CN111262804B - Frequency offset estimation method and device, storage medium and terminal - Google Patents
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Abstract
A frequency offset estimation method and device, a storage medium and a terminal are provided, wherein the frequency offset estimation method comprises the following steps: determining an expression of a received signal, and processing the expression of the received signal to obtain a real part expression of N-point FFT (fast Fourier transform), wherein N is a positive integer; determining a first frequency offset estimation value based on the normalized frequency offset in the real part expression; performing frequency offset estimation on the sum of the frequency of the received signal and the first frequency offset estimation value to obtain a second frequency offset estimation value; and determining the sum of the first frequency offset estimation value and the second frequency offset estimation value as a frequency offset estimation result. By the technical scheme provided by the invention, the frequency offset estimation can be carried out in a larger frequency offset range, and the frequency offset estimation error can be reduced.
Description
Technical Field
The present invention relates to the field of wireless communications technologies, and in particular, to a frequency offset estimation method and apparatus, a storage medium, and a terminal.
Background
In a wireless communication system, existing frequency offset estimation schemes rely on the approximate satisfaction of the condition | x | < 1 to utilize the formula
And calculating the frequency offset, wherein x represents the normalized frequency offset. Therefore, when the frequency offset is small and the approximate condition is met, the calculation result is a biased estimation; when the frequency offset is large and the approximation condition is not satisfied, a large calculation error is generated.
Disclosure of Invention
The invention solves the technical problem of how to reduce the frequency offset estimation error so as to more accurately estimate the frequency offset in a larger frequency offset range.
To solve the foregoing technical problem, an embodiment of the present invention provides a frequency offset estimation method, including: determining an expression of a received signal, and processing the expression of the received signal to obtain a real part expression of N-point FFT (fast Fourier transform), wherein N is a positive integer; determining a first frequency offset estimation value based on the normalized frequency offset in the real part expression; performing frequency offset estimation on the sum of the frequency of the received signal and the first frequency offset estimation value to obtain a second frequency offset estimation value; and determining the sum of the first frequency offset estimation value and the second frequency offset estimation value as a frequency offset estimation result.
Optionally, the processing the expression of the received signal to obtain a real part expression of N-point FFT transform includes: obtaining a likelihood function expression containing the normalized frequency offset according to the expression of the received signal; substituting the channel estimation result into the likelihood function expression to obtain an optimized expression containing the normalized frequency offset; and calculating to obtain a real part expression of the N-point FFT transformation by maximizing the optimized expression.
Optionally, the received signal is a vector X, and the optimized expression is g (v) ═ X H Γ(v)BΓ H (v) X, where Γ (v) represents a diagonal matrix,
B＝A H (A H A) -1 a, v represents the normalized frequency deviation, A represents a preset local signal, X H Transpose, Γ, representing X H Denotes the transposition of Γ, A H Representing the transpose of a.
Optionally, the performing equivalent transformation on the optimized expression to obtain a real part expression of N-point FFT transformation includes: substituting v-k/N into the optimized expression and performing an equivalent transformation to obtain the following formula:
where FFT [ rho ]]Denotes the FFT transformation of the vector ρ, Re { FFT [ ρ ]]Denotes the expression of the real part of the vector p after FFT,
x (k) denotes the kth element of the vector X, k being a positive integer from m to (N-1), X * (k-m) denotes the conjugate of x (k-m), and ρ (m) denotes the mth element of the vector ρ.
Optionally, the determining a first frequency offset estimation value based on the normalized frequency offset in the real expression includes: selecting a maximum value from the real part expression to obtain a maximum value of l (k/N), and determining a k value;
substituting the k value into the following formula to obtain the first frequency offset estimation value:
where Δ f represents the first frequency offset estimate, f s Representing a preset symbol sampling rate.
Optionally, the received signal is a vector X, and the optimized expression is g (v) ═ X H Γ(v)BΓ H (v) X, where Γ (v) represents a diagonal matrix,
B＝A H a, v represents the normalized frequency deviation, A represents a preset local signal, X H Transpose, Γ, representing X H Denotes the transposition of Γ, A H Representing the transpose of a.
To solve the foregoing technical problem, an embodiment of the present invention further provides a frequency offset estimation apparatus, including: the processing module is suitable for determining an expression of a received signal and processing the expression of the received signal to obtain a real part expression of N-point FFT (fast Fourier transform), wherein N is a positive integer; a first determining module, adapted to determine a first frequency offset estimation value based on the normalized frequency offset in the real expression; the estimation module is suitable for carrying out frequency offset estimation on the sum of the frequency of the received signal and the first frequency offset estimation value to obtain a second frequency offset estimation value; and a second determining module, adapted to determine a sum of the first frequency offset estimation value and the second frequency offset estimation value as a frequency offset estimation result.
In order to solve the foregoing technical problem, an embodiment of the present invention further provides a storage medium, on which computer instructions are stored, and when the computer instructions are executed, the steps of the foregoing method are performed.
In order to solve the foregoing technical problem, an embodiment of the present invention further provides a terminal, including a memory and a processor, where the memory stores computer instructions executable on the processor, and the processor executes the computer instructions to perform the steps of the foregoing method.
Compared with the prior art, the technical scheme of the embodiment of the invention has the following beneficial effects:
the embodiment of the invention provides a frequency offset estimation method, which comprises the following steps: determining an expression of a received signal, and processing the expression of the received signal to obtain a real part expression of N-point FFT (fast Fourier transform), wherein N is a positive integer; determining a first frequency offset estimation value based on the normalized frequency offset in the real part expression; performing frequency offset estimation on the sum of the frequency of the received signal and the first frequency offset estimation value to obtain a second frequency offset estimation value; and determining the sum of the first frequency offset estimation value and the second frequency offset estimation value as a frequency offset estimation result. Compared with the prior art, the technical scheme provided by the embodiment of the invention firstly processes the received signal to realize FFT conversion, so that a coarse-precision frequency offset estimation value can be obtained, the embodiment of the invention can carry out frequency offset estimation in a larger frequency offset range, and the frequency offset estimation error caused by the condition that approximate processing conditions are not met under the condition of large frequency offset is avoided. And then, the fine frequency offset estimation can be carried out on the frequency offset within the coarse precision range by adopting the prior art scheme, and at the moment, the approximate processing condition can be met, so that a high-precision frequency offset estimation value can be obtained.
Further, the received signal is a vector X, and the optimized expression is g (v) ═ X H Γ(v)BΓ H (v) X, where Γ (v) represents a diagonal matrix,
B＝A H a, v represents the normalized frequency deviation, A represents a preset local signal, X H Denotes the transposition of X, A H Representing the transpose of a. The embodiment of the invention adopts B ═ A H A instead of B ═ A H (A H A) -1 A, the performance loss is small, but the calculation process can be greatly simplified, and the calculation complexity is reduced.
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FIG. 1 is a diagram illustrating the error between the GSM frequency offset estimate and the actual frequency offset;
FIG. 2 is a flow chart of a method of frequency offset estimation according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a frequency offset estimation apparatus according to an embodiment of the present invention.
Detailed Description
As will be appreciated by those skilled in the art, as mentioned in the background, the existing frequency offset estimation method is biased estimation, and the frequency offset estimation accuracy is low.
The prior art scheme may employ an optimization method to calculate the frequency offset estimate. Specifically, the received signal x (n) obtained by the terminal device from the air interface may be represented as follows:
where N is a positive integer, e.g., N ═ 512; v ═ Δ f/f s To represent normalized frequency offset; Δ f is the frequency deviation, f s Represents the symbol sampling rate; w (n) represents channel noise; h (k) denotes a wireless channel; a is n-k Represents a preset local signal; l represents the number of multipath channels; θ represents the initial phase.
Converting X (n) into matrix form to obtain vector X ═ e jθ Γ(v)AH+W。
Where, X ═ { X (0), X (1), …, X (N-1) }. Γ (v) denotes a diagonal matrix,
A＝{a 0 ，a 1 ，...，a N-1 }， W＝{w(0)，w(1)，...，w(N-1)}。
further, transforming the vector X, a likelihood function can be obtained: Λ (θ, v, H) | | | X-e jθ Γ(v)AH|| 2 。
When θ and v are fixed, the value of H can be obtained by maximizing Λ (θ, v, H): h ═ e -jθ (A H A) -1 AΓ H (v)X。
Then, substituting H into Λ (θ, v, H) can result in the optimization formula: g (v) ═ X H Γ(v)BΓ H (v)X。
Wherein B is A H (A H A) -1 A. For simple calculation, B is approximately equal to A H A, simulation verification adopts A H A approximates the value of B with only a small loss in performance. Further, X H 、A H Each representing a transpose of X, A.
Further, maximizing g (v) is equivalent to maximizing the following:
wherein,
if the normalized frequency offset v is small, then the following approximation can be used:
a simplified formula can be obtained:
to obtain an optimal solution for l (v), derivative may be taken on l (v). Order to
Thus, the optimal solution for v is obtained:
however, since the frequency offset estimation relies on approximately satisfying the condition: only when | x | < 1,
x denotes a normalized frequency offset. When this condition is not satisfied, a large calculation error occurs.
Gaussian filtered minimum frequency shift keying (Gauss) of Global system for Mobile communications (GSM)Taking an ian filtered Minimum Shift Keying (GMSK for short) modulation signal as an example, the simulation modulation sequence is a random sequence, and the symbol sampling rate f s At 270.833 kilohertz (kHz), assuming af 'is the frequency offset estimate, the relationship between the frequency offset estimate error value (af' -af) and the actual frequency offset value af is shown in fig. 1.
Referring to fig. 1, in the range of-500 Hz < Δ f < 500Hz, the error of frequency offset estimation is within 20Hz, and basically meets the condition of frequency offset approximation processing. However, as the frequency offset Δ f increases, the frequency offset estimation error increases sharply due to difficulty in satisfying the frequency offset processing condition. When Δ f is 1000Hz, the frequency offset estimation error reaches 1600 Hz.
Therefore, the frequency offset estimation error is large, and further research on a frequency offset estimation method is needed to accurately estimate the frequency offset value.
To solve the foregoing technical problem, an embodiment of the present invention provides a frequency offset estimation method, including: determining an expression of a received signal, and processing the expression of the received signal to obtain a real part expression of N-point FFT (fast Fourier transform), wherein N is a positive integer; determining a first frequency offset estimation value based on the normalized frequency offset in the real part expression; performing frequency offset estimation on the sum of the frequency of the received signal and the first frequency offset estimation value to obtain a second frequency offset estimation value; and determining the sum of the first frequency offset estimation value and the second frequency offset estimation value as a frequency offset estimation result.
Compared with the prior art, the technical scheme provided by the embodiment of the invention firstly processes the received signal to realize FFT conversion, so that a coarse-precision frequency offset estimation value can be obtained, the embodiment of the invention can carry out frequency offset estimation in a larger frequency offset range, and the frequency offset estimation error caused by the condition that approximate processing conditions are not met under the condition of large frequency offset is avoided. And then, the fine frequency offset estimation can be carried out on the frequency offset within the coarse precision range by adopting the prior art scheme, and at the moment, the approximate processing condition can be met, so that a high-precision frequency offset estimation value can be obtained.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
Fig. 2 is a flowchart illustrating a frequency offset estimation method according to an embodiment of the present invention. The frequency offset estimation method can be used for a GSM system. Referring to fig. 2, the frequency offset estimation method may include the steps of:
step S201, determining an expression of a received signal, and processing the expression of the received signal to obtain a real part expression of N-point FFT, wherein N is a positive integer;
step S202, determining a first frequency offset estimation value based on the normalized frequency offset in the real part expression;
step S203, performing frequency offset estimation on the sum of the frequency of the received signal and the first frequency offset estimation value to obtain a second frequency offset estimation value;
step S204, determining the sum of the first frequency offset estimation value and the second frequency offset estimation value as a frequency offset estimation result.
Specifically, in step S201, a terminal device (e.g., a User Equipment (UE)) may obtain a received signal from a base station on the network side. Thereafter, an expression of the received signal may be determined:
wherein n represents the nth received signal of x (n). N is a positive integer, for example, N is 512, 1024, or the like. v ═ Δ f/f s Denotes normalized frequency deviation,. DELTA.f denotes frequency deviation, f s Representing a preset symbol sampling rate. w (n) represents channel noise; h (k) denotes a radio channel; a is n-k An element representing a preset local signal a; l represents the number of multipath channels, and k represents the multipath channel index; θ represents an initial phase of the received signal.
If X (n) is converted into a matrix form, the vector X ═ e is obtained jθ Γ (v) AH + W. Where, X ═ { X (0), X (1), …, X (N-1) }.
Γ (v) denotes a diagonal matrix，A＝{a 0 ，a 1 ，...，a N-1 }，W＝{w(0)，w(1)，...，w(N-1)}。
Then, the expression of the received signal is transformed to obtain a likelihood function expression including a parameter θ, a parameter v, and a parameter H, where the likelihood function expression is Λ (θ, v, H) | | X-e jθ Γ(v)AH|| 2 。
When θ and v are fixed, the value of H can be obtained by maximizing Λ (θ, v, H): h-e -jθ (A H A) -1 AΓ H (v)X，Γ H Denoting the transposition of Γ, A H Representing the transpose of a.
Substituting the calculation result of the parameter H into the likelihood function expression Λ (θ, v, H) to obtain an optimized expression containing the parameter v. Those skilled in the art will appreciate that the optimized expression can be calculated as g (v) ═ X H Γ(v)BΓ H (v)X，X H Representing the transpose of X. Wherein B ═ A H (A H A) -1 A。
Since B ≈ A H A, and simulation verification adopts A H A approximates the value of B with only a small loss in performance. Therefore, for simplicity of calculation, as a variation, B ═ a may be given H A. At this time, the optimized expression is:
wherein Γ (v) represents a diagonal matrix,
v denotes the normalized frequency offset, A denotes a predetermined local signal, X H Transpose, Γ, representing X H Denotes the transposition of Γ, A H Representing the transpose of a.
It is understood by those skilled in the art that maximizing g (v) is equivalent to maximizing the following equation:
wherein,
x (k) denotes the kth element of the vector X, k being a positive integer from m to (N-1), X * (k-m) denotes the conjugate of x (k-m), and ρ (m) denotes the mth element of the vector ρ.
Further, let
It is possible to obtain:
in step S202, l (v) may be maximized to calculate v. Specifically, l (k/N) may be calculated by FFT, where k is 0, 1, 2, …, (N-1). Further, the first frequency offset estimation value is obtained by using the following formula:
the frequency offset estimation precision obtained at this time is
Taking GSM system as an example, the symbol sampling rate f of GSM s When N is 512, the frequency offset estimation precision obtained by FFT conversion calculation is 270.833kHz
In step S203, the receiving frequency of the received signal may be added to the first frequency offset estimation value to control the frequency offset at
Within the range. In the frequency offset range, a second frequency offset estimation value with higher precision can be obtained by adopting the prior art scheme to carry out frequency offset estimation.
On toolIn a bulk implementation, the frequency offset estimation may range from
Using GSM as an example, the frequency offset Δ f ∈ [ -135.416kHz, 135.416kHz]. Considering the complexity and precision of the operation, a first frequency offset estimation value with coarse precision may be estimated by using 512-point FFT, and at this time, the participating frequency offset is controlled within 528.97Hz, as can be seen from fig. 1, at this time, a second frequency offset estimation value with higher precision may be obtained by using the prior art scheme.
In step S204, the sum of the first frequency offset estimation value and the second frequency offset estimation value may be determined as a frequency offset estimation result, so as to complete frequency offset calculation and achieve the purpose of correcting frequency offset.
Therefore, the embodiment of the invention can carry out frequency offset estimation in a larger frequency offset range, avoids frequency offset estimation errors caused by approximate processing under the condition of large frequency offset, and is beneficial to improving the frequency offset estimation precision.
Fig. 3 is a schematic structural diagram of a frequency offset estimation apparatus according to an embodiment of the present invention. The frequency offset estimation apparatus 3 can be applied to a terminal device. Those skilled in the art will appreciate that embodiments of the present invention may be used to implement the method solution illustrated in fig. 2.
Specifically, the frequency offset estimation apparatus 3 may include: a processing module 31, adapted to determine an expression of a received signal, and process the expression of the received signal to obtain a real part expression of an N-point FFT transform, where N is a positive integer; a first determining module 32 adapted to determine a first frequency offset estimate based on the normalized frequency offset in the real expression; an estimating module 33, adapted to perform frequency offset estimation on the sum of the frequency of the received signal and the first frequency offset estimation value to obtain a second frequency offset estimation value; a second determining module 34, adapted to determine a sum of the first frequency offset estimation value and the second frequency offset estimation value as a frequency offset estimation result.
In a specific implementation, the processing module 31 may include: the first processing sub-module 311 is adapted to obtain a likelihood function expression including the normalized frequency offset according to the expression of the received signal; a first import sub-module 312 adapted to import the channel estimation result into the likelihood function expression to obtain an optimized expression containing the normalized frequency offset; and the second processing submodule 313 is suitable for calculating a real part expression of the N-point FFT transformation by maximizing the optimized expression.
In a specific implementation, the received signal is a vector X, and the optimized expression may be g (v) ═ X H Γ(v)BΓ H (v) X, where Γ (v) represents a diagonal matrix,
B＝A H (A H A) - 1 a, v represents the normalized frequency deviation, A represents a preset local signal, X H Transpose of X, Γ H Denotes the transposition of Γ, A H Representing the transpose of a.
As a variant, the received signal is a vector X, and the optimized expression is g (v) -X H Γ(v)BΓ H (v) X, wherein,
Γ (v) denotes a diagonal matrix, B ═ a H A, v represents the normalized frequency deviation, A represents a preset local signal, X H Transpose of X, Γ H Denoting the transposition of Γ, A H Representing the transpose of a.
In a specific implementation, the second processing submodule 313 is further adapted to substitute v ═ k/N into the optimized expression, and perform an equivalent transformation to obtain the following equation:
where FFT [ rho ]]Denotes the FFT transformation of the vector ρ, Re { FFT [ ρ ]]Denotes the expression of the real part of the vector p after FFT transformation,
x (k) representsThe kth element of the vector X, k being a positive integer from m to (N-1), X * (k-m) represents the conjugate of x (k-m) and ρ (m) represents the mth element of the vector ρ.
In a specific implementation, the first determining module 32 may include: a selecting submodule 321 adapted to select a maximum value from the real part expression to obtain a maximum value of l (k/N), and determine a k value; a second generation-in module 322, adapted to substitute the k value into the following formula to obtain the first frequency offset estimation value:
where Δ f represents the first frequency offset estimate, f s Representing a preset symbol sampling rate.
For more contents of the operation principle and the operation mode of the frequency offset estimation apparatus 3, reference may be made to the related description in fig. 2, which is not described herein again.
Further, the embodiment of the present invention also discloses a storage medium, on which a computer instruction is stored, and when the computer instruction runs, the technical solution of the method in the embodiment shown in fig. 2 is executed. Preferably, the storage medium may include a computer-readable storage medium such as a non-volatile (non-volatile) memory or a non-transitory (non-transient) memory. The computer readable storage medium may include ROM, RAM, magnetic or optical disks, and the like.
Further, an embodiment of the present invention further discloses a terminal, which includes a memory and a processor, where the memory stores a computer instruction capable of running on the processor, and the processor executes the technical solution of the method in the embodiment shown in fig. 2 when running the computer instruction. In particular, the terminal may be a user equipment.
Although the present invention is disclosed above, the present invention is not limited thereto. Various changes and modifications may be effected by one skilled in the art without departing from the spirit and scope of the invention, as defined in the appended claims.
Claims (8)
1. A method of frequency offset estimation, comprising:
determining an expression of a received signal, and processing the expression of the received signal to obtain a real part expression of N-point FFT (fast Fourier transform), wherein N is a positive integer;
determining a first frequency offset estimation value based on the normalized frequency offset in the real part expression;
performing frequency offset estimation on the sum of the frequency of the received signal and the first frequency offset estimation value to obtain a second frequency offset estimation value;
determining the sum of the first frequency offset estimation value and the second frequency offset estimation value as a frequency offset estimation result;
wherein the processing the expression of the received signal to obtain a real part expression of an N-point FFT comprises:
obtaining a likelihood function expression containing the normalized frequency offset according to the expression of the received signal;
substituting the channel estimation result into the likelihood function expression to obtain an optimized expression containing the normalized frequency offset;
and calculating to obtain a real part expression of the N-point FFT transformation by maximizing the optimized expression.
2. The frequency offset estimation method of claim 1 wherein said received signal is a vector X and said optimized expression is g (v) -X H Γ(v)BΓ H (v) X, where Γ (v) represents a diagonal matrix,
B＝A H (A H A) -1 a, v represents the normalized frequency deviation, A represents a preset local signal, X H Transpose, Γ, representing X H Denotes the transposition of Γ, A H Representing the transpose of a.
3. The frequency offset estimation method of claim 2 wherein said equivalently transforming said optimized representation to obtain a real representation of an N-point FFT transform comprises:
substituting v-k/N into the optimized expression and performing an equivalent transformation to obtain the following formula:
wherein FFT [ ρ ]]Denotes the FFT transformation of the vector ρ, Re { FFT [ ρ ]]Denotes the expression of the real part of the vector p after FFT,
1, 2, N-1; x (k) denotes the kth element of the vector X, k being a positive integer from m to (N-1), X * (k-m) represents the conjugate of x (k-m) and ρ (m) represents the mth element of the vector ρ.
4. The frequency offset estimation method of claim 3 wherein said determining a first frequency offset estimate based on the normalized frequency offset in the real expression comprises:
selecting a maximum value from the real part expression to obtain a maximum value of l (k/N), and determining a k value;
substituting the k value into the following formula to obtain the first frequency offset estimation value:
where Δ f represents the first frequency offset estimate, f s Representing a preset symbol sampling rate.
5. The frequency offset estimation method of claim 1 wherein said received signal is a vector X and said optimized expression is g (v) -X H Γ(v)BΓ H (v) X, where Γ (v) represents a diagonal matrix,
B＝A H a, v represents the normalized frequency deviation, A represents a preset local signal, X H Transpose, Γ, representing X H Denotes the transposition of Γ, A H Representing the transpose of a.
6. A frequency offset estimation apparatus, comprising:
the processing module is suitable for determining an expression of a received signal and processing the expression of the received signal to obtain a real part expression of N-point FFT (fast Fourier transform), wherein N is a positive integer;
a first determining module, adapted to determine a first frequency offset estimation value based on the normalized frequency offset in the real expression;
the estimation module is suitable for carrying out frequency offset estimation on the sum of the frequency of the received signal and the first frequency offset estimation value to obtain a second frequency offset estimation value;
a second determining module, adapted to determine a sum of the first frequency offset estimation value and the second frequency offset estimation value as a frequency offset estimation result;
wherein the processing module comprises:
the first processing submodule is suitable for obtaining a likelihood function expression containing the normalized frequency offset according to the expression of the received signal;
the first generation submodule is suitable for substituting the channel estimation result into the likelihood function expression to obtain an optimized expression containing the normalized frequency offset;
and the second processing submodule is suitable for calculating to obtain a real part expression of the N-point FFT transformation by maximizing the optimized expression.
7. A storage medium having stored thereon computer instructions, which, when executed by a processor, perform the steps of the method of any one of claims 1 to 5.
8. A terminal comprising a memory and a processor, the memory having stored thereon computer instructions executable on the processor, wherein the processor, when executing the computer instructions, performs the steps of the method of any one of claims 1 to 5.
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