It can be seen that if the modulation order α of the transmitting end is within an interval of 0 to 2, the demodulated data D '(n) is the real data x (n), and if the modulation order α of the transmitting end is within an interval of 2 to 4, the demodulated data D' (n) is the inverted data x (-n) of the real data.
Figure BDA0002312203310000113
Because it cannot be determined whether the original modulation order is within 0-2 or within 2-4, the data D ' (n) and the data D ' (-n) after D ' (n) inversion are output simultaneously, and the 2-path data analysis process is far more complicated than the 400-path data analysis process.
A high resolution blind scanning method for WFRFT signals carries out modulation order estimation and communication data reception under the condition of unknown modulation order (parameter), so that the same scanning conclusion can be reached no matter the modulation order is in a fixed form or a dynamic change form. In addition, since all the multiple-term WFRFT systems can be converted into corresponding 4-term WFRFT systems, a high-resolution blind scanning method for WFRFT signals is not only applicable to the 4-term WFRFT systems, but also applicable to the multiple-term WFRFT systems.

Claims (1)

1. A method for high resolution blind scanning of WFRFT signals is characterized in that: firstly, establishing a regular relation between a modulation order error and an error rate under a theoretical condition, and determining a minimum main value window; establishing a multi-channel demodulation order in a main value window, setting a left modulation order and a right modulation order in each channel, further performing WFRFT inverse processing of two branches on a received signal by each channel, performing correlation operation by using the inverse processing results of the two branches in each channel, and calculating a peak-to-average ratio; establishing a rectangular correlation interval by using the theoretical correlation degree, and obtaining a theoretical boundary value; calculating a mapping channel by using the peak-to-average ratios of a plurality of channels, and further calculating a demodulation order corresponding to the channel; calculating an estimated modulation order by using the calculation result; performing WFRFT inverse processing by using the estimated modulation order and the received signal, and obtaining demodulation data;
The method specifically comprises the following steps:
establishing a regular relation between modulation order error delta beta and an error rate under a theoretical condition, setting a minimum main value window K to be 2, and setting a stepping amount to be 0.01;
in a minimum principal value period, namely 0-2 intervals, carrying out multichannel scanning by taking lambda as a stepping quantity, wherein the scanning upper limit is N:
Figure FDA0003467782070000011
defining a demodulation order set betaiFormula (7), wherein i ∈ [1N ]]，
βi＝i·λ (7)
Assuming the estimated modulation order is α ', the error between the demodulation order of each channel and α' is:
Δβi＝α'-βi (8)
will betaiIs subjected to periodic continuation to obtain
Figure FDA0003467782070000012
Then, the reverse rotation and the translation are carried out to obtain
Figure FDA0003467782070000021
And
Figure FDA0003467782070000022
in each channel betaiOn the basis, the right modulation order beta is carried outiRLeft modulation order betaiLAnd (3) calculating:
Figure FDA0003467782070000023
Figure FDA0003467782070000024
using two branches beta per channeliRAnd betaiLPerforming WFRFT inverse processing on the received signals S (n):
Figure FDA0003467782070000025
Figure FDA0003467782070000026
two-branch inverse processing result S in each channeliR(n) and SiL(n) performing correlation operation to obtain correlation result C of each channeli(n), wherein fft (-), ifft (-) are fast fourier transform and inverse transform processing functions;
Figure FDA0003467782070000027
by Ci(n) calculating the Peak-to-average ratio PiWhere max (·) is a maximum calculation function;
Figure FDA0003467782070000031
Figure FDA0003467782070000032
Figure FDA0003467782070000033
ΔβRis the right boundary of the rectangular correlation interval, Δ βLIs the left boundary of the rectangular correlation interval;
using peak-to-average ratio P of N channels iComparing with a threshold G, and further calculating to obtain a continuous sequence R (j), wherein mod (·) is a modular operation function;
Figure FDA0003467782070000034
and (3) performing minimum value calculation on the continuous sequence R (j) by using a minimum value calculation function min (·), and performing minimum periodic processing to obtain a mapping channel H corresponding to a rectangular correlation interval:
H＝mod(min[R(j)],N) (18)
calculating the demodulation order beta corresponding to the channel by using the mapping channel HH：
Figure FDA0003467782070000035
By using betaHAnd the right boundary Δ β of the rectangular intervalRAnd combining with equation (8), the estimated modulation order α' can be calculated:
Figure FDA0003467782070000041
wherein m is an integer and is more than or equal to 0, and the alpha' is the minimum positive value in the range of [04 ] by selecting m;
performing WFRFT inverse processing by using the estimated alpha' and a receiving signal S (n):
Figure FDA0003467782070000042
calculating to obtain data D' (n) after WFRFT inverse processing as a formula (22); if the modulation order alpha of the transmitting end is within the range of 0-2, the demodulated data D '(n) is real data x (n), and if the modulation order alpha of the transmitting end is within the range of 2-4, the demodulated data D' (n) is inverted data x (-n) of the real data;
Figure FDA0003467782070000043
the data D ' (n) and the data D ' (-n) obtained by inverting the data D ' (n) are outputted simultaneously.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103441822A (en) * 2013-09-16 2013-12-11 哈尔滨工业大学 Signal modulation method based on weighted-type fractional Fourier transform and energy spreading transform
WO2017054632A1 (en) * 2015-09-29 2017-04-06 华为技术有限公司 Signal sending method, signal receiving method, transmitting terminal and receiving terminal
CN107682297A (en) * 2017-09-06 2018-02-09 西北工业大学 A kind of mobile underwater sound communication method
CN108920419A (en) * 2018-06-20 2018-11-30 沈阳理工大学 Scan method is classified based on one-parameter Fractional Fourier inverse transformation

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103441822A (en) * 2013-09-16 2013-12-11 哈尔滨工业大学 Signal modulation method based on weighted-type fractional Fourier transform and energy spreading transform
WO2017054632A1 (en) * 2015-09-29 2017-04-06 华为技术有限公司 Signal sending method, signal receiving method, transmitting terminal and receiving terminal
CN107682297A (en) * 2017-09-06 2018-02-09 西北工业大学 A kind of mobile underwater sound communication method
CN108920419A (en) * 2018-06-20 2018-11-30 沈阳理工大学 Scan method is classified based on one-parameter Fractional Fourier inverse transformation

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