CN106254046B - Method for selecting length of pilot symbol signal - Google Patents

Method for selecting length of pilot symbol signal Download PDF

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CN106254046B
CN106254046B CN201510308682.7A CN201510308682A CN106254046B CN 106254046 B CN106254046 B CN 106254046B CN 201510308682 A CN201510308682 A CN 201510308682A CN 106254046 B CN106254046 B CN 106254046B
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signal
prefix
sampling
time domain
preamble symbol
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CN106254046A (en
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张文军
徐洪亮
史毅俊
管云峰
郭序峰
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Shanghai National Engineering Research Center of Digital Television Co Ltd
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Priority to CN201710091674.0A priority patent/CN106936757B/en
Priority to CN201710090760.XA priority patent/CN107017976B/en
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00Arrangements affording multiple use of the transmission path
    • H04L5/003Arrangements for allocating sub-channels of the transmission path
    • H04L5/0048Allocation of pilot signals, i.e. of signals known to the receiver
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/26Systems using multi-frequency codes
    • H04L27/2601Multicarrier modulation systems
    • H04L27/2602Signal structure
    • H04L27/261Details of reference signals
    • H04L27/2613Structure of the reference signals
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/26Systems using multi-frequency codes
    • H04L27/2601Multicarrier modulation systems
    • H04L27/2647Arrangements specific to the receiver only
    • H04L27/2655Synchronisation arrangements
    • H04L27/2689Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation
    • H04L27/2692Link with other circuits, i.e. special connections between synchronisation arrangements and other circuits for achieving synchronisation with preamble design, i.e. with negotiation of the synchronisation sequence with transmitter or sequence linked to the algorithm used at the receiver

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  • Engineering & Computer Science (AREA)
  • Signal Processing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Synchronisation In Digital Transmission Systems (AREA)
  • Transmission Systems Not Characterized By The Medium Used For Transmission (AREA)

Abstract

The invention provides a method for selecting the signal length of a leading symbol, which is used for a multi-sampling rate system with different sampling frequencies of the leading symbol and the corresponding data symbol, and is characterized by comprising the following steps: the length of the signal corresponding to the time domain main signal, the suffix or prefix and the prefix in the preamble symbol without sampling frequency conversion is selected based on all different sampling frequencies in the multi-sampling rate system, thereby ensuring that the selected time domain structure can avoid signal distortion caused by the incomplete division of the number of sampling points when sampling rate conversion is carried out in the multi-sampling rate broadcast communication system.

Description

Method for selecting length of pilot symbol signal
Technical Field
The present invention relates to preamble symbols of a physical frame in a broadcast communication system, and more particularly, to a method for selecting a time domain structure of preamble symbols suitable for multiple sampling frequencies, especially a method for selecting a signal length.
Background
The preamble symbol plays an important role in broadcast and communication systems, and is an indispensable part in system discovery, timing synchronization, channel estimation and signaling transmission. Therefore, the preamble symbols are required to have high robustness and extremely low detection threshold. DVB-T2 uses a three-segment structured time domain symbol but is not suitable for coherent detection due to the absence of a cyclic prefix. Accordingly, those skilled in the relevant art will recognize that a three-segment time domain structure with a cyclic prefix structure can solve the above-mentioned deficiencies.
When the time domain symbol with the three-segment structure is used in a multi-sampling frequency broadcast communication system, the sampling rate of the preamble symbol is different from that of other data symbols in the system. After the preamble symbol is generated, sampling rate conversion needs to be performed first to make the sampling rates of the preamble symbol and other symbols uniform, and then the sampling rates are sent to the digital-to-analog converter for output.
However, because the three-segment time domain structure design does not consider the process of conversion processing due to different sampling rates, the number of sampling points after sampling rate conversion may be non-integer, and therefore, rounding operation needs to be performed on the number of sampling points, and once rounding operation is performed, the problem of signal distortion may be caused.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method for selecting signal length in preamble symbol, which aims to avoid the above distortion problem when sampling rate conversion is performed on the specific time domain structure, i.e. the time domain main signal, the suffix or prefix and the prefix, so that the method is suitable for being used in a multisampling frequency broadcast communication system.
The invention provides a method for selecting the signal length of a leading symbol, which is used for a multi-sampling rate system with different sampling frequencies of the leading symbol and the corresponding data symbol, and is characterized by comprising the following steps: the length of the preamble symbols corresponding to the time domain body signal, suffix or prefix and prefix, without sample frequency translation, is selected based on all the different sampling frequencies in the multiple sampling rate system.
Further, when the lengths of the signals corresponding to the first three parts without sample rate conversion are selected, the method comprises the following steps: according to all different sampling frequencies in the multi-sampling rate system, the preset basic frequency is determined based on the following conditions: all different sampling frequencies can be obtained by multiplying the same basic frequency by a plurality of corresponding integer multiples; selecting an integer multiple corresponding to the sampling frequency of the preamble symbol from a plurality of integer multiples as a reference multiple; and designing the lengths of signals corresponding to the time domain main body signal, the suffix or prefix and the prefix in the preamble symbols which are not subjected to sampling rate conversion to be integral multiples of the reference multiple.
Further, the greatest common divisor between all the integer multiples multiplied by the same predetermined basic frequency is a positive integer greater than or equal to 1.
Further, wherein the length of the time domain body signal is selected to be an integer power of the value 2.
Further, the length of the suffix or the super prefix is less than or equal to the length of the prefix.
Further, wherein the preamble symbol comprises: based on the time domain main signal, the suffix or the prefix and the prefix respectively formed by the signals with the selected lengths, when the sampling frequency of the preamble symbol needs to be converted into the sampling frequency of the data symbol, the signal lengths of the time domain main signal, the suffix or the prefix and the prefix in the preamble symbol after the sampling rate conversion are all integers.
Further, the lengths of the time domain body signal, the suffix or prefix and the prefix respectively correspond to 2048 points, 496 points and 528 points.
Further, the preamble symbol comprises at least one three-segment structured time domain symbol, the three-segment structured time domain symbol comprising a first partial signal being a time domain main signal, a second partial signal being a postfix or a superpacket of the first partial signal based on the partial time domain main signal, and a third partial signal being a prefix of the first partial signal based on the partial time domain main signal.
Further, the preamble symbol with the first sampling rate is processed into an equivalent signal with the second sampling rate by the following method, and the concatenation in the time domain is realized with the data symbol with the second sampling rate: time domain resampling method: resampling the sampling signal of the preamble symbol; or frequency domain direct transform: filling zeros at two sides of the frequency domain main body signal with the first sampling rate, and then performing IFFT to obtain a time domain main body signal which needs to be sampled and has a second sampling rate; then according to the original prefix, suffix or super prefix selecting rule respectively from the time domain main signal to be sampled selecting the sampling point of the specific length, after the proper phase shift, the time domain main signal is spliced to form the preamble symbol, the specific length is: the length of the original prefix, suffix or prefix is divided by the first sampling rate and multiplied by the second sampling rate.
Further, in the time domain resampling method: the interpolation coefficient and the extraction coefficient used in resampling are respectively the integral multiple corresponding to the sampling frequency of the preamble symbol and the integral multiple corresponding to the sampling frequency of the data symbol, so that the number of waveforms obtained after resampling is an integer; in the frequency domain direct transform method: the number of zeros to be zero-padded is obtained by multiplying the length of the time domain subject signal by a predetermined coefficient, which is a positive integer, and the predetermined coefficient is determined by a ratio between a difference obtained by subtracting the sampling frequency of the preamble symbol from the sampling frequency of the data symbol and the sampling frequency of the preamble symbol; the length of the prefix, suffix or super-prefix after the sampling frequency conversion is the corresponding length before the sampling frequency conversion divided by the first sampling rate and then multiplied by the second sampling rate, and the lengths before and after the sampling frequency conversion are positive integers.
Effects and effects of the invention
According to the method for selecting the signal length in the preamble symbol provided by the invention, all different sampling frequencies in a multi-sampling rate system can be considered, the sampling frequency of the preamble symbol and the sampling frequency of the data symbol are considered, and the method is used for determining the time length (namely the number of points) of the three-section structure of the preamble symbol, namely the time domain main body signal, the suffix or the prefix and the prefix, so that the signal distortion caused by the fact that the number of sampling points is not divided exactly is avoided when the designed time domain structure is used for carrying out sampling rate conversion in a multi-sampling rate broadcast communication system.
Drawings
FIG. 1 is a flow chart of the design of signal length in preamble symbols according to an embodiment of the present invention;
fig. 2 is a time domain structure diagram of a first preamble symbol in an embodiment of the present invention; and
fig. 3 is a time domain structure diagram of a second preamble symbol in the embodiment of the present invention.
Detailed Description
The inventor finds that in the prior art, the problem of signal distortion caused by rounding the number of sampling points due to the fact that the number of non-integer sampling points after sampling rate conversion is not considered in the design of a three-stage time domain structure of a preamble symbol, namely a time domain main signal, a suffix or an prefix and a prefix.
In view of the above problem, the inventor has studied to provide a method for selecting a length of a preamble symbol signal for use in a multi-sampling rate system in which a preamble symbol has a sampling frequency different from a sampling frequency of a corresponding data symbol, the method comprising: the length of the preamble symbols corresponding to the time domain body signal, suffix or prefix and prefix, without sample frequency translation, is selected based on all the different sampling frequencies in the multiple sampling rate system.
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 time domain structure diagram of a first preamble symbol in an embodiment of the present invention. Fig. 3 is a time domain structure diagram of a second preamble symbol in the embodiment of the present invention.
As shown in fig. 2 and fig. 3, two general preamble symbols can be generated based on a segment of time domain main signal (marked as a in fig. 2 and fig. 3), respectively, and fig. 2 shows a preamble symbol having a first three-segment structure; fig. 3 shows a preamble symbol having a second three-segment structure. The invention does not only comprise a single three-segment structure time domain symbol shown in fig. 2 or fig. 3, the preamble symbol comprises at least one three-segment structure time domain symbol, and the preamble symbol can comprise a first three-segment structure, a second three-segment structure or a free combination of any plurality of first three-segment structures and second three-segment structures without any sequence.
The three-segment structure time-domain symbol includes a first partial signal that is a time-domain body signal a, a second partial signal B that is a suffix or a super-prefix of the first partial signal a based on the partial time-domain body signal a, and a third partial signal C that is a prefix of the first partial signal a based on the partial time-domain body signal.
Specifically, a part is taken out from the rear of a as a prefix (the prefix is identified as C in fig. 2 and 3), subjected to necessary processing, and copied to the front of a; while a portion is taken from the rear of a as a suffix or super-prefix (labeled as B in fig. 2 and 3), it can be seen that the portion B of the preamble symbol of the first three-segment structure of fig. 2 is prefixed; the portion B of the preamble symbol of the second three-part structure of FIG. 3 is suffixed. The preamble symbol designed with the first three-segment structure then contains the resulting combination of signals C-a-B as shown in fig. 2, and accordingly, may be combined in the order of B-C-a as shown in fig. 3.
Where necessary, each sample of the signal may be multiplied by a fixed coefficient, or each sample may be multiplied by a different coefficient, for the C and B portions.
Let the lengths of parts a, B and C be denoted as NA, NB and NC, respectively, it being clear that NA, NB and NC are positive integers and NA > NB, NC.
Since the time domain body signal a part is the result of inverse fourier transform of a frequency domain body, in order to reduce the computational complexity, the length of a is usually selected to be an integer power of 2, for example: the length of A is 512 or 1024 or 2048, etc. In the present embodiment, 2048 is taken as an example for explanation.
For the preamble symbol of the first three-segment structure, the C portion functions as a guard interval, and therefore needs to have a certain length to eliminate inter-symbol interference (ISI) caused by multipath, for example, if the maximum multipath to be considered is 500 sampling periods, the length of the C portion needs to be at least 500 at this time. Still further consider that: in the delayed autocorrelation receiving, since the second half of C needs to be correlated with B, the length of B should be less than or equal to C, however, considering various channel factors that may exist, if the lengths of B and C are the same, they will fail at the same time in a certain multipath, it should be avoided that the lengths of B and C are the same, and the invention is not limited in this respect; meanwhile, the length of B should be a large value within an allowable range to obtain good delay autocorrelation performance.
Therefore, considering the above conditions together, the length parameters of the obtained group of time domain body signals, suffixes or prefix and prefixes may be NA 2048, NC 500 and NB 499, and this embodiment is performed according to this technical idea, and the analyzed drawback is that, because only the above conditions are considered, the selection of the group of parameters is still relatively blind and random, but the adverse effect of distortion caused by the non-satisfaction of the integer relationship during the later resampling is not considered.
Therefore, the preferred embodiment is further adopted in this embodiment, and the specific selection method of the length of A, B, C is described as follows:
for a multi-sampling rate system, there are only two different sampling frequencies in a set of configurations of the system, for example, (F1, F2), or (F1, F3), or (F1, F4), and in this embodiment, the preamble symbol has a sampling frequency of F1 and the data symbol has a sampling frequency of F2, and so on. Wherein the sampling frequency of the preamble symbol is F1, the frequency of the data symbol is F2 or F3 or F4, etc., and F1 is less than F2 or F3 or F4.
In order to process the preamble symbol with the first sampling frequency (i.e., F1) into the equivalent signal with the second sampling frequency (i.e., F2), the preamble symbol with the first sampling frequency needs to be processed to obtain its equivalent signal with the second sampling frequency, so as to implement the splicing in the time domain with the data symbol with the second sampling frequency. The specific methods are two types: time domain resampling or frequency domain direct transformation methods.
[ time-domain resampling method ]
The time domain resampling method is used for resampling the sampled signal of the preamble symbol. The interpolation coefficient and the decimation coefficient used in resampling are respectively an integer multiple M1 corresponding to the sampling frequency of the preamble symbol and an integer multiple M2 corresponding to the sampling frequency of the data symbol, so that the number of waveforms obtained after resampling is an integer.
In the time domain resampling method: and the interpolation coefficient and the extraction coefficient used in resampling are respectively the integer multiple corresponding to the sampling frequency of the preamble symbol and the integer multiple corresponding to the sampling frequency of the data symbol, so that the number of waveforms obtained after resampling is an integer. Specifically, the time domain resampling method resamples the generated preamble symbol sample signal by a resampler, thereby obtaining a new sample signal. If the number of waveforms before resampling is N1, the number of waveforms after resampling, N2-N1-M2/M1, must be an integer to ensure that no signal is lost before and after resampling, thereby ensuring that the total duration is equal and the signal is not distorted, where M2 is a decimation coefficient and M1 is an interpolation coefficient.
The time domain resampling may be performed separately for A, B and C portions and then concatenated, or may be performed together for the entire preamble symbol of the CAB or BCA structure, or may be performed together for multiple preamble symbols concatenated from multiple CAB and/or BCA structures.
[ frequency domain direct conversion method ]
In general, the frequency domain direct conversion method can directly convert the preamble symbol frequency domain main signal into the time domain main signal of the required sampling rate. Namely, after zero filling is carried out on two sides of the frequency domain main body signal before transformation, IFFT is carried out to obtain the time domain main body signal to be sampled; then, according to the selection rule of the original prefix, suffix or super prefix, respectively selecting sampling points with a specific length from the time domain main body signal to be sampled, and splicing with the time domain main body signal after proper phase shift to form the preamble symbol, wherein the specific length is as follows: the length of the original prefix, suffix or prefix is divided by the first sampling frequency and multiplied by the second sampling frequency.
Recording the frequency domain main signal before transformation as X1, wherein the frequency domain main signal X1 and the time domain main signal A1 before sampling frequency transformation have FFT corresponding relation, and then adding the same number of zeros on two sides of X1 to obtain a frequency domain main signal X2 after zero padding, wherein the total number of zeros is N _ z-N _ A (F2-F1)/F1; then performing IFFT on the X2 to obtain a time domain main signal A2 after sampling rate conversion; then, according to the selection rule of the original prefix, suffix or super prefix, respectively selecting sampling points with specific length from A2, and after proper phase shift, splicing with A2 to form a new preamble symbol. However, in this process, the specific length is determined by the following method: the lengths N _ B2 and N _ C2 of the B, C parts after sample rate conversion are the lengths N _ B1 and N _ B2 of the B, C parts before sample rate conversion, respectively, divided by the first sampling frequency and multiplied by the second sampling frequency.
In order to ensure that the designed time domain structure scheme can be suitable for the two sampling rate conversion methods, the following requirements should be met: the number of the sampled waveforms N2 during the time domain resampling meets the condition that: n2 ═ N1 × F2/F1 and N2 are positive integers; in the case of frequency domain direct conversion, the number of zeros to be zero-padded is determined by multiplying the length of the time domain body signal by a predetermined coefficient, which is a positive integer, where the predetermined coefficient is determined by a ratio between a difference obtained by subtracting the sampling frequency of the preamble symbol from the sampling frequency of the data symbol, and the sampling frequency of the preamble symbol, that is, N _ z is N _ a (F2 to F1)/F1 is a positive integer, and ratios between the lengths of the prefix and the suffix or the length of the super prefix after the sample rate conversion and before the sample rate conversion are determined by the sampling frequency of the data symbol and the sampling frequency of the preamble symbol, respectively, and the lengths before and after the sample rate conversion are both positive integers, that is, N _ B2 is N _ B1F 2/F1, and N _ C5 is N _ C2F 2/F1 is a positive integer.
Therefore, when the lengths of the signals corresponding to the three parts before the sampling frequency conversion are selected, the method is as follows:
first, all the different sampling frequencies that may occur within the system (denoted as F1, F2, F3, etc.) are written as multiples of some base frequency F0:
F1=F0*M1,
F2=F0*M2,
F3=F0*M3,
wherein M1, M2 and M3 are multiples of the basic frequency. The greatest common divisor of all multiples of M1, M2, M3, etc. is required to be 1, and in the present invention, the greatest common divisor may be a positive integer greater than or equal to 1.
Taking M1 as a reference multiple; and determines the lengths of the A, B and C triples having the first sampling frequency to be integer multiples of the reference multiple.
For example, if in a multi-sample rate system, the sample rate of the preamble symbol is 6.144MHz, and the sample rates of the other symbols are: 6.912MHz,8.064MHz,9.216MHz, i.e.:
F1=6.144,
F2=6.912,
F3=8.064
F4=9.216
the base frequency may be determined to be 0.384MHz, and each sampling rate may be written as:
F1=F0*N1,N1=16
F2=F0*N2,N2=18
F3=F0*N3,N3=21
F4=F0*N4,N4=24
the greatest common divisor of N1, N2, N3 and N4 is 1, and the requirements are met.
In the foregoing example, NA is 2048, NB is 500, and NC is 499 obviously not in accordance with the above requirement that the lengths of the A, B, C three parts are all integer multiples of the reference multiple N1, and no matter which sampling rate conversion method is used, signal distortion is introduced. The parameters redesigned using the method described above were as follows:
the NA is 2048 which is an integral multiple of N1 which is 16, and meets the requirement;
NC needs to be an integer multiple of N1 and not less than 500, and the available NC values are: 512. 528, 540, and so on.
NB needs to be an integer multiple of N1, close to but less than NC, and optional values for visible NB can be: 512. 496, 480, and so on.
From the above alternatives, it can be obtained that a set of NA, NB, and NC values (2048, 496, and 528) satisfy the respective requirements, and this value also considers that when performing delayed autocorrelation reception, since the second half of C needs to be correlated with B, the length of B should be equal to or less than C.
The pilot symbol obtained by the method can ensure that an integer number of sampling points can be obtained no matter a time domain resampling method or a frequency domain direct transformation method is used, and signal distortion cannot be caused.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.

Claims (9)

1. A method for selecting a signal length of a preamble symbol for use in a multiple sampling rate system in which the preamble symbol has a sampling frequency different from a sampling frequency of a corresponding data symbol, comprising:
the length of the signal corresponding to the time domain main signal, the suffix or prefix and the prefix in the preamble symbol without sampling frequency conversion is selected based on all different sampling frequencies in the multi-sampling rate system;
when the lengths of the signals corresponding to the three parts before sampling rate conversion are selected, the method comprises the following steps:
according to all different sampling frequencies in the multi-sampling rate system, the preset basic frequency is determined based on the following conditions: all the different sampling frequencies can be obtained by multiplying the same basic frequency by a plurality of corresponding integer multiples;
selecting the integer multiple corresponding to the sampling frequency of the preamble symbol from the multiple integer multiples as a reference multiple; and
and designing the lengths of signals corresponding to the time domain main body signal, the suffix or prefix and the prefix in the preamble symbols which are not subjected to sampling rate conversion to be integral multiples of the reference multiple.
2. A method for selecting a preamble symbol signal length according to claim 1, characterized by:
wherein the greatest common divisor between all the integer multiples multiplied by the same preset basic frequency is a positive integer which is greater than or equal to 1.
3. A method for selecting a preamble symbol signal length according to claim 1, characterized by:
wherein the length of the time domain subject signal is selected to be an integer power of a value of 2.
4. A method for selecting a preamble symbol signal length according to claim 1, characterized by:
wherein the length of the suffix or super prefix is less than or equal to the length of the prefix.
5. A method for selecting a preamble symbol signal length according to claim 1, characterized by:
wherein the preamble symbol comprises: based on the time domain main body signal, the suffix or the prefix and the prefix respectively formed by the signals with the selected lengths, when the sampling frequency of the preamble symbol is required to be converted into the sampling frequency of the data symbol, the signal lengths of the time domain main body signal, the suffix or the prefix and the prefix in the preamble symbol after the sampling rate conversion are all integers.
6. The method for selecting a preamble symbol signal length according to claim 1,
the lengths of the time domain body signal, the suffix or prefix and the prefix are respectively 2048 points, 496 points and 528 points.
7. A method for selecting a preamble symbol signal length according to claim 1, characterized by:
the preamble symbol includes at least one three-segment structure time domain symbol, and the three-segment structure time domain symbol includes a first partial signal as the time domain main signal, a second partial signal generated as the suffix or the super-prefix of the first partial signal based on a part of the time domain main signal, and a third partial signal generated as the prefix of the first partial signal based on a part of the time domain main signal.
8. A method for selecting a preamble symbol signal length according to claim 1, characterized by:
processing the preamble symbol with the first sampling rate into an equivalent signal with the second sampling rate, and splicing the equivalent signal with the data symbol with the second sampling rate in a time domain by the following method:
time domain resampling method: resampling the sampling signals of the preamble symbols; or
Frequency domain direct conversion method: filling zeros on two sides of the frequency domain main signal with the first sampling rate, and then performing IFFT to obtain the time domain main signal with the second sampling rate and needing sampling; then respectively selecting sampling points with specific length from the time domain main body signal to be sampled according to the selection rule of the original prefix, suffix or super prefix, splicing with the time domain main body signal after proper phase shift to form the preamble symbol,
the specific length is as follows: the length of the original prefix, suffix or prefix is divided by the first sampling rate and multiplied by the second sampling rate.
9. The method for selecting a preamble symbol signal length according to claim 8, wherein:
in the time-domain resampling method: the interpolation coefficient and the extraction coefficient used in resampling are respectively the integer multiple corresponding to the sampling frequency of the preamble symbol and the integer multiple corresponding to the sampling frequency of the data symbol, so that the number of waveforms obtained after resampling is an integer;
in the frequency domain direct conversion method:
the number of zeros to be zero-padded is obtained by multiplying the length of the time domain subject signal by a predetermined coefficient, which is a positive integer, and the predetermined coefficient is determined by a ratio between a difference obtained by subtracting the sampling frequency of the preamble symbol from the sampling frequency of the data symbol and the sampling frequency of the preamble symbol;
the length of the prefix, suffix or super-prefix after the sampling frequency conversion is the corresponding length before the sampling frequency conversion divided by the first sampling rate and then multiplied by the second sampling rate, and the lengths before and after the sampling frequency conversion are positive integers.
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