CN107919940A - Suitable for the smooth interpretation method of forward-backward algorithm, device and the OvXDM systems of OvXDM systems - Google Patents
Suitable for the smooth interpretation method of forward-backward algorithm, device and the OvXDM systems of OvXDM systems Download PDFInfo
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Abstract
This application discloses a kind of smooth interpretation method of forward-backward algorithm, device and OvXDM systems suitable for OvXDM systems.The thought of statistics is introduced decoding process by it, by preceding to smooth and backward smooth two processes, make full use of interparticle mutual information, realize the decoding of OvXDM systems, the coding sequence made more approaching to reality value, at the same time with the increase of overlapping number, comparing traditional interpretation method reduces decoding complexity, improves decoding efficiency and system performance.
Description
Technical Field
The application relates to the field of decoding, in particular to a forward and backward smooth decoding method and device suitable for an OvXDM system and the OvXDM system.
Background
For the OvXDM system of the overlapping multiplexing system, the conventional decoding needs to constantly access the nodes in the Trellis diagram (Trellis), and two memories are provided for each node, one for storing the relative best path to the node, and one for storing the corresponding measure of the relative best path to the node.
Taking the OvTDM system as an example, since the decoding process needs to be performed for each node in the trellis diagramThe number of nodes determines the complexity of decoding, and for a system with K number of overlaps and M modulation dimension (M is an integer greater than or equal to 2), the number of nodes in steady state in the corresponding trellis diagram is M K-1 Therefore, the decoding complexity increases exponentially with the number of overlaps K. In the OvTDM system, the spectral efficiency of the system is 2K/symbol, so the spectral efficiency is higher when the number of times of overlapping K is larger. Therefore, on one hand, the larger the overlap number K is, the better it is for the requirement of improving the spectral efficiency, and on the other hand, the smaller the overlap number K is, the better it is for the requirement of reducing the decoding complexity, and particularly, when the overlap number K is increased to a certain value, for example, K is greater than 8, the decoding complexity is increased sharply, the existing decoding method is difficult to meet the requirement of real-time decoding, and the spectral efficiency, the decoding complexity and the decoding efficiency form a pair of contradictory requirements.
Disclosure of Invention
In order to solve the above problems, the present application provides a forward and backward smooth decoding method and apparatus suitable for an OvXDM system, and an OvXDM system.
According to a first aspect of the present application, the present application provides a forward and backward smoothing decoding method suitable for an OvXDM system, comprising the following steps:
a forward smoothing step: sequentially calculating the importance weight of each particle in the particle set corresponding to each symbol from the first symbol to the last symbol in an estimation sequence to obtain the importance weight of the particles in the forward smoothing process;
and a backward smoothing step: sequentially calculating the importance weight of each particle in the particle set corresponding to each symbol by referring to the importance weight of the particles obtained in the forward smoothing step from the last symbol to the end of the first symbol in the estimation sequence to obtain the importance weight of the particles in the backward smoothing process;
an output step: and taking the particle with the maximum particle importance weight in the backward smoothing process in the particle set corresponding to each symbol as an estimated value of the symbol, and outputting a final decoding sequence.
According to a second aspect of the present application, there is provided a forward and backward smooth decoding apparatus suitable for an OvXDM system, comprising:
a forward smoothing unit, configured to calculate importance weights of particles in a particle set corresponding to each symbol in sequence from a first symbol to a last symbol in an estimation sequence, so as to obtain a particle importance weight in a forward smoothing process;
a backward smoothing unit, configured to calculate importance weights of particles in a particle set corresponding to each symbol in sequence by referring to the importance weights of the particles obtained in the forward smoothing unit from a last symbol to a first symbol in the estimation sequence, so as to obtain an importance weight of the particles in a backward smoothing process;
and the output unit is used for taking the particle with the maximum particle importance weight in the backward smoothing process in the particle set corresponding to each symbol as an estimated value of the symbol and outputting a final decoding sequence.
According to a third aspect of the present application, there is provided an OvXDM system, including the above forward and backward smooth decoding apparatus suitable for the OvXDM system, wherein the OvXDM system is an OvTDM system, an OvFDM system, an OvCDM system, an OvSDM system, or an OvHDM system.
The beneficial effect of this application is:
according to the forward and backward smooth decoding method, the device and the OvXDM system which are applied to the OvXDM system, the statistical idea is introduced into the decoding process, the mutual information among particles is fully utilized through the forward smooth process and the backward smooth process, the decoding of the OvXDM system is realized, the obtained decoding sequence is closer to a true value, and meanwhile, along with the increase of the overlapping times, the decoding complexity is reduced compared with the traditional decoding method, and the decoding efficiency and the system performance are improved.
Drawings
Fig. 1 is a schematic structural diagram of a transmitting end of a conventional OvTDM system;
fig. 2 is a schematic diagram of a parallelogram rule of an OvTDM system for performing overlapping multiplexing coding on input symbols;
fig. 3 (a) and (b) respectively illustrate a preprocessing unit and a sequence detection unit of a conventional OvTDM receiving end;
FIG. 4 is a tree diagram of the I/O code of the system when the system has the number of times of overlap multiplexing K = 3;
FIG. 5 is a node state transition diagram for the system of FIG. 4;
FIG. 6 is a Trellis (Trellis) diagram of the system of FIG. 4 or FIG. 5, respectively;
fig. 7 is a schematic flowchart of a forward and backward smooth decoding method applied to an OvXDM system according to an embodiment of the present application;
FIG. 8 is a diagram of an OvXDM system equivalent convolutional coding model;
FIG. 9 is a schematic flow chart of a forward smoothing step according to an embodiment of the present application;
FIG. 10 is a schematic illustration of a resampling step in an embodiment of the present application;
FIG. 11 is a flow chart illustrating a backward smoothing step according to an embodiment of the present application;
fig. 12 is a schematic structural diagram of a forward/backward smoothing decoding apparatus suitable for the OvXDM system in an embodiment of the present application;
FIG. 13 is a schematic diagram of a forward smoothing unit in one embodiment of the present application;
FIG. 14 is a schematic diagram of a backward smoothing unit in an embodiment of the present application.
Detailed Description
The present application will be described in further detail below with reference to the accompanying drawings by way of specific embodiments.
The application provides a forward and backward smooth decoding method and device suitable for an OvXDM system, and the OvXDM system, wherein the OvXDM system is an Overlapped Time Division Multiplexing (OvTDM) system, an Overlapped Frequency Division Multiplexing (OvFDM) system, an Overlapped Code Division Multiplexing (OvCDM) system, an Overlapped Space Division Multiplexing (OvSDM) system, or an Overlapped Hybrid Division Multiplexing (OvHDM) system.
Taking the OvTDM system as an example, a brief description will be given to the transmitting and receiving end of the system.
As shown in fig. 1, a sending process of an OvTDM sending end includes the following specific steps:
(1) First, the envelope waveform h (t) for generating the transmission signal is designed.
(2) And (3) after the envelope waveform h (T) designed in the step (1) is shifted by a specific time, forming the envelope waveform h (T-i multiplied by delta T) of the transmission signal at other times.
(3) The symbol x to be transmitted i Multiplying the envelope waveform h (T-i multiplied by delta T) generated in the step (2) at the corresponding moment to obtain a signal waveform x to be transmitted at each moment i h(t-i×ΔT)。
(4) Performing x on each waveform to be transmitted formed in the step (3) i h (T-i multiplied by delta T) are superposed to form a transmitting signal waveform. The transmitted signal may be represented as:
wherein the overlap-and-multiplex method follows the parallelogram rule as shown in fig. 2.
The transmitting end transmits the coded and modulated signals through an antenna, the signals are transmitted in a wireless channel, the receiving end performs matched filtering on the received signals, then samples and decodes the signals respectively, and finally, the output bit stream is judged.
As shown in fig. 3, a receiving process of an OvTDM receiving end is shown, where 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:
(5) Firstly, the received signals are synchronized, including carrier synchronization, frame synchronization, symbol time synchronization, etc.
(6) The received signal in each frame is digitized according to the sampling theorem.
(7) The received waveform is sliced according to the waveform transmission time interval.
(8) And decoding the cut waveform according to a certain decoding algorithm. For example, decoding is performed by viterbi decoding.
Fig. 4 to 6 show a tree diagram of the system i/o code when the number of overlapping multiplexing K =3 in the decoding process, fig. 5 shows a corresponding node state transition diagram of the system, and fig. 6 shows a Trellis diagram of the system.
As described above, in the conventional decoding method (typically, viterbi decoding), as the number of overlapping times increases, the decoding complexity increases sharply, the requirement on hardware accuracy is high, and the system performance is reduced. In order to solve the problem, the inventor introduces the statistical idea into the decoding process through research and practice, fully utilizes the mutual information between particles through two processes of forward smoothing and backward smoothing, realizes the decoding of the OvXDM system, enables the obtained decoding sequence to be closer to a true value, and simultaneously reduces the decoding complexity and improves the decoding efficiency and the system performance compared with the traditional decoding method along with the increase of the overlapping times. The inventive concepts and principles of the present application are described below.
The decoding process mainly comprises 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 method (Monte Carlo methods). The Monte Carlo method is a very important numerical calculation method which is applied to statistics and guided by probability statistics theory, and the basic idea is that when the problem to be solved is the probability of occurrence of a certain random event or the expected value of a certain random variable, the probability of the random event is estimated by using the frequency of occurrence of the event through a certain 'experiment' method, or certain digital characteristics of the random variable are obtained and taken as the solution of the problem. The method is called a monte carlo method in statistics, and is called Particle Filter (PF) in engineering correspondingly. The particle filtering idea is based on a Monte Carlo method, the particle set is used for representing the probability, the particle set can be used on any form of state space model, and the posterior probability distribution based on the observed quantity and the controlled quantity can be more accurately expressed. The core idea of particle filtering is to express the distribution of random-state particles by extracting them from the posterior probability, which is a Sequential Importance Sampling method (Sequential Importance Sampling). Particle filtering is a process of finding a group of random samples propagating in a state space to approximate a probability density function, and substituting an integral operation with a sample mean value to obtain a minimum variance estimate of a system state. Any form of probability density distribution can be approximated as the number of samples approaches infinity.
The backward smoothing process is to smooth the estimated particles again according to the sequence estimated by the forward smoothing and the corresponding particle weight after the forward smoothing process and the sequence from the backward to the forward to obtain a more real estimated sequence.
Thus, in summary, the Forward-Backward Smoothing (FBS) process is based on the following relation:
wherein, p (x) t |y 1:t ) And p (x) t+1 |y 1:t ) Respectively, the filter density and the forward prediction density at time t. According to the above formula, from p (x) T |y 1:T ) Initially, p (x) is repeatedly acquired t |y 1:T ) To p (x) t+1 |y 1:T ). Through the above repeated iterations, the edge smoothing distribution can be approximately described by the weighted particle cloud. The forward particle filter can be expressed as:the backward smooth distribution is represented as:the smoothing weight is repeatedly and iteratively calculated by the following formula:
wherein the content of the first and second substances,
the above is a description of the principle of the forward smoothing process and the backward smoothing process, and the forward smoothing process and the backward smoothing process are specifically described below.
1. A forward smoothing process:
(1) Subset of structuring granulesWherein
(2) Calculating an importance weight for each particle in the set of particlesWhereinAnd isSatisfy the requirements of
(3) Resampling the particle set when it meets a certain conditionTo obtain a new set of particles.
In the forward smoothing process, t is more than or equal to 1, and i takes a value of 1-Ns. And finally finding the particle distribution closest to the real sequence through the repeated iterative operation.
2. And (3) backward smoothing process:
as described above, the backward smoothing is to perform smoothing processing on the estimated particles again in the order from the backward to the forward according to the sequence estimated by the forward smoothing and the corresponding particle weights thereof on the basis of the forward smoothing to obtain a more realistic estimated sequence.
(4) FBS initialization
Setting p (x) 0 |x -1 )＝p(x 0 )；i＝1～NS。
(5) Calculating the probability density of the current symbol and the next symbol
(6) Calculating a normalization factorWhereinIs calculated in the forward smoothing process.
(7) Computing backward smoothing weightsIn particular, according to the formulaTo calculate the weight of each particle in the backward smoothing process.
(8) And selecting the closest particle as an estimated value of the current symbol according to a certain rule, for example, searching the particle with the largest weight as the estimated value.
(9) And (5) repeating the steps (5) to (8) until the estimated values of all the symbols are calculated, and ending the backward smoothing process. And the sequence formed by the estimation values of all the symbols is the final decoding sequence.
The above is the concept and principle of the forward and backward smooth decoding method and apparatus suitable for the OvXDM system, and the OvXDM system of the present application, and the present application is described in detail below.
In an embodiment, referring to fig. 7, the forward and backward smoothing decoding method for OvXDM system disclosed in the present application includes a forward smoothing step S100, a backward smoothing step S300, and an output step S500, where the OvXDM system may be an OvTDM system, an OvFDM system, an OvCDM system, an OvSDM system, or an OvHDM system, and as shown in fig. 8, is an equivalent convolutional coding model of the OvXDM system.
Forward smoothing step S100: and sequentially calculating the importance weight of each particle in the particle set corresponding to each symbol from the first symbol to the last symbol in an estimation sequence to obtain the particle importance weight in the forward smoothing process. Specifically, referring to fig. 9, the forward smoothing step S100 includes steps S101 to S109.
Step S101: an estimation sequence X is initialized. Since this is in the forward smoothing process, the estimation sequence X is not called a forward smoothed estimation sequence Xf, and its sequence length is the same as the sequence length to be decoded. For example, the OvXDM system receiving end is not allowed to receive a symbol sequence y with a length of N, where the symbol sequence y is a sequence to be decoded, the number of times of overlapping is K, and a rectangular wave is used as a multiplexing waveform; if the number of particles of each symbol is Ns, each particle corresponds to an importance weight value. The forward smoothing estimation sequence Xf is Ns × N, and the set Wf of importance weights corresponding to each particle is Ns × N.
Step S103: starting from the first symbol to the last symbol in the forward smoothed estimate sequence Xf, a set of particles is generated for the current symbol, where the number of particles in the set corresponding to each symbol is N, as described above s . For example, in OvXDM system, taking the binary data stream { +1, -1} as an example, there are only two possible values for each symbol: and +1 or-1, so that the particle set corresponding to each symbol comprises two particles, and the values are +1 and-1 respectively. There are many ways to generate particle sets for the current symbol as long as the distribution of the generated particle sets approaches the theoretical distribution.
Step S105: after generating the particle set for the current symbol, calculating the importance probability density of each particle of the current symbol and the sequence to be decoded, and calculating the importance weight of each particle. In one embodiment, the importance weight of each particle in the particle set corresponding to the current symbol is calculated according to the following formula:
wherein, wf i,j Is the importance weight of the particle, 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 probability density of importance of the particle. It can be seen that wf i,j In effect, the normalized importance weight of the particle.
In an embodiment, when i >1, that is, when the current symbol is the 2 nd symbol or a symbol after, the importance probability density of the particles in the particle set of the current symbol and the sequence to be decoded is calculated, and the importance probability density of the particles in the particle set of the previous symbol and the sequence to be decoded may be referred to.
It should be noted that, in the OvXDM system, since the received symbol sequence y is OvXDM-coded, the estimated symbol Xf also needs to be mapped to i,j OvXDM encoding was performed, and the importance probability density was calculated.
After the importance weight of each particle in the particle set corresponding to the current symbol is calculated, step S107 is performed.
Step S107: and judging whether the particle set corresponding to the current symbol meets a preset particle degradation condition or not, and if not, performing the next symbol, namely performing the next symbol from the step S103. If yes, go to step S109. In step S107, it is determined whether the degradation phenomenon of the particles in the particle set corresponding to the current symbol is significant. For example, the effective particle capacity of the corresponding particle set when the symbol corresponds to the particle set can be setBelow a certain threshold, then the particle set corresponding to the symbol is resampled. It should be noted that the above-mentioned condition of not satisfying the predetermined particle degradation condition isIf the particle set degradation phenomenon corresponding to the current symbol is not serious, the particle set degradation condition is met, and the particle set degradation phenomenon corresponding to the current symbol is serious, so that resampling is needed.
Step S109: the particle set of the current symbol is resampled. The resampling is to eliminate low-weight particles and concentrate on high-weight particles to suppress the degradation phenomenon. The resampling method has various methods, including importance resampling, residual resampling, layered resampling, optimized combined resampling and the like, and the basic idea is to copy particles with large weight, eliminate particles with small weight, and finally generate a new particle set through resampling, wherein a resampling schematic diagram is shown in fig. 10.
In the specific implementation of "from the first symbol to the last symbol in the forward smoothing estimation sequence Xf" mentioned in step S103, step S101 may be performed from the first symbol, and when the determination result in step S107 is not satisfied and after step S109, a determination is performed to determine whether the last symbol is reached, if so, the forward smoothing step S100 is completed, otherwise, the next symbol is processed, that is, the next symbol is started from step S103, and the steps are performed downward according to the flow shown in fig. 9.
Through the forward smoothing step S100, i.e., steps S101 to S109, each symbol in the estimation sequence X (forward smoothing estimation sequence Xf) has a corresponding particle set, and each particle in each particle set has an importance weight.
Backward smoothing step S300: the importance weight of each particle in the particle set corresponding to each symbol is sequentially calculated with reference to the importance weight of the particle obtained in the forward smoothing step S100 from the last symbol to the end of the first symbol in the estimation sequence X (forward smoothing estimation sequence Xf), and the importance weight of the particle in the backward smoothing process is obtained. In one embodiment, referring to fig. 11, the backward smoothing step S300 includes steps S301 to S305.
Step S301: according to the result calculated in the forward smoothing step S100, the particle with the largest importance weight in the particle set corresponding to the last symbol in the estimation sequence X (forward smoothing estimation sequence Xf) is used as the estimation value of the symbol, and the particle importance weight of each particle in the particle set corresponding to the last symbol in the estimation sequence X (forward smoothing estimation sequence Xf) in the forward smoothing process is used as the particle importance weight of each particle in the particle set corresponding to the last symbol in the estimation sequence X (forward smoothing estimation sequence Xf) in the backward smoothing process. In an embodiment, a backward smoothing sequence Xb may be additionally provided, which has a length N, and the set of particles corresponding to the last symbol in the estimation sequence X (forward smoothing estimation sequence Xf) with the largest importance weight may be represented as an estimation value of the last symbol in the backward smoothing sequence Xb as follows: xb (N) = Xf (max, N). Meanwhile, the importance weight of each particle in the particle set corresponding to the last symbol in the estimation sequence X (forward smoothed estimation sequence Xf) is given to the importance weight Wb of the backward smoothed sequence Xb, and can be represented as Wb (1 to Ns, N) = Wf (1 to Ns, N).
Step S303: calculating the probability density between the current symbol and the following symbol starting from the last but one symbol of the estimated sequence X to the end of the first symbolIt should be noted that, since the sequence estimated in the forward smoothing process is not encoded, the current time symbol and the next time symbol need to be encoded by K-fold OvXDM with respect to the multiplexed waveform first and then the probability density of the multiplexed waveform needs to be calculated. This case employs a multi-dimensional normal distribution (mvnpdf) probability density.
Step S305: and calculating the particle importance weight of the backward smoothing process of the current symbol according to the probability density calculated in the step S303, the particle importance weight of the backward smoothing process of the next symbol and the particle importance weight of the forward smoothing process of the current symbol. In one embodiment, the normalization factor may be calculated firstWhereinIs the result of the calculation by the forward smoothing step S100. In one embodiment, the importance weight of each particle in the particle set corresponding to the current symbol is calculated by the following formula:
ns represents the number of particles, i, j represents the particle index, and the value is 1-Ns; x is the number of t (k) The kth particle in the symbol representing time t;
wherein, ω is t The particle importance weight of the forward smoothing process for the current symbol,is the probability density, ω, between the current symbol and the following symbol t|T Is the particle importance weight of the backward smoothing process for the current symbol.
Of course, the "from the last symbol to the end of the first symbol in the estimation sequence X" mentioned in step S303 may also be similar to the "from the first symbol to the end of the last symbol in the forward smoothed estimation sequence Xf" mentioned in step S103, and is not described herein again.
Step S500: and taking the particle with the maximum particle importance weight in the backward smoothing process in the particle set corresponding to each symbol as an estimated value of the symbol, and outputting a final decoding sequence. In other words, the particle with the largest particle importance weight in the backward smoothing process in the particle set corresponding to each symbol in the sequence X is estimated as the estimated value of the symbol, and the final decoded sequence is output.
The above is the flow of the forward and backward smooth decoding method applicable to the OvXDM system disclosed in the present application, and accordingly, the present application also discloses an OvXDM system, which may be an OvTDM system, an OvFDM system, an OvCDM system, an OvSDM system or an OvHDM system, and which includes a forward and backward smooth decoding apparatus applicable to the OvXDM system. Referring to fig. 12, the forward and backward smoothing decoding apparatus for 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 sequentially calculate importance weights of particles in a particle set corresponding to each symbol from a first symbol to a last symbol in an estimation sequence, so as to obtain the importance weights of the particles in the forward smoothing process. In an embodiment, referring to fig. 13, the forward smoothing unit 100 includes an initialization unit 101, a particle set generation unit 103, an importance probability density calculation unit 105, an importance weight calculation unit 107, a judgment unit 109, and a resampling unit 111.
The initialization unit 101 is configured to initialize an estimation sequence X, where the length of the estimation sequence X is the same as the length of the sequence to be decoded. Since this is in the process of forward smoothing, the estimation sequence X is not called a forward smoothed estimation sequence Xf, and its sequence length is the same as that of the sequence to be decoded. For example, the OvXDM system receiving end is not allowed to receive a symbol sequence y with a length of N, where the symbol sequence y is a sequence to be decoded, the number of times of overlapping is K, and a rectangular wave is used as a multiplexing waveform; if the number of particles of each symbol is Ns, each particle corresponds to an importance weight value. The size of the forward smoothing estimation sequence Xf is Ns × N, and the size of the set Wf of importance weights corresponding to each particle is Ns × N.
The kernel set generating unit 103 is configured to generate a kernel set for a current symbol starting from a first symbol to an end of a last symbol in the estimated sequence X. As described above, the number of particles in the particle set corresponding to each symbol is N s . For example, in the OvXDM system, taking the binary data stream { +1, -1} as an example, the possible values of each symbol are only two: +1 or-1, so that the corresponding particle set of each symbol includes two particles, which take values of +1 and-1, respectively. There are many ways to generate particle sets for the current symbol, as long as the distribution of the generated particle sets approaches the theoretical distribution.
The importance probability density calculation unit 105 is used for calculating the importance probability density of each particle of the current symbol and the sequence to be decoded after the current symbol generates the particle setAnd (4) degree. In one embodiment, when i> 1, i.e. when the current symbol is the 2 nd symbol or the following symbol, the importance probability density calculation unit 105 calculates the importance probability density of the particles in the particle set of the current symbol and the sequence to be decoded, which can refer to the importance probability density of the particles in the particle set of the previous symbol and the sequence to be decoded i,j OvXDM encoding was performed, and the importance probability density was calculated.
The importance weight calculation unit 107 is configured to calculate an importance weight for each particle based on the importance probability density. In an embodiment, the importance weight calculating unit 107 calculates the importance weight of each particle in the particle set corresponding to the current symbol according to the following formula:
wherein, wfi i,j Is the importance weight of the particle, 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 probability density of importance of the particle. It can be seen that wf i,j In effect, the normalized importance weight of the particle.
The determining unit 109 is configured to determine whether the particle set corresponding to the current symbol satisfies a predetermined particle degradation condition, and if not, notify the particle set generating unit 103 to generate a particle subset for a next symbol. The determining unit 109 is used for determining whether the degradation phenomenon of the particles in the particle set corresponding to the current symbol is obvious. For example, the effective particle capacity of the corresponding particle set when the symbol is setBelow 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. Resampling section 111 performs resampling so as to eliminate low-weight particles and concentrate on high-weight particles, thereby suppressing degradation. The resampling method has various methods, including importance resampling, residual resampling, hierarchical resampling, optimized combined resampling, etc., and the basic idea is to copy particles with large weight, eliminate particles with small weight, and finally generate a new particle set through resampling, wherein the schematic diagram of resampling is shown in fig. 10. The resampling unit 111 resamples the grain of the current symbol, and notifies the grain set generating unit 103 to generate a grain set for the next symbol.
The backward smoothing unit 300 is configured to calculate the importance weights of the particles in the particle set corresponding to each symbol in sequence by referring to the importance weights of the particles obtained in the forward smoothing unit 100 from the last symbol to the end of the first symbol in the estimation sequence X (forward smoothed estimation sequence Xf), so as to obtain the importance weights of the particles in the backward smoothing process. In one embodiment, referring to fig. 14, 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, according to the result calculated by the forward smoothing unit 100, take the particle with the largest importance weight of the particle set corresponding to the last symbol in the estimation sequence X (forward smoothed estimation sequence Xf) as the estimation value of the symbol, and take the particle importance weight of each particle in the particle set corresponding to the last symbol in the estimation sequence X (forward smoothed estimation sequence Xf) in the forward smoothing process as the particle importance weight of each particle in the particle set corresponding to the last symbol in the estimation sequence in the backward smoothing process. In an embodiment, a backward smoothing sequence Xb may also be additionally provided, and the length of the backward smoothing sequence Xb is N, and the setting unit 301 uses the particle with the largest importance weight in the particle set corresponding to the last symbol in the estimation sequence X (forward smoothing estimation sequence Xf) as the estimation value of the last symbol in the backward smoothing sequence Xb, and may be represented as follows: xb (N) = Xf (max, N). Meanwhile, setting section 301 assigns an importance weight of each particle in the particle set corresponding to the last symbol in estimation sequence X (forward smoothed estimation sequence Xf) to importance weight Wb of backward smoothed sequence Xb, which can be expressed as Wb (1 to Ns, N) = Wf (1 to Ns, N).
A probability density calculation unit 303 for calculating the probability density between the current symbol and the next symbol from the last symbol to the end of the first symbol of the estimated sequenceIt should be noted that, since the sequence estimated in the forward smoothing process is not encoded, the current time symbol and the next time symbol need to be encoded by K-fold OvXDM with respect to the multiplexed waveform first and then the probability density of the current time symbol and the next time symbol is calculated. In this case, a multi-dimensional normal distribution (mvnpdf) probability density is adopted.
And an importance weight recalculating unit 305, configured to calculate the particle importance of the backward smoothing process of the current symbol according to the probability density calculated by the probability density calculating unit 303, the particle importance weight of the backward smoothing process of the next symbol, and the particle importance weight of the forward smoothing process of the current symbol after the probability density between the current symbol and the next symbol is calculated. In one embodiment, the importance weight recalculation unit 305 may calculate the normalization factor firstWhereinIs the result of the calculation by the forward smoothing unit 100. In an embodiment, the importance weight recalculating unit 305 calculates the importance weight of each particle 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 the value is 1-Ns; x is the number of t (k) Symbol representing time tThe kth particle of (1)
Wherein, ω is t The particle importance weight of the forward smoothing process for the current symbol,is the probability density, ω, between the current symbol and the following symbol t|T Is the particle importance weight of the backward smoothing process of the current symbol.
The output unit 500 is configured to output a final decoding sequence by taking the particle with the largest particle importance weight in the backward smoothing process after the particle corresponding to each symbol is collected as an estimation value of the symbol. In other words, the particle with the largest particle importance weight in the backward smoothing process in the particle set corresponding to each symbol in the sequence X is estimated as the estimated value of the symbol, and the final decoded sequence is output.
The above is the OvXDM system and the forward and backward smooth decoding device suitable for the OvXDM system disclosed in the present application.
In the decoding process, when particle subsets are generated for each symbol, for an unknown sequence, because the particle distribution of the unknown sequence is unknown in the initial stage, a group of samples can be randomly generated at first, the reliability of the particles is judged by calculating the importance weights of the particles and the observed values, the particle samples are resampled according to a certain criterion, the particles with small weights are eliminated, the particles with large weights are copied, iterative calculation is sequentially repeated, and finally, a reliable output value is obtained through calculation. The higher the number of iterations, the more accurate the result is. In addition, the degradation phenomenon of the particles is the biggest defect of the particle filter, the development of the particle filter is restricted, and one effective method for solving the problem of the degradation of the particles is to resample the particles. Particle filtering has unique advantages in parameter estimation and state filtering for solving nonlinear and non-Gaussian problems, so that the method has a large development space, and a plurality of mature different optimization methods can be introduced into a resampling process so as to extract typical 'particles' reflecting the probability characteristics of a system more quickly.
According to the method, the statistical thought is introduced into the decoding process, mutual information among particles is fully utilized through a forward smoothing process and a backward smoothing process, the decoding of the OvXDM system is achieved, the obtained decoding sequence is enabled to be closer to a true value, and meanwhile, along with the increase of the overlapping times, compared with a traditional decoding method, the decoding complexity is reduced, and the decoding efficiency and the system performance are improved.
The foregoing is a more detailed description of the present application in connection with specific embodiments thereof, and it is not intended that the present application be limited to the specific embodiments thereof. It will be apparent to those skilled in the art from this disclosure that many more simple derivations or substitutions can be made without departing from the inventive concepts herein.
Claims (12)
1. A forward and backward smooth decoding method suitable for an OvXDM system is characterized by comprising the following steps:
a forward smoothing step: sequentially calculating the importance weight of each particle in the particle set corresponding to each symbol from the first symbol to the last symbol in an estimation sequence to obtain the importance weight of the particles in the forward smoothing process;
and a backward smoothing step: sequentially calculating the importance weight of each particle in the particle set corresponding to each symbol by referring to the importance weight of the particles obtained in the forward smoothing step from the last symbol to the end of the first symbol in the estimation sequence to obtain the importance weight of the particles in the backward smoothing process;
an output step: and taking the particle with the maximum particle importance weight in the backward smoothing process in the particle set corresponding to each symbol as an estimated value of the symbol, and outputting a final decoding sequence.
2. The forward backward smoothing decoding method for OvXDM system as claimed in claim 1, wherein said forward smoothing step comprises:
initializing an estimation sequence, wherein the length of the estimation sequence is the same as the length of a sequence to be coded;
starting from the first symbol to the end of the last symbol in the estimated sequence: generating a set of particles for the current symbol; calculating the importance probability density of each particle of the current symbol and the sequence to be decoded, and calculating the importance weight of each particle; judging whether the particle set corresponding to the current symbol meets a preset particle degradation condition or not, and if so, resampling the particle set of the current symbol; if not, the next symbol is carried out.
3. The forward-backward smoothing decoding method for OvXDM system as claimed in claim 1 or 2, wherein in the forward-smoothing step, the importance weight of each particle in the particle set corresponding to the current symbol is calculated according to the following formula:
wherein, wf i,j Is the importance weight of the particle, 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 probability density of importance of the particle.
4. The forward backward smoothing decoding method for OvXDM system as claimed in claim 1, wherein said backward smoothing step comprises:
according to the result calculated in the forward smoothing step, taking the particle with the largest importance weight in the particle set corresponding to the last symbol in the estimation sequence as the estimation value of the symbol, and taking the particle importance weight of each particle in the particle set corresponding to the last symbol in the estimation sequence in the forward smoothing process as the particle importance weight of each particle in the particle set corresponding to the last symbol in the estimation sequence in the backward smoothing process;
starting from the second last symbol to the end of the first symbol of the estimation sequence: calculating a probability density between a current symbol and a subsequent symbol; and calculating to obtain the particle importance weight of the backward smoothing process of the current symbol according to the probability density, the particle importance weight of the backward smoothing process of the next symbol and the particle importance weight of the forward smoothing process of the current symbol.
5. The forward-backward smoothing decoding method for OvXDM system as defined in claim 1 or 4, wherein in the backward smoothing step, the importance weight of each particle in the particle set corresponding to each symbol is calculated according to the following formula:
ns is the number of particles in the particle set corresponding to the current symbol, i and j represent particle indexes, and the value is 1-Ns; x is a radical of a fluorine atom t A symbol indicating time t;
wherein, ω is t The particle importance weight of the forward smoothing process for the current symbol,is the probability density, ω, between the current symbol and the following symbol t|T Is the particle importance weight of the current symbol backward smoothing process.
6. The forward and backward smooth decoding method for OvXDM system as claimed in claim 1, wherein the OvXDM system is an OvTDM system, an OvFDM system, an OvCDM system, an OvSDM system or an OvHDM system.
7. A forward and backward smoothing decoding apparatus suitable for OvXDM system, comprising:
a forward smoothing unit, configured to calculate importance weights of particles in a particle set corresponding to each symbol in sequence from a first symbol to a last symbol in an estimation sequence, so as to obtain a particle importance weight in a forward smoothing process;
a backward smoothing unit, configured to calculate importance weights of particles in the particle set corresponding to each symbol in sequence with reference to the particle importance weights obtained in the forward smoothing unit from a last symbol to a first symbol in the estimation sequence, so as to obtain a particle importance weight in a backward smoothing process;
and the output unit is used for taking the particle with the maximum particle importance weight in the backward smoothing process in the particle set corresponding to each symbol as an estimated value of the symbol and outputting a final decoding sequence.
8. The forward backward smoothing decoding apparatus for an OvXDM system according to claim 7, wherein the forward smoothing unit comprises:
the device comprises an initialization unit, a decoding unit and a decoding unit, wherein the initialization unit is used for initializing an estimation sequence, and the length of the estimation sequence is the same as that of a sequence to be decoded;
a particle set generating unit, configured to generate a particle set for a current symbol from a first symbol to a last symbol in an estimation sequence;
the importance probability density calculation unit is used for calculating the importance probability density of each particle of the current symbol and the sequence to be decoded after the current symbol generates the particle subset;
an importance weight calculation unit for calculating an importance weight of each particle based on the importance probability density;
the judging unit is used for judging whether the particle set corresponding to the current symbol meets a preset particle degradation condition or not, and if not, the particle set generating unit is informed to generate a particle set for the next symbol;
and the resampling unit is used for resampling the particle set of the current symbol when the result of the judging unit is satisfied.
9. The forward-backward smoothing decoding apparatus for OvXDM system as claimed in claim 7 or 8, wherein the importance weight calculating unit calculates the importance weight according to the following formula in the forward smoothing unit:
wherein, w i,j Is the importance weight of the particle, 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 probability density of importance of the particle.
10. The forward backward smoothing decoding apparatus for an OvXDM system according to claim 7, wherein the backward smoothing unit comprises:
a setting unit, configured to use, according to a result calculated by the forward smoothing unit, a particle with a largest importance weight in the particle set corresponding to the last symbol in the estimation sequence as an estimation value of the symbol, and use a particle importance weight of a forward smoothing process of each particle in the particle set corresponding to the last symbol in the estimation sequence as a particle importance weight of a backward smoothing process of each particle in the particle set corresponding to the last symbol in the estimation sequence;
a probability density calculation unit for calculating a probability density between a current symbol and a subsequent symbol starting from a last-but-one symbol of the estimation sequence to an end of the first symbol;
and the importance weight recalculation unit is used for calculating the particle importance weight of the backward smoothing process of the current symbol according to the probability density, the particle importance weight of the backward smoothing process of the next symbol and the particle importance weight of the forward smoothing process of the current symbol after the probability density between the current symbol and the next symbol is calculated.
11. The forward-backward smoothing decoding apparatus for OvXDM system as claimed in claim 7 or 10, wherein the importance weight recalculating unit in the backward smoothing unit recalculates the importance weight of each particle in the particle set corresponding to the current symbol according to the following formula:
ns represents the number of particles in a particle set corresponding to the current symbol, i and j represent particle indexes, and the value is 1-Ns;
wherein, ω is t The particle importance weight of the forward smoothing process for the current symbol,is the probability density, ω, between the current symbol and the following symbol t|T Is the particle importance weight of the backward smoothing process of the current symbol.
12. An OvXDM system, comprising the forward and backward smooth decoding apparatus suitable for the OvXDM system as claimed in any one of the claims 7 to 11, wherein the OvXDM system is an OvTDM system, an OvFDM system, an OvCDM system, an OvSDM system or an OvHDM system.
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| CN201610886190.0A CN107919940A (en) | 2016-10-10 | 2016-10-10 | Suitable for the smooth interpretation method of forward-backward algorithm, device and the OvXDM systems of OvXDM systems |
| KR1020197013014A KR102239746B1 (en) | 2016-10-10 | 2017-09-26 | Anterior and posterior smoothing decoding method, apparatus and system |
| PCT/CN2017/103311 WO2018068630A1 (en) | 2016-10-10 | 2017-09-26 | Forward and backward smooth decoding method, device, and system |
| EP17861037.4A EP3525372A4 (en) | 2016-10-10 | 2017-09-26 | Forward and backward smooth decoding method, device, and system |
| JP2019518947A JP6857720B2 (en) | 2016-10-10 | 2017-09-26 | Front-back smooth decoding method, equipment and system |
| US16/379,622 US10707896B2 (en) | 2016-10-10 | 2019-04-09 | Forward and backward smooth decoding method, device, and system |
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