CN106941470A - A kind of method of signal peak-to-average ratio in reduction FBMC systems - Google Patents

A kind of method of signal peak-to-average ratio in reduction FBMC systems Download PDF

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CN106941470A
CN106941470A CN201710094515.6A CN201710094515A CN106941470A CN 106941470 A CN106941470 A CN 106941470A CN 201710094515 A CN201710094515 A CN 201710094515A CN 106941470 A CN106941470 A CN 106941470A
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data
signal
upsi
peak
phase rotation
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徐平平
柳颖
王潍潍
肖霖
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Southeast University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/32Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/3405Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power
    • H04L27/3411Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power reducing the peak to average power ratio or the mean power of the constellation; Arrangements for increasing the shape gain of a signal set
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00Modulated-carrier systems
    • H04L27/32Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/345Modifications of the signal space to allow the transmission of additional information
    • H04L27/3461Modifications of the signal space to allow the transmission of additional information in order to transmit a subchannel
    • H04L27/3483Modifications of the signal space to allow the transmission of additional information in order to transmit a subchannel using a modulation of the constellation points

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  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Digital Transmission Methods That Use Modulated Carrier Waves (AREA)

Abstract

The invention discloses a kind of method of signal peak-to-average ratio in reduction FBMC systems, signal is pre-processed in signal sending end first, even if data are carried out to be multiplied by phase rotation coefficient after constellation mapping, data will not also produce overlapping;It is combined again with traditional PTS method and is split data, one group of data for selecting peak-to-average force ratio minimum from multi-group data are transmitted, can be very good to reduce the peak-to-average force ratio of signal;The demodulation of signal can be carried out with the decision rule of basis signal in receiving terminal, the transmission of side information can be so avoided.Present invention reduces the peak-to-average force ratio of FBMC systems, it is not necessary to transmit and improve the utilization rate of frequency spectrum resource under the demodulation that phase rotation coefficient is used to receive client information, the same terms, so as to improve the service efficiency of whole system.

Description

A kind of method of signal peak-to-average ratio in reduction FBMC systems
Technical field
The present invention relates to reduce the side of signal peak-to-average ratio by constellation mapping and partial transmission sequence in a kind of FBMC systems Method, belongs to wireless communication technology research field.
Abbreviation and Key Term definition
Background technology
With the raising of wireless communication technology, people also uprise therewith to the quality requirement of communication.Due to multi-carrier communication System has the advantages such as spectrum efficiency is high, spectrum utilization is flexible so that multi-carrier communications systems turn into main direction of studying.Many The signal of a part of subchannel in parallel transmission signal is only influenced whether in carrier system, when which part signal is interfered Transmission quality, and whole communication can not be influenceed.Although multi-carrier communication has more advantage, there is higher peak in signal Compare, be easily caused the overall communication performance of the distorted signals influence of nearby frequency bands.Therefore, PAR of carrier signal is reduced Research is just particularly important.
The need for developing due to various technologies and frequency spectrum resource distribution the factor, OFDM such as unreasonable (OFDM) technology is arisen at the historic moment.It is next in order to meet there is also various shortcoming although OFDM technology has carried out commercialization The need for for 5G communication system high data rate transfers, FBMC-OQAM systems technologies have attracted the interest of many people.It is a kind of The communication mode of use based on multicarrier staggeredly quadrature amplitude modulation.Compared with ofdm system, be most intuitively in FBMC- Signal does not need recycling-guard in OQAM systems, therefore, and FBMC-OQAM message transmission rates compare OFDM at identical conditions It is high.
Peak-to-average force ratio reduction technical research has had long time, and researcher considers from different scene angles, proposes The methods of many reduction signal peak-to-average ratios, can be largely classified into anti-aliasing techniques and undistorted technology.Scheme that signal is undistorted In, signal will not be distorted;And in signal has distortion scheme, the basic thought of its process signal is to carry out non-thread to signal Property processing, so as to reduce the peak-to-average ratio of signal, although this method it is fairly simple but receiving terminal demodulate come signal The higher bit error rate can be produced.
(1) the undistorted technology of signal:Coding class technology is mainly performed the encoding operation to signal, utilizes the code word set of transmission Conjunction is handled signal, is selected those that peak-to-average force ratio can be made to reduce or minimum code word, is then selected from codeword set The peak amplitude of signal is used to transmit than relatively low codeword set, higher peak value can be avoided to occur, this outer coding class technology Also distorted signals and out-of-band radiation will not be caused.Proposed in document 1 based on BCH code, M sequence, Golay complementary series and The coding class technologies of Hadamard codes reduces peak-to-average force ratio.The method of probability class be mainly reduction signal in peak value occur it is general The maximum of power in rate rather than reduction signal.Choose for user method (SLM) is proposed in document 2, its basic thought is The signal of the input vectorial X of M statistical iterationm(1≤m≤M) is indicated, and is occurred by conversion reduction signal peak-to-average ratio Probability.
(2) signal has anti-aliasing techniques:The basic thought of companding class technical method is to original time-domain signal in transmitting terminal Nonlinear conversion is carried out, the signal larger to wherein Amplitude Ration is compressed, the less signal of Amplitude Ration is enlarged, but Need keep convert after mean power and primary signal mean power it is equal.Amplitude limit class method is proposed in document 3, Its simplest reduction peak-to-average force ratio scheme, the basic thought of such method is an initial threshold value to be set, when the width of signal When degree is higher than the threshold value, the amplitude of signal is maintained for, and phase invariant identical with the threshold value of the setting.Although this method Realize fairly simple, but signal carried out signal can be made to produce inband distortion after peak clipping, so that BER hydraulic performance declines, produced Out-of-band radiation, the problems such as interference is produced to adjacent channel.
The technological difficulties of signal peak-to-average ratio are reduced, mainly there is the following aspects:
(1) frequency spectrum resource utilization rate:In existing probability class method, in order to accurately demodulate transmission in receiving terminal Signal is, it is necessary to know phase place information of the signal in transmitting terminal.Therefore, need to revolve phase while useful signal is sent Transposon is transmitted as side information.The utilization rate of frequency spectrum resource can thus be reduced.
(2) peak regeneration:If the peak-to-average force ratio for reducing signal uses nonlinear processing, although can in certain degree To reduce the out-of-band interference and in-band noise of signal, but still easily there is showing for peak regeneration afterwards after filtering in signal As.
(3) transmission rate:Signal is handled using the codeword set of transmission, select those can make peak reduce or The minimum code word of person, then the peak amplitude of select-out signal is used to transmit than relatively low codeword set from codeword set, can be with Higher peak value is avoided to occur, still, the transmission rate of signal also can be reduced substantially.
Signal is by being formed by stacking through ovennodulation and several separate sub-carrier signals, so when subcarrier letter Number phase it is same or similar when the output signal of system will be made to produce higher peak-to-average force ratio.PTS be (PTS algorithm models Block diagram is shown in accompanying drawing 1) main thought be to be multiplied using the data of multiple separate phase sequences and input, the multigroup sequence of generation Arrange to represent same group of identical signal, so under conditions of given PAPR threshold values are met, selection wherein PAPR values are minimum That group signal be transmitted, reduce height power ratio produce probability.
Fractional transmission (PTS) technology is that data X is divided into V groups are continuously distributed, size is identical and mutually disjoint sub- load Ripple block, the form that can be expressed as:
X=[X1,X2,…,Xυ]T
Wherein, XυRepresent the υ block of sub-carriers, υ=1,2 ..., V.We can see that PTS method is to every from Fig. 1 One block of sub-carriers carries out independent phase rotation.From phase rotatable sequence set B={ ej2πi/W| i=0,1 ..., W-1 in for the υ block of sub-carriers XυSelect a phase rotation coefficient bυ, form phase rotation coefficient sequence b=[b1,…,bV], the υ son Carrier block XυWith corresponding phase rotation coefficient bυAfter multiplication, then by IFFT conversion and superposition can obtain phase place because The alternative transmission data x obtained in the case of subsequence b, the form being expressed as:
Wherein, xυFor XυResult after being converted through IFFT, W is the system number that phase rotation coefficient is selected.
The alternative peak-to-average power ratio PAPR for sending data x is calculated, from all phase rotation coefficient sequence b situations, is chosen Alternative transmission data x minimum peak-to-average power ratio PAPR is used as data to be sentData to be sentCorresponding phase place because Subsequence b is used as optimum angle twiddle factor sequenceThe form being expressed as:
Wherein, xυIncluding N number of frequency domain symbol, xυ[n] is xυIn n-th of frequency domain symbol.
The step of PTS method is illustrated with W=2 situation below, as W=2, B={ 1, -1 }, namely bυ's Selectable value is 1 and -1 two kind, and algorithm steps are as follows:
With reference to above example, it can be seen that existing PTS method has following technical disadvantages:
(1) because needing to consider the complexity issue that system is realized in actual application, in order to reduce complexity Spend phase rotation coefficientOnly in a limited phase place arrangement set B={ ej2πi/W| i=0,1 ..., W-1 } in Choose;Despite this, optimum angle rotating vectorChoice Theory on need for carry out WVIt is secondary to calculate, and And the complexity calculated also can exponentially increase with the increase of block of sub-carriers number.
(2) under normal circumstances, in order to improve system bit error rate performance, it is necessary to will produce minimum PAPR values phase place The factor is sent together as side information with the data with minimum PAPR, so can accurately be recovered in receiving terminal Go out primary signal.But meanwhile, side information will reduce the transmission rate of system data, if receiving terminal can not be solved accurately Side information is recalled, the bit error rate performance of system can be also reduced.
Bibliography
[1].Meymanatabadi,Saber,Niya,Javad Musevi,and Mozaffari, Behzad.Selected mapping technique for PAPR reduction without side information based on m-sequence[J].Wireless personal communications,2013,71(4):2523–2534.
[2].Alsusa,Emad and Rabie,Khaled M.Dynamic peak-based threshold estimation method for mitigating impulsive noise in power-line communication systems[J].IEEE Transactions on Power Delivery,2013,28(4):2201–2208.
[3].Sharma,Chhavi,Sharma,Pankaj Kumar,Tomar,SK,et al.A modified Iterative Amplitude clipping and filtering technique for PAPR reduction in OFDM systems[C].In:Emerging Trends in Networks and Computer Communications (ETNCC),2011International Conference on.2011.365–368.
The content of the invention
Goal of the invention:In order to overcome the deficiencies in the prior art, the present invention is to traditional fractional transmission (PTS) technology It is improved, proposes a kind of method that signal peak-to-average ratio is reduced by constellation mapping and partial transmission sequence.
Technical scheme:To achieve the above object, the technical solution adopted by the present invention is:
A kind of method of signal peak-to-average ratio in reduction FBMC systems, the data processing of transmitting terminal comprises the following steps:
(1) by encoding operation by the former data conversion to be sent of transmitting terminal into quaternary number evidence, then by after conversion Quaternary number forms data X according to being respectively mapped on constellation circle;
(2) data X is divided into V group block of sub-carriers X=[X after string and conversion1,X2,…,XV]T, XυRepresent the υ son load Ripple block, υ=1,2 ..., V;
(3) it is the υ block of sub-carriers X from phase rotatable sequence set BυSelect a phase rotation coefficient bυ, form phase Position twiddle factor sequence b=[b1,…,bV], the υ block of sub-carriers XυWith corresponding phase rotation coefficient bυAfter multiplication, then pass through IFFT is converted and superposition can obtain the alternative transmission data x obtained in the case of phase rotation coefficient sequence b, is expressed as Form:
Wherein, xυFor XυResult after being converted through IFFT;Calculate the alternative peak-to-average power ratio PAPR for sending data x;
(4) calculating of step (3) is based on, from all phase rotation coefficient sequence b situations, peak-to-average power ratio PAPR is chosen Minimum alternative transmission data x is used as data to be sentData to be sentCorresponding phase rotation coefficient sequence b is as most Excellent phase rotation coefficient sequenceThe form being expressed as:
Wherein, xυIncluding N number of frequency domain symbol, xυ[n] is xυIn n-th of frequency domain symbol.
Specifically, in the step (1), data 0 are mapped to constellation circle by the quaternary number evidence after conversion On, data 1 are mapped on constellation circle (0,2j), data 2 are mapped on constellation circle (- 4,0), data 3 are mapped to constellation CircleOn.
Specifically, in the step (4), phase place arrangement set B is B={ e(2πj/2)i, i=0,1 }.
Specifically, in the step (2), data X is after string and conversion, and the group technology for being divided into V groups is adjacent packets, Interleaved packet or random packet, wherein being grouped into best practice at random.
Traditional PTS schemes can effectively reduce the peak-to-average force ratio of signal, but be due to need to transmit phase place information, Therefore the efficiency of transmission of system is reduced;In addition, the overall computation complexity of traditional PTS schemes is than larger.The present invention is to hair The data of sending end are handled, even if the data after carrying out constellation mapping are multiplied by after phase rotation coefficient, all points Data are not in overlapping all on concentric circles and during being mapped;So, do not needed in receiving terminal any auxiliary The information helped can just come out data recovery, and the availability of frequency spectrum is improved compared to traditional PTS schemes.
The present invention is mapped the data on circle first, and the data after mapping use all subcarriers by serioparallel exchange The method of adjacent segmentation is divided into V groups, and each packet is separate;Each group of subcarrier is multiplied by a phase rotation respectively Transposon, then all Signal averagings are got up, select the less one group of data of peak-to-average force ratio to carry out in all candidate signals Transmission, so as to realize the target algorithm block diagram of reduction peak-to-average force ratio, as shown in Figure 3.Signal is after IFFT conversion, the letter of time domain Number displacement is circulated, signal is equivalent on frequency domain and carries out phase place, therefore the amplitude of signal will not change, that is, become Constellation point is still on original position after alternatively.
After receiving terminal carries out FFT, time-domain signal becomes frequency-region signal.And the amplitude of signal is constant, so Re can be expressed as in receiving end signal, r is the amplitude for receiving signal, and θ is the phase angle for receiving signal.Therefore, in receiving terminal four The decision rule of binary data is as shown in algorithm 2.It can just connect using the method for constellation mapping according to following decision method Receiving end recovers the quaternary number evidence of transmission, it is not necessary to recovers transmission data in the case of extra transmission side information, improves The transmission rates of data.
The constellation mapping PTS schemes of algorithm 2, receiving end signal decision rule
Beneficial effect:The method of signal peak-to-average ratio in the reduction FBMC systems that the present invention is provided, employ constellation mapping with The method that partial transmission sequence is combined, relative to prior art, with following advantage:
1st, traditional PTS schemes are simply to be believed during Signal Pretreatment during signal peak-to-average ratio is reduced Phase rotation coefficient operation is multiplied by after number packet, causes to need the side information that additionally transmits to carry out signal demodulation in receiving terminal; The present invention has carried out signal constellation (in digital modulation) mapping in Signal Pretreatment, so that the utilization rate of frequency spectrum resource is improved, reduction signal demodulation Computation complexity;
2nd, traditional PTS schemes are during signal peak-to-average ratio is reduced, due to being adopted in the case where sub-carrier number is more Complexity with PTS algorithm search optimum angles twiddle factor vector is higher;The present invention due to having carried out constellation mapping operation, Therefore the computation complexity of phase rotation coefficient search is reduced, efficiency reduction is improved and calculates cost;
3rd, traditional PTS schemes are during signal peak-to-average ratio is reduced, and transmitting terminal needs accurately to send out side information Receiving terminal is given, such receiving terminal can accurately demodulate the information of transmission, can thus reduce the frequency spectrum of signal Resource utilization;The present invention uses constellation mapping algorithm, and side information is solved the problems, such as while reduction peak-to-average force ratio is ensured.
Brief description of the drawings
Fig. 1 is traditional PTS scheme transmitting terminal data process diagrams;
Fig. 2 is that data constellation maps schematic diagram;
Fig. 3 is transmitting terminal data process diagram of the present invention;
Primary signals and the CCDF of ofdm system primary signal comparison of the Fig. 4 for FBMC systems;
Fig. 5 is comparison of the FBMC-OQAM signals using CCDF during different number of piecemeal;
Fig. 6 is comparison of the FBMC-OQAM systems using constellation mapping and the CCDF of PTS method.
Embodiment
The present invention is further described below in conjunction with the accompanying drawings.
The data handling procedure block diagram of transmitting terminal in this example is illustrated in figure 3, is comprised the following steps:
(1) by encoding operation by the former data conversion to be sent of transmitting terminal into quaternary number evidence, then by after conversion Quaternary number forms data X according to being respectively mapped on constellation circle;
(2) data X is after string and conversion, is divided into that V groups are continuously distributed, size is identical and mutually disjoint block of sub-carriers X =[X1,X2,…,XV]T, XυRepresent the υ block of sub-carriers, υ=1,2 ..., V;
(3) from phase rotatable sequence set B={ e(2πj/2)i, i=0,1 } in for the υ block of sub-carriers XυSelect a phase Position twiddle factor bυ, form phase rotation coefficient sequence b=[b1,…,bV], the υ block of sub-carriers XυWith corresponding phase place Factor bυAfter multiplication, then convert by IFFT and superposition can obtain obtain in the case of phase rotation coefficient sequence b alternative Send data x, the form being expressed as:
Wherein, xυFor XυResult after being converted through IFFT;Calculate the alternative peak-to-average power ratio PAPR for sending data x;
(4) calculating of step (3) is based on, from all phase rotation coefficient sequence b situations, peak-to-average power ratio PAPR is chosen Minimum alternative transmission data x is used as data to be sentData to be sentCorresponding phase rotation coefficient sequence b is as most Excellent phase rotation coefficient sequenceThe form being expressed as:
Wherein, xυIncluding N number of frequency domain symbol, xυ[n] is xυIn n-th of frequency domain symbol.
The phase place arrangement set that this case is used is B={ e(2πj/2)i, i=0,1 }, i.e. W=2 so can not only drop The computation complexity of low optimum angle factor search can also play the excellent of partial transmission sequence reduction signal peak-to-average ratio well Gesture.Traditional PTS schemes need to transmit demodulation of the side information for receiving end signal, if the side information of transmission is in demodulation Distortion serious Shi Fasheng, can cause signal not demodulate.In the present case because employing the scheme of annular mapping, Receiving terminal can be made decisions with the phase and amplitude of basis signal to signal, not need the side information of PTS algorithms;So not The utilization rate that improve only signal spectrum also improves the degree of accuracy of signal.
Fig. 2 is the schematic diagram that data carry out constellation mapping progress, initial data is pre-processed, by the data of the quaternary Be respectively mapped on the circle that radius is 2 and radius is 4 as shown in Fig. 2 left hand views, such data carry out PTS algorithm operatings when, Data are multiplied by different phase rotation coefficients respectively, the phenomenon that will not be overlapped, so can be with basis signal in receiving terminal Amplitude and phase make decisions to data, so as to avoid the need for transmitting the situation of side information, reduce the complexity of calculating.
Fig. 4 is that the primary signal of FBMC systems is compared with the CCDF of ofdm system primary signal, it can be seen that FBMC signals PAPR have dropped 0.1dB than OFDM on the CCDF=0.001 orders of magnitude.Thus, it is possible to draw a conclusion, FBMC compared to OFDM has preferable peak-to-average force ratio characteristic.
When Fig. 5 is that FBMC-OQAM systems use PTS method (sub-block number of variations), under the conditions of different piecemeal numbers The PAPR of FBMC-OQAM system signals CCDF performances.As can be seen from the figure being continuously increased with sub-block number, i.e. V= The PAPR performances of 1,2,4,8,16 systems are improved.
Fig. 6 is the analogous diagram that FBMC-OQAM systems use constellation mapping PTS schemes, for comparative analysis, in other emulation Under the same conditions, the block count that two schemes are used is all for 4, i.e. V=4 for parameter.As can be seen from the figure the PTS of constellation mapping Scheme and traditional PTS schemes have same reduction PAPR effect (being better than traditional PTS schemes), but constellation mapping PTS Scheme need not transmit side information compared to traditional PTS schemes, improve frequency spectrum resource utilization rate.Meanwhile, in receiving terminal Constellation mapping PTS schemes recover transmission data it is more easier than traditional PT schemes because side information need not be transmitted, this Sample (receiving terminal can not accurately obtain side information) under more severe transmission environment also ensure that data transfer Bit error rate performance.
The above is only the preferred embodiment of the present invention, it should be pointed out that:For the ordinary skill people of the art For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should It is considered as protection scope of the present invention.

Claims (5)

1. a kind of method of signal peak-to-average ratio in reduction FBMC systems, it is characterised in that:The data processing of transmitting terminal includes as follows Step:
(1) by encoding operation by the former data conversion to be sent of transmitting terminal into quaternary number evidence, then four after conversion are entered Data processed are respectively mapped on constellation circle, form data X;
(2) data X is divided into V group block of sub-carriers X=[X after string and conversion1,X2,…,XV]T, XυRepresent the υ subcarrier Block, υ=1,2 ..., V;
(3) it is the υ block of sub-carriers X from phase rotatable sequence set BυSelect a phase rotation coefficient bυ, form phase rotation Transposon sequence b=[b1,…,bV], the υ block of sub-carriers XυWith corresponding phase rotation coefficient bυAfter multiplication, then by IFFT Conversion and superposition can obtain the alternative transmission data x obtained in the case of phase rotation coefficient sequence b, the shape being expressed as Formula:
x = I F F T { Σ υ = 1 V b υ X υ } = Σ υ = 1 V b υ · I F F T { X υ } = Σ υ = 1 V b υ x υ
Wherein, xυFor XυResult after being converted through IFFT;Calculate the alternative peak-to-average power ratio PAPR for sending data x;
(4) calculating of step (3) is based on, from all phase rotation coefficient sequence b situations, peak-to-average power ratio PAPR is chosen minimum Alternative transmission data x be used as data to be sentData to be sentCorresponding phase rotation coefficient sequence b is used as optimal phase Position twiddle factor sequenceThe form being expressed as:
[ b ~ 1 , ... , b ~ V ] = arg m i n [ b 1 , ... , b V ] ( m a x [ n = 0 , 1 , ... , N - 1 ] | Σ υ = 1 V b υ x υ [ n ] | )
x ~ = Σ υ = 1 V b ~ υ x υ
Wherein, xυIncluding N number of frequency domain symbol, x υ [n] are xυIn n-th of frequency domain symbol.
2. the method for signal peak-to-average ratio in reduction FBMC systems according to claim 1, it is characterised in that:The step (1) in, data 0 are mapped to constellation circle by the quaternary number evidence after conversionOn, by data 1 be mapped to constellation circle (0, On 2j), data 2 are mapped on constellation circle (- 4,0), data 3 are mapped to constellation circleOn.
3. the method for signal peak-to-average ratio in reduction FBMC systems according to claim 1, it is characterised in that:The step (4) in, phase place arrangement set B is B={ e(2πj/2)i, i=0,1 }.
4. the method for signal peak-to-average ratio in reduction FBMC systems according to claim 1, it is characterised in that:The step (2) in, data X is divided into the group technology of V groups for adjacent packets after string and conversion, interleaved packet or random packet, wherein Random to be grouped into best practice, this case carries out simulating, verifying using the method for adjacent packets.
5. the method for signal peak-to-average ratio in reduction FBMC systems according to claim 1, it is characterised in that:Receiving terminal according to The following decision rule docking collection of letters number is demodulated:
1. as r < 3, ifIt is 0 then to receive signal;
2. as r < 3, ifIt is 1 then to receive signal;
3. as r >=3, ifIt is 2 then to receive signal;
4. as r >=3, ifIt is 3 then to receive signal;
Wherein, r is receives the amplitude of signal, and θ is the phase angle for receiving signal.
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