A frequency offset estimation method for communication system based on block pilot

Abstract

The present invention discloses a method for estimating frequency offset of a communication system based on block pilot. The method comprises the following steps: extracting the received signals corresponding to the front and rear pilot blocks, filling the middle data part with zeros, and obtaining a signal sequence y(n); calculating the N=D+2P point discrete Fourier transform of y(n) to obtain a discrete spectrum Y(k), and searching for the value with the largest amplitude in Y(k); constructing an ideal signal function containing unknown parameters; constructing an objective function for frequency offset estimation, and obtaining a frequency offset estimation result by solving the minimum value of the objective function. The present invention uses an approximate expression based on Taylor expansion to obtain a closed-form expression of the estimation result, without the need for searching and solving, and is convenient for engineering implementation. The present invention is applicable to systems using block pilots, and compared with continuous single-block pilots, more accurate estimation results can be obtained under the same number of pilots.

Description

Technical Field

[0001] The present invention relates to a communication system receiving end processing technology, and in particular to a communication system frequency offset estimation method based on block pilot. Background Art

[0002] There are two main reasons for carrier frequency deviation. One is that the frequency of the local clock is inconsistent with the clock frequency of the transmitting end, resulting in a deviation between the local carrier frequency and the received carrier frequency. The other is that the Doppler effect caused by the relative movement of the transmitting and receiving ends causes the carrier frequency to shift. Carrier frequency deviation will significantly increase the error probability of symbol detection at the receiving end. Therefore, the receiving end of the communication system needs to estimate and compensate for the carrier frequency deviation of the received signal.

[0003] The Chinese invention patent "A method and device for frequency offset estimation based on discrete pilot assistance" (CN201910630157.5) discloses a carrier frequency offset estimation method based on pilots. This method uses a pilot signal to improve the accuracy of frequency offset estimation by padding the receiving channel corresponding to the pilot with zeros and then performing Fourier transform. The Chinese invention patent "A method and device for frequency offset estimation based on combined pilots (CN200910088046.2)" discloses a frequency offset estimation method based on continuous pilots / discrete pilots. The continuous pilot is used to make a rough estimate of the frequency offset, and then the discrete pilot is used to make a fine estimate of the frequency offset.

[0004] Increasing the number of pilot symbols can improve the accuracy of frequency offset estimation, but pilot symbols themselves do not convey information, and too many pilot symbols will reduce the transmission efficiency of the system. Therefore, it is necessary to further explore new frequency offset estimation methods under limited pilot symbols. Existing methods mostly use single-block pilots, which limits the space for performance improvement. Even methods based on combined pilots use one continuous pilot and one discrete pilot. There is currently no frequency offset estimation method based on block pilots. Summary of the invention

[0005] The object of the present invention is to provide a pilot-based communication system carrier frequency offset estimation method.

[0006] The purpose of the present invention is achieved by at least one of the following technical solutions.

[0007] A method for estimating frequency offset of a communication system based on block pilot comprises the following steps:

[0008] S1, extract the received signals corresponding to the front and rear pilot blocks, fill the middle data part with zeros, and obtain the signal sequence y(n);

[0009] S2. Calculate the N = D + 2P discrete Fourier transform of y(n), obtain the discrete spectrum Y(k), and search for the value with the largest amplitude in Y(k);

[0010] S3, construct an ideal signal function containing unknown parameters;

[0011] S4. Construct an objective function for frequency offset estimation, and obtain a frequency offset estimation result by solving the minimum value of the objective function.

[0012] Furthermore, the block pilots are located at the beginning and the end of the data frame respectively, and the pilot blocks are of equal length and the pilot sequence has a constant modulus.

[0013] Furthermore, in step S1, the conjugate of the pilot symbol is multiplied by the corresponding received signal to obtain a signal sequence y(n), where y(n) takes non-zero values ​​in the range of 0≤n≤P-1, D+P≤n≤D+2P and takes zero values ​​in other ranges, wherein n represents the timing, P represents the length of the pilot block, that is, the number of pilot symbols; and D represents the distance between two pilot blocks measured in the number of symbols.

[0014] Further, in step S2, the N=D+2P point discrete Fourier transform of the signal sequence y(n) is calculated to obtain a discrete spectrum Y(k); wherein N is the length of the signal frame;

[0015] Search for the value Y(k) with the largest amplitude in the discrete spectrum Y(k) 0 ), the corresponding spectrum position is a rough estimate of the discrete spectrum Y(k), k 0 It is a rough estimate.

[0016] Furthermore, in step S3, the following ideal signal function including unknown parameters is constructed, as follows:

[0017]

[0018] Among them, A is the signal amplitude, ω∈[-π,π] is the signal carrier frequency deviation, which is the parameter to be estimated; is the signal phase; are all unknown constants, and j is the imaginary number sign.

[0019] Further, in step S4, let U(k,ω)=|P(k,ω)| 2 , construct the following objective function for frequency offset estimation:

[0020]

[0021] where |Y(k)| 2 is the square of the absolute value of the discrete spectrum Y(k), called the energy spectrum of y(n); Q is a given positive integer ranging from 1 to 3.

[0022] Further, in step S4, the minimum value of the objective function for frequency offset estimation is solved to obtain the frequency offset estimation result

[0023] Furthermore, a method for solving the minimum value without iterative solution is used to solve the minimum value of the objective function of the frequency offset estimation, as follows:

[0024] remember is a rough estimate of the frequency deviation. The actual frequency deviation is expressed as ω = ω * +ω α , where ω α is the offset to be estimated. α The value of is relatively small, U(k,ω) is * Approximate by Taylor expansion, we get

[0025] U(k,ω)=U(k,ω * )+ωαU′(k,ω * )

[0026] in,

[0027] Further, remember

[0028] p=[U(k 0 -Q,ω * ),…,U(k 0 ,ω * ),…,U(k 0 +Q,ω * )] T

[0029] p′=[U′(k 0 -Q,ω * ),…,U′(k 0 ,ω * ),…,U′(k 0 +Q,ω * )] T

[0030] y=[|Y(k 0 -Q)| 2 ,…,|Y(k 0 )| 2 ,…,|Y(k 0 +Q)| 2 ] T

[0031] Calculate the following intermediate variables:

[0032] ε=p T p

[0033] β=p′ T p

[0034] τ=p′ Tp′

[0035]

[0036]

[0037] Among them, ε, β, π, a and c are all intermediate variables.

[0038] Furthermore, according to the intermediate variables, the final frequency offset estimation result is obtained, as follows:

[0039]

[0040]

[0041] Compared with the prior art, the advantages of the present invention are:

[0042] (1) The frequency offset estimation result of the present invention is obtained through closed-form calculation without the need for iterative solution.

[0043] (2) The present invention is applicable to a system using block pilots. Compared with continuous single-block pilots, the present invention can greatly reduce the number of pilots at the same accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Schematic diagram of a data frame structure with a block pilot structure in an embodiment of the present invention;

[0045] Figure 2 It is a processing flow chart of a method for estimating frequency offset of a communication system based on block pilot in an embodiment of the present invention;

[0046] Figure 3 Schematic diagram of a data frame structure with a continuous single-block pilot structure in an embodiment of the present invention;

[0047] Figure 4 Schematic diagram of length comparison between continuous pilot and block pilot at the same estimation accuracy in an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The following description combines specific illustrations to explain the technical solution so as to fully understand the present invention. However, the present invention can be implemented in many other ways different from those described herein, and similar generalized embodiments made by ordinary technicians in the field without creative work are all within the scope of protection of the present invention.

[0049] The terms used in this specification are for the purpose of describing specific embodiments only and are not intended to limit this specification. The singular forms of "a", "the" and "the" used in one or more embodiments of this specification and the appended claims are also intended to include plural forms unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used in one or more embodiments of this specification refers to and includes any or all possible combinations of one or more associated listed items.

[0050] The present invention is further described in detail below in conjunction with examples. This example illustrates a use of the present invention, but the implementation mode of the present invention is not limited thereto.

[0051] Embodiment 1:

[0052] Assume that the communication system data frame adopts Figure 1 In the structure shown, the block pilots are located at the beginning and the end of the data frame respectively, and the pilot blocks are of equal length and the pilot sequence has a constant modulus; the pilot length and distance are both calculated in units of the number of symbols.

[0053] A frequency offset estimation method for a communication system based on block pilot, such as Figure 2 As shown, the following steps are included:

[0054] S1, extract the received signals corresponding to the front and rear pilot blocks, fill the middle data part with zeros, and obtain the signal sequence y(n);

[0055] In this embodiment, the received data corresponding to the pilot symbol can be expressed as:

[0056]

[0057] Among them, A is the unknown signal amplitude, ω∈[-π,π] is the signal carrier frequency deviation, which is the parameter to be estimated. is the signal phase; is an unknown constant, and j is an imaginary symbol. z(n) is a complex Gaussian white noise with zero mean and unknown variance, and s(n) is a pilot symbol; the conjugate of the pilot symbol s(n) is multiplied by the corresponding received signal, and assuming that the modulus of the pilot symbol is 1, the signal sequence y(n) is obtained, as follows:

[0058]

[0059] y(n) takes non-zero values ​​in the range of 0≤n≤P-1, D+P≤n≤D+2P, and takes zero values ​​in other ranges, where n represents the timing, P represents the length of the pilot block, that is, the number of pilot symbols; and D represents the distance between two pilot blocks measured in the number of symbols.

[0060] S2. Calculate the N=D+2P discrete Fourier transform of the signal sequence y(n) to obtain the discrete spectrum Y(k), whose sample point interval is N is the length of the signal frame;

[0061] Search for the value Y(k) with the largest amplitude in the discrete spectrum Y(k) 0 ), the corresponding spectrum position is a rough estimate of the discrete spectrum Y(k), k 0 To roughly estimate the sequence number, record it as:

[0062] ω * =k 0 ω s (3).

[0063] S3. The theoretical discrete Fourier transform of the received signal can be expressed as

[0064]

[0065] Ignore the influence of noise for now.

[0066]

[0067] Among them, A is the signal amplitude, ω∈[-π,π] is the signal carrier frequency deviation, which is the parameter to be estimated; is the signal phase; are all unknown constants, and j is the imaginary number sign.

[0068] S4, constructing an objective function for frequency offset estimation, and obtaining a frequency offset estimation result by solving the minimum value of the objective function;

[0069] Let U(k,ω)=|P(k,ω)| 2 , represents the theoretical ideal energy spectrum. The criterion for frequency offset estimation is to make the theoretical ideal energy spectrum and the actual energy spectrum as consistent as possible, and construct an objective function with frequency offset ω as an unknown parameter:

[0070]

[0071] The above formula uses all spectral lines for calculation, which is quite complex. 0 Therefore, the above calculation can only take k 0 The nearby spectral lines are used to replace them and the following simplified objective function is constructed:

[0072]

[0073] where |Y(k)| 2 The square of the absolute value of the Fourier transform result Y(k) in claim 4 is called the energy spectrum of y(n); Q is a given positive integer ranging from 1 to 3.

[0074] Solve the minimum value of the objective function used for frequency offset estimation and obtain the frequency offset estimation result The minimum value of J(ω) can be solved by classical mathematical methods, for example, taking the rough estimate of formula (3) as the initial value and using the gradient descent method for iterative solution.

[0075] Embodiment 2:

[0076] The iterative solution method has high computational complexity and its convergence characteristics are difficult to predict. In Example 2, the present invention introduces a method that does not require iterative calculation. Based on formula (3), the real frequency deviation can be expressed as ω=ω * +ω α , where ω α The value is It can be seen that the estimation of the real frequency offset is equivalent to the estimation of ω α Next, consider the estimation of ω α Estimates.

[0077] Formula (5) can be expressed as

[0078]

[0079] Notice

[0080]

[0081] Therefore, the ideal energy spectrum can be expressed as

[0082]

[0083] Because α is very small, U(k,ω) is in ω * Approximate by Taylor expansion, we get

[0084] U(k,ω)=U(k,ω * )+ω α U ′ (k,ω * ) (11)

[0085] in Substituting (11) into (10) yields

[0086]

[0087] Where a = 4A 2 , c = 4A 2 ω αIt is related to the amplitude and the residual frequency. Without loss of generality, we only consider Q = 1. To obtain the optimal solution for a and c, we set the partial derivatives of the approximate error with respect to a and c to zero, that is,

[0088]

[0089]

[0090] After calculation, the frequency estimation expression is obtained

[0091]

[0092] where w u (k) and w v (k) is the energy spectrum weighting coefficient. Definition

[0093] p=[P 0 (-1),P 0 (0),P 0 (1)] T (16)

[0094] p′=[P 0 ′(-1),P 0 ′(0),P 0 ′(1)] T (17)

[0095] y=[|Y -1 | 2 ,|Y 0 | 2 ,|Y 1 | 2 ] T (18)

[0096] definition

[0097] ε=p T p (19)

[0098] β=p′ T p (20)

[0099] τ=p′ T p′ (21)

[0100] in

[0101]

[0102]

[0103]

[0104] Solving (13) and (14) and rearranging them, we can obtain

[0105]

[0106]

[0107] The optimal weighting coefficient is

[0108] w u (k) = (εP′ 0 (k)-βP 0 (k)) (26)

[0109] w v (k)=(τP 0 (k)-βP′ 0 (k)) (27)

[0110] Since p is even symmetric and p′ is odd symmetric, β = 0, so we have

[0111]

[0112]

[0113] From this we can get

[0114] w u (k)=εP′0(k) (30)

[0115] w v (k) = τP 0 (k) (31)

[0116] Substituting (17) and (18) into (11), we can get the frequency estimator expression as

[0117]

[0118] In calculating ω α Then, based on formula (3) and ω = ω * +ω α The final frequency offset estimation can be obtained.

[0119] Embodiment 3:

[0120] In this embodiment, the objective function is applied to the continuous single-block pilots, that is, Figure 3 The pilot results shown in FIG. 1 are the methods reported in the existing literature and the block pilot method proposed in the present invention. The number of pilot symbols required by the two methods is compared under the same accuracy requirement. The comparison results are shown in FIG. Figure 4 Compared with continuous single-block pilots, the system using block pilots proposed by the present invention can greatly reduce the number of pilots under the same accuracy.

[0121] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

[0122] The preferred embodiments of the present application disclosed above are only used to help understand the present invention and its core ideas. For those skilled in the art, according to the ideas of the present invention, there will be changes in specific application scenarios and implementation operations, and this specification should not be interpreted as limiting the present invention. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A method for estimating frequency offset of a communication system based on block pilot, characterized in that: The following steps are involved: S1, extract the received signals corresponding to the front and rear pilot blocks, fill the middle data part with zeros, and obtain the signal sequence y(n); S2. Calculate the N = D + 2P discrete Fourier transform of y(n), obtain the discrete spectrum Y(k), and search for the value with the largest amplitude in Y(k); S3. Construct an ideal signal function including unknown parameters; construct the following ideal signal function including unknown parameters, as follows: Among them, A is the signal amplitude, ω∈[-π,π] is the signal carrier frequency deviation, which is the parameter to be estimated; is the signal phase; they are all unknown constants, j is the imaginary number sign; S4. Construct an objective function for frequency offset estimation, and obtain the frequency offset estimation result by solving the minimum value of the objective function; let U(k,ω)=|P(k,ω)| 2 , construct the following objective function for frequency offset estimation: where |Y(k)| 2 is the square of the absolute value of the discrete spectrum Y(k), called the energy spectrum of y(n); Q is a given positive integer ranging from 1 to 3; Solve the minimum value of the objective function used for frequency offset estimation and obtain the frequency offset estimation result A method for solving the minimum value without iterative solution is used to solve the minimum value of the objective function of frequency offset estimation, as follows: remember is a rough estimate of the frequency deviation. The actual frequency deviation is expressed as ω = ω * +ω α , where ω α is the offset to be estimated; because ω α The value of is relatively small, U(k,ω) is * Approximate by Taylor expansion, we get U(k,ω)=U(k,ω * )+ω α U′(k,ω * ) in, remember p=[U(k0-Q,ω * ),…,U(k0,ω * ),…,U(k0+Q,ω * )] T p′=[U′(k0-Q,ω * ),…,U′(k0,ω * ),…,U′(k0+Q,ω * )] T y=[|Y(k0-Q)| 2 ,…,|Y(k0)| 2 ,…,|Y(k0+Q)| 2 ] T Calculate the following intermediate variables: e=p T p β=p′ T p τ=p′ T p′ Among them, ε, β, τ, a and c are all intermediate variables; According to the intermediate variables, the final frequency offset estimation result is obtained as follows:

2. A method for estimating frequency offset of a communication system based on block pilot according to claim 1, characterized in that: The block pilots are located at the beginning and end of the data frame respectively, and the pilot blocks are of equal length and the pilot sequence has a constant modulus.

3. The method for estimating frequency offset of a communication system based on block pilot according to claim 1, characterized in that: In step S1, the conjugate of the pilot symbol is multiplied by the corresponding received signal to obtain a signal sequence y(n), where y(n) takes non-zero values ​​in the range of 0≤n≤P-1, D+P≤n≤D+2P and takes zero values ​​in other ranges, wherein n represents the timing, P represents the length of the pilot block, that is, the number of pilot symbols; and D represents the distance between two pilot blocks measured in terms of the number of symbols.

4. The method for estimating frequency offset of a communication system based on block pilot according to claim 1, characterized in that: In step S2, the N=D+2P point discrete Fourier transform of the signal sequence y(n) is calculated to obtain a discrete spectrum Y(k); wherein N is the length of the signal frame; Search for the value Y(k0) with the largest amplitude in the discrete spectrum Y(k), and the corresponding spectrum position is the rough estimate of the discrete spectrum Y(k), and k0 is the rough estimate sequence number.

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