CN109547370B - Symbol estimation method of super-Nyquist system based on joint equalization and interference cancellation - Google Patents
Symbol estimation method of super-Nyquist system based on joint equalization and interference cancellation Download PDFInfo
- Publication number
- CN109547370B CN109547370B CN201910013077.5A CN201910013077A CN109547370B CN 109547370 B CN109547370 B CN 109547370B CN 201910013077 A CN201910013077 A CN 201910013077A CN 109547370 B CN109547370 B CN 109547370B
- Authority
- CN
- China
- Prior art keywords
- symbol
- super
- nyquist system
- receiver
- iteration
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L25/03012—Arrangements for removing intersymbol interference operating in the time domain
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
- H04L25/03006—Arrangements for removing intersymbol interference
- H04L2025/03433—Arrangements for removing intersymbol interference characterised by equaliser structure
- H04L2025/03439—Fixed structures
- H04L2025/03445—Time domain
Abstract
The invention discloses a symbol estimation method of a super-Nyquist system by combining equalization and interference cancellation, which comprises the following steps: acquiring an input symbol; training an equalizer; judging whether the training times of the equalizer are smaller than the threshold value of the equalizer or not; calculating the equalized symbols; calculating an interference elimination factor of the super-Nyquist system; eliminating intersymbol interference in the first iteration; eliminating intersymbol interference through iteration; judging whether the iteration times are smaller than an estimation threshold value; and acquiring a final estimation symbol. Compared with the prior art, the method can ensure that the super-Nyquist system has better bit error rate performance even under the condition of more serious intersymbol interference, and has low symbol estimation complexity and higher practicability.
Description
Technical Field
The invention belongs to the technical field of communication, and further relates to a symbol estimation method of a super-Nyquist system for combined equalization and interference cancellation in the technical field of wireless communication. The method can be used for eliminating intersymbol interference in the super-Nyquist system so as to estimate the sending symbol of the transmitter of the super-Nyquist system.
Background
In designing conventional communication systems, the nyquist first criterion is followed in order to avoid intersymbol interference of the system. However, orthogonality between symbols transmitted without intersymbol interference in nyquist transmission systems comes at the expense of spectral efficiency. By artificially introducing intersymbol interference, the faster-than-nyquist system can support higher transmission rates and spectral efficiency. Accordingly, the super-nyquist system requires higher complexity to eliminate the intersymbol interference, thereby estimating the transmission symbols of the super-nyquist system transmitter.
Ebrahim Beder proposed a low complexity symbol estimation method based on backoff and interference cancellation in its published paper "A very low complexity available symbol-by-symbol sequence estimator for fast-through-Nyquist signaling" (IEEE Access, 2017, 5: 7414-. After receiving a symbol, the method firstly estimates the current received symbol by using the current received symbol and the symbol estimated before, then re-estimates the front end number of symbols of the current estimated symbol by using the estimated symbol of the current symbol, and finally re-estimates the current symbol by using the re-estimated symbol. The method can effectively eliminate the intersymbol interference of the super-Nyquist system under the condition that the super-Nyquist system adopts a low-order modulation mode and slight intersymbol interference, and achieves good performance. The method has the disadvantages that the estimation precision is low because the interference of the front symbol of the current receiving symbol is eliminated, and the symbol estimation performance is poor when the super-nyquist system adopts a high-order modulation mode or under the condition of more serious intersymbol interference (the super-nyquist acceleration factor is smaller or a receiver matching filter adopts a smaller roll-off factor).
Ebrahim Beder proposes a symbol estimation method based on semi-definite relaxation in its published paper "Low-complex detection of high-order QAMfast-than-Nyquist signaling" (IEEE Access, 2017, 5: 14579-. The method has the disadvantages that the complexity is positively correlated with the order of the selected modulation mode, and the high complexity of the super-Nyquist system when the modulation mode with higher order is adopted causes the method to have no practicability.
The patent document "bidirectional serial interference cancellation method in super-nyquist communication system" (patent application No. 201810744483.4, publication No. CN108632182A) filed by the university of west ann electronic technology proposes a bidirectional serial inter-symbol interference cancellation method for super-nyquist system. The method uses a truncated waveform shaping filter to carry out forward and backward bidirectional serial interference elimination on sampling data, namely, firstly, a demodulation code element in front of a current code element is used for eliminating forward serial interference to obtain a temporary decision value of a demodulation signal, and then, the temporary decision value of the demodulation signal is used for eliminating backward serial interference to obtain a final demodulation signal. The method improves the demodulation performance of the receiving end of the super-Nyquist communication system, reduces the complexity of the receiving end, is suitable for the condition of slight intersymbol interference, but is difficult to approach the theoretical performance limit, and has larger performance loss particularly under the condition of serious intersymbol interference.
Disclosure of Invention
The present invention aims to provide a method for estimating symbols of a super-nyquist system by combining equalization and interference cancellation, which overcomes the shortcomings of the prior art.
The idea of achieving the purpose of the invention is that under the condition of serious intersymbol interference, when iterative cancellation of intersymbol interference is adopted, better performance can not be achieved even in subsequent iteration due to poor performance of the bit error rate of the super-nyquist system after first iterative estimation, so that a symbol after equalization can be obtained by performing one-time equalization operation after a receiver matched filter output symbol is obtained, and then intersymbol interference is cancelled on the equalized symbol through iteration to obtain a final estimated symbol.
The method comprises the following specific steps:
(1) obtaining input symbols:
receiving symbols output by a matched filter of a receiver corresponding to symbols transmitted by a transmitter of the super-Nyquist system in real time, and taking the symbols output by the matched filter of the receiver of the super-Nyquist system at each moment as input symbols corresponding to the symbols transmitted by the transmitter for symbol estimation;
(2) training the equalizer of the receiver of the super-Nyquist system:
(2a) calculating the error value of the receiver equalizer of the super-Nyquist system according to the following formula:
e(k)＝[d(k)d(k-1)…d(k-ψ+1)]T-YT(k)w*
wherein e (k) represents the error value of the receiver equalizer of the super-Nyquist system at the k-th time, k represents the sequence number of the time corresponding to each input symbol, d (k) represents the known transmission signal corresponding to the symbol in the theta-th tap of the receiver equalizer of the super-Nyquist system at the k-th time,
k represents the total number of taps coefficients of the receiver equalizer of the super-nyquist system, which has an odd number,
denotes a rounding-up operation, psi denotes the number of data reuses of the equalizer of the super-nyquist system receiver, T denotes a transposition operation, y (K) denotes an input symbol matrix of dimension K x psi at the K-th time instant, ykRepresenting the input symbol at the k-th moment, w represents the column vector of the tap coefficient of the equalizer of the receiver of the super-Nyquist system, the initial value is zero vector, and x represents the conjugate operation;
(2b) calculating the tap coefficient vector of the equalizer of the super-Nyquist system receiver according to the following formula:
wherein the content of the first and second substances,
representing a vector of equalizer tap coefficients of a receiver of the super-Nyquist system, mu representing a step size of the receiver of the super-Nyquist system, said step size being a decimal selected in a range of (0,1), H representing a conjugate transpose operation, gamma representing a constant selected in a range of (0,1), E representing a unit matrix having dimensions of psi x psi, ()-1Representing an inversion operation;
(2c) receiver equalizer tap coefficient vector with super-Nyquist system
Updating element values of corresponding positions in a tap coefficient column vector w of the equalizer of the super-Nyquist system receiver before the equalization by each element value in the sequence;
(3) judging whether the current training times of the equalizer of the receiver of the super-Nyquist system is smaller than the threshold value of the equalizer, if so, adding 1 to the current training times and then executing the step (2), otherwise, executing the step (4) after finishing the training of the equalizer;
(4) using input symbol vector ykyk-1… yk-K+1]Multiplying the conjugate vector of the tap coefficient sequence vector w of the receiver equalizer of the super-Nyquist system to obtain a symbol after equalizing the input symbol at the k-theta +1 th moment
(5) The interference cancellation factor of the super-nyquist system is calculated according to the following formula:
Gj＝gP+jτQ(h)
wherein G isjRepresents the jth interference elimination factor in the super-Nyquist system, j represents the serial number of the interference elimination factor, and the value range of j is
Denotes a rounding-down operation, P denotes a total number of all time-domain response coefficients of a receiver matched filter in the super-Nyquist system, τ denotes a super-Nyquist system acceleration factor, said acceleration factor being a fraction selected in the range of (0,1), Q denotes a down-sampling multiple of the matched filter of the system receiver in the super-Nyquist system, said down-sampling multiple being at [2,10 ]]An integer selected in the range represents multiplication operation, g () represents self-convolution operation, h represents the time domain response coefficient of the matched filter of the receiver of the super-Nyquist system generated according to the total time domain response coefficient P of the matched filter of the receiver of the super-Nyquist system and roll-off factors, and subscript P + j tauQ represents the number of the obtained coefficient;
(6) the first iteration eliminates intersymbol interference:
(6a) the intersymbol interference in the input symbol at each time instant at the first iteration is calculated according to the following equation:
wherein, χk-θ-L+1The method comprises the steps of representing intersymbol interference in input symbols at the k-theta-L +1 th moment in the first iteration, calculating the intersymbol interference in symbols before the current input symbol in each iteration due to the fact that the intersymbol interference generated by symbols at the front side and the rear side in each symbol needs to be eliminated, wherein L represents the unilateral symbol length used for symbol estimation in all iteration processes set according to the total number P of time domain response coefficients of a matched filter of a receiver of a super-Nyquist system, and the value range of L is
Representing the symbol after the first iteration of the input symbol at the k-theta-2L +1 th moment;
(6b) using input symbols y at the k-theta-L +1 time instantk-θ-L+1Subtracting the intersymbol interference χ at the first iterationk-θ-L+1Obtaining β a symbol after eliminating intersymbol interference in the first iterationk-θ-L+1；
(6c) Symbol β for intersymbol interference cancellation after first iterationk-θ-L+1Performing hard decision operation to obtain a symbol after first iteration of the input symbol at the k-theta-L +1 th moment
(7) Intersymbol interference is eliminated by iteration:
(7a) the intersymbol interference in the input symbol at the current iteration is calculated according to the following equation:
wherein, χk-θ-cL+1Represents the intersymbol interference in the input symbol at the k-theta-cL +1 th moment of the current iteration, c represents the sequence number of the current iteration,
represents the symbol after the input symbol at the k-theta-cL-L +1 time point is iterated for the same number of times as the current iteration,
representing the symbol after one iteration less than the current iteration times is carried out on the input symbol at the k-theta-cL +2 th moment;
(7b) using input symbols y at the k-theta-cL +1 timek-θ-cL+1Subtracting the intersymbol interference χ at the current iterationk-θ-cL+1Eliminating the intersymbol interference to obtain the symbol β of the input symbol at the k-theta-cL +1 th moment in the current iteration after eliminating the intersymbol interferencek-θ-cL+1；
(7c) Symbol β after eliminating intersymbol interference for input symbol at k-theta-cL +1 time of current iterationk-θ-cL+1Performing hard decision operation to obtain the symbol after current iteration of the input symbol at the k-theta-cL +1 th moment
(8) Judging whether the current iteration number is smaller than an estimation threshold value, if so, adding 1 to the current iteration number and then executing the step (7), otherwise, eliminating the intersymbol interference in each input symbol and terminating the symbol estimation process executing step (9);
(9) obtaining the final estimated symbol:
and taking the estimation symbol after the iteration is terminated as an estimation symbol corresponding to the symbol sent by the transmitter, and finishing the symbol estimation process of the super-Nyquist system.
Compared with the prior art, the invention has the following advantages:
firstly, the equalization is carried out by utilizing the equalizer, and then intersymbol interference is eliminated by iteration on the equalized symbols, so that the problem of poor symbol estimation performance when a high-order modulation mode is selected by the super-Nyquist system or under the condition of more serious intersymbol interference in the prior art is solved, the estimation method has higher estimation precision, can more accurately estimate the transmitted symbols of the super-Nyquist system, and is particularly suitable for the super-Nyquist system under the condition of adopting the high-order modulation mode and more serious intersymbol interference.
Secondly, because the invention eliminates the intersymbol interference through iteration on the basis of equalization, the intersymbol interference is eliminated and is independent of a modulation mode, and the complexity of the equalizer is lower, the problem that the complexity of the prior art is positively correlated with the modulation mode, which causes the complexity to be too high when the high-order modulation mode is selected by the super-Nyquist system is solved, the intersymbol interference of the super-Nyquist system can be eliminated with lower complexity even in the super-Nyquist system adopting the high-order modulation mode, and the invention has stronger practicability.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph of simulation results of the present invention.
Detailed Description
The present invention is described in further detail below with reference to the attached drawing figures.
The steps of the present invention will be described in further detail with reference to fig. 1.
Step 1, obtaining an input symbol.
And receiving the symbols output by the matched filter of the receiver corresponding to the symbols transmitted by the transmitter of the super-Nyquist system in real time, and taking the symbols output by the matched filter of the receiver of the super-Nyquist system at each moment as input symbols corresponding to the symbols transmitted by the transmitter for symbol estimation.
The sending symbols are generated according to a constellation diagram of a super-Nyquist system, and the constellation diagram of the super-Nyquist system is a distribution diagram formed by all the sending symbols after the super-Nyquist system transmitter is modulated.
And 2, training an equalizer of the receiver of the super-Nyquist system.
Calculating the error value of the receiver equalizer of the super-Nyquist system according to the following formula:
e(k)＝[d(k)d(k-1)...d(k-ψ+1)]T-YT(k)w*
wherein e (k) represents the error value of the receiver equalizer of the super-Nyquist system at the k-th time, k represents the sequence number of the time corresponding to each input symbol, d (k) represents the known transmission signal corresponding to the symbol in the theta-th tap of the receiver equalizer of the super-Nyquist system at the k-th time,
k represents the total number of taps coefficients of the receiver equalizer of the super-nyquist system, which has an odd number,
denotes a rounding-up operation, ψ denotes the number of data reuses of an equalizer of a super-nyquist system receiver, T denotes a transposition operation,
input symbol matrix with dimension K x psi representing the K-th time instant, ykDenotes the input symbol at the k-th time instant, w denotes the column vector of the tap coefficients of the equalizer of the super-nyquist system receiver, whose initial value is the zero vector, and x denotes the conjugation operation.
Calculating the tap coefficient vector of the equalizer of the super-Nyquist system receiver according to the following formula:
wherein the content of the first and second substances,
represents a super-nyquist system receiver equalizer tap coefficient vector, mu represents a step size of the super-nyquist system receiver, the step size is a decimal selected in a range of (0,1),h denotes a conjugate transpose operation, γ denotes a constant selected in the range of (0,1), and E denotes an identity matrix having dimensions of ψ × ψ, ()-1Representing an inversion operation.
Receiver equalizer tap coefficient vector with super-Nyquist system
Each element value in the vector updates the element value of the corresponding position in the tap coefficient sequence w of the equalizer of the receiver of the super-Nyquist system before the equalization.
And 3, judging whether the current training times of the equalizer of the receiver of the super-Nyquist system is smaller than an equalizer threshold value, if so, adding 1 to the current training times and then executing the step 2, otherwise, executing the step 4 after finishing the training of the equalizer.
The equalizer threshold is a parameter when the equalizer of the super-Nyquist system receiver terminates training, and the value of the equalizer threshold is as follows: when the acceleration factor of the super-Nyquist system is less than or equal to 0.8 or the roll-off factor of a matched filter of a receiver is less than or equal to 0.3, the training threshold value is 400000; when the acceleration factor of the super-Nyquist system is greater than or equal to 0.9 or the roll-off factor of the matched filter of the receiver is greater than or equal to 0.5, the training threshold value is 10000; in other cases, the training threshold is 200000.
And 5, calculating an interference elimination factor of the super-Nyquist system according to the following formula.
Gj＝gP+jτQ(h)
Wherein G isjRepresents the jth interference elimination factor in the super-Nyquist system, j represents the serial number of the interference elimination factor, and the value range of j is
Denotes a rounding-down operation, P denotes a total number of all time-domain response coefficients of a receiver matched filter in the super-Nyquist system, τ denotes a super-Nyquist system acceleration factor, said acceleration factor being a fraction selected in the range of (0,1), Q denotes a down-sampling multiple of the matched filter of the system receiver in the super-Nyquist system, said down-sampling multiple being at [2,10 ]]The range is selected to be an integer, the integer represents multiplication operation, g () represents self-convolution operation, h represents the time domain response coefficient of the matched filter of the receiver of the super-Nyquist system generated according to the total number P of the time domain response coefficients of the matched filter of the receiver of the super-Nyquist system and a roll-off factor, and a subscript P + j tau Q represents the serial number of the obtained coefficient.
And 6, eliminating intersymbol interference in the first iteration.
The intersymbol interference in the input symbol at each time instant at the first iteration is calculated according to the following equation:
wherein, χk-θ-L+1The method comprises the steps of representing intersymbol interference in input symbols at the k-theta-L +1 th moment in the first iteration, calculating the intersymbol interference in symbols before the current input symbol in each iteration due to the fact that the intersymbol interference generated by symbols at the front side and the rear side in each symbol needs to be eliminated, wherein L represents the unilateral symbol length used for symbol estimation in all iteration processes set according to the total number P of time domain response coefficients of a matched filter of a receiver of a super-Nyquist system, and the value range of L is
Representing the input symbols at the k-theta-2L +1 th time instant after the first iterationAnd (4) a symbol.
Using input symbols y at the k-theta-L +1 time instantk-θ-L+1Subtracting the intersymbol interference χ at the first iterationk-θ-L+1Obtaining β a symbol after eliminating intersymbol interference in the first iterationk-θ-L+1。
Symbol β for intersymbol interference cancellation after first iterationk-θ-L+1Performing hard decision operation to obtain a symbol after first iteration of the input symbol at the k-theta-L +1 th moment
The steps of the hard decision operation are as follows:
step 1, calculating the distance between each symbol in the constellation diagram and the symbol after eliminating the intersymbol interference according to the following formula:
wherein, κiThe distance between the ith symbol in the constellation diagram and the symbol after eliminating the intersymbol interference is represented, i represents the serial number of the symbol in the constellation diagram, and the value range is [1, v ]]V denotes the total number of different symbols in the constellation diagram, siIndicating the ith symbol in the constellation, β indicating the symbol after intersymbol interference cancellation,
the open square root operation is denoted and the conjugate operation is denoted.
And 2, selecting a minimum value from all distances between each symbol in the constellation diagram and the symbol after intersymbol interference elimination, and taking the symbol in the constellation diagram corresponding to the minimum value as the symbol after hard decision.
And 7, eliminating intersymbol interference through iteration.
The intersymbol interference in the input symbol at the current iteration is calculated according to the following equation:
wherein, χk-θ-cL+1Represents the intersymbol interference in the input symbol at the k-theta-cL +1 th moment of the current iteration, c represents the sequence number of the current iteration,
represents the symbol after the input symbol at the k-theta-cL-L +1 time point is iterated for the same number of times as the current iteration,
the symbol after one iteration less than the current iteration number is carried out on the input symbol at the k-theta-cL + 2 th time.
Using input symbols y at the k-theta-cL +1 timek-θ-cL+1Subtracting the intersymbol interference χ at the current iterationk-θ-cL+1Eliminating the intersymbol interference to obtain the symbol β of the input symbol at the k-theta-cL +1 th moment in the current iteration after eliminating the intersymbol interferencek-θ-cL+1。
Symbol β after eliminating intersymbol interference for input symbol at k-theta-cL +1 time of current iterationk-θ-cL+1Performing hard decision operation to obtain the symbol after current iteration of the input symbol at the k-theta-cL +1 th moment
The steps of the hard decision operation are as follows:
step 1, calculating the distance between each symbol in the constellation diagram and the symbol after eliminating the intersymbol interference according to the following formula:
wherein, κiThe distance between the ith symbol in the constellation diagram and the symbol after eliminating the intersymbol interference is represented, i represents the serial number of the symbol in the constellation diagram, and the value range is [1, v ]]V denotes the total number of different symbols in the constellation diagram, siIndicating the ith symbol in the constellation, β indicating the symbol after intersymbol interference cancellation,
the open square root operation is denoted and the conjugate operation is denoted.
And 2, selecting a minimum value from all distances between each symbol in the constellation diagram and the symbol after intersymbol interference elimination, and taking the symbol in the constellation diagram corresponding to the minimum value as the symbol after hard decision.
And 8, judging whether the current iteration frequency is smaller than an estimation threshold value, if so, adding 1 to the current iteration frequency and executing the step 7, otherwise, eliminating the intersymbol interference in each input symbol and terminating the symbol estimation process to execute the step 9.
The estimation threshold refers to a parameter when iteration is terminated, and the value of the estimation threshold is as follows: when the acceleration factor of the super-Nyquist system is less than 0.8 and the roll-off factor of the matched filter of the receiver is less than 0.3, the iteration threshold value is 8; when the acceleration factor of the super-Nyquist system is greater than or equal to 0.9 or the roll-off factor of a matched filter of the receiver is greater than or equal to 0.3, the iteration threshold value is 3; in the remaining cases, the iteration threshold is taken as 6.
And 9, acquiring a final estimated symbol.
And taking the estimation symbol after the iteration is terminated as an estimation symbol corresponding to the symbol sent by the transmitter, and finishing the symbol estimation process of the super-Nyquist system.
The sending symbols are generated according to a constellation diagram of a super-Nyquist system, and the constellation diagram of the super-Nyquist system is a distribution diagram formed by all the sending symbols after the super-Nyquist system transmitter is modulated.
The effect of the present invention will be further explained with the simulation experiment.
1. Simulation conditions are as follows:
the simulation experiment of the invention is carried out under MATLAB 2017B software. In the simulation experiment of the present invention, the total number of all time domain response coefficients of the matched filter of the receiver in the super-nyquist system is 161 and the down-sampling multiple thereof is 10. In the simulation of the symbol estimation method of the super-Nyquist system of the combined equalization and interference cancellation, the acceleration factor of the super-Nyquist system is 0.8, and the roll-off factor of a matched filter of a receiver in the super-Nyquist system is 0.3. In the simulation process, the noise type of the super-Nyquist system is Gaussian white noise.
2. Simulation content and result analysis:
the simulation experiment adopts the invention and two existing methods (frequency domain equalization method, method based on backspacing and interference elimination) to respectively eliminate intersymbol interference of the super-Nyquist system and estimate the transmitted symbol, and the simulation total bit number of single bit signal-to-noise ratio is 1 multiplied by 108The modulation mode of the super-Nyquist system adopts quadrature phase shift keying QPSK (quadrature phase shift keying), eight-system phase shift keying 8-PSK (8 phase shift keying), 16-Amplitude Phase Shift Keying (APSK) (amplitude phase shift keying) and 32/64/128/256-APSK.
To verify the effect of the simulation experiment, the performance of the present invention and two existing methods were evaluated using the bit error rate curves. The method for acquiring the bit error rate curve comprises the following steps: comparing the bit data corresponding to the transmitted symbol and the estimated symbol of the super-nyquist system under the condition of one bit signal-to-noise ratio, counting the total number of different bits in the bit data, and dividing the total number by the total bit number to obtain the simulated bit error rate of the super-nyquist system under the condition of the signal-to-noise ratio, and obtaining 10 different bit error rates by simulating 10 different bit signal-to-noise ratios, and further drawing a bit error rate curve, wherein the simulation result of the simulation experiment is as shown in figure 2.
The horizontal axis in fig. 2 represents the bit signal to noise ratio of the super-nyquist system in db (decibel), and the vertical axis represents the bit error rate of the super-nyquist system. Fig. 2 has 7 solid lines, 7 cross-marked curves, 7 diamond-marked curves, and 7 circular-marked curves, wherein the solid lines represent the theoretical bit error rate curves of the super-nyquist system, and the curves are plotted according to the theoretical bit error rates corresponding to the 7 modulation schemes, and the theoretical bit error rates are theoretically derived optimal bit error rates. The curve denoted by crosses represents the bit error rate curve of the faster-than-nyquist system when the symbols are transmitted, estimated using the prior art frequency domain equalization method. The curve marked with diamonds represents the bit error rate curve for the faster-than-nyquist system when estimating transmitted symbols using the prior art back-off and interference cancellation based method. The curve marked with circles represents the bit error rate curve of the faster-than-nyquist system when the symbols are estimated using the method of the present invention.
Fixing the abscissa in fig. 2, observing and comparing 4 curves (solid line, curve marked with crosses, curve marked with diamonds, and curve marked with circles) using QPSK, it can be known that, under the same bit signal to noise ratio, the position of the corresponding point on the bit error rate curve of the faster-than-nyquist system when symbols are estimated using the method of the present invention is lower than the position of the corresponding point on the bit error rate curve of the faster-than-nyquist system when symbols are estimated using two prior art techniques (frequency domain equalization method, method based on back-off and interference cancellation). By observing and comparing 4 curves adopting any one of the other 6 modulation modes by adopting the same method, the corresponding points on the bit error rate curves using the method of the invention are lower than the corresponding points on the bit error rate curves using the two prior art. This shows that the method of the present invention can estimate the transmitted symbol more accurately in the scene of more serious intersymbol interference of the super-nyquist system, so that the super-nyquist system has better bit error rate performance.
Claims (5)
1. A method for estimating symbols of a super-Nyquist system by combining equalization and interference cancellation is characterized in that equalization operation is carried out once after symbols output by a matched filter of a receiver of the super-Nyquist system are obtained to obtain equalized symbols, and intersymbol interference is cancelled on the equalized symbols through iteration, and the method comprises the following steps:
(1) obtaining input symbols:
receiving symbols output by a matched filter of a receiver corresponding to symbols transmitted by a transmitter of the super-Nyquist system in real time, and taking the symbols output by the matched filter of the receiver of the super-Nyquist system at each moment as input symbols corresponding to the symbols transmitted by the transmitter for symbol estimation;
(2) training the equalizer of the receiver of the super-Nyquist system:
(2a) calculating the error value of the receiver equalizer of the super-Nyquist system according to the following formula:
e(k)＝[d(k)d(k-1)...d(k-ψ+1)]T-YT(k)w*
wherein e (k) represents the error value of the receiver equalizer of the super-Nyquist system at the k-th time, k represents the sequence number of the time corresponding to each input symbol, d (k) represents the known transmission signal corresponding to the symbol in the theta-th tap of the receiver equalizer of the super-Nyquist system at the k-th time,
k represents the total number of taps coefficients of the receiver equalizer of the super-nyquist system, which has an odd number,
denotes a rounding-up operation, psi denotes the number of data reuses of the equalizer of the super-nyquist system receiver, T denotes a transposition operation, y (K) denotes an input symbol matrix of dimension K x psi at the K-th time instant, ykRepresenting the input symbol at the k-th moment, w represents the column vector of the tap coefficient of the equalizer of the receiver of the super-Nyquist system, the initial value is zero vector, and x represents the conjugate operation;
(2b) calculating the tap coefficient vector of the equalizer of the super-Nyquist system receiver according to the following formula:
wherein the content of the first and second substances,
representing a tap coefficient vector of an equalizer of a super-Nyquist system receiver, mu representing a step size of the super-Nyquist system receiver, the step size being a decimal selected in a range of (0,1), H representing a conjugate transpose operation, gamma representing a constant selected in a range of (0,1), and E representing a unit having a dimension of ψ x ψMatrix, ()-1Representing an inversion operation;
(2c) receiver equalizer tap coefficient vector with super-Nyquist system
Updating element values of corresponding positions in a tap coefficient column vector w of the equalizer of the super-Nyquist system receiver before the equalization by each element value in the sequence;
(3) judging whether the current training times of the equalizer of the receiver of the super-Nyquist system is smaller than the threshold value of the equalizer, if so, adding 1 to the current training times and then executing the step (2), otherwise, executing the step (4) after finishing the training of the equalizer;
(4) using input symbol vector ykyk-1…yk-K+1]Multiplying the conjugate vector of the tap coefficient sequence vector w of the receiver equalizer of the super-Nyquist system to obtain a symbol after equalizing the input symbol at the k-theta +1 th moment
(5) The interference cancellation factor of the super-nyquist system is calculated according to the following formula:
Gj＝gP+jτQ(h)
wherein G isjRepresents the jth interference elimination factor in the super-Nyquist system, j represents the serial number of the interference elimination factor, and the value range of j is
Denotes a rounding-down operation, P denotes a total number of all time-domain response coefficients of a receiver matched filter in the super-Nyquist system, τ denotes a super-Nyquist system acceleration factor, said acceleration factor being a fraction selected in the range of (0,1), Q denotes a down-sampling multiple of the matched filter of the system receiver in the super-Nyquist system, said down-sampling multiple being at [2,10 ]]An integer selected in the range represents multiplication operation, g () represents self-convolution operation, h represents a time domain response coefficient of the matched filter of the receiver of the super-Nyquist system generated according to the total number P of the time domain response coefficients of the matched filter of the receiver of the super-Nyquist system and a roll-off factor, and a subscript P + j tau Q represents the serial number of the obtained coefficient;
(6) the first iteration eliminates intersymbol interference:
(6a) the intersymbol interference in the input symbol at each time instant at the first iteration is calculated according to the following equation:
wherein, χk-θ-L+1The method comprises the steps of representing intersymbol interference in input symbols at the k-theta-L +1 th moment in the first iteration, calculating the intersymbol interference in symbols before the current input symbol in each iteration due to the fact that the intersymbol interference generated by symbols at the front side and the rear side in each symbol needs to be eliminated, wherein L represents the unilateral symbol length used for symbol estimation in all iteration processes set according to the total number P of time domain response coefficients of a matched filter of a receiver of a super-Nyquist system, and the value range of L is
Representing the symbol after the first iteration of the input symbol at the k-theta-2L +1 th moment;
(6b) using input symbols y at the k-theta-L +1 time instantk-θ-L+1Subtracting the intersymbol interference χ at the first iterationk-θ-L+1Obtaining β a symbol after eliminating intersymbol interference in the first iterationk-θ-L+1；
(6c) Symbol β for intersymbol interference cancellation after first iterationk-θ-L+1Performing hard decision operation to obtain a symbol after first iteration of the input symbol at the k-theta-L +1 th moment
(7) Intersymbol interference is eliminated by iteration:
(7a) the intersymbol interference in the input symbol at the current iteration is calculated according to the following equation:
wherein, χk-θ-cL+1Represents the intersymbol interference in the input symbol at the k-theta-cL +1 th moment of the current iteration, c represents the sequence number of the current iteration,
represents the symbol after the input symbol at the k-theta-cL-L +1 time point is iterated for the same number of times as the current iteration,
representing the symbol after one iteration less than the current iteration times is carried out on the input symbol at the k-theta-cL +2 th moment;
(7b) using input symbols y at the k-theta-cL +1 timek-θ-cL+1Subtracting the intersymbol interference χ at the current iterationk-θ-cL+1Eliminating the intersymbol interference to obtain the symbol β of the input symbol at the k-theta-cL +1 th moment in the current iteration after eliminating the intersymbol interferencek-θ-cL+1；
(7c) Symbol β after eliminating intersymbol interference for input symbol at k-theta-cL +1 time of current iterationk-θ-cL+1Performing hard decision operation to obtain the symbol after current iteration of the input symbol at the k-theta-cL +1 th moment
(8) Judging whether the current iteration number is smaller than an estimation threshold value, if so, adding 1 to the current iteration number and then executing the step (7), otherwise, eliminating the intersymbol interference in each input symbol and terminating the symbol estimation process executing step (9);
(9) obtaining the final estimated symbol:
and taking the estimation symbol after the iteration is terminated as an estimation symbol corresponding to the symbol sent by the transmitter, and finishing the symbol estimation process of the super-Nyquist system.
2. The method for joint equalization and interference cancellation faster-than-nyquist system symbol estimation according to claim 1, wherein: the sending symbols in the step (1) and the step (9) are generated according to a constellation diagram of a super-nyquist system, wherein the constellation diagram of the super-nyquist system is a distribution diagram formed by all the sending symbols after the constellation of a transmitter of the super-nyquist system is modulated.
3. The method for joint equalization and interference cancellation faster-than-nyquist system symbol estimation according to claim 1, wherein: the equalizer threshold in step (3) refers to a parameter when the equalizer of the super-nyquist system receiver terminates training, and the value of the parameter is as follows: when the acceleration factor of the super-Nyquist system is less than or equal to 0.8 or the roll-off factor of a matched filter of a receiver is less than or equal to 0.3, the training threshold value is 400000; when the acceleration factor of the super-Nyquist system is greater than or equal to 0.9 or the roll-off factor of the matched filter of the receiver is greater than or equal to 0.5, the training threshold value is 10000; in other cases, the training threshold is 200000.
4. The method for joint equalization and interference cancellation faster-than-nyquist system symbol estimation according to claim 1, wherein: the hard decision operation in step (6c) and step (7c) comprises the following steps:
firstly, calculating the distance between each symbol in the constellation diagram and the symbol after eliminating the intersymbol interference according to the following formula:
wherein, κiRepresenting the symbol between the ith symbol and the symbol after intersymbol interference cancellation in a constellation diagramThe distance i represents the serial number of the symbol in the constellation diagram and has a value range of [1, v]V denotes the total number of different symbols in the constellation diagram, siIndicating the ith symbol in the constellation, β indicating the symbol after intersymbol interference cancellation,
represents the open square root operation and represents the conjugate operation;
and secondly, selecting a minimum value from all distances between each symbol in the constellation diagram and the symbol subjected to intersymbol interference elimination, and taking the symbol in the constellation diagram corresponding to the minimum value as the symbol subjected to hard decision.
5. The method for joint equalization and interference cancellation faster-than-nyquist system symbol estimation according to claim 1, wherein: the estimation threshold value in step (8) refers to a parameter when iteration is terminated, and the value of the estimation threshold value is as follows: when the acceleration factor of the super-Nyquist system is less than 0.8 and the roll-off factor of the matched filter of the receiver is less than 0.3, the iteration threshold value is 8; when the acceleration factor of the super-Nyquist system is greater than or equal to 0.9 or the roll-off factor of a matched filter of the receiver is greater than or equal to 0.3, the iteration threshold value is 3; in the remaining cases, the iteration threshold is taken as 6.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910013077.5A CN109547370B (en) | 2019-01-07 | 2019-01-07 | Symbol estimation method of super-Nyquist system based on joint equalization and interference cancellation |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910013077.5A CN109547370B (en) | 2019-01-07 | 2019-01-07 | Symbol estimation method of super-Nyquist system based on joint equalization and interference cancellation |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109547370A CN109547370A (en) | 2019-03-29 |
| CN109547370B true CN109547370B (en) | 2020-06-05 |
Family
ID=65834455
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910013077.5A Active CN109547370B (en) | 2019-01-07 | 2019-01-07 | Symbol estimation method of super-Nyquist system based on joint equalization and interference cancellation |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109547370B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110149287B (en) * | 2019-06-18 | 2021-06-25 | 西安电子科技大学 | Linear precoding-based super-Nyquist system and symbol estimation method thereof |
| CN112235217B (en) * | 2020-10-16 | 2023-02-03 | 兰州理工大学 | Self-adaptive pre-equalization method based on wireless optical fiber to the home (FTN) communication system |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106549892A (en) * | 2016-11-22 | 2017-03-29 | 北京理工大学 | A kind of joint time-frequency doubly selective channel is estimated and super Nyquist signal detecting method |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR102455847B1 (en) * | 2016-07-29 | 2022-10-19 | 한국전자통신연구원 | Apparatus for receiving signal based on faster-than-nyquist and method for using the same |
-
2019
- 2019-01-07 CN CN201910013077.5A patent/CN109547370B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106549892A (en) * | 2016-11-22 | 2017-03-29 | 北京理工大学 | A kind of joint time-frequency doubly selective channel is estimated and super Nyquist signal detecting method |
Non-Patent Citations (2)
| Title |
|---|
| REDUCED COMPLEXITY OPTIMAL DETECTION OF BINARY FASTER-THAN-NTQUIST SIGNALING;EBRAHIM BEDEER；HALIM YANIKOMEROGLU；MOHAMED HOSSAM AHMED;<2017 IEEE INTERNATIONAL CONFERENCE ON COMMUNICATIONS(ICC)>;IEEE;20170731 * |
| 多径信道下基于频域均衡的超奈奎斯特传输;王志峰 白勇 唐啸宇 黄梦醒;《高技术通讯》;20170730;第27卷(第7期);619-624 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109547370A (en) | 2019-03-29 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110266617B (en) | Multipath channel estimation method of super-Nyquist system | |
| CN110149287B (en) | Linear precoding-based super-Nyquist system and symbol estimation method thereof | |
| CN109246039B (en) | Soft information iteration receiving method based on bidirectional time domain equalization | |
| EP1856797B1 (en) | Wireless communications device performing block equalization based upon prior, current and/or future autocorrelation matrix estimates and related methods | |
| EP2420033B1 (en) | Method and receiver for jointly decoding received communication signals using maximum likelihood detection | |
| CN112866151B (en) | Underwater sound MPSK signal blind Turbo equalization method based on channel blind estimation | |
| CN112003804B (en) | Multipath multivariate differential chaotic shift keying iterative receiving method | |
| CN109547370B (en) | Symbol estimation method of super-Nyquist system based on joint equalization and interference cancellation | |
| CN108600140B (en) | Anti-impulse interference channel estimation method in OFDM system | |
| US20030115061A1 (en) | MPSK equalizer | |
| CN110753011B (en) | Single carrier equalization method for GMSK signal | |
| CN109861939B (en) | OQPSK frequency domain equalization wireless data transmission method | |
| US8189709B2 (en) | Frequency domain equalization method for continuous phase modulated signals | |
| CN110324271A (en) | A kind of F-OFDM system transceiver design method of compressed sensing based clipping | |
| US20130064282A1 (en) | Frequency-domain equalization and combining for single carrier transmission | |
| CN109743271B (en) | Symbol estimation method of super-Nyquist system based on iterative interference cancellation | |
| CN109818894B (en) | GMSK signal detection method and detection device under multipath channel | |
| AU765972B2 (en) | Method and apparatus for interference rejection | |
| Raphaeli | A reduced complexity equalizer for OQPSK | |
| CN108521311B (en) | Signal-to-noise ratio estimation method based on Gray sequence | |
| CN110912651A (en) | FTN index modulation signal detection method | |
| CN116633737B (en) | Low-complexity SVD precoding method for super Nyquist system | |
| CN116668246B (en) | Frequency domain equalization method of super Nyquist system without cyclic prefix | |
| CN1443011A (en) | Equilized demodulation method used in mobile communication system | |
| Xu et al. | Low-complexity fractional-spaced equalization approach in the frequency domain for CPM |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |