WO2018068630A1 - 前向后向平滑译码方法、装置及系统 - Google Patents

前向后向平滑译码方法、装置及系统 Download PDF

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WO2018068630A1
WO2018068630A1 PCT/CN2017/103311 CN2017103311W WO2018068630A1 WO 2018068630 A1 WO2018068630 A1 WO 2018068630A1 CN 2017103311 W CN2017103311 W CN 2017103311W WO 2018068630 A1 WO2018068630 A1 WO 2018068630A1
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particle
symbol
sequence
importance
weight
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PCT/CN2017/103311
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English (en)
French (fr)
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刘若鹏
季春霖
徐兴安
张莎莎
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深圳超级数据链技术有限公司
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Priority claimed from CN201610886190.0A external-priority patent/CN107919940A/zh
Priority claimed from CN201610886096.5A external-priority patent/CN107919939B/zh
Application filed by 深圳超级数据链技术有限公司 filed Critical 深圳超级数据链技术有限公司
Priority to EP17861037.4A priority Critical patent/EP3525372A4/en
Priority to JP2019518947A priority patent/JP6857720B2/ja
Priority to KR1020197013014A priority patent/KR102239746B1/ko
Publication of WO2018068630A1 publication Critical patent/WO2018068630A1/zh
Priority to US16/379,622 priority patent/US10707896B2/en

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    • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
    • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
    • H03M7/3002—Conversion to or from differential modulation
    • H03M7/3004—Digital delta-sigma modulation
    • H03M7/3015—Structural details of digital delta-sigma modulators
    • H03M7/3031—Structural details of digital delta-sigma modulators characterised by the order of the loop filter, e.g. having a first order loop filter in the feedforward path
    • H03M7/3033—Structural details of digital delta-sigma modulators characterised by the order of the loop filter, e.g. having a first order loop filter in the feedforward path the modulator having a higher order loop filter in the feedforward path, e.g. with distributed feedforward inputs
    • H03M7/3037—Structural details of digital delta-sigma modulators characterised by the order of the loop filter, e.g. having a first order loop filter in the feedforward path the modulator having a higher order loop filter in the feedforward path, e.g. with distributed feedforward inputs with weighted feedforward summation, i.e. with feedforward paths from more than one filter stage to the quantiser input
    • H—ELECTRICITY
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    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
    • H04L1/0015—Systems modifying transmission characteristics according to link quality, e.g. power backoff characterised by the adaptation strategy
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03178—Arrangements involving sequence estimation techniques
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
    • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
    • H03M7/3002—Conversion to or from differential modulation
    • H03M7/3004—Digital delta-sigma modulation
    • H03M7/3015—Structural details of digital delta-sigma modulators
    • H03M7/3031—Structural details of digital delta-sigma modulators characterised by the order of the loop filter, e.g. having a first order loop filter in the feedforward path
    • H03M7/3033—Structural details of digital delta-sigma modulators characterised by the order of the loop filter, e.g. having a first order loop filter in the feedforward path the modulator having a higher order loop filter in the feedforward path, e.g. with distributed feedforward inputs
    • H03M7/304—Structural details of digital delta-sigma modulators characterised by the order of the loop filter, e.g. having a first order loop filter in the feedforward path the modulator having a higher order loop filter in the feedforward path, e.g. with distributed feedforward inputs with distributed feedback, i.e. with feedback paths from the quantiser output to more than one filter stage
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
    • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
    • H03M7/3059—Digital compression and data reduction techniques where the original information is represented by a subset or similar information, e.g. lossy compression
    • H03M7/3062—Compressive sampling or sensing
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
    • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
    • H03M7/60—General implementation details not specific to a particular type of compression
    • H03M7/6005—Decoder aspects
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0059—Convolutional codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03171—Arrangements involving maximum a posteriori probability [MAP] detection
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03343—Arrangements at the transmitter end
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/38—Synchronous or start-stop systems, e.g. for Baudot code
    • H04L25/40—Transmitting circuits; Receiving circuits
    • H04L25/49—Transmitting circuits; Receiving circuits using code conversion at the transmitter; using predistortion; using insertion of idle bits for obtaining a desired frequency spectrum; using three or more amplitude levels ; Baseband coding techniques specific to data transmission systems
    • H04L25/497—Transmitting circuits; Receiving circuits using code conversion at the transmitter; using predistortion; using insertion of idle bits for obtaining a desired frequency spectrum; using three or more amplitude levels ; Baseband coding techniques specific to data transmission systems by correlative coding, e.g. partial response coding or echo modulation coding transmitters and receivers for partial response systems
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    • G06F11/07—Responding to the occurrence of a fault, e.g. fault tolerance
    • G06F11/08—Error detection or correction by redundancy in data representation, e.g. by using checking codes
    • G06F11/10—Adding special bits or symbols to the coded information, e.g. parity check, casting out 9's or 11's
    • G06F11/1004—Adding special bits or symbols to the coded information, e.g. parity check, casting out 9's or 11's to protect a block of data words, e.g. CRC or checksum
    • G—PHYSICS
    • G11—INFORMATION STORAGE
    • G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
    • G11B20/00—Signal processing not specific to the method of recording or reproducing; Circuits therefor
    • G11B20/10—Digital recording or reproducing
    • G11B20/12—Formatting, e.g. arrangement of data block or words on the record carriers
    • G11B20/1217—Formatting, e.g. arrangement of data block or words on the record carriers on discs
    • G11B2020/1218—Formatting, e.g. arrangement of data block or words on the record carriers on discs wherein the formatting concerns a specific area of the disc
    • G11B2020/1222—ECC block, i.e. a block of error correction encoded symbols which includes all parity data needed for decoding
    • G—PHYSICS
    • G11—INFORMATION STORAGE
    • G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
    • G11B20/00—Signal processing not specific to the method of recording or reproducing; Circuits therefor
    • G11B20/10—Digital recording or reproducing
    • G11B20/18—Error detection or correction; Testing, e.g. of drop-outs
    • G11B20/1833—Error detection or correction; Testing, e.g. of drop-outs by adding special lists or symbols to the coded information
    • G11B2020/1859—Error detection or correction; Testing, e.g. of drop-outs by adding special lists or symbols to the coded information wherein a trellis is used for decoding the error correcting code

Definitions

  • the present invention relates to the field of decoding, and in particular, to a forward-backward smooth decoding method, apparatus and system.
  • the number of nodes determines the complexity of decoding, and for systems with overlapping times K and modulation dimension M ( M is an integer greater than or equal to 2), and the number of nodes in the steady state in the corresponding trellis diagram is M K-1 , so the decoding complexity increases exponentially with the number of overlaps K.
  • the spectral efficiency of the system is 2K/symbol, so the larger the number of overlaps K, the higher the spectral efficiency.
  • the requirement of improving the spectral efficiency is such that the larger the number of overlaps K is, the better, and on the other hand, the smaller the number of times of overlap K is, the better, in order to reduce the decoding complexity, in particular, when the number of overlaps K is increased to a certain extent.
  • the value for example, if K is greater than 8, the decoding complexity increases sharply.
  • the existing decoding method is difficult to meet the requirements of real-time decoding, and the spectral efficiency, decoding complexity and decoding efficiency form a contradiction requirement.
  • the present application provides a forward backward smooth decoding method suitable for an OvXDM system, including the following steps:
  • the forward smoothing step starting from the first symbol in an estimated sequence to the end of the last symbol, sequentially calculating the importance weights of the particles in the particle set corresponding to each symbol, and obtaining the particle importance weight of the forward smoothing process;
  • a backward smoothing step starting from the last symbol in the estimated sequence to the end of the first symbol, referring to the importance weight of the particles obtained in the forward smoothing step, and sequentially calculating the importance weights of the particles in the particle set corresponding to each symbol , obtaining the particle importance weight of the backward smoothing process;
  • Output step the particle with the largest weight importance of the particle smoothing process after each symbol is used as the estimated value of the symbol, and the final decoding sequence is output.
  • the present application provides a forward backward smooth decoding apparatus suitable for an OvXDM system, including:
  • the forward smoothing unit is configured to calculate the importance weight of each particle in the particle set corresponding to each symbol from the first symbol in the estimation sequence to the end of the last symbol, and obtain the particle importance weight of the forward smoothing process;
  • a backward smoothing unit for starting from the last symbol in the estimated sequence to the end of the first symbol, referring to the importance weight of the particles obtained in the forward smoothing unit, and sequentially calculating the importance of each particle in the particle set corresponding to each symbol Sexual weight, the particle importance weight of the backward smoothing process;
  • the output unit is configured to use the particle with the highest weight importance of the particle smoothing process for each symbol to be the estimated value of the symbol, and output the final decoding sequence.
  • the present application provides an OvXDM system, including the foregoing forward backward smooth decoding apparatus applicable to an OvXDM system, wherein the OvXDM system is an OvTDM system, an OvFDM system, an OvCDM system, and an OvSDM system. Or OvHDM system.
  • the statistical idea is introduced into the decoding process, and the two processes of forward smoothing and backward smoothing are utilized to fully utilize the mutual interaction between the particles.
  • the information realizes the decoding of the OvXDM system, so that the obtained decoding sequence is closer to the true value.
  • the decoding complexity is reduced compared with the traditional decoding method, and the decoding efficiency and system performance are improved. .
  • FIG. 1 is a schematic structural view of a transmitting end of a conventional OvTDM system
  • FIG. 2 is a schematic diagram of a parallelogram rule for overlapping multiplexing coding of input symbols by an OvTDM system
  • Figure 3 (a), (b) respectively, the preprocessing unit and the sequence detecting unit of the conventional OvTDM receiving end;
  • Figure 5 is a node state transition diagram of the corresponding system of Figure 4.
  • Figure 6 is a Trellis diagram of the corresponding system of Figure 4 or Figure 5;
  • FIG. 7 is a schematic flowchart of a forward-backward smooth decoding method applicable to an OvXDM system according to an embodiment of the present application.
  • Figure 8 is a diagram of an equivalent convolutional coding model of the OvXDM system
  • FIG. 9 is a schematic flowchart of a forward smoothing step in an embodiment of the present application.
  • FIG. 10 is a schematic diagram of a resampling step in an embodiment of the present application.
  • FIG. 11 is a schematic flowchart of a backward smoothing step in an embodiment of the present application.
  • FIG. 12 is a schematic structural diagram of a forward backward smooth decoding apparatus applicable to an OvXDM system according to an embodiment of the present application
  • FIG. 13 is a schematic structural diagram of a forward smoothing unit in an embodiment of the present application.
  • FIG. 14 is a schematic structural diagram of a backward smoothing unit in an embodiment of the present application.
  • FIG. 15 is a schematic flowchart of a forward backward decoding method applicable to an OvXDM system according to another embodiment of the present application.
  • 16 is a schematic flow chart of a forward step in another embodiment of the present application.
  • FIG. 17 is a schematic structural diagram of a decoding apparatus according to another embodiment of the present application.
  • FIG. 18 is a schematic structural diagram of a forward unit according to another embodiment of the present application.
  • FIG. 19 is a schematic structural diagram of a backward unit in another embodiment of the present application.
  • the forward step and the backward step are employed in the embodiment of the present invention.
  • the forward step may include a forward smoothing step or a forward filtering step;
  • the backward step may include a backward smoothing step or a backward direction Filtering step.
  • the present application proposes a forward-backward smooth decoding method and apparatus for an OvXDM system, and an OvXDM system, wherein the OvXDM system is an Overlapped Time Division Multiplexing (OvTDM) system and an overlapping frequency division multiplexing (OvFDM, Overlapped Frequency Division Multiplexing System, Overlapped Code Division Multiplexing (OvCDM) system, Overlapped Space Division Multiplexing (OvSDM) system or Overlapped Hybrid Division Multiplexing (OvHDM) system .
  • OvTDM Overlapped Time Division Multiplexing
  • OFDM Overlapped Frequency Division Multiplexing
  • OFDM Overlapped Code Division Multiplexing
  • OFDM Overlapped Space Division Multiplexing
  • OFHDM Overlapped Hybrid Division Multiplexing
  • the sending process of the OvTDM sender is as follows:
  • the respective waveforms to be transmitted formed by (3) are superposed by x i h(ti ⁇ ⁇ T) to form a waveform of the transmission signal.
  • the signal sent can be expressed as:
  • the overlapping multiplexing method follows the parallelogram rule as shown in FIG. 2.
  • the transmitting end transmits the coded and modulated signal through the antenna, and the signal is transmitted in the wireless channel, and the receiving end performs matching filtering on the received signal, and then separately samples and decodes the signal, and finally determines the output bit stream.
  • FIG. 3 it is a receiving process of the OvTDM receiving end, wherein FIG. 3(a) is a preprocessing unit of the OvTDM receiving end, and FIG. 3(b) is a sequence detecting unit of the OvTDM receiving end, and the specific steps are as follows:
  • the received signal is synchronized, including carrier synchronization, frame synchronization, symbol time synchronization, and the like.
  • the received signal in each frame is digitized.
  • the received waveform is cut according to the waveform transmission time interval.
  • FIG. 5 is a corresponding node state transition diagram of the system, and
  • FIG. 6 is a grid shape of the system. (Trellis) map.
  • the conventional decoding method typically, Viterbi decoding
  • the decoding complexity increases sharply, the hardware precision is required to be high, and the system performance is lowered.
  • the inventor introduced the statistical idea into the decoding process through research and practice, and made full use of the mutual information between the particles to realize the decoding of the OvXDM system through the two processes of forward smoothing and backward smoothing.
  • the decoding sequence is closer to the true value, and as the number of overlaps increases, the decoding complexity is reduced compared with the conventional decoding method, and the decoding efficiency and system performance are improved.
  • the decoding process in this embodiment mainly includes a forward smoothing process and a backward smoothing process.
  • the principle of the forward smoothing process is the same as that of the Monte Carlo methods.
  • the Monte Carlo method is a kind of very important numerical calculation method which is applied to statistics and guided by probability and statistics theory.
  • the basic idea is that when the problem is solved, the probability of a random event appears, or a random
  • the probability of the random event is estimated by the frequency of the occurrence of such an event by an "experimental” method, or some numerical characteristics of the random variable are obtained and used as a solution to the problem.
  • Monte Carlo method Monte Carlo method in statistics
  • the corresponding one is called Particle Filter (PF) in engineering.
  • the idea of particle filtering is based on the Monte Carlo method, which uses particle sets to represent probabilities.
  • particle filtering It can be used on any form of state space model to accurately express posterior probability distributions based on observations and control quantities.
  • the core idea of particle filtering is to express its distribution by extracting random state particles from the posterior probability. It is a sequential importance sampling method (Sequential Importance Sampling). Therefore, particle filtering is to approximate the probability density function by finding a set of random samples propagating in the state space, and replace the integral operation with the sample mean, and then obtain the process of estimating the minimum variance of the system state. These samples are called “ Particles, so called particle filtering. Any form of probability density distribution can be approximated when the number of samples approaches infinity.
  • the backward smoothing process is based on the forward smoothing process and the corresponding particle weights in the forward smoothing process.
  • the estimated particles are smoothed again in order from the back to the front to obtain a more realistic estimation. sequence.
  • the forward-backward smoothing (FBS) process is based on the following relationship:
  • y 1:t ) are the filter density and the forward prediction density at time t , respectively.
  • y 1:T ) is repeatedly obtained to p(x t+1
  • the edge smooth distribution can be approximated by a weight particle cloud.
  • the forward particle filter can be expressed as:
  • the backward smooth distribution is expressed as: Its smoothing weight is calculated iteratively by the following formula:
  • the backward smoothing is based on the forward smoothing, and the estimated particles are smoothed again according to the sequence of the backward smoothing and the corresponding particle weights. A more realistic estimate of the sequence.
  • the forward backward decoding method applicable to the OvXDM system disclosed in the present application includes a forward smoothing step S100, a backward smoothing step S300, and an output step S500, wherein the OvXDM system may be The OvTDM system, the OvFDM system, the OvCDM system, the OvSDM system, or the OvHDM system, as shown in FIG. 8, is an equivalent convolutional coding model of the OvXDM system.
  • the forward smoothing step S100 starting from the first symbol in an estimated sequence to the end of the last symbol, sequentially calculating the importance weights of the particles in the particle set corresponding to each symbol, and obtaining the particle importance weight of the forward smoothing process. Specifically, referring to FIG. 9, the forward smoothing step S100 includes steps S101 to S109.
  • Step S101 Initialize the estimated sequence X. Since this is in the forward smoothing process, it is possible to refer to the estimated sequence X as a forward smoothing estimation sequence Xf whose sequence length is the same as the length of the sequence to be decoded.
  • the receiving end of the OvXDM system may receive the symbol sequence y of length N, which is the sequence to be decoded, the number of times of overlap is K, and the rectangular wave is a multiplexed waveform; if the number of particles of each symbol For Ns, each particle corresponds to an importance weight value.
  • the size of the forward smoothing estimation sequence Xf is Ns ⁇ N
  • the size of the set Wf of importance weight values corresponding to each particle is Ns ⁇ N.
  • Step S103 Starting from the first symbol in the forward smoothing estimation sequence Xf to the end of the last symbol, generating a particle set for the current symbol.
  • the number of particles in the particle concentration corresponding to each symbol is N s .
  • the particle set corresponding to each symbol includes two Particles, with values +1 and -1 respectively.
  • Step S105 After generating the particle set for the current symbol, calculate the importance probability density of each particle of the current symbol and the sequence to be decoded, and calculate the importance weight of each particle.
  • calculating the importance weight of each particle in the particle set corresponding to the current symbol is calculated according to the following formula:
  • N is the length of the sequence to be decoded
  • Ns is the number of particles in the particle set corresponding to the current symbol
  • P i,j is the importance probability density of the particle. It can be seen that wf i,j is actually the normalized importance weight of the particles.
  • the importance probability density of the particle in the particle set of the current symbol and the sequence to be decoded is calculated, and the previous symbol can be referred to.
  • the probability density of the particles in the particle set and the importance of the sequence to be decoded is calculated.
  • step S107 After calculating the importance weights of the particles in the particle set corresponding to the current symbol, step S107 is performed.
  • Step S107 It is determined whether the particle set corresponding to the current symbol satisfies a preset particle degradation condition. If not, the next symbol is performed, that is, the next symbol is started from step S103. If yes, step S109 is performed.
  • This step S107 is for determining whether the degradation phenomenon of the particle-concentrated particles corresponding to the current symbol is obvious. For example, you can set the effective particle capacity of the particle set corresponding to the symbol. Below a certain threshold, then the particle set corresponding to the symbol is resampled.
  • the above-mentioned particle degradation condition that does not satisfy the preset means that the particle set degradation phenomenon corresponding to the current symbol is not serious, and the predetermined particle degradation condition is satisfied, which means that the particle set degradation phenomenon corresponding to the current symbol is serious. It therefore needs to be resampled.
  • Step S109 Resampling the particle set of the current symbol. Resampling is to eliminate particles with low weight and concentrate on particles with high weight, thus suppressing degradation. There are many methods for resampling, including importance resampling, residual resampling, layered resampling, and optimized combined resampling. The basic idea is to reproduce the particles with heavy weight and eliminate the particles with small weights. Finally, a new particle set is generated, and the resampling schematic is shown in FIG.
  • the "starting from the first symbol in the forward smoothing estimation sequence Xf to the end of the last symbol" mentioned in the step S103 may be performed from the first symbol to the step S101 first, and the result of the determination in the step S107. If it is not satisfied and after step S109, a judgment is made to determine whether the last symbol is reached, and if so, the forward smoothing step S100 ends, otherwise the next symbol is processed, that is, the next symbol starts from step S103. According to the flow shown in Fig. 9, the steps are performed downward.
  • each symbol in the sequence X (forward smoothing estimation sequence Xf) has a corresponding particle set, and each particle in each particle set has an importance weight.
  • the backward smoothing step S300 starting from the last symbol in the estimated sequence X (forward smoothing estimation sequence Xf) to the end of the first symbol, referring to the importance weight of the particles obtained in the forward smoothing step S100, sequentially calculating the corresponding correspondence of each symbol The importance weight of each particle in the particle concentration is obtained, and the particle importance weight of the backward smoothing process is obtained.
  • the backward smoothing step S300 includes steps S301 to S305.
  • Step S301 According to the result calculated by the forward smoothing step S100, the particle with the highest importance weight of the particle corresponding to the last symbol in the estimated sequence X (forward smoothing estimation sequence Xf) is used as an estimated value of the symbol, and the estimated sequence is The particle importance weight of the forward smoothing process of each particle in the particle set corresponding to the last symbol in X (forward smoothing estimation sequence Xf) is the particle concentration corresponding to the last symbol in the estimated sequence X (forward smoothing estimation sequence Xf) The importance of the particles of the backward smoothing process of each particle.
  • a backward smoothing sequence Xb may be additionally provided, the length of which is N, and the particle with the highest importance weight of the particle corresponding to the last symbol in the estimated sequence X (forward smoothing estimation sequence Xf) is used as
  • Step S303 calculating the probability density between the current symbol and the latter symbol from the second last symbol of the estimated sequence X to the end of the first symbol. It should be noted that since the sequence estimated in the forward smoothing process is not encoded, it is necessary to calculate the probability density of the current time symbol and the subsequent time symbol respectively after the multiplexed waveform is subjected to K-weight OvXDM coding. . In this case, the multivariate normal probability density (mvnpdf) probability density is used.
  • Step S305 Calculate the particle of the backward smoothing process of the current symbol according to the probability density calculated in step S303, the particle importance weight of the backward smoothing process of the latter symbol, and the particle importance weight of the forward smoothing process of the current symbol. Importance weight.
  • the normalization factor can be calculated first. among them It is the result calculated by the forward smoothing step S100.
  • the importance weights of the particles in the particle set corresponding to the current symbol are calculated by the following formula:
  • Ns represents the number of particles, i, j represents the particle index, and takes a value of 1 to Ns;
  • x t (k) represents the kth particle in the symbol at time t;
  • ⁇ t is the particle importance weight of the forward smoothing process of the current symbol
  • Is the probability density between the current symbol and the latter symbol
  • T is the particle importance weight of the backward smoothing process of the current symbol.
  • the "from the second to last symbol of the estimated sequence X to the end of the first symbol" mentioned in the step S303 may also start from the first symbol in the forward smooth estimation sequence Xf to the last mentioned in the above step S103.
  • the implementation of a symbol end is similar and will not be described here.
  • Step S500 The particles corresponding to each symbol are concentrated and the particles with the highest weight importance of the smoothing process are used as the estimated values of the symbols, and the final decoding sequence is output.
  • the particle having the largest weight importance of the backward smoothing process of the particle corresponding to each symbol in the sequence X is used as an estimated value of the symbol, and the final decoding sequence is output.
  • a forward backward smooth decoding apparatus suitable for an OvXDM system includes a forward smoothing unit 100, a backward smoothing unit 300, and an output unit 500.
  • the forward smoothing unit 100 is configured to calculate the importance weights of the particles in the particle set corresponding to each symbol from the first symbol in the estimation sequence to the end of the last symbol, and obtain the particle importance weight of the forward smoothing process.
  • the forward smoothing unit 100 includes an initializing unit 101, a particle set generating unit 103, an importance probability density calculating unit 105, an importance weight calculating unit 107, a determining unit 109, and a resampling unit 111.
  • the initialization unit 101 is used to initialize the estimated sequence X, wherein the length of the estimated sequence X is the same as the length of the sequence to be coded. Since this is in the pre-smoothing process, it is possible to refer to the estimated sequence X as the forward smoothing estimation sequence Xf whose sequence length is the same as the length of the sequence to be decoded.
  • the receiving end of the OvXDM system may receive the symbol sequence y of length N, which is the sequence to be decoded, the number of times of overlap is K, and the rectangular wave is a multiplexed waveform; if the number of particles of each symbol For Ns, each particle corresponds to an importance weight value. Then, the size of the forward smoothing estimation sequence Xf is Ns ⁇ N, and the size of the set Wf of importance weight values corresponding to each particle is Ns ⁇ N.
  • the particle set generation unit 103 is configured to generate a particle set for the current symbol from the first symbol in the estimated sequence X to the end of the last symbol.
  • the number of particles in the particle set corresponding to each symbol is N s .
  • the particle set corresponding to each symbol includes two Particles, with values +1 and -1 respectively.
  • the importance probability density calculation unit 105 calculates the importance probability density of each particle of the current symbol and the sequence to be decoded after the current symbol generation particle set is used. In an embodiment, when i>1, that is, when the current symbol is the second symbol or the following symbol, the importance probability density calculation unit 105 calculates the importance probability of the particle in the particle set of the current symbol and the sequence to be decoded. For the density, reference may be made to the importance probability density of the particles in the particle set of the previous symbol and the sequence to be decoded. It should be noted that in the OvXDM system, since the received symbol sequence y is encoded by OvXDM, the estimated symbol is also needed. Xf i,j performs OvXDM encoding and then calculates its importance probability density.
  • the importance weight calculation unit 107 is configured to calculate the importance weight of each particle based on the importance probability density. In an embodiment, the importance weight calculation unit 107 calculates the importance weight of each particle in the particle set corresponding to the current symbol according to the following formula:
  • N is the length of the sequence to be decoded
  • Ns is the number of particles in the particle set corresponding to the current symbol
  • P i,j is the importance probability density of the particle. It can be seen that wf i,j is actually the normalized importance weight of the particles.
  • the determining unit 109 is configured to determine whether the particle set corresponding to the current symbol satisfies a preset particle degradation condition, and if not, notify the particle set generating unit 103 to generate a particle set for the latter symbol.
  • the determining unit 109 is for determining whether the degradation phenomenon of the particle-concentrated particles corresponding to the current symbol is obvious. For example, you can set the effective particle capacity of the particle set corresponding to the symbol. Below a certain threshold, then the particle set corresponding to the symbol is resampled.
  • the resampling unit 111 is configured to resample the particle set of the current symbol when the result of the determining unit 109 is satisfied.
  • the resampling unit 111 performs resampling in order to eliminate particles with low weight and concentrate on particles with high weight. Sub, thereby suppressing degradation.
  • the backward smoothing unit 300 is configured to start from the last symbol in the estimated sequence X (forward smoothing estimation sequence Xf) to the end of the first symbol, and refer to the importance weight of the particles obtained in the forward smoothing unit 100, and sequentially calculate each symbol. The importance weight of each particle in the corresponding particle concentration is obtained, and the particle importance weight of the backward smoothing process is obtained.
  • the backward smoothing unit 300 includes a setting unit 301, a probability density calculating unit 303, and an importance weight recalculating unit 305.
  • the setting unit 301 is configured to use, as a result of the calculation by the forward smoothing unit 100, a particle having the largest particle set importance weight corresponding to the last symbol in the estimated sequence X (forward smoothing estimation sequence Xf) as an estimated value of the symbol, and Estimating the particle importance weight of the forward smoothing process of each particle in the particle set corresponding to the last symbol in the sequence X (forward smoothing estimation sequence Xf) as the backward direction of each particle corresponding to the last symbol in the estimated sequence The importance of the particle importance of the smoothing process.
  • a backward smoothing sequence Xb may be additionally provided, the length of which is N, and the setting unit 301 maximizes the weight importance of the particle concentration corresponding to the last symbol in the estimated sequence X (forward smoothing estimation sequence Xf).
  • the setting unit 301 assigns the importance weight of each particle in the particle set corresponding to the last symbol in the estimated sequence X (forward smoothing estimation sequence Xf) to the importance weight Wb of the backward smoothing sequence Xb, which can be expressed as Wb (1).
  • ⁇ Ns, N) Wf (1 to Ns, N).
  • the probability density calculation unit 303 is configured to calculate the probability density between the current symbol and the latter symbol from the second last symbol of the estimation sequence to the end of the first symbol. It should be noted that since the sequence estimated in the forward smoothing process is not encoded, it is necessary to calculate the probability density of the current time symbol and the subsequent time symbol respectively after the multiplexed waveform is subjected to K-weight OvXDM coding. . In this case, the multivariate normal probability density (mvnpdf) probability density is used.
  • the importance weight recalculating unit 305 is configured to calculate the probability density according to the probability density calculation unit 303 and the particle importance of the backward smoothing process of the latter symbol, after the probability density between the current symbol and the latter symbol is calculated. Weight, the particle importance weight of the forward smoothing process of the current symbol, and the particle importance of the backward smoothing process of the current symbol is calculated. In an embodiment, the importance weight recalculation unit 305 may first calculate the normalization factor. among them It is the result calculated by the forward smoothing unit 100. In an embodiment, the importance weight recalculation unit 305 calculates the importance weights of the particles in the particle set corresponding to the current symbol by the following formula:
  • Ns represents the number of particles, i, j represents the particle index, and takes a value of 1 to Ns; x t (t) represents the kth particle in the symbol at time t.
  • ⁇ t is the particle importance weight of the forward smoothing process of the current symbol
  • Is the probability density between the current symbol and the latter symbol
  • T is the particle importance weight of the backward smoothing process of the current symbol.
  • the output unit 500 is configured to use the particle with the highest weight importance of the particle smoothing process for each symbol to be the estimated value of the symbol, and output the final decoding sequence. In other words, it is estimated that the particle having the largest weight importance of the backward smoothing process of the particle corresponding to each symbol in the sequence X is used as an estimated value of the symbol, and the final decoding sequence is output.
  • a set of samples may be randomly generated first, and the importance weight of the particle and the observed value is calculated.
  • the particle samples are resampled, the particles with small weights are eliminated, and the particles with significant weights are repeatedly iteratively calculated in turn, and finally the more reliable output values are obtained.
  • the degradation of particles is the biggest defect of particle filters, which restricts the development of particle filters.
  • One of the effective methods to solve the problem of particle degradation is to resample the particles.
  • Particle filtering has unique advantages in solving parameter estimation and state filtering of nonlinear and non-Gaussian problems. Therefore, there is a great room for development, and a variety of mature optimization methods can be introduced into the resampling process for faster Extracted to a typical "particle" that reflects the probabilistic characteristics of the system.
  • the two processes of forward smoothing and backward smoothing are utilized to fully utilize the mutual information between the particles to realize the decoding of the OvXDM system, so that the obtained decoding sequence is closer to the true value, and at the same time, with the number of overlaps Compared with the traditional decoding method, the decoding complexity is reduced, and the decoding efficiency and system performance are improved.
  • the decoding process of another embodiment of the present application mainly includes a forward filtering process and a backward information filtering process.
  • the principle of the forward filtering process is the same as that of the Monte Carlo methods.
  • the Monte Carlo method is a kind of very important numerical calculation method which is applied to statistics and guided by probability and statistics theory.
  • the basic idea is that when the problem is solved, the probability of a random event appears, or a random
  • the probability of the random event is estimated by the frequency of the occurrence of such an event by an "experimental” method, or some numerical characteristics of the random variable are obtained and used as a solution to the problem.
  • Statistics It is called the Monte Carlo method, and the corresponding one is called Particle Filter (PF) in engineering.
  • PF Particle Filter
  • the idea of particle filtering is based on the Monte Carlo method, which uses particle sets to represent probabilities.
  • particle filtering It can be used on any form of state space model to accurately express posterior probability distributions based on observations and control quantities.
  • the core idea of particle filtering is to express its distribution by extracting random state particles from the posterior probability. It is a sequential importance sampling method (Sequential Importance Sampling). Therefore, particle filtering is to approximate the probability density function by finding a set of random samples propagating in the state space, and replace the integral operation with the sample mean, and then obtain the process of estimating the minimum variance of the system state. These samples are called “ Particles, so called particle filtering. Any form of probability density distribution can be approximated when the number of samples approaches infinity.
  • the backward information filtering process is performed after the forward filtering process, according to the sequence estimated by the forward filtering and its corresponding particle weight, and the estimated particles are filtered again in order from the backward to the forward to obtain a more realistic Estimate the sequence.
  • x t ) represents the backward information filtering, which is composed of p(y t+1:T
  • Double filter smoothing whose smooth distribution is through forward filtering and auxiliary probability distribution on x t Calculated.
  • This auxiliary density is defined by the artificial distribution sequence ⁇ t (x t ): Therefore, combined with the above formula can be expressed as:
  • the process of generating weighted particles recursively by backward information filtering can be expressed as:
  • y 1:T ) is calculated by a combination of forward filtering (FF) and backward information filtering (BIF):
  • particle clouds use backward filtering clouds Expressed as:
  • the particle weight is expressed as:
  • the backward information filtering is based on the forward filtering, and according to the sequence estimated by the forward filtering and its corresponding particle weight, the estimated particle is subjected to the backward filtering process again in the order from the back to the front.
  • the particle weight obtained by filtering the backward information is calculated by the artificial distribution sequence ⁇ t (x t ).
  • This step is not necessary in the backward information filtering process, and can be determined according to actual system requirements. The purpose is to ensure that the estimated particles are closest to the real sequence and improve the accuracy of the estimation.
  • the particle importance weight of the forward filtering process of each symbol in the estimated sequence and the particle importance weight of the backward information filtering process are obtained, according to the particle importance weight and backward direction of the forward filtering process.
  • the particle importance weight of the information filtering process calculating the particle importance weight of the double filtering process, for example, for each symbol in the estimation sequence, according to the formula Calculate the particle importance weight of the double filtering process for each symbol, where Represents the importance weight of the particles in the double filtering process, Represents the importance weight of the particles of the same symbol forward filtering process, Represents the weight importance of the particle of the same symbol backward information filtering process.
  • the particles closest to the real symbol are selected from the estimated sequence. For example, the particle with the highest weight importance of the double-filtering process for each symbol-corresponding particle is used as the estimated value of the symbol to output the final Decoding sequence.
  • the dual filtering smooth decoding method applicable to the OvXDM system disclosed in the present application includes a forward filtering step S100, a backward information filtering step S300, a dual filtering weight calculation step S400, and an output step S500.
  • the OvXDM system may be an OvTDM system, an OvFDM system, an OvCDM system, an OvSDM system, or an OvHDM system, as shown in FIG. 8, which is an equivalent convolutional coding model of the OvXDM system.
  • the forward filtering step S100 starting from the first symbol in an estimated sequence to the end of the last symbol, sequentially calculating the importance weights of the particles in the particle set corresponding to each symbol, and obtaining the particle importance weight of the forward filtering process. Specifically, referring to FIG. 9, the forward filtering step S100 includes steps S101 to S109.
  • Step S101 Initialize the estimated sequence X. Since this is in the forward filtering process, it is possible to refer to the estimated sequence X as a forward filtered estimation sequence Xf whose sequence length is the same as the length of the sequence to be decoded.
  • the receiving end of the OvXDM system may receive the symbol sequence y of length N, which is the sequence to be decoded, the number of times of overlap is K, and the rectangular wave is a multiplexed waveform; if the number of particles of each symbol For Ns, each particle corresponds to an importance weight value. Then, the size of the forward filter estimation sequence Xf is Ns ⁇ N, and the size of the set Wf of importance weight values corresponding to each particle is Ns ⁇ N.
  • Step S103 Starting from the first symbol in the forward filter estimation sequence Xf to the end of the last symbol, generating a particle set for the current symbol.
  • the number of particles in the particle concentration corresponding to each symbol is N s .
  • the particle set corresponding to each symbol includes two Species, with values +1 and -1, respectively.
  • There are many ways to generate a particle set for the current symbol as long as the distribution of the generated particle set approaches the theoretical distribution.
  • Step S105 After generating the particle set for the current symbol, calculate the importance probability density of each particle of the current symbol and the sequence to be decoded, and calculate the importance weight of each particle.
  • calculating the importance weight of each particle in the particle set corresponding to the current symbol is calculated according to the following formula:
  • N is the length of the sequence to be decoded
  • N s is the number of particles in the particle set corresponding to the current symbol
  • P i,j is the importance probability density of the particle.
  • the importance probability density of the particle in the particle set of the current symbol and the sequence to be decoded is calculated, and the previous symbol can be referred to.
  • the probability density of the particles in the particle set and the importance of the sequence to be decoded is calculated.
  • step S107 After calculating the importance weights of the particles in the particle set corresponding to the current symbol, step S107 is performed.
  • Step S107 It is determined whether the particle set corresponding to the current symbol satisfies a preset particle degradation condition. If not, the next symbol is performed, that is, the next symbol is started from step S103. If yes, step S109 is performed.
  • This step S107 is for determining whether the degradation phenomenon of the particle-concentrated particles corresponding to the current symbol is obvious. For example, you can set the effective particle capacity of the particle set corresponding to the symbol. Below a certain threshold, then the particle set corresponding to the symbol is resampled.
  • the above-mentioned particle degradation condition that does not satisfy the preset means that the particle set degradation phenomenon corresponding to the current symbol is not serious, and the predetermined particle degradation condition is satisfied, which means that the particle set degradation phenomenon corresponding to the current symbol is serious. It therefore needs to be resampled.
  • Step S109 Resampling the particle set of the current symbol. Resampling is to eliminate particles with low weight and concentrate on particles with high weight, thus suppressing degradation. There are many methods for resampling, including importance resampling, residual resampling, layered resampling, and optimized combined resampling. The basic idea is to reproduce the particles with heavy weight and eliminate the particles with small weights. Finally, a new particle set is generated, and the resampling schematic is shown in FIG.
  • the "starting from the first symbol in the forward filter estimation sequence Xf to the end of the last symbol" mentioned in the step S103 may be performed from the first symbol to the step S101, and the result of the determination in the step S107. If it is not satisfied and after step S109, a judgment is made to determine whether the last symbol is reached, and if so, the forward smoothing step S100 ends, otherwise the next symbol is processed, that is, the next symbol starts from step S103. According to the flow shown in Fig. 16, the steps are performed downward.
  • each symbol in the sequence X (forward filtering estimation sequence Xf) has a corresponding particle set, and each particle in each particle set has an importance weight.
  • the backward information filtering step S300 starting from the last symbol in the estimated sequence X (forward filtering estimation sequence Xf) to the end of the first symbol, sequentially calculating the importance weights of the particles in the particle set corresponding to each symbol, and obtaining the backward direction The particle importance weight of the information filtering process.
  • the backward information filtering step S300 includes steps S301 to S311.
  • Step S301 According to the result of the forward filtering step S100, the particle with the highest importance weight of the particle corresponding to the last symbol in the estimated sequence X (forward filtering estimation sequence Xf) is used as an estimated value of the symbol, and the estimated sequence is X (forward filtering estimation sequence Xf) the last symbol corresponding to the particle concentration of each particle.
  • the particle importance weight of the forward filtering process of the sub-segment is used as the particle importance weight of the backward information filtering process corresponding to each particle in the particle set corresponding to the last symbol in the estimated sequence X.
  • Step S303 Construct an artificial distribution sequence, wherein the length of the artificial distribution sequence is the same as the length of the sequence to be decoded.
  • the constructed artificial distribution sequence is:
  • ⁇ t (x t ) represents the artificial distribution sequence
  • x t represents the symbol at time t.
  • Step S305 calculating the probability density of each particle of the sequence to be decoded and the current symbol from the last symbol of the estimated sequence X to the end of the first symbol; and according to the probability density of each particle of the sequence to be decoded and the current symbol,
  • the artificial distribution sequence calculates the auxiliary probability density of the backward information filtering process for each particle of the current symbol.
  • calculating the auxiliary probability density of the backward information filtering process for each particle of the current symbol is according to a formula Calculated, where f(x t+1
  • step S305 may also be the same as the "first symbol from the forward filter estimation sequence Xf" to the last symbol mentioned in the above step S103.
  • end is similar and will not be described here.
  • Step S307 Calculate the importance weights of the backward information filtering process of each particle according to the auxiliary probability density of the backward information filtering process of each particle of the current symbol.
  • the importance weight of the backward information filtering process for calculating each particle is according to a formula Calculated, of which The importance weight is filtered for the backward information of the particle, N is the length of the sequence to be decoded, N s is the number of particles in the particle set corresponding to the current symbol, and ⁇ i, j is the auxiliary probability density of the particle. It can be seen that the calculated importance weight of the backward information filtering process of each particle is actually the normalized importance weight.
  • Step S309 determining, according to the importance weight of the backward information filtering process of the current symbol, whether the particle set corresponding to the current symbol satisfies a predetermined particle degradation condition, and if not, performing the previous symbol, that is, the current symbol The previous symbol of the number proceeds from step S305. If yes, step S311 is performed.
  • the purpose of this step S309 is the same as that of step S107, and the particle degradation conditions in the two steps may be the same or different.
  • Step S311 Resampling the particle set of the current symbol.
  • the method and principle of the step S311 are similar to the step S109, and details are not described herein again.
  • Step S309 and step S311 are not necessary and may be determined according to actual system requirements, and the purpose is to ensure that the estimated particles are closest to the real sequence and improve the accuracy of the estimation.
  • the dual filtering weight calculation step S400 calculating the particle importance weight of the double filtering process according to the particle importance weight of the forward filtering process and the particle importance weight of the backward information filtering process.
  • the particle importance weight of the double filtering process is calculated according to the following formula:
  • Output step S500 The calculation result of step S400 is calculated based on the double filter weight, and the decoding sequence is output.
  • the outputting step S500 outputs, as an estimated value of the symbol, the particle having the largest particle importance weight of the dual filtering process corresponding to each symbol, and outputs the final decoding sequence.
  • the present application also discloses an OvXDM system, which may be an OvTDM system, an OvFDM system, an OvCDM system, an OvSDM system, or
  • the OvHDM system includes a dual filtering smooth decoding device suitable for the OvXDM system.
  • the dual filter smoothing decoding apparatus applicable to the OvXDM system includes a forward filtering unit 100, a backward information filtering unit 300, a dual filtering weight calculating unit 400, and an output unit 500.
  • the forward filtering unit 100 is configured to calculate the importance weights of the particles in the particle set corresponding to each symbol from the first symbol in the estimation sequence to the end of the last symbol, and obtain the particle importance weight of the forward filtering process.
  • the forward filtering unit 100 includes an initializing unit 101, a particle set generating unit 103, an importance probability density calculating unit 105, an importance weight calculating unit 107, a first determining unit 109a, and a first Resampling unit 111a.
  • the initialization unit 101 is used to initialize the estimated sequence X, wherein the length of the estimated sequence X is the same as the length of the sequence to be coded. Since this is in the forward filtering process, it is possible to refer to the estimated sequence X as a forward filtered estimation sequence Xf whose sequence length is the same as the length of the sequence to be decoded.
  • the receiving end of the OvXDM system may receive the symbol sequence y of length N, which is the sequence to be decoded, the number of times of overlap is K, and the rectangular wave is a multiplexed waveform; if the number of particles of each symbol For Ns, each particle corresponds to an importance weight value. Then, the size of the forward filter estimation sequence Xf is Ns ⁇ N, and the size of the set Wf of importance weight values corresponding to each particle is Ns ⁇ N.
  • the particle set generation unit 103 is configured to generate a particle set for the current symbol from the first symbol in the estimated sequence X to the end of the last symbol.
  • the number of particles in the particle set corresponding to each symbol is N s .
  • the particle set corresponding to each symbol includes two Species, with values +1 and -1, respectively.
  • There are many ways to generate a particle set for the current symbol as long as the distribution of the generated particle set approaches the theoretical distribution.
  • the importance probability density calculation unit 105 calculates the importance probability density of each particle of the current symbol and the sequence to be decoded after the current symbol generation particle set is used. In an embodiment, when i>1, that is, when the current symbol is the second symbol or the following symbol, the importance probability density calculation unit 105 calculates the importance probability of the particle in the particle set of the current symbol and the sequence to be decoded. Density, can refer to the importance probability density of the particles in the particle set of the previous symbol and the sequence to be decoded. It should be noted that in the OvXDM system, since the received symbol sequence y is encoded by OvXDM, it is also necessary to estimate the The symbol particle Xf i,j is OvXDM encoded, and its importance probability density is calculated.
  • the importance weight calculation unit 107 is configured to calculate the importance weight of each particle based on the importance probability density. In an embodiment, the importance weight calculation unit 107 calculates the normalized importance weight of each particle in the particle set corresponding to the current symbol according to the following formula:
  • N is the length of the sequence to be decoded
  • N s is the number of particles in the particle set corresponding to the current symbol
  • P i,j is the importance probability density of the particle.
  • the first determining unit 109a is configured to determine whether the particle set corresponding to the current symbol satisfies a preset particle degradation condition, and if not, notify the particle set generating unit 103 to generate a particle set for the latter symbol.
  • the determining unit 109 is for determining whether the degradation phenomenon of the particle-concentrated particles corresponding to the current symbol is obvious. For example, you can set the effective particle capacity of the particle set corresponding to the symbol. Below a certain threshold, then the particle set corresponding to the symbol is resampled.
  • the first resampling unit 111a is configured to resample the particle set of the current symbol when the result of the first determining unit 109a is satisfied. After the first resampling unit 111a resamples the particle set of the current symbol, it notifies the particle set generation unit 103 to generate a particle set for the latter symbol.
  • the first resampling unit 111a performs resampling in order to eliminate particles having a low weight and concentrate on particles having a high weight, thereby suppressing the degradation phenomenon.
  • the backward information filtering unit 300 starts from the last symbol in the estimated sequence X (forward filtering estimation sequence Xf) to the end of the first symbol, and sequentially calculates the importance weights of the particles in the particle set corresponding to each symbol. The weight importance of the particles to the backward information filtering process.
  • the backward information filtering unit 300 includes a setting unit 301, an artificial distribution sequence construction unit 302, a probability density calculation unit 303, an auxiliary probability density calculation unit 307, and an importance weight recalculation unit 305.
  • the second determining unit 311 and the second resampling unit 313 may also be included.
  • the setting unit 301 is configured to use, as a result of the calculation by the forward filtering unit 100, a particle having the largest weight concentration importance of the particle corresponding to the last symbol in the estimated sequence X (forward filtering estimation sequence Xf) as an estimated value of the symbol, and Estimating the particle importance weight of the forward filtering process of each particle in the particle set corresponding to the last symbol in the sequence X (forward filtering estimation sequence Xf) as the backward information corresponding to each particle in the particle set corresponding to the last symbol in the estimated sequence X The particle importance weight of the filtering process.
  • a backward smoothing sequence Xb may be additionally provided, the length of which is N, and the setting unit 301 maximizes the weight importance of the particle concentration corresponding to the last symbol in the estimated sequence X (forward filtering estimation sequence Xf).
  • the setting unit 301 assigns the importance weight of each particle in the particle set corresponding to the last symbol in the estimated sequence X (forward filtering estimation sequence Xf) to the importance weight Wb of the backward smoothing sequence Xb, which can be expressed as Wb (1).
  • ⁇ Ns, N) Wf (1 to Ns, N).
  • the artificial distribution sequence construction unit 302 is configured to construct an artificial distribution sequence, wherein the length of the artificial distribution sequence is the same as the length of the sequence to be decoded.
  • the artificial distribution sequence construction unit 302 constructs the artificial distribution sequence according to the following formula:
  • ⁇ t (x t ) represents the artificial distribution sequence described above.
  • the probability density calculation unit 303 is configured to start from the last symbol of the estimation sequence to the end of the first symbol: calculate a probability density of each particle of the sequence to be coded and the current symbol. It should be noted that since the sequence estimated in the forward filtering process is not encoded, it is necessary to calculate the probability density of the estimated particle first and the multiplexed waveform after K-weight OvXDM encoding, and then the sequence to be decoded. In this case, the multivariate normal probability density (mvnpdf) probability density is used.
  • the auxiliary probability density calculation unit 307 is configured to calculate an auxiliary probability density of the backward information filtering process of each particle of the current symbol according to the probability density of each particle of the to-be-decoded sequence and the current symbol and the artificial distribution sequence.
  • the auxiliary probability density calculation unit 307 is based on a formula Calculated, where f(x t+1
  • the auxiliary probability density of the process is calculated separately for the importance weight of the backward information filtering process of each particle.
  • the importance weight of the backward information filtering process for calculating each particle is based on a formula Calculated, where The importance weight is filtered for the backward information of the particle, N is the length of the sequence to be decoded, N s is the number of particles in the particle set corresponding to the current symbol, and ⁇ i, j is the auxiliary probability density of the particle. It can be seen that the calculated importance weight of the backward information filtering process of each particle is actually the normalized importance weight.
  • the second determining unit 311 is configured to determine, according to the importance weight of the backward information filtering process of the current symbol, whether the particle set corresponding to the current symbol satisfies a preset particle degradation condition, and if yes, notify the second resampling unit to the current The particle set of the symbol is resampled, and if not, the notification probability density calculation unit 307 calculates the previous symbol.
  • the second determining unit 311 is similar to the first determining unit 109a, and the particle degradation conditions of the two determining units 311 may be the same or different, and are not described herein again.
  • the second resampling unit 313 is configured to resample the particle set of the current symbol when the result of the second determining unit 311 is satisfied.
  • the second resampling unit 313 resamples the particle set of the current symbol, and notifies the probability density calculation unit 307 to calculate the previous symbol.
  • the second resampling unit 313 is similar to the first resampling unit 111a, and details are not described herein again.
  • the dual filtering weight calculation unit 400 is configured to calculate the particle importance weight of the double filtering process according to the particle importance weight of the forward filtering process and the particle importance weight of the backward information filtering process.
  • the dual filter weight calculation unit 50 calculates the particle importance weight of the double filtering process according to the following formula:
  • Represents the importance weight of the particles in the double filtering process Represents the weight importance of the forward filtering process
  • the output unit 500 is configured to output a decoding sequence according to the calculation result of the dual filtering weight calculation unit 400.
  • the output unit 500 is configured to use the particle having the largest particle importance weight of the particle filtering process corresponding to each symbol as the estimated value of the symbol, and output the final decoding sequence.
  • a set of samples may be randomly generated first, and the importance weight of the particle and the observed value is calculated.
  • the particle samples are resampled, the particles with small weights are eliminated, and the particles with significant weights are repeatedly iteratively calculated in turn, and finally the more reliable output values are obtained.
  • the degradation of particles is the biggest defect of particle filters, which restricts the development of particle filters.
  • One of the effective methods to solve the problem of particle degradation is to resample the particles.
  • Particle filtering has unique advantages in solving parameter estimation and state filtering of nonlinear and non-Gaussian problems. Therefore, there is a great room for development, and many different optimization methods can be introduced into the resampling process for faster The ground is extracted to a typical "particle" that reflects the probability characteristics of the system.
  • the present application calculates the importance weights of the particles in the particle set corresponding to the symbols by forward filtering and backward information filtering, and then combines the particle importance weights of the forward filtering and the particle importance weights of the backward information filtering to filter the output.
  • the final decoding sequence in this process, makes full use of the mutual information between the particles, realizes the decoding of the 0vXDM system, so that the decoded sequence is closer to the true value, and at the same time, as the number of overlaps increases, compared with the traditional
  • the decoding method reduces the decoding complexity and improves the decoding efficiency and system performance.

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Abstract

本申请公开了一种适用于OvXDM系统的译码方法、装置及系统，通过前向过程和后向过程分别计算符号对应的粒子集中各粒子的重要性权重，再结合前向粒子重要性权重和后向粒子重要性权重进行筛选，以输出最终的译码序列，在这过程中，充分利用了粒子间的互信息，实现OvXDM系统的译码，使得到的译码序列更加逼近真实值，同时随着重叠次数的增加，相较传统的译码方法降低了译码复杂度，提升了译码效率和系统性能。

Description

前向后向平滑译码方法、装置及系统 技术领域
本发明涉及一种涉及译码领域，具体涉及一种前向后向平滑译码方法、装置及系统。
背景技术
对于重叠复用系统OvXDM系统，其传统的译码中都需要不断访问格状图(Trellis)中的节点，并为每一个节点设置两个存储器，一个用于存储到达该节点的相对最佳路径，一个用于存储到达该节点的相对最佳路径对应的测度。
不妨以OvTDM系统为例，由于译码过程中，需要对格状图中每个节点进行扩展，因此节点数决定了译码的复杂度，而对于重叠次数为K和调制维度为M的系统(M是大于等于2的整数)，其对应的格状图中稳定状态的节点数为MK-1，因此译码复杂度会随着重叠次数K而指数增加。而在OvTDM系统中，系统的频谱效率为2K/符号，因此重叠次数K越大频谱效率越高。因此，一方面出于提高频谱效率的要求使得重叠次数K越大越好，另一方面出于降低译码复杂度的要求使得重叠次数K越小越好，特别地，当重叠次数K增加到一定值，例如K大于8后，译码复杂度急剧增加，现有的译码方法难以满足实时译码的要求，频谱效率与译码复杂度、译码效率形成了一对矛盾需求。
发明内容
根据本申请的第一方面，本申请提供一种适用于OvXDM系统的前向后向平滑译码方法，包括以下步骤：
前向平滑步骤：从一估计序列中第一个符号开始到最后一个符号结束，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到前向平滑过程的粒子重要性权重；
后向平滑步骤：从所述估计序列中最后一个符号开始到第一个符号结束，参照前向平滑步骤中得到的粒子重要性权重，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到后向平滑过程的粒子重要性权重；
输出步骤：将每一个符号对应的粒子集中后向平滑过程的粒子重要性权重最大的粒子作为此符号的估计值，输出最终的译码序列。
根据本申请的第二方面，本申请提供一种适用于OvXDM系统的前向后向平滑译码装置，包括：
前向平滑单元，用于从一估计序列中第一个符号开始到最后一个符号结束，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到前向平滑过程的粒子重要性权重；
后向平滑单元，用于从所述估计序列中最后一个符号开始到第一个符号结束，参照前向平滑单元中得到的粒子重要性权重，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到后向平滑过程的粒子重要性权重；
输出单元，用于将每一个符号对应的粒子集中后向平滑过程的粒子重要性权重最大的粒子作为此符号的估计值，输出最终的译码序列。
根据本申请的第三方面，本申请提供一种OvXDM系统，包括上述的适用于OvXDM系统的前向后向平滑译码装置，其中所述OvXDM系统为OvTDM系统、OvFDM系统、OvCDM系统、OvSDM系统或OvHDM系统。
本申请的有益效果是：
依上述实施的适用于OvXDM系统的前向后向平滑译码方法、装置及OvXDM系统，将统计的思想引入译码过程，通过前向平滑和后向平滑两个过程，充分利用粒子间的互信息，实现OvXDM系统的译码，使得到的译码序列更加逼近真实值，同时随着重叠次数的增加，相较传统的译码方法降低了译码复杂度，提升了译码效率和系统性能。
附图说明
图1为传统OvTDM系统的发射端的结构示意图；
图2为OvTDM系统对输入符号进行重叠复用编码的平行四边形规则示意图；
图3(a)、(b)分别传统OvTDM接收端的预处理单元、序列检测单元；
图4为系统重叠复用次数K＝3时，系统输入-输出码树图；
图5为图4相应的系统的节点状态转移图；
图6为图4或图5相应的系统的格状(Trellis)图；
图7为本申请一种实施例中适用于OvXDM系统的前向后向平滑译码方法的流程示意图；
图8为OvXDM系统等效卷积编码模型图；
图9为本申请一种实施例中前向平滑步骤的流程示意图；
图10为本申请一种实施例中重采样步骤的示意图；
图11为本申请一种实施例中后向平滑步骤的流程示意图；
图12为本申请一种实施例中适用于OvXDM系统的前向后向平滑译码装置的结构示意图；
图13本申请一种实施例中前向平滑单元的结构示意图；
图14本申请一种实施例中后向平滑单元的结构示意图；
图15为本申请另一实施例中适用于OvXDM系统的前向后向译码方法的流程示意图；
图16为本申请另一实施例中前向步骤的流程示意图；
图17为本申请另一实施例中译码装置的结构示意图；
图18为本申请另一种实施例中前向单元的结构示意图；
图19为本申请另一种实施例中后向单元的结构示意图。
具体实施方式
下面通过具体实施方式结合附图对本申请作进一步详细说明。
本发明的实施例中采用了前向步骤和后向步骤，在后续的实施例中，前向步骤可以包括前向平滑步骤或者前向滤波步骤；后向步骤可以包括后向平滑步骤或者后向滤波步骤。
本申请提出一种适用于OvXDM系统的前向后向平滑译码方法、装置及OvXDM系统，其中OvXDM系统为重叠时分复用(OvTDM，Overlapped Time Division Multiplexing)系统、重叠频分复用(OvFDM，Overlapped Frequency Division Multiplexing)系统、重叠码分复用(OvCDM，Overlapped Code Division Multiplexing)系统、重叠空分复用(OvSDM，Overlapped Space Division Multiplexing)系统或重叠混合复用(OvHDM，Overlapped Hybrid Division Multiplexing)系统。
不妨以OvTDM系统为例，先简要说明一下系统的收发端。
如图1所示，为OvTDM发送端的发送过程，具体步骤如下：
(1)首先设计生成发送信号的包络波形h(t)。
(2)将(1)中所设计的包络波形h(t)经特定时间移位后，形成其它各个时刻发送信号包络波形h(t-i×ΔT)。
(3)将所要发送的符号xi与(2)生成的相应时刻的包络波形h(t-i×ΔT)相乘，得到各个时刻的待发送信号波形xih(t-i×ΔT)。
(4)将(3)所形成的各个待发送波形进行xih(t-i×ΔT)叠加，形成发射信号波形。发送的信号可以表示为：
Figure PCTCN2017103311-appb-000001
其中，重叠复用方法遵循如图2所示的平行四边形规则。
发送端将编码调制后的信号通过天线发射出去，信号在无线信道中传输，接收端对接收信号进行匹配滤波，再对信号分别进行抽样、译码，最终判决输出比特流。
如图3所示，为OvTDM接收端的接收过程，其中，图3(a)为OvTDM接收端的预处理单元，图3(b)为OvTDM接收端的序列检测单元，具体步骤如下：
(5)首先对接收信号进行同步，包括载波同步、帧同步、符号时间同步等。
(6)根据取样定理，对每一帧内的接收信号进行数字化处理。
(7)对接收到的波形按照波形发送时间间隔切割。
(8)按照一定的译码算法对切割后的波形进行译码。例如，以维特比译码进行 译码。
其中，译码过程请参照图4～6，图4为重叠复用次数K＝3时，系统输入-输出码树图，图5为系统相应的节点状态转移图，图6为系统的格状(Trellis)图。
如上所述，传统的译码方法(典型如维特比译码)，随着重叠次数的增加，译码复杂度急剧增加，对硬件精度要求较高，降低了系统性能。为解决这个问题，发明人通过研究和实践，将统计的思想引入译码过程，通过前向平滑和后向平滑两个过程，充分利用粒子间的互信息，实现OvXDM系统的译码，使得到的译码序列更加逼近真实值，同时随着重叠次数的增加，相较传统的译码方法降低了译码复杂度，提升了译码效率和系统性能。下面先对本申请的发明构思和原理进行说明。
本实施例中的译码过程主要包括前向平滑过程和后向平滑过程。
前向平滑过程的原理与蒙特卡洛方法(Monte Carlo methods)的原理是相同的。蒙特卡洛方法是应用于统计学中的一种以概率统计理论为指导的一类非常重要的数值计算方法，其基本思想是当所求解问题是某种随机事件出现的概率，或者是某个随机变量的期望值时，通过某种“实验”的方法，以这种事件出现的频率估计这一随机事件的概率，或者得到这个随机变量的某些数字特征，并将其作为问题的解。统计学中称之为蒙特卡洛方法，对应的在工程中称为粒子滤波(PF，Particle Filter)。粒子滤波的思想是基于蒙特卡洛方法，利用粒子集来表示概率，可以用于任何形式的状态空间模型上，能够比较精确地表达基于观测量和控制量的后验概率分布。粒子滤波的核心思想是通过从后验概率中抽取的随机状态粒子来表达其分布，是一种顺序重要性采样法(Sequential Importance Sampling)。因此粒子滤波就是通过寻找一组在状态空间中传播的随机样本来近似的表示概率密度函数，用样本均值代替积分运算，进而获得系统状态的最小方差估计的过程，这些样本被形象的称为“粒子”，故而叫粒子滤波。当样本数量趋近无穷大时可以逼近任何形式的概率密度分布。
后向平滑过程是在前向平滑过程之后，根据前向平滑估计出的序列及其对应粒子权重，按照由后向前的顺序，对估计出的粒子再次进行平滑处理，以得到更真实的估计序列。
因此，综合来看，前向后向平滑(FBS，Forward-Backward Smoothing)过程是基于以下关系式：
Figure PCTCN2017103311-appb-000002
其中，p(xt|y1：t)和p(xt+1|y1：t)分别是t时刻的滤波密度和前向预测密度。根据上面的公式，由p(xT|y1：T)开始，反复的获取p(xt|y1：T)到p(xt+1|y1：T)。经过上述的反复迭代，边缘平滑分布可近似的用权重粒子云来描述。前向粒子滤波器可表示为：
Figure PCTCN2017103311-appb-000003
后向平滑分布表示为：
Figure PCTCN2017103311-appb-000004
其平滑权重是由如下公式反复迭代计算的：
Figure PCTCN2017103311-appb-000005
其中，
Figure PCTCN2017103311-appb-000006
上面的是前向平滑过程和后向平滑过程的原理说明，下面对前向平滑过程和后向平滑过程作具体的说明。
一、前向平滑过程：
(1)构造粒子集
Figure PCTCN2017103311-appb-000007
其中
Figure PCTCN2017103311-appb-000008
(2)计算粒子集中每个粒子的重要性权重
Figure PCTCN2017103311-appb-000009
其中
Figure PCTCN2017103311-appb-000010
且
Figure PCTCN2017103311-appb-000011
满足
Figure PCTCN2017103311-appb-000012
(3)当粒子集满足一定条件时对其进行重采样
Figure PCTCN2017103311-appb-000013
以得到新的粒子集。
上述的前向平滑过程中，t≥1，i的取值为1～Ns。经过上述反复迭代运算，最终找到最接近真实序列的粒子分布。
二、后向平滑过程：
如上所述，后向平滑是在前向平滑的基础上，根据前向平滑估计出的序列及其对应粒子权重，按照由后向前的顺序，对估计出的粒子再次进行平滑处理，以得到更真实的估计序列。
(4)FBS初始化
设置p(x0|x-1)＝p(x0)；
Figure PCTCN2017103311-appb-000014
i＝1～NS。
(5)计算当前符号与后一符号的概率密度
Figure PCTCN2017103311-appb-000015
(6)计算归一化因子
Figure PCTCN2017103311-appb-000016
其中
Figure PCTCN2017103311-appb-000017
是前向平滑过程中计算得到的。
(7)计算后向平滑权重
Figure PCTCN2017103311-appb-000018
具体地，根据公式
Figure PCTCN2017103311-appb-000019
来计算后向平滑过程中每个粒子的权重。
(8)根据一定规则选出最为接近的粒子作为当前符号的估计值，例如寻找权重最大的粒子，作为估计值。
(9)重复上步骤(5)～(8)，直到计算完所有符号的估计值，后向平滑过程结束。各个符号的估计值组成的序列，即为最终的译码序列。
上为本申请的适用于OvXDM系统的前向后向平滑译码方法、装置及OvXDM系统的构思及原理，下面对本申请进行详细说明。
在一实施例中，请参照图7，本申请公开的适用于OvXDM系统的前向后向平滑译码方法包括前向平滑步骤S100、后向平滑步骤S300和输出步骤S500，其中OvXDM系统可以为OvTDM系统、OvFDM系统、OvCDM系统、OvSDM系统或OvHDM系统，如图8所示，为OvXDM系统等效卷积编码模型。
前向平滑步骤S100：从一估计序列中第一个符号开始到最后一个符号结束，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到前向平滑过程的粒子重要性权重。具体地，请参照图9，前向平滑步骤S100包括步骤S101～S109。
步骤S101：初始化估计序列X。由于这是在前向平滑过程中，因此不妨将估计序列X称为前向平滑估计序列Xf，其序列长度与待译码序列长度相同。例如，不妨令OvXDM系统接收端接收到长度为N的符号序列y，此符号序列y即为待译码序列，其重叠次数为K，以矩形波为复用波形；若每个符号的粒子数为Ns，每个粒子对应一个重要性权重值。则前向平滑估计序列Xf的大小为Ns×N，各粒子对应的重要性权重值的集合Wf的大小为Ns×N。
步骤S103：从前向平滑估计序列Xf中第一个符号开始到最后一个符号结束，对当前符号生成一个粒子集，如上所述，每个符号对应的粒子集中粒子个数为Ns。例如，在OvXDM系统中，以二元数据流{+1，-1}为例，每个符号的可能取值只有两种：+1或者-1，因此每个符号对应的粒子集就是包括两个粒子，取值分别+1和-1。对当前符号生成粒子集的方法很多，只要生成的粒子集的分布趋近理论分布即可。
步骤S105：在对当前符号生成粒子集后，计算当前符号每个粒子与待译码序列的重要性概率密度，并计算每个粒子的重要性权重。在一实施例中，计算当前符号对应的粒子集中每个粒子的重要性权重是根据下述公式进行计算的：
Figure PCTCN2017103311-appb-000020
其中，wfi，j为粒子的重要性权重，N为待译码序列长度，Ns为当前符号对应的粒子集中的粒子数，Pi，j为粒子的重要性概率密度。可以看到，wfi，j实际为粒子的归一化重要性权重。
在一实施例中，当i＞1时，即当前符号为第2个符号或之后的符号时，计算当前符号的粒子集中的粒子与待译码序列的重要性概率密度，可以参考前一符号的粒子集中的粒子与待译码序列的重要性概率密度。
需要说明的是，在OvXDM系统中，由于接收符号序列y是经过OvXDM编码的，因此也需要对估计符号Xfi，j进行OvXDM编码，再计算其重要性概率密度。
计算完当前符号对应的粒子集中各粒子的重要性权重后，再进行步骤S107。
步骤S107：判断当前符号对应的粒子集是否满足预设的粒子退化条件，若不满足，则进行下一符号，即下一符号从步骤S103开始进行。若满足，则进行步骤S109。本步骤S107是用于判断当前符号对应的粒子集中粒子的退化现象是否明显。例如，可以设定当符号对应的粒子集的有效粒子容量
Figure PCTCN2017103311-appb-000021
低于某个阈值时，那么该符号对应的粒子集就要进行重采样。需要说明的是，上述不满足预设的粒子退化条件，指的是当前符号对应的粒子集退化现象不严重，满足预设的粒子退化条件，指的是当前符号对应的粒子集退化现象严重，因而需要被重采样。
步骤S109：对当前符号的粒子集进行重采样。重采样是为了淘汰权重低的粒子，而集中于权重高的粒子，从而抑制退化现象。重采样的方法有多种，包括重要性重采样、残差重采样、分层重采样和优化组合重采样等，其基本思路就是复制权重大的粒子，淘汰权重小的粒子，通过重采样，最后生成一个新的粒子集，重采样示意图如附图10所示。
另外，步骤S103提到的“从前向平滑估计序列Xf中第一个符号开始到最后一个符号结束”在具体实现时，可以从第一个符号开始先进行步骤S101，当在步骤S107的判断结果为不满足以及步骤S109之后，都进行一个判断，判断是否到达最后一个符号，若是，则前向平滑步骤S100结束，否则的话就进行下一符号的处理，即下一符号又从步骤S103开始，按照图9所示的流程，往下进行各步骤。
通过前向平滑步骤S100，即步骤S101～S109，估计序列X(前向平滑估计序列Xf)中各符号都具有对应的粒子集，各粒子集中的每个粒子都具有一个重要性权重。
后向平滑步骤S300：从估计序列X(前向平滑估计序列Xf)中最后一个符号开始到第一符号结束，参照前向平滑步骤S100中得到的粒子重要性权重，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到后向平滑过程的粒子重要性权重。在一实施例中，请参照图11，后向平滑步骤S300包括步骤S301～S305。
步骤S301：根据前向平滑步骤S100计算的结果，将估计序列X(前向平滑估计序列Xf)中最后一个符号对应的粒子集中重要性权重最大的粒子作为此符号的估计值，以及将估计序列X(前向平滑估计序列Xf)中最后一个符号对应的粒子集中各粒子的前向平滑过程的粒子重要性权重作为估计序列X(前向平滑估计序列Xf)中最后一个符号对应的粒子集中对应各粒子的后向平滑过程的粒子重要性权重。在一实施例中，也可以另外设置一个后向平滑序列Xb，其长度为N，将估计序列X(前向平滑估计序列Xf)中最后一个符号对应的粒子集中重要性权重最大的粒子，作为后向平滑序列Xb最后一个符号的估计值，可表示为如下形式：Xb(N)＝Xf(max，N)。同时， 将估计序列X(前向平滑估计序列Xf)中最后一个符号对应的粒子集中各粒子的重要性权重赋给后向平滑序列Xb的重要性权重Wb，可表示为Wb(1～Ns，N)＝Wf(1～Ns，N)。
步骤S303：从估计序列X倒数第二个符号开始到第一个符号结束，计算当前符号和后一符号之间的概率密度
Figure PCTCN2017103311-appb-000022
需要说明的是，由于前向平滑过程中估计出的序列是没有经过编码的，因此需要对当前时刻符号和后一时刻符号分别先和复用波形经过K重OvXDM编码后，再计算其概率密度。本案例采用多维正态分布(Multivariate normal probability density function，mvnpdf)概率密度。
步骤S305：根据步骤S303计算得到的概率密度、后一符号的后向平滑过程的粒子重要性权重、当前符号的前向平滑过程的粒子重要性权重，计算得到当前符号的后向平滑过程的粒子重要性权重。在一实施例中，可以先计算归一化因子
Figure PCTCN2017103311-appb-000023
其中
Figure PCTCN2017103311-appb-000024
是由前向平滑步骤S100计算得到的结果。在一实施例中，通过下述公式计算当前符号对应的粒子集中各粒子的重要性权重：
Figure PCTCN2017103311-appb-000025
Ns表示粒子数，i，j表示粒子索引，取值为1～Ns；xt (k)表示t时刻的符号中的第k个粒子；
其中，ωt为当前符号的前向平滑过程的粒子重要性权重，
Figure PCTCN2017103311-appb-000026
是当前符号和后一符号之间的概率密度，ωt|T是当前符号的后向平滑过程的粒子重要性权重。
当然，步骤S303中提到的“从估计序列X倒数第二个符号开始到第一个符号结束”也可以和上面步骤S103提到的“从前向平滑估计序列Xf中第一个符号开始到最后一个符号结束”的实现类似，在此不再赘述。
步骤S500：将每一个符号对应的粒子集中后向平滑过程的粒子重要性权重最大的粒子作为此符号的估计值，输出最终的译码序列。换句话说，估计序列X中每个符号对应的粒子集中后向平滑过程的粒子重要性权重最大的粒子作为此符号的估计值，输出最终的译码序列。
以上就是本申请公开的适用于OvXDM系统的前向后向平滑译码方法的流程，相应地，本申请还公开了一种OvXDM系统，此OvXDM系统可以为OvTDM系统、OvFDM系统、OvCDM系统、OvSDM系统或OvHDM系统，其包括一种适用于OvXDM系统的前向后向平滑译码装置。请参照图12，适用于OvXDM系统的前向后向平滑译码装置包括前向平滑单元100、后向平滑单元300和输出单元500。
前向平滑单元100用于从一估计序列中第一个符号开始到最后一个符号结束，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到前向平滑过程的粒子重要性权重。在一实施例中，请参照图13，前向平滑单元100包括初始化单元101、粒子集生成单元103、重要性概率密度计算单元105、重要性权重计算单元107、判断单元109和重采样单元111。
初始化单元101用于初始化估计序列X，其中估计序列X的长度与待译码序列长度相同。由于这是在前平滑过程中，因此不妨将估计序列X称为前向平滑估计序列Xf，其序列长度与待译码序列长度相同。例如，不妨令OvXDM系统接收端接收到长度为N的符号序列y，此符号序列y即为待译码序列，其重叠次数为K，以矩形波为复用波形；若每个符号的粒子数为Ns，每个粒子对应一个重要性权重值。则前向平滑估计序列Xf的大小为Ns×N，各粒子对应的重要性权重值的集合Wf的大小为Ns×N。
粒子集生成单元103用于从估计序列X中第一个符号开始到最后一个符号结束，对当前符号生成一个粒子集。如上所述，每个符号对应的粒子集中粒子个数为Ns。例如，在OvXDM系统中，以二元数据流{+1，-1}为例，每个符号的可能取值只有两种：+1或者-1，因此每个符号对应的粒子集就是包括两个粒子，取值分别+1和-1。对当前符号生成粒子集的方法很多，只要生成的粒子集的分布趋近理论分布即可。
重要性概率密度计算单元105用于当前符号生成粒子集后，计算当前符号每个粒子与待译码序列的重要性概率密度。在一实施例中，当i＞1时，即当前符号为第2个符号或之后的符号时，重要性概率密度计算单元105计算当前符号的粒子集中的粒子与待译码序列的重要性概率密度，可以参考前一符号的粒子集中的粒子与待译码序列的重要性概率密度，需要说明的是，在OvXDM系统中，由于接收符号序列y是经过OvXDM编码的，因此也需要对估计符号Xfi，j进行OvXDM编码，再计算其重要性概率密度。
重要性权重计算单元107用于根据重要性概率密度计算每个粒子的重要性权重。在一实施例中，重要性权重计算单元107计算当前符号对应的粒子集中每个粒子的重要性权重是根据下述公式进行计算的：
Figure PCTCN2017103311-appb-000027
其中，wfi，j为粒子的重要性权重，N为待译码序列长度，Ns为当前符号对应的粒子集中的粒子数，Pi，j为粒子的重要性概率密度。可以看到，wfi，j实际为粒子的归一化重要性权重。
判断单元109用于判断当前符号对应的粒子集是否满足预设的粒子退化条件，若不满足，则通知粒子集生成单元103对后一个符号生成粒子集。本判断单元109是用于判断当前符号对应的粒子集中粒子的退化现象是否明显。例如，可以设定当符号对应的粒子集的有效粒子容量
Figure PCTCN2017103311-appb-000028
低于某个阈值时，那么该符号对应的粒子集就要进行重采样。
重采样单元111用于当判断单元109的结果为满足时，对当前符号的粒子集进行重采样。重采样单元111进行重采样是为了淘汰权重低的粒子，而集中于权重高的粒 子，从而抑制退化现象。重采样的方法有多种，包括重要性重采样、残差重采样、分层重采样和优化组合重采样等，其基本思路就是复制权重大的粒子，淘汰权重小的粒子，通过重采样，最后生成一个新的粒子集，重采样示意图如上面的附图10所示。重采样单元111对当前符号的粒子进行重采样后，通知粒子集生成单元103对后一个符号生成粒子集。
后向平滑单元300用于从估计序列X(前向平滑估计序列Xf)中最后一个符号开始到第一个符号结束，参照前向平滑单元100中得到的粒子重要性权重，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到后向平滑过程的粒子重要性权重。在一实施例中，请参照图14，后向平滑单元300包括设置单元301、概率密度计算单元303和重要性权重再计算单元305。
设置单元301用于根据前向平滑单元100计算的结果，将估计序列X(前向平滑估计序列Xf)中最后一个符号对应的粒子集重要性权重最大的粒子作为此符号的估计值，以及将估计序列X(前向平滑估计序列Xf)中最后一个符号对应的粒子集中各粒子的前向平滑过程的粒子重要性权重作为所述估计序列中最后一个符号对应的粒子集中对应各粒子的后向平滑过程的粒子重要性权重。在一实施例中，也可以另外设置一个后向平滑序列Xb，其长度为N，设置单元301将估计序列X(前向平滑估计序列Xf)中最后一个符号对应的粒子集中重要性权重最大的粒子，作为后向平滑序列Xb最后一个符号的估计值，可表示为如下形式：Xb(N)＝Xf(max，N)。同时，设置单元301将估计序列X(前向平滑估计序列Xf)中最后一个符号对应的粒子集中各粒子的重要性权重赋给后向平滑序列Xb的重要性权重Wb，可表示为Wb(1～Ns，N)＝Wf(1～Ns，N)。
概率密度计算单元303，用于从估计序列倒数第二个符号开始到第一个符号结束，计算当前符号和后一符号之间的概率密度
Figure PCTCN2017103311-appb-000029
需要说明的是，由于前向平滑过程中估计出的序列是没有经过编码的，因此需要对当前时刻符号和后一时刻符号分别先和复用波形经过K重OvXDM编码后，再计算其概率密度。本案例采用多维正态分布(Multivariate normal probability density function，mvnpdf)概率密度。
重要性权重再计算单元305，用于当前符号和后一符号之间的概率密度被计算得到后，根据概率密度计算单元303计算得到的概率密度、后一符号的后向平滑过程的粒子重要性权重、当前符号的前向平滑过程的粒子重要性权重，计算得到当前符号的后向平滑过程的粒子重要性。在一实施例中，重要性权重再计算单元305可以先计算归一化因子
Figure PCTCN2017103311-appb-000030
其中
Figure PCTCN2017103311-appb-000031
是前向平滑单元100计算得到的结果。在一实施例中，重要性权重再计算单元305通过下述公式计算当前符号对应的粒子集中各粒 子的重要性权重：
Figure PCTCN2017103311-appb-000032
Ns表示粒子数，i，j表示粒子索引，取值为1～Ns；xt (t)表示t时刻的符号中的第k个粒子
其中，ωt为当前符号的前向平滑过程的粒子重要性权重，
Figure PCTCN2017103311-appb-000033
是当前符号和后一符号之间的概率密度，ωt|T是当前符号的后向平滑过程的粒子重要性权重。
输出单元500用于将每一个符号对应的粒子集中后向平滑过程的粒子重要性权重最大的粒子作为此符号的估计值，输出最终的译码序列。换句话说，估计序列X中每个符号对应的粒子集中后向平滑过程的粒子重要性权重最大的粒子作为此符号的估计值，输出最终的译码序列。
以上就是本申请公开的OvXDM系统及适用于OvXDM系统的前向后向平滑译码装置。
本申请在译码过程中，在对各符号生成粒子集时，对于一个未知的序列，由于初始阶段不知道其粒子分布，可先随机生成一组样本，通过计算粒子与观测值的重要性权重，判断粒子的可靠性，依据一定的准则，对粒子样本进行重采样，淘汰权重小得粒子，复制权重大的粒子，依次反复迭代计算，最终计算得到较为可靠的输出值。迭代次数越高，得到的结果越精确。另外，粒子的退化现象是粒子滤波器的最大缺陷，制约着粒子滤波器的发展，解决粒子退化问题的有效方法之一就是对粒子进行重采样。粒子滤波在解决非线性、非高斯问题的参数估计和状态滤波方面有着独到的优势，因此有很大的发展空间，可以将成熟的多种不同的寻优方法引入重采样过程，以便更快地提取到反映系统概率特征的典型“粒子”。
上述的实施例中，通过前向平滑和后向平滑两个过程，充分利用粒子间的互信息，实现OvXDM系统的译码，使得到的译码序列更加逼近真实值，同时随着重叠次数的增加，相较传统的译码方法降低了译码复杂度，提升了译码效率和系统性能。
本申请的另外一个实施例的译码过程主要包括前向滤波过程和后向信息滤波过程。
前向滤波过程的原理与蒙特卡洛方法(Monte Carlo methods)的原理是相同的。蒙特卡洛方法是应用于统计学中的一种以概率统计理论为指导的一类非常重要的数值计算方法，其基本思想是当所求解问题是某种随机事件出现的概率，或者是某个随机变量的期望值时，通过某种“实验”的方法，以这种事件出现的频率估计这一随机事件的概率，或者得到这个随机变量的某些数字特征，并将其作为问题的解。统计学 中称之为蒙特卡洛方法，对应的在工程中称为粒子滤波(PF，Particle Filter)。粒子滤波的思想是基于蒙特卡洛方法，利用粒子集来表示概率，可以用于任何形式的状态空间模型上，能够比较精确地表达基于观测量和控制量的后验概率分布。粒子滤波的核心思想是通过从后验概率中抽取的随机状态粒子来表达其分布，是一种顺序重要性采样法(Sequential Importance Sampling)。因此粒子滤波就是通过寻找一组在状态空间中传播的随机样本来近似的表示概率密度函数，用样本均值代替积分运算，进而获得系统状态的最小方差估计的过程，这些样本被形象的称为“粒子”，故而叫粒子滤波。当样本数量趋近无穷大时可以逼近任何形式的概率密度分布。
后向信息滤波过程是在前向滤波过程之后，根据前向滤波估计出的序列及其对应粒子权重，按照由后向前的顺序，对估计出的粒子再次进行滤波处理，以得到更真实的估计序列。
因此，综合来看，双滤波平滑(TFS，Two-Filter Smoothing)过程中，p(yt：T|xt)表示后向信息滤波，它是由p(yt+1：T|xt+1)根据下面公式计算得到的：
p(yt：T|xt)＝p(yt|xt)∫p(xt+1|xt)p(yt+1：T|xt+1)dxt+1；
其中，p(yt：T|xt)并不是指xt的概率密度，因为实际上它在xt上的积分有可能不是有限的。
双滤波平滑，其平滑分布是通过前向滤波和在xt上的辅助概率分布
Figure PCTCN2017103311-appb-000034
计算得到的。该辅助密度是通过人工分布序列γt(xt)定义的：
Figure PCTCN2017103311-appb-000035
因此和上式结合起来可表示为：
Figure PCTCN2017103311-appb-000036
反过来，由后向信息滤波递归的产生加权粒子的过程可表示为：
Figure PCTCN2017103311-appb-000037
边缘平滑p(xt|y1：T)是通过前向滤波(FF，Forward Filter)和后向信息滤波(BIF，Backward Information Filter)的组合计算得到的：
Figure PCTCN2017103311-appb-000038
将上式中的积分用蒙特卡洛前向滤波云
Figure PCTCN2017103311-appb-000039
表示为：
Figure PCTCN2017103311-appb-000040
最后，粒子云使用后向滤波云
Figure PCTCN2017103311-appb-000041
表示为：
Figure PCTCN2017103311-appb-000042
其中，粒子权重表示为：
Figure PCTCN2017103311-appb-000043
上面是包括前向滤波和后向信息滤波的双滤波的原理说明，下面对前向滤波过程和后向信息滤波过程作具体的说明。
一、前向滤波过程：
(1)构造粒子集
Figure PCTCN2017103311-appb-000044
其中
Figure PCTCN2017103311-appb-000045
(2)计算粒子集中每个粒子的重要性权重
Figure PCTCN2017103311-appb-000046
其中
Figure PCTCN2017103311-appb-000047
满足
Figure PCTCN2017103311-appb-000048
(3)当粒子集满足一定条件时对其进行重采样
Figure PCTCN2017103311-appb-000049
以得到新的粒子集。
上述过程中，t≥1，i的取值为1～N。经过上述反复迭代运算，最终得到前向滤波最接近真实序列的粒子分布。
二、后向信息滤波过程：
如上所述，后向信息滤波是在前向滤波的基础上，根据前向滤波估计出的序列及其对应粒子权重，按照由后向前的顺序，对估计出的粒子再次进行后向滤波处理，以得到更真实的估计序列，其中后向信息滤波得到的粒子权重是通过人造分布序列γt(xt)计算得到的。
(4)BIF初始化
初始化后向信息滤波序列的最后一个符号的粒子集及其对应的粒子权重。
(5)构造人工分布序列γt(xt)：
Figure PCTCN2017103311-appb-000050
(6)计算后向信息滤波过程的粒子权重
计算待译码序列与估计粒子间的概率密度f(xt+1|xt)，再根据公式
Figure PCTCN2017103311-appb-000051
将其作为后向信息滤波过程的辅助概率密度，通过得到的后向信息滤波辅助概率密度再对每个粒子求其后向信息粒子归一化权重
Figure PCTCN2017103311-appb-000052
(7)当粒子集满足一定条件时对其进行重采样。这一步骤在后向信息滤波过程中不是必须的，可以根据实际系统需求而定，目的都是确保估计的粒子最逼近真实序列，提高估计的准确性。
在步骤(7)之后，就得到了估计序列中各符号的前向滤波过程的粒子重要性权重和后向信息滤波过程的粒子重要性权重，根据前向滤波过程的粒子重要性权重和后向信息滤波过程的粒子重要性权重，计算双滤波过程的粒子重要性权重，例如，对于估计序列中每一个符号，根据公式
Figure PCTCN2017103311-appb-000053
计算各符号的双滤波过 程的粒子重要性权重，其中
Figure PCTCN2017103311-appb-000054
表示双滤波过程的粒子重要性权重，
Figure PCTCN2017103311-appb-000055
表示同一符号前向滤波过程的粒子重要性权重，
Figure PCTCN2017103311-appb-000056
表示同一符号后向信息滤波过程的粒子重要性权重。最后根据一定的规则从估计序列中选出最为接近真实符号的粒子，例如，将每一个符号对应的粒子集中双滤波过程的粒子重要性权重最大的粒子作为此符号的估计值，以输出最终的译码序列。
上为本申请的适用于OvXDM系统的双滤波平滑译码方法、装置及OvXDM系统的构思及原理，下面对本申请进行详细说明。
在一实施例中，请参照图15，本申请公开的适用于OvXDM系统的双滤波平滑译码方法包括前向滤波步骤S100、后向信息滤波步骤S300、双滤波权重计算步骤S400和输出步骤S500，其中OvXDM系统可以为OvTDM系统、OvFDM系统、OvCDM系统、OvSDM系统或OvHDM系统，如图8所示，为OvXDM系统等效卷积编码模型。
前向滤波步骤S100：从一估计序列中第一个符号开始到最后一个符号结束，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到前向滤波过程的粒子重要性权重。具体地，请参照图9，前向滤波步骤S100包括步骤S101～S109。
步骤S101：初始化估计序列X。由于这是在前向滤波过程中，因此不妨将估计序列X称为前向滤波估计序列Xf，其序列长度与待译码序列长度相同。例如，不妨令OvXDM系统接收端接收到长度为N的符号序列y，此符号序列y即为待译码序列，其重叠次数为K，以矩形波为复用波形；若每个符号的粒子数为Ns，每个粒子对应一个重要性权重值。则前向滤波估计序列Xf的大小为Ns×N，各粒子对应的重要性权重值的集合Wf的大小为Ns×N。
步骤S103：从前向滤波估计序列Xf中第一个符号开始到最后一个符号结束，对当前符号生成一个粒子集，如上所述，每个符号对应的粒子集中粒子个数为Ns。例如，在OvXDM系统中，以二元数据流{+1，-1}为例，每个符号的可能取值只有两种：+1或者-1，因此每个符号对应的粒子集就是包括两种粒子，取值分别+1和-1。对当前符号生成粒子集的方法很多，只要生成的粒子集的分布趋近理论分布即可。
步骤S105：在对当前符号生成粒子集后，计算当前符号每个粒子与待译码序列的重要性概率密度，并计算每个粒子的重要性权重。在一实施例中，计算当前符号对应的粒子集中每个粒子的重要性权重是根据下述公式进行计算的：
Figure PCTCN2017103311-appb-000057
其中，
Figure PCTCN2017103311-appb-000058
为粒子的重要性权重，N为待译码序列长度，Ns为当前符号对应的粒子集中的粒子数，Pi，j为粒子的重要性概率密度。可以看到，
Figure PCTCN2017103311-appb-000059
实质上是归一化重 要性权重。
在一实施例中，当i＞1时，即当前符号为第2个符号或之后的符号时，计算当前符号的粒子集中的粒子与待译码序列的重要性概率密度，可以参考前一符号的粒子集中的粒子与待译码序列的重要性概率密度。
需要说明的是，在OvXDM系统中，由于接收符号序列y是经过OvXDM编码的，因此也需要对估计的符号粒子进行OvXDM编码，再计算其重要性概率密度。
计算完当前符号对应的粒子集中各粒子的重要性权重后，再进行步骤S107。
步骤S107：判断当前符号对应的粒子集是否满足预设的粒子退化条件，若不满足，则进行下一符号，即下一符号从步骤S103开始进行。若满足，则进行步骤S109。本步骤S107是用于判断当前符号对应的粒子集中粒子的退化现象是否明显。例如，可以设定当符号对应的粒子集的有效粒子容量
Figure PCTCN2017103311-appb-000060
低于某个阈值时，那么该符号对应的粒子集就要进行重采样。需要说明的是，上述不满足预设的粒子退化条件，指的是当前符号对应的粒子集退化现象不严重，满足预设的粒子退化条件，指的是当前符号对应的粒子集退化现象严重，因而需要被重采样。
步骤S109：对当前符号的粒子集进行重采样。重采样是为了淘汰权重低的粒子，而集中于权重高的粒子，从而抑制退化现象。重采样的方法有多种，包括重要性重采样、残差重采样、分层重采样和优化组合重采样等，其基本思路就是复制权重大的粒子，淘汰权重小的粒子，通过重采样，最后生成一个新的粒子集，重采样示意图如附图10所示。
另外，步骤S103提到的“从前向滤波估计序列Xf中第一个符号开始到最后一个符号结束”在具体实现时，可以从第一个符号开始先进行步骤S101，当在步骤S107的判断结果为不满足以及步骤S109之后，都进行一个判断，判断是否到达最后一个符号，若是，则前向平滑步骤S100结束，否则的话就进行下一符号的处理，即下一符号又从步骤S103开始，按照图16所示的流程，往下进行各步骤。
通过前向平滑步骤S100，即步骤S101～S109，估计序列X(前向滤波估计序列Xf)中各符号都具有对应的粒子集，各粒子集中的每个粒子都具有一个重要性权重。
后向信息滤波步骤S300：从估计序列X(前向滤波估计序列Xf)中最后一个符号开始到第一个符号结束，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到后向信息滤波过程的粒子重要性权重。在一实施例中，请参照图16，后向信息滤波步骤S300包括步骤S301～S311。
步骤S301：根据前向滤波步骤S100计算的结果，将估计序列X(前向滤波估计序列Xf)中最后一个符号对应的粒子集中重要性权重最大的粒子作为此符号的估计值，以及将估计序列X(前向滤波估计序列Xf)中最后一个符号对应的粒子集中各粒 子的前向滤波过程的粒子重要性权重作为估计序列X中最后一个符号对应的粒子集中对应各粒子的后向信息滤波过程的粒子重要性权重。在一实施例中，也可以另外设置一个后向信息滤波序列Xb，其长度为N，将估计序列X(前向滤波估计序列Xf)中最后一个符号对应的粒子集中重要性权重最大的粒子，作为后向信息滤波序列Xb最后一个符号的估计值，可表示为如下形式：Xb(N)＝Xf(max，N)。同时，将估计序列X(前向滤波估计序列Xf)中最后一个符号对应的粒子集中各粒子的重要性权重赋给后向信息滤波序列Xb的重要性权重Wb，可表示为Wb(1～Ns，N)＝Wf(1～Ns，N)。
步骤S303：构造一人工分布序列，其中该人工分布序列的长度与待译码序列长度相同。在一实施例中，所构造的人工分布序列为：
Figure PCTCN2017103311-appb-000061
其中，γt(xt)表示该人工分布序列；xt表示t时刻的符号。
步骤S305：从估计序列X最后一个符号开始到第一个符号结束，计算待译码序列与当前符号每个粒子的概率密度；并根据待译码序列与当前符号每个粒子的概率密度与上述人工分布序列，计算当前符号每个粒子的后向信息滤波过程的辅助概率密度。在一实施例中，计算当前符号每个粒子的后向信息滤波过程的辅助概率密度，是根据公式
Figure PCTCN2017103311-appb-000062
计算的，其中f(xt+1|xt)表示待译码序列与当前符号每个粒子的概率密度。需要说明的是，由于前向滤波过程中估计出的序列是没有经过编码的，因此需要对估计的粒子先和复用波形经过K重OvXDM编码后，再与待译码序列计算其概率密度。本案例采用多维正态分布(Multivariate normal probability density function，mvnpdf)概率密度。
当然，步骤S305中提到的“从估计序列X最后一个符号开始到第一个符号结束”也可以和上面步骤S103提到的“从前向滤波估计序列Xf中第一个符号开始到最后一个符号结束”的实现类似，在此不再赘述。
步骤S307：根据当前符号每个粒子的后向信息滤波过程的辅助概率密度，分别计算各粒子的后向信息滤波过程的重要性权重。在一实施例中，计算各粒子的后向信息滤波过程的重要性权重是根据公式
Figure PCTCN2017103311-appb-000063
计算的，其中其中
Figure PCTCN2017103311-appb-000064
为粒子的后向信息滤波重要性权重，N为待译码序列长度，Ns为当前符号对应的粒子集中的粒子数，γi，j为粒子的辅助概率密度。可以看到，计算得到的各粒子的后向信息滤波过程的重要性权重，实际为归一化重要性权重。
步骤S309：根据当前符号的后向信息滤波过程的重要性权重来判断当前符号对应的粒子集是否满足一预设的粒子退化条件，若不满足，则进行前一符号，即当前符 号的前一符号从步骤S305开始进行。若满足，则进行步骤S311。本步骤S309与步骤S107的目的是一样，两步骤中的粒子退化条件可以相同，也可以不同。
步骤S311：对当前符号的粒子集进行重采样。本步骤S311的方法和原理与步骤S109类似，在此不再赘述。步骤S309和步骤S311不是必须的，可以根据实际系统需求而定，目的都是确保估计的粒子最逼近真实序列，提高估计的准确性。
双滤波权重计算步骤S400：根据前向滤波过程的粒子重要性权重和后向信息滤波过程的粒子重要性权重，计算双滤波过程的粒子重要性权重。在一实施例中，双滤波权重计算步骤中，计算双滤波过程的粒子重要性权重是根据下面的公式计算的：
Figure PCTCN2017103311-appb-000065
其中，
Figure PCTCN2017103311-appb-000066
表示双滤波过程的粒子重要性权重，
Figure PCTCN2017103311-appb-000067
表示前向滤波过程的粒子重要性权重，
Figure PCTCN2017103311-appb-000068
表示后向信息滤波过程的粒子重要性权重；xt (k)表示t时刻的符号的第k个粒子，符号～表示后向过程。
输出步骤S500：根据双滤波权重计算步骤S400的计算结果，输出译码序列。在一实施例中，输出步骤S500将每一个符号对应的粒子集中双滤波过程的粒子重要性权重最大的粒子作为此符号的估计值，输出最终的译码序列。
以上就是本申请公开的适用于OvXDM系统的双滤波平滑译码方法的流程，相应地，本申请还公开了一种OvXDM系统，此OvXDM系统可以为OvTDM系统、OvFDM系统、OvCDM系统、OvSDM系统或OvHDM系统，其包括一种适用于OvXDM系统的双滤波平滑译码装置。请参照图17，适用于OvXDM系统的双滤波平滑译码装置包括前向滤波单元100、后向信息滤波单元300、双滤波权重计算单元400和输出单元500。
前向滤波单元100用于从一估计序列中第一个符号开始到最后一个符号结束，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到前向滤波过程的粒子重要性权重。在一实施例中，请参照图18，前向滤波单元100包括初始化单元101、粒子集生成单元103、重要性概率密度计算单元105、重要性权重计算单元107、第一判断单元109a和第一重采样单元111a。
初始化单元101用于初始化估计序列X，其中估计序列X的长度与待译码序列长度相同。由于这是在前向滤波过程中，因此不妨将估计序列X称为前向滤波估计序列Xf，其序列长度与待译码序列长度相同。例如，不妨令OvXDM系统接收端接收到长度为N的符号序列y，此符号序列y即为待译码序列，其重叠次数为K，以矩形波为复用波形；若每个符号的粒子数为Ns，每个粒子对应一个重要性权重值。则前向滤波估计序列Xf的大小为Ns×N，各粒子对应的重要性权重值的集合Wf的大小为Ns×N。
粒子集生成单元103用于从估计序列X中第一个符号开始到最后一个符号结束， 对当前符号生成一个粒子集。如上所述，每个符号对应的粒子集中粒子个数为Ns。例如，在OvXDM系统中，以二元数据流{+1，-1}为例，每个符号的可能取值只有两种：+1或者-1，因此每个符号对应的粒子集就是包括两种粒子，取值分别+1和-1。对当前符号生成粒子集的方法很多，只要生成的粒子集的分布趋近理论分布即可。
重要性概率密度计算单元105用于当前符号生成粒子集后，计算当前符号每个粒子与待译码序列的重要性概率密度。在一实施例中，当i＞1时，即当前符号为第2个符号或之后的符号时，重要性概率密度计算单元105计算当前符号的粒子集中的粒子与待译码序列的重要性概率密度，可以参考前一符号的粒子集中的粒子与待译码序列的重要性概率密度，需要说明的是，在OvXDM系统中，由于接收符号序列y是经过OvXDM编码的，因此也需要对估计的符号粒子Xfi，j进行OvXDM编码，再计算其重要性概率密度。
重要性权重计算单元107用于根据重要性概率密度计算每个粒子的重要性权重。在一实施例中，重要性权重计算单元107计算当前符号对应的粒子集中每个粒子的归一化重要性权重是根据下述公式进行计算的：
Figure PCTCN2017103311-appb-000069
其中，
Figure PCTCN2017103311-appb-000070
为粒子的重要性权重，N为待译码序列长度，Ns为当前符号对应的粒子集中的粒子数，Pi，j为粒子的重要性概率密度。可以看到，
Figure PCTCN2017103311-appb-000071
实质上是归一化重要性权重。
第一判断单元109a用于判断当前符号对应的粒子集是否满足预设的粒子退化条件，若不满足，则通知粒子集生成单元103对后一个符号生成粒子集。本判断单元109是用于判断当前符号对应的粒子集中粒子的退化现象是否明显。例如，可以设定当符号对应的粒子集的有效粒子容量
Figure PCTCN2017103311-appb-000072
低于某个阈值时，那么该符号对应的粒子集就要进行重采样。
第一重采样单元111a用于当第一判断单元109a的结果为满足时，对当前符号的粒子集进行重采样。第一重采样单元111a对当前符号的粒子集进行重采样后，通知粒子集生成单元103对后一个符号生成粒子集。
第一重采样单元111a进行重采样是为了淘汰权重低的粒子，而集中于权重高的粒子，从而抑制退化现象。重采样的方法有多种，包括重要性重采样、残差重采样、分层重采样和优化组合重采样等，其基本思路就是复制权重大的粒子，淘汰权重小的粒子，通过重采样，最后生成一个新的粒子集，重采样示意图如上面的附图10所示。
后向信息滤波单元300从估计序列X(前向滤波估计序列Xf)中最后一个符号开始到第一个符号结束，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得 到后向信息滤波过程的粒子重要性权重。在一实施例中，请参照图19，后向信息滤波单元300包括设置单元301、人工分布序列构造单元302、概率密度计算单元303、辅助概率密度计算单元307和重要性权重再计算单元305，在一实施例中，还可以包括第二判断单元311和第二重采样单元313。
设置单元301用于根据前向滤波单元100计算的结果，将估计序列X(前向滤波估计序列Xf)中最后一个符号对应的粒子集中重要性权重最大的粒子作为此符号的估计值，以及将估计序列X(前向滤波估计序列Xf)中最后一个符号对应的粒子集中各粒子的前向滤波过程的粒子重要性权重作为估计序列X中最后一个符号对应的粒子集中对应各粒子的后向信息滤波过程的粒子重要性权重。在一实施例中，也可以另外设置一个后向平滑序列Xb，其长度为N，设置单元301将估计序列X(前向滤波估计序列Xf)中最后一个符号对应的粒子集中重要性权重最大的粒子，作为后向平滑序列Xb最后一个符号的估计值，可表示为如下形式：Xb(N)＝Xf(max，N)。同时，设置单元301将估计序列X(前向滤波估计序列Xf)中最后一个符号对应的粒子集中各粒子的重要性权重赋给后向平滑序列Xb的重要性权重Wb，可表示为Wb(1～Ns，N)＝Wf(1～Ns，N)。
人工分布序列构造单元302用于构造一人工分布序列，其中该人工分布序列的长度与待译码序列长度相同。在一实施例中，人工分布序列构造单元302依据下式构造上述人工分布序列：
Figure PCTCN2017103311-appb-000073
其中，γt(xt)表示上述人工分布序列。
概率密度计算单元303用于从所述估计序列最后一个符号开始到第一个符号结束：计算待译码序列与当前符号每个粒子的概率密度。需要说明的是，由于前向滤波过程中估计出的序列是没有经过编码的，因此需要对估计的粒子先和复用波形经过K重OvXDM编码后，再与待译码序列计算其概率密度。本案例采用多维正态分布(Multivariate normal probability density function，mvnpdf)概率密度。
辅助概率密度计算单元307用于根据待译码序列与当前符号每个粒子的概率密度与所述人工分布序列，计算当前符号每个粒子的后向信息滤波过程的辅助概率密度。在一实施例中，辅助概率密度计算单元307依据公式
Figure PCTCN2017103311-appb-000074
进行计算的，其中f(xt+1|xt)表示待译码序列与当前符号每个粒子的概率密度，重要性权重再计算单元305用于根据当前符号每个粒子的后向信息滤波过程的辅助概率密度，分别计算各粒子的后向信息滤波过程的重要性权重。在一实施例中，计算各粒子的后向信 息滤波过程的重要性权重是根据公式
Figure PCTCN2017103311-appb-000075
计算的，其中
Figure PCTCN2017103311-appb-000076
为粒子的后向信息滤波重要性权重，N为待译码序列长度，Ns为当前符号对应的粒子集中的粒子数，γi，j为粒子的辅助概率密度。可以看到，计算得到的各粒子的后向信息滤波过程的重要性权重，实际为归一化重要性权重。
第二判断单元311用于根据当前符号的后向信息滤波过程的重要性权重来判断当前符号对应的粒子集是否满足一预设的粒子退化条件，若满足，则通知第二重采样单元对当前符号的粒子集进行重采样，若不满足，则通知概率密度计算单元307对前一符号进行计算。第二判断单元311与第一判断单元109a类似，两者的粒子退化条件可以相同，也可以不同，在此不再赘述。
第二重采样单元313用于当第二判断单元311的结果为满足时，对当前符号的粒子集进行重采样。第二重采样单元313对当前符号的粒子集进行重采样，通知概率密度计算单元307对前一符号进行计算。第二重采样单元313与第一重采样单元111a类似，在此不再赘述。
双滤波权重计算单元400用于根据前向滤波过程的粒子重要性权重和后向信息滤波过程的粒子重要性权重，计算双滤波过程的粒子重要性权重。在一实施例中，双滤波权重计算单元50计算双滤波过程的粒子重要性权重是根据下面的公式计算的：
Figure PCTCN2017103311-appb-000077
其中，
Figure PCTCN2017103311-appb-000078
表示双滤波过程的粒子重要性权重，
Figure PCTCN2017103311-appb-000079
表示前向滤波过程的粒子重要性权重，
Figure PCTCN2017103311-appb-000080
表示后向信息滤波过程的粒子重要性权重。
输出单元500用于根据双滤波权重计算单元400的计算结果，输出译码序列。在一实施例中，输出单元500用于将每一个符号对应的粒子集中双滤波过程的粒子重要性权重最大的粒子作为此符号的估计值，输出最终的译码序列。
以上就是本申请公开的OvXDM系统及适用于OvXDM系统的双滤波平滑译码装置。
本申请在译码过程中，在对各符号生成粒子集时，对于一个未知的序列，由于初始阶段不知道其粒子分布，可先随机生成一组样本，通过计算粒子与观测值的重要性权重，判断粒子的可靠性，依据一定的准则，对粒子样本进行重采样，淘汰权重小得粒子，复制权重大的粒子，依次反复迭代计算，最终计算得到较为可靠的输出值。迭代次数越高，得到的结果越精确。另外，粒子的退化现象是粒子滤波器的最大缺陷，制约着粒子滤波器的发展，解决粒子退化问题的有效方法之一就是对粒子进行重采样。粒子滤波在解决非线性、非高斯问题的参数估计和状态滤波方面有着独到的优势，因此有很大的发展空间，可以将成熟的多种不同的寻优方法引入重采样过程，以便更快 地提取到反映系统概率特征的典型“粒子”。
本申请通过前向滤波和后向信息滤波分别计算符号对应的粒子集中各粒子的重要性权重，再结合前向滤波的粒子重要性权重和后向信息滤波的粒子重要性权重进行筛选，以输出最终的译码序列，在这过程中，充分利用了粒子间的互信息，实现0vXDM系统的译码，使得到的译码序列更加逼近真实值，同时随着重叠次数的增加，相较传统的译码方法降低了译码复杂度，提升了译码效率和系统性能。
以上内容是结合具体的实施方式对本申请所作的进一步详细说明，不能认定本申请的具体实施只局限于这些说明。对于本申请所属技术领域的普通技术人员来说，在不脱离本申请发明构思的前提下，还可以做出若干简单推演或替换。

Claims (25)

  1. 一种前向后向译码方法，其特征在于，包括以下步骤：
    前向步骤：从一估计序列中第一个符号开始到最后一个符号结束，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到前向过程的粒子重要性权重；
    后向步骤：从所述估计序列中最后一个符号开始到第一个符号结束，参照前向步骤中得到的粒子重要性权重，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到后向过程的粒子重要性权重；
    输出步骤：取每一个符号对应的估计值，输出最终的译码序列。
  2. 如权利要求1所述译码方法，其特征在于，所述输出步骤为：将每一个符号对应的粒子集中后向过程的粒子重要性权重最大的粒子作为此符号的估计值，输出最终的译码序列。
  3. 如权利要求1所述的译码方法，其特征在于，所述后向步骤后还包括：
    双滤波权重计算步骤：根据前向过程的粒子重要性权重和后向过程的粒子重要性权重，计算双滤波过程的粒子重要性权重；
    所述输出步骤为：将每一个符号对应的粒子集中双滤波过程的粒子重要性权重最大的粒子作为此符号的估计值，输出最终的译码序列。
  4. 如权利要求1所述的译码方法，其特征在于，所述前向步骤包括：
    初始化估计序列，其中所述估计序列的长度与待译码序列长度相同；
    从估计序列中第一个符号开始到最后一个符号结束：对当前符号生成一个粒子集；计算当前符号每个粒子与待译码序列的重要性概率密度，并计算每个粒子的重要性权重；判断当前符号对应的粒子集是否满足预设的粒子退化条件，若满足，则对当前符号的粒子集进行重采样；若不满足，则进行下一符号。
  5. 如权利要求4所述的译码方法，其特征在于，在前向步骤中，计算当前符号对应的粒子集中每一个粒子的重要性权重是根据下述公式进行计算的：
    Figure PCTCN2017103311-appb-100001
    其中，wfi，j为粒子的重要性权重，N为待译码序列长度，Ns为当前符号对应的粒子集中的粒子数，Pi，j为粒子的重要性概率密度。
  6. 如权利要求2所述的译码方法，其特征在于，所述后向步骤包括：
    根据前向步骤计算的结果，将所述估计序列中最后一个符号对应的粒子集中重要性权重最大的粒子作为此符号的估计值，以及将所述估计序列中最后一个符号对应的粒子集中各粒子的前向过程的粒子重要性权重作为所述估计序列 中最后一个符号对应的粒子集中对应各粒子的后向过程的粒子重要性权重；
    从所述估计序列倒数第二个符号开始到第一个符号结束：计算当前符号和后一符号之间的概率密度；根据此概率密度、后一符号的后向过程的粒子重要性权重、当前符号的前向过程的粒子重要性权重，计算得到当前符号的后向过程的粒子重要性权重。
  7. 如权利要求6所述的译码方法，其特征在于，在后向步骤中，计算各符号对应的粒子集中各粒子的重要性权重是根据下述公式进行计算的：
    Figure PCTCN2017103311-appb-100002
    Ns为当前符号对应的粒子集中的粒子数，i和j表示粒子索引，取值为1～Ns；xt表示t时刻的符号；
    其中，ωt为当前符号的前向过程的粒子重要性权重，
    Figure PCTCN2017103311-appb-100003
    是当前符号和后一符号之间的概率密度，ωt|T是当前符号后向过程的粒子重要性权重。
  8. 如权利要求3所述的译码方法，其特征在于，所述后向步骤包括：根据前向步骤计算的结果，将所述估计序列中最后一个符号对应的粒子集中重要性权重最大的粒子作为此符号的估计值，以及将所述估计序列中最后一个符号对应的粒子集中各粒子的前向滤波过程的粒子重要性权重作为所述估计序列中最后一个符号对应的粒子集中对应各粒子的后向信息滤波过程的粒子重要性权重；
    构造一人工分布序列，其中所述人工分布序列的长度与待译码序列长度相同；
    从所述估计序列最后一个符号开始到第一个符号结束：计算待译码序列与当前符号每个粒子的概率密度；并根据待译码序列与当前符号每个粒子的概率密度与所述人工分布序列，计算当前符号每个粒子的后向信息滤波过程的辅助概率密度；
    根据当前符号每个粒子的后向信息滤波过程的辅助概率密度，分别计算各粒子的后向信息滤波过程的重要性权重。
  9. 如权利要求8所述的译码方法，其特征在于，在后向步骤中，还根据当前符号的后向信息滤波过程的重要性权重来判断当前符号对应的粒子集是否满足一预设的粒子退化条件，若满足，则对当前符号的粒子集进行重采样；若不满足，则进行前一符号。
  10. 如权利要求9所述的译码方法，其特征在于：
    所构造的人工分布序列为：
    Figure PCTCN2017103311-appb-100004
    其中，γt(xt)表示所述人工分布序列；
    计算当前符号每个粒子的后向信息滤波过程的辅助概率密度，是根据公式
    Figure PCTCN2017103311-appb-100005
    计算的，其中f(xt+1|xt)表示待译码序列与当前符号每个粒子的概率密度；xt表示t时刻的符号；
    计算各粒子的后向信息滤波过程的重要性权重是根据下述公式计算的，
    Figure PCTCN2017103311-appb-100006
    其中
    Figure PCTCN2017103311-appb-100007
    为粒子的后向信息滤波重要性权重，N为待译码序列长度，Ns为当前符号对应的粒子集中的粒子数，γi，j为粒子的辅助概率密度。
  11. 如权利要求10所述的译码方法，其特征在于，双滤波权重计算步骤中，计算双滤波过程的粒子重要性权重是根据下面的公式计算的：
    Figure PCTCN2017103311-appb-100008
    其中，
    Figure PCTCN2017103311-appb-100009
    表示双滤波过程的粒子重要性权重，
    Figure PCTCN2017103311-appb-100010
    表示前向滤波过程的粒子重要性权重，
    Figure PCTCN2017103311-appb-100011
    表示后向信息滤波过程的粒子重要性权重；xt (k)表示t时刻的符号的第k个粒子，符号～表示后向过程。
  12. 如权利要求1中所述的译码方法，其特征在于，所述OvXDM系统为OvTDM系统、OvFDM系统、OvCDM系统、OvSDM系统或OvHDM系统。
  13. 一种前向后向译码装置，其特征在于，包括：
    前向单元，用于从一估计序列中第一个符号开始到最后一个符号结束，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到前向平滑过程的粒子重要性权重；
    后向单元，用于从所述估计序列中最后一个符号开始到第一个符号结束，参照前向平滑单元中得到的粒子重要性权重，依次计算每一个符号对应的粒子集中各粒子的重要性权重，得到后向平滑过程的粒子重要性权重；
    输出单元，用于输出最终的译码序列。
  14. 如权利要求13所述的译码装置，其特征在于，所述输出单元将每一个符号对应的粒子集中后向过程的粒子重要性权重最大的粒子作为此符号的估计值，输出最终的译码序列。
  15. 如权利要求13所述的译码装置，其特征在于，还包括：
    双滤波权重计算单元，用于根据前向滤波过程的粒子重要性权重和后向信息滤波过程的粒子重要性权重，计算双滤波过程的粒子重要性权重；
    所述输出单元将每一个符号对应的粒子集中双滤波过程的粒子重要性权重最大的粒子作为此符号的估计值，输出最终的译码序列。
  16. 如权利要求13所述的译码装置，其特征在于，所述前向单元包括：
    初始化单元，用于初始化估计序列，其中所述估计序列的长度与待译码序列长度相同；
    粒子集生成单元，用于从估计序列中第一个符号开始到最后一个符号结束，对当前符号生成一个粒子集；
    重要性概率密度计算单元，用于当前符号生成粒子集后，计算当前符号每个粒子与待译码序列的重要性概率密度；
    重要性权重计算单元，用于根据重要性概率密度计算每个粒子的重要性权重；
    判断单元，用于判断当前符号对应的粒子集是否满足预设的粒子退化条件，若不满足，则通知粒子集生成单元对下一个符号生成粒子集；
    重采样单元，用于当判断单元的结果为满足时，对当前符号的粒子集进行重采样。
  17. 如权利要求16所述的译码装置，其特征在于，在前向单元中所述重要性权重计算单元根据下述公式进行计算重要性权重：
    Figure PCTCN2017103311-appb-100012
    其中，wi，j为粒子的重要性权重，N为待译码序列长度，Ns为当前符号对应的粒子集中的粒子数，Pi，j为粒子的重要性概率密度。
  18. 如权利要求13所述的译码装置，其特征在于，所述后向单元包括：
    设置单元，用于根据前向单元计算的结果，将所述估计序列中最后一个符号对应的粒子集中重要性权重最大的粒子作为此符号的估计值，以及将所述估计序列中最后一个符号对应的粒子集中各粒子的前向过程的粒子重要性权重作为所述估计序列中最后一个符号对应的粒子集中对应各粒子的后向过程的粒子重要性权重；
    概率密度计算单元，用于从所述估计序列倒数第二个符号开始到第一个符号结束，计算当前符号和后一符号之间的概率密度；
    重要性权重再计算单元，用于当前符号和后一符号之间的概率密度被计算得到后，根据此概率密度、后一符号的后向过程的粒子重要性权重、当前符号 的前向过程的粒子重要性权重，计算得到当前符号的后向过程的粒子重要性权重。
  19. 如权利要求13所述的译码装置，其特征在于，在后向单元中重要性权重再计算单元是根据下述公式来重新计算当前符号对应的粒子集中各粒子的重要性权重：
    Figure PCTCN2017103311-appb-100013
    Ns表示当前符号对应的粒子集中的粒子数，i和j表示粒子索引，取值为1～Ns；
    其中，ωt为当前符号的前向过程的粒子重要性权重，
    Figure PCTCN2017103311-appb-100014
    是当前符号和后一符号之间的概率密度，ωt|T是当前符号的后向过程的粒子重要性权重。
  20. 如权利要求13所述的的译码装置，其特征在于，所述前向单元包括：
    初始化单元，用于初始化估计序列，其中所述估计序列的长度与待译码序列长度相同；
    粒子集生成单元，用于从估计序列中第一个符号开始到最后一个符号结束，对当前符号生成一个粒子集；
    重要性概率密度计算单元，用于当前符号生成粒子集后，计算当前符号每个粒子与待译码序列的重要性概率密度；
    重要性权重计算单元，用于根据重要性概率密度计算每个粒子的重要性权重；
    第一判断单元，用于判断当前符号对应的粒子集是否满足预设的粒子退化条件，若不满足，则通知粒子集生成单元对下一个符号生成粒子集；
    第一重采样单元，用于当第一判断单元的结果为满足时，对当前符号的粒子集进行重采样。
  21. 如权利要求20所述的译码装置，其特征在于，在前向单元中所述重要性权重计算单元根据下述公式进行计算重要性权重：
    Figure PCTCN2017103311-appb-100015
    其中，wi，j为粒子的前向滤波重要性权重，N为待译码序列长度，Ns为当前符号对应的粒子集中的粒子数，Pi，j为粒子的重要性概率密度。
  22. 如权利要求20所述的译码装置，其特征在于，所述后向单元包括：
    设置单元，用于根据前向滤波单元计算的结果，将所述估计序列中最后一个符号对应的粒子集中重要性权重最大的粒子作为此符号的估计值，以及将所述估计序列中最后一个符号对应的粒子集中各粒子的前向滤波过程的粒子重要 性权重作为所述估计序列中最后一个符号对应的粒子集中对应各粒子的后向信息滤波过程的粒子重要性权重；
    人工分布序列构造单元，用于构造一人工分布序列，其中所述人工分布序列的长度与待译码序列长度相同；
    概率密度计算单元，用于从所述估计序列最后一个符号开始到第一个符号结束：计算待译码序列与当前符号每个粒子的概率密度；
    辅助概率密度计算单元，用于根据待译码序列与当前符号每个粒子的概率密度与所述人工分布序列，计算当前符号每个粒子的后向信息滤波过程的辅助概率密度；
    重要性权重再计算单元，用于根据当前符号每个粒子的后向信息滤波过程的辅助概率密度，分别计算各粒子的后向信息滤波过程的重要性权重。
  23. 如权利要求20所述译码装置，其特征在于，还包括第二判断单元和第二重采样单元；所述第二判断单元用于根据当前符号的后向信息滤波过程的重要性权重来判断当前符号对应的粒子集是否满足一预设的粒子退化条件，若满足，则通知第二重采样单元对当前符号的粒子集进行重采样，若不满足，则通知概率密度计算单元对前一符号进行计算。
  24. 如权利要求22所述的译码装置，其特征在于，所述人工分布序列构造单元依据下式构造所述人工分布序列：
    Figure PCTCN2017103311-appb-100016
    其中，γt(xt)表示所述人工分布序列；xt表示t时刻的符号；
    所述辅助概率密度计算单元依据公式
    Figure PCTCN2017103311-appb-100017
    进行计算的，其中f(xt+1|xt)表示待译码序列与当前符号每个粒子的概率密度；
    所述重要性权重再计算单元是根据下述公式计算的，
    Figure PCTCN2017103311-appb-100018
    其中
    Figure PCTCN2017103311-appb-100019
    为粒子的后向信息滤波重要性权重，N为待译码序列长度，Ns为当前符号对应的粒子集中的粒子数，γi，j为粒子的辅助概率密度。
  25. 如权利要求24所述译码装置，其特征在于，双滤波权重计算单元中，计算双滤波过程的粒子重要性权重是根据下面的公式计算的：
    Figure PCTCN2017103311-appb-100020
    其中，
    Figure PCTCN2017103311-appb-100021
    表示双滤波过程的粒子重要性权重，
    Figure PCTCN2017103311-appb-100022
    表示前向滤波过程的粒子重要性权重，
    Figure PCTCN2017103311-appb-100023
    表示后向信息滤波过程的粒子重要性权重；xt (k)表示t时刻的符号的第k个粒子，符号～表示后向过程。
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109545113A (zh) * 2018-09-30 2019-03-29 合肥鑫晟光电科技有限公司 一种异常数据处理方法及装置

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101340266A (zh) * 2008-06-06 2009-01-07 山东大学 一种基于粒子滤波器和神经网络的双选择性信道跟踪方法
CN101425870A (zh) * 2007-11-01 2009-05-06 中兴通讯股份有限公司 一种Turbo码迭代译码方法
WO2014052252A2 (en) * 2012-09-28 2014-04-03 Qualcomm Incorporated Techniques for faster time-to-first-fix
CN104899921A (zh) * 2015-06-04 2015-09-09 杭州电子科技大学 基于多模态自编码模型的单视角视频人体姿态恢复方法
US20160084869A1 (en) * 2014-09-23 2016-03-24 Fitbit, Inc. Hybrid angular motion sensors

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP3888135B2 (ja) * 2001-11-15 2007-02-28 日本電気株式会社 誤り訂正符号復号装置
GB2395871B (en) * 2002-11-28 2006-01-11 Toshiba Res Europ Ltd Signal estimation methods and apparatus
US20110141918A1 (en) * 2009-09-13 2011-06-16 Research Institute Of Tsinghua University In Shenzhen Time division multiplexing method and system
CN113395136B (zh) * 2015-04-06 2023-06-23 Lg电子株式会社 用于处理广播信号的广播发送器、广播接收器和方法

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101425870A (zh) * 2007-11-01 2009-05-06 中兴通讯股份有限公司 一种Turbo码迭代译码方法
CN101340266A (zh) * 2008-06-06 2009-01-07 山东大学 一种基于粒子滤波器和神经网络的双选择性信道跟踪方法
WO2014052252A2 (en) * 2012-09-28 2014-04-03 Qualcomm Incorporated Techniques for faster time-to-first-fix
US20160084869A1 (en) * 2014-09-23 2016-03-24 Fitbit, Inc. Hybrid angular motion sensors
CN104899921A (zh) * 2015-06-04 2015-09-09 杭州电子科技大学 基于多模态自编码模型的单视角视频人体姿态恢复方法

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
See also references of EP3525372A4 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109545113A (zh) * 2018-09-30 2019-03-29 合肥鑫晟光电科技有限公司 一种异常数据处理方法及装置

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