CN109217933B - Carrier-free amplitude and phase modulation method and demodulation method based on probability forming - Google Patents
Carrier-free amplitude and phase modulation method and demodulation method based on probability forming Download PDFInfo
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Abstract
The invention discloses a carrier-free amplitude phase modulation and demodulation method based on probability forming, which comprises a probability forming constellation mapping step, a demapping step, a carrier-free amplitude phase modulation step and a demodulation step, wherein the probability forming constellation mapping step comprises three substeps of determining a non-uniform probability forming constellation mapping table, carrying out non-uniform distribution bit interleaving and carrying out constellation mapping, and the probability forming constellation demapping step comprises three substeps of determining the non-uniform probability forming constellation mapping table, carrying out constellation demapping and non-uniform distribution bit deinterleaving. The invention can reduce the emission probability of the constellation points with higher energy, improve the emission probability of the constellation points with lower energy, reduce the average emission power of the system through the forming gain caused by probability forming, and realize the improvement of the transmission capacity of the short-distance communication system. Meanwhile, the bits in the bit stream are rearranged, so that errors are randomized, the burst error influence in a channel is reduced, and the performance improvement in the aspect of the error rate is realized.
Description
Technical Field
The invention relates to a carrier-free amplitude and phase modulation method and a carrier-free amplitude and phase demodulation method, in particular to a carrier-free amplitude and phase modulation method and a carrier-free amplitude and phase demodulation method based on probability forming.
Background
In recent years, the explosive development of the information industry has led to an explosive increase in the demand for data communication bandwidth, and the global data volume in 2014 is 6 × 1021Bits, almost equivalent to the data size of 10000 billion 720P movies, which number would reach 4X 10 in 202025. While these large amounts of data are transmitted over long distances, it is more necessary to store and process large amounts of data in terminals, including data centers and even personal computers. With the development of cloud computing, big data and the internet of things, more data are mainly stored in a data center. Data calling, online playing, downloading, operation, program running and the like need to be exchanged in a large amount in a data center, short-distance broadband interconnection is the main bottleneck of the data center, optical interconnection is the only option for solving the bottleneck, and electrical interconnection is completely replaced by the optical interconnection in a newly-built high-speed large-scale data center.
In a short-distance optical interconnection communication system, an advanced modulation format is one of key technologies for realizing high-spectrum-efficiency large-capacity transmission. For the scene characteristics of short-distance optical interconnection, the main modulation formats include Pulse Amplitude Modulation (PAM), discrete multi-tone (DMT) modulation, Carrierless Amplitude Phase (CAP) modulation and the like, wherein the CAP modulation is realized by adopting a digital filter-based DSP technology, and the modulation format has the advantages of low overhead cost, simple realization, high spectrum utilization rate, and has become a very promising modulation technology in a short-distance optical transmission system. However, in the constellation mapping used in the CAP modulation technology at present, each symbol point in the constellation is represented by the same bit number, and an inner circle constellation point with lower energy required for transmission and an outer circle constellation point with higher energy required for transmission are transmitted with the same probability, which has the disadvantages of higher transmission power and weak transmission performance.
Disclosure of Invention
The purpose of the invention is as follows: the technical problem to be solved by the invention is to provide a carrier-free amplitude and phase modulation method and a carrier-free amplitude and phase demodulation method based on probability forming, wherein the mapping probability distribution of constellation points at different positions is optimally designed in constellation mapping, so that inner-circle constellation points with lower energy required for emission are mapped with higher probability, outer-circle constellation points with higher energy required for emission are mapped with lower probability, the average emission power of a system can be reduced, and the transmission performance of the system is improved.
The technical scheme is as follows: the invention provides a carrier-free amplitude phase modulation method based on probability forming, which comprises a probability forming constellation mapping step and a carrier-free amplitude phase modulation step, wherein the probability forming constellation mapping step comprises the following steps: the method comprises the steps of firstly, determining a probability forming constellation mapping table which corresponds input bit symbols and constellation positions one by one, wherein constellation points in the constellation mapping table are in non-uniform distribution, the probability of the constellation points in the inner circle is high, the probability of the constellation points in the outer circle is low, secondly, filling an input single-path original binary bit sequence m (k) into a bit interleaver for carrying out non-uniform distribution bit interleaving, realizing rearrangement of bits in a bit stream, thirdly, forming the constellation mapping table according to the probability, carrying out non-uniform distribution constellation mapping on output symbols after passing through the bit interleaver, and outputting a path of complex signal A (i).
In order to reduce the error rate, the probability-shaped constellation mapping is further set as a non-uniformly distributed twelve-point square constellation mapping, and the steps are as follows: firstly, determining a probability forming constellation mapping table as a twelve-point square constellation mapping table, setting 4 constellation points at the inner circle of the constellation map, wherein each constellation point corresponds to 3 bits, the constellation points are 000, 001, 010 and 011 respectively, and the occurrence probability of each constellation point is 1/8; setting 8 constellation points at the outer circle of a constellation diagram, wherein each constellation point corresponds to 4 bits and is respectively 1000, 1001, 1010, 1011, 1100, 1101, 1110 and 1111, and the occurrence probability of each constellation point is 1/16; secondly, non-uniformly distributed bit interleaving is carried out, an input single-path original binary bit sequence m (k) is sequentially filled into a 1 st row, a 2 nd row and a 3 rd row in a 4 xL interleaver, bit data in the first three rows are read from top to bottom according to columns, if three bits are any one of 000, 001, 010 and 011, a specified bit B is filled in the 4 th row, and otherwise, the bit sequence is continuously filled in the 4 th row; thirdly, constellation mapping is carried out, 3-bit or 4-bit data in each row in the interleaver is mapped into a constellation diagram row by row according to the twelve-point square constellation mapping table to form a non-uniformly distributed twelve-point square constellation mapping, and a path of complex signal A (i) is output.
For the CAP modulation, the carrier-free amplitude-phase modulation step is set as follows: the method comprises the following steps of firstly, performing up-sampling on a single-path complex signal A (i) by M times to obtain an up-sampled single-path complex signal A (n), wherein M can be set to be 4 for optimal combination of multi-sampling and a small amount of data; secondly, real part and imaginary part separation is carried out on the up-sampled complex data A (n), the up-sampled complex data A (n) is divided into two paths of real number signals a (n) and b (n) which are parallel after processing, and then the two paths of real number signals are respectively sent into two digital shaping filter units for processing; and the third step is shaping filtering: respectively carrying out shaping filtering on a (n) and b (n) by adopting a shaping filter to obtain s1(t) and s2(t); subtracting the two paths of signals in the fourth step to obtain the two paths of parallel signals s1(t) and s2(t) subtracting the two signals by an adder unit to obtain a single real signal s (t) s1(t)-s2And (t) outputting. The expressions of the two shaping filters are respectively:
The invention also provides a carrier-free amplitude and phase demodulation method based on probability forming, which comprises a carrier-free amplitude and phase demodulation step and a probability forming constellation demapping step, wherein the probability forming constellation demapping step comprises the following steps: firstly, forming a constellation mapping table according to the probability determined in the modulation process, and carrying out constellation demapping on a non-uniform distribution on a received complex signal A' (i); and secondly, filling the bit symbols obtained by constellation demapping into a bit interleaver for bit deinterleaving in a non-uniform distribution manner, reading the deinterleaved bit data, and outputting a single-path binary bit stream m' (k), namely the information data obtained by demodulation at the receiving end.
Further, the probability forming constellation mapping is set as a non-uniformly distributed twelve-point square constellation mapping, and the probability forming constellation demapping step is as follows: firstly, determining a probability forming constellation mapping table, wherein the constellation mapping table is a twelve-point square constellation mapping table determined in the modulation process; secondly, constellation demapping is carried out, probability forming constellation demapping is carried out on the received single-path complex signal A' (i) according to the twelve-point square constellation mapping table, and each constellation point in the twelve-point square constellation map is demapped to 3-bit or 4-bit data; thirdly, bit de-interleaving in non-uniform distribution, writing the bit data obtained in the last step into an interleaver in sequence to obtain a data matrix with the size of 4 xL, reading the bit data in the first three rows from top to bottom according to the columns, if the bit data in the first three rows is any one of 000, 001, 010 and 011, filling the specified bit B in the 4 th row of the column, and otherwise, counting the information bit in the 4 th row of the column; and sequentially reading the data, and recovering to obtain a single-path binary bit stream m '(k) output, wherein m' (k) is information data obtained by demodulation of a receiving end.
For the CAP demodulation, the carrier-free amplitude-phase demodulation step is set as follows: the first step of orthogonal separation, namely, multiplying the received one-way real number signal r (t) by the original carrier function under the action of an orthogonal separation unit respectively to obtain two-way orthogonal and in-phase real number signal r1(t) and r2(t); second step of matched filtering, r1(t) and r2(t) performing matched filtering under the action of two matched filter units to obtaina '(n) and b' (n); combining real parts and imaginary parts, combining the real parts and the imaginary parts of the two paths of parallel real signals a ' (n) and b ' (n) processed by the matched filter, and processing by the unit to obtain a path of complex data A ' (n), wherein A ' (n) is a (n) + jb ' (n); and a fourth step of down-sampling, in which the complex data A '(n) is subjected to M' times down-sampling processing by a down-sampling unit to obtain A '(i), wherein M' is the same as the value M during modulation. The expressions of the two matched filters are respectively:
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages: 1. the transmitting probability of the constellation points with higher energy is reduced, the transmitting probability of the constellation points with lower energy is improved, the average transmitting power of the system is reduced through the forming gain caused by probability forming, and the transmission capacity of the short-distance communication system is effectively improved; 2. by rearranging the bits in the bit stream, errors are randomized, the burst error influence in a channel is reduced, and the performance improvement in the aspect of the error rate is realized.
Drawings
FIG. 1 is a flow chart of a carrier-free amplitude-phase modulation method based on probability shaping according to the present invention;
fig. 2 is a schematic diagram of a probability shaping constellation mapping unit interleaver;
fig. 3 is a mapping rule diagram of a probability shaping constellation mapping unit;
fig. 4 is a probability distribution diagram of constellation points of a probability shaping constellation mapping unit;
FIG. 5 is a non-uniformly distributed twelve-point square constellation;
FIG. 6 is a graph of the impulse response of a quadrature, in-phase two-way filter;
FIG. 7 is a graph of a root-raised cosine filter impulse response;
fig. 8 is a flow chart of the carrierless amplitude phase demodulation method based on probability shaping.
Detailed Description
As shown in fig. 1, the working flow of the modulation method of the present invention is: inputting a single-path binary bit stream to a probability forming constellation mapping unit, completing the twelve-point square constellation mapping with non-uniform distribution after the single m (k) element processing, and outputting a single-path complex signal generated by a path of complex signal to an up-sampling unit root A (i). And performing M times of upsampling according to the sampling rate of the filter to realize M times of period prolongation of the signal on a frequency spectrum, and dividing the single-path complex signal subjected to upsampling into complex signals A (n) through a real part and imaginary part separation unit. The real part and imaginary part of A (n) are divided into two parallel real signals a (n) and b (n). Then, a (n) and b (n) enter finite impulse response filter to carry out shaping filtering to obtain s1(t) and s2(t) of (d). Finally, two paths of parallel signals are subtracted under the action of an adder unit to obtain a single-path real number signal s (t) which is the CAP-12 signal based on probability forming and is output.
The specific workflow of each module of the part is as follows:
(1) probability shaping constellation mapping unit
The probability forming constellation mapping unit is a core module in the modulation part, and the realization of the module can be divided into three steps of determination of a probability forming constellation mapping table, non-uniform distribution bit interleaving and constellation forming mapping.
Determining a probability forming constellation mapping table: according to a basic principle of probability forming, determining a twelve-point square constellation mapping table shown in table 1 as a probability forming constellation mapping table, wherein {000, 001, 010, 011} corresponds to four constellation points at the inner circle in a constellation diagram, each constellation point corresponds to 3 bits, and the probability of each constellation point is 1/8; {1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111} corresponds to eight constellation points in the outer circle of the constellation diagram, each constellation point corresponds to 4 bits, and the probability of each constellation point is 1/16.
TABLE 1 twelve-point Square constellation mapping table
| Bits | Probability of | Bits | Probability of |
| 000 | 1/8 | 1010 | 1/16 |
| 001 | 1/8 | 1011 | 1/16 |
| 010 | 1/8 | 1100 | 1/16 |
| 011 | 1/8 | 1101 | 1/16 |
| 1000 | 1/16 | 1110 | 1/16 |
| 1001 | 1/16 | 1111 | 1/16 |
Non-uniformly distributed bit interleaving: bit interleaving may rearrange bits in the bit stream, randomize errors, and convert burst errors in the channel into random errors over time, thereby increasing the robustness of the encoding. The specific principle is as shown in fig. 2, an input single-path original binary bit sequence m (k) is sequentially filled into the 1 st line, the 2 nd line and the 3 rd line in a 4 × L interleaver; reading the bit data in the first three rows from top to bottom according to the column, if any one of the three bits is {000, 001, 010, 011}, filling the specified bit B in the 4 th row position of the column, otherwise, continuing filling the information bit in the 4 th row position of the column.
Constellation forming and mapping: according to a twelve-point square constellation mapping table, sequentially mapping each row of 3-bit or 4-bit data into a constellation diagram, wherein a specific mapping rule is shown in fig. 3, a probability distribution condition of each constellation point in the constellation diagram is shown in fig. 4, finally realizing non-uniformly distributed twelve-point square constellation mapping through probability shaping, and a constellation diagram is shown in fig. 5, and outputting a path of complex signal A (i).
(2) Upsampling unit
The up-sampling unit performs M times up-sampling on the single-path complex signal A (i) according to the sampling rate of the filter, so as to realize M times period extension of the signal on a frequency spectrum and obtain the up-sampled single-path complex signal A (n). Taking M ═ 4 as an example, assuming that a (i) ═ 1+ i, 1-i, 3+ i, -3-i, ·, then a (n) · after M-fold upsampling [1+ i, 0, 0, 0, 1-i, 0, 0, 3+ i, 0, 0, 0, -3-i, 0, 0, 0, · ].
(3) Real part and imaginary part separation unit
The real part and imaginary part separation unit realizes real-imaginary part separation of up-sampled complex data A (n), and A (n) ═ a (n) + jb (n) is processed by the real part and imaginary part separation unit, then is divided into two parallel real number signals a (n) and b (n), and then is respectively sent into two digital shaping filter units for processing.
(4) Shaping filter unit
The shaping filter unit adopts a traditional shaping filter to respectively carry out shaping filtering on a (n) and b (n) to obtain s1(t) and s2(t) of (d). The expression of the shaping filter is as follows, wherein g (t) is a root raised cosine roll-off function, the impulse response of the orthogonal and in-phase filters is as shown in fig. 6, and the impulse response of the root raised cosine filter is as shown in fig. 7.
(5) Adder unit
Two parallel signals s1(t) and s2(t) subtracting the two signals by an adder unit to obtain a single real signal s (t) s1(t)-s2(t) output, s (t) is the CAP-12 signal shaped based on probability.
As shown in fig. 8, the work flow of the demodulation method of the present invention is: the received single-path real signal r (t) is divided into two paths of orthogonal and in-phase real signals r under the action of an orthogonal separation unit1(t) and r2(t) of (d). Then r1(t) and r2And (t) performing matched filtering under the action of the two matched filter units to recover and obtain a '(n) and b' (n). and a '(n) and b' (n) are subjected to real-imaginary part combination unit to be combined into a complex data A '(n), wherein A' (n) is a '(n) + jb' (n). Next, a '(n) is subjected to M-fold down-sampling corresponding to the up-sampling unit in the modulation process, resulting in a' (i). Finally, in a probability forming constellation demapping unit, A ' (i) recovers and obtains a single-path binary bit stream m ' (k) output, wherein m ' (k) is the information number obtained by demodulation of a receiving endAccordingly.
The specific workflow of each module of the part is as follows:
(1) orthogonal separation unit
Because the carrier phases of the orthogonal and in-phase signals have a 90-degree phase difference in the modulation process, the received single-path real number signal r (t) can be respectively multiplied by the original carrier function under the action of an orthogonal separation unit to obtain two paths of orthogonal and in-phase real number signals r1(t) and r2(t)。
(2) Matched filter unit
The matched filter unit corresponds to the shaping filter unit in the modulation process, and the adopted matched filter expression is consistent with the shaping filter.
(3) Real part and imaginary part combining unit
And the real part and imaginary part combining unit is used for combining the real parts and the imaginary parts of the two paths of parallel real signals a ' (n) and b ' (n) processed by the matched filter, and obtaining a path of complex data A ' (n) after the processing of the real part and imaginary part combining unit, wherein A ' (n) is a (n) + jb ' (n).
(4) Down sampling unit
The down-sampling unit and the up-sampling unit in the modulation process are opposite to A '(n), and the down-sampling unit obtains A' (i) after M times down-sampling processing of the down-sampling unit.
(5) Probability shaping constellation demapping unit
The probability forming constellation demapping unit is a core module in the demodulation part, and the implementation of the module can be divided into three steps of constellation forming demapping, non-uniform distribution bit deinterleaving and received data reading.
Constellation shaping and demapping: according to the twelve-point square constellation mapping table shown in table 1 and the corresponding mapping rule shown in fig. 3, constellation forming demapping is performed on the received single-path complex signal a' (i), and each constellation point in the non-uniformly distributed twelve-point square constellation map is demapped to 3-bit or 4-bit data.
Non-uniformly distributed bit de-interleaving: sequentially writing the data obtained in the first step into an interleaver to obtain a data matrix with the size of 4 xL, and sequentially reading the data according to the sequence of the 1 st row, the 2 nd row and the 3 rd row; reading the bit data in the first three rows from top to bottom according to the columns, if any one of the three bits is {000, 001, 010, 011}, filling the specified bit B in the 4 th row position of the column, not counting as information data, otherwise, counting as information bit in the 4 th row position of the column;
receiving data reading: and sequentially reading the data in the previous step, and recovering to obtain a single-path binary bit stream m '(k) output, wherein m' (k) is information data obtained by demodulation of a receiving end.
Claims (6)
1. A carrier-free amplitude phase modulation method based on probability forming comprises a probability forming constellation mapping step and a carrier-free amplitude phase modulation step, and is characterized in that the probability forming constellation mapping step is as follows:
(11) determining a probability forming constellation mapping table which corresponds input bit symbols and constellation positions one by one, wherein constellation points in the constellation mapping table are in non-uniform distribution, the probability of the constellation points at the inner circle is high, and the probability of the constellation points at the outer circle is low; the probability forming constellation mapping table is a twelve-point square constellation mapping table: setting 4 constellation points at the inner circle of a constellation diagram, wherein each constellation point corresponds to 3 bits, the number of the constellation points is 000, 001, 010 and 011 respectively, and the occurrence probability of each constellation point is 1/8; setting 8 constellation points at the outer circle of a constellation diagram, wherein each constellation point corresponds to 4 bits and is respectively 1000, 1001, 1010, 1011, 1100, 1101, 1110 and 1111, and the occurrence probability of each constellation point is 1/16;
(12) filling an input single-path original binary bit sequence m (k) into a bit interleaver for carrying out non-uniformly distributed bit interleaving, and realizing the rearrangement of bits in a bit stream; the non-uniformly distributed bit interleaving specifically comprises: sequentially filling an input single-path original binary bit sequence m (k) into a 1 st row, a 2 nd row and a 3 rd row in a 4 xL interleaver, wherein L is the bit number of each row of the interleaver, reading bit data in the first three rows from top to bottom according to a column, filling a specified bit B into the 4 th row of the column if three bits are any one of 000, 001, 010 and 011, and otherwise, continuously filling a bit sequence into the 4 th row of the column;
(13) according to the probability forming constellation mapping table, carrying out non-uniformly distributed constellation mapping on output symbols after passing through a bit interleaver, and outputting a path of complex signal A (i); the constellation mapping specifically comprises: and mapping 3-bit or 4-bit data in each column in the interleaver into a constellation diagram column by column to form a non-uniformly distributed twelve-point square constellation mapping.
2. The method as claimed in claim 1, wherein the step of modulating the carrierless amplitude and phase comprises:
(21) and (3) upsampling: performing M times of up-sampling on the single-path complex signal A (i), wherein M is more than or equal to 3, and obtaining an up-sampled single-path complex signal A (n);
(22) and (3) separating a real part and an imaginary part: performing real-imaginary part separation on the up-sampled complex data A (n), dividing the processed complex data A (n) into two paths of parallel real signals a (n) and b (n), and then respectively sending the two paths of parallel real signals a (n) and b (n) to two digital shaping filter units for processing;
(23) and (3) shaping and filtering: respectively carrying out shaping filtering on a (n) and b (n) by adopting a shaping filter to obtain s1(t) and s2(t), the two shaping filter expressions are:
wherein g (t) is a root-raised cosine roll-off function:
(24) Subtracting the two signals: combining the two paths of parallel signals s1(t) and s2(t) subtracting the two signals by an adder unit to obtain a single real signal s (t) s1(t)-s2And (t) outputting.
3. The method of claim 2, wherein M in step (21) is 4.
4. A carrier-free amplitude and phase demodulation method based on probability forming comprises a carrier-free amplitude and phase demodulation step and a probability forming constellation demapping step, and is characterized in that the probability forming constellation demapping step is as follows:
(41) the probability forming constellation mapping table according to claim 1, performing constellation demapping of non-uniform distribution on the received complex signal a' (i);
(42) filling the bit symbols obtained by constellation demapping into a bit interleaver for bit deinterleaving in non-uniform distribution, reading the bit data after deinterleaving, and outputting a single-path binary bit stream m' (k), namely the information data obtained by demodulation at the receiving end.
5. The method according to claim 4, wherein the probability forming constellation demapping step is:
(51) determining the probability forming constellation mapping table as the twelve-point square constellation mapping table in claim 1;
(52) performing probability forming constellation demapping: performing probability forming constellation demapping on the received single-path complex signal A' (i) according to the probability forming constellation mapping table, and demapping each constellation point in a non-uniformly distributed twelve-point square constellation map to 3-bit or 4-bit data;
(53) non-uniformly distributed bit de-interleaving: sequentially writing the bit data obtained in the last step into an interleaver to obtain a data matrix with the size of 4 xL, wherein L is the bit number of each row of the interleaver, reading the bit data in the first three rows from top to bottom according to the rows, if the bit data in the first three rows is any one of 000, 001, 010 and 011, the 4 th row position in the row is filled with a specified bit B, and otherwise, the 4 th row position in the row is an information bit; and sequentially reading the data, and recovering to obtain a single-path binary bit stream m '(k) output, wherein m' (k) is information data obtained by demodulation of a receiving end.
6. The method as claimed in claim 4, wherein the step of carrierless amplitude phase demodulation comprises:
(61) orthogonal separation: multiplying the received single-path real number signal r (t) by the original carrier function under the action of an orthogonal separation unit to obtain two paths of orthogonal and in-phase real number signals r1(t) and r2(t)；
(62) Matched filtering: r is1(t) and r2(t) performing matched filtering under the action of the two matched filter units to obtain a '(n) and b' (n), wherein the expressions of the two matched filters are respectively as follows:
(63) And combining the real part and the imaginary part: combining real and imaginary parts of two paths of parallel real signals a '(n) and b' (n) processed by the matched filter, and obtaining a path of complex data A '(n) after the real and imaginary parts are processed by the unit, wherein A' (n) is a '(n) + jb' (n);
(64) down-sampling: the complex data A '(n) is subjected to M' times downsampling processing by a downsampling unit to obtain A '(i), wherein M' is equal to M, and M is an upsampling multiple.
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| CN111049586B (en) * | 2019-12-25 | 2020-11-03 | 南京信息工程大学 | Pulse amplitude position modulation system based on amplitude reduction type probability forming |
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| CN107682298A (en) * | 2017-10-18 | 2018-02-09 | 北京邮电大学 | A kind of signal modulation/demodulation method and device based on wavelet transform |
| EP3306884A1 (en) * | 2016-10-06 | 2018-04-11 | Alcatel Lucent | Frequency offset estimation for probabilistically shaped qam signal |
| CN108574650A (en) * | 2017-03-10 | 2018-09-25 | 中兴通讯股份有限公司 | Probability shaping orthogonal frequency division multiplexing |
| CN108631879A (en) * | 2018-05-14 | 2018-10-09 | 华侨大学 | A kind of light orthogonal frequency division multiplexing communication method and system based on probability shaping mapping |
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| CN103036845A (en) * | 2012-12-05 | 2013-04-10 | 清华大学 | Non-equal probability constellation labeling method based on absolute phase shift keying (APSK) constellation diagram |
| EP3306884A1 (en) * | 2016-10-06 | 2018-04-11 | Alcatel Lucent | Frequency offset estimation for probabilistically shaped qam signal |
| CN108574650A (en) * | 2017-03-10 | 2018-09-25 | 中兴通讯股份有限公司 | Probability shaping orthogonal frequency division multiplexing |
| CN107682298A (en) * | 2017-10-18 | 2018-02-09 | 北京邮电大学 | A kind of signal modulation/demodulation method and device based on wavelet transform |
| CN108631879A (en) * | 2018-05-14 | 2018-10-09 | 华侨大学 | A kind of light orthogonal frequency division multiplexing communication method and system based on probability shaping mapping |
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