Detailed Description
The present application will be described in further detail below with reference to the accompanying drawings by way of specific embodiments.
In this application, ovXDM (Overlapped X Division Multiplexing) is used to refer to an overlap Multiplexing system, where X may represent time T, frequency F, code domain C, space S, or hybrid H, and accordingly, the OvXDM system is an OvTDM system, an OvFDM system, an OvCDM system, an OvSDM system, or an OvHDM system. The inventive concept of the present application resides in: the head and the tail of the data which are subjected to the overlapping multiplexing coding are overlapped at a sending end or a receiving end, so that all data symbols are fully overlapped before the data are decoded according to a certain decoding algorithm, thereby solving the problem of higher error rate of the last symbols in the traditional technology and greatly reducing the error rate of a system on one hand, and not requiring the data to have large length on the other hand, and obtaining a stable decoding path even if the data has short length, thereby reducing the decoding processing time delay and improving the processing time precision and the transmission speed of the system. The present application discloses an OvXDM system, which comprises the complementary encoding apparatus disclosed in the following embodiment one, or comprises the complementary decoding apparatus disclosed in the following embodiment two.
Example one
Referring to fig. 2, the present embodiment discloses a complementary coding method suitable for OvXDM system, which includes steps S01 to S09.
And S01, generating an initial envelope waveform in a first domain according to the design parameters.
And S03, shifting the initial envelope waveform on a first domain according to the overlapping multiplexing times at preset intervals to obtain shifted envelope waveforms of all fixed intervals.
Step S05, multiplying the digital signals in the input sequence by the corresponding displacement envelope waveforms to obtain modulation envelope waveforms;
and S07, overlapping the modulation envelope waveforms on a first domain to obtain a complex modulation envelope waveform on the first domain, wherein the complex modulation envelope waveform comprises a first section which is not fully overlapped, a main section which is fully overlapped and a tail section which is not fully overlapped.
And S09, superposing the first segment of the complex modulation envelope waveform to the tail segment, or superposing the tail segment to the first segment to generate a complementary complex modulation envelope waveform, and then carrying out subsequent processing.
In one embodiment, the OvXDM system is an OvFDM system, and accordingly, the first domain is a frequency domain. In step S09, the generated complementary complex modulation envelope waveform is subsequently processed, in one embodiment, by transforming it into a time domain complementary complex modulation envelope waveform by, for example, inverse fourier transform, for transmission.
In one embodiment, the OvXDM system is an OvTDM system, and accordingly, the first domain is a time domain at this time. Subsequent processing of the generated complementary complex modulation envelope waveform, in one embodiment, transmits it, at step S09.
Correspondingly, referring to fig. 3, the present embodiment further provides a complementary encoding apparatus suitable for the OvXDM system, which includes a waveform generating module 01, a shifting module 03, a multiplying module 05, a superimposing module 07, and a complementary module 09, and in an embodiment, may further include a subsequent processing module 11.
The waveform generating module 01 is configured to generate an initial envelope waveform in a first domain according to the design parameters.
The shifting module 03 is configured to shift the initial envelope waveform in the first domain at predetermined intervals according to the number of overlapping multiplexing to obtain shifted envelope waveforms at fixed intervals.
The multiplication module 05 is configured to multiply the digital signal in the input sequence by the respective corresponding shifted envelope waveform to obtain each modulated envelope waveform.
The superposition module 07 is configured to superpose the modulation envelope waveforms in a first domain to obtain a complex modulation envelope waveform in the first domain, where the complex modulation envelope waveform includes a first segment that is not sufficiently superposed, a main segment that is sufficiently superposed, and a last segment that is not sufficiently superposed.
The complementary module 09 is configured to superimpose the first segment of the complex modulation envelope waveform onto the last segment, or superimpose the last segment onto the first segment, so as to generate a complementary complex modulation envelope waveform;
the post-processing module 11 is configured to perform post-processing on the complementary complex modulation envelope waveform.
In one embodiment, when the OvXDM system is an OvFDM system, accordingly, the first domain is a frequency domain. The subsequent processing of the generated complementary complex modulation envelope waveform by the subsequent processing module 11 may be, in one embodiment, transforming it into a time domain complementary complex modulation envelope waveform by, for example, inverse fourier transform, for transmission.
In one embodiment, the OvXDM system is an OvTDM system, and accordingly, the first domain is a time domain at this time. Subsequent processing of the generated complementary complex modulation envelope waveform by the subsequent processing module 11, in one embodiment, transmits it.
Example two
As shown in fig. 4, the present embodiment proposes a complementary decoding method suitable for OvXDM system, which includes steps S31 to S35.
Step S31, receiving a signal and processing the received signal to obtain a digital signal in a first domain, where the digital signal in the first domain includes a first segment that is not sufficiently superimposed, a main segment that is sufficiently superimposed, and a last segment that is not sufficiently superimposed.
In one embodiment, the OvXDM system is an OvFDM system, and accordingly, the first domain is a frequency domain. In one embodiment, specifically, in step S31, symbol synchronization is first formed in the time domain for the received signal; then, the signal of each symbol time interval is subjected to digital processing, including sampling and quantization, and is changed into a received digital signal sequence; then, carrying out Fourier transform on the received digital signal sequence of each time symbol interval to form an actual received signal frequency spectrum of each time symbol interval; and segmenting the actual received signal spectrum of each time symbol interval in a frequency domain at subcarrier spectrum intervals to obtain the actual received signal segmented spectrum.
In one embodiment, the OvXDM system is an OvTDM system, and accordingly, the first domain is a time domain. In an embodiment, specifically, in step S31, the received signal is synchronized first, including carrier synchronization, frame synchronization, symbol time synchronization, and the like; then according to the sampling theorem, the received signal in each frame is processed digitally; and cutting the received waveform according to the waveform sending time interval.
And step S33, superposing the head segment of the digital signal in the first domain to the tail segment, or superposing the tail segment to the head segment, so as to generate a complementary digital signal.
And S35, decoding the digital signal according to a certain decoding algorithm. The decoding algorithm may employ existing or future-occurrence decoding algorithms, for example, the decoding algorithm may be a viterbi decoding algorithm, an iterative decoding algorithm, or the like.
In one embodiment, the OvXDM system is an OvFDM system, and accordingly, the first domain is a frequency domain.
In one embodiment, the OvXDM system is an OvTDM system, and accordingly, the first domain is a time domain.
In one embodiment, the OvXDM system is an OvCDM system, and accordingly, the first domain is a code division domain.
In an embodiment, the OvXDM system is an OvSDM system and accordingly, the first domain is a spatial domain.
In one embodiment, the OvXDM system is an OvHDM system, and accordingly, the first domain is a hybrid domain
Accordingly, as shown in fig. 5, the present embodiment further proposes a complementary decoding apparatus suitable for the OvXDM system, which includes a receiving module 31, a complementary module 33, and a decoding module 35.
The receiving module 31 is configured to receive a signal and process the received signal to obtain a digital signal in a first domain, where the digital signal in the first domain includes a first segment that is not sufficiently superimposed, a main segment that is sufficiently superimposed, and a last segment that is not sufficiently superimposed.
The complementary module 33 is configured to superimpose the first segment of the digital signal in the first domain onto the last segment, or the last segment onto the first segment, to generate a complementary digital signal.
The decoding module 35 is configured to decode the digital signal according to a certain decoding algorithm. The decoding algorithm may be an existing or future-appearing decoding algorithm, for example, the decoding algorithm may be a viterbi decoding algorithm, an iterative decoding algorithm, or the like.
The above embodiments are explained and illustrated below in two practical examples.
The first example is not illustrated with an OvFDM system.
The existing OvFDM system is in a parallelogram shape for overlapping data, a first section and a tail section are respectively arranged in front of and behind the coded data, and the shapes of the sections are in an upper triangle shape and a lower triangle shape and are just complementary. The 'tail segment' of the encoded data is moved to the position of the 'head segment', or the 'head segment' is moved to the position of the 'tail segment', namely, the lower triangle and the upper triangle are complementarily superposed to form a rectangular shape, and the superposition can be called as a complementary OvFDM system. The complemented data is in a rectangular shape, and each data is overlapped for K times, so that the problems in the prior art in the background technology are solved.
The encoding process is shown in fig. 6:
(1) An initial envelope waveform H (f) within the spectrum is generated in accordance with the design parameters.
(2) And (3) shifting the initial envelope waveform H (f) designed in the step (1) by a specific carrier spectrum interval delta B to form other subcarrier envelope waveforms H (f-i multiplied by delta B) with respective spectrum intervals delta B. The spectrum interval is a subcarrier spectrum interval delta B, wherein the subcarrier spectrum interval delta B = B/K, B is the bandwidth of the initial envelope waveform, and K is the number of overlapping multiplexes. In an embodiment, the subcarrier spectral spacing Δ B is greater than or equal to the inverse of the system samples.
(3) Symbol X to be transmitted i Respectively multiplying the envelope waveforms H (f-i multiplied by delta B) of the corresponding subcarriers generated in the step (2) to obtain modulation envelope waveforms X modulated by the subcarriers i H(f-i×ΔB)。
(4) Subjecting each modulation envelope waveform formed in (3) to X
i H (f-i × Δ B) superposition, forming a complex modulation envelope waveform, the complex modulation envelope waveform superposition process can be expressed as:
(5) And (3) performing inverse discrete fourier transform on the complex modulation envelope waveform generated in the step (4) to finally form a complex modulation envelope waveform of a time domain, wherein a transmission signal can be expressed as: signal (t) TX =ifft(S(f))。
The above is the encoding process of the conventional OvFDM system. (4) The superposition process in (2) is reflected on the encoding of the data, as shown in fig. 1. For data with a symbol length of N, the length of the data is changed into N + K-1 after modulation and coding, and the data has a first section with the length of K-1 and not subjected to K-time superposition and a tail section with the length of K-1 and not subjected to K-time superposition.
The decoding process is shown in fig. 7:
the transmitting end transmits the coded and modulated signal through the antenna, the signal is transmitted in a wireless channel, the receiving end performs matched filtering on the received signal, and the received signal is a time domain signalTherefore, it is necessary to perform fourier transform on the time domain signal to convert it into a frequency domain signal, and then perform decoding processing on the signal, where the inverse fourier transform and the fourier transform in the OvFDM system both involve setting the number of sampling points, and the number of sampling points should be kept consistent and should be 2 n . Then the signals are respectively sampled and decoded, and finally the output bit stream is judged. Specifically, the method comprises the following steps:
(6) Symbol synchronization is formed in the time domain for the received signal.
(7) The signal for each symbol time interval is digitally processed, including sampling and quantization, into a sequence of received digital signals.
(8) The received digital signal sequence for each time symbol interval is fourier transformed to form an actual received signal spectrum for each time symbol interval. The expression is as follows: signal (f) RX =fft(s(t))。
(9) And segmenting the actual received signal spectrum of each time symbol interval in a frequency domain by a subcarrier spectrum interval delta B to obtain the actual received signal segmented spectrum.
(10) And decoding the cut frequency spectrum waveform according to a certain decoding algorithm.
The above is the encoding process of the conventional OvFDM system, and in the decoding process, the data in the tail segment is not decoded, and because the length of the useful information stream is N, only the first N data in the data with the length of N + K-1 are decoded.
The inventive concept of the present application is to shift the first segment of the encoded data with the length of N + K-1 to the last segment, and superimpose the first segment with the original last segment to form a new last segment, so as to form a new complementary encoded data with the data length of N, and certainly, shift the last segment to the first segment to superimpose, as shown in fig. 8. The moving process can be put into the programming process or the decoding process. In one embodiment, if the move process is put into the programming process, the first/last segment of data may be moved to the last/first segment for superposition before (5). In one embodiment, if the moving process is put into the decoding process, the first segment/last segment of the data can be moved to the last segment/first segment for superposition before (10).
(10) The decoding algorithm in (1) includes various algorithms, such as a viterbi decoding algorithm and an iterative decoding algorithm. The following description will not be made by taking the viterbi decoding method as an example.
After the application, when the decoding is carried out to (10), the sequence y with the length of N is used i (i = 1-N), each symbol is the result of the superposition of K symbols, i.e. the decoding of a complementary data sequence. .
Firstly, generating a possible state after K paths of symbols are superposed, namely an ideal symbol S theory (j),j=1~2 K In total 2 K And (4) seed preparation.
The K-way symbol is represented as:
the corresponding representation form after superposition is
If +1 is used to represent the superposed output level, K +1 symbol levels are included in total, namely +/-K, +/- (K-2) and +/-2
k ) K =1 to K/2, and is denoted as Y
theory (index),index=1~
K+1。
For example, when K =3, the symbols are superimposed to have 8 states in total, which are:
four kinds of output symbol levels of + -3, + -1, namely Y
theory (1)=-3,Y
theory (2)=-1,Y
theory (3)=1,Y
theory (4)=3。
And secondly, calculating the measure distance of the current symbol.
The metric distance represents the distance between two signals and is defined as
When p =2, i.e. the euclidean distance, which is the true distance between two signals, the distance between the actual signal and the ideal signal can be truly reflected, which is defined as the distance between the actual signal and the ideal signal
In this embodiment, the euclidean distance is used as an example.
Using the current symbol y
i (i =1 to N) and 2 produced
K Ideal symbol S
theory (j) Sequentially calculating Euclidean distance to obtain 2
k The euclidean distance. Is marked as
And thirdly, calculating the accumulated distance of the current symbol.
When comparing the euclidean distances, if only comparing the euclidean distances between the current symbol and the theoretical symbol, the optimal path may have a deviation with the increase of the decoding depth, resulting in a decrease in the success rate of the final decoding.
Since the symbol superposition process is that K symbols are mutually overlapped, the correlation between the front and the back of the symbols is large, the sum of the current Euclidean distance and the previously accumulated Euclidean distance is adopted for judgment, so that the optimal path can be judged more accurately along with the increase of the decoding depth, and the decoding success rate is improved.
The cumulative euclidean distance expression is noted as:
wherein D i,j Representing the Euclidean distance after the accumulation of the current symbol, wherein only the current distance d is calculated because the first symbol has no accumulated distance current . i denotes the index of the current symbol in the whole received symbol sequence, j denotes the index of the accumulated symbol, totaling 2 K And (4) seed selection.
D prev_i-1 Representing the current node y i The sum of the Euclidean distances after the previous screening is 2 in total K-1 I.e. 2 K-1 Seed D prev_i-1 Is from 2 K Seed D i-1,j And (4) screening. Due to 2 K The middle state is different only in the first path of symbols and finally only keeps 2 K-1 Seed Euclidean distance and 2 K-1 Strip optimal path, hence D prev_i-1 In total 2 K-1 Euclidean distance, since the first symbol does not accumulate distance, there is no D prev_i-1 。
d current Always being the euclidean distance of the current symbol from the theoretical symbol.
Fourth, select the best path
After the treatment of the third step, 2 is obtained K Accumulation Euclidean distance D i,j And path j ,j=1~2 K Due to this 2 K The seed path can be roughly divided into 2 sections, i.e., whether the previous state was input +1 or input-1. Therefore we will 2 K Each path is divided into two parts, each part comprising 2 K-1 And the strip path divides the corresponding accumulative Euclidean distance into two parts.
Comparing the accumulated Euclidean distances of each row corresponding to each part pairwise to obtain the minimum, namely comparing the first row of the first part with the first row of the second part, comparing the second row of the first part with the second row of the second part, and so on to obtain the minimum Euclidean distance of each row, and recording the accumulated Euclidean distance D corresponding to the row i,j And labeled as the new filtered cumulative Euclidean distance D prev_i Which is to calculate the cumulative Euclidean distance D of the i +1 node i+ 1 ,j The accumulated Euclidean distances of the previous i nodes are used, meanwhile, a symbol path corresponding to the accumulated Euclidean distances is reserved, the current symbol is input with +1 or-1 according to the transfer path, and the depth of the corresponding path is added with 1.
After the treatment of the steps, the compound is obtained by 2 K-1 Euclidean distance D prev_i And corresponding 2 K-1 A symbol path.
Fifth, last symbol processing
According to the first to fourth stepsProcessing the rest symbols, and when the last symbol y is processed N Then, through screening, 2 is obtained K-1 Euclidean distance d j And corresponding 2 K-1 A path of symbols, where the depth of the path is N. To 2 K-1 And sequencing the Euclidean distances from small to large, finding out the Euclidean distance with the minimum accumulated distance to obtain the corresponding index, and taking out the decoding symbol sequence of the index corresponding to the path according to the index to obtain the final decoding result.
Noting the decoded sequence as S decode (i) I =1 to N. Comparison decoding sequence S decode (i) And input sequence x i And whether the decoding result is correct can be checked, and the error rate of the system is calculated.
The decoding process refers to the code tree diagram of the overlapping time division input-output relationship with K =3 in fig. 9, the node state transition diagram in fig. 10, and the trellis diagram of the ovfdm system with K =3 in fig. 11.
Generally, because the length of data to be decoded is long, and the accumulated distance is larger and larger as the decoding depth is deeper, the system consumes system resources if the system decodes all the data and then outputs the decoded data, and therefore, a better processing method is adopted for storing the storage capacity and the distance of the path. Generally selecting a path memory length of 4K-5K, and if the path memory is full and the decoding decision output is not forced to be output, outputting initial nodes with the same path first; the accumulated distance is larger and larger as the decoding depth is deeper, the accumulated distance can be stored as a relative distance, that is, a reference distance is defined, the value of the reference distance depends on different systems, and the distance storage records the relative value of the second distance of each path relative to the reference distance, and the comparison is performed through the relative distance when the optimal path is screened.
For example, in this case, we use square waves as the multiplexing waveform to illustrate the encoding and decoding process. Setting the number of overlapping multiplexing times K =3, the length of an input sequence N =9, and a symbol sequence x i With { -1, +1, -1, +1, +1, +1, -1, +1, -1}, the output sequence length becomes 11 (N + K-1) after being coded by the OvFDM system, and the output symbol sequence s' (t) = { -1,0, -1, +1, +1, +3, +1, +1, -1,0, -1}, the symbol superposition process of this case is shown in fig. 12, and it can be seen that the first two and the last two symbols in the superposed symbol sequence are not superposed in 3 ways, so we add these two signals complementarily and put them in front of the middle symbol to form a complementary ovdm mode, and the output symbol sequence after complementary superposition is s (t) = { -1, -1, -1, +1, +1, +3, +1, +1, -1}. The coded signal is transmitted through an actual channel, and the symbol sequence received at the receiving end has deviation, which is marked as y i I =1 to 9. The sequence of symbols received in this case is:
y i ={-0.9155,-1.4137,0.0825,0.5699,0.5244,3.7270,0.2254,1.9963,-2.1995};
all symbols are decoded one by one according to the viterbi decoding method described above, and the symbol detection path in the decoding process is shown in fig. 13. After decoding of all symbols is completed, four optimal paths and corresponding euclidean distances thereof are obtained as follows:
path 1 :{-1,1,-1,1,1,1,-1,1,1};
path 2 :{-1,1,-1,1,1,1,-1,1,-1};
path 3 :{-1,1,-1,1,1,1,-1,-1,1};
path 4 :{-1,1,-1,1,1,1,-1,-1,-1};
the corresponding Euclidean distance is d in sequence 1 =8.1839,d 2 =6.1839,d 3 =8.1839,d 4 =7.7848, and these four distances are compared in magnitude to obtain d 2 Has the minimum Euclidean distance, the corresponding path 2 Is selected as the output symbol sequence. I.e. the sequence of symbols S we consider to output decode =1,1, -1,1,1,1, -1,1, -1}, and the input symbol sequence x i { -1, +1, -1, +1, +1, +1, -1, +1, -1}, comparative S decode And x i If the two sequences are identical, the decoding result is correct.
The second example is not illustrated with an OvTDM system.
The existing OvTDM system is in a parallelogram for overlapping data, a section of 'first section' and a section of 'last section' are respectively arranged in front of and behind the encoded data, and the shapes of the sections are in an upper triangle shape and a lower triangle shape and are just complementary. We move the "end segment" of the encoded data to the position of the "first segment", or move the "first segment" to the position of the "end segment", i.e. the lower triangle and the upper triangle are complementarily superimposed to form a rectangle, which can be called complementary OvTDM system. The complemented data is in a rectangular shape, and each data is overlapped for K times, so that the problems in the prior art in the background technology are solved.
The encoding process is shown in fig. 14:
(1) And generating an initial envelope waveform h (t) in the time domain according to the design parameters.
(2) And (3) after the envelope waveform h (T) designed in the step (1) is subjected to specific time shift, forming offset envelope waveforms h (T-i multiplied by delta T) of the transmission signals at other moments.
(3) The symbol x to be transmitted i Multiplying the generated offset envelope waveform h (T-i multiplied by delta T) at the corresponding moment in the step (2) to obtain a modulation envelope waveform x at each moment i h(t-i×ΔT)。
(4) Forming a modulation envelope waveform x of each time instant in (3)
i h (T-i x delta T) are superposed to form a complex modulation envelope waveform for transmission. The complex modulation envelope waveform may be expressed as follows:
the above is the encoding process of the conventional OvTDM system. (4) The superposition process in (2) is reflected on the encoding of the data, as shown in fig. 1. For data with a symbol length of N, the length of the data is changed into N + K-1 after modulation and coding, and the data has a first section with the length of K-1 and not subjected to K-time superposition and a tail section with the length of K-1 and not subjected to K-time superposition. The data in fig. 1 are arranged into a parallelogram, the left end triangle is the 'first segment data', the right end triangle is the 'last segment data', and the middle is the fully overlapped data.
The decoding process is shown in fig. 15:
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. Specifically, the method comprises the following steps:
(5) Firstly, the received signals are synchronized, including carrier synchronization, frame synchronization, symbol time synchronization, etc.
(6) The received signal within 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.
The above is the encoding process of the conventional OvTDM system, and in the decoding process, the data in the tail segment is not decoded, and because the length of the useful information stream is N, only the first N data in the data with the length of N + K-1 are decoded.
The inventive concept of the present application is to shift the first segment of the encoded data with the length of N + K-1 to the last segment, and superimpose the first segment with the original last segment to form a new last segment, so as to form a new complementary encoded data with the data length of N, and certainly, the last segment may be shifted to the first segment to superimpose, as shown in fig. 16. The moving process can be put into the programming process or the decoding process. In one embodiment, if the move process is put into the programming process, the first segment/end segment of the data may be moved to the end segment/first segment for superposition in (4). In one embodiment, if the above-mentioned moving process is put into the decoding process, the first segment/last segment of the data can be moved to the last segment/first segment for superposition before (8). A
(8) The decoding algorithm in (1) includes various algorithms, such as a viterbi decoding algorithm and an iterative decoding algorithm. The following description will not be made by taking the viterbi decoding method as an example.
After the present application, when the decoding to (8) is performed, the sequence y with the length of N is used i (i = 1-N), each symbol is the result of the superposition of K symbols, i.e. the decoding of a complementary data sequence.
Firstly, generating possible states after superposition of K paths of symbolsI.e. the ideal symbol S theory (j),j=1~2 K In total 2 K And (4) seed preparation.
The K-way symbol is represented as:
the corresponding representation form after superposition is
If +1 is used to represent the superposed output level, K +1 symbol levels are included in total, namely +/-K, +/- (K-2) and +/-2
k ) K =1 to K/2, and is denoted as Y
theory (index),index=1~
K+1。
For example, when K =3, the symbols are superimposed to have 8 states in total, which are:
the corresponding output symbol levels are four, namely Y, of +/-3 and +/-1
theory (1)=-3,Y
theory (2)=-1,Y
theory (3)=1,Y
theory (4)=3。
And secondly, calculating the measure distance of the current symbol.
The metric distance represents the distance between two signals and is defined as
When p =2, i.e. the euclidean distance, which is the true distance between two signals, the distance between the actual signal and the ideal signal can be truly reflected, which is defined as the distance between the actual signal and the ideal signal
In this embodiment, the euclidean distance is used as an example.
Using the current symbol y
i (i =1 to N) and(1) 2 of (2)
K Ideal symbol S
theory (j) Sequentially calculating Euclidean distances to obtain 2
k The euclidean distance. Is marked as
And thirdly, calculating the accumulated distance of the current symbol.
When comparing the euclidean distances, if only comparing the euclidean distances between the current symbol and the theoretical symbol, the optimal path may have a deviation with the increase of the decoding depth, resulting in a decrease in the success rate of the final decoding.
Since the symbol superposition process is that K symbols are mutually overlapped and the correlation between the front symbol and the rear symbol is large, the sum of the current Euclidean distance and the previously accumulated Euclidean distance is adopted for judgment, so that the optimal path can be judged more accurately along with the increase of the decoding depth, and the decoding success rate is improved.
The cumulative euclidean distance expression is noted as:
wherein D i,j Representing the Euclidean distance after the accumulation of the current symbol, wherein only the current distance d is calculated because the first symbol has no accumulated distance current . i denotes the index of the current symbol in the whole received symbol sequence, j denotes the index of the accumulated symbol, totaling 2 K And (4) seed preparation.
D prev_i-1 Representing the current node y i The sum of the Euclidean distances after the previous screening is 2 in total K-1 I.e. 2 K-1 Seed D prev_i-1 Is from 2 K Seed D i-1,j And (4) screening. Due to 2 K The middle state is different only in the first path of symbols and finally only keeps 2 K-1 Seed Euclidean distance and 2 K-1 Strip optimal path, hence D prev_i-1 In total 2 K-1 Euclidean distance, since the first symbol does not accumulate distance, there is no D prev_i-1 。d current Always being the euclidean distance of the current symbol from the theoretical symbol.
Fourthly, selecting the best path.
After the treatment of the third step, 2 is obtained K Accumulation Euclidean distance D i,j And path j ,j=1~2 K Due to this 2 K The seed path can be divided into 2 parts, i.e. whether the previous state is input +1 or input-1. Therefore we will 2 K Each path is divided into two parts, each part comprising 2 K-1 And the strip path divides the corresponding accumulative Euclidean distance into two parts.
Comparing the accumulated Euclidean distances of each row corresponding to each part pairwise to obtain the minimum, namely comparing the first row of the first part with the first row of the second part, comparing the second row of the first part with the second row of the second part, and so on to obtain the minimum Euclidean distance of each row, and recording the accumulated Euclidean distance D corresponding to the row i,j And labeled as the new filtered cumulative Euclidean distance D prev_i Which is to calculate the cumulative Euclidean distance D of the i +1 node i+1,j The accumulated Euclidean distances of the previous i nodes are used, meanwhile, a symbol path corresponding to the accumulated Euclidean distances is reserved, the current symbol is input with +1 or-1 according to the transfer path, and the depth of the corresponding path is added with 1.
After the treatment of the steps, the compound is obtained by 2 K-1 Euclidean distance D prev_i And corresponding 2 K-1 A symbol path.
Fifth, last symbol processing.
Processing the rest symbols according to the first to the fourth steps in sequence, and when the last symbol y is processed N Then, through screening, 2 is obtained K-1 Euclidean distance d j And corresponding 2 K-1 A path of symbols, where the depth of the path is N. To 2 K-1 And sequencing the Euclidean distances from small to large, finding out the Euclidean distance with the minimum accumulated distance to obtain the corresponding index, and taking out the decoding symbol sequence of the index corresponding to the path according to the index to obtain the final decoding result.
Noting the decoded sequence as S decode (i) I =1 to N. Comparison decoding sequence S decode (i) And input sequence x i And whether the decoding result is correct can be checked, and the error rate of the system is calculated.
The decoding process refers to the code tree diagram of fig. 17 with K =3 overlapping time division input-output relationship, the node state transition diagram of fig. 18, and the K =3, ovtdm trellis (trellis) diagram of fig. 19.
Generally, because the length of data to be decoded is long, and the accumulated distance is larger and larger as the decoding depth is deeper, the system consumes system resources if the system decodes all the data and then outputs the decoded data, and therefore, a better processing method is adopted for storing the storage capacity and the distance of the path. Generally selecting a path memory length of 4K-5K, and if the path memory is full and the decoding decision output is not forced to be output, outputting initial nodes with the same path first; the accumulated distance is larger and larger as the decoding depth is deeper, the accumulated distance can be stored as a relative distance, that is, a reference distance is defined, the value of the reference distance depends on different systems, and the distance storage records the relative value of the second distance of each path relative to the reference distance, and the comparison is performed through the relative distance when the screening of the optimal path is performed.
For example, in this case, we use square waves as the multiplexing waveform to illustrate the encoding and decoding process. Setting the number of overlapping multiplexing times K =3, the length of an input sequence N =9, and a symbol sequence x i The length of an output sequence becomes 11 (N + K-1) after being coded by an OvTDM series, an output symbol sequence s' (t) = -1,0, -1, +1, +1, +3, +1, +1, -1,0, -1} in this case, the symbol superposition process of this case is as shown in fig. 20, and it can be seen that the first two and the last two symbols in the superposed symbol sequence are not superposed by 3 paths, so that the two signals are complementarily superposed and placed in front of the middle symbol to form a complementary OvTDM mode, and the output symbol sequence after complementary superposition is s (t) = { -1, -1, -1, +1, +3, +1, +1, -1}. The coded signal is transmitted through an actual channel, and the symbol sequence received at the receiving end has deviation, which is marked as y i I =1 to 9. The sequence of symbols received in this case is:
y i ={-0.9155,-1.4137,0.0825,0.5699,0.5244,3.7270,0.2254,1.9963,-2.1995};
all the symbols are decoded one by one according to the above-mentioned viterbi decoding method, and the symbol detection path in the decoding process is shown in fig. 21. After decoding of all symbols is completed, four optimal paths and corresponding euclidean distances thereof are obtained as follows:
path 1 :{-1,1,-1,1,1,1,-1,1,1};
path 2 :{-1,1,-1,1,1,1,-1,1,-1};
path 3 :{-1,1,-1,1,1,1,-1,-1,1};
path 4 :{-1,1,-1,1,1,1,-1,-1,-1};
the corresponding Euclidean distances are d in sequence 1 =8.1839,d 2 =6.1839,d 3 =8.1839,d 4 =7.7848, and these four distances are compared in magnitude to obtain d 2 Has the minimum Euclidean distance, the corresponding path 2 Is selected as the output symbol sequence. I.e. the sequence of symbols S we consider to output decode =1,1, -1,1,1,1, -1,1, -1}, and the input symbol sequence x i =1, +1, -1, +1, +1, +1, -1, +1, -1}, comparative S decode And x i If the two sequences are identical, the decoding result is correct.
The complementary coding method and device, and the complementary decoding method and device can achieve higher decoding success rate under the condition of the same signal to noise ratio, can be widely applied to actual mobile communication systems such as TD-LTE and TD-SCDMA and the like besides the systems such as OvTDM and OvFDM, and can also be widely applied to any wireless communication systems such as satellite communication, microwave line-of-sight communication, scattering communication, atmospheric optical communication, infrared communication and aquatic communication. The method can be applied to large-capacity wireless transmission and also can be applied to a small-capacity light radio system.
The foregoing is a more detailed description of the present application in connection with specific embodiments thereof, and it is not intended to limit the present application to the particular forms disclosed. 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.