CN110099437B - Frequency offset estimation method and device of GSM system and mobile terminal - Google Patents

Frequency offset estimation method and device of GSM system and mobile terminal Download PDF

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CN110099437B
CN110099437B CN201810085075.2A CN201810085075A CN110099437B CN 110099437 B CN110099437 B CN 110099437B CN 201810085075 A CN201810085075 A CN 201810085075A CN 110099437 B CN110099437 B CN 110099437B
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茆晓军
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Spreadtrum Communications Shanghai Co Ltd
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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
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W56/00—Synchronisation arrangements
    • H04W56/0035—Synchronisation arrangements detecting errors in frequency or phase
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
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Abstract

The invention provides a frequency offset estimation method and device of a GSM system and a mobile terminal. The frequency offset estimation method provided by the invention considers two constraint conditions of the phase difference delta phi ' (k) with the symbol interval of k and the difference value between the phase difference delta phi ' (k) with the current symbol interval of k and the adjacent phase difference delta phi ' (k +1) at the same time, and determines the positive and negative of the frequency offset according to the position relation between the two adjacent phase differences. The invention can improve the frequency offset estimation range, so that the value of the symbol interval can be further increased, thereby reducing the deviation of frequency offset estimation and overcoming the phase ambiguity problem in the prior art.

Description

Frequency offset estimation method and device of GSM system and mobile terminal
Technical Field
The present invention relates to the field of communications technologies, and in particular, to a frequency offset estimation method and apparatus for a GSM system, and a mobile terminal.
Background
In the GSM system, a precondition for normal communication between a mobile station and a base station of a serving cell is to achieve frequency Synchronization and time Synchronization between the mobile station and the base station, and specifically, the mobile station must acquire frequency and time Synchronization with the base station through a frequency Correction signal fcch (frequency Correction Channel) and a Synchronization Channel SCH (Synchronization Channel) to perform normal communication.
The frequency correction channel FCCH is used to transmit a frequency correction signal (i.e., FCCH signal) to the mobile station to cause the mobile station to perform frequency offset correction based on the received FCCH signal so that the mobile station can tune to the corresponding frequency, wherein the frequency correction signal is a sinusoidal signal having a frequency of 66.7 kHz. The existing frequency offset estimation method of the GSM system is as follows:
ideally, the phase of the FCCH received signal is:
Figure BDA0001562174610000011
wherein, Ts＝1/f s1/270.833kbps, one symbol period.
But the actual environment has phase noise epsilonnAssuming that the frequency offset of the received signal is Δ f, the FCCH received signal can be expressed as:
Figure BDA0001562174610000012
let t equal to iTsThen the discrete form of the FCCH received signal is:
Figure BDA0001562174610000013
to phi (i) in turn
Figure BDA0001562174610000014
After the phase compensation, the following can be obtained:
φ‘(i)＝φ0+2πΔf·Ts·i+εn(i)；
the phase difference with symbol interval k is:
Δφ‘(k)＝φ’(i+k)-φ‘(i)＝2πΔf·k·Ts+εn(i+k)-εn(i)；
assuming that the phase noise is white noise characterized, then εn(i+k)-εn(i) Is a white noise with an average value of 0 independent of k and i, and is set as EnThen the frequency offset estimate is
Figure BDA0001562174610000021
Wherein E isn/(2π·k·Ts) For the noise term of the frequency offset estimation, it can be seen that the symbol interval k should take a larger value as possible to reduce the deviation of the frequency offset estimation, but in practical application, the above calculation formula of the frequency offset estimation value needs to satisfy the following condition: Δ φ' (k) e [ - π, π]Otherwise, phase ambiguity exists, as shown in FIG. 1, which is an illustrative schematic diagram of phase ambiguity, when the positive frequency phase difference Δ φ ' (k) (shown as a solid line) falls in quadrant 3 or quadrant 4 (i.e., Δ φ ' (k) is greater than π), since Δ φ ' (k) e [ - π, π [ - π []The positive frequency phase difference is treated as a negative frequency phase difference (as shown by the dashed line).
Disclosure of Invention
The frequency offset estimation method, the frequency offset estimation device and the mobile terminal of the GSM system can improve the frequency offset estimation range, so that the value of the symbol interval can be further increased, the deviation of frequency offset estimation can be reduced, and the phase ambiguity problem in the prior art is also overcome.
In a first aspect, the present invention provides a frequency offset estimation method for a GSM system, including:
sequentially carrying out the phase of the FCCH discrete signal
Figure BDA0001562174610000022
Phase compensation of (2):
φ‘(i)＝φ0+2πΔf·Ts·i+εn(i)；
wherein,
Figure BDA0001562174610000023
phi (i) is the FCCH discrete signal, phi0To an initial phase, TsIs the symbol period, Δ f is the frequency offset, ε, of the FCCH received signaln(i) Phase noise existing in the actual environment;
calculating the phase difference between two FCCH discrete signals with symbol interval k:
Δφ‘(k)＝φ’(i+k)-φ‘(i)＝2πΔf·k·Ts+En；
wherein E isn＝εn(i+k)-εn(i) Is white noise with an average value of 0 independent of k and i, and k is greater than 1;
calculating a difference between the phase difference Δ φ '(k) for the current symbol interval k and the adjacent phase difference Δ φ' (k + 1):
Δφ‘(k+1)-Δφ‘(k)＝2π·Δf·Ts；
calculating a frequency offset estimation value:
Figure BDA0001562174610000031
wherein, the frequency offset estimation value satisfies the following two constraint conditions:
1) the phase difference with symbol interval k is less than 2 pi, namely | delta phi' (k) | < 2 pi;
2) the difference value between two adjacent phase differences is less than pi, namely | delta phi '(k +1) -delta phi' (k) | < pi;
and determining the positive and negative of the frequency deviation estimated value according to the position relation of two adjacent phase differences.
Optionally, the determining the positive or negative of the frequency offset estimation value according to the position relationship between two adjacent phase differences includes:
if the phase difference delta phi ' (k) with the current symbol interval of k is positioned above the adjacent phase difference delta phi ' (k +1), the phase difference delta phi ' (k) with the current symbol interval of k is formed by positive frequency offset, so that the corresponding frequency offset is determined to be positive frequency offset;
if the phase difference Δ φ ' (k) of the current symbol interval k is located below the phase difference Δ φ ' (k +1) adjacent thereto, the phase difference Δ φ ' (k) of the current symbol interval k is formed from a negative frequency offset, thereby determining that the corresponding frequency offset is a negative frequency offset.
Optionally, the phase of the FCCH discrete signal is sequentially performed
Figure BDA0001562174610000032
Before the phase compensation, the method further comprises:
extracting a Frequency Correction Channel (FCCH) received signal
Figure BDA0001562174610000033
Wherein phi is0To an initial phase, TsIs the symbol period, Δ f is the frequency offset, ε, of the FCCH received signaln(t) is the phase noise present in the actual environment;
performing discrete processing on the FCCH received signal to obtain an FCCH discrete signal:
Figure BDA0001562174610000041
in a second aspect, the present invention provides a frequency offset estimation apparatus for a GSM system, including:
a phase compensation module for sequentially performing the phase of the FCCH discrete signal
Figure BDA0001562174610000042
The phase compensation formula is as follows: phi' (i) being phi0+2πΔf·Ts·i+εn(i)；
Wherein,
Figure BDA0001562174610000043
phi (i) is the FCCH discrete signal, phi0To an initial phase, TsIs the symbol period, Δ f is the frequency offset, ε, of the FCCH received signaln(i) Phase noise existing in the actual environment;
a phase difference calculating module, configured to calculate a phase difference between two FCCH discrete signals with a symbol interval of k, where the phase difference calculating formula is: Δ Φ ' (k) ═ Φ ' (i + k) - Φ ' (i) ═ 2 pi Δ f · k · Ts+En；
Wherein E isn＝εn(i+k)-εn(i) Is white noise with an average value of 0 independent of k and i, and k is greater than 1;
and an adjacent phase difference value calculating module, configured to calculate a difference value between the phase difference Δ Φ '(k) with the current symbol interval k and the adjacent phase difference Δ Φ' (k + 1): Δ φ '(k +1) - Δ φ' (k) ═ 2 π Δ f · Ts；
A first frequency offset calculation module, configured to calculate a frequency offset estimation value:
Figure BDA0001562174610000044
wherein, the frequency offset estimation value satisfies the following two constraint conditions:
1) the phase difference with symbol interval k is less than 2 pi, namely | delta phi' (k) | < 2 pi;
2) the difference value between two adjacent phase differences is less than pi, namely | delta phi '(k +1) -delta phi' (k) | < pi;
and the second frequency offset calculation module is used for determining the positive and negative of the frequency offset estimation value according to the position relation of two adjacent phase differences.
Optionally, the second frequency offset calculating module is configured to determine that the phase difference Δ Φ ' (k) with the current symbol interval k is formed by a positive frequency offset when the phase difference Δ Φ ' (k) with the current symbol interval k is located above the adjacent phase difference Δ Φ ' (k +1), so as to determine that the corresponding frequency offset is a positive frequency offset; and determining that the phase difference delta phi ' (k) of the current symbol interval k is formed by a negative frequency offset when the phase difference delta phi ' (k) of the current symbol interval k is located below the phase difference delta phi ' (k +1) adjacent thereto, thereby determining that the corresponding frequency offset is a negative frequency offset.
Optionally, the apparatus further comprises:
a signal extraction module for extracting a Frequency Correction Channel (FCCH) receiving signal
Figure BDA0001562174610000051
Wherein phi is0To an initial phase, TsIs the symbol period, Δ f is the frequency offset, ε, of the FCCH received signaln(t) is the phase noise present in the actual environment;
a discrete processing module for performing discrete processing on the FCCH received signal to obtain an FCCH discrete signal
Figure BDA0001562174610000052
In a third aspect, the present invention provides a mobile terminal, where the user equipment includes the frequency offset estimation apparatus of the GSM system.
The frequency offset estimation method, the device and the mobile terminal of the GSM system provided by the embodiment of the invention simultaneously consider two constraint conditions of the phase difference delta phi ' (k) with the symbol interval of k and the difference value between the phase difference delta phi ' (k) with the current symbol interval of k and the adjacent phase difference delta phi ' (k +1), and determine the positive and negative of the frequency offset according to the position relationship between the two adjacent phase differences. Compared with the prior art, the method can improve the frequency offset estimation range, namely, the original delta phi '(k) epsilon [ -pi, pi ] is changed into delta phi' (k) epsilon [ -2 pi, 2 pi ], so that the value of the symbol interval can be further increased, the deviation of frequency offset estimation can be reduced, and the phase ambiguity problem in the prior art is also solved.
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FIG. 1 is a schematic diagram illustrating phase ambiguity in the prior art;
FIG. 2 is a flowchart of a frequency offset estimation method of a GSM system according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating the determination of the sign of a frequency offset estimation value according to the position relationship between two adjacent phase differences;
fig. 4 is a schematic structural diagram of a frequency offset estimation apparatus of a GSM system according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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.
The invention provides a frequency offset estimation method of a GSM system, as shown in FIG. 2, the method comprises:
s11, sequentially carrying out the phase of the FCCH discrete signal
Figure BDA0001562174610000061
Phase compensation of (2):
φ‘(i)＝φ0+2πΔf·Ts·i+εn(i) wherein
Figure BDA0001562174610000062
phi (i) is the FCCH discrete signal, phi0To an initial phase, TsIs the symbol period, Δ f is the frequency offset, ε, of the FCCH received signaln(i) Is the phase noise present in the actual environment.
S12, calculating the phase difference between two FCCH discrete signals with symbol interval k:
Δφ‘(k)＝φ’(i+k)-φ‘(i)＝2πΔf·k·Ts+Enwherein E isn＝εn(i+k)-εn(i) Is white noise with an average of 0 independent of k and i, and k is greater than 1.
S13, calculating a difference between the phase difference Δ Φ '(k) of the current symbol interval k and the adjacent phase difference Δ Φ' (k + 1): Δ φ '(k +1) - Δ φ' (k) ═ 2 π Δ f · Ts。
S14, calculating a frequency offset estimation value:
Figure BDA0001562174610000063
wherein, the frequency offset estimation value satisfies the following two constraint conditions:
1) the phase difference with symbol interval k is less than 2 pi, namely | delta phi' (k) | < 2 pi;
2) the difference between two adjacent phase differences is less than pi, i.e., | Δ φ '(k +1) - Δ φ' (k) | < pi.
S15, determining the positive and negative of the frequency deviation estimated value according to the position relation of two adjacent phase differences.
The frequency offset estimation method of the GSM system provided in the embodiment of the present invention considers two constraint conditions of the phase difference Δ Φ ' (k) with the symbol interval k and the difference between the phase difference Δ Φ ' (k) with the current symbol interval k and the adjacent phase difference Δ Φ ' (k +1) at the same time, and determines the positive and negative of the frequency offset according to the position relationship between the two adjacent phase differences. Compared with the prior art, the method can improve the frequency offset estimation range, namely, the original delta phi '(k) epsilon [ -pi, pi ] is changed into delta phi' (k) epsilon [ -2 pi, 2 pi ], so that the value of the symbol interval can be further increased, the deviation of frequency offset estimation can be reduced, and the phase ambiguity problem in the prior art is also solved.
As shown in fig. 3, the determining the positive or negative of the frequency offset estimation value according to the position relationship between two adjacent phase differences includes:
as shown in the left diagram, if the phase difference Δ Φ ' (k) of the current symbol interval k is located above the phase difference Δ Φ ' (k +1) adjacent thereto, the phase difference Δ Φ ' (k) of the current symbol interval k is formed by a positive frequency offset, thereby determining that the corresponding frequency offset is a positive frequency offset;
as shown in the right diagram, if the phase difference Δ Φ ' (k) of the current symbol interval k is located below the phase difference Δ Φ ' (k +1) adjacent thereto, the phase difference Δ Φ ' (k) of the current symbol interval k is formed by a negative frequency offset, thereby determining that the corresponding frequency offset is a negative frequency offset.
Further, before the step S11, the method further includes the following steps:
1) extracting a Frequency Correction Channel (FCCH) received signal
Figure BDA0001562174610000074
Wherein phi is0To an initial phase, TsIs the symbol period, Δ f is the frequency offset, ε, of the FCCH received signaln(t) is the phase noise present in the actual environment;
2) performing discrete processing on the FCCH received signal to obtain an FCCH discrete signal:
Figure BDA0001562174610000071
an embodiment of the present invention further provides a frequency offset estimation apparatus of a GSM system, as shown in fig. 4, the apparatus includes a phase compensation module, a phase difference calculation module, an adjacent phase difference calculation module, a first frequency offset calculation module, and a second frequency offset calculation module.
The phase compensation module is used for sequentially carrying out phase compensation on the FCCH discrete signals
Figure BDA0001562174610000072
The phase compensation formula is as follows: phi' (i) being phi0+2πΔf·Ts·i+εn(i)；
Wherein,
Figure BDA0001562174610000073
phi (i) is the FCCH discrete signal, phi0To an initial phase, TsIs the symbol period, Δ f is the frequency offset, ε, of the FCCH received signaln(i) Phase noise existing in the actual environment;
the phase difference calculating module is used for calculating two FCCH discrete signals with symbol interval of kA phase difference between the signals, the phase difference being calculated by: Δ Φ ' (k) ═ Φ ' (i + k) - Φ ' (i) ═ 2 pi Δ f · k · Ts+En；
Wherein E isn＝εn(i+k)-εn(i) Is white noise with an average value of 0 independent of k and i, and k is greater than 1;
the adjacent phase difference calculating module is used for calculating the difference value between the phase difference delta phi '(k) with the current symbol interval being k and the adjacent phase difference delta phi' (k + 1): Δ φ '(k +1) - Δ φ' (k) ═ 2 π Δ f · Ts；
The first frequency offset calculation module is configured to calculate a frequency offset estimation value:
Figure BDA0001562174610000081
wherein, the frequency offset estimation value satisfies the following two constraint conditions:
1) the phase difference with symbol interval k is less than 2 pi, namely | delta phi' (k) | < 2 pi;
2) the difference value between two adjacent phase differences is less than pi, namely | delta phi '(k +1) -delta phi' (k) | < pi;
and the second frequency offset calculation module is used for determining the positive and negative of the frequency offset estimation value according to the position relationship of two adjacent phase differences.
The frequency offset estimation device of the GSM system provided in the embodiment of the present invention considers two constraint conditions of the phase difference Δ Φ ' (k) with the symbol interval k and the difference between the phase difference Δ Φ ' (k) with the current symbol interval k and the adjacent phase difference Δ Φ ' (k +1) at the same time, and determines the positive and negative of the frequency offset according to the position relationship between the two adjacent phase differences. Compared with the prior art, the method can improve the frequency offset estimation range, namely, the original delta phi '(k) epsilon [ -pi, pi ] is changed into delta phi' (k) epsilon [ -2 pi, 2 pi ], so that the value of the symbol interval can be further increased, the deviation of frequency offset estimation can be reduced, and the phase ambiguity problem in the prior art is also solved.
Optionally, the second frequency offset calculating module is configured to determine that the phase difference Δ Φ ' (k) with the current symbol interval k is formed by a positive frequency offset when the phase difference Δ Φ ' (k) with the current symbol interval k is located above the adjacent phase difference Δ Φ ' (k +1), so as to determine that the corresponding frequency offset is a positive frequency offset; and determining that the phase difference delta phi ' (k) of the current symbol interval k is formed by a negative frequency offset when the phase difference delta phi ' (k) of the current symbol interval k is located below the phase difference delta phi ' (k +1) adjacent thereto, thereby determining that the corresponding frequency offset is a negative frequency offset.
Optionally, the apparatus further comprises a signal extraction module and a discrete processing module.
The signal extraction module is used for extracting a Frequency Correction Channel (FCCH) receiving signal, wherein the FCCH receiving signal is
Figure BDA0001562174610000091
Wherein phi is0To an initial phase, TsIs the symbol period, Δ f is the frequency offset, ε, of the FCCH received signaln(t) is the phase noise present in the actual environment;
the discrete processing module is used for performing discrete processing on the FCCH received signal to obtain an FCCH discrete signal
Figure BDA0001562174610000092
The embodiment of the invention also provides a mobile terminal, and the user equipment comprises the frequency offset estimation device of the GSM system.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (5)

1. A method for estimating frequency offset in a GSM system, comprising:
sequentially carrying out the phase of the FCCH discrete signal
Figure FDA0003037219140000011
Phase compensation of (2):
φ‘(i)＝φ0+2πΔf·Ts·i+εn(i)；
wherein,
Figure FDA0003037219140000012
phi (i) is the FCCH discrete signal, phi0To an initial phase, TsIs the symbol period, Δ f is the frequency offset, ε, of the FCCH received signaln(i) I is a natural number greater than or equal to 1, which is phase noise existing in an actual environment;
calculating the phase difference between two FCCH discrete signals with symbol interval k:
Δφ‘(k)＝φ’(i+k)-φ‘(i)＝2πΔf·k·Ts+En；
wherein E isn＝εn(i+k)-εn(i) Is white noise with an average value of 0 independent of k and i, and k is greater than 1;
calculating a difference between the phase difference Δ φ '(k) for the current symbol interval k and the adjacent phase difference Δ φ' (k + 1):
Δφ‘(k+1)-Δφ‘(k)＝2π·Δf·Ts；
calculating a frequency offset estimation value:
Figure FDA0003037219140000013
wherein, the frequency offset estimation value satisfies the following two constraint conditions:
1) symbolThe phase difference at the interval k being less than 2 pi, i.e.
Figure FDA0003037219140000014
2) The difference between two adjacent phase differences being less than pi, i.e.
Figure FDA0003037219140000015
Determining the positive and negative of the frequency deviation estimated value according to the position relation of two adjacent phase differences;
the determining the positive and negative of the frequency deviation estimated value according to the position relationship of the two adjacent phase differences comprises: if the phase difference delta phi ' (k) with the current symbol interval of k is positioned above the adjacent phase difference delta phi ' (k +1), the phase difference delta phi ' (k) with the current symbol interval of k is formed by positive frequency offset, so that the corresponding frequency offset is determined to be positive frequency offset; if the phase difference Δ φ ' (k) of the current symbol interval k is located below the phase difference Δ φ ' (k +1) adjacent thereto, the phase difference Δ φ ' (k) of the current symbol interval k is formed from a negative frequency offset, thereby determining that the corresponding frequency offset is a negative frequency offset.
2. The method according to claim 1, wherein the phase of the FCCH discrete signal is sequentially performed
Figure FDA0003037219140000021
Before the phase compensation, the method further comprises:
extracting a Frequency Correction Channel (FCCH) received signal
Figure FDA0003037219140000022
Wherein phi is0To an initial phase, TsIs the symbol period, Δ f is the frequency offset, ε, of the FCCH received signaln(t) is the phase noise present in the actual environment;
performing discrete processing on the FCCH received signal to obtain an FCCH discrete signal:
Figure FDA0003037219140000023
3. a frequency offset estimation apparatus of a GSM system, comprising:
a phase compensation module for sequentially performing the phase of the FCCH discrete signal
Figure FDA0003037219140000024
The phase compensation formula is as follows: phi' (i) being phi0+2πΔf·Ts·i+εn(i)；
Wherein,
Figure FDA0003037219140000025
phi (i) is the FCCH discrete signal, phi0To an initial phase, TsIs the symbol period, Δ f is the frequency offset, ε, of the FCCH received signaln(i) I is a natural number greater than or equal to 1, which is phase noise existing in an actual environment;
a phase difference calculating module, configured to calculate a phase difference between two FCCH discrete signals with a symbol interval of k, where the phase difference calculating formula is: Δ Φ ' (k) ═ Φ ' (i + k) - Φ ' (i) ═ 2 pi Δ f · k · Ts+En；
Wherein E isn＝εn(i+k)-εn(i) Is white noise with an average value of 0 independent of k and i, and k is greater than 1;
and an adjacent phase difference value calculating module, configured to calculate a difference value between the phase difference Δ Φ '(k) with the current symbol interval k and the adjacent phase difference Δ Φ' (k + 1): Δ φ '(k +1) - Δ φ' (k) ═ 2 π Δ f · Ts；
A first frequency offset calculation module, configured to calculate a frequency offset estimation value:
Figure FDA0003037219140000026
wherein, the frequency offset estimation value satisfies the following two constraint conditions:
1) the phase difference being less than 2 pi with a symbol interval k, i.e.
Figure FDA0003037219140000027
2) The difference between two adjacent phase differences being less than pi, i.e.
Figure FDA0003037219140000028
The second frequency offset calculation module is used for determining the positive and negative of the frequency offset estimation value according to the position relation of two adjacent phase differences;
the second frequency offset calculating module is further configured to determine that the phase difference Δ Φ ' (k) with the current symbol interval k is formed by positive frequency offset when the phase difference Δ Φ ' (k) with the current symbol interval k is located above the phase difference Δ Φ ' (k +1) adjacent to the current symbol interval k, so as to determine that the corresponding frequency offset is positive frequency offset; and determining that the phase difference delta phi ' (k) of the current symbol interval k is formed by a negative frequency offset when the phase difference delta phi ' (k) of the current symbol interval k is located below the phase difference delta phi ' (k +1) adjacent thereto, thereby determining that the corresponding frequency offset is a negative frequency offset.
4. The apparatus of claim 3, further comprising:
a signal extraction module for extracting a Frequency Correction Channel (FCCH) receiving signal
Figure FDA0003037219140000031
Wherein phi is0To an initial phase, TsIs the symbol period, Δ f is the frequency offset, ε, of the FCCH received signaln(t) is the phase noise present in the actual environment;
a discrete processing module for performing discrete processing on the FCCH received signal to obtain an FCCH discrete signal
Figure FDA0003037219140000032
5. A mobile terminal, characterized in that it comprises the frequency offset estimation means of the GSM system of any one of claims 3 to 4.
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