CN116633735A - GMD pre-coding method of super Nyquist system with higher estimation precision - Google Patents
GMD pre-coding method of super Nyquist system with higher estimation precision Download PDFInfo
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- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
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Abstract
The application discloses a GMD pre-coding method of a super Nyquist system with higher estimation precision, which comprises the steps of obtaining a sending symbol block and an intersymbol interference matrix; GMD decomposition is carried out on the intersymbol interference matrix to generate a unitary matrix and an upper triangular matrix; GMD precoding is carried out on the sent symbol blocks through an upper triangular matrix; adding a cyclic prefix and a cyclic suffix to the precoded transmitting symbol blocks, and performing baseband forming and transmitting; receiving a transmitted symbol block, and sequentially carrying out matched filtering, downsampling and cyclic prefix and cyclic suffix removal on the received symbol block; GMD decoding is carried out on the symbol blocks with the cyclic prefix and the cyclic postfix removed through the unitary matrix, and estimated symbol blocks are generated. Through the technical scheme, the symbol estimation precision of the super Nyquist system can be improved, and the bit error rate performance of the super Nyquist system can be improved.
Description
Technical Field
The application relates to the technical field of communication, in particular to a GMD pre-coding method of a super Nyquist system with higher estimation precision, which can be used for the design of a transmission scheme of the super Nyquist system.
Background
In designing a conventional communication system, the communication system complies with the nyquist first criterion 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 super-Nyquist (FTN) system can support higher transmission rates and spectral efficiency. Accordingly, the super nyquist system requires higher complexity to cancel the intersymbol interference, thereby estimating the transmitted symbols of the super nyquist system transmitter.
Shinya Sugiura, in its published paper "Frequency-domain equalization of faster-than-Nyquist signaling" (IEEE wireless communications letters,2013, 2:555-558), proposes a cyclic prefix-based Frequency domain equalization method that fully considers colored noise in the super Nyquist system and performs noise whitening on it using minimum mean square error criteria, and can effectively eliminate intersymbol interference in the case of low-order modulation mode, with good bit error rate performance. The method has the defects that when the super Nyquist system adopts a modulation mode with higher order, the symbol estimation accuracy is lower, and the bit error rate performance is poor.
Guo Mingxi, et al, of the university of Chinese's Jib's paper "Simulation of precoding algorithms based on matrix decomposition for faster-than-Nyquist signaling" (Wireless and optical communication conference,2016,1-5) proposes a precoding method based on geometric mean decomposition (Geometric Mean Decomposition, GMD) that directly divides the transmitted symbols into symbol blocks, then performs GMD decomposition on the intersymbol interference matrix, and performs precoding with the aid of the GMD decomposition result. The method has the defects that the constructed intersymbol interference matrix is incomplete, so that the method cannot effectively eliminate the intersymbol interference, and therefore, the symbol estimation precision is low, and the bit error rate performance is poor.
The university of western electronic technology Gong Fengkui et al in its published paper "Beyond DVB-S2X: fast-than-Nyquist signaling with linear precoding" (IEEE transactions on broadcasting,2020, 66: 620-629) proposes a cyclic prefix and cyclic suffix based singular value decomposition precoding method that inserts a cyclic prefix and a cyclic suffix respectively in the front and rear of each transmitted symbol block and constructs an accurate intersymbol interference matrix, then performs singular value decomposition on it, and implements precoding by means of the matrix decomposition result, thereby eliminating intersymbol interference. The method has the defects that the symbol energy cannot be distributed evenly, so that the symbol estimation accuracy is low and the bit error rate performance is poor.
Disclosure of Invention
In order to solve the problems in the prior art, the application provides a super Nyquist system GMD precoding method based on a cyclic prefix and a cyclic suffix, which constructs a complete intersymbol interference matrix to improve the symbol estimation precision of the super Nyquist system and improve the bit error rate performance of the super Nyquist system.
In order to achieve the technical purpose, the application provides the following technical scheme: the GMD pre-coding method of the super Nyquist system with higher estimation precision comprises the following steps:
acquiring a sending symbol block and an intersymbol interference matrix;
GMD decomposition is carried out on the intersymbol interference matrix to generate a unitary matrix and an upper triangular matrix;
GMD precoding is carried out on the sending symbol block through an upper triangular matrix;
adding a cyclic prefix and a cyclic suffix to the precoded transmitting symbol block, and performing baseband forming and transmitting;
receiving a transmitted symbol block, and sequentially carrying out matched filtering, downsampling and cyclic prefix and cyclic suffix removal on the received symbol block;
GMD decoding is carried out on the symbol blocks with the cyclic prefix and the cyclic postfix removed through the unitary matrix, and estimated symbol blocks are generated.
Optionally, the acquiring process of the sending symbol block includes:
and obtaining bit data, mapping the bit data to obtain a transmission symbol, and dividing the transmission symbol to generate a transmission symbol block.
Optionally, the process of obtaining the intersymbol interference matrix includes:
and acquiring an intersymbol interference factor, and acquiring an intersymbol interference matrix according to the intersymbol interference factor and the length of a transmitted symbol block.
Optionally, the process of GMD decomposition of the intersymbol interference matrix includes:
G＝QRP H
wherein Q and P are respectively different unitary matrices, R is an upper triangular matrix, and the superscript H represents conjugate transpose operation.
Optionally, for the transmitted symbol block a k The process of GMD precoding includes:
s k ＝Pa k
wherein ,sk Representing the kth precoded block of transmitted symbols of the super nyquist system transmitter.
Optionally, the process of adding the cyclic prefix and the cyclic suffix includes:
inserting a cyclic prefix and a cyclic suffix into a front portion and a rear portion of the precoded transmission symbol block, respectively, wherein the cyclic prefix and the cyclic suffix are a rearmost and a foremost portion of the precoded transmission symbol block, respectivelyColumn vectors of individual symbols, < >>Representing the single-sided length of the intersymbol interference of the super nyquist system.
Optionally, the process of removing the cyclic prefix and the cyclic suffix includes:
deleting the front most and rear most symbol blocks after downsamplingAnd obtaining symbol blocks with the cyclic prefix and the cyclic suffix removed.
Optionally, for symbol block r from which cyclic prefix and cyclic suffix are removed k GMD decoding:
wherein ,representing the kth estimated symbol block of the receiver of the super nyquist system after intersymbol interference cancellation, (·) -1 Representing matrix inversion.
The application has the following technical effects:
the application inserts the cyclic prefix and the cyclic suffix at the front part and the rear part of the pre-coding symbol block respectively, fully considers the interference of the cyclic prefix and the cyclic suffix to the transmitting symbol block, constructs a complete intersymbol interference matrix, carries out GMD decomposition by means of the accurate intersymbol interference matrix, and respectively realizes GMD pre-coding and decoding at a super Nyquist system transmitter and a receiver by the aid of the complete intersymbol interference matrix, thereby eliminating intersymbol interference, recovering the transmitting symbol, overcoming the problem of poor symbol estimation performance in the prior art and realizing better bit error rate performance.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a block diagram of a super Nyquist system;
FIG. 2 is a flow chart of an implementation of the present application for symbol estimation based on the system of FIG. 1;
fig. 3 is a diagram of simulation results of symbol estimation under QPSK, 8-PSK, and 16-APSK conditions using the method of the present application, where (a) is a diagram of simulation results of symbol estimation using QPSK as its modulation scheme; (b) A simulation result diagram for carrying out symbol estimation by adopting 8-PSK as a modulation mode; (c) A simulation result diagram for carrying out symbol estimation by adopting 16-APSK as a modulation mode;
FIG. 4 is a diagram of simulation results of symbol estimation under the conditions of 32-APSK, 64-APSK, 128-APSK and 256-APSK using the method of the application, wherein (a) is a diagram of simulation results of symbol estimation using 32-APSK as its modulation scheme; (b) A simulation result diagram for carrying out symbol estimation by adopting 64-APSK as a modulation mode; (c) A simulation result diagram for carrying out symbol estimation by adopting 128-APSK as a modulation mode; (d) The simulation result diagram is used for carrying out symbol estimation by adopting 256-APSK as a modulation mode.
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
Aiming at the defects of the prior art, the application provides a GMD pre-coding method of a super Nyquist system based on a cyclic prefix and a cyclic suffix, which constructs a complete intersymbol interference matrix to improve the symbol estimation precision of the super Nyquist system and improve the bit error rate performance of the super Nyquist system.
The method comprises the steps of inserting a cyclic prefix and a cyclic suffix after precoding of a transmitter of a super Nyquist system, converting an intersymbol interference matrix after precoding of the super Nyquist system into a circularly symmetric matrix, performing GMD decomposition on the intersymbol interference matrix, and performing GMD precoding based on the GMD decomposition to eliminate intersymbol interference.
According to the above thought, the implementation steps of the application are as follows:
1) Dividing a transmitting symbol of a super Nyquist system after constellation mapping into a transmitting symbol block a with the length L k, wherein ak The column vector represents the kth transmitted symbol block, k is more than or equal to 1 and less than or equal to N, and N represents the total number of transmitted symbol blocks;
2) Obtaining an intersymbol interference matrix G of a super Nyquist system;
3) GMD decomposition is carried out on the intersymbol interference matrix:
G＝QRP H
wherein Q and P are different unitary matrices, R is an upper triangular matrix, and the upper label H represents conjugate transposition operation;
4) For each transmitted symbol block a of the super Nyquist system transmitter, according to k Precoding:
s k ＝Pa k
wherein ,sk Representing a kth precoded block of transmitted symbols of the super nyquist system transmitter;
5) Transmitting symbol block s pre-coded at transmitter k The front part and the rear part are respectively inserted with a cyclic prefix f k And suffix b k ，f k and bk Respectively represent s k Rearmost and frontmostColumn vectors of individual symbols, < >>Single side length representing intersymbol interference of the super Nyquist system and then obtaining a block of transmitted symbols with cyclic prefix and cyclic suffix added +.>
6) Acquiring downsampled received symbolsDelete received symbol block->Foremost and rearmost +.>Symbols, obtaining deleted cyclic prefix and cyclic postfixReceiving symbol block r k ；
7) For symbol blocks r with cyclic prefixes and cyclic suffixes deleted, according to the following k GMD decoding is performed and estimated symbols are obtained:
wherein ,represents the kth estimated symbol block of the receiver of the super nyquist system, (·) -1 Representing matrix inversion.
The technical scheme is described in detail with reference to the accompanying drawings:
referring to fig. 1, the super nyquist system adopted in the present application mainly comprises a data source, constellation mapping, GMD precoding, cyclic prefix and cyclic suffix insertion, baseband shaping, channel, matched filtering, cyclic prefix and cyclic suffix deletion, GMD decoding, demapping and bit error rate module, wherein:
the data source module generates bit data required to be transmitted by the transmission system and transmits the bit data to the constellation mapping module;
the constellation mapping module maps the bit data into symbols according to constellation mapping rules and transmits the mapped symbols to the GMD precoding module;
the GMD pre-coding module divides the symbol after constellation mapping into symbol blocks, then performs GMD pre-coding by utilizing a pre-coding matrix, and transmits the pre-coded symbol blocks to the cyclic prefix and cyclic suffix inserting module;
a cyclic prefix and cyclic suffix module is inserted, a cyclic prefix and a cyclic suffix are respectively inserted in the front part and the rear part of the pre-coded symbol block, and the symbol block inserted with the cyclic prefix and the cyclic suffix is transmitted to a baseband forming module;
the baseband forming module performs FTN forming on the symbol block inserted with the cyclic prefix and the cyclic postfix, and transmits the symbol after baseband forming to the channel module;
the channel module is used for adding Gaussian white noise to the symbol after the baseband forming to simulate a channel environment and transmitting the symbol after the Gaussian white noise addition to the matched filtering module;
the matched filtering module performs matched filtering operation on the symbol added with Gaussian white noise, then performs downsampling, and transmits the downsampled symbol to the cyclic prefix and cyclic suffix removal module;
a module for deleting the cyclic prefix and cyclic suffix, deleting the cyclic prefix and cyclic suffix in the filtered symbol, and transmitting the symbol with the cyclic prefix and cyclic suffix deleted to the GMD decoding module;
the GMD decoding module eliminates intersymbol interference in the symbols by using a GMD decoding matrix, estimates the transmitted symbols, and transmits the estimated symbols to the demapping module;
the demapping module restores the estimated symbol into bit data and transmits the bit data to the bit error rate module;
and the bit error rate module is used for counting the bit error rate of the bit data recovered by the demapping module.
Referring to fig. 2, the implementation steps of GMD precoding using the above-mentioned ultranyquist system of the present application are as follows:
and step 1, dividing the sending symbol blocks.
Acquiring a transmitting symbol of a super Nyquist system after constellation mapping, and dividing the transmitting symbol into a transmitting symbol block a with the length L k, wherein ak And the column vector represents the kth transmitted symbol block, k is more than or equal to 1 and less than or equal to N, and N represents the total number of the transmitted symbol blocks.
And step 2, obtaining an intersymbol interference matrix of the super Nyquist system.
Transmitted symbol block length L and intersymbol interference factor g in accordance with the super Nyquist system j By means of the cyclic symmetry characteristic, an intersymbol interference matrix G of the super Nyquist system is obtained:
where j denotes the sequence number of the intersymbol interference factor and lxl denotes the dimension of the intersymbol interference matrix G.
And 3, performing GMD decomposition on the intersymbol interference matrix.
GMD decomposition of the intersymbol interference matrix of the nyquist system is performed according to the following:
G＝QRP H
wherein, Q and P are unitary matrices, R is an upper triangular matrix, and the upper label H represents conjugate transpose operation.
And 4, performing GMD precoding on the sending symbol block.
For each transmitted symbol block a of the super Nyquist system transmitter, according to k Precoding:
s k ＝Pa k
wherein ,sk Representing the kth precoded block of transmitted symbols of the super nyquist system transmitter.
And 5, inserting a cyclic prefix and a cyclic postfix by the transmitter.
Transmitting symbol block s pre-coded at transmitter k The front part and the rear part are respectively inserted with a cyclic prefix f k And suffix b k ，f k and bk Respectively represent s k Rearmost and frontmostColumn vectors of individual symbols, < >>Single side length representing intersymbol interference of the super Nyquist system and then obtaining a block of transmitted symbols with cyclic prefix and cyclic suffix added +.>
And 6, deleting the cyclic prefix and the cyclic postfix by the receiver.
Receiving symbol block after obtaining downsampled by receiver of super Nyquist systemDelete received symbol block->Foremost and rearmost +.>The symbol blocks r of the cyclic prefix and the cyclic suffix are obtained k 。
And 7, performing GMD decoding by the receiver of the super Nyquist system.
For symbol block r with cyclic prefix and cyclic postfix deleted k GMD decoding is performed and estimated symbols are obtained:
wherein ,representing the kth estimated symbol block of the receiver of the super nyquist system after intersymbol interference cancellation, (·) -1 Representing matrix inversion.
The effects of the present application will be further described with reference to simulation experiments.
1. Simulation conditions:
the simulation experiments of the present application were performed under MATLAB 2022B software. In the simulation experiment of the application, the total number P of time domain response coefficients of receiver matched filtering in the super Nyquist system is 201, the downsampling multiple B is 10, and the length of a transmitting symbol block is 512.
The acceleration factor of the super Nyquist system is set to be 0.9, and the matched filter roll-off factor of the receiver in the super Nyquist system is set to be 0.25.
Setting the simulated total bit number of single bit signal-to-noise ratio to be 1×10 7 。
2. Simulation content and result analysis:
simulation 1, under the above conditions, adopts QPSK, 8-PSK and 16-APSK as modulation modes, and respectively carries out symbol estimation by using the method and the existing singular value decomposition precoding method and GMD precoding method, and the result is shown in figure 3, wherein:
fig. 3 (a) is a diagram of simulation results of symbol estimation using QPSK as its modulation scheme;
fig. 3 (b) is a diagram of simulation results of symbol estimation using 8-PSK as its modulation scheme;
fig. 3 (c) is a diagram of simulation results of symbol estimation using 16-APSK as the modulation scheme.
Simulation 2, under the above conditions, adopting 32-APSK, 64-APSK, 128-APSK and 256-APSK as modulation modes, and respectively performing symbol estimation by using the method and the existing singular value decomposition precoding method and GMD precoding method, wherein the result is shown in fig. 4, and the method comprises the following steps:
fig. 4 (a) is a diagram of simulation results of symbol estimation using 32-APSK as its modulation scheme;
fig. 4 (b) is a diagram of simulation results of symbol estimation using 64-APSK as its modulation scheme;
fig. 4 (c) is a diagram of simulation results of symbol estimation using 128-APSK as its modulation scheme;
fig. 4 (d) is a simulation result diagram of symbol estimation using 256-APSK as its modulation scheme.
The horizontal axis in fig. 3 and 4 represents the bit signal-to-noise ratio of the nyquist system in dB (decibel), and the vertical axis represents the bit error rate of the nyquist system.
As can be seen from fig. 3 and fig. 4, for all modulation modes, the bit error rate curve using the method of the present application is lower than the bit error rate curve using the existing singular value decomposition precoding method and GMD precoding method, which indicates that the method of the present application can more accurately estimate the transmitted symbol in the nyquist system, so that the nyquist system has better bit error rate performance, and the higher the modulation mode adopted by the nyquist system, the more significant the bit error rate performance advantage of the present application.
The present application is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present application are intended to be included in the scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.
Claims (8)
1. The GMD pre-coding method of the super Nyquist system with higher estimation precision is characterized by comprising the following steps:
acquiring a sending symbol block and an intersymbol interference matrix;
GMD decomposition is carried out on the intersymbol interference matrix to generate a unitary matrix and an upper triangular matrix;
GMD precoding is carried out on the sending symbol block through an upper triangular matrix;
adding a cyclic prefix and a cyclic suffix to the precoded transmitting symbol block, and performing baseband forming and transmitting;
receiving a transmitted symbol block, and sequentially carrying out matched filtering, downsampling and cyclic prefix and cyclic suffix removal on the received symbol block;
GMD decoding is carried out on the symbol blocks with the cyclic prefix and the cyclic postfix removed through the unitary matrix, and estimated symbol blocks are generated.
2. The super nyquist system GMD precoding method of claim 1, wherein:
the process for acquiring the sending symbol block comprises the following steps:
and obtaining bit data, mapping the bit data to obtain a transmission symbol, and dividing the transmission symbol to generate a transmission symbol block.
3. The super nyquist system GMD precoding method of claim 1, wherein:
the process for obtaining the intersymbol interference matrix comprises the following steps:
and acquiring an intersymbol interference factor, and acquiring an intersymbol interference matrix according to the intersymbol interference factor and the length of a transmitted symbol block.
4. The super nyquist system GMD precoding method of claim 1, wherein:
the process of GMD decomposition of the intersymbol interference matrix includes:
G＝QRP H
wherein Q and P are respectively different unitary matrices, R is an upper triangular matrix, and the superscript H represents conjugate transpose operation.
5. The super nyquist system GMD precoding method of claim 1, wherein:
for transmitting symbol block a k The process of GMD precoding includes:
s k ＝Pa k
wherein ,sk Representing the kth precoded block of transmitted symbols of the super nyquist system transmitter.
6. The super nyquist system GMD precoding method of claim 1, wherein:
the process of adding the cyclic prefix and the cyclic suffix comprises the following steps:
inserting a cyclic prefix and a cyclic suffix into a front portion and a rear portion of the precoded transmission symbol block, respectively, wherein the cyclic prefix and the cyclic suffix are a rearmost and a foremost portion of the precoded transmission symbol block, respectivelyColumn vectors of individual symbols, < >>Representing the single-sided length of the intersymbol interference of the super nyquist system.
7. The method of GMD precoding for the super nyquist system of claim 6, wherein:
the process of removing the cyclic prefix and cyclic suffix includes:
under deletionThe front most and rear most symbol blocks after samplingAnd obtaining symbol blocks with the cyclic prefix and the cyclic suffix removed.
8. The super nyquist system GMD precoding method of claim 1, wherein:
for symbol block r with cyclic prefix and cyclic postfix removed k GMD decoding:
wherein ,representing the kth estimated symbol block of the receiver of the super nyquist system after intersymbol interference cancellation, (·) -1 Representing matrix inversion.
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| US20160308697A1 (en) * | 2013-12-09 | 2016-10-20 | Telefonaktiebolaget Lm Ericsson (Publ) | Pre-Coding in a Faster-Than-Nyquist Transmission System |
| CN110149287A (en) * | 2019-06-18 | 2019-08-20 | 西安电子科技大学 | Super Nyquist system and its symbol estimation method based on linear predictive coding |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US20160308697A1 (en) * | 2013-12-09 | 2016-10-20 | Telefonaktiebolaget Lm Ericsson (Publ) | Pre-Coding in a Faster-Than-Nyquist Transmission System |
| CN110149287A (en) * | 2019-06-18 | 2019-08-20 | 西安电子科技大学 | Super Nyquist system and its symbol estimation method based on linear predictive coding |
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