CN1567764A - New sub-channel generating and allocating method of multi-user OFDMA system - Google Patents
New sub-channel generating and allocating method of multi-user OFDMA system Download PDFInfo
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Abstract
The invention is a method of generating and allocating new subchannel in a multiuser orthogonal frequency division multiplex (OFDM) access system, including the steps: the system has 256 sub-carrier waves whose mark numbers are [-128 : 127]; the number of usable useful sub-carrier waves are 200, and their mark numbers are [-100 : -1, 1 : 100], where the sub-carrier waves -88, -63, -38, -13, 13, 38, 63, and 88 are used to transmit guide frequency signals; as all the useful sub-carrier waves are divided into two subchannels, the mark numbers of sub-carrier waves contained by one subchannel are [-100: -76, -50: -26, 1 : 25, 51 : 75], where the sub-carrier waves -38, -88, 13 and 88 are placed with guide frequency signals; and those of sub-carrier waves contained by the other subchannel are [-75: -51:, -25: -1, 26: 50, 76: 100], where the sub-carrier waves -13, 88, -63 and 38 are placed with guide frequency signals. The subchannels have the characters as follows: they have good frequency separately collecting effect; their guide frequency signals are uniformly allocated and dispersively distributed and it is extremely easy to obtain the access front guide of the subchannel with very-low power peak average and to apply to multiantenna system. It introduces a new subchannel access front guide, which has lower power peak average ratio.
Description
Technical field
The present invention relates to orthogonal frequency division multiplexing multiple access and insert (OFDMA) communication technical field, specifically, the present invention relates to subchannel new in the ofdma communication system physical layer and produce and distribution method.
Background technology
OFDM (OFDM) technology has just put forward as far back as the sixties as a kind of high speed transmission technology of wireless communication system.In the last few years, because the develop rapidly of Digital Signal Processing and asic technology, the realization of ofdm system became a reality, and the OFDM technology receives publicity once again and studies.OFDM has obtained generally acknowledging both at home and abroad as mobile radio communications system technology of future generation.
The OFDMA system is based on the multiple access to communication system of OFDM technology, and in the OFDMA system, all available subcarriers are divided into subchannel, and according to the division methods difference, subchannel can contain one or more subcarriers.Different subchannels is distributed to different users in can be at one time.More effective like this frequency band that utilizes improves power system capacity.Because the use of subchannel has reduced the power peak-to-average ratio, help the mobile of user terminal and improve the coverage of sub-district simultaneously.
When a certain user used a certain subchannel, this user only need be at the subchannel transmitting data of this appointment.In a lot of OFDMA systems, for the purpose of synchronous and channel estimating, the user is some training symbols of transmission before the transmission data or in transmission course, and we are called access lead (Preamble).
Preamble in the actual OFDMA system obtains on the frequency domain known sequences being IFFT on specific subchannel, and we claim that this kind sequence is a frequency domain training sequence.
In the 256FFTOFDM physical layer of high-performance metropolitan area network standard Hiperman and IEEE802.16e, have 256 subcarriers, label is-128 to 127, but the actual label of only having used is 200 subcarriers of-100 to 100, wherein zero subcarrier need not.
Except the 256FFTOFDM pattern, Hiperman also adopts the 256FFTOFDMA pattern, and 802.16e also adopts the 256FFTOFDMA pattern at present.The 256OFDMA pattern is that whole available subcarrier is divided into 16 subchannels.The user can use these subchannel combinations when using these subchannels.Corresponding each subchannel combinations all should have a kind of frequency domain training sequence.
When the design subchannel is divided, should consider following design principle:
1: the subcarrier of subchannel distributes have good frequency diversity effect.Require the subcarrier in the subchannel to disperse so as far as possible.
2: the pilot signal quantity of each subchannel should equate as far as possible.
3: the distribution of pilot signal in subchannel should disperse as far as possible.
5: the access lead of corresponding subchannel requires to have very low power peak-to-average ratio, can avoid nonlinear distortion like this, the synchronous and channel parameter of better estimation.
In the current system for example the 256OFDMA physical layer sub-channels of high-performance metropolitan area network standard (Hiperman) and 802.16e divide and do not meet above-mentioned design principle fully
Summary of the invention
At the technical problem of above-mentioned existence, the purpose of this invention is to provide a kind of new subchannel and divide and distribution method.
For achieving the above object, subchannel new in a kind of multi-user orthogonal frequency division multiplexing multiple access to communication system generates and distribution method, comprises step:
The orthogonal frequency division multiplexing multiple access access communication system has 256 subcarriers, and label is [128:127];
Spendable useful subcarrier is 200, and label is [100:-1,1:100], and wherein label is-88 ,-63 ,-38 ,-13, and 13,38,63,88 are used for transmitting pilot signal;
When all useful subcarriers were divided into two subchannels, S1: the label that comprises subcarrier was [100:-76 ,-50:-26,1:25,51:75], and wherein label be-the subcarrier placement pilot signal of 38-88 13 88;
S2: the label that comprises subcarrier is [75:-51 ,-25:-1,26:50,76:100], and wherein label is the subcarrier placement pilot signal of-13 88-63 38.
The subchannel that the inventive method is divided has following characteristics, and subchannel has good frequency diversity effect; The pilot signal of subchannel obtains mean allocation and dispersed and distributed, is very easy to obtain the access lead of the very low subchannel of power peak-to-average ratio, is easy to be applied to multiaerial system.Introduce a kind of new subchannel access lead, this subchannel access lead has the lower-wattage peak-to-average ratio.
Description of drawings
Fig. 1 is the OFDMA transmitter;
Fig. 2 is the OFDM transmitter;
Fig. 3 is the time-domain signal after the Cyclic Prefix operation, and CP represents Cyclic Prefix;
Fig. 4 is the access lead of subchannel.Wherein Tg represents the length of Cyclic Prefix, and Tb represents the length of an OFDM data symbol.
Embodiment
Ofdma communication system is to be a kind of communication system of core with the OFDM technology.OFDM is the high speed transmission technology under a kind of wireless environment.The frequency response curve of wireless channel is non-flat forms mostly, and the main thought of OFDM technology is divided into many orthogonal sub-carriers with allocated frequency band exactly in frequency domain, on each subcarrier, modulate, and each subcarrier parallel transmission.Like this, although total wireless channel be non-flat forms, have frequency selectivity, but each subcarrier is a relatively flat, what carry out on each subcarrier is narrow band transmission, and signal bandwidth is less than the respective bandwidth of wireless channel, so the just interference between the erasure signal waveform greatly.Because each subcarrier is mutually orthogonal in ofdm system, their frequency spectrum is overlapped, has so not only reduced the phase mutual interference between subcarrier, has improved the availability of frequency spectrum simultaneously again.
OFDMA system basic principle is to divide whole OFDM subcarrier into a lot of sub carrier group, and we are referred to as subchannel.Different users can use different subchannels at one time.The advantage of OFDM has not only been inherited by the OFDMA system, also has data transmission rate more flexibly simultaneously, bigger power system capacity and bigger coverage.In the OFDMA system, except being used for the transmitting useful data, estimate channel parameter for better, a spot of subcarrier also is used for transmitting pilot signal.
The OFDMA system is divided into N subcarrier from low to high with whole frequency band, and label is [N/2:N/2-1], and generally speaking, in order to prevent monkey chatter, the subcarrier that is positioned at the band edge edge is not used.For the convenience on realizing, label is that zero subcarrier is not used yet simultaneously.Any signal is not promptly placed in obsolete subcarrier zero setting.
The OFDMA system basic parameter that the present invention is directed to is:
1) total number of sub carrier wave is 256, and label is [128:127].
2) number of sub carrier wave of Shi Yonging is 200, label [100:-1,1:100];
3) number of sub carrier wave that is used to transmit pilot tone is 8, and label is [88 ,-63 ,-38 ,-13,13,38,63,88];
4) subcarrier that is positioned at boundary belt is 55, and label is [128:-101,101:127];
In the ofdm system, as shown in Figure 2, the serial data symbol is divided into piece { p
j| j=-N/2 ..., N/2-1} (wherein N is an IFFT length, the corresponding OFDM modulated sub-carriers of j label), parallel being placed on carried out quick inverse-Fourier transform (IFFT) and obtained the OFDM symbol on the corresponding subcarrier
Behind the IFFT, this OFDM data-signal is carried out launching by antenna through digital to analog conversion and up-conversion after the Cyclic Prefix operation.
p
jCan contain pilot signal, in addition, if p
jBe to be frequency domain training sequence, the OFDM symbol that obtains so is an access lead.
Time-domain signal after the Cyclic Prefix operation as shown in Figure 3.
Corresponding to system parameters of the present invention, p
jBeing that label is to be placed with on [100:1,1:100] with symbol (data symbol, pilot tone or frequency domain training sequence) at the subcarrier that uses only, is zero on other subcarrier.
Corresponding to the OFDMA system, as Fig. 1, when if a certain user makes a certain subchannel, when generating data symbol, the data modulation symbol that modulation mapper comes out generates and the subchannel corresponding symbol piece that uses through deserializer, select corresponding subchannel by the subchannel maker, load mapper by subchannel and the corresponding symbol piece is placed on accordingly on the subcarrier of subchannel, on corresponding subcarrier, place pilot signal simultaneously.。In the time will generating the access lead of subchannel, behind generation of subchannel frequency domain sequence maker and the corresponding frequency domain sequence of this subchannel, select corresponding subchannel by the subchannel maker, load mapper by subchannel then corresponding frequency domain sequence is placed on the subcarrier of subchannel accordingly.Subchannel loads the p that mapper comes out
jOnly containing useful signal on the subcarrier on the subchannel that this user uses, is zero on other subcarrier.Then to p
jCarry out the IFFT operation.
Subchannel division methods of the present invention is as follows:
1) when all useful subcarriers are divided into two subchannels:
S1:[-100:-76 ,-50:-26,1:25,51:75], wherein label be-subcarrier of 38-881388 places pilot signal.
S2:[-75:-51 ,-25:-1,26:50,76:100], wherein label be-subcarrier of 1388-6338 places pilot signal.
2) when all useful subcarriers are divided into four subchannels:
S3:[-100:-89,-50:-39,1:12,51:62];
S4:[-87:-76,-37:-26,12:25,64:75];
S5:[-75:-64,-25:-14,26:37,76:87];
S6:[-64:-51,-12:-1,39:50,89:100];
S3 and S4 use the pilot tone rule to be:
Rule one: when one of them subchannel uses label be-38,63 subcarrier when placing pilot tone, and can only to use label be-88,13 subcarrier placement pilot signal to the another one subchannel so.
Rule two: when one of them subchannel uses label be-88,63 subcarrier when placing pilot tone, and can only to use label be-38,13 subcarrier placement pilot tone to the another one subchannel so
S5 and S6 use the rule of pilot tone to be
Rule one: when one of them subchannel uses label be-13,88 subcarrier when placing pilot tone, and can only to use label be-63,38 subcarrier placement pilot signal to the another one subchannel so.
Rule two: when one of them subchannel uses label be-13,38 subcarrier when placing pilot tone, and can only to use label be-63,88 subcarrier placement pilot tone to the another one subchannel so
3) when all useful subcarriers are divided into eight subchannels
S7:[-94:-89,-44:-39,1:651:56];
S8:[-100:-95,-50:-45,7:12,57:62];
S9:[-81:-76,-31:-26,14:19,64:69];
S10:[-87:-82,-37:-32,20:25,70:75];
S11:[-69:-64,-19:-14,26:31,76:81];
S12:[-75:-70,-25:-20,32:37,82:87];
S13:[-56:-51,-6:-1,39:44,89:94];
S14:[-62:-57,-12:-7,45:51,95:100];
S7, S8, S9, S10 use the pilot tone rule to be:
Rule one: it is-38,63,13 that S7, S8, S9, S10 use label respectively, and-88 subcarrier is placed pilot tone.
Rule two: it is-38,13,63 that S7, S8, S9, S10 use label respectively, and-88 subcarrier is placed pilot tone.
Rule three: it is-88,63,13 that S7, S8, S9, S10 use label respectively, and-38 subcarrier is placed pilot tone.
Rule four: it is-88,13,63 that S7, S8, S9, S10 use label respectively, and-38 subcarrier is placed pilot tone.
S11, S12, S13, S14 use the pilot tone rule to be:
Rule one: it is-13,88,38 that S11, S12, S13, S14 use label respectively, and-63 subcarrier is placed pilot tone.
Rule two: it is-13,38,88 that S11, S12, S13, S14 use label respectively, and-63 subcarrier is placed pilot tone.
Rule three: it is-63,88,38 that S11, S12, S13, S14 use label respectively, and-13 subcarrier is placed pilot tone.
Rule four: it is-63,38,88 that S11, S12, S13, S14 use label respectively, and-13 subcarrier is placed pilot tone.
4) when all useful subcarriers are divided into 16 subchannels:
S15:[-91:-89?-41:-39?1:3;51:53];
S16:[-94:-92,-44:-42,4:6,54:56];
S17:[-97:-95;-47:-45;7:9;57:59];
S18:[-100:-98;-50:-48;10:12;60:62];
S19:[-78:-76,-28:-26,14:16,64:66];
S20:[-81:-79;-31:-29;17:19;67:69];
S21:[-84:-82;-34:-32?20:22;70:72];
S22:[-87:-85;-37:-35?23:25?73:75];
S23:[-66:-64?-16:-14?26:28?76:78];
S24:[-69:-67,-19:-17,29:31?79:81];
S25:[-72:-70,-22:-20,32:34?82:84];
S26:[-75:-73,-25:-23,35:37,85:87];
S27:[-53:-51?-3:-1?39:41,89:91];
S28:[-56:-54,-6:-4,42:44,92:94];
S29:[-59:-57,-9:-7,45:47,95:97];
S30:[-62:-60,-12:-10,48:51?98:100];
S15 does not use any subcarrier to place pilot tone to S30.
Above-mentioned 1) 2) 3) and 4) arbitrary subchannel of dividing can distribute to Any user, specifically this user uses that subchannel, depends on communication environment.
As the specific operating position of subchannel that the present invention divides, when a certain user uses following arbitrary subchannel:
S1,S2。
Using label be that-38,63 subcarrier places the S3 of pilot tone and use label is the S4 of-88,13 subcarrier placement pilot tone
Using label be that-13,88 subcarrier places the S5 of pilot tone and use label is the S6 of-63,38 subcarrier placement pilot tone
Using label respectively is-38,63,13, and-88 ,-13,88,38 ,-63 subcarrier is placed the S7 of pilot tone, S8, S9, S10, S11, S12, S13, S14.
S15 is to S30
When generating the access lead of above a certain subchannel, can and get from the following sequences extraction corresponding to the frequency domain training sequence of this subchannel:
Seq(-100:100)=[-1-i1+i1+i-1-i-1+i-1-i-1-i1+i1+i-1-i-1+i-1-i-1+i-1-i1+i1+i-1-i-1+i-1-i-1-i1+i1+i-1-i-1+i-1-i-1-i1-i-1-i-1-i1+i1+i-1-i1-i-1-i-1-i1+i1+i1-i-1-i1-i-1-i-1-i1+i1+i-1-i1-i-1-i-1-i1+i1+i-1+i-1-i-1+i-1+i-1+i1-i-1+i-1-i-1+i-1+i-1+I1-i-1-i1-i1+i1-i1-i1-i-1+i1-i1+i1-i1-i1-i-1+i1+i1+i-1-i1+i1-i1+i1+i1+i-1-i1+i1-i1+i-1-i-1-i-1-i1+i-1-i-1+i-1-i-1-i-1-i1+i-1-i-1+i-1-i0-1+i1-i1-i1-i-1-i1-i1-i-1+i-1+i-1+i1+i-1+i-1+i-1+i1-i1-i1-i-1-i1-i1-i-1+i-1+i-1+i1+i-1+i1-i1+i1-i-1+i1-i1-i-1+i-1-i-1+i1-i-1+i-1+i1+i1-i1+i1-i-1+i1-i1-i-1+i-1-i-1+i1-i-1+i-1+i1+i-1+i1+i-1-i-1-i1+i-1-i1-i-1-i1+i1+i-1-i1+i-1-i1-i-1-i1+i1+i-1-i1+i-1+i1+i-1-i-1-i1+i-1+i-1+i1-i1-i-1-i1-i1-i1-i-1+i-1+i1+i-1+i-1+i1-i1-i-1+i-1+i1+i-1+i-1+i-1+i1-i1-i-1-i1-i]*W;
Here only provide the value of label for training symbol on from-100 to 100 subcarriers, other positions are zero, and promptly label is for being zero on-128 to-101 and 101 to 127 the subcarrier, and wherein W is a coefficient of determining, can be any real number or plural number.This sequence is a sequence of complex numbers, and the element of sequence is a plural number, represents the QPSK modulation.
According to above-mentioned frequency domain training sequence, when the user who uses a certain subchannel will generate access lead corresponding to this subchannel, on sequence Seq, be placed on the subcarrier of this subchannel corresponding to extracting the element correspondence on the position of the subcarrier label in this subchannel.If this subchannel uses pilot tone, on the position of the pilot tone label that uses corresponding to this subchannel on the sequence Seq, extract the element correspondence so simultaneously and be placed on the subcarrier of corresponding pilot tone.Other subcarrier does not use, and promptly places zero.Carry out the IFFT operation then.The access lead that generates as shown in Figure 4.
Claims (12)
1. new subchannel generates and distribution method in the multi-user orthogonal frequency division multiplexing multiple access to communication system, comprises step:
The orthogonal frequency division multiplexing multiple access access communication system has 256 subcarriers, and label is [128:127];
Spendable useful subcarrier is 200, and label is [100:-1,1:100], and wherein label is-88 ,-63 ,-38 ,-13, and 13,38,63,88 are used for transmitting pilot signal;
When all useful subcarriers were divided into two subchannels, S1: the label that comprises subcarrier was [100:-76 ,-50:-26,1:25,51:75], and wherein label is-38-88 13 88 subcarrier placement pilot signal;
S2: the label that comprises subcarrier is [75:-51 ,-25:-1,26:50,76:100], and wherein label is-13 88-63 38 subcarrier placement pilot signal.
2. by the described method of claim 1, it is characterized in that:
When all useful subcarriers are divided into four subchannels:
S3: the label that comprises subcarrier is [100:-89 ,-50:-39,1:12,51:62];
S4: the label that comprises subcarrier is [87:-76 ,-37:-26,12:25,64:75];
S5: the label that comprises subcarrier is [75:-64 ,-25:-14,26:37,76:87];
S6: the label that comprises subcarrier is [64:-51 ,-12:-1,39:50,89:100];
Simultaneously, each subchannel also contains two other subcarrier and transmits pilot signal, and service regeulations are:
S3 and S4 use the pilot tone rule to be:
When one of them subchannel uses label be-38,63 subcarrier when placing pilot tone, and can only to use label be-88,13 subcarrier placement pilot signal to the another one subchannel so;
S5 and S6 use the rule of pilot tone to be
When one of them subchannel uses label be-13,88 subcarrier when placing pilot tone, and can only to use label be-63,38 subcarrier placement pilot signal to the another one subchannel so.3. by the described method of claim 2, it is characterized in that: S3 and S4 use the pilot tone rule to be:
When one of them subchannel uses label be-88,63 subcarrier when placing pilot tone, and can only to use label be-38,13 subcarrier placement pilot tone to the another one subchannel so;
4. by the described method of claim 2, it is characterized in that: S5 and S6 use the rule of pilot tone to be:
When one of them subchannel uses label be-13,38 subcarrier when placing pilot tone, and can only to use label be-63,88 subcarrier placement pilot tone to the another one subchannel so.
5. by the described method of claim 1, it is characterized in that:
When all useful subcarriers are divided into eight subchannels
S7: the subcarrier label that comprises is [94:-89 ,-44:-39,1:6 51:56];
S8: the subcarrier label that comprises is [100:-95 ,-50:-45,7:12,57:62];
S9: the subcarrier label that comprises is [81:-76 ,-31:-26,14:19,64:69];
S10: the subcarrier label that comprises is [87:-82 ,-37:-32,20:25,70:75];
S11: the subcarrier label that comprises is [69:-64 ,-19:-14,26:31,76:81];
S12: the subcarrier label that comprises is [75:-70 ,-25:-20,32:37,82:87];
S13: the subcarrier label that comprises is [56:-51 ,-6:-1,39:44,89:94];
S14: the subcarrier label that comprises is [62:-57 ,-12:-7,45:51,95:100];
Simultaneously, each subchannel also contains the another one subcarrier and transmits pilot signal, and service regeulations are:
S7, S8, S9, S10 use the pilot tone rule to be:
It is-38,63,13 that S7, S8, S9, S10 use label respectively, and-88 subcarrier is placed pilot tone;
S11, S12, S13, S14 use the pilot tone rule to be:
It is-13,88,38 that S11, S12, S13, S14 use label respectively, and-63 subcarrier is placed pilot tone.
6. by the described method of claim 5, it is characterized in that: S7, S8, S9, S10 use the pilot tone rule to be:
It is-38,13,63 that S7, S8, S9, S10 use label respectively, and-88 subcarrier is placed pilot tone;
S11, S12, S13, S14 use the pilot tone rule to be:
It is-13,38,88 that S11, S12, S13, S14 use label respectively, and-63 subcarrier is placed pilot tone.
7. by the described method of claim 5, it is characterized in that: S7, S8, S9, S10 use the pilot tone rule to be:
It is-88,63,13 that S7, S8, S9, S10 use label respectively, and-38 subcarrier is placed pilot tone;
S11, S12, S13, S14 use the pilot tone rule to be:
It is-63,88,38 that S11, S12, S13, S14 use label respectively, and-13 subcarrier is placed pilot tone.
8. by the described method of claim 5, it is characterized in that: S7, S8, S9, S10 use the pilot tone rule to be:
It is-88,13,63 that S7, S8, S9, S10 use label respectively, and-38 subcarrier is placed pilot tone.
S11, S12, S13, S14 use the pilot tone rule to be:
It is-63,38,88 that S11, S12, S13, S14 use label respectively, and-13 subcarrier is placed pilot tone.
9. by the described method of claim 1, it is characterized in that: when all useful subcarriers are divided into 16 subchannels:
S15: the subcarrier label that comprises is [91:-89 ,-41:-39,1:3,51:53];
S16: the subcarrier label that comprises [94:-92 ,-44:-4,4:6,54:56];
S17: the subcarrier label that comprises is [97:-95;-47:-45; 7:9; 57:59];
S18: the subcarrier label that comprises is [100:-98;-50:-48; 10:12; 60:62];
S19: the subcarrier label that comprises is [78:-76 ,-28:-26,14:16,64:66];
S20: the subcarrier label that comprises is [81:-79;-31:-29; 17:19; 67:69];
S21: the subcarrier label that comprises is [84:-82;-34:-32 20:22; 70:72];
S22: the subcarrier label that comprises is [87:-85;-37:-35 23:25 73:75];
S23: the subcarrier label that comprises is [66:-64-16:-14 26:28 76:78];
S24: the subcarrier label that comprises is [69:-67 ,-19:-17,29:31 79:81];
S25: the subcarrier label that comprises is [72:-70 ,-22:-20,32:34 82:84];
S26: the subcarrier label that comprises is [75:-73 ,-25:-23,35:37,85:87];
S27: the subcarrier label that comprises is [53:-51-3:-1 39:41,89:91];
S28: the subcarrier label that comprises is [56:-54 ,-6:-4,42:44,92:94];
S29: the subcarrier label that comprises is [59:-57 ,-9:-7,45:47,95:97];
S30: the subcarrier label that comprises is [62:-60 ,-12:-10,48:5198:100];
Each subchannel does not use any subcarrier to place pilot tone.
10. by one of aforementioned claim described method, it is characterized in that: system can distribute arbitrary subchannel to use for a certain user.When this user used a certain subchannel, only transmission signals was placed useful signal on this subchannel, and other subcarrier does not use, i.e. zero setting.
11. by the described method of claim 1, it is characterized in that: place frequency domain training sequence in the subcarrier of user in the subchannel that uses, other no subchannels place zero, carry out inverse-Fourier transform and form OFDM subchannel access lead.
12., it is characterized in that by one of aforementioned claim described method:
The user can use following arbitrary subchannel:
S1,S2,
Using label be that-38,63 subcarrier places the S3 of pilot tone and use label is the S4 of-88,13 subcarrier placement pilot tone,
Using label be that-13,88 subcarrier places the S5 of pilot tone and use label is the S6 of-63,38 subcarrier placement pilot tone,
Using label respectively is-38,63,13, and-88 ,-13,88,38 ,-63 subcarrier is placed the S7 of pilot tone, S8, and S9, S10, S11, S12, S13, S14,
S15 is to S30.
13., it is characterized in that by the described method of claim 11:
When generating the access lead of a certain subchannel, can extract and get from following sequences corresponding to the frequency domain training sequence of this subchannel:
Seq(-100:100)=[-1-i1+i1+i-1-i-1+i-1-i-1-i1+i1+i-1-i-1+i-1-i-1+i-1-i1+i1+i-1-i-1+i-1-i-1-i1+i1+i-1-i-1+i-1-i-1-i1-i-1-i-1-i1+i1+i-1-i1-i-1-i-1-i1+i1+i1-i-1-i1-i-1-i-1-i1+i1+i-1-i1-i-1-i-1-i1+i1+i-1+i-1-i-1+i-1+i-1+i1-i-1+i-1-i-1+i-1+i-1+i1-i-1-i1-i1+i1-i1-i1-i-1+i1-i1+i1-i1-i1-i-1+i1+i1+i-1-i1+i1-i1+i1+i1+i-1-i1+i1-i1+i-1-i-1-i-1-i1+i-1-i-1+i-1-i-1-i-1-i1+i-1-i-1+i-1-i0-1+i1-i1-i1-i-1-i1-i1-i-1+i-1+i-1+i1+i-1+i-1+i-1+i1-i1-i1-i-1-i1-i1-i-1+i-1+i-1+i1+i-1+i1-i1+i1-i-1+i1-i1-i-1+i-1-i-1+i1-i-1+i-1+i1+i1-i1+i1-i-1+i1-i1-i-1+i-1-i-1+i1-i-1+i-1+i1+i-1+i1+i-1-i-1-i1+i-1-i1-i-1-i1+i1+i-1-i1+i-1-i1-i-1-i1+i1+i-1-i1+i-1+i1+i-1-i-1-i1+i-1+i-1+i1-i1-i-1-i1-i1-i1-i-1+i-1+i1+i-1+i-1+i1-i1-i-1+i-1+i1+i-1+i-1+i-1+i1-i1-i-1-i1-i]*W。
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