CN116633737B - Low-complexity SVD precoding method for super Nyquist system - Google Patents
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Abstract
The invention discloses a low-complexity SVD precoding method aiming at a super Nyquist system, which comprises the steps of obtaining a sending symbol block and an intersymbol interference matrix; SVD decomposition is carried out on the intersymbol interference matrix to obtain a diagonal matrix; SVD pre-coding is carried out on the sent symbol blocks; adding a cyclic prefix and a cyclic suffix to the precoded transmitting symbol blocks, and transmitting after baseband shaping; receiving a transmitted symbol block, and sequentially carrying out matched filtering, downsampling and cyclic prefix and cyclic suffix removal on the received symbol block; and carrying out SVD decoding on the symbol blocks with the cyclic prefix and the cyclic suffix removed through the diagonal matrix to obtain estimated symbol blocks. Through the technical scheme, the complexity of the super Nyquist system is improved, the symbol estimation precision of the super Nyquist system is improved, and the bit error rate performance of the super Nyquist system is improved.
Description
Technical Field
The invention relates to the technical field of communication, in particular to a low-complexity SVD precoding method aiming at a super-Nyquist system, 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 a high-order modulation mode is adopted by the super Nyquist system, the symbol estimation accuracy is low, and the bit error rate performance is poor.
Ebrahim Bedeer in its published paper "A very low complexity successive symbol-by-symbol sequence estimator for faster-thian-Nyquist signaling" (IEEE access,2017, 5:7414-7422) proposes a low complexity symbol estimation method based on back-off repetition estimation. The method firstly utilizes the symbol estimated before to estimate the current received symbol, and then utilizes the estimated symbol of the current symbol to re-estimate a plurality of symbols at the front end of the current estimated symbol. The method has lower complexity, and can effectively eliminate the intersymbol interference of the super Nyquist system under the condition of light intersymbol interference. The disadvantage of this method is that the performance of bit error rate is poor when the super nyquist system adopts a high order modulation scheme or under severe intersymbol interference conditions (the super nyquist acceleration factor is smaller or the receiver matched filtering adopts a smaller roll factor).
The university of the Chinese people's free army's college Liu Aijun et al in its published paper "Linear precoding for faster-than-Nyquist signaling" (IEEE international conference on computer and communications,2017, 52-56) proposes a symbol estimation method based on singular value decomposition (SingularValue Decomposition, SVD) precoding, which constructs an intersymbol interference matrix for each transmitted symbol block, then performs SVD decomposition on it, and implements precoding by means of the SVD decomposition result, thereby eliminating intersymbol interference. The method has the defects that the required complexity is high, the constructed intersymbol interference matrix ignores the intersymbol interference, so that when a high-order modulation mode is adopted by a super Nyquist system, the method cannot effectively eliminate the intersymbol interference, and therefore, the symbol estimation precision is low and the bit error rate performance is poor.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a low-complexity SVD precoding method for a super-Nyquist system, so as to reduce the complexity of the super-Nyquist system adopting SVD precoding, 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 invention provides the following technical scheme: a low-complexity SVD pre-coding method aiming at a super Nyquist system comprises the following steps:
acquiring a sending symbol block and an intersymbol interference matrix;
SVD decomposition is carried out on the intersymbol interference matrix to obtain a diagonal matrix;
SVD pre-coding is carried out on the sent symbol blocks;
adding a cyclic prefix and a cyclic suffix to the precoded transmitting symbol blocks, and transmitting after baseband shaping;
receiving a transmitted symbol block, and sequentially carrying out matched filtering, downsampling and cyclic prefix and cyclic suffix removal on the received symbol block;
and carrying out SVD decoding on the symbol blocks with the cyclic prefix and the cyclic suffix removed through the diagonal matrix to obtain estimated symbol blocks.
Optionally, the acquiring process of the sending symbol block includes:
and acquiring bit data, mapping the bit data into transmission symbols, and dividing the transmission symbols by a fixed length, wherein the fixed length is an exponent based on 2.
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 fixed length calculation based on the cyclic symmetry characteristic.
Optionally, the process of performing SVD decomposition on the intersymbol interference matrix includes:
acquiring a Fourier transform matrix:
wherein q l,η Elements of the first row and the eta column of the Fourier transformation matrix Q, lambda represents imaginary units, and the value ranges of l and eta are 1, L]L is the length of the transmitted symbol block;
SVD decomposition is carried out on the intersymbol interference matrix G through a Fourier transform matrix:
G＝Q T ΛQ *
the superscript T denotes a transpose operation, and the superscript is a conjugate operation.
Optionally, the process of performing SVD precoding on the sent symbol block includes:
precoding the block of transmit symbols SVD by a fourier transform matrix, transmitting a block of symbols a k Conversion from time domain to frequency domain:
s k ＝Q T a k
wherein s is k 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 the front part and the rear part of the pre-coded transmitting symbol block respectively; the cyclic prefix and the cyclic suffix are column vectors formed by symbols with the rearmost and foremost cyclic lengths of the precoded transmitting symbol blocks respectively, and the cyclic lengths are unilateral lengths of intersymbol interference of the super Nyquist system.
Optionally, the process of removing the cyclic prefix and the cyclic suffix includes:
and respectively removing the cyclic length symbols from the front part and the rear part of the downsampled symbol block to obtain a symbol block with the cyclic prefix and the cyclic suffix removed.
Optionally, the SVD decoding the symbol blocks from which the cyclic prefix and the cyclic suffix are removed includes:
converting the symbol blocks with the cyclic prefixes and cyclic suffixes removed to a time domain through a fourier transform matrix:
wherein,a kth symbol block representing a transition back to the time domain;
SVD decoding is carried out on the symbol blocks with the cyclic prefix and the cyclic postfix removed through the diagonal matrix:
wherein,represents the kth estimated symbol block of the receiver of the super nyquist system, (·) -1 Representing matrix inversion.
The invention has the following technical effects:
compared with the prior art, the invention has the following advantages:
firstly, the invention 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 SVD decomposition on the accurate intersymbol interference matrix by means of a Fourier transform matrix, and respectively realizes SVD pre-coding and decoding at a super Nyquist system transmitter and a receiver by the SVD pre-coding and decoding, thereby eliminating intersymbol interference and recovering the transmitting symbol, overcoming the problem of poor estimation performance of the symbol in the prior art, being capable of more accurately estimating the transmitting symbol of the super Nyquist system and being particularly suitable for the super Nyquist system adopting a high-order modulation mode.
Secondly, because the invention adds the cyclic prefix and the cyclic suffix to the transmitted symbol block after the transmitter of the super Nyquist system performs precoding, the intersymbol interference matrix of the super Nyquist system is a cyclic symmetric matrix, and SVD precoding and decoding are realized by utilizing a Fourier transform matrix which can be realized by fast Fourier transform and inverse transform thereof, therefore, the invention can be realized rapidly only by 1 pair of fast Fourier transform and inverse transform intellectual property cores thereof and 1 complex multiplier, reduces the realization complexity of the prior SVD precoding method and has stronger practicability.
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In order to more clearly illustrate the embodiments of the present invention 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 invention, 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 invention for symbol estimation based on the system of FIG. 1;
FIG. 3 is a graph of simulation results of symbol estimation under 64-APSK, 128-APSK and 256-APSK conditions using the method of the invention, wherein: (a) A simulation result diagram for carrying out symbol estimation by adopting 64-APSK as a modulation mode; (b) A simulation result diagram for carrying out symbol estimation by adopting 128-APSK as a modulation mode; (c) 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 invention 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 invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims at overcoming the defects of the prior art, and provides a low-complexity SVD precoding method for a super-Nyquist system, so that the complexity of the super-Nyquist system adopting SVD precoding is reduced, the symbol estimation precision of the super-Nyquist system is improved, and the bit error rate performance of the super-Nyquist system is improved.
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 cyclic symmetry matrix, then carrying out SVD decomposition on the cyclic symmetry matrix by means of a Fourier transform matrix, and carrying out SVD precoding based on the cyclic symmetry matrix to eliminate intersymbol interference.
According to the above thought, the implementation steps of the invention 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 a is k For column vectors, the k-th transmitted symbol block is represented, k is not less than 1 and not more than N, N represents the total number of transmitted symbols, and L takes an exponent (such as 256, 512 and 1024) with 2 as a base number;
2) Obtaining an intersymbol interference matrix of a super Nyquist system;
3) Calculating a Fourier transform matrix Q, and carrying out SVD (singular value decomposition) on an intersymbol interference matrix by using the Fourier transform matrix Q to obtain a diagonal matrix Λ of the intersymbol interference matrix;
4) The transmitted symbol blocks of the super nyquist system transmitter are precoded with a fourier transform matrix, thereby converting them to the frequency domain:
s k ＝Q T a k
wherein s is k Representing a kth precoded transmitted symbol block of the super nyquist system transmitter, and superscript T represents a transpose operation;
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 b k 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) Receiver acquires downsampled received symbolsDelete received symbol block->Foremost and rearmost +.>The received symbol block r with the cyclic prefix and the cyclic postfix removed is obtained k ；
7) The received symbol block r is transformed by a fourier transform matrix k Conversion back to the time domain:
wherein,the kth symbol block representing the conversion back to the time domain is superscript by conjugate;
8) The estimated symbol blocks are calculated using the diagonal matrix of the intersymbol interference matrix as follows:
wherein,represents the kth estimated symbol block of the receiver of the super nyquist system, (·) -1 Representing matrix inversion.
The technical contents described above are explained in detail with reference to the accompanying drawings:
referring to fig. 1, the super nyquist system adopted in the present invention mainly comprises a data source, constellation mapping, SVD precoding, insertion of cyclic prefix and cyclic suffix, baseband shaping, channel, matched filtering, removal of cyclic prefix and cyclic suffix, SVD 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 SVD precoding module;
the SVD pre-coding module divides the symbol mapped by the constellation into symbol blocks, then performs SVD 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 an FTN 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 7 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;
the module for removing the cyclic prefix and the cyclic suffix removes the cyclic prefix and the cyclic suffix in the filtered symbols and transmits the symbols after removing the cyclic prefix and the cyclic suffix to the SVD decoding module;
the SVD decoding module eliminates intersymbol interference in the symbol after removing the cyclic prefix and the cyclic postfix by utilizing the SVD decoding matrix, estimates a sending symbol, and transmits the estimated symbol 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 symbol estimation by using the above-mentioned nyquist system of the present invention 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 a is k For column vectors, the kth transmitted symbol block is represented, 1.ltoreq.k.ltoreq.N, N represents the total number of transmitted symbol blocks, L takes an exponent based on 2 (e.g., 256, 512, and 1024), which is taken as 1024 in this example.
And step 2, obtaining an intersymbol interference matrix of the super Nyquist system.
By means of the cyclic symmetry property, the intersymbol interference matrix G of the super Nyquist system is calculated:
wherein g j Representing the jth intersymbol interference factor in the super nyquist system, L x L represents the dimension of the intersymbol interference matrix G.
And step 3, performing SVD decomposition on an intersymbol interference matrix of the super Nyquist system.
3.1 A fourier transform matrix Q) is obtained as follows:
wherein q l,η Elements of the first row and the eta column of the Fourier transformation matrix Q, lambda represents imaginary units, and the value ranges of l and eta are 1, L]；
3.2 SVD (singular value decomposition) is carried out on the intersymbol interference matrix by utilizing a Fourier transform matrix Q, so as to obtain a diagonal matrix Λ of the intersymbol interference matrix:
G＝Q T ΛQ *
the superscript T denotes a transpose operation, and the superscript is a conjugate operation.
And 4, SVD precoding is carried out on the sent symbol blocks.
The transmitted symbol block of the ultranyquist system transmitter is precoded with a fourier transform matrix, thereby being converted into the frequency domain, according to the following:
s k ＝Q T a k
wherein s is k 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 b k 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, the receiver removes the cyclic prefix and the cyclic suffix.
Receiver acquires downsampled received symbolsDelete received symbol block->Foremost and rearmost +.>The received symbol block r with the cyclic prefix and the cyclic postfix removed is obtained k ；
And 7, SVD decoding is carried out by the receiver of the super Nyquist system.
7.1 Using fourier transform matrix to receive symbol block r k Conversion back to the time domain:
wherein,a kth symbol block representing a transition back to the time domain;
7.2 Using the diagonal matrix of the intersymbol interference matrix to obtain estimated symbols according to:
wherein,represents the kth estimated symbol block of the receiver of the super nyquist system, (·) -1 Representing matrix inversion.
The effects of the present invention will be further described with reference to simulation experiments.
1. Simulation conditions:
the simulation experiments of the present invention were performed under MATLAB 2022B software. In the simulation experiment of the invention, the total number P of time domain response coefficients of receiver matched filtering in the super Nyquist system is 201, and the downsampling multiple B is 10.
The acceleration factor of the super Nyquist system is set to be 0.9, and the matched filtering roll-off factor of the receiver in the super Nyquist system is set to be 0.3.
Setting the simulated total bit number of single bit signal-to-noise ratio to be 1×10 7 。
2. Simulation content and result analysis:
under the above conditions, 64-APSK, 128-APSK and 256-APSK are adopted as modulation modes, and symbol estimation is respectively carried out by using the method and the prior frequency domain equalization method and SVD precoding method, and the result is shown in fig. 3, wherein:
fig. 3 (a) is a diagram of simulation results of symbol estimation using 64-APSK as its modulation scheme;
fig. 3 (b) is a diagram of simulation results of symbol estimation using 128-APSK as its modulation scheme;
fig. 3 (c) is a simulation result diagram of symbol estimation using 256-APSK as its modulation scheme.
The horizontal axis in fig. 3 represents the bit signal-to-noise ratio of the super nyquist system in decibels dB (decibel), and the vertical axis represents the bit error rate of the super nyquist system.
As can be seen from fig. 3, when the nyquist system adopts a high-order modulation mode, the bit error rate curves of the method of the present invention are lower than those of the existing frequency domain equalization method and SVD precoding method, which indicates that the method of the present invention can effectively eliminate intersymbol interference when the nyquist system adopts a high-order modulation mode, so as to more accurately estimate the transmission symbol, and make the nyquist system have better bit error rate performance.
The foregoing is merely a preferred embodiment of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions easily conceivable by those skilled in the art within the technical scope of the present application should be covered in the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (6)
1. The low-complexity SVD pre-coding method for the super Nyquist system is characterized by comprising the following steps:
acquiring a sending symbol block and an intersymbol interference matrix; SVD decomposition is carried out on the intersymbol interference matrix to obtain a diagonal matrix;
SVD pre-coding is carried out on the sending symbol block; adding a cyclic prefix and a cyclic suffix to the precoded transmitting symbol blocks, and transmitting after baseband shaping;
receiving a transmitted symbol block, and sequentially carrying out matched filtering, downsampling and cyclic prefix and cyclic suffix removal on the received symbol block;
SVD decoding is carried out on the symbol blocks with the cyclic prefix and the cyclic suffix removed through the diagonal matrix, so that estimated symbol blocks are obtained;
the SVD pre-coding process of the sending symbol block comprises the following steps:
precoding the block of transmit symbols SVD by a fourier transform matrix, transmitting a block of symbols a k Conversion from time domain to frequency domain:
s k ＝Q T a k
wherein s is k Representing a kth precoded block of transmitted symbols of the super nyquist system transmitter;
the SVD decoding of the symbol blocks from which the cyclic prefix and the cyclic suffix are removed includes:
converting the symbol blocks with the cyclic prefixes and cyclic suffixes removed to a time domain through a fourier transform matrix:
wherein,a kth symbol block representing a transition back to the time domain;
SVD decoding is carried out on the symbol blocks with the cyclic prefix and the cyclic postfix removed through the diagonal matrix:
wherein,represents the kth estimated symbol block of the receiver of the super nyquist system, (·) -1 Representing matrix inversion.
2. The low complexity SVD precoding method of claim 1, wherein:
the process for acquiring the sending symbol block comprises the following steps:
and acquiring bit data, mapping the bit data into transmission symbols, and dividing the transmission symbols by a fixed length, wherein the fixed length is an exponent based on 2.
3. The low complexity SVD precoding method of claim 2, further comprising:
the process for obtaining the intersymbol interference matrix comprises the following steps:
and acquiring an intersymbol interference factor, and calculating to acquire an intersymbol interference matrix according to the intersymbol interference factor and the fixed length based on the cyclic symmetry characteristic.
4. The low complexity SVD precoding method of claim 1, wherein:
the SVD decomposition process of the intersymbol interference matrix comprises the following steps:
acquiring a Fourier transform matrix:
wherein q l,η Elements of the first row and the eta column of the Fourier transformation matrix Q, lambda represents imaginary units, and the value ranges of l and eta are 1, L]L is hairThe length of the symbol block is sent;
SVD decomposition is carried out on the intersymbol interference matrix G through a Fourier transform matrix:
G＝Q T ΛQ *
the superscript T denotes a transpose operation, and the superscript is a conjugate operation.
5. The low complexity SVD 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 the front part and the rear part of the pre-coded transmitting symbol block respectively; the cyclic prefix and the cyclic suffix are column vectors formed by symbols with the rearmost and foremost cyclic lengths of the precoded transmitting symbol blocks respectively, and the cyclic lengths are unilateral lengths of intersymbol interference of the super Nyquist system.
6. The low complexity SVD precoding method of claim 1, wherein:
the process of removing the cyclic prefix and cyclic suffix includes:
and respectively removing the cyclic length symbols from the front part and the rear part of the downsampled symbol block to obtain a symbol block with the cyclic prefix and the cyclic suffix removed.
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