CN109600330B - Simplified diagonal cross-correlation carrier frequency offset estimation method - Google Patents

Simplified diagonal cross-correlation carrier frequency offset estimation method Download PDF

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CN109600330B
CN109600330B CN201811409953.8A CN201811409953A CN109600330B CN 109600330 B CN109600330 B CN 109600330B CN 201811409953 A CN201811409953 A CN 201811409953A CN 109600330 B CN109600330 B CN 109600330B
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correlation
frequency offset
diagonal cross
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CN109600330A (en
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朱海
徐恒舟
许蒙蒙
周慢杰
车景平
朱思峰
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Zhoukou Normal University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/18—Phase-modulated carrier systems, i.e. using phase-shift keying
    • H04L27/20—Modulator circuits; Transmitter circuits
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/0014—Carrier regulation
    • H04L2027/0024—Carrier regulation at the receiver end
    • H04L2027/0026—Correction of carrier offset

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Abstract

The invention discloses a simplified estimation method of carrier frequency offset of cross-angle correlation, which comprises the following steps: s1: setting a PSAM frame structure; s2: obtaining a baseband receiving signal Z; s3: obtaining a demodulated signal Z 'by a demodulation operation based on the baseband received signal Z'm(ii) a S4: using the unmodulated signal Z'mObtaining a cross-correlation operator R through a time domain cross-correlation algorithmCC(ii) a S5: using cross correlation operator RCCObtaining the diagonal cross-correlation operator R through an autocorrelation algorithmDCC(ii) a S6: using diagonal cross-correlation operator RDCCObtaining the diagonal cross-correlation frequency offset estimator by amplitude-angle operation
Figure DDA0001878255640000011
S7: frequency offset estimator using diagonal cross-correlation
Figure DDA0001878255640000012
Simplified diagonal cross-correlation frequency offset estimator by using exponential approximation of complex signal
Figure DDA0001878255640000013
S8: frequency offset estimator using reduced diagonal cross-correlation
Figure DDA0001878255640000014
Obtaining simplified diagonal cross-correlation frequency offset estimator for resolving phase ambiguity by combining phase ambiguity resolving algorithm
Figure DDA0001878255640000015
The method is low in overall complexity, and can give consideration to a large estimation range and high estimation precision.

Description

Simplified diagonal cross-correlation carrier frequency offset estimation method
Technical Field
The invention relates to the technical field of wireless communication, in particular to a simplified diagonal cross-correlation carrier frequency offset method.
Background
The short burst communication system is widely applied to the fields of high-speed mobile communication, satellite communication, military communication and the like, and Doppler effect generated by relative movement of two communication parties enables a received signal to generate certain frequency offset. The large frequency offset can cause the error code performance of the synchronous receiver to be rapidly deteriorated, thereby causing the serious reduction of the communication quality.
Conventional frequency offset estimation techniques may be classified into data-aided DA, non-data-aided NDA, decision-directed DD, and the like, depending on whether or not a pilot is utilized. The signal-to-noise threshold of both the NDA and DD estimators is high relative to the DA estimator. Therefore, in short burst communication with a low signal-to-noise ratio, a DA estimator that estimates frequency offset and phase offset by means of a pilot sequence is commonly used. The pilot sequences may be inserted at different locations in the data frame to form different data frame structures. In the Second generation digital Video Broadcasting standard (DVB-S2) (ESTI EN 302.307, V1.2.1digital Video Broadcasting; continuous generation from structure, channel coding and modulation systems for Broadcasting, Interactive Service, News heating and other base and satellite applications, April 2009), a new data frame structure is proposed, which has the main idea of dividing a pilot of a certain length into several blocks and inserting the blocks into a data frame. Lo, d.lee and j.a.gansman propose a data frame structure based on Pilot Symbol Assisted Modulation (PSAM) in "a satellite of non-uniform Pilot Modulation for PSAM" (processing IEEE International Conference Communication, PP322-325, 2000). It divides the pilot sequence into two parts, one part contains several continuous pilot symbols and is placed in the frame head, and the other part is subdivided into discrete pilot symbols and inserted into the frame and the frame tail.
From the specific algorithm adopted, the DA estimation algorithm can be further divided into a frequency domain estimation algorithm and a time domain estimation algorithm. Under the limited pilot overhead, the estimation range of the former is larger, and the estimation precision of the latter is higher. Therefore, the joint time-frequency DA estimation algorithm can combine the advantages of the two algorithms, but the problems of high complexity and difficult optimal parameter configuration are brought. Therefore, researchers in the related art have proposed frequency offset estimation algorithms with high accuracy, wide range and low complexity, which all use time domain correlation algorithms with low complexity directly or indirectly. The autocorrelation algorithm using an equivalent/single pilot block is proposed in "Carrier frequency recovery in all-digital models for burst-mode transmissions" (IEEE transmission Communication, PP1169-1178, 1995) by m.luise, r.regianni, which has a low signal-to-noise ratio threshold and complexity but a low estimation accuracy. In the 'joint pilot frequency and iterative decoding carrier synchronization of short burst transmission system' (journal of the university of western electronics and technology, 29-36, 41(1), 2014), the sunglowa, wangxuemei and the like propose a cross-correlation algorithm using two or more disjoint pilot frequency blocks, and under the same pilot frequency length and signal-to-noise ratio, the estimation precision is far higher than that of the algorithms proposed by m.luise and r.reggiannini and the complexity is moderate. However, the same drawback exists in time domain correlation algorithms based on multiple disjoint pilot blocks, i.e., the frequency offset estimation range is narrow and inversely proportional to the pilot symbol interval. The root of the method is that a time domain correlation algorithm under the frame structure has phase ambiguity. Since the phase increment in the estimator of such algorithms is mainly affected by the normalized frequency offset, the pilot spacing and the noise, the phase ambiguity is caused by the larger frequency offset or pilot spacing. A.Barbieri, G.Colavolpe proposed a simplified M & M estimation algorithm based On DVB-S2 frame structure in "On pilot-system-assisted carrier synchronization for DVB-S2 systems" (IEEE Transactions On Broadcasting, PP685-692, 53(3), 2007), and the problem of phase ambiguity was solved by using check bits of LDPC decoding. Palm, m.rice in "Low-Complexity Frequency Estimation Using Multiple discrete pilot Blocks in Burst-Mode Communications" (IEEE transmission Communications, PP3135-3145, 59(11), 2011) proposes a non-coding method for iteratively updating the estimated Frequency offset by Using a kalman filter and solves the phase ambiguity, and combines with an autocorrelation Estimation algorithm AC (Auto-Correlation) to obtain a larger Estimation range, but the Complexity is very high and a specific step of the phase ambiguity resolution algorithm is not given.
In summary, a need exists in the art for a carrier frequency offset estimation method that can effectively consider both estimation performance and complexity under large frequency offset to solve the problem of phase ambiguity existing under the PSAM frame.
Disclosure of Invention
In view of this, the present invention provides a simplified diagonal cross-correlation carrier frequency offset method, which not only has low overall complexity, but also can give consideration to a larger estimation range and higher estimation accuracy.
In order to achieve the purpose, the invention adopts the following technical scheme:
a simplified diagonal cross-correlation carrier frequency offset estimation method comprises the following steps:
step S1: setting a PSAM frame structure;
step S2: obtaining a baseband receiving signal Z;
step S3: obtaining a demodulation signal Z 'by demodulation operation based on the baseband receiving signal Z'm；
Step S4: using the unmodulated signal Z'mObtaining a cross-correlation operator R through a time domain cross-correlation algorithmCC；
Step S5: using cross correlation operator RCCObtaining a diagonal cross-correlation operator R through an autocorrelation algorithmDCC；
Step S6: using diagonal cross-correlation operator RDCCObtaining a diagonal cross-correlation frequency offset estimator by amplitude and angle taking operation
Figure BDA0001878255620000031
Step S7: frequency offset estimator using diagonal cross-correlation
Figure BDA0001878255620000032
Obtaining a simplified diagonal cross-correlation frequency offset estimator by using an exponential approximation of a complex signal
Figure BDA0001878255620000033
Step S8: frequency offset estimator using reduced diagonal cross-correlation
Figure BDA0001878255620000034
By combining a phase ambiguity resolution algorithm, a simplified diagonal cross-correlation frequency offset estimator for resolving phase ambiguity is obtained
Figure BDA0001878255620000035
Preferably, step S1 specifically includes:
s11: generating data of length LPAnd equally divide it into m small blocks PmGenerating a binary data bit sequence D with a data length D' ═ m-1 x t, wherein LPL and m are positive integers, t is a single data block DmLength of (d);
s12: using m pilot blocks PmAnd m-1 data blocks DmAnd obtaining the PSAM-like frame structure in a multiplexing mode.
Preferably, step S2 specifically includes:
s21: based on a PSAM frame structure, obtaining a modulated signal S through quadrature phase shift keying modulation;
s22: and obtaining a baseband receiving signal Z by using the modulation signal S through a Gaussian white noise channel and adding the frequency offset f.
Compared with the prior art, the simplified diagonal cross-correlation carrier frequency offset method disclosed by the invention uses the principles of autocorrelation estimation and complex signal exponential approximation and the idea of phase ambiguity resolution algorithm, so that the overall complexity is low, and a larger estimation range and higher estimation accuracy can be considered. The method provided by the invention is not limited by a specific modulation mode and has general applicability.
The method provided by the invention is suitable for a large-frequency-offset short burst communication system, and can also be applied to a coding system to adapt to a short burst communication environment under a low signal-to-noise ratio.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a flow chart of a simplified diagonal cross-correlation carrier frequency offset method provided by the present invention;
fig. 2 is a schematic diagram of a PSAM-like frame structure provided in the present invention;
FIG. 3 is a plot of the root mean square error of the frequency offset estimation of the present invention using diagonal cross-correlation, simplified diagonal cross-correlation and full cross-correlation simulations at different signal-to-noise ratios;
FIG. 4 is a plot of the root mean square error of the frequency offset estimation of the simplified diagonal cross-correlation simulation with simplified diagonal cross-correlation and de-phase ambiguity, under different frequency offsets in accordance with the present invention;
figure 5 is a plot of the root mean square error of frequency offset estimates simulated using M & M, AC and the present invention at different frequency offsets.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, an embodiment of the present invention discloses a simplified diagonal cross-correlation carrier frequency offset method, including:
step S1: setting a PSAM frame structure;
step S2: obtaining a baseband receiving signal Z;
step S3: obtaining a demodulation signal Z 'by demodulation operation based on the baseband receiving signal Z'm；
Step (ii) ofS4: using the unmodulated signal Z'mObtaining a cross-correlation operator R through a time domain cross-correlation algorithmCC；
Step S5: using cross correlation operator RCCObtaining a diagonal cross-correlation operator R through an autocorrelation algorithmDCC；
Step S6: using diagonal cross-correlation operator RDCCObtaining a diagonal cross-correlation frequency offset estimator by amplitude and angle taking operation
Figure BDA0001878255620000051
Step S7: frequency offset estimator using diagonal cross-correlation
Figure BDA0001878255620000052
Obtaining a simplified diagonal cross-correlation frequency offset estimator by using an exponential approximation of a complex signal
Figure BDA0001878255620000053
Step S8: frequency offset estimator using reduced diagonal cross-correlation
Figure BDA0001878255620000054
By combining a phase ambiguity resolution algorithm, a simplified diagonal cross-correlation frequency offset estimator for resolving phase ambiguity is obtained
Figure BDA0001878255620000055
The technical solution of the present invention is further explained with reference to specific steps, embodiments and simulation results.
Step 1, a data frame structure (PSAM-like frame) is set, please refer to fig. 2.
(1a) A pilot block P of a certain data length is generated and equally divided into m small blocks PmEach small block has a length L, and a binary data bit sequence D with a data length D ═ m-1 x t is generated, wherein L and m are positive integers, and t is a single data block DmLength of (d);
(1b) using m pilot blocks PmAnd m-1 data blocks DmAnd obtaining the PSAM-like frame structure in a multiplexing mode.
And step 2, obtaining a baseband receiving signal.
(2a) Obtaining a modulation signal S by utilizing the obtained PSAM frame structure and through Quadrature Phase Shift Keying (QPSK) modulation;
(2b) and obtaining a baseband receiving signal Z by using the modulation signal S through a Gaussian white noise channel and adding the frequency offset f.
Step 3, determining a specific algorithm of a diagonal cross correlation operator:
(3a) sending the received baseband signal Z to a carrier estimator, taking the first L data of the baseband signal Z as a first section pilot P1 of the baseband signal Z, and taking the data from the L + t +1 th symbol to the 2L + t +1 th symbol of the baseband signal Z as a second section pilot P2 of the baseband signal Z;
(3b) the first pilot frequency de-modulation signal P1 is obtained by utilizing the first pilot frequency P1 and the second pilot frequency P2d＝P1×(P1′)*And a second pilot unmodulated signal P2d＝P2×(P2′)*Wherein P1 ' and P2 ' are the first pilot and the second pilot of the transmission signal agreed in advance by the transmitter and receiver (P1 ')*Is the conjugate of P1 '(P2')*Is the conjugate of P2';
(3c) signal P1 is unmodulated using a first segment pilotdAnd a second pilot unmodulated signal P2dObtaining a cross-correlation operator R through a time domain cross-correlation algorithmCC：
Figure BDA0001878255620000061
D is the interval between the first pilot segment and the second pilot segment, i.e., D ═ L + t;
(3d1) using cross correlation operator RCCObtaining a cross-correlation operator frequency offset estimator by amplitude-angle operation
Figure BDA0001878255620000071
Figure BDA0001878255620000072
Wherein T issIs a symbol period and Ts＝1/(1×104) Second, arg {. is operated by taking argument;
it should be noted that step (3d1) is not necessary, and is listed here because it is necessary to use this parameter in the course of the comparative simulation.
(3d2) Using cross correlation operator RCCObtaining a diagonal cross-correlation operator R through an autocorrelation algorithmDCC：
Figure BDA0001878255620000073
(3e) Using diagonal cross-correlation operator RDCCObtaining a diagonal cross-correlation frequency offset estimator by amplitude and angle taking operation
Figure BDA0001878255620000074
Figure BDA0001878255620000075
Step 4, determining a specific algorithm of the simplified diagonal cross-correlation estimator:
(4a) first, the complex signal exponential approximation principle is given: when signal-to-noise ratio Es/N0When > 1, the complex signal P1 is unmodulateddIs approximately 1, and utilizes the exponential form of the complex number to obtain P1d＝|P1d|exp(jarg(P1d))≈exp(jarg(P1d) In which | is a modulo operation, exp (-) is a natural exponential operation, j is a unit imaginary number;
(4b) utilizing the diagonal cross-correlation frequency offset estimator obtained in the step (3)
Figure BDA0001878255620000076
Obtaining a simplified diagonal cross-correlation frequency offset estimator through the complex signal exponential approximation operation of the step (4a)
Figure BDA0001878255620000077
Figure BDA0001878255620000078
Wherein
Figure BDA0001878255620000079
(4c) Utilizing the cross-correlation frequency offset estimator obtained in the step (3) and the step (4b)
Figure BDA00018782556200000710
Diagonal cross-correlation frequency offset estimator
Figure BDA00018782556200000711
And simplified diagonal cross-correlation frequency offset estimator
Figure BDA00018782556200000712
Obtaining w-th frequency deviation estimated values through Monte Carlo simulation
Figure BDA00018782556200000713
And
Figure BDA00018782556200000714
(4d) repeating the steps (3) - (4b) for W times to obtain W frequency deviation estimated values
Figure BDA0001878255620000081
Figure BDA0001878255620000082
And
Figure BDA0001878255620000083
calculating normalized residual frequency deviation E by using the frequency deviation estimated values and the added frequency deviation fCC、EDCCAnd ESDCC：
Figure BDA0001878255620000084
Figure BDA0001878255620000085
Figure BDA0001878255620000086
It should be noted here that the purpose of multiple simulations is to obtain data points in the simulation graph, and thus obtain a statistical average value to avoid occasional errors due to a single estimation.
In this embodiment, the number of pilot blocks m is 2, the pilot symbol length L is 25, the single data symbol length t is 250, and the pilot symbol interval D is 275. Additional frequency offset f of 10Hz, symbol period Ts＝1/(1×104) And second. And (4) performing simulation according to the steps (3) to (4d), wherein each data point is simulated for 5000 times by using Monte Carlo, and obtaining a diagram 3, namely, a frequency deviation estimation root mean square error curve simulated by using diagonal cross-correlation, simplified diagonal cross-correlation and cross-correlation algorithms under different signal to noise ratios. As can be seen from fig. 3, the estimated performance of the simplified diagonal cross-correlation algorithm is comparable to and close to the estimated performance of the diagonal cross-correlation algorithm. Therefore, the dephasing ambiguity algorithm is hereinafter applied to the reduced diagonal cross-correlation algorithm.
And 5, determining a simplified diagonal cross-correlation algorithm for phase ambiguity resolution.
Firstly, a phase ambiguity resolution algorithm principle is given:
(5a) utilizing the simplified diagonal cross-correlation operator R obtained in step (4b)SDCCAnd obtaining a phase increment delta phi through amplitude angle taking operation: Δ Φ ═ arg { RSDCC}≈2πfTsD；
(5b) And obtaining the value limit of the delta phi by utilizing the phase increment delta phi and taking a single mapping relation of the amplitude angle operation: i delta phi I is approximately equal to |2 pi fTsD | < pi, where | is absolute value operation, | f | < 1/(2 DT)s)；
(5c) Using a value ofTaking a value restriction inequality, and introducing a parameter q to obtain delta phi' under large frequency offset: i delta phi '| approximately equals |2 pi f' TsD +/-2 pi q | is less than pi, wherein | f' | is less than 1/(2T)s)；
(5d) Obtaining a frequency deviation estimated value of phase ambiguity resolution by using delta phi' under large frequency deviation through absolute value removal operation
Figure BDA0001878255620000091
Figure BDA0001878255620000092
(5e) Frequency offset estimation using phase deblurring
Figure BDA0001878255620000093
Obtaining accurate parameters by dichotomy search
Figure BDA0001878255620000094
The method comprises the following specific steps:
suppose that the initial search step length of a given pilot frequency interval D and a parameter q
Figure BDA0001878255620000095
And an estimation accuracy epsilon.
(5e1) By using
Figure BDA0001878255620000096
The frequency deviation estimated value obtained by the step (5d)
Figure BDA0001878255620000097
To obtain
Figure BDA0001878255620000098
Figure BDA0001878255620000099
Wherein
Figure BDA00018782556200000910
Is the initial value of q and is,
Figure BDA00018782556200000911
is an initial value of the frequency deviation f';
(5e2) by using
Figure BDA00018782556200000912
By comparison
Figure BDA00018782556200000913
And ε/TsIs obtained when
Figure BDA00018782556200000914
When the temperature of the water is higher than the set temperature,
Figure BDA00018782556200000915
get
Figure BDA00018782556200000916
Otherwise, entering a step (5e 3);
(5e3) by using
Figure BDA00018782556200000917
The frequency deviation estimated value obtained by the step (5d)
Figure BDA00018782556200000918
To obtain
Figure BDA00018782556200000919
Figure BDA00018782556200000920
(5e4) By using
Figure BDA00018782556200000921
By comparison
Figure BDA00018782556200000922
And ε/TsIs obtained when
Figure BDA00018782556200000923
When the temperature of the water is higher than the set temperature,
Figure BDA00018782556200000924
get
Figure BDA00018782556200000925
Otherwise, otherwise go to step (5e 5);
(5e5) using the first search
Figure BDA00018782556200000926
The frequency deviation estimated value obtained by the step (5d)
Figure BDA00018782556200000927
To obtain
Figure BDA00018782556200000928
Figure BDA00018782556200000929
Wherein l is a positive integer;
(5e6) by using
Figure BDA00018782556200000930
By comparison
Figure BDA00018782556200000931
And ε/TsIs obtained when
Figure BDA00018782556200000932
When the temperature of the water is higher than the set temperature,
Figure BDA00018782556200000933
get
Figure BDA00018782556200000934
At this time
Figure BDA00018782556200000935
Otherwise, let l be l +1, return to step (5e 5);
(5f) obtaining the precise value of the parameter q using steps (5e1) - (5e6)
Figure BDA00018782556200000936
Estimating the frequency offset by simplified diagonal cross-correlation with step (4b)
Figure BDA00018782556200000937
Combining to obtain simplified diagonal cross-correlation frequency offset estimator for resolving phase ambiguity
Figure BDA00018782556200000938
Figure BDA00018782556200000939
Wherein
Figure BDA00018782556200000940
So far, the specific flow of the algorithm has been explained in detail. Next, the simulation result is further explained.
(5g) Utilizing the simplified diagonal cross-correlation frequency offset estimator obtained in the steps (4b) and (5f)
Figure BDA0001878255620000101
Simplified diagonal cross-correlation frequency offset estimator for resolving phase ambiguity
Figure BDA0001878255620000102
Respectively obtaining w' th frequency deviation estimated values through Monte Carlo simulation
Figure BDA0001878255620000103
And
Figure BDA0001878255620000104
(5h) repeating the steps (3) - (4b) and the steps (5e) - (5f) for W 'times to obtain W' frequency deviation estimated values
Figure BDA0001878255620000105
And
Figure BDA0001878255620000106
utilizing the frequency deviation estimated values and the frequency deviation f with the added normalized value of-0.5iCalculating normalized residual frequency deviation ESDCC,iAnd EPUW-SDCC,i：
Figure BDA0001878255620000107
Figure BDA0001878255620000108
Wherein the added frequency offset fi∈[-0.5,0.5]/Ts。
In this embodiment, the number of pilot blocks m is 2, the pilot symbol length L is 25, the single data symbol length t is 250, and the pilot symbol interval D is 275. Additional frequency offset fi∈[-0.5,0.5]/TsSymbol period Ts＝1/(1×104) And second. And (5) performing simulation according to the steps (3) to (4b) and the steps (5e) to (5f), wherein each data point is simulated by using Monte Carlo (W' 5000 times), and obtaining a graph shown in the figure 4, namely, a frequency offset estimation root mean square error curve of simplified diagonal cross-correlation simulation of simplified diagonal cross-correlation and phase ambiguity resolution under different frequency offsets.
As can be seen from fig. 4, compared with the simplified diagonal cross-correlation algorithm, the normalized estimated frequency offset of the simplified diagonal cross-correlation algorithm for resolving the phase ambiguity is close to 0.5, and the estimation performance of the simplified diagonal cross-correlation algorithm under a larger frequency offset still obtains the estimation effect of the simplified diagonal cross-correlation algorithm within 1/(2D) ═ 1/550, which is shown in a partially enlarged view.
And 6, comparing the estimation effects of the simplified diagonal cross-correlation algorithm of the phase ambiguity resolution.
And comparing the performance with the existing classical carrier estimation algorithm. In this example, assume Eb/N08dB and fiTs∈[-0.5,0.5]A carrier estimation algorithm suitable for large frequency offset, i.e., M, proposed in Data-aided frequency estimation for burst digital transmission (IEEE transmission Communication, PP23-25, 45(1), 1997) is selected&M algorithm and j.palmer, m.rice.g., AC algorithm, in "Low-Complexity Frequency Estimation Using Multiple discrete Pilot Blocks in Burst-Mode Communications" (IEEE Transaction Communications, PP3135-3145, 59(11), 2011). Each data point was simulated 5000 times using monte carlo to obtain fig. 5, i.e. using M at different frequency offsets&M algorithm, AC algorithm and frequency deviation estimation root mean square error curve simulated by the invention. As can be seen from fig. 5, the estimation range of the present invention is the same as that of the other two algorithms, but the estimation precision is the highest. The estimation value of the invention is more accurate, and the effectiveness of the invention is further shown.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (3)

1. A simplified diagonal cross-correlation carrier frequency offset estimation method is characterized by comprising the following steps:
step S1: setting a PSAM frame structure;
step S2: obtaining a baseband receiving signal Z;
step S3: obtaining a demodulation signal Z 'by demodulation operation based on the baseband receiving signal Z'm；
Step S4: using the unmodulated signal Z'mDisclosure of the inventionObtaining cross-correlation operator R by time domain cross-correlation algorithmCC(ii) a Diagonal cross correlation operator RCCThe calculation process of (2) is as follows:
sending the received baseband signal Z to a carrier estimator, taking the first L data of the baseband signal Z as a first section pilot P1 of the baseband signal Z, and taking the data from the L + t +1 th symbol to the 2L + t +1 th symbol of the baseband signal Z as a second section pilot P2 of the baseband signal Z;
the first pilot frequency de-modulation signal P1 is obtained by utilizing the first pilot frequency P1 and the second pilot frequency P2dP1 × (P1')/and a second pilot unmodulated signal P2dP2 × (P2 '), (P1 ') is the conjugate of P1 ', and (P2 ') is the conjugate of P2 ', where P1 ' and P2 ' are the first pilot and the second pilot of the transmission signal previously agreed by both the transmitter and the receiver;
signal P1 is unmodulated using a first segment pilotdAnd a second pilot unmodulated signal P2dAnd obtaining a cross-correlation operator RCC through a time domain cross-correlation algorithm:
Figure FDA0003333520080000011
d is the interval between the first pilot segment and the second pilot segment, i.e., D ═ L + t;
step S5: using cross correlation operator RCCObtaining a diagonal cross-correlation operator R through an autocorrelation algorithmDCC(ii) a Diagonal cross correlation operator RDCCThe calculation formula of (2) is as follows:
Figure FDA0003333520080000012
step S6: using diagonal cross-correlation operator RDCCObtaining a diagonal cross-correlation frequency offset estimator by amplitude and angle taking operation
Figure FDA0003333520080000013
Diagonal cross-correlation frequency offset estimator
Figure FDA0003333520080000014
The calculation formula of (2) is as follows:
Figure FDA0003333520080000015
step S7: frequency offset estimator using diagonal cross-correlation
Figure FDA0003333520080000021
Obtaining a simplified diagonal cross-correlation frequency offset estimator by using an exponential approximation of a complex signal
Figure FDA0003333520080000022
Determining reduced diagonal cross-correlation estimator
Figure FDA0003333520080000023
The specific algorithm of (1):
(4a) first, the complex signal exponential approximation principle is given: when signal-to-noise ratio Es/N0When > 1, the complex signal P1 is unmodulateddIs approximately 1, and utilizes the exponential form of the complex number to obtain P1d＝|P1d|exp(jarg(P1d))≈exp(jarg(P1d) In which | is a modulo operation, exp (-) is a natural exponential operation, j is a unit imaginary number;
(4b) utilizing the diagonal cross-correlation frequency offset estimator obtained in the step (3)
Figure FDA0003333520080000024
Obtaining a simplified diagonal cross-correlation frequency offset estimator through the complex signal exponential approximation operation of the step (4a)
Figure FDA0003333520080000025
Figure FDA0003333520080000026
Wherein
Figure FDA0003333520080000027
Wherein, TsIs a symbol period;
(4c) utilizing the cross-correlation frequency offset estimator obtained in the step (3) and the step (4b)
Figure FDA0003333520080000028
Diagonal cross-correlation frequency offset estimator
Figure FDA0003333520080000029
And simplified diagonal cross-correlation frequency offset estimator
Figure FDA00033335200800000210
Obtaining w-th frequency deviation estimated values through Monte Carlo simulation
Figure FDA00033335200800000211
And
Figure FDA00033335200800000212
(4d) repeating the steps (3) - (4b) for W times to obtain W frequency deviation estimated values
Figure FDA00033335200800000213
Figure FDA00033335200800000214
And
Figure FDA00033335200800000215
calculating normalized residual frequency deviation E by using the frequency deviation estimated values and the added frequency deviation fCC、EDCCAnd ESDCC：
Figure FDA0003333520080000031
Figure FDA0003333520080000032
Figure FDA0003333520080000033
Step S8: frequency offset estimator using reduced diagonal cross-correlation
Figure FDA0003333520080000034
By combining a phase ambiguity resolution algorithm, a simplified diagonal cross-correlation frequency offset estimator for resolving phase ambiguity is obtained
Figure FDA0003333520080000035
2. The simplified diagonal cross-correlation carrier frequency offset estimation method according to claim 1, wherein step S1 specifically includes:
s11: generating data of length LPAnd equally divide it into m small blocks PmGenerating a binary data bit sequence D with a data length D' ═ m-1 x t, wherein LPL and m are positive integers, t is a single data block DmLength of (d);
s12: using m pilot blocks PmAnd m-1 data blocks DmAnd obtaining the PSAM-like frame structure in a multiplexing mode.
3. The simplified diagonal cross-correlation carrier frequency offset estimation method according to claim 2, wherein step S2 specifically includes:
s21: based on a PSAM frame structure, obtaining a modulated signal S through quadrature phase shift keying modulation;
s22: and obtaining a baseband receiving signal Z by using the modulation signal S through a Gaussian white noise channel and adding the frequency offset f.
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