A truncated singular value decomposition dft spread frequency division multiplexing method

Abstract

This invention proposes a truncated singular value decomposition (SVDe) DFT-spread frequency division multiplexing (FDM) method, which can improve the bit error rate (BER) curve performance of a single-carrier high-spectral-efficiency FDM communication system while maintaining spectral efficiency. This invention pads the end of the modulation symbol vector *s* input to the DFT-spread FDM communication system with zeros, and discards these zeros in the output symbol vector *S* at the receiver, obtaining a symbol vector *P*. The symbol vector *P* is then fed into a decoder for decoding to obtain the decoded symbol vector. This method can improve the BER vsE of a single-carrier high-spectral-efficiency FDM communication system while maintaining spectral efficiency. b / N0 curve performance.

Description

Technical Field

[0001] This invention relates to the field of information and communication engineering technology, specifically to a truncated singular value decomposition DFT spread frequency division multiplexing method. Background Technology

[0002] To further improve the spectral efficiency of communication systems based on Orthogonal Frequency Division Multiplexing (OFDM) technology, High Spectral Efficiency Frequency Division Multiplexing (SEFDM) technology was proposed. Compared to OFDM, SEFDM multiplies the subcarrier frequency spacing f by a compression factor α, achieving higher spectral efficiency by sacrificing the orthogonality between subcarriers, but this poses a greater challenge to the receiver's detection capability. On the other hand, to reduce the peak-to-average power ratio (PAPR) of SEFDM, Discrete Fourier Transform (DFT) was introduced, leading to the proposed Discrete Fourier Transform Extended SEFDM (DFT-s-SEFDM) scheme. However, this scheme further exacerbates crosstalk between subcarriers, requiring further system optimization.

[0003] The transmitting signal of a SEFDM system can be represented as X = ΦS, where S represents the data symbol and Φ represents...

[0004] This demonstrates the fractional inverse Fourier transform (iFrFT) operation. The signal obtained at the receiving end is then R = ΦΦS + W.

[0005] Where Φ is the conjugate transpose of Φ, which is the fractional Fourier transform (FrFT) operation, and W represents the result after FrFT transformation.

[0006] The Gaussian white noise vector is then processed. The cross-correlation coefficient matrix C = ΦΦ is defined, and the elements of matrix C are:

[0007]

[0008] This causes matrix C to become increasingly ill-conditioned as the spectral compression factor α of SEFDM decreases, eventually approaching a singular matrix. Furthermore, in DFT-s-SEFDM systems incorporating DFT operations, the ill-conditioning of matrix C is further exacerbated. Therefore, the selection of the receiver detector and the system design are crucial in DFT-s-SEFDM systems. Maximum likelihood detection (ML) is an ideal detector, but its exponential complexity makes it unusable; equalizers such as zero-forcing (ZF) equalization and minimum mean square error (MMSE) equalization exhibit extremely poor performance due to the ill-conditioning of matrix C. To address the ill-conditioning problem of matrix C in DFT-s-SEFDM systems, existing technologies employ a transmit / receive scheme that pads the data header with zeros and uses zero-forcing equalization at the receiver, thus improving the BER vs E of the DFT-s-SEFDM system. bThe performance of the / N0 curve is improved, but the spectral efficiency is low because too many zeros are added. There is also a truncated singular value decomposition-fixed complexity sphere decoder for SEFDM systems, but the performance of this detector is poor in the DFT-s-SEFDM system. SUMMARY

[0009] Therefore, the application provides a truncated singular value decomposition DFT spread frequency division multiplexing method, which can improve the bit error rate curve performance of the single-carrier high spectral efficiency frequency division multiplexing communication system while ensuring the spectral efficiency.

[0010] To achieve the above object, the technical scheme of the application is as follows:

[0011] A truncated singular value decomposition DFT spread frequency division multiplexing method, in a high spectral efficiency frequency division multiplexing communication system, a transmitter adds a plurality of zeros to the tail of an input modulated symbol vector s and outputs to a receiver; the receiver discards the symbols in the tail of the symbol vector S output by the transmitter to obtain a symbol vector P, and sends the symbol vector P into a decoder for decoding to obtain a decoded symbol vector;

[0012] The decoder selects a fixed complexity sphere decoder, and a TSVD-FSD joint detection decoding is used in the system receiver;

[0013] The specific steps of the truncated singular value decomposition DFT spread frequency division multiplexing are as follows:

[0014] Step 1, selecting a truncation coefficient ξ of TSVD, a FFT point number N, and a compression factor coefficient α of the SEFDM system;

[0015] Step 2, the transmitter performs grouping processing on the input data symbols, specifically: every ξ data symbols are grouped, and zeros are added to the tail to N to obtain a symbol vector X;

[0016] Step 3, the symbol vector X is sent into an N-point FFT module to perform DFT extension on the symbol vector X to obtain a symbol vector S;

[0017] Step 4, the symbol vector S is sent into an N-point iFrFT module to modulate the symbol vector S by iFrFT to obtain a modulated symbol vector s;

[0018] Step 5, the transmitter performs serial-parallel conversion on the modulated symbol vector s to obtain a signal and sends it into a channel; the receiver performs serial-parallel conversion on the received signal to obtain a symbol vector r and sends it into an FrFT demodulation module;

[0019] Step 6, the FrFT demodulation module is used to demodulate the received symbol vector r to obtain a demodulated symbol vector s';

[0020] Step 7, TSVD equalization processing is conducted on the demodulated symbol vector s', and a symbol vector y is obtained;

[0021] Step 8, N-point ifft transformation is conducted on the symbol vector y, and the first ξ symbol data are reserved as an input symbol vector P input to the FSD decoder;

[0022] Step 9, the FSD decoder is used to decode the symbol vector P, and a decoded data vector is obtained, and frequency division multiplexing is completed.

[0023] In the step 1, it is set that Wherein, ξ is a natural number, N is a power of 2, and the symbol Indicates rounding up.

[0024] In the step 7, the specific mode that the symbol vector s is subjected to TSVD equalization processing is that the demodulated symbol vector s' is multiplied by the pseudo-inverse C_xi of the cross correlation coefficient matrix C calculated by TSVD.

[0025] Beneficial effects:

[0026] 1, the application adds a plurality of zeros to the tail of the modulation symbol vector s input by the DFT extended high frequency spectrum efficiency frequency division multiplexing communication system sending end, and the symbols in the tail are discarded in the output symbol vector S of the receiving end, so that the symbol vector P is obtained. The symbol vector P is sent into the decoder for decoding, and the decoded symbol vector can be obtained, so that the BER vs E b / N0 curve performance of the single carrier high frequency spectrum efficiency frequency division multiplexing communication system is improved while the spectrum efficiency is ensured.

[0027] 2, in the receiving end of the system, the decoder can select a maximum likelihood (ML) decoder, a spherical decoder (SD), a fixed complexity spherical decoder (FSD) or a traditional hard decision decoder, and the selection range is wide.

[0028] 3, in the receiving end of the system, a fixed complexity spherical decoder (FSD) is further selected, since the decoding performance of the hard decision decoder is poor, the ML decoder and the SD decoder have the best performance, but the complexity is too large and does not have practical value, the FSD decoder can balance the decoding accuracy and the complexity, the application adopts TSVD-FSD joint detection decoding, compared with the ZH-DFT-s-SEFDM scheme, the BER vs E b / N0 curve performance of the system is better under the same spectrum efficiency. DETAILED DESCRIPTION

[0029] Figure 1 It is a TSVD-DFT-s-SEFDM signal analysis model schematic diagram in the application.

[0030] Figure 2 The simulation calculation result schematic diagram of the transfer matrix T of the TSVD-DFT-s-SEFDM system in different parameter selection cases in the application.

[0031] Figure 3 The system model block diagram of the ZT-TSVD-DFT-s-SEFDM sending end in the application.

[0032] Figure 4 The system model block diagram of the ZT-TSVD-DFT-s-SEFDM receiving end in the application.

[0033] Figure 5 The system model block diagram of the ZT-TSVD-DFT-s-SEFDM in the embodiment of the application. DETAILED DESCRIPTION

[0034] The application will be described in detail below with reference to the drawings and embodiments.

[0035] The application provides a truncated singular value decomposition DFT spread frequency division multiplexing method, in particular a zero tail-truncated singular value decomposition DFT spread high frequency spectrum efficiency frequency division multiplexing (ZT-TSVD-DFT-s-SEFDM) method, which comprises the following steps:

[0036] Step 1, selecting a TSVD truncation coefficient ξ, an FFT point number N and an SEFDM system compression factor coefficient α. Setting Wherein ξ is a natural number, N is a power of 2, represents the minimum integer greater than x.

[0037] Step 2, grouping processing of input data symbols, specifically: every ξ data symbols are grouped into a group, and zero is supplemented to N in the tail to obtain a symbol vector X.

[0038] Step 3, sending the symbol vector X into an N-point FFT module to perform DFT spreading on X to obtain a symbol vector S.

[0039] Step 4, sending the symbol vector S into an N-point iFrFT module to modulate the symbol vector by iFrFT to obtain a modulated symbol vector s.

[0040] Step 5, performing serial-parallel conversion on the modulated symbol vector s to obtain a signal and sending the signal into a channel. At the receiving end, performing serial-parallel conversion on the received signal to obtain a symbol vector r and sending the symbol vector r into an FrFT demodulation module.

[0041] Step 6, using the FrFT module to demodulate the received symbol vector r to obtain a symbol vector s'.

[0042] Step 7, multiply the symbol vector s' with the pseudo-inverse C_xi of the cross correlation coefficient matrix C calculated by TSVD, that is, TSVD equalization processing is performed, and a symbol vector y is obtained.

[0043] Step 8, perform N-point ifft transformation on the symbol vector y, and retain the first ξ symbol data as an input symbol vector P, which is input to the FSD decoder.

[0044] Step 9, use the FSD decoder to perform decoding processing on the vector P, and obtain a decoding data Y vector, thereby completing the zero-tail-truncated singular value decomposition DFT spread high spectrum efficiency frequency division multiplexing.

[0045] Specifically, the application supplements a plurality of zeros at the tail of a modulation symbol vector s input by a DFT spread high spectrum efficiency frequency division multiplexing communication system at a sending end, and discards the symbols at the tail in an output symbol vector S at a receiving end, so as to obtain a symbol vector P. The symbol vector P is input into a decoder to perform decoding, so as to obtain a decoded symbol vector, which can improve the BER vs E b / N0 curve performance of the single-carrier high spectrum efficiency frequency division multiplexing communication system while guaranteeing the spectrum efficiency.

[0046] Further, the decoder at the receiving end of the system can select a maximum likelihood (ML) decoder, a sphere decoder (SD), a fixed complexity sphere decoder (FSD), or a traditional hard decision decoder, and the selection range is wide.

[0047] Preferably, the fixed complexity sphere decoder (FSD) is further selected at the receiving end of the system, because the decoding performance of the hard decision decoder is poor, the ML decoder and the SD decoder have the best performance, but the complexity is too large to have practical value, the FSD decoder can balance the decoding accuracy and the complexity, and can improve the BER vs E b / N0 curve performance of the single-carrier high spectrum efficiency frequency division multiplexing communication system while guaranteeing the spectrum efficiency, and has the effect of reducing the peak-to-average power ratio of the system.

[0048] In the ZH-DFT-s-SEFDM method of the prior art, zeros are supplemented at the head of a signal vector S, and the head of a symbol vector P is discarded at the receiving end, while in the application, zeros are supplemented at the tail of the signal vector, and the tail of the symbol vector P is discarded at the receiving end; and the ZH-DFT-s-SEFDM method uses a zero-forcing equalization algorithm as a detection decoder at the receiving end of the system, while the application uses a TSVD-FSD joint detection decoding. Compared with the ZH-DFT-s-SEFDM scheme, the application has better performance of the BER vs E b / N0 curve of the system under the same spectrum efficiency.

[0049] Figure 1The transformation of the signal vector in a TSVD-DFT-s-SEFDM system without noise is described in the form of a flow chart. Since all the transformations are linear transformations, the present application uses the method of matrix multiplication to represent the transformations. Define F FFT represents the FFT transformation matrix, and Φ represents the IFFr transformation matrix, then the N-point IFFr transformation matrix can be represented by the matrix Φ, and the TSVD transformation can be represented by the matrix C ξ The matrix multiplication is replaced by N-point IFFT can be represented by F IFFT Therefore, the transformation of the signal in the TSVD-DFT-s-SEFDM system can be represented by the method of matrix multiplication as

[0050]

[0051] Define the system transfer matrix T as

[0052] T=F IFFT ·C ξ ·Φ·Φ·F FFT ,

[0053] Therefore, the transformation of the signal vector in the system can be represented as

[0054]

[0055] Since the matrix T is the system transfer matrix of the entire DFT-s-SEFDM system, it is known that when the ZF algorithm is used as the detector by the receiver detector, T=I according to the principle of the ZF detector N is an N×N identity matrix, but due to the ICI interference in the SEFDM system, the matrix C is ill-conditioned, which leads to poor BER vs E b / N0 curve performance in a noisy environment, so the TSVD detector needs to be used instead.

[0056] In the simulation, it is found that when the TSVD detector parameters are selected to meet , the upper left corner of the matrix T is approximately an identity matrix I ξ , and the rest of the energy is very low, which is approximately a zero matrix. At this time, the matrix T is approximately diag(1,1,1,…,1,0,…,0), that is, a diagonal matrix with the first ξ values on the diagonal being 1 and the rest being 0. The simulation calculation of the matrix T under the selection of different carriers N and compression factors a is shown in Figure 2 . Figure 2In the middle, respectively, to the compression factor α takes 0.8 and 0.6 and the selection of carrier number N=8, 12, 16, 32 under TSVD-DFT-s-SEFDM system transfer matrix T is carried out numerical calculation. It can be seen that, with the increase of carrier number N and the decrease of compression factor α, the low energy area of the tail of transfer matrix T expands constantly, which conforms to the description of T in the previous paragraph, and the mathematical expression is

[0057]

[0058] According to the properties of matrix T, it can be known that if the data vector is supplemented with N-ξ zeros to obtain the symbol vector X, the BER vs E b / N0 curve of TSVD-DFT-s-SEFDM system can be improved. It can be seen that, compared with the prior art, the method can improve the BER vs E b / N0 curve performance of the single carrier high spectral efficiency frequency division multiplexing communication system while ensuring the spectral efficiency, and has the effect of reducing the peak-to-average ratio of system transmission power.

[0059] Taking α=0.8 and N=8, it has To verify the method, a zero tail-truncated singular value decomposition DFT extended high spectral efficiency frequency division multiplexing system is designed, and the ZT-TSVD-DFT-s-SEFDM transmitter system model block diagram in the application is shown in Figure 3 The transceiver structure of the ZT-TSVD-DFT-s-SEFDM receiver system model block diagram is shown in Figure 4 The ZT-TSVD-DFT-s-SEFDM system model of the embodiment is shown in Figure 5 It can be seen from Figure 5 that the number of iFrFT / FrFT and IFFT / FFT points is 8.

[0060] At the input of the FFT module in the transmitter, the input data symbols are grouped, 7 symbols are grouped as a group, and one zero is supplemented after each group of symbols. The signal vector is sequentially subjected to FFT processing, iFrFT operation and parallel-to-serial conversion to obtain a signal that can be transmitted to the channel. The pseudo-inverse C_xi of the cross-correlation coefficient matrix C is calculated, and the calculation method is

[0061] C=U·S·V'

[0062] C_xi=V·S xi ·U'

[0063] Where S=diag{s1,s2,…,s N} is a diagonal matrix, S xi =diag{1 / s1,1 / s2,…,1 / s xi,0,…,0}. That is, S xi is to take inverse of the first xi elements of diagonal matrix S, and set the elements with order number greater than xi to zero, xi = ξ = 7.

[0064] At the receiving end, the received symbol vector r is respectively subjected to serial-parallel conversion and 8-point FrFT, and the symbol vector is multiplied by matrix C_xi to obtain vector y, and the first 7 bits of y are sent into the FSD decoder for decoding, and the decoded data vector Y can be obtained at the output end of the FSD.

[0065] To sum up, the above is only a preferred embodiment of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A truncated singular value decomposition (DFT-spread frequency division multiplexing (DFT-S-OFDM) method, characterized in that, In a high spectral efficiency frequency division multiplexing communication system, a transmitter appends zeros to the tail of an input modulated symbol vector s and outputs to a receiver; the receiver discards the symbols in the tail of the symbol vector S output by the transmitter and obtains a symbol vector P, and sends the symbol vector P into a decoder for decoding to obtain a decoded symbol vector; The decoder selects a fixed complexity sphere decoder, and TSVD-FSD joint detection decoding is used in the system receiver; The specific steps of the truncated singular value decomposition DFT spread frequency division multiplexing are as follows: Step 1, selecting the truncation coefficient of TSVD , the number of FFT points N and the compression factor coefficient a of SEFDM system Step 2, the transmitter groups the input data symbols, specifically, each data symbol is grouped into a group, and zero padding is performed to N at the tail to obtain a symbol vector X. Step 2, the transmitter groups the input data symbols, specifically, each data symbol is grouped into a group, and zero padding is performed to N at the tail to obtain a symbol vector X. Step 3, sending the symbol vector X into an N-point FFT module to perform DFT spreading on the symbol vector X to obtain a symbol vector S; Step 4, sending the symbol vector S into an N-point iFrFT module to modulate the symbol vector S by iFrFT to obtain a modulated symbol vector s; Step 5, the transmitter performs serial-parallel conversion on the modulated symbol vector s to obtain a signal and sends the signal into a channel; the receiver performs serial-parallel conversion on the received signal to obtain a symbol vector r and sends the symbol vector r into an FrFT demodulation module; Step 6, demodulate the received symbol vector r using the FrFT demodulation module to obtain a demodulated symbol vector ; Step 7, the demodulated symbol vector TSVD equalization is performed to obtain a symbol vector y; Step 8, N-point ifft transform is performed on the symbol vector y, and the first symbol data is reserved to obtain a symbol vector P, which is input to the FSD decoder. Step 9, using an FSD decoder to decode and process the symbol vector P to obtain a decoded data vector, and completing frequency division multiplexing.

2. The method of claim 1, wherein, In the step 1, set wherein is a natural number, N is a power of 2, and the symbol denotes the ceiling function.

3. The method of claim 1, wherein, In step 7, the specific way of TSVD equalization processing of the symbol vector s is: multiplying the demodulated symbol vector s with the pseudo-inverse C_xi of the cross correlation coefficient matrix C calculated by TSVD. with the pseudo-inverse C_xi of the cross correlation coefficient matrix C calculated by TSVD.

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