CN116405356B - Method and system for expanding frequency offset estimation range based on extended Chinese remainder theorem - Google Patents

Abstract

A method and system for extending the frequency offset estimation range based on the extended Chinese remainder theorem, firstly, the pilot is divided into n parts, each part is composed of two completely equal pilot sequences, and the result of dividing the interval of each pilot sequence by the common divisor of all pilot sequence intervals needs to meet the condition of not completely equal; then, the pilot sequences of each part are cross-correlated and phase angle operations are taken to calculate the phase estimation results of each part; then, the influence of noise is ignored, and a linear congruential equation group for frequency offset estimation is constructed according to the relationship between the real phase offset and the estimated phase offset; then, the linear congruential equation group is solved based on exCRT to perform phase unwrapping; finally, the normalized frequency offset results of the pilot sequences of each part after phase unwrapping are calculated, and the frequency offset results of each part are weighted summed according to the interval to obtain the final frequency offset estimation result; the present invention expands the frequency offset estimation range of the cross-correlation algorithm, can flexibly adjust the center value of the frequency offset estimation range, has low calculation complexity and is simple to implement.

Description

Method and system for extending frequency offset estimation range based on extended Chinese remainder theorem

Technical Field

The present invention belongs to the technical field of radio transmission, and in particular relates to a method and system for extending a frequency offset estimation range based on an extended Chinese Remainder Theorem (exCRT).

Background Art

In mobile communication systems, due to the Doppler effect caused by the relative motion between the transmitter and the receiver, as well as the problem of crystal oscillator accuracy at both ends, there will be a certain deviation in the carrier frequency between the transmitter and the receiver. The larger the frequency offset value, the more serious the distortion of the received signal waveform. Effective measures need to be taken to estimate the frequency deviation and compensate the estimated frequency deviation value to the received signal to ensure that the receiving end receives the signal correctly and effectively.

Depending on whether a known pilot sequence is used, the frequency offset estimation method can be divided into two categories: data-assisted and non-data-assisted. The frequency offset estimation method based on non-data assistance uses an unknown data sequence to estimate the frequency offset. Generally, the demodulation soft information after the received sequence is demodulated is used for estimation. The calculation complexity is high, and the estimation accuracy depends on the length of the data sequence and the reliability of the demodulation soft information. In the frequency offset estimation method based on data assistance, the receiver can use a known pilot sequence to estimate the frequency offset. The calculation complexity is low. Different pilot sequence lengths and structures will affect the estimation range and accuracy. This method introduces additional system overhead and reduces the spectrum utilization of the overall system. Therefore, the pilot sequence length is often limited.

Among the frequency offset estimation methods based on data assistance, the most commonly used one is the estimation method based on phase increment. This type of method is based on the autocorrelation operation of the received signal or the cross-correlation operation with the known pilot sequence, from which the phase information is extracted to perform frequency offset estimation. Among them, T.M.Schmidl proposed a cross-correlation synchronization method in the paper "Robust frequency and timing synchronization for OFDM", which can be used for both time synchronization and frequency synchronization, and is widely used in various communication systems. The cross-correlation synchronization method uses two pilot sequences to perform cross-correlation operations, accumulates the phase angles, and then averages to obtain the frequency offset estimation value. The computational complexity is low, but the estimation range and accuracy cannot be consistent. The longer the pilot length, the higher the estimation accuracy. The smaller the frequency offset estimation range, the more likely it is to have phase ambiguity.

Summary of the invention

In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a method and system for expanding the frequency offset estimation range based on the extended Chinese remainder theorem, which expands the frequency offset estimation range of the cross-correlation synchronization method, can flexibly adjust the center value of the frequency offset estimation range, has low computational complexity and is simple to implement.

In order to achieve the above object, the technical solution adopted by the present invention is:

A method for expanding a frequency offset estimation range based on an extended Chinese remainder theorem comprises the following steps:

1) The pilot is divided into n parts, each part is composed of two completely equal pilot sequences, and the result of dividing the interval of each pilot sequence by the common divisor of all pilot sequence intervals needs to meet the condition of not being completely equal;

2) Based on the cross-correlation synchronization method, the estimated phase offset of each pilot sequence is calculated through cross-correlation and phase angle calculation.

3) Ignoring the influence of noise, according to the actual phase offset θ _di of each part of the pilot sequence and the estimated phase offset The linear congruence equations (S ₃ ) for frequency offset estimation are constructed based on the relationship between ;

4) Solve the linear congruential equations (S ₃ ) based on exCRT to perform phase unwrapping:

4.1) Simplify linear congruence equations according to Euclid's algorithm and Pei Shu's theorem, and solve the general solution of linear congruence equations;

4.2) Substitute the general solution of K _r+1 in the linear congruence equation system (S ₃ ) into the linear congruence equation (r), construct a new linear congruence equation system and find the general solution;

4.3) Find a special solution within the corresponding frequency offset estimation range according to the actual situation;

5) Calculate the normalized frequency offset results based on each part of the pilot sequence according to the special solution The frequency offset results are weighted and summed according to the interval length to obtain the final frequency offset estimation result.

A system for implementing the above method for extending the frequency offset estimation range based on the extended Chinese remainder theorem comprises:

Fixed parameter storage module: Calculate the special solution of m _r and the linear congruential equation D _r K′ _r+1 +m _r t′ _r =gcd(D _r ,m _r ) according to the pilot length and interval and and storing the calculation results in a local storage unit;

Estimated phase offset calculation module: Based on the cross-correlation synchronization method, the estimated phase offset of each part of the pilot sequence is calculated through cross-correlation and phase angle calculation.

Module for calculating coefficients of the general solution of linear congruential equations: estimated phase offset based on each part of the pilot sequence Calculate the coefficients of the general solution of a linear congruential system of equations

Linear congruential equation group special solution calculation module: within the determined frequency offset estimation range, based on the general solution of the linear congruential equation group, solve the special solution of K _i (i＝1,2,...,n);

Frequency offset estimation result calculation module: calculates the normalized frequency offset result based on each part of the pilot sequence according to the special solution The frequency offset results are weighted and summed according to the interval length to obtain the final frequency offset estimation result.

Compared with the prior art, the present invention has the following advantages:

1. Expanded frequency offset range: In the cross-correlation synchronization method, the longer the pilot sequence length and interval, the higher the estimation accuracy, but the smaller the frequency offset estimation range, the estimation range and accuracy cannot be consistent. The present invention uses pilot sequences of different lengths and can effectively expand the frequency offset estimation range based on exCRT.

2. The center value of the frequency offset estimation range can be flexibly adjusted according to actual conditions: Based on the general solution form of the frequency offset estimation linear congruential equation group, the frequency offset estimation range of the present invention is fixed, but the center value of the frequency offset estimation range can be flexibly adjusted.

3. Low computational complexity and simple implementation: After the length and interval of each pilot sequence of the present invention are determined, the general solution of the linear congruential equation system is The values of m _r and D _r no longer change. We only need to solve g _r(r+1) according to the phase estimation result to directly obtain the general solution of the linear congruential equation, and then perform addition and subtraction operations in a suitable range to solve the special solution.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of a flow chart of a method according to an embodiment of the present invention.

FIG. 2 is a diagram showing the structure of the system according to the embodiment of the present invention.

FIG3 is a frame structure provided by a method according to an embodiment of the present invention.

FIG. 4 is a simulation comparison diagram of the estimated frequency offset range of the method according to the embodiment of the present invention and the cross-correlation synchronization method.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the method of the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

1 , a method for extending a frequency offset estimation range based on an extended Chinese remainder theorem comprises the following steps:

1) Divide the pilot of length L into n parts, each part consists of two completely equal pilot sequences i of length L _i and interval D _i (i＝1,2,...,n), wherein D ₁ ≥D ₂ ≥…≥D _n , the common divisor of D ₁ ,D ₂ ,...,D _n is D _gcd ; D _{i_p} ＝D _i /D _gcd , D _{i_p} needs to meet the condition of not completely equal;

2) Calculate the estimated phase offset of each part based on the pilot sequence of each part Take the conjugate of the first pilot sequence i of each part, and perform cross-correlation calculation with the second pilot sequence i of each part, and take the argument:

Wherein, _yi k) represents the pilot sequence i, angle (·) represents the angle operation;

3) Ignore the influence of noise and construct a linear congruential equation system for frequency offset estimation. Due to the phase ambiguity phenomenon, the actual phase offset and the estimated phase offset may be inconsistent, and the relationship between the two is:

Wherein, θ _di is the actual phase offset of each part, θ is the unit phase offset, and _Ki is the multiple of 2π between the actual phase offset of pilot sequence i and the estimated phase offset; sub-equation (r+1) and sub-equation (r) (r＝1,2,…,n-1) of equation group (S ₁ ) are calculated without θ, and the linear congruential equation group (S ₂ ) for frequency offset estimation is obtained after sorting:

According to Pei Shu's theorem, when the linear congruence equation system (S ₂ ) has a solution, we have:

in is an integer, gcd(D _r ,-D _r+1 ) represents the common divisor of D _r and -D _r+1 ;

4) Solve the linear congruential equations (S ₃ ) based on exCRT to perform phase unwrapping:

4.1) Simplify the linear congruential equation and calculate the general solution of the linear congruential equation; let m ₁ = -D ₂ , t ₁ = K ₁ , The linear congruence equation (1) in the equation system (S ₃ ) becomes:

In order to make the solution universal, the subscript of the above formula is changed to r (1 = 1, 2, ..., n-1), and we have:

make have

D _r K′ _r+1 +m _r t′ _r =gcd(D _r ,m _r )

Simplify the above linear congruential equation according to the Euclidean algorithm:

When gcd(D _{r_sq} ,0) appears on the right side of the equation, the simplification ends; q is the number of simplifications, D _{r_sp} = m _{r_s(p-1)} , m _{r_sp} = D _{r_s(p-1)} %(m _{r_s(p-1)} )(p=1,2,...,q), % is the remainder calculation; according to Pei Shu's theorem, each simplification process has:

According to the corresponding relationship between the left and right sides of the equal sign, we have:

After simplification q times, the simplified equation is D _{r_sq} K′ _{r+1_sq} ＝gcd(D _{r_sq} ,0), and there is a special solution

Substituting the above special solution (S ₅ ) into the corresponding relationship of (S ₄ ), we can reversely obtain the special solutions of K′ _r+1 and t′ _r Finally, the general solution of the linear congruential equation can be obtained as:

When r=1, the general solution of the linear congruence equation (1) in the equation group (S ₃ ) is:

in, is a particular solution of the linear congruential equation _Dr K′ _r+1 +m _r t′ _r =gcd(D _r ,m _r );

4.2) Construct a new linear congruence equation system and find the general solution; Substitute the general solution of K ₂ into the linear congruence equation (2) in the equation system (S ₃ ) and rearrange it to obtain:

make Form new linear congruential equations:

in

Repeat the above operation, that is, substitute the general solution of K _r+1 into the linear congruence equation (r) in the equation system (S ₃ ), and let

Arrange and get the new linear congruential equations:

in According to the algorithm in step 4.1), the general solution of each linear congruential equation in the equation group (S ₆ ) is:

When the length and interval of the pilot sequence are determined, m _r , D _r are determined, and the general solution of the linear congruential equation for frequency offset estimation can be determined by simply solving g _r(r+1) according to step 3);

4.3) Solve the special solution according to the actual situation; the center value of the estimation range changes with the change of _tn value in the general solution _Kn , so different frequency offset estimation ranges can be selected according to the actual situation; when the frequency offset estimation range is centered at 0Hz, the range of _Kn is:

in, To round down, is rounded up; when K _n satisfies the above conditions, t _n is determined and the result is substituted into the general solution (S ₇ ), the special solution of each K _i (i＝1,2,...,n) can be obtained;

5) Solve the final frequency offset estimation result:

5.1) Based on the special solution K _i, the normalized frequency offset results based on each pilot sequence are solved separately Where _fs is the symbol rate:

5.2) Perform weighted summation of each normalized frequency offset result according to the interval to obtain the final frequency offset estimation result

2 , a system for implementing the method for extending the frequency offset estimation range based on the extended Chinese remainder theorem includes:

Fixed parameter module: When the pilot length and interval are determined, according to m ₁ = -D ₂ , Calculate m _r and calculate the specific solution of the linear congruential equation D _r K′ _r+1 +m _r t′ _r =gcd(D _r ,m _r ) and Finally, the calculation results are stored in the local storage unit;

Estimated phase offset calculation module: Based on the cross-correlation synchronization method, the estimated phase offset of each part of the pilot sequence is calculated through cross-correlation and phase angle calculation.

Where _yi (k) represents the pilot sequence i, angle(·) represents the angle operation;

Module for calculating coefficients of the general solution of linear congruential equations: estimated phase offset based on each part of the pilot sequence Calculate the coefficients of the general solution of a linear congruential system of equations

Module for calculating the special solution of linear congruential equations: select the appropriate t _r+1 so that K _r+1 satisfies a certain range, and then calculate the special solution of K _i (i＝1,2,...,n) according to the following formula;

Frequency offset estimation result calculation module: based on the special solution Ki _, the normalized frequency offset results based on each pilot sequence are solved separately The normalized frequency offset results are weighted and summed according to the interval to obtain the final frequency offset estimation result.

Where _fs is the symbol rate.

The following is a simulation experiment to further illustrate the technical effect of the present invention:

1. Simulation conditions: The simulation uses Matlab R2021b simulation software and adopts a pilot-prepended frame structure, as shown in Figure 3. The total length of the pilot is L=192, and the pilot is divided into two parts: pilot sequence 1 and pilot sequence 2. The length of pilot sequence 1 is L ₁ =60, and the length of pilot sequence 2 is L ₂ =36. The pilot sequences are arranged in the order of pilot sequence 1, pilot sequence 1, pilot sequence 2, and pilot sequence 2. The pilot intervals of each part are D ₁ =60 and D ₂ =36, and the symbol rate is f _s =100 kHz.

2. Analysis of simulation content and results: Under the condition of equal overhead length, the cross-correlation synchronization method is used as a comparison method to compare the frequency deviation ranges that can be estimated by the two methods. The simulation results are shown in Figure 4. The simulation results show that the method based on exCRT to expand the frequency deviation estimation range proposed in the present invention has a wider estimation range than the cross-correlation synchronization method.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (5)

1. The method for expanding the frequency offset estimation range based on the extended Chinese remainder theorem is characterized by comprising the following steps:

1) Dividing the pilot frequency into n parts, wherein each part consists of two completely equal pilot frequency sequences, and the result of dividing the interval of each pilot frequency sequence by the common divisor of the intervals of all pilot frequency sequences is required to meet the condition of incomplete equality;

2) Based on the cross-correlation synchronization algorithm, calculating the estimated phase offset of each partial pilot sequence through cross-correlation and argument operation

3) Neglecting the effect of noise, based on the true and estimated phase offsets θ _di and θ _di of each partial pilot sequenceA linear congruence equation set of frequency offset estimates is constructed (S ₃);

Because of the phase ambiguity phenomenon, the true phase offset and the estimated phase offset may not be identical, and the relationship between the two is:

Wherein, θ _di is the real phase offset of each part, θ is the unit phase offset, and K _i is the multiple of the difference of 2 pi between the real phase offset and the estimated phase offset of the pilot sequence i; and (3) calculating theta removal by using a sub-equation (r+1) and a sub-equation (r) (r=1, 2, …, n-1) of the equation set (S ₁), and obtaining a linear congruence equation set (S ₂) of frequency offset estimation after finishing:

According to Pei Shu theorem, when a solution is given to the system of linear congruence equations (S ₂), there are:

Wherein the method comprises the steps of Gcd (D _r,-D_r+1) is expressed as a common divisor of D _r and-D _r+1;

4) Phase unwrapping is performed based on exCRT solving a system of linear congruence equations (S ₃):

4.1 Simplifying the linear congruence equation according to the Euclidean algorithm and Pei Shu theorem, and solving the general solution of the linear congruence equation;

linear congruence equation for simplifying frequency offset estimation based on Euclidean algorithm and Pei Shu theorem The general solution obtained is:

wherein, A special solution for the linear congruence equation D _rK′_r+1+m_rt′_r＝gcd(D_r,m_r);

4.2 Bringing the full solution of K _r+1 in the linear congruence equation set (S ₃) into the linear congruence equation (r), constructing a new linear congruence equation set and solving the full solution;

The new set of linear congruence equations is:

Wherein:

According to the method for solving the general solution of the linear congruence equation in the step 4.1), the general solution of the new linear congruence equation set is as follows:

When the length and interval of the pilot sequence are determined, the method is performed M _r,D_r, determining the general solution of the frequency offset estimation linear congruence equation only by solving g _r(r+1) according to the step 3);

4.3 Solving the special solution in the corresponding frequency offset estimation range according to the actual situation;

Based on the general solution and the actual situation, determining the special solution, when the frequency offset estimation range is 0Hz as the center, the range of K _n is:

wherein, In order to take the whole downwards,Is rounded upwards; when K _n satisfies the above conditions, at this time, t _n determines and brings the result into a full solution (S ₇), and obtains a special solution for each K _i (i=1, 2,., n);

5) Calculating normalized frequency offset result based on pilot frequency sequences of all parts according to special solution And carrying out weighted summation on each frequency offset result according to the interval length to obtain a final frequency offset estimation result.

2. The method according to claim 1, wherein step 1) is specifically: the pilot of length L is divided into n parts, each of which is divided by two identical pilot segments of length L _i, spacing D _i (i=1, 2, pilot sequence i composition of n), wherein a common divisor of D ₁≥D₂≥…≥D_n,D₁,D₂,...,D_n of D _gcd;D_{i_p}＝D_i/D_gcd,D_{i_p} is required to satisfy the condition of not being exactly equal.

3. The method according to claim 2, wherein step 2) is specifically: conjugation is taken for the first pilot sequence i of each part, cross-correlation calculation is carried out on the first pilot sequence i of each part and the second pilot sequence i of each part, and an amplitude angle is taken:

Where y _i (k) is denoted as pilot sequence i and angle (·) is denoted the argument operation.

4. The method according to claim 1, wherein: solving the normalized frequency offset result of each pilot sequence based on the special solution K _i in the step 5)And weighting and summing all normalized frequency offset results according to intervals to obtain a final frequency offset estimation result

Where f _s is the symbol rate.

5. A system for implementing a method for extending a range of frequency offset estimates based on the extended chinese remainder theorem as recited in claim 1, comprising:

The fixed parameter storage module: calculating a special solution of m _r and a linear congruence equation D _rK′_r+1+m_rt′_r＝gcd(D_r,m_r) according to the pilot length and the interval AndStoring the calculation result into a local storage unit;

An estimated phase offset calculation module: based on the cross-correlation synchronization method, the estimated phase offset of each partial pilot sequence is calculated through cross-correlation and argument operation

And the linear congruence equation set general solution coefficient calculating module is used for: estimated phase offset based on partial pilot sequencesCalculating the general solution coefficient of the linear congruence equation set

And a linear congruence equation set special solution calculation module: solving a special solution of K _i (i=1, 2,., n) based on a linear congruence system of equations general solution within the determined frequency offset estimation range;

And a frequency offset estimation result calculation module: calculating normalized frequency offset result based on pilot frequency sequences of all parts according to special solution And carrying out weighted summation on each frequency offset result according to the interval length to obtain a final frequency offset estimation result.