CN101119177A - Bit-symbol signal processing method for coherent communication machine - Google Patents
Bit-symbol signal processing method for coherent communication machine Download PDFInfo
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Abstract
The present invention discloses a bit-symbol signal processing method which is applicable for a self-adapting adjudication feedback equalizer and decoder connection and iteration signal process, comprising the following steps: 1 confirm the expression which is the most corresponding to the posterior probability of the signal of the communication receiving; 2 according to SOVA arithmetic, make the highest expression value of the process 1, thereby the posterior probability of the signal of the communication receiving is the highest and the flexible adjudication of the signal is acquired; 3 according to SOVA arithmetic, make the highest expression value of the process 1, thereby the posterior probability of the signal of the communication receiving is the highest and the rigid adjudication is acquired.
Description
Technical Field
The invention relates to a signal processing technology, in particular to a bit-symbol signal processing method suitable for cascade connection of a self-adaptive decision feedback equalizer and a decoder and iterative signal processing.
Background
An underwater acoustic channel is a multipath, time-varying, and dispersive channel. Due to the multi-path effect, the transmitting end transmits one sound pulse, and the receiving end can receive a plurality of pulses, so that time delay diffusion is generated. Due to carrier motion, as well as channel interface and medium motion, various motions cause these pulses to produce doppler shifts and doppler spreads. The speed of sound in water is about 1500m/s, and these velocities of motion are not negligible compared to the speed of sound, which makes the doppler spread quite severe. For the reasons mentioned above, the hydroacoustic channel is often referred to as a delay and doppler spread channel. Moreover, the characteristics of the underwater acoustic channel vary with time and place, and its effective transmission bandwidth is limited, which makes it more difficult to transmit information in the underwater acoustic channel.
In order to transmit information at high speed in an underwater acoustic channel, an underwater acoustic coherent communication technology is generally adopted, and a multi-phase shift keying (MPSK) or multi-quadrature amplitude Modulation (MQAN) signal is transmitted at a transmitting end, so that the bandwidth utilization rate of the signals is high. The effect of the underwater acoustic channel is overcome by adopting an adaptive equalizer or a decoder for coding signals at a receiving end, but the effect of overcoming the effect of the underwater acoustic channel is difficult to achieve by adopting one technology alone. In recent years, people start to cascade an adaptive equalizer and a decoder to perform iterative signal processing operation, output symbol information of the adaptive equalizer is sent to the decoder, output bit information of the decoder is fed back to the adaptive equalizer, and iteration is stopped after a certain standard is reached. For example, the technique disclosed in U.S. patent "Iterative decision feedback adaptive equalizer" published by US 6819630B1 and m. Marandian et al 2001 "Low complex Iterative decision feedback equalizer for 8PSK modulation in time discrete channel", IEEE International Symposium, vol 1.30sept 3-oct 2001.Pp 102-a106", was obtained from f.a. blackman et al 2004, 11, 16. The above document discloses that the decision feedback adaptive equalizer is connected in series with the decoder to perform iterative operations, but does not mention how to convert the bit information output by the decoder into the symbol information required by the decision feedback adaptive equalizer.
In fact, the bit information output by the decoder must be converted into symbol information when the iterative operation is performed, and since the adaptive equalizer only performs the operation on the symbol information, in practical applications, there is a problem of signal processing in which the bit information is converted into the symbol information.
In the prior art, a key technology of an underwater acoustic coherent communication system is to cascade a decision feedback adaptive equalizer and a Turbo-TCM (Trellis Coded Modulation) decoder and perform iterative operation. The soft output of the Turbo-TCM decoder is the probability information of systematic bits, which is used to generate an estimate of the transmitted symbols, and the prior art is hard decision re-encoding of the probability information of systematic bits, which is known as the technique disclosed in the document "Proakis, j.g., digital Communications, beijing, publishing House of Electronics Industry, 2001". This re-encoding method works well and is easy to implement if the output of the decoder reaches zero bit error rate. However, in practical applications, error bits often appear at the output of the decoder, and during re-encoding, the state transition path in the trellis diagram is changed by the error bit information, so that a plurality of symbol sequences different from the transmitted symbols are generated, and a large number of error transmissions are generated during joint iteration of the equalizer and the decoder. Therefore, the signal processing method of converting bit information into symbol information in the prior art is relatively easy to implement, but has poor performance.
In summary, due to the deficiencies of the prior art, a signal processing method for converting bit information output by a decoder into symbol information required by a decision feedback adaptive equalizer with good performance is needed.
Disclosure of Invention
The present invention is directed to overcome the deficiencies of the prior art and to provide a method for processing a bit-symbol signal for coherent communication.
In order to achieve the above object, the present invention adopts the following technical solutions.
A bit-symbol signal processing method for a coherent communication device, comprising the steps of:
1) Determining the expression corresponding most to the a posteriori probability of the symbols received by the communicator as follows:
wherein p is t (s t ) Is a prior probability, r t，I And r t，Q Imaginary and real parts of the received symbol, s, respectively at time t t，I i And s t ，Q i Respectively an imaginary part and a real part of a corresponding signal in a signal constellation diagram;
2) According to the SOVA algorithm, the expression value in the step 1) is maximized, so that the posterior probability of the symbol received by the communication machine is maximized, and the soft decision of the symbol is obtained;
3) According to the SOVA algorithm, the expression value in the step 1) is maximized, so that the posterior probability of the symbol received by the communication machine is maximized, and the hard decision of the symbol is obtained.
Further, the step 2) specifically comprises the following steps:
(1) Determining branch metrics of a transfer path in a component convolutional code grid graph according to an SOVA algorithm;
(2) Determining a path metric;
(3) For the MPSK modulation mode, determining the metric value of a survival path, and determining the metric value of a competition path corresponding to the signal point;
(4) Determining prior probabilities that systematic bits are 0 and 1, respectively;
(5) Determining a received symbol r at a time t t Euclidean distances from each point in the constellation diagram;
(6) Obtaining the probability of the check bit at the time t according to the constellation diagram in the last step (5);
(7) And obtaining the probability of each symbol point in the constellation diagram, and forming the probability into the soft decision of the symbol for the soft iterative signal processing of the decision feedback adaptive equalizer and the decoder.
Further, the step 3) specifically comprises the following steps:
(1) Determining branch metrics of a transfer path in a component convolutional code grid graph according to an SOVA algorithm;
(2) Determining a path metric;
(3) For the MPSK modulation mode, determining the metric value of a survival path, and determining the metric value of a competition path corresponding to the signal point;
(4) Determining prior probabilities that system bits are 0 and 1 respectively;
(5) Determining a received symbol r at a time t t Euclidean distances from each point in the constellation diagram;
(6) By step 5), obtaining the probability of the check bit at the time t according to the constellation diagram;
(7) Deciding the symbol transmitted at time t if Λ(s) t i ) At a minimum, the symbol transmitted at that time is s i Forming hard decisions for the symbols.
A bit-symbol signal processing method for coherent communication, comprising the steps of
1) Determining an expression corresponding to a maximum a posteriori probability of symbols received by the communicator, by which expression the maximum a posteriori probability of symbols received by the communicator is determined;
wherein r is t，l And r t，Q The imaginary and real parts of the received symbol at time t, respectively.
2) According to the SOVA (Soft Output Viterbi Algorithm) Algorithm, the branch metric of the transfer path in the component convolutional code trellis diagram is determined as follows:
3) For the transfer path X, the path metric is determined as:
4) For the MPSK modulation mode, at any moment, the survival path corresponds to M-1 competition paths, and the metric value of the survival path is determined as follows:
determining the sum signal point s 1 ，s 2 ，……s M-1 The metric values of the corresponding competition paths are:
wherein, the symbol s in the constellation diagram corresponds to the survival path at the time t 0 M-1 competition paths respectively correspond to the signal points s at the time 1 、s 2 、……s M-1 ，μ t，si I =1,2, \8230; \ 8230;, M-1 is the signal point s 1 ，s 2 ，……s M-1 The corresponding metric value of the competition path; and l si ′，
Representing the state of adjacent time instants, M S Is the number of states in the trellis diagram, μ t-1 f (l si ') is the forward survival path metric at time t-1, μ t b (l si ) Measure of reverse survival path at time t, v t si (l si ′，l si ) Generating a symbol s for time t i State transition branch metrics of (c);
5) Determining the probability of each symbol point in the constellation diagram as follows:
6) Determining systematic bit c t The prior probabilities of 0 and 1, respectively, are:
wherein the prior probability estimate Λ (c) t ) Systematic bit probability soft information output by the decoder;
7) Determining a received symbol r at a time t t The Euclidean distances from each point in the constellation diagram are respectively as follows:
8) And 7), obtaining the probability of the check bit at the time t according to the constellation diagram:
9) Obtaining p according to the constellation diagram by the results of the step 6), the step 7) and the step 8) t (s t )；
10 P (\58411) t ＝s i ) And becomes the soft decision of the symbol, which is used for the soft iterative signal processing of the decision feedback adaptive equalizer and the decoder.
In the above technical solution, further, step 11) is further included, that is, the symbol transmitted at time t is directly decided by step 4) and step 9), if Λ(s) (i.e. the symbol is a symbol transmitted at time t in the symbol), and the symbol is a symbol transmitted at time t in the symbol if Λ (i.e. the symbol is a symbol transmitted at time t in the symbol is a symbol transmitted in the symbol), and the symbol is a symbol transmitted at time t in the symbol if Λ (i.e. the symbol is a symbol transmitted in the symbol) t i ) At a minimum, the symbol transmitted at that time is s i And forming hard decision of the symbol, and applying the hard iteration signal processing of the decision feedback adaptive equalizer and the decoder.
Compared with the prior art, the invention has the beneficial effects that:
1) The invention realizes the signal processing of converting bit information into symbol information based on the SOVA (Soft Output Viterbi Algorithm) Algorithm, has good performance, and has the symbol error rate of converting the bit information into the symbol information which is two orders of magnitude better than the prior art under the condition that the decoder outputs error bits, thereby obviously improving the performance of the cascade connection and iterative signal processing of the decision feedback adaptive equalizer and the decoder.
2) The main part of the signal processing of the invention adopts the SOVA algorithm which is widely applied to the decoder, so the invention has wide application range.
Drawings
FIG. 1 is a flow chart of a bit-symbol signal processing method of the present invention;
fig. 2 is a schematic diagram of the application of the bit-symbol signal processing method of the present invention in coherent communication.
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
the signal processing method for converting the bit information output by the decoder into the symbol information required by the decision feedback adaptive equalizer can be called as a 'bit-to-symbol converter' module in application. The invention adopts a method based on SOVA (Soft Output Viterbi Algorithm) Algorithm according to the systematic bit probability information Output by the Turbo-TCM decoder, and can obtain the estimated value of the receiving symbol of the receiver. The invention always has few error symbols and excellent performance. The operation complexity related by the invention is similar to that of the SOVA algorithm, and the application range is wide in practical application.
The SOVA algorithm is often used in Turbo decoders, and in this case, the SOVA algorithm should also be used in bit-to-symbol conversion. And the absolute value of the systematic bit probability estimation (also called systematic bit log-likelihood ratio) obtained by the decoder by the SOVA algorithm is not too large, and overflow phenomenon can not occur during exponential operation.
For convenience of description, the bit-symbol signal processing method of the present invention will be described in detail below by taking a QPSK modulated signal as an example. Of course, the invention is also applicable to all MPSK modulated signals.
The posterior probability of the symbol received by the receiving end of the coherent communication machine is
From this, obtain
Wherein S = { S = 1 ，s 2 ，…，s T Represents the desired symbol sequence, r 1 T Representing the sequence of symbols from time 1 to time T that the equalizer outputs to the decoder. To maximize the posterior probability, only p is needed for a set of equi-probability symbol sequences r (S，r 1 T ) And max. Logarithm is calculated on two sides of the formula (2) to obtain
Assuming that the noise of the transmission channel is independent gaussian noise, equation (3) is expressed as
Wherein r is t，I And r t，Q Imaginary and real parts of the received symbol, s, respectively at time t t，I i And s t，Q i I =0,1,2,3, respectively, for the imaginary and real parts of the corresponding signal in the signal constellation. p is a radical of t (s t ) Is a prior probability. n is the length of the component code. If the symbol at any given time is different from the signal corresponding to each point in the signal constellation diagram, then the posterior probability is maximized by maximizing the following equation:
according to the SOVA algorithm, branch metrics of a transition path in a trellis diagram of a component convolutional code are defined as
For the branch path X, define the path metric as
For the QPSK modulation scheme, the survival path corresponds to 3 contention paths at any time, and it is assumed that the symbol s in the constellation diagram corresponds to the survival path at time t 0 Then the three contention paths correspond to the signal point s at this time 1 、s 2 And s 3 . Definition of mu T，min For the metric value of the survival path, mu t，si I =1,2,3 is the and signal point s 1 ，s 2 ，s 3 The metric value of the corresponding competition path can be obtained by the formula (7) as
The quantities in the above formula are represented by the following formulas
Wherein l si ′， 
Representing the state of adjacent time instants, M S Is the number of states in the trellis diagram. Competition path in grid diagram at t-1 from state l si ', i =1,2,3, transition to state l si I =1,2,3, generating the symbol s i ，i＝1，2，3，μ t-1 f (l si ') is the forward survivor path metric at time t-1, μ t b (l si ) Measure of reverse survival path at time t, v t si (l si ′，l si ) Generating a symbol s for time t i State transition branch metrics. Probability p (\58411; = s) of each symbol point in the constellation diagram i ) Is composed of
Since the prior probability of the symbol is used in equation (6), the prior probability of each point in the constellation should be obtained from the systematic bit probability output by the decoder and the probability of the symbol check bit currently received by the receiver. The soft information of systematic bit probability output by the decoder is the prior probability estimation lambda (c) t ) Is represented by the following formula
A systematic bit c is obtained t A priori probabilities of 0 and 1, respectively
Obtained by SOVA algorithm t ) Is not large and its exponent does not overflow. MAP algorithm derived Λ (c) t ) Is relatively large and its exponent will overflow. If the received symbol at time t is r t The Euclidean distance between the symbol and each point in the constellation diagram is
The probability of the check bit at time t is respectively
The bits in each codeword can be considered to be independent of each other, so that the prior probabilities that the current transmission symbol is each point in the constellation diagram are
This yields the symbol prior probability p required in equation (6) t (s t )。
Equations (6) to (15) give the algorithm of the bit-to-symbol conversion signal processing.
P (\\ 58411 t ＝s i ) The symbol soft decision can also be made by directly deciding the symbol transmitted at time t according to equations (8), (9) and (15), if Λ(s) t i ) At a minimum, the symbol transmitted at that time is s i Hard decisions of the symbols are formed. The above described symbol soft and hard decisions are applied to soft and hard iterative algorithms of the decision feedback adaptive equalizer and decoder, respectively.
The present invention is applicable to MPSK modulated signals, and is described below in terms of the signal processing flow of the present invention, which is illustrated by QPSK as an example in fig. 1. Soft information output by decoder is prior probability estimation lambda (c) t ) Is input to a bitP (c) in operation block 101 of symbol converter 100 using equation (12) t ). Data stream r received by a receiver 1 T Input to an operation block 104, and L(s) is obtained from the equation (13) i )。L(s i ) Input to the operation block 103 to obtain p (Check). r is 1 T 、 p(c t ) The sum p (Check) is input to the operation block 102, and p(s) is obtained by the formula (15) t )。{r t H and p(s) t ) V is obtained from equation (6) and input to operation block 105 t st 。v t st Input to the operation block 106, the value of μ is obtained by equation (7) t x 。μ t x Sent to an operation block 107 to obtain mu by using the expressions (9 a) and (9 b) T，min And mu t，st From this,. Lambda.'(s) is obtained t i ) Hard iterative algorithms for decision feedback adaptive equalizers and decoders. Mu.s T，min And mu t，st An input operation block 108 for calculating p (\58411 t ＝s i ) And the soft iterative algorithm is used for a decision feedback adaptive equalizer and a decoder. The operation blocks 105, 106, 107 and 108 constitute an operation block 109, which is the SOVA algorithm. The operation block may be implemented by software or by an electrical device. The invention can be popularized and applied to MQAM modulation signals。
The following compares the performance of two methods of deriving a transmitted symbol stream from the decoder output bit stream, one being the bit-to-symbol converter output and the other being the re-encoded output. Testing 8PSKTurbo-TCM coded signals with component code generator polynomial {23, 35, 33}, frame length 1936, adding sigma to the coded output 2 =0.07 white gaussian noise, and the number of decoder iterations is 0 (output directly without iterative operation). Table 1 gives the output results of arbitrarily selected 10 frames of data. It can be seen that when the bit error rate of the decoder output is 0, the performance of the re-encoded output is slightly better than that of the bit-to-symbol converter, which may have a few error symbols at the output, and the symbol error rate of the re-encoded output is 0. Once the decoder output has erroneous bits, the symbol error rate of the re-encoded output becomes dramatically greater, while the bit-to-symbol converter output is much better, the latter performing two orders of magnitude better than the former. This is because when the decoder outputs erroneous bits, the state transition path of the encoder is erroneous and results in many erroneous symbols when re-encoded with these bits. The results are similar when different white noise is added to the coded output.
TABLE 1 comparison of the Performance of two methods for obtaining a stream of transmitted symbols from a decoder output bit stream
| Frame number | Decoding output error bit Rate of change | Bit-to-symbol conversion Symbol error rate of output | Recoding output Symbol error rate |
| 1 | 0.00077 | 0.01085 | 0.26033 |
| 2 | 0.00387 | 0.00981 | 0.19421 |
| 3 | 0.00646 | 0.02273 | 0.25362 |
| 4 | 0.00000 | 0.00413 | 0.00000 |
| 5 | 0.00000 | 0.00568 | 0.00000 |
| 6 | 0.00310 | 0.01188 | 0.25981 |
| 7 | 0.00207 | 0.01446 | 0.22521 |
| 8 | 0.00077 | 0.00878 | 0.18957 |
| 9 | 0.00129 | 0.00723 | 0.17252 |
| 10 | 0.00336 | 0.00981 | 0.24948 |
The adaptive decision of the present invention is described below with reference to FIG. 2Use of a block feedback equalizer in cascade with a decoder. See fig. 2. Data stream r output by equalizer 1 T Is divided into two paths, one path is directly input into the first bit-to-symbol converter 201, and the other path is input into the second bit-to-symbol converter 204 via the interleaver 203. Output prior probability estimate Λ (c) of decoder 200 t ) The input is divided into two paths, one path is input to a first bit-to-symbol converter 201 via a deinterleaver 202, and the other path is input to a second bit-to-symbol converter 204. The output of the first bit-to-symbol converter 201 and the output of the second bit-to-symbol converter 204 via the deinterleaver 205 are subjected to a deletion operation to obtain Λ'(s) t i ) Or p (\58411 t ＝s i ) Obtaining the required symbol estimation after hard or soft decision 206 { \58411 t }。
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the specific embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (5)
1. A bit-symbol signal processing method for coherent communication, comprising the steps of:
1) Determining the expression corresponding most to the a posteriori probability of the symbols received by the communicator as follows:
wherein p is t (s t ) Is a prior probability, r t，I And r t，Q Imaginary and real parts of the received symbol, s, respectively at time t t，I i And s t，Q i Respectively an imaginary part and a real part of a corresponding signal in a signal constellation diagram;
2) According to the SOVA algorithm, the expression value in the step 1) is maximized, so that the posterior probability of the symbol received by the communication machine is maximized, and the soft decision of the symbol is obtained;
3) According to the SOVA algorithm, the expression value in the step 1) is maximized, so that the posterior probability of the symbol received by the communication machine is maximized, and the hard decision of the symbol is obtained.
2. The bit-symbol signal processing method for a coherent communication device according to claim 1, wherein said step 2) comprises the steps of:
(1) Determining branch measurement of a transfer path in a component convolutional code grid graph according to an SOVA algorithm;
(2) Determining a path metric;
(3) For the MPSK modulation mode, determining the metric value of a survival path, and determining the metric value of a competition path corresponding to the signal point;
(4) Determining prior probabilities that systematic bits are 0 and 1, respectively;
(5) Determining a received symbol r at a time t t Euclidean distances between the constellation diagram and each point;
(6) Obtaining the probability of the check bit at the time t according to the constellation diagram in the last step (5);
(7) And obtaining the probability of each symbol point in the constellation diagram, and forming the probability into the soft decision of the symbol for the soft iterative signal processing of the decision feedback adaptive equalizer and the decoder.
3. The bit-symbol signal processing method for the coherent communication device according to claim 1, wherein the step 3) comprises the steps of:
(1) Determining branch measurement of a transfer path in a component convolutional code grid graph according to an SOVA algorithm;
(2) Determining a path metric;
(3) For the MPSK modulation mode, determining the metric value of a survival path, and determining the metric value of a competition path corresponding to the signal point;
(4) Determining prior probabilities that system bits are 0 and 1 respectively;
(5) Determining a received symbol r at a time t t Euclidean distances from each point in the constellation diagram;
(6) By step 5), obtaining the probability of the check bit at the time t according to the constellation diagram;
(7) Deciding the symbol transmitted at time t if Λ(s) t i ) At a minimum, the symbol transmitted at that time is s i Hard decisions of the symbols are formed.
4. A bit-symbol signal processing method for coherent communication, comprising the steps of:
1) The expression that determines the maximum posterior probability for a symbol received by the communicator is as follows:
wherein p is t (s t ) Is a priori probability, r t，I And r t，Q Imaginary and real parts of the received symbol, s, respectively at time t t，I i And s t，Q i Respectively an imaginary part and a real part of a corresponding signal in a signal constellation diagram;
2) According to the SOVA algorithm, the branch metric of the transfer path in the component convolutional code grid graph is determined as follows:
3) For the transfer path X, the path metric is determined as:
4) For the MPSK modulation mode, the survival path corresponds to M-1 competition paths at any moment,
determining the metric value of the survival path as follows:
determining the sum signal point s 1 ，s 2 ，……s M-1 The metric values of the corresponding competition paths are:
wherein, the symbol s in the constellation diagram corresponds to the survival path at the time t 0 M-1 competition paths respectively correspond to the signal points s at the time 1 、s 2 、……s M-1 ，μ t，si I =1,2, \8230; \ 8230;, M-1 is the signal point s 1 ，s 2 ，……s M-1 The corresponding metric value of the competition path; and l si ′，
Representing the state of adjacent time instants, M S Is the number of states in the trellis diagram, μ t-1 f (l si ') is the forward survivor path metric at time t-1, μ t b (l si ) Measure value of reverse survival path at time t, v t si (l si ′，l si ) Generating a symbol s for time t i State transition branch metrics of;
5) Determining the probability of each symbol point in the constellation diagram as follows:
6) Determining systematic bit c t The prior probabilities of 0 and 1, respectively, are:
wherein the prior probability estimate Λ (c) t ) Systematic bit probability soft information output by a decoder;
7) Determining a received symbol r at a time t t The Euclidean distances between the constellation diagram and each point are respectively as follows:
8) By step 7), according to the constellation diagram, the probability of the check bit at the time t is obtained:
9) Obtaining p according to the constellation diagram by the results of the step 6), the step 7) and the step 8) t (s t )；
10 From the results of step 4), step 5) and step 9)
Becomes the soft decision of the symbol for the soft iterative signal processing of decision feedback adaptive equalizer and decoder.
5. The bit-symbol signal processing method for a coherent communication device according to claim 4, further comprising:
step 11): from said step 4) and said step 9), the symbol transmitted at time t is decided, if Λ(s) t i ) At a minimum, the symbol transmitted at that time is s i Hard decisions of the symbols are formed.
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| CN102413089A (en) * | 2011-08-16 | 2012-04-11 | 上海交通大学 | Shannon limit coding GMSK demodulation method used for satellite communication system |
| CN102413089B (en) * | 2011-08-16 | 2014-04-02 | 上海交通大学 | Shannon limit coding GMSK demodulation method used for satellite communication system |
| CN103401826A (en) * | 2013-08-09 | 2013-11-20 | 电子科技大学 | Multi-carrier frequency hopping communication soft-decision method based on OOK modulation |
| CN103401826B (en) * | 2013-08-09 | 2016-10-26 | 电子科技大学 | The soft decision method of multi-carrier frequency hopping communication based on OOK modulation |
| CN105227509A (en) * | 2014-07-03 | 2016-01-06 | 扬智科技股份有限公司 | Mixing decision method in quadrature amplitude modulation code demodulating system and receiving system thereof |
| CN105227509B (en) * | 2014-07-03 | 2018-04-13 | 扬智科技股份有限公司 | Mixing decision method and its reception device in quadrature amplitude modulation code demodulating system |
| CN107086972A (en) * | 2017-05-12 | 2017-08-22 | 南京信息工程大学 | The adaptive decision feedback filtering system and method limited based on constellation |
| CN110784282A (en) * | 2019-09-12 | 2020-02-11 | 浙江大学 | Underwater acoustic communication data reuse method based on soft information transfer |
| CN110784282B (en) * | 2019-09-12 | 2021-02-19 | 浙江大学 | Underwater acoustic communication data reuse method based on soft information transfer |
| US11533126B1 (en) | 2021-08-20 | 2022-12-20 | Cisco Technology, Inc. | Soft-output Viterbi equalizer for non-binary modulation |
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