阅读说明：本技术 一种基于对角分块带状矩阵增强的正交信分复用均衡方法 (Orthogonal signal division multiplexing equalization method based on diagonal block banded matrix enhancement ) 是由 韩晶 张群飞 马胜前 王玉洁 于 2019-10-02 设计创作，主要内容包括：本发明提供了一种基于对角分块带状矩阵增强的正交信分复用均衡方法,采用时变信道OSDM系统模型得到接收信号；基于带限的多普勒扩展,完成接收信号中复合信道矩阵的DBB近似；基于时域接收窗函数,对接收信号中的DBB近似结构进行增强处理；基于接收信号中的DBB矩阵增强方法,设计低复杂度OSDM均衡算法。本发明改善了系统的归一化均方误差性能,提高了系统误码性能,有效降低了多普勒效应引起的性能损失,通信系统性能得到了显著提高,计算量得到很大的降低,具有很好的应用前景。(The invention provides an orthogonal signal division multiplexing equalization method based on diagonal block banded matrix enhancement, which adopts a time-varying channel OSDM system model to obtain a received signal; completing DBB approximation of a composite channel matrix in a received signal based on band-limited Doppler spread; based on a time domain receiving window function, enhancing a DBB approximate structure in a received signal; and designing a low-complexity OSDM equalization algorithm based on a DBB matrix enhancement method in the received signal. The invention improves the normalized mean square error performance of the system, improves the error code performance of the system, effectively reduces the performance loss caused by the Doppler effect, obviously improves the performance of the communication system, greatly reduces the calculated amount and has good application prospect.)

1. An orthogonal signal division multiplexing equalization method based on diagonal block banded matrix enhancement is characterized by comprising the following steps:

(1) in an OSDM transmission system, assuming that a symbol block d of length K ═ MN is transmitted, OSDM modulation generates a transmission signal

(2) Based on band-limited Doppler spread, assume that when | Q | > Q

Wherein the content of the first and second substances,C＝TCT^H，

(3) matrix arrayIs replaced by its direct DBB approximation, denoted as

(4) based on received signalsMiddle DBB matrix enhancing method, low complexity OSDM equalization algorithmWherein the content of the first and second substances,

2. the orthogonal signal division multiplexing equalization method based on diagonal block band matrix enhancement of claim 1, characterized in that: the step (3) selects MBAE-SOE window, and the corresponding window function w is [ f ═ f_-Q,...,f₀,...,f_Q]a, wherein,

Technical Field

The invention belongs to the field of wireless communication, and particularly relates to a low-complexity equalization method of an orthogonal signal division multiplexing system in a time-varying multipath dual-selective fading channel.

Background

Orthogonal Signal-Division Multiplexing (OSDM), which is a new generalized modulation framework, unifies OFDM (Orthogonal Frequency-Division Multiplexing) and SCBT (Single-Carrier Block Transmission) into two extreme examples. Specifically, the OSDM divides K ═ MN symbols into N symbol vectors of length M in one data block, and performs Inverse Discrete Fourier Transform (IDFT) on an element-by-element basis to realize modulation. Because the values of M and N can be flexibly configured according to actual conditions, the OSDM modulation method has higher degree of freedom in balancing the design requirements of the system compared with OFDM and SCBT.

Existing research on OSDM modulation in time-varying channels is mainly based on simplified channel models, which typically assume that the same doppler effect exists for all channel transmission paths. Under the condition, the OSDM receiving end only needs to perform phase compensation first, and design a time-invariant channel equalizer. In addition, in some studies, the channel is based on a complex exponential basis expansion model (CE-BEM) to adapt to more complicated doppler modeling independent of each path. The model respectively simulates the time-varying characteristic of each channel delay tap through an exponential function, thereby realizing more elastic Doppler compensation and equalization. However, the actual effect of this equalization process is also affected due to errors introduced by the CE-BEM channel approximation.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a low-complexity channel equalization algorithm based on Diagonal-Block-Banded (DBB) matrix enhancement.

The technical scheme adopted by the invention for solving the technical problem comprises the following steps:

(1) in an OSDM transmission system, assuming that a symbol block d of length K ═ MN is transmitted, OSDM modulation generates a transmission signal

Wherein, F_NRepresenting an N-point Fourier transform unitary matrix, (-)^HHermitian transpose, I, of the representation matrix_MAnd e_M(M) represents M-dimensional unit momentsThe M-th column of the matrix and M-dimensional identity matrix,

represents the kronecker product; a baseband receiving signal block r of a communication receiving end is Cs + n, wherein n represents K multiplied by 1 dimension noise item,representing a K x K dimensional channel matrix; then K x K dimensional composite channel matrix

(2) Based on band-limited Doppler spread, assume that when | Q | > Q

Each element b of_q,i0, corresponding matrix

Is a strip matrix; further assume Q < N/2, for the matrix

Performing interleaving operation to obtain matrix

Is a block banded matrix; placing 2Q zero vectors across the transmit data block,

dcomprisesNN-2Q vectors; at the receiving end, by intercepting the middle of the received blockNIndividual vector derivationxTx, where T ═ I_K]_QM:(N-Q)M-1(ii) a Then

Wherein the content of the first and second substances,C＝TCT^H，

z＝Tz，by intercepting the effective channel matrix

The resulting matrix

Is in the form of a block strip, the corresponding matrix structure is called DBB structure;

(3) matrix array

Is replaced by its direct DBB approximation, denoted as

M_CThe DBB mask matrix is formed, the elements on the diagonal lines of the blocks of the main block band are 1, and other elements are 0; adding a time domain window function at a receiving end, wherein the receiver window function with the length of K is W ═ diag { W }, and carrying out windowing on a received signal r_w＝C_ws+n_w， r_w＝Wr，n_w＝Wn，C_wWC; further define the

Optimal window pass solution

s.t.w^Hw-N, wherein,C _w＝TC_wT^H，

(4) based on the DBB matrix enhancement method in the received signal,designing low complexity OSDM equalization algorithms

Wherein the content of the first and second substances,is a matrix of the DBB, and,

the step (3) selects MBAE-SOE window, and the corresponding window function w is [ f ═ f_-Q,...,f₀,...,f_Q]a, wherein,the value range of Q is Q ═ Q., Q, and the design parameter coefficient vector a ═ a ·_-Q,，..a,₀...,a_Q,^T。

The invention has the beneficial effects that: compared with a system using direct DBB approximation, the invention improves the normalized mean square error performance of the system, improves the error code performance of the system, effectively reduces the performance loss caused by Doppler effect, and obviously improves the performance of the communication system. The transform domain equalization method designed by the present invention uses block LDLs^HThe method is realized by decomposition, only has linear complexity, greatly reduces the calculated amount compared with the directly balanced cubic complexity, and has good application prospect.

Drawings

FIG. 1 is a general block diagram of the system of the present invention;

FIG. 2 is a channel Doppler frequency response matrix

And is composed of

Matrix obtained by interleaving

Schematic structural diagram ofThe parameters are set as M-4, N-8 and Q-2;

FIG. 3 is a graphical comparison of normalized mean square error performance of a direct diagonal blocking strip approximation and an enhanced diagonal blocking strip approximation;

FIG. 4 is a schematic diagram of performance simulation of an orthogonal signal division multiplexing wireless communication equalization algorithm based on diagonal block banded matrix enhancement, and parameters are set to be M-4, f_dT＝0.5；

Fig. 5 is a schematic diagram of performance simulation of an orthogonal signal division multiplexing wireless communication equalization algorithm based on diagonal block banded matrix enhancement, and parameters are set to be SNR 20dB and Q2.

Detailed Description

The invention researches an OSDM channel matrix structure under the condition of time-varying multipath double-selective fading channel, and designs a low-complexity channel equalization algorithm based on Diagonal-Block-Banded (DBB) matrix enhancement. Finally, the performance of the proposed OSDM equalization method is evaluated through numerical simulation, and the effectiveness of the method in a time-varying channel is verified.

The invention provides an orthogonal signal division multiplexing wireless communication equalization method based on DBB matrix enhancement, which comprises the following steps: (1) adopting a time-varying channel OSDM system model, and obtaining a received signal through researching a composite channel matrix; (2) completing DBB approximation of a composite channel matrix in the received signal based on band-limited Doppler spread; (3) based on a time domain receiving window function, enhancing a DBB approximate structure in a received signal; (4) and designing a low-complexity OSDM equalization algorithm based on a DBB matrix enhancement method in the received signal.

(1) Aiming at an OSDM system model of a time-varying channel, a received signal is obtained through researching a composite channel matrix, and the method comprises the following steps:

in an OSDM transmission system, assuming that a symbol block d of length K ═ MN is transmitted, the OSDM modulation generated transmission signal s is represented as

Wherein, F_NRepresenting an N-point Fourier transform unitary matrix, (-)^HHermitian transpose, I, of the representation matrix_MAnd e_M(M) M columns of the M-dimensional identity matrix and the M-dimensional identity matrix, respectively,

representing the kronecker product. The baseband received signal block r of the communication receiving end is represented as

r＝Cs+n， (2)

Wherein n represents a K × 1 dimensional noise term,

representing a K x K dimensional channel matrix. The OSDM demodulation is expressed as

In the formula (I), the compound is shown in the specification,

where C denotes a K × K-dimensional composite channel matrix and z denotes a K × 1-dimensional demodulation noise term.

Under time-varying channel, the channel impulse response is denoted as { c_k,lWhere k denotes a time index and l denotes a time delay index, the cyclic channel matrix in (2) is expressed as

Wherein K is more than or equal to 0, and K' is more than or equal to K-1. Further, a DFT matrix with K-MN dimension is decomposed into

Wherein the content of the first and second substances,

P_N,Mis expressed as a K x K dimensional permutation matrix

Analogous to equation (7), the equivalent form of the composite channel matrix is expressed as

Wherein the content of the first and second substances,

representing the channel doppler frequency response matrix.

Each element in (1) is represented as

b_q,iIs expressed as

Where q and i are the doppler index and the frequency index, respectively. In the time-varying channel, the composite channel matrix C no longer has a block diagonal structure, and is now divided into blocks of size M × M, denoted as

C_n,n′＝[C]_{nM:nM+M-1,n′M:n′M+M-1}, (11)

0≤n,n′≤N-1。

(2) Based on band-limited Doppler spread, the DBB approximation of the composite channel matrix in the received signal is completed, the steps are as follows:

to achieve low complexity OSDM equalization over time-varying channels, further matrix studies are needed

Sum matrixThe structure of (1). Based on band-limited Doppler spread, let b be assumed when | Q | > Q _q,i0, corresponding matrix

In the form of a (circular) ribbon matrix. Further assume Q < N/2, for the matrixPerforming interleaving operation to obtain matrix

Is a (cyclic) block-wise banded matrix. As can be seen from FIG. 2, the matrix

The block matrices in all main block bands are diagonal matrices,

wherein | n-n' | is less than or equal to Q,

is that

The (n, n') th block of (a).

To remove the matrixNon-diagonal blocks at two corners, 2Q zero vectors are placed at two ends of the transmission data block,

dcomprisesNN-2Q vectors. At the receiving end, by intercepting the middle of the received blockNIndividual vector derivationxTx, where T ═ I_K]_{QM:(N-Q)M-1,:}。

In conjunction with equation (9), equation (3) is rewritten as

Wherein the content of the first and second substances,C＝TCT^H，

z＝Tz，

by intercepting the effective channel matrix

The resulting matrix

Is block-banded and the corresponding matrix structure is called DBB structure.

(3) And performing time domain windowing, and performing enhancement processing on the DBB matrix approximate structure. The method comprises the following steps:

modeling a time-varying channel by adopting a CE-BEM model, and expressing a channel impulse response vector as

Wherein Q < N/2 denotes Doppler spread, c_k,lRepresents the channel impulse response, h, of the ith path at the kth sample point_q,lDenotes c_k,lThe q-base component of (1). Obtained from the formula (10) and the formula (14)

In this case, the matrix

Is actually replaced by its direct DBB approximation, denoted as

Wherein M is_CThe DBB mask matrix has elements 1 on the diagonal of the block of the main block band, and other elements are all 0. To cancel the direct sum matrix in equation (16)

The partial elements tend to 0 to cause channel approximation error, and the invention adds a time domain window function at a receiving end to enhance a matrix

The DBB structure of (1). The receiver window function with length K is W ═ diag { W }, and the received signal after windowing is represented as W

r_w＝C_ws+n_w, (17)

Wherein r is_w＝Wr，n_w＝Wn，C_wWC. Further define the

The derivation in equation (13) is repeated

Wherein the content of the first and second substances,C _w＝TC_wT^H，

to enhance the matrixThe degree of approximation of the DBB of (c),the optimal window is obtained by solving the following equation,

the invention selects MBAE-SOE window, and the corresponding window function is expressed as

w＝[f_-Q,...,f₀,...,f_Q]a, (20)

Wherein the content of the first and second substances,the value range of Q is Q ═ Q., Q, and the design parameter coefficient vector can be calculated by the MBAE-SOE design rule and is expressed as a ═ a ·_-Q,...,a₀,...,a_Q]^T。

(4) And designing a low-complexity OSDM equalization algorithm based on a DBB matrix enhancement method in the received signal. The method comprises the following steps:

suppose the noise term n in equation (2) is white gaussian noise (mean 0, variance σ)²) Then E { zz^H}＝E{nn^H}＝σ²I_K. After windowing, the white gaussian noise becomes colored noisez _wWhose covariance matrix is expressed as

Wherein the content of the first and second substances,

analogy to equation (9) to obtain

Wherein the content of the first and second substances,

by definition

Formula (21) is rewritten as

Assuming efficient transmission of symbol itemsdIs independently and equally distributed in unit power, Edd ^H}＝I_{M N} . Directly performing MMSE block equalization to obtain a pair based on the formulas (18) to (21)dIs expressed as

However, the matrix inversion operation in the formula (24) brings cubic computation, and is not easy to be implemented in engineering. To this end, the present invention uses matrix factorization in equations (18) and (23) while taking into account

With an enhanced DBB structure, equation (24) becomes

Wherein the content of the first and second substances,

is a DBB matrix.

The algorithm represented by equation (25) is the transform domain channel equalization algorithm. Specifically, the channel equalization is not directly paired as in equation (24)x _wDone but in its transform domain. At the same time, using a matrix

DBB structure of (3), binding Block LDL^HDecomposition, the above-mentioned equalization algorithm only having

Of the system.

The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.

The specific method of the embodiment of the invention is as follows: (1) obtaining a received signal by adopting an OSDM system model under a time-varying channel; (2) the DBB approximation of the composite channel matrix in the received signal is completed by researching the structure of the composite channel matrix in the received signal and based on band-limited Doppler expansion; (3) adding a time domain window function at a receiving end, and enhancing the approximation degree of the DBB matrix in the received signal; (4) based on a DBB matrix enhancement method in a received signal, a corresponding low-complexity equalization algorithm is designed. The general structural block diagram of the invention is shown in fig. 2.

The method comprises the following steps:

step 1: obtaining a received signal by adopting an OSDM system model under a time-varying channel

In an OSDM transmission system, assuming that a symbol block d of length K ═ MN is transmitted, the OSDM modulation generated transmission signal s is represented as

Wherein, F_NRepresenting an N-point Fourier transform unitary matrix, (-)^HHermitian transpose, I, of the representation matrix_MAnd e_M(M) M columns of the M-dimensional identity matrix and the M-dimensional identity matrix, respectively,

representing the kronecker product. The signal is added with a cyclic prefix, modulated by a carrier wave and then sent to a channel.

At the communication receiving end, the baseband receiving signal block r after removing the carrier and the cyclic prefix is expressed as

r＝Cs+n， (27)

Wherein n represents a K × 1 dimensional noise term,representing K x K dimensional cyclic letterA lane matrix. Specifically, let c be ═ c₀,c₁,...,c_L]^TRepresenting a channel impulse response vector, where L represents a channel memory length, thenThe first column element of

Here 0_K-L-1Representing an all-zero vector of length K-L-1.

OSDM demodulation is performed by performing an element-by-element N-point Discrete Fourier Transform (DFT) to obtain a block of received symbols x, denoted as received symbol x

In the formula (I), the compound is shown in the specification,

where C denotes a K × K-dimensional composite channel matrix and z denotes a K × 1-dimensional demodulation noise term.

Under time-varying channel, the channel impulse response is denoted as { c_k,lWhere k denotes the time index and l denotes the time delay index. The cyclic channel matrix in (27) is represented as

Wherein K is more than or equal to 0, and K' is more than or equal to K-1.

Here, a DFT matrix of K-MN dimension is decomposed into

Wherein the content of the first and second substances,P_N,Mis expressed as a K x K dimensional permutation matrix

Analogous to equation (32), the equivalent of the composite channel matrix is expressed as

Wherein the content of the first and second substances,

representing the channel doppler frequency response matrix.

Each element in (1) is represented as

b_q,iIs expressed as

Where q and i are the doppler index and the frequency index, respectively.

In the time-varying channel, the composite channel matrix C no longer has a block diagonal structure, and is now divided into blocks of size M × M, denoted as

C_n,n′＝[C]_{nM:nM+M-1,n′M:n′M+M-1}, (36)

N is more than or equal to 0, N' is more than or equal to N-1, and the N-th OSDM demodulation vector is obtained by substituting the N-th OSDM demodulation vector into the formula (28)

Formula (37) In

Representing IVI, this means that in time-varying channels, orthogonality between OSDM vectors is destroyed.

Step 2: the DBB approximation of the composite channel matrix in the received signal is accomplished by studying the structure of the composite channel matrix in the received signal and based on band-limited Doppler spread.

To achieve low complexity OSDM equalization over a time-varying channel, further study of the channel doppler frequency response matrix is required

And is composed of

Matrix obtained by interleaving

The structure of (1). Matrix array

Element { b }_q,iIs stored in a circulating way

Among the diagonals, the case where the doppler index q is 0 corresponds to the main diagonal line, q>0(q<0) Corresponding to the qth lower (upper) diagonal. By means of a pair matrix

Left rideAnd right multiply by P_N,MRespectively complete the pair matrix

Interleaving of rows and columns.

Based on band-limited Doppler spread, let b be assumed when | Q | > Q _q,i0, thisTime matrix

In the form of a (circular) strip matrix. Further assume Q < N/2, via the pairwise matrixBy interleaving operations, resulting matrix

Is a (cyclic) block-wise strip matrix. To more intuitively see its structure, the channel doppler frequency response matrix

And is composed ofMatrix obtained by interleaving

An example of (2) is shown in figure 2.

As can be seen from FIG. 2, the matrix

The matrices in all main blockbands are diagonal matrices,

wherein | n-n' | is less than or equal to Q,

is that

The (n, n') th block of (a).

To remove the matrix

Two cornersThe off-diagonal block is placed with 2Q zero vectors at the two ends of the transmitting data block,

dcomprisesNN-2Q vectors. At the OSDM receiver end, by intercepting the middle of the received blockNThe vector can be obtainedxTx, where T ═ I_K]_{QM:(N-Q)M-1,:}。

According to the formula (28) and the formula (34), the signal model at this time is

Wherein the content of the first and second substances,C＝TCT^H，

z＝Tz，

after interception, the obtained matrix

Is BSB beta_C＝min{Q,N-1} of a block banded matrix, all non-zero blocks of which are diagonal matrices.The matrix structure of (2) is called a DBB structure, and a specific form thereof can be referred to fig. 2.

And step 3: adding a time domain window function at a receiving end, and enhancing the approximation degree of the DBB matrix in the received signal

Modeling a time-varying channel by adopting a CE-BEM model, and expressing a channel impulse response vector as

Wherein Q < N/2 denotes Doppler spread, c_k,lRepresents the channel impulse response, h, of the ith path at the kth sample point_q,lDenotes c_k,lThe q-base component of (1). From the formula (35) and the formula (40), it can be obtained

In this case, the matrix

Is actually replaced by its direct DBB approximation, denoted as

Wherein M is_CThe DBB mask matrix has elements 1 on the diagonal of the block of the main block band, and other elements are all 0. However, the effective channel matrix is directly mapped in equation (42)

Tends to 0 resulting in large channel approximation errors. Therefore, the invention adds a time domain window function and enhances a matrix at a receiving end

The DBB structure of (1). Assuming that the length of the receiving window is K, the window function is represented as W ═ diag { W }, similar to equation (27), and the received signal is represented as the received signal

r_w＝C_ws+n_w, (43)

Wherein r is_w＝Wr，n_w＝Wn，C_wWC. Further, define

The derivation in equation (39) is repeated

Wherein the content of the first and second substances,C _w＝TC_wT^H，

to enhance the matrix

The optimum window is obtained by solving equation (45) for the approximate structure of DBB (B), which is expressed as

While taking into account

AndC _wthe optimal problem in equation (45) is transformed into

Wherein the corresponding scalar strip mask matrix is represented as

The invention selects MBAE-SOE window, and the corresponding window function is expressed as

w＝[f_-Q,…,f₀,…,f_Q]a, (47)

Wherein the content of the first and second substances,

the value range of Q is Q-Q, …, Q, and the design parameter coefficient vector can be calculated by the MBAE-SOE design rule and is expressed as a-a_-Q,…,a₀,…,a_Q]^T。

And 4, step 4: based on DBB matrix enhancement method in received signal, corresponding low-complexity equalization algorithm is designed

Suppose the noise term n in equation (27) is white gaussian noise (mean 0, variance σ)²) Then E { zz^H}＝E{nn^H}＝σ²I_K. After windowing, the white gaussian noise becomes colored noisez _wWhose covariance matrix is expressed as

Wherein the content of the first and second substances,

analogy equation (34) can be obtained

Wherein the content of the first and second substances,

by definition

Equation (48) is rewritten as

Assuming efficient transmission of symbol itemsdIs independently and equally distributed in unit power, Edd ^H}＝I_{M N} . Directly performing MMSE block equalization to obtain pairs based on equations (44) to (48)dIs expressed as

However, the matrix inversion operation in equation (51) may bring cubic computation and is not easy to be implemented in engineering. To this end, the present invention alternates the matrix factorization in equations (44) and (50) while taking into account

With an enhanced DBB structure, equation (51) becomes

Wherein the content of the first and second substances,

is a DBB matrix. In addition, the algorithm represented by equation (52) is a transform domain channel equalization algorithm. Specifically, the channel equalization is not directly paired as in equation (51)x _wDone but in its transform domain. At the same time, using a matrixDBB structure of (3), binding Block LDL^HDecomposition, the above-mentioned equalization algorithm only having

Of the system.

And performing performance analysis on the orthogonal signal division multiplexing wireless communication equalization algorithm based on DBB matrix enhancement through a numerical simulation result. Considering a dual selective fading channel in a wireless communication scenario, given an OSDM data block length K of 1024, QPSK is used for information transmission, and a symbol sampling period T is used_sT/K is 0.25ms (where T is 256ms), the channel memory length is L24, and the multipath delay spread is τ_max＝LT_s＝256ms。

Fig. 3 compares the normalized mean square error performance of the direct DBB approximation and the enhanced DBB approximation. At this point, the fixed OSDM vector length is M4, and the normalized doppler spread f is_dT range is [0.1,0.5 ]]. From equation (47), it can be confirmed that the DBB matrix enhancement and the direct DBB approximation are equivalent when Q is 0. When the value of Q is continuously increased, the normalized mean square error under the enhancement of the DBB matrix is far better than that of the direct DBB approximation. FIG. 3 demonstrates the effectiveness of DBB enhancement structures while also making the design less complexA degree OSDM equalizer becomes possible.

Fig. 4 shows the error rate performance of a low complexity OSDM equalization algorithm at different signal to noise ratios. At this time, the vector length is fixed to M4, and the normalized doppler spread is fixed to f_dT is 0.5. Obviously, the equalization performance is always better than the direct DBB approximation when the DBB matrix enhancement method is adopted, and the bit error rate is reduced along with the increase of Q.

Fig. 5 shows the error rate performance of the low complexity OSDM equalization algorithm at different doppler spreads. At this time, the fixed snr is 20dB, Q2. As can be seen from fig. 5, the error rate gradually decreases as M increases. However, with f_dThe error code rate performance is rapidly deteriorated when the direct DBB approximation is adopted due to the increase of T, and the performance loss caused by the Doppler effect can be effectively reduced by an OSDM equalization algorithm when a DBB matrix enhancement method is adopted.