CN101155164A

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Publication number: CN101155164A
Application number: CNA2006101166033A
Authority: CN
Inventors: 李明齐; 芮赟; 张小东; 李元杰; 胡宏林
Original assignee: Shanghai Institute of Microsystem and Information Technology of CAS
Current assignee: Shanghai Han Xun Information Technology Ltd By Share Ltd
Priority date: 2006-09-27
Filing date: 2006-09-27
Publication date: 2008-04-02
Anticipated expiration: 2026-09-27
Also published as: CN101155164B

Abstract

一种DFT扩频的广义多载波系统的SINR估计方法，其通过首先建立所述离散傅立叶变换(DFT)扩频的广义多载波传输系统的信号输入输出之间的数学关系，然后根据信道频率响应、信道噪声方差和均衡方法，设定所述DFT扩频的广义多载波传输系统的频域均衡子载波的均衡系数，再根据所述数学关系及所述频域均衡系数分别计算所述DFT扩频的广义多载波传输系统接收端有用信号的平均功率、信号间干扰的平均功率以及噪声方差，再计算有效信干噪比(SINR)，如此以实现对广义多载波传输系统的有效信干噪比的准确计算，该有效信干噪比估计方法可用于基于离散傅立叶变换扩频的广义多载波传输系统的链路自适应传输方案和无线资源管理方面。A kind of SINR estimation method of the generalized multi-carrier system of DFT spread spectrum, it by first establishing the mathematical relationship between the signal input and output of the generalized multi-carrier transmission system of described discrete Fourier transform (DFT) spread spectrum, then according to the channel frequency response , channel noise variance and equalization method, setting the equalization coefficient of the frequency domain equalization subcarrier of the generalized multi-carrier transmission system of the DFT spread spectrum, and then calculating the DFT spread respectively according to the mathematical relationship and the frequency domain equalization coefficient The average power of the useful signal at the receiving end of the generalized multi-carrier transmission system, the average power of the interference between signals, and the noise variance, and then calculate the effective signal-to-interference-noise ratio (SINR), so as to achieve the effective SINR of the generalized multi-carrier transmission system The effective SINR estimation method can be used in the link adaptive transmission scheme and radio resource management of the generalized multi-carrier transmission system based on discrete Fourier transform spread spectrum.

Description

Translated fromChinese

一种DFT扩频的广义多载波系统的SINR估计方法A SINR Estimation Method for Generalized Multi-Carrier Systems Based on DFT Spread Spectrum

技术领域technical field

本发明涉及一种DFT扩频的广义多载波传输系统的SINR估计方法。The invention relates to a method for estimating SINR of a generalized multi-carrier transmission system of DFT spreading.

背景技术Background technique

单载波频分多址(SC-FDMA)是近年来国际上提出来的一种新型频分多址通信系统，其既具备单载波通信峰均比特性，同时又具备多载波通信的实现简单及资源调度灵活等特性，主要应用于宽带移动通信的上行链路解决方案。目前，SC-FDMA有以下两种实现方式：Single-carrier frequency-division multiple access (SC-FDMA) is a new type of frequency-division multiple access communication system proposed internationally in recent years. Flexible resource scheduling and other features are mainly used in uplink solutions for broadband mobile communications. Currently, SC-FDMA has the following two implementation methods:

1、基于正交频分多址(OFDMA)技术的SC-FDMA；1. SC-FDMA based on Orthogonal Frequency Division Multiple Access (OFDMA) technology;

2、基于滤波器组变换的SC-FDMA。2. SC-FDMA based on filter bank transformation.

其中，对于基于OFDMA技术的SC-FDMA又有以下两种实现形式：Among them, SC-FDMA based on OFDMA technology has the following two implementation forms:

1、通过频域处理的SC-FDMA，也就是基于离散傅立叶变换扩频的正交频分复用多址(DFT-S-OFDMA)，在该系统，各个用户编码调制后的数据符号先经过一个较小点数(通常该点数与分配的子载波数目相同)的离散傅立叶变换(DFT)变换，然后将变换后的数据映射到分配的子载波上传输。由于DFT-S-OFDMA将每个数据符号扩频到所有分配的子载波上传输，使得其传输信号具有单载波信号的特性。因此，与OFDMA系统相比，该系统可明显降低传输信号峰均比，然而，由于DFT-S-OFDM也是基于正交频分复用(OFDM)传输的，因此也具有对同步误差导致的多址干扰敏感的缺陷；1. SC-FDMA through frequency domain processing, that is, Orthogonal Frequency Division Multiple Access (DFT-S-OFDMA) based on discrete Fourier transform spread spectrum. In this system, the coded and modulated data symbols of each user first pass through A discrete Fourier transform (DFT) transformation with a small number of points (usually the number of points is the same as the number of allocated subcarriers), and then the transformed data is mapped to the allocated subcarriers for transmission. Since DFT-S-OFDMA spreads each data symbol to all allocated sub-carriers for transmission, its transmission signal has the characteristics of a single-carrier signal. Therefore, compared with the OFDMA system, this system can significantly reduce the peak-to-average ratio of the transmitted signal. However, since DFT-S-OFDM is also based on Orthogonal Frequency Division Multiplexing (OFDM) transmission, it also has many effects on synchronization errors. Defects sensitive to address interference;

2、通过时域处理的SC-FDMA。时域处理的SC-FDMA也有两种实现方法，一种是将已调制符号数据块直接添加循环前缀，经过成形滤波后，再通过用户特定的频谱搬移，实现频分多址，其传输信号具有连续频谱；另一种是将已调制符号数据块先重复级联，然后添加循环前缀，接着经过成形滤波后，再通过用户特定的频谱搬移，实现频分多址，其传输信号具有离散频谱。事实上，采用该实现方法的系统也称为交织频分复用多址(IFDMA)系统。时域处理的SC-FDMA比DFT-S-OFDMA具有更低的峰均比，但是相对于基于OFDM技术的DFT-S-OFDMA，其频谱利用率明显降低。此外，IFDMA对于对同步误差导致的多址干扰同样非常敏感。2. SC-FDMA through time domain processing. SC-FDMA with time domain processing also has two implementation methods. One is to directly add a cyclic prefix to the modulated symbol data block, after shaping and filtering, and then through user-specific spectrum shifting, frequency division multiple access is realized. The transmission signal has Continuous spectrum; the other is to repeatedly concatenate the modulated symbol data blocks first, then add a cyclic prefix, and then pass through shaping filtering, and then move through user-specific spectrum to realize frequency division multiple access. The transmission signal has a discrete spectrum. In fact, the system using this implementation method is also called an Interleaved Frequency Division Multiple Access (IFDMA) system. SC-FDMA processed in time domain has a lower peak-to-average ratio than DFT-S-OFDMA, but compared with DFT-S-OFDMA based on OFDM technology, its spectrum utilization is significantly lower. In addition, IFDMA is also very sensitive to multiple access interference caused by synchronization errors.

基于滤波器组变换的SC-FDMA，即基于离散傅立叶变换的广义多载波频分多址(DFT-S-GMC)方案，与DFT-S-OFDM类似，即采用DFT进行频域扩频，以降低传输信号峰均比，但是与DFT-S-OFDM不同的是，DFT-S-GMC采用逆滤波器组变换(IFBT)实现频分复用和频分多址，如图1及图2所示，其中，图1为DFT-S-GMC系统的发射机的结构示意图，图2为DFT-S-GMC系统的接收机的结构示意图，以下将对发射机的结构进行分析：SC-FDMA based on filter bank transform, that is, a generalized multi-carrier frequency division multiple access (DFT-S-GMC) scheme based on discrete Fourier transform, is similar to DFT-S-OFDM, that is, DFT is used for frequency domain spreading to Reduce the peak-to-average ratio of the transmission signal, but unlike DFT-S-OFDM, DFT-S-GMC uses inverse filter bank transform (IFBT) to realize frequency division multiplexing and frequency division multiple access, as shown in Figure 1 and Figure 2 Show, wherein, Fig. 1 is the structural representation of the transmitter of DFT-S-GMC system, Fig. 2 is the structural representation of the receiver of DFT-S-GMC system, will analyze the structure of transmitter below:

首先假设第n个IFBT变换时刻输入的第k个已调制符号为a_k(n)，0≤k≤K-1；0≤n≤D-1，K为当前用户占用的子带数目，D表示在每个传输的数据块中复用的IFBT符号数目。经过K点离散傅立叶变换，输出信号为First assume that the kth modulated symbol input at the nth IFBT transformation time is a_k (n), 0≤k≤K-1; 0≤n≤D-1, K is the number of subbands occupied by the current user, D Indicates the number of IFBT symbols multiplexed in each transmitted data block. After K-point discrete Fourier transform, the output signal is

${A A}_{{k k}^{' '}} ((n no)) = = \frac{11}{\sqrt{K K}} {Σ Σ}_{k k = = 00}^{K K - - 11} {a a}_{k k} ((n no)) exp exp ((- - j j 22 πk πk {k k}^{' '} / / K K)),, 00 \leq \leq {k k}^{' '} \leq \leq K K - - 11;; 00 \leq \leq n no \leq \leq D D. - - 11 - - - - - - ((11))$

子带映射将DFT扩频输出信号序列中的每个元素映射到相应的子带上传输。映射方式可以为集中映射和分散映射两种方式。The subband mapping maps each element in the DFT spread spectrum output signal sequence to the corresponding subband for transmission. There are two ways of mapping: centralized mapping and decentralized mapping.

对于分散映射，映射输出为For a scatter map, the map output is

对于集中映射，映射输出为For a centralized map, the map output is

其中，C是特定用户的子带偏移量，M是系统的子带总数，R为子带映射间隔。Wherein, C is the subband offset of a specific user, M is the total number of subbands in the system, and R is the subband mapping interval.

经过逆滤波器组变换(IFBT)，发送的第n个IFBT符号的L个离散值为After inverse filter bank transformation (IFBT), the L discrete values of the nth IFBT symbol sent are

${g g}_{t t} ((n no)) = = {Σ Σ}_{m m = = 00}^{M m - - 11} {b b}_{m m} ((n no)) {f f}_{p p} ((t t)) exp exp ((j j 22 πmt πmt / / M m)),, 00 \leq \leq t t \leq \leq L L - - 11,, 00 \leq \leq n no \leq \leq D D. - - 11 - - - - - - ((33))$

其中f_p(t)为滤波器组原型滤波器的冲击响应，该原型滤波器满足移位正交条件where f_p (t) is the impulse response of the filter bank prototype filter that satisfies the shifted quadrature condition

${Σ Σ}_{t t = = 00}^{L L - - 11} {f f}_{p p} ((t t)) {f f}_{p p}^{* *} ((t t - - kN kN)) = = \{\begin{matrix} 11,, & k k = = 00 \\ 00,, & k k &NotEqual; &NotEqual; 00 \end{matrix} - - - - - - ((44))$

其中，N是原型滤波器的移位正交间隔，上标“*”表示共轭。逆滤波器组变换将宽带信道分割为若干子带传输信号，并且各子带之间是拟正交的。为减小各子带间干扰，原型滤波器满足频域拟正交条件where N is the shifted quadrature interval of the prototype filter, and the superscript "*" indicates the conjugate. The inverse filter bank transform divides the wideband channel into several subbands for transmission, and the subbands are quasi-orthogonal. In order to reduce the interference between sub-bands, the prototype filter satisfies the quasi-orthogonal condition in the frequency domain

${Σ Σ}_{t t = = 00}^{L L - - 11} {f f}_{p p} ((t t)) {f f}_{p p}^{* *} ((t t)) exp exp [[j j 22 π π ((m m - - {m m}^{' '})) t t / / M m]] \{\begin{matrix} = = 11,, & m m = = {m m}^{' '} \\ < < ξ ξ,, & m m &NotEqual; &NotEqual; {m m}^{' '} \end{matrix} - - - - - - ((55))$

其中ξ为比1小得多的常数，表示各子带之间的最大干扰。若设计原型滤波器的移位正交间隔N大于系统子带总数M，可使得各子带之间存在一定的保护频带，以减小相邻子带之间的干扰。原型滤波器可采用根升余弦滤波器，通过尾部补零构成长度为L的滤波器，并且设计L为系统子带总数M的整数倍，则IFBT可用基于FFT的快速算法实现。Where ξ is a constant much smaller than 1, representing the maximum interference between subbands. If the shifted orthogonal interval N of the designed prototype filter is greater than the total number of system subbands M, a certain guard band can exist between each subband to reduce the interference between adjacent subbands. The prototype filter can use a root-raised cosine filter, and a filter of length L is formed by trailing zero padding, and the design L is an integer multiple of the total number of system subbands M, then IFBT can be realized by a fast algorithm based on FFT.

随后，按原型滤波器的移位正交间隔N，移位累加D个长度为L的IFBT符号，其输出为Then, according to the shifted orthogonal interval N of the prototype filter, D IFBT symbols with a length of L are shifted and accumulated, and the output is

$s the s ((t t)) = = {Σ Σ}_{n no = = 00}^{D D. - - 11} {g g}_{t t - - nN n} ((n no)),, 00 \leq \leq t t \leq \leq ((D D. - - 11)) N N + + L L - - 11 - - - - - - ((66))$

为降低子带间的干扰，子带的频率响应的过渡带应尽量陡峭。此时，多子带滤波器组对应的原型滤波器系数将很长，从而导致移位累加输出的信号有很长的拖尾。如果将该信号直接发送出去，将极大降低系统的频谱利用率。为提高频谱效率，经过多子带滤波的信号必须先经过波形截短后再发送出去。如果直接将经过多子带滤波的信号中的拖尾截去，则一方面会导致信号失真，另一方面导致发射信号的频谱泄漏，造成信号的带外干扰。为克服上述缺陷，DFT-S-GMC系统采用循环数据成块方法，即先将移位累加输出的长度为(D-1)N+L的数据序列分割为长度分别为T₁＝(L-N)/2，T₂＝D×N和T₃＝(L-N)/2的三段数据块；然后将第一段数据块累加到第二段数据块的尾部，将第三段数据块累加到第二段数据块的首部，获得的数据块，即S-GMC符号的有效部分，为一首尾连续的循环数据块。循环累加输出为In order to reduce the interference between the sub-bands, the transition band of the frequency response of the sub-bands should be as steep as possible. At this time, the prototype filter coefficients corresponding to the multi-subband filter bank will be very long, resulting in a very long tail of the signal output by shift-accumulation. If the signal is sent out directly, the spectrum utilization rate of the system will be greatly reduced. To improve spectral efficiency, the multi-subband filtered signal must be truncated before being sent out. If the smear in the multi-subband filtered signal is directly truncated, on the one hand, it will cause signal distortion, and on the other hand, it will cause spectrum leakage of the transmitted signal, resulting in out-of-band interference of the signal. In order to overcome the above-mentioned defects, the DFT-S-GMC system adopts a cyclic data block method, that is, first divide the data sequence whose length is (D-1)N+L output by the shift and accumulation into segments whose lengths are respectively T₁ =(LN) /2, three data blocks of T₂ =D×N and T₃ =(LN)/2; then add the first data block to the end of the second data block, and add the third data block to the end of the second data block The header of the two-segment data block, the obtained data block, that is, the effective part of the S-GMC symbol, is a continuous cyclic data block from the beginning to the end. The output of the loop accumulation is

$s^{'} (t) = s (t + T_{1}) R_{T_{2}} (t) + s (t + T_{1} + T_{2}) R_{T_{3}} (t) + s (t) R_{T_{1}} (t),$ 0≤t≤N×D-1(7) ${the s}^{'} (t) = the s (t + T_{1}) R_{T_{2}} (t) + the s (t + T_{1} + T_{2}) R_{T_{3}} (t) + the s (t) R_{T_{1}} (t),$ 0≤t≤N×D-1(7)

其中in

${R R}_{T T} ((t t)) = = \{\begin{matrix} 11,, & 00 \leq \leq t t \leq \leq T T - - 11 \\ 00,, & otherwise otherwise \end{matrix} - - - - - - ((88))$

最后，将生成的循环数据块添加循环前缀，构成完整的S-GMC符号后，经成形滤波，数模转换，上变频，由射频发射即完成信号的发射工作，而接收端完成的是与发射端相反的逆操作(参见文献李明齐，张小东，李元杰，周斌，“基于DFT扩频的广义多载波频分多址上行链路传输方案——DFT-S-GMC”，电信科学，第6期，2006(Xiaodong Zhang，Mingqi Li，Honglin Hu Haifeng Wang Bin Zhou，Xiaohu You，“Dft Spread Generalized Multi-CarrierScheme For Broadband Mobile Communications”，PIMRC 2006；)；张小东李明齐周斌卜智勇，专利“基于多子带滤波器组的发射、接收装置及其方法”，申请号：200510030276.5，申请日期：2005.09.30；3GPP提案，R1-051388，上海无线通信研究中心，“适用于通用陆地无线接入演进上行技术-基于DFT扩频的广义多载波传输方案”，韩国，首尔，11月，2005年(3GPP，R1-051388，SHRCWC，“DFT-S-GMC for EUTRA Uplink”，SHRCWC，Seoul，Korea，Nov.2005))，这里就不再详细赘述。Finally, add a cyclic prefix to the generated cyclic data block to form a complete S-GMC symbol. After shaping and filtering, digital-to-analog conversion, and up-conversion, the signal transmission is completed by radio frequency transmission, and the receiving end completes the same as the transmission. The inverse operation opposite to the terminal (see literature Li Mingqi, Zhang Xiaodong, Li Yuanjie, Zhou Bin, "Generalized Multi-Carrier Frequency Division Multiple Access Uplink Transmission Scheme Based on DFT Spread Spectrum-DFT-S-GMC", Telecommunications Science, No. 6, 2006 (Xiaodong Zhang, Mingqi Li, Honglin Hu Haifeng Wang Bin Zhou, Xiaohu You, "Dft Spread Generalized Multi-CarrierScheme For Broadband Mobile Communications", PIMRC 2006;); 3GPP proposal, R1-051388, Shanghai Wireless Communication Research Center, "Applicable to Universal Terrestrial Wireless Access Evolution Uplink Technology-Based on DFT Spread Spectrum Generalized Multi-Carrier Transmission Scheme", Seoul, Korea, November, 2005 (3GPP, R1-051388, SHRCWC, "DFT-S-GMC for EUTRA Uplink", SHRCWC, Seoul, Korea, Nov.2005)) , which will not be described in detail here.

由于DFT-S-GMC系统每个子带的带宽相对于载波频偏和多普勒频移较大，同时每个子带之间具有一定的频域保护间隔，此外每个子带的频谱具有陡峭的带外衰减，这些特征使得该方案对载波频偏和定时误差引起的多用户间干扰具有较强的鲁棒性，除了具有鲁棒的多址干扰性能外，DFT-S-GMC传输方案还可支持灵活的频域调度和自适应编码调制等链路自适应技术。然而，实现这些技术的关键是必须能在接收端(对于上行链路即为基站)准确估计接收信号的有效信干噪比，而目前还没有针对基于DFT扩频的广义多载波传输方案(DFT-S-GMC)的有效信干噪比(SINR)估计方法，因此，如何解决现有DFT-S-GMC存在的问题实已成为本领域技术人员亟待解决的技术问题。Because the bandwidth of each subband of the DFT-S-GMC system is relatively large relative to the carrier frequency offset and Doppler frequency shift, and there is a certain frequency domain guard interval between each subband, and the spectrum of each subband has a steep band External attenuation, these characteristics make the scheme more robust to multi-user interference caused by carrier frequency offset and timing error. In addition to having robust multiple access interference performance, the DFT-S-GMC transmission scheme can also support Link adaptive technologies such as flexible frequency domain scheduling and adaptive coding and modulation. However, the key to realizing these technologies is to be able to accurately estimate the effective signal-to-interference-noise ratio of the received signal at the receiving end (for the uplink, the base station), and there is no generalized multi-carrier transmission scheme based on DFT spreading (DFT -S-GMC) effective signal-to-interference-noise ratio (SINR) estimation method, therefore, how to solve the existing problems of DFT-S-GMC has become a technical problem to be solved urgently by those skilled in the art.

发明内容Contents of the invention

本发明的目的在于提供一种DFT扩频的广义多载波传输系统的SINR估计方法，以实现准确计算基于DFT扩频的广义多载波传输系统的信干噪比。The purpose of the present invention is to provide a method for estimating SINR of a generalized multi-carrier transmission system based on DFT spreading, so as to realize accurate calculation of the SINR of the generalized multi-carrier transmission system based on DFT spreading.

为了达到上述目的，本发明提供的DFT扩频的广义多载波传输系统的SINR估计方法，其包括步骤：1)建立所述DFT扩频的广义多载波传输系统的信号输入输出之间的数学关系；2)根据所述DFT扩频的广义多载波传输系统的信道频率响应、信道噪声方差和均衡方法，设定所述DFT扩频的广义多载波传输系统的频域均衡子载波的均衡系数；3)根据所述数学关系及所述频域均衡系数计算所述DFT扩频的广义多载波传输系统接收端有用信号的平均功率；4)根据所述接收端有用信号的平均功率计算所述接收端信号间干扰的平均功率；5)根据所述数学关系及所述频域均衡系数计算所述接收端相应噪声的噪声方差；6)根据所述有用信号的平均功率、所述信号间干扰的平均功率、所述噪声方差计算所述SINR。In order to achieve the above object, the SINR estimation method of the generalized multi-carrier transmission system of DFT spreading provided by the present invention comprises the steps of: 1) establishing the mathematical relationship between the signal input and output of the generalized multi-carrier transmission system of DFT spreading ; 2) according to the channel frequency response, the channel noise variance and the equalization method of the generalized multi-carrier transmission system of the DFT spreading, the equalization coefficient of the frequency domain equalization subcarrier of the generalized multi-carrier transmission system of the DFT spreading is set; 3) Calculate the average power of the useful signal at the receiving end of the DFT spread generalized multi-carrier transmission system according to the mathematical relationship and the frequency domain equalization coefficient; 4) Calculate the receiving end according to the average power of the useful signal at the receiving end 5) Calculate the noise variance of the corresponding noise at the receiving end according to the mathematical relationship and the frequency domain equalization coefficient; 6) According to the average power of the useful signal and the power of the inter-signal interference The average power, the noise variance calculates the SINR.

所述数学关系为：The mathematical relationship is:

$\overset{^^}{D D.} = = {F f}_{K K}^{H h} {T T}_{M m,, K K}^{T T} {F f}_{M m} {Γ Γ}_{L L,, M m}^{T T} {γ γ}_{L L}^{H h} {Ω Ω}_{N N,, L L}^{H h} {F f}_{N N}^{H h} {H h}^{H h} WR WR$

$= = {F f}_{K K}^{H h} {T T}_{M m,, K K}^{T T} {F f}_{M m} {Γ Γ}_{L L,, M m}^{T T} {γ γ}_{L L}^{H h} {Ω Ω}_{N N,, L L}^{H h} {F f}_{N N}^{H h} {H h}^{H h} {WHF WHF}_{N N} {Ω Ω}_{N N,, L L} {γ γ}_{L L} {Γ Γ}_{L L,, M m} {F f}_{M m}^{H h} {T T}_{M m,, K K} {F f}_{K K} {D D.}_{K K}$

$+ + {F f}_{K K}^{H h} {T T}_{M m,, K K}^{T T} {F f}_{M m} {Γ Γ}_{L L,, M m}^{T T} {γ γ}_{L L}^{H h} {Ω Ω}_{N N,, L L}^{H h} {F f}_{N N}^{H h} {H h}^{H h} WZ WZ$

其中，上标“H”表示共轭转置，F_MΓ_L，M^TΥ_L^H为M点滤波器组变换(FBT)矩阵；T_M，K^T为K×M子带解映射矩阵；F_K^H为K×K IDFT解扩矩阵； $Ω_{N, L} = [\begin{matrix} I_{L} \\ 0_{(N - L) \times L} \end{matrix}],$ I_L为L×L的单位矩阵，0_(N-L)×L为(N-L)×L零矩阵；H为N×N对角矩阵，其对角元素矢量[H₀ H₁ …H_N-1]^T为频域均衡子载波的信道频率响应；W为N×N对角矩阵，其对角元素矢量[ω₀ ω₁ …ω_m…ω_N-1]^T为频域均衡系数；F_M是M点DFT变换矩阵，并且 $F_{M} F_{M}^{H} = I_{M};$ Υ_LΓ_L，MF_M^H为M点逆滤波器组变换(IFBT)矩阵，其中，F_M是M点FFT变换酉矩阵，并且 $F_{M} F_{M}^{H} = I_{M},$ Γ_L，M为L×M的级联扩展矩阵，并且Γ_L，M＝[I_M，I_M，…，I_M]^T，I_M为M×K的单位矩阵，L为M的整数倍，Υ_L为L×L为对角矩阵，其对角元素为多子带滤波器组原型滤波器L点系数f_p(t)，t＝0，1，...，L-1；D_K为长度为K的调制符号矢量；Z是方差为σ²的时域加性高斯白噪声矢量的N点DFT变换输出矢量。Wherein, the superscript "H" represents the conjugate transpose, F_M Γ_{L, M}^T Y_L^H is an M-point filter bank transformation (FBT) matrix; T_{M, K}^T is a K×M subband demapping matrix; F_K^H is the K×K IDFT despreading matrix; $Ω_{N, L} = [\begin{matrix} I_{L} \\ 0_{(N - L) \times L} \end{matrix}],$ I_L is a unit matrix of L×L, 0_(NL)×L is a (NL)×L zero matrix; H is an N×N diagonal matrix, and its diagonal element vector [H₀ H₁ ...H_N-1 ]^T is the channel frequency response of frequency-domain equalized subcarriers; W is an N×N diagonal matrix, and its diagonal element vector [ω₀ ω₁ …ω_m …ω_N-1 ]^T is the frequency-domain equalization coefficient; F_M is M-point DFT transformation matrix, and $f_{m} f_{m}^{h} = I_{m};$ Υ_L Γ_{L, M} F_M^H is an M-point inverse filter bank transform (IFBT) matrix, wherein, F_M is an M-point FFT transformation unitary matrix, and $f_{m} f_{m}^{h} = I_{m},$ Γ_{L, M} is a concatenated expansion matrix of L×M, and Γ_{L, M} =[I_M , I_M ,…, I_M ]^T , I_M is an identity matrix of M×K, and L is an integer multiple of M , Υ_L is L×L is a diagonal matrix, and its diagonal elements are multi-subband filter bank prototype filter L point coefficient f_p (t), t=0,1,...,L-1; D_K is the modulation symbol vector with length K; Z is the N-point DFT transform output vector of time-domain additive Gaussian white noise vector with variance^σ2 .

当所述DFT扩频的广义多载波传输系统为包含1个发射天线及1个接收天线的DFT扩频的广义多载波传输系统时，若所述DFT扩频的广义多载波传输系统采用迫零均衡，所述步骤2)中设定第m个频域均衡子载波对应的均衡系数ω_m为 $ω_{m} = \frac{1}{{| H_{m} |}^{2}},$ 其中，H_m为第m个频域均衡子载波的信道频率响应；若所述DFT扩频的广义多载波传输系统采用最小均方误差均衡，所述步骤2)中设定第m个频域均衡子载波对应的均衡系数ω_m为 $ω_{m} = \frac{1}{{| H_{m} |}^{2} + σ^{2}},$ 其中，H_m为第m个频域均衡子载波的信道频率响应，σ²为频域均衡子载波的噪声方差，而当所述DFT扩频的广义多载波传输系统为包含1个发射天线及多个接收天线的DFT扩频的广义多载波传输系统时，若所述DFT扩频的广义多载波传输系统采用迫零均衡，所述步骤2)中设定第m个频域均衡子载波对应的均衡系数ω_m为 ${\tilde{ω}}_{m} = \frac{1}{Σ_{n = 1}^{Nr} {| H_{m}^{n} |}^{2}},$ 其中，H_mⁿ为发射天线到第n个接收天线之间的多径信道中第m个频域均衡子载波的信道频率响应；若所述DFT扩频的广义多载波传输系统采用最小均方误差均衡，所述步骤2)中设定第m个频域均衡子载波对应的均衡系数ω_m为 ${\tilde{ω}}_{m} = \frac{1}{Σ_{n = 1}^{Nr} {| H_{m}^{n} |}^{2} + σ^{2}},$ 其中，H_mⁿ为发射天线到第n个接收天线之间的多径信道中第m个频域均衡子载波的信道频率响应，σ²为频域均衡子载波的噪声方差。When the generalized multi-carrier transmission system of DFT spreading is a generalized multi-carrier transmission system of DFT spreading comprising 1 transmitting antenna and 1 receiving antenna, if the generalized multi-carrier transmission system of DFT spreading adopts zero-forcing equalization, the equalization coefficient_ωm corresponding to the mth frequency domain equalization subcarrier is set in the step 2) as $ω_{m} = \frac{1}{{| h_{m} |}^{2}},$ Wherein, H_m is the channel frequency response of the equalized subcarrier in the m frequency domain; if the generalized multi-carrier transmission system of the DFT spread spectrum adopts minimum mean square error equalization, the m frequency domain is set in the step 2) The equalization coefficient ω_m corresponding to the equalized subcarrier is $ω_{m} = \frac{1}{{| h_{m} |}^{2} + σ^{2}},$ Wherein, H_m is the channel frequency response of the mth frequency-domain equalized subcarrier,^σ2 is the noise variance of the frequency-domain equalized subcarrier, and when the generalized multi-carrier transmission system of DFT spread spectrum includes 1 transmitting antenna and During the generalized multi-carrier transmission system of the DFT spread spectrum of multiple receiving antennas, if the generalized multi-carrier transmission system of the DFT spread spectrum adopts zero-forcing equalization, the mth frequency domain equalization subcarrier is set in the step 2) to correspond to The equalization coefficient ω_m is ${\tilde{ω}}_{m} = \frac{1}{Σ_{no = 1}^{Nr} {| h_{m}^{no} |}^{2}},$ Wherein, H_mⁿ is the channel frequency response of the mth frequency-domain equalized subcarrier in the multipath channel between the transmitting antenna and the nth receiving antenna; if the generalized multi-carrier transmission system of DFT spread spectrum adopts the least mean square Error equalization, the equalization coefficient_ωm corresponding to the mth frequency domain equalization subcarrier is set in the step 2) as ${\tilde{ω}}_{m} = \frac{1}{Σ_{no = 1}^{Nr} {| h_{m}^{no} |}^{2} + σ^{2}},$ Among them, H_mⁿ is the channel frequency response of the mth frequency domain equalized subcarrier in the multipath channel between the transmitting antenna and the nth receiving antenna, and^σ2 is the noise variance of the frequency domain equalized subcarrier.

所述步骤3)中的有用信号的平均功率计算式为：The average power calculation formula of useful signal in described step 3) is:

${E E.}_{s the s}^{' '} = = {| | \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {\overset{~ ~}{H h}}_{k k} | |}^{22}$

其中，E_s′为有用信号的平均功率，所述步骤4)中信号间干扰的平均功率计算式为：Wherein, E_s ' is the average power of the useful signal, and the average power calculation formula of the inter-signal interference in the step 4) is:

${σ σ}_{ISI ISI}^{22} = = \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {| | {\overset{~ ~}{H h}}_{k k} | |}^{22} - - {| | \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {\overset{~ ~}{H h}}_{k k} | |}^{22}$

其中，σ_ISI²为信号间干扰的平均功率，所述步骤5)中噪声方差计算式为：Wherein, σ_ISI² is the average power of inter-signal interference, and the noise variance calculation formula in the step 5) is:

${σ σ}_{n no}^{22} = = \frac{{σ σ}^{22}}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {\overset{~ ~}{H h}}_{k k}^{' '}$

其中，σ_n²为噪声方差，所述步骤6)中有效信干噪比计算式为：Wherein, σ_n² is the noise variance, and the effective SINR calculation formula in the step 6) is:

$SINR SINR = = \frac{{E E.}_{s the s}^{' '}}{{σ σ}_{n no}^{22} + + {σ σ}_{ISI ISI}^{22}}$

$= = \frac{{| | \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {\overset{~ ~}{H h}}_{k k} | |}^{22}}{\frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {\overset{&OverBar; &OverBar;}{H h}}_{k k} {σ σ}^{22} + + \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {| | {\overset{~ ~}{H h}}_{k k} | |}^{22} - - {| | \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {\overset{~ ~}{H h}}_{k k} | |}^{22}}$

综上所述，本发明的DFT扩频的广义多载波传输系统的有效信干噪比估计方法是针对多径慢时变信道下的DFT-S-GMC系统，提出一种有效信干噪比估计方法，实现了对有效信干噪比的估计。In summary, the effective SINR estimation method of the DFT spread spectrum generalized multi-carrier transmission system of the present invention is aimed at the DFT-S-GMC system under the multipath slow time-varying channel, and proposes an effective SINR The estimation method realizes the estimation of the effective SINR.

附图说明Description of drawings

图1为DFT扩频的广义多载波传输系统的发射机的结构示意图。FIG. 1 is a structural schematic diagram of a transmitter of a generalized multi-carrier transmission system of DFT spread spectrum.

图2为DFT扩频的广义多载波传输系统的接收机的结构示意图。FIG. 2 is a schematic structural diagram of a receiver of a generalized multi-carrier transmission system of DFT spreading.

图3为本发明的DFT扩频的广义多载波传输系统的有效信干噪比映射性能示意图。FIG. 3 is a schematic diagram of the effective SINR mapping performance of the DFT spread spectrum generalized multi-carrier transmission system of the present invention.

图4为本发明的DFT扩频的广义多载波传输系统的有效信干噪比映射性能示意图。FIG. 4 is a schematic diagram of the effective SINR mapping performance of the DFT spread spectrum generalized multi-carrier transmission system of the present invention.

具体实施方式Detailed ways

一、当本发明的DFT扩频的广义多载波传输系统为包含1个发射天线1个接收天线的DFT-S-GMC系统时，主要执行以下步骤：One, when the generalized multi-carrier transmission system of DFT spread spectrum of the present invention is the DFT-S-GMC system that comprises 1 transmitantenna 1 receive antenna, mainly perform the following steps:

步骤1)：建立所述DFT扩频的广义多载波传输系统的信号输入输出之间的数学关系，即建立1个发射天线1个接收天线的DFT-S-GMC信号模型，由现有DFT-S-GMC传输方案可知，每个接收的数据块是由若干个时域波形符号移位累加(复用)而得到(可参见背景技术中的第6式)。但由于原型滤波器满足移位正交性(可参见背景技术中的第4式)，所以可以近似认为均衡后的数据块中复用的各时域波形符号是互不干扰的，这可以在后续仿真中得以证实。因此，为分析简便，在此仅考虑一个时域波形复用的情况：Step 1): establish the mathematical relationship between the signal input and output of the generalized multi-carrier transmission system of DFT spread spectrum, that is, establish the DFT-S-GMC signal model of 1 transmitting antenna and 1 receiving antenna, by the existing DFT- It can be seen from the S-GMC transmission scheme that each received data block is obtained by shifting and accumulating (multiplexing) several time-domain waveform symbols (refer to Equation 6 in the background art). However, since the prototype filter satisfies shift orthogonality (refer to Equation 4 in the background art), it can be approximately considered that the multiplexed time-domain waveform symbols in the equalized data block do not interfere with each other, which can be obtained in It was confirmed in subsequent simulations. Therefore, for the convenience of analysis, only one time-domain waveform multiplexing situation is considered here:

假设，在发送端，长度为K的调制符号矢量D_K，可以表示为：Suppose, at the sending end, the modulation symbol vector D_K with length K can be expressed as:

${D D.}_{K K} = = [\begin{matrix} {d d}_{11} \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ {d d}_{K K} \end{matrix}] - - - - - - ((99))$

所以D_K经过K点DFT扩频，子带映射，M点逆滤波器组变换(IFBT)后，形成长度为L点的并行序列Therefore, after D_K undergoes K-point DFT spreading, sub-band mapping, and M-point inverse filter bank transformation (IFBT), a parallel sequence with a length of L points is formed.

${s the s}^{' '} = = {γ γ}_{L L} {Γ Γ}_{L L,, M m} {F f}_{M m}^{H h} {T T}_{M m,, K K} {F f}_{K K} {D D.}_{K K} - - - - - - ((1010))$

这里，F_K为K×KDFT扩频矩阵，并且Here, F_K is the K×KDFT spreading matrix, and

${F f}_{K K} = = \frac{11}{\sqrt{K K}} {(\begin{matrix} 11 & {W W}_{K K}^{00 - - 11} & \cdot \cdot \cdot &Center Dot; \cdot \cdot & {W W}_{K K}^{00 - - ((K K - - 11))} \\ 11 & {W W}_{K K}^{11 - - 11} & \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot & {W W}_{K K}^{11 - - ((K K - - 11))} \\ \cdot \cdot \cdot &Center Dot; \cdot &Center Dot; & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & \cdot \cdot \cdot &Center Dot; \cdot \cdot & \cdot \cdot \cdot &Center Dot; \cdot &Center Dot; \\ 11 & {W W}_{K K}^{((K K - - 11)) \cdot &Center Dot; 11} & \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot & {W W}_{K K}^{((K K - - 11)) \cdot &Center Dot; ((K K - - 11))} \end{matrix})}_{K K \times \times K K} - - - - - - ((1111))$

其中 $W_{K}^{x} = \exp (- j 2 πx / K),$ $F_{K}^{H} F_{K} = F_{K} F_{K}^{H} = I_{K},$ I_K为K×K的单位矩阵，上标“H”表示共轭转置；in $W_{K}^{x} = \exp (- j 2 πx / K),$ $f_{K}^{h} f_{K} = f_{K} f_{K}^{h} = I_{K},$ I_K is the identity matrix of K×K, and the superscript "H" means conjugate transpose;

T_M，K为M×K子带映射矩阵，其M×K个元素中只有K个元素为“1”，其余为“0”，如果希望将经过K点快速傅里叶变换(FFT变换)输出的第k个元素映射到第m个子带上传输，则将T_M，K的第m行第k列的元素置为“1”：T_{M, K} is the M×K subband mapping matrix, only K elements are “1” among the M×K elements, and the rest are “0”. The kth element of the output is mapped to the mth subband for transmission, then the element in the mth row and kth column of_{TM, K} is set to "1":

Υ_LΓ_L，MF_M^H为M点逆滤波器组变换(IFBT)矩阵，其中F_M是M点FFT变换酉矩阵，并且 $F_{M} F_{M}^{H} = I_{M};$ Υ_L Γ_{L, M} F_M^H is an M-point inverse filter bank transform (IFBT) matrix, where F_M is an M-point FFT transform unitary matrix, and $f_{m} f_{m}^{h} = I_{m};$

Γ_L，M为L×M的级联扩展矩阵，并且Γ_L，M＝[I_M，I_M，…，I_M]^T，I_M为M×K的单位矩阵，L为M的整数倍；Γ_{L, M} is a concatenated expansion matrix of L×M, and Γ_{L, M} =[I_M , I_M ,…, I_M ]^T , I_M is an identity matrix of M×K, and L is an integer multiple of M ;

Υ_L为L×L为对角矩阵，其对角元素为多子带滤波器组原型滤波器L点系数f_p(t)，t＝0，1，...，L-1。Υ_L is L×L is a diagonal matrix, and its diagonal elements are the multi-subband filter bank prototype filter L-point coefficients f_p (t), t=0, 1, ..., L-1.

由于只考虑一个时域波形复用的情况，输出的数据矢量为IFBT变换输出数据矢量尾部添加N-L个零，以形成长度为N的并行数据矢量Since only one time-domain waveform multiplexing is considered, the output data vector adds N-L zeros to the end of the IFBT transformation output data vector to form a parallel data vector of length N

$s the s = = {Ω Ω}_{N N,, L L} {γ γ}_{L L} {Γ Γ}_{L L,, M m} {F f}_{M m}^{H h} {T T}_{M m,, K K} {F f}_{K K} {D D.}_{K K} - - - - - - ((1212))$

其中， $Ω_{N, L} = [\begin{matrix} I_{L} \\ 0_{(N - L) \times L} \end{matrix}],$ I_L为L×L的单位矩阵，0_(N-L)×L为(N-L)×L零矩阵。最后序列s添加循环前缀后发射输出。in, $Ω_{N, L} = [\begin{matrix} I_{L} \\ 0_{(N - L) \times L} \end{matrix}],$ I_L is a unit matrix of L×L, and 0_(NL)×L is a (NL)×L zero matrix. The final sequence s emits the output after adding the cyclic prefix.

接着经过多径信道后，在接收端，首先将接收到的数据去除循环前缀后，经过N点DFT变换，得到频域数据矢量R，R可以表示为：Then after passing through the multipath channel, at the receiving end, first remove the cyclic prefix from the received data, and then undergo N-point DFT transformation to obtain the frequency domain data vector R, which can be expressed as:

$R R = = {HF HF}_{N N} {Ω Ω}_{N N,, L L} {γ γ}_{L L} {Γ Γ}_{L L,, M m} {F f}_{M m}^{H h} {T T}_{M m,, K K} {F f}_{K K} {D D.}_{K K} + + Z Z - - - - - - ((1313))$

其中，Z是方差为σ²的时域加性高斯白噪声(AWGN噪声)矢量的N点DFT变换输出矢量；Wherein, Z is the N-point DFT transform output vector of the time-domain additive white Gaussian noise (AWGN noise) vector whose variance is^σ2 ;

F_M是M点DFT变换矩阵，并且 $F_{M} = F_{M}^{H} = I_{M};$ F_M is the M-point DFT transformation matrix, and $f_{m} = f_{m}^{h} = I_{m};$

H为N×N对角矩阵，其对角元素矢量[H₀ H₁ …H_N-1]^T为频域均衡子载波的信道频率响应。信道频率响应在实际的系统中可通过导频估计得到，而在仿真中认为完全己知。H is an N×N diagonal matrix, and its diagonal element vector [H₀ H₁ ...H_N-1 ]^T is the channel frequency response of the frequency domain equalized subcarrier. The channel frequency response can be obtained through pilot estimation in the actual system, but it is considered completely known in the simulation.

经过频域均衡后，可得时域数据矢量After frequency domain equalization, the time domain data vector can be obtained

${R R}^{' '} = = {F f}_{N N}^{H h} {H h}^{H h} WR WR - - - - - - ((1414))$

其中，W为N×N对角矩阵，其对角元素矢量[ω₀ ω₁ …ω_m…ω_N-1]^T为频域均衡系数。对频域均衡后的数据矢量，先截取前L点数据，并对该L点数据进行M点滤波器组变换(FBT)后，子带解映射，再经过K点离散傅里叶反变换(IDFT)解扩，可得估计的K点数据符号矢量即信号输入输出之间的关系：Among them, W is an N×N diagonal matrix, and its diagonal element vector [ω₀ ω₁ ...ω_m ...ω_N-1 ]^T is the frequency domain equalization coefficient. For the data vector after frequency domain equalization, the first L point data is intercepted, and after the M point filter bank transformation (FBT) is performed on the L point data, the subband is demapped, and then the K point discrete Fourier inverse transform ( IDFT) despreading, the estimated K-point data symbol vector, that is, the relationship between the signal input and output can be obtained:

$+ + {F f}_{K K}^{H h} {T T}_{M m,, K K}^{T T} {F f}_{M m} {Γ Γ}_{L L,, M m}^{T T} {γ γ}_{L L}^{H h} {Ω Ω}_{N N,, L L}^{H h} {F f}_{N N}^{H h} {H h}^{H h} WZ WZ - - - - - - ((1515))$

上式中第一项为有用信号和符号间干扰分量，第二项为噪声分量。The first item in the above formula is the useful signal and the intersymbol interference component, and the second item is the noise component.

并且(17)式中，与发射端相对应And in formula (17), corresponding to the transmitter

F_MΓ_L，M^TΥ_L^H为M点滤波器组变换(FBT)矩阵；F_M Γ_{L, M}^T Υ_L^H is an M-point filter bank transformation (FBT) matrix;

T_M，K^T为K×M子带解映射矩阵；T_{M, K}^T is the K×M subband demapping matrix;

F_K^H为K×K IDFT解扩矩阵。F_K^H is a K×K IDFT despreading matrix.

步骤2)：根据所述DFT扩频的广义多载波传输系统的信道频率响应、信道噪声方差和均衡方法，设定所述DFT扩频的广义多载波传输系统的频域均衡子载波的均衡系数，在本实施例中，信道噪声采用AWGN噪声，对于迫零(ZF)均衡，设定第m个频域均衡子载波对应的均衡系数ω_m为：Step 2): According to the channel frequency response, channel noise variance and equalization method of the generalized multi-carrier transmission system of DFT spreading, the equalization coefficient of the frequency domain equalization subcarrier of the generalized multi-carrier transmission system of DFT spreading is set , in this embodiment, the channel noise adopts AWGN noise, and for zero-forcing (ZF) equalization, the equalization coefficient ω_m corresponding to the mth frequency-domain equalization subcarrier is set as:

${ω ω}_{m m} = = \frac{11}{{| | {H h}_{m m} | |}^{22}} - - - - - - ((1616))$

而对于最小均方误差(MMSE)均衡，则设定第m个频域均衡子载波对应的均衡系数ω_m为：For minimum mean square error (MMSE) equalization, the equalization coefficient ω_m corresponding to the mth frequency domain equalized subcarrier is set as:

${ω ω}_{m m} = = \frac{11}{{| | {H h}_{m m} | |}^{22} + + {σ σ}^{22}} - - - - - - ((1717))$

其中，H_m为第m个频域均衡子载波的信道频率响应，σ²为频域均衡子载波的噪声方差。Among them, H_m is the channel frequency response of the mth frequency domain equalization subcarrier, and^σ2 is the noise variance of the frequency domain equalization subcarrier.

步骤3)：根据所述数学关系及所述频域均衡系数计算所述DFT扩频的广义多载波传输系统接收端有用信号的平均功率，其包括以下步骤：Step 3): Calculate the average power of the useful signal at the receiving end of the generalized multi-carrier transmission system of the DFT spread spectrum according to the mathematical relationship and the frequency domain equalization coefficient, which includes the following steps:

第一步：由所建立的数学关系式(15)第一项可得The first step: from the established mathematical relation (15) the first item can be obtained

${D D.}^{' '} = = {F f}_{K K}^{H h} {T T}_{M m,, K K}^{T T} {F f}_{M m} {Γ Γ}_{L L,, M m}^{T T} {γ γ}_{L L}^{H h} {Ω Ω}_{N N,, L L}^{H h} {F f}_{N N}^{H h} {H h}^{H h} {WHF WHF}_{N N} {Ω Ω}_{N N,, L L} {γ γ}_{L L} {Γ Γ}_{L L,, M m} {F f}_{M m}^{H h} {T T}_{M m,, K K} {F f}_{K K} {D D.}_{K K} - - - - - - ((1818))$

根据频域均衡子载波的信道频率响应[H₀ H₁ ... H_N-1]^T和所设定的频域均衡子载波对应的均衡系数[ω₀ ω₁ …ω_m …ω_N-1]^T(即第(16)及(17)式)，计算对角矩阵According to the channel frequency response [H₀ H₁ ... H_N-1 ]^T of the frequency domain equalization subcarrier and the equalization coefficient corresponding to the set frequency domain equalization subcarrier [ω₀ ω₁ ...ω_m ...ω_{N- 1} ]^T (i.e. (16) and (17)), calculate the diagonal matrix

Λ_N＝H^HWH＝diag{|H₀|²ω₀，|H₁|²ω₁，...，|H_N-1|²ω_N-1} (19)Λ_N ＝H^H WH＝diag{|H₀ |² ω₀ , |H₁ |² ω₁ ,..., |H_N-1 |² ω_N-1 } (19)

diag{A}表示以矢量A为对角元素的对角矩阵。diag{A} represents a diagonal matrix with vector A as the diagonal elements.

第二步：计算矩阵Step 2: Calculate the Matrix

$h h = = {F f}_{N N}^{H h} {Λ Λ}_{N N} {F f}_{N N} - - - - - - ((2020))$

由于Λ_N为对角阵，所以h为一循环对称矩阵，并且h第一列元素矢量为Since Λ_N is a diagonal matrix, h is a cyclic symmetric matrix, and the element vector of the first column of h is

${h h}_{00} = = \frac{11}{\sqrt{N N}} {F f}_{N N}^{H h} {[\begin{matrix} {| | {H h}_{00} | |}^{22} {ω ω}_{00} & {| | {H h}_{11} | |}^{22} {ω ω}_{11} & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {| | {H h}_{N N - - 11} | |}^{22} {ω ω}_{N N - - 11} \end{matrix}]}^{T T}$

h的其余列矢量可由h₀循环移位获得。The remaining column vectors of h can be obtained by h₀ cyclic shift.

第三步：截取矩阵h左上角的前L行和前L列，构成的L×L矩阵Step 3: Intercept the first L rows and first L columns in the upper left corner of the matrix h to form an L×L matrix

$\overset{~ ~}{h h} = = {Ω Ω}_{N N,, L L}^{H h} h h {Ω Ω}_{N N,, L L} - - - - - - ((21 twenty one))$

第四步：将矩阵分割成(L/M)×(L/M)的块矩阵，每个矩阵块的大小为M×M，其中第i行和前j列的矩阵块可表示为Step 4: Convert the matrix Divided into (L/M)×(L/M) block matrix, the size of each matrix block is M×M, where the matrix block in the i-th row and the first j column can be expressed as

其中

为矩阵

第i行第j列元素；in

for the matrix

element in row i and column j;

第五步：分别计算P_ih_i，jP_j第一列向量Step 5: Calculate the first column vector of P_i h_{i, j} P_j respectively

${b b}_{i i,, j j} = = {P P}_{i i} {h h}_{i i,, j j} {P P}_{} j j [\begin{matrix} 11 \\ 00_{((M m - - 11)) \times \times 11} \end{matrix}] - - - - - - ((23 twenty three))$

其中P_i为M×M对角阵，其对角元素为{f_p(i×M)，f_p(i×M+1)，…，f_p(i×M+M-1)}，f_p(t)，t＝0，1，...，L-1为多子带滤波器组原型滤波器系数。0_(M-t)×1为(M-1)×1零列向量。Among them, P_i is an M×M diagonal matrix, and its diagonal elements are {f_p (i×M), f_p (i×M+1),…, f_p (i×M+M-1)}, f_p (t), t=0, 1, . . . , L-1 are the prototype filter coefficients of the multi-subband filter bank. 0_(Mt)×1 is a (M-1)×1 zero column vector.

第六步：叠加b_i，j，并进行M点DFT变换，可得列向量Step 6: Superimpose b_{i, j} and perform M-point DFT transformation to obtain a column vector

$B B = = \sqrt{M m} {F f}_{M m} {{{Σ Σ}_{i i,, j j = = 00}^{L L / / M m - - 11} {b b}_{i i,, j j}}} - - - - - - ((24 twenty four))$

第七步：经过子带解映射，提取占用子带上的信号分量Step 7: After subband demapping, extract the signal components on the occupied subbands

${[\begin{matrix} {\overset{~ ~}{H h}}_{00} & {\overset{~ ~}{H h}}_{11} & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {\overset{~ ~}{H h}}_{K K - - 11} \end{matrix}]}^{T T} = = {T T}_{M m,, K K}^{H h} B B - - - - - - ((2525))$

第八步：计算有用信号平均功率Step 8: Calculate the average power of the useful signal

${E E.}_{s the s}^{' '} = = {| | \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {\overset{~ ~}{H h}}_{k k} | |}^{22} - - - - - - ((2626))$

事实上，矩阵 $Γ_{L, M}^{T} γ_{L}^{H} \tilde{h} γ_{L} Γ_{L, M} = Σ_{i, j = 0}^{L / M - 1} P_{i} h_{i, j} P_{j}$ 可近似为循环矩阵，则 $F_{M} {Σ_{i, j = 0}^{L / M - 1} P_{i} h_{i, j} P_{j}} F_{M}^{H}$ 为M×M对角阵，其对角元素矢量与B相同，并且In fact, the matrix $Γ_{L, m}^{T} γ_{L}^{h} \tilde{h} γ_{L} Γ_{L, m} = Σ_{i, j = 0}^{L / m - 1} P_{i} h_{i, j} P_{j}$ can be approximated as a circular matrix, then $f_{m} {Σ_{i, j = 0}^{L / m - 1} P_{i} h_{i, j} P_{j}} f_{m}^{h}$ is an M×M diagonal matrix with the same diagonal element vectors as B, and

${T T}_{M m,, K K}^{T T} {F f}_{M m} {{{Σ Σ}_{i i,, j j = = 00}^{L L / / M m - - 11} {P P}_{i i} {h h}_{i i,, j j} {P P}_{j j}}} {F f}_{M m}^{H h} {T T}_{M m,, K K} = = diag diag (({\overset{~ ~}{H h}}_{00},, {\overset{~ ~}{H h}}_{11},, . . . . . .,, {\overset{~ ~}{H h}}_{K K - - 11})) = = {Λ Λ}_{K K} - - - - - - ((2727))$

由DFT变换性质可知，F_K^HΛ_KF_K为循环矩阵。令According to the properties of DFT transformation, F_K^H Λ_K F_K is a circular matrix. make

${F f}_{K K}^{H h} {Λ Λ}_{K K} {F f}_{K K} = = (\begin{matrix} {h h}_{00} & {h h}_{K K - - 11} & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & {h h}_{11} \\ {h h}_{11} & {h h}_{00} & \cdot \cdot & \cdot \cdot & \cdot &Center Dot; & {h h}_{22} \\ \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ {h h}_{K K - - 11} & {h h}_{K K - - 22} & \cdot \cdot & \cdot \cdot & \cdot &Center Dot; & {h h}_{00} \end{matrix}) - - - - - - ((2828))$

其中in

${[\begin{matrix} {h h}_{00} & {h h}_{11} & \cdot &Center Dot; \cdot \cdot \cdot &Center Dot; & {h h}_{K K - - 11} \end{matrix}]}^{T T} = = \frac{11}{\sqrt{K K}} {F f}_{K K}^{H h} {[\begin{matrix} {\overset{~ ~}{H h}}_{00} & {\overset{~ ~}{H h}}_{11} & \cdot &Center Dot; \cdot \cdot \cdot &Center Dot; & {\overset{~ ~}{H h}}_{K K - - 11} \end{matrix}]}^{T T} - - - - - - ((2929))$

这样，(18)式可表示为In this way, (18) can be expressed as

${D D.}^{' '} = = (\begin{matrix} {h h}_{00} & {h h}_{K K - - 11} & \cdot \cdot & \cdot \cdot & \cdot &Center Dot; & {h h}_{11} \\ {h h}_{11} & {h h}_{00} & \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; & {h h}_{22} \\ \cdot \cdot & \cdot \cdot & \cdot &Center Dot; \\ \cdot \cdot & \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot \cdot \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ {h h}_{K K - - 11} & {h h}_{K K} & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & {h h}_{00} \end{matrix}) [\begin{matrix} {d d}_{11} \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot \cdot \\ {d d}_{K K} \end{matrix}] = = [\begin{matrix} {h h}_{00} {d d}_{11} + + {ISI ISI}_{11} \\ {h h}_{00} {d d}_{22} + + {ISI ISI}_{22} \\ \cdot \cdot \\ \cdot \cdot \\ \cdot \cdot \\ {h h}_{00} {d d}_{K K} + + {ISI ISI}_{K K} \end{matrix}] - - - - - - ((3030))$

假设发射的信号矢量中每个调制符号元素的能量已归一化，即其平均功率 $E_{s} = E [{| d_{k} |}^{2}] = 1, k = 1,2, . . ., K,$ 这样，有用信号的平均能量为Assume that the energy of each modulation symbol element in the transmitted signal vector is normalized, i.e. its average power ${E.}_{the s} = E. [{| d_{k} |}^{2}] = 1, k = 1,2, . . ., K,$ Thus, the average energy of the useful signal is

E_s′＝|h₀|²E_s＝|h₀|² (31)E_s ′＝|h₀ |² E_s ＝|h₀ |² (31)

由(29)式可得From (29) can get

${| | {h h}_{00} | |}^{22} = = {| | \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {\overset{~ ~}{H h}}_{k k} | |}^{22} - - - - - - ((3232))$

步骤4)：根据所述接收端有用信号的平均功率计算所述接收端信号间干扰的平均功率：Step 4): Calculate the average power of interference between signals at the receiving end according to the average power of the useful signal at the receiving end:

由(30)式可知，对于独立同分布，能量归一化调制符号矢量D_K，所有解调符号上的平均符号间干扰分量相同，并且符号间干扰能量为It can be known from (30) that for independent and identically distributed, energy-normalized modulation symbol vector D_K , the average intersymbol interference components on all demodulated symbols are the same, and the intersymbol interference energy is

${σ σ}_{ISI ISI}^{22} = = {| | {h h}_{11} | |}^{22} + + {| | {h h}_{22} | |}^{22} + + . . . . . . {| | {h h}_{K K - - 11} | |}^{22} - - - - - - ((3333))$

又由(29)式可得And from (29) we can get

${| | {h h}_{00} | |}^{22} + + {| | {h h}_{11} | |}^{22} + + {| | {h h}_{22} | |}^{22} + + \cdot \cdot \cdot \cdot \cdot \cdot {| | {h h}_{K K - - 11} | |}^{22} = = \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {| | {\overset{~ ~}{H h}}_{k k} | |}^{22} - - - - - - ((3434))$

即Right now

${| | {h h}_{11} | |}^{22} + + {| | {h h}_{22} | |}^{22} + + \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; {| | {h h}_{K K - - 11} | |}^{22} = = \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {| | {\overset{~ ~}{H h}}_{k k} | |}^{22} - - {| | {h h}_{00} | |}^{22} - - - - - - ((3535))$

因此，计算符号间干扰平均功率可估计为：Therefore, calculating the average power of intersymbol interference can be estimated as:

${σ σ}_{ISI ISI}^{22} = = \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {| | {\overset{~ ~}{H h}}_{k k} | |}^{22} - - {| | \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {\overset{~ ~}{H h}}_{k k} | |}^{22} - - - - - - ((3636))$

步骤5)：根据所述数学关系及所述频域均衡系数计算所述接收端相应噪声的噪声方差，其主要包括以下步骤：Step 5): calculating the noise variance of the corresponding noise at the receiving end according to the mathematical relationship and the frequency domain equalization coefficient, which mainly includes the following steps:

由所建立的数学关系式(15)第二项可知：From the second term of the established mathematical relation (15), it can be seen that:

$\overset{^^}{Z Z} = = {F f}_{K K}^{H h} {T T}_{M m,, K K}^{T T} {F f}_{M m} {Γ Γ}_{L L,, M m}^{T T} {γ γ}_{L L}^{H h} {Ω Ω}_{N N,, L L}^{H h} {F f}_{N N}^{H h} {H h}^{H h} WZ WZ$

$= = {F f}_{K K}^{H h} {T T}_{M m,, K K}^{T T} {F f}_{M m} {Γ Γ}_{L L,, M m}^{T T} {γ γ}_{L L}^{H h} {Ω Ω}_{N N,, L L}^{H h} {F f}_{N N}^{H h} {H h}^{H h} W W {F f}_{N N} z z - - - - - - ((3737))$

其中z为方差为σ²的加性高斯白噪声的时域噪声矢量，所以噪声矢量协方差矩阵为：where z is the time domain noise vector of additive Gaussian white noise with variance σ² , so the noise vector covariance matrix is:

$E E. ((\overset{~ ~}{Z Z} {\overset{~ ~}{Z Z}}^{H h})) = = E E. (({F f}_{K K}^{H h} {T T}_{M m,, K K}^{T T} {F f}_{M m} {Γ Γ}_{L L,, M m}^{T T} {γ γ}_{L L}^{H h} {Ω Ω}_{N N,, L L}^{H h} {F f}_{N N}^{H h} {H h}^{H h} {WF WF}_{N N} z z {z z}^{H h} {F f}_{N N}^{H h} {W W}^{H h} {HF HF}_{N N} {Ω Ω}_{N N,, L L} {γ γ}_{L L} {Γ Γ}_{L L,, M m} {F f}_{M m}^{H h} {T T}_{M m,, K K} {F f}_{K K}))$

$= = {σ σ}^{22} {F f}_{K K}^{H h} {T T}_{M m,, K K}^{T T} {F f}_{M m} {Γ Γ}_{L L,, M m}^{T T} {γ γ}_{L L}^{H h} {Ω Ω}_{N N,, L L}^{H h} {F f}_{N N}^{H h} {H h}^{H h} {W W}^{22} {HF HF}_{N N} {Ω Ω}_{N N,, L L} {γ γ}_{L L} {Γ Γ}_{L L,, M m} {F f}_{M m}^{H h} {T T}_{M m,, K K} {F f}_{K K}$

第一步：根据频域均衡子载波的信道频率响应[H₀ H₁ …H_N-1]^T和所设定的频域均衡子载波对应的均衡系数[ω₀ ω₁ …ω_m…ω_N-1]^T(即第(16)及(17)式)，计算对角矩阵Step 1: According to the channel frequency response [H₀ H₁ ...H_N-1 ]^T of the frequency domain equalization subcarrier and the equalization coefficient corresponding to the set frequency domain equalization subcarrier [ω₀ ω₁ ...ω_m ...ω_N-1 ]^T (i.e. (16) and (17)), calculate the diagonal matrix

${Λ Λ}_{N N}^{' '} = = {H h}^{H h} {W W}^{22} H h = = diag diag {{{| | {H h}_{00} | |}^{22} {ω ω}_{00}^{22},, {| | {H h}_{11} | |}^{22} {ω ω}_{11}^{22},, . . . . . .,, {| | {H h}_{N N - - 11} | |}^{22} {ω ω}_{N N - - 11}^{22}}} . . - - - - - - ((3838))$

第二步：计算矩阵Step 2: Calculate the Matrix

${h h}^{' '} = = {F f}_{N N}^{H h} {Λ Λ}_{N N}^{' '} {F f}_{N N} - - - - - - ((3939))$

由于Λ_N′为对角阵，所以h′为一循环对称矩阵，并且h′第一列元素矢量为Since Λ_N ′ is a diagonal matrix, h′ is a cyclic symmetric matrix, and the element vector of the first column of h′ is

${h h}_{00}^{' '} = = \frac{11}{\sqrt{N N}} {F f}_{N N}^{H h} {[\begin{matrix} {| | {H h}_{00} | |}^{22} {ω ω}_{00}^{22} & {| | {H h}_{11} | |}^{22} {ω ω}_{11}^{22} & \cdot \cdot \cdot \cdot \cdot \cdot & {| | {H h}_{N N - - 11} | |}^{22} {ω ω}_{N N - - 11}^{22} \end{matrix}]}^{T T}$

h′的其余列矢量可由h₀′循环移位获得。The remaining column vectors of h' can be obtained by cyclic shifting of h₀ '.

第三步：截取矩阵h′左上角的前L行和前L列，构成的L×L矩阵Step 3: Intercept the first L rows and first L columns in the upper left corner of the matrix h′ to form an L×L matrix

${\overset{~ ~}{h h}}^{' '} = = {Ω Ω}_{N N,, L L}^{H h} {h h}^{' '} {Ω Ω}_{N N,, L L} - - - - - - ((4040))$

第四步：将矩阵

分割成(L/M)×(L/M)的块矩阵，每个矩阵块的大小为M×M，其中第i行和前j列的矩阵块可表示为Step 4: Convert the matrix

Divided into (L/M)×(L/M) block matrix, the size of each matrix block is M×M, where the matrix block in the i-th row and the first j column can be expressed as

其中

为矩阵

第i行第j列元素；in

for the matrix

element in row i and column j;

第五步：分别计算P_ih_i，j′P_j第一列向量Step 5: Calculate the first column vector of P_i h_{i, j} ′P_j respectively

${b b}_{i i,, j j}^{' '} = = {P P}_{i i} {h h}_{i i,, j j}^{' '} {P P}_{j j} [\begin{matrix} 11 \\ 00_{((M m - - 11)) \times \times 11} \end{matrix}] - - - - - - ((4242))$

其中P_i为M×M对角阵，其对角元素为{f_p(i×M)，f_p(i×M+1)，…，f_p(i×M+M-1)}，f_p(t)，t＝0，1，...，L-1为多子带滤波器组原型滤波器系数。0_(M-1)×1为(M-1)×1零列向量。Among them, P_i is an M×M diagonal matrix, and its diagonal elements are {f_p (i×M), f_p (i×M+1),…, f_p (i×M+M-1)}, f_p (t), t=0, 1, . . . , L-1 are the prototype filter coefficients of the multi-subband filter bank. 0_(M-1)×1 is a (M-1)×1 zero column vector.

第六步：叠加b_i，j′，并进行M点DFT变换，可得Step 6: Superimposing b_{i, j} ′, and performing M-point DFT transformation, we can get

${B B}^{' '} = = \sqrt{M m} {F f}_{M m} {{{Σ Σ}_{i i,, j j = = 00}^{L L / / M m - - 11} {b b}_{i i,, j j}^{' '}}} - - - - - - ((4343))$

第七步：经过子带解映射，提取占用子带上的噪声分量Step 7: After subband demapping, extract the noise component on the occupied subband

${[\begin{matrix} {\overset{~ ~}{H h}}_{00}^{' '} & {\overset{~ ~}{H h}}_{11}^{' '} & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {\overset{~ ~}{H h}}_{K K - - 11}^{' '} \end{matrix}]}^{T T} = = {T T}_{M m,, K K}^{T T} {B B}^{' '} - - - - - - ((4444))$

第八步：计算噪声方差Step 8: Calculate the noise variance

${σ σ}_{n no}^{22} = = \frac{{σ σ}^{22}}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {\overset{~ ~}{H h}}_{k k}^{' '} - - - - - - ((4545))$

事实上，矩阵 $Γ_{L, M}^{T} γ_{L}^{H} {\tilde{h}}^{'} γ_{L} Γ_{L, M} = Σ_{i, j = 0}^{L / M - 1} P_{i} h_{i, j}^{'} P_{j}$ 可近似为循环矩阵，则 $F_{M} {Σ_{i, j = 0}^{L / M - 1} P_{i} h_{i, j}^{'} P_{j}} F_{M}^{H}$ 为M×M对角阵，其对角元素矢量与B′相同，并且In fact, the matrix $Γ_{L, m}^{T} γ_{L}^{h} {\tilde{h}}^{'} γ_{L} Γ_{L, m} = Σ_{i, j = 0}^{L / m - 1} P_{i} h_{i, j}^{'} P_{j}$ can be approximated as a circular matrix, then $f_{m} {Σ_{i, j = 0}^{L / m - 1} P_{i} h_{i, j}^{'} P_{j}} f_{m}^{h}$ is an M×M diagonal matrix with the same diagonal element vectors as B′, and

${T T}_{M m,, K K}^{T T} {F f}_{M m} {{{Σ Σ}_{i i,, j j = = 00}^{L L / / M m - - 11} {P P}_{i i} {h h}_{i i,, j j}^{' '} {P P}_{j j}}} {F f}_{M m}^{H h} {T T}_{M m,, K K} = = diag diag (({\overset{~ ~}{H h}}_{00}^{' '},, {\overset{~ ~}{H h}}_{11}^{' '},, . . . . . .,, {\overset{~ ~}{H h}}_{K K - - 11}^{' '})) = = {Λ Λ}_{K K}^{' '} - - - - - - ((4646))$

由DFT变换性质可知，F_K^HΛ_K′F_K为循环矩阵。令According to the properties of DFT transformation, F_K^H Λ_K ′F_K is a circular matrix. make

${F f}_{K K}^{H h} {Λ Λ}_{K K}^{' '} {F f}_{K K} = = (\begin{matrix} {h h}_{00}^{' '} & {h h}_{K K - - 11} & \cdot &Center Dot; & \cdot &Center Dot; & \cdot \cdot & {h h}_{11}^{' '} \\ {h h}_{11}^{' '} & {h h}_{00}^{' '} & \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; & {h h}_{22}^{' '} \\ \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ {h h}_{K K - - 11}^{' '} & {h h}_{K K - - 22}^{' '} & \cdot \cdot & \cdot &Center Dot; & \cdot \cdot & {h h}_{00}^{' '} \end{matrix}) - - - - - - ((4747))$

其中 $h_{0}^{'} = \frac{1}{K} Σ_{k = 0}^{K - 1} {\tilde{H}}_{k}^{'},$ 这样in $h_{0}^{'} = \frac{1}{K} Σ_{k = 0}^{K - 1} {\tilde{h}}_{k}^{'},$ so

$E E. ((\overset{~ ~}{Z Z} {\overset{~ ~}{Z Z}}^{H h})) = = {σ σ}^{22} (\begin{matrix} {h h}_{00}^{' '} & {h h}_{K K - - 11} & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & {h h}_{11}^{' '} \\ {h h}_{11}^{' '} & {h h}_{00}^{' '} & \cdot \cdot & \cdot \cdot & \cdot &Center Dot; & {h h}_{22}^{' '} \\ \cdot \cdot & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ {h h}_{K K - - 11}^{' '} & {h h}_{K K - - 22}^{' '} & \cdot \cdot & \cdot \cdot & \cdot \cdot & {h h}_{00}^{' '} \end{matrix}) - - - - - - ((4848))$

噪声矢量协方差矩阵对角元素即为噪声方差。The diagonal elements of the noise vector covariance matrix are the noise variances.

步骤6)根据所述有用信号的平均功率、所述信号间干扰的平均功率、所述噪声方差计算有效信干噪比，其计算公式为：

Step 6) Calculate the effective signal-to-interference-noise ratio according to the average power of the useful signal, the average power of the inter-signal interference, and the noise variance, and its calculation formula is:

由(26)，(33)和(45)式，可得有效SINR表达式为From (26), (33) and (45), the effective SINR expression can be obtained as

$= = \frac{{| | \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {\overset{~ ~}{H h}}_{k k} | |}^{22}}{\frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {\overset{&OverBar; &OverBar;}{H h}}_{k k} {σ σ}^{22} + + \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {| | {\overset{~ ~}{H h}}_{k k} | |}^{22} - - {| | \frac{11}{K K} {Σ Σ}_{k k = = 00}^{K K - - 11} {\overset{~ ~}{H h}}_{k k} | |}^{22}} - - - - - - ((4949))$

二、当本发明的DFT扩频的广义多载波传输系统为包含1个发射天线多天线的DFT-S-GMC系统时，主要执行的步骤与前述包含1个发射天线1个天线的DFT-S-GMC系统所执行的步骤相似，首先执行步骤1)，建立DFT-S-GMC系统的数学关系，该数学关系与式(15)相同。Two, when the generalized multi-carrier transmission system of DFT spread spectrum of the present invention is the DFT-S-GMC system that comprises 1 transmitting antenna multi-antenna, the main steps of execution are the same as the aforementioned DFT-S comprising 1 transmitting antenna and 1 antenna -The steps performed by the GMC system are similar. First, step 1) is performed to establish the mathematical relationship of the DFT-S-GMC system, which is the same as the formula (15).

接着执行步骤2)，根据信道频率响应、信道噪声方差和均衡方法，设定均衡系数及噪声类型，假设有Nr个接收天线：Then execute step 2), set the equalization coefficient and noise type according to the channel frequency response, channel noise variance and equalization method, assuming that there are Nr receiving antennas:

对于迫零(ZF)均衡，则设定第m个频域均衡子载波对应的均衡系数

为：For zero-forcing (ZF) equalization, set the equalization coefficient corresponding to the mth frequency domain equalization subcarrier

for:

${\overset{~ ~}{ω ω}}_{m m} = = \frac{11}{{Σ Σ}_{n no = = 11}^{Nr Nr} {| | {H h}_{m m}^{n no} | |}^{22}} - - - - - - ((5050))$

对于最小均方误差(MMSE)均衡，则设定第m个频域均衡子载波对应的均衡系数

为：For minimum mean square error (MMSE) equalization, set the equalization coefficient corresponding to the mth frequency domain equalization subcarrier

for:

${\overset{~ ~}{ω ω}}_{m m} = = \frac{11}{{Σ Σ}_{n no = = 11}^{Nr Nr} {| | {H h}_{m m}^{n no} | |}^{22} + + {σ σ}^{22}} - - - - - - ((5151))$

其中，H_mⁿ为发射天线到第n个接收天线之间的多径信道中第m个频域均衡子载波的信道频率响应，σ²为频域均衡子载波的噪声方差。Among them, H_mⁿ is the channel frequency response of the mth frequency domain equalized subcarrier in the multipath channel between the transmitting antenna and the nth receiving antenna, and^σ2 is the noise variance of the frequency domain equalized subcarrier.

执行步骤3)，计算有用信号平均功率时，根据所设定的均衡系数，由发射天线到第n个接收天线之间的信道对应的频域均衡子载波的信道频率响应[H₀ⁿ H₁ⁿ …H_N-1ⁿ]^T和频域均衡子载波对应的均衡系数 ${[\begin{matrix} {\tilde{ω}}_{0} & {\tilde{ω}}_{1} & \cdot \cdot \cdot & {\tilde{ω}}_{m} & \cdot \cdot \cdot & {\tilde{ω}}_{N - 1} \end{matrix}]}^{T},$ 计算对角矩阵Execute step 3), when calculating the average power of the useful signal, according to the set equalization coefficient, the channel frequency response of the frequency domain equalization subcarrier corresponding to the channel between the transmitting antenna and the nth receiving antenna [H₀ⁿ H₁ⁿ …H_N-1ⁿ ]^T and equalization coefficients corresponding to frequency domain equalized subcarriers ${[\begin{matrix} {\tilde{ω}}_{0} & {\tilde{ω}}_{1} & \cdot &Center Dot; &Center Dot; & {\tilde{ω}}_{m} & \cdot &Center Dot; \cdot & {\tilde{ω}}_{N - 1} \end{matrix}]}^{T},$ Compute Diagonal Matrix

${\overset{~ ~}{Λ Λ}}_{N N} = = {Σ Σ}_{n no = = 11}^{Nr Nr} {(({H h}^{n no}))}^{H h} \overset{~ ~}{W W} {H h}^{n no} = = diag diag {{{Σ Σ}_{n no = = 11}^{Nr Nr} {| | {H h}_{m m}^{n no} | |}^{22} {\overset{~ ~}{ω ω}}_{00},, {Σ Σ}_{n no = = 11}^{Nr Nr} {| | {H h}_{m m}^{n no} | |}^{22} {\overset{~ ~}{ω ω}}_{11},, . . . . . .,, {Σ Σ}_{n no = = 11}^{Nr Nr} {| | {H h}_{m m}^{n no} | |}^{22} {\overset{~ ~}{ω ω}}_{N N - - 11}}} - - - - - - ((5252))$

和对角矩阵and a diagonal matrix

${\overset{&OverBar; &OverBar;}{Λ Λ}}_{N N} = = {Σ Σ}_{n no = = 11}^{Nr Nr} {(({H h}^{n no}))}^{H h} {\overset{~ ~}{W W}}^{22} {H h}^{n no} = = diag diag {{{Σ Σ}_{n no = = 11}^{Nr Nr} {| | {H h}_{m m}^{n no} | |}^{22} {\overset{~ ~}{ω ω}}_{00}^{22},, {Σ Σ}_{n no = = 11}^{Nr Nr} {| | {H h}_{m m}^{n no} | |}^{22} {\overset{~ ~}{ω ω}}_{11}^{22},, . . . . . .,, {Σ Σ}_{n no = = 11}^{Nr Nr} {| | {H h}_{m m}^{n no} | |}^{22} {\overset{~ ~}{ω ω}}_{N N - - 11}^{22}}} - - - - - - ((5353))$

其中Hⁿ为N×N对角矩阵，其对角元素矢量为[H₀ⁿ H₁ⁿ …H_N-1ⁿ]^T。为N×N对角矩阵，其对角元素矢量为 ${[\begin{matrix} {\tilde{ω}}_{0} & {\tilde{ω}}_{1} & \cdot \cdot \cdot & {\tilde{ω}}_{m} & \cdot \cdot \cdot & {\tilde{ω}}_{N - 1} \end{matrix}]}^{T} .$ Where Hⁿ is an N×N diagonal matrix, and its diagonal element vector is [H₀ⁿ H₁ⁿ …H_N-1ⁿ ]^T . It is an N×N diagonal matrix, and its diagonal element vector is ${[\begin{matrix} {\tilde{ω}}_{0} & {\tilde{ω}}_{1} & &Center Dot; &Center Dot; \cdot & {\tilde{ω}}_{m} & &Center Dot; &Center Dot; &Center Dot; & {\tilde{ω}}_{N - 1} \end{matrix}]}^{T} .$

如此仅需要将(52)式中的矩阵

代替(19)式中的Λ_N，并采用式(20)到式(26)步骤进行计算即可得到有用信号平均功率。In this way, only the matrix in (52) needs to be

Substitute Λ_N in formula (19), and use formula (20) to formula (26) to calculate the average power of the useful signal.

再执行步骤4)即采用式(23)，计算一个发射天线多个接收天线的DFT-S-GMC的检测信号符号间干扰平均功率。Step 4) is executed again, that is, the formula (23) is used to calculate the average power of the intersymbol interference of the detection signal of DFT-S-GMC with one transmitting antenna and multiple receiving antennas.

再执行步骤5)将(53)式中的矩阵

代替(38)式中的Λ_N′，采用(39)式到(45)式步骤，计算一个发射天线多个接收天线的DFT-S-GMC的检测信号噪声方差。Execute step 5 again) the matrix in (53) formula

Instead of Λ_N ' in formula (38), the steps from formula (39) to formula (45) are used to calculate the detection signal noise variance of DFT-S-GMC with one transmitting antenna and multiple receiving antennas.

最后执行步骤6)采用(49)式，计算一个发射天线多个接收天线的DFT-S-GMC的有效信干噪比。Finally, step 6 is performed to calculate the effective signal-to-interference-noise ratio of the DFT-S-GMC of one transmitting antenna and multiple receiving antennas by using formula (49).

根据下表1及表2的参数以及前述的计算即可得到的有信干噪比，图3及图4比较了不同占用子带数目(1和8个)、采用一个发射天线和一个接收天线(1x1)和一个发射天线和两个接收天线(1x2)配置，DFT-S-GMC在PB-3km/h信道下基于有效信干噪比(eSINR)的误帧率与其在加性高斯白噪声(AWGN)信道下基于信噪比(Eb/N0)的误帧率性能。需要说明的是本发明方法估计的DFT-S-GMC系统有效信干噪比相当于符号信噪比，即Es/N0。因此可以根据调制编码方式直接求出相应的比特信噪比Eb/N0。由结果可知，利用本发明方法估计的DFT-S-GMC系统有效信干噪比，其多径信道下的性能曲线可以很好地匹配其在高斯白噪声信道下的性能曲线，两者的信噪比误差约为0.1分贝(dB)左右。According to the parameters in Table 1 and Table 2 below and the SINR that can be obtained from the aforementioned calculations, Figure 3 and Figure 4 compare different numbers of occupied subbands (1 and 8), using one transmitting antenna and one receiving antenna (1x1) and one transmit antenna and two receive antennas (1x2) configuration, DFT-S-GMC under the PB-3km/h channel based on the effective signal-to-interference-noise ratio (eSINR) of the frame error rate and its additive white Gaussian noise Frame error rate performance based on signal-to-noise ratio (Eb/N0) in (AWGN) channel. It should be noted that the effective SINR of the DFT-S-GMC system estimated by the method of the present invention is equivalent to the symbol SNR, that is, Es/N0. Therefore, the corresponding bit signal-to-noise ratio Eb/N0 can be directly obtained according to the modulation and coding method. As can be seen from the results, the effective SINR of the DFT-S-GMC system estimated by the method of the present invention, its performance curve under the multipath channel can well match its performance curve under the Gaussian white noise channel, and the signal-to-interference-noise ratio of the two The noise ratio error is about 0.1 decibel (dB).

表1 系统参数Table 1 System parameters

系统参数 System parameters 载波频率(MHz)Carrier frequency (MHz) 700700 载波带宽BWc(MHz)Carrier bandwidth BWc(MHz) 55 采样频率(MHz)Sampling frequency (MHz) 5.65.6 信道模型Channel model ITU-PBITU-PB 移动速度 Moving speed 3km/h3km/h 信道均衡channel equalization MMSEMMSE 信道估计channel estimation 理想 ideal 编码encoding 涡轮码(Turbo码)Turbo code (Turbo code) 码率code rate 1/21/2 调制方式 Modulation 四相相移键控调制(QPSK)，16正交幅度调制(16QAM)Quadrature Phase Shift Keying Modulation (QPSK), 16 Quadrature Amplitude Modulation (16QAM)

表2 DFT-S-GMC参数Table 2 DFT-S-GMC parameters

DFT-S-GMC参数DFT-S-GMC parameters 子带总数MThe total number of subbands M 2828 有效子带数NocbEffective number of subbands Nocb 24 twenty four 虚拟子带数NvbNumber of virtual subbands Nvb 44 占用带宽BWocc(MHz)Occupied bandwidth BWocc(MHz) 4.84.8 子带间隔BWband(kHz)Subband spacing BWband(kHz) 200200 每个长数据块复用的波形符号数DNumber of waveform symbols multiplexed per long data block D 1616 原型滤波器类型Prototype filter type 根升余弦root raised cosine 滚降系数Roll-off coefficient 0.20.2 原型滤波器上采样率NPrototype filter upsampling rate N 3232 原型滤波器长度LPrototype filter length L 392392 GMC数据块长度GMC data block length 512512 频域均衡点数Frequency Domain Equalization Points 512512 数据块个数/每子帧Number of data blocks/per subframe 55

理论分析和仿真结果表明，本发明的方法可准确估计DFT-S-GMC系统的有效信干噪比，其多径慢时变信道下的基于有效信干噪比(eSINR)的等效性能与高斯白噪声下的性能误差只有0.1dB左右，该有效信干噪比估计方法可用于基于离散傅立叶变换扩频的广义多载波传输系统的链路自适应传输方案和无线资源管理方面。Theoretical analysis and simulation results show that the method of the present invention can accurately estimate the effective SINR of the DFT-S-GMC system, and the equivalent performance based on the effective SINR (eSINR) under its multipath slow time-varying channel is the same as The performance error under Gaussian white noise is only about 0.1dB. This effective SINR estimation method can be used in the link adaptive transmission scheme and wireless resource management of the generalized multi-carrier transmission system based on discrete Fourier transform spread spectrum.

Claims

1. the SINR method of estimation of the generalized multi-carrier transmission system of a DFT spread spectrum is characterized in that may further comprise the steps:

1) sets up mathematical relationship between the signal input and output of generalized multi-carrier transmission system of described DFT spread spectrum;

2), set the equalizing coefficient of frequency domain equalization subcarrier of the generalized multi-carrier transmission system of described DFT spread spectrum according to channel frequency response, interchannel noise variance and the equalization methods of the generalized multi-carrier transmission system of described DFT spread spectrum;

3) according to the average power of the generalized multi-carrier transmission system receiving terminal useful signal of described mathematical relationship and the described DFT spread spectrum of described frequency domain equalization coefficient calculations;

4) calculate the average power of disturbing between described receiving end signal according to the average power of described receiving terminal useful signal;

5) according to the noise variance of described mathematical relationship and the corresponding noise of the described receiving terminal of described frequency domain equalization coefficient calculations;

6) calculate described SINR according to the average power of disturbing between the average power of described receiving terminal useful signal, described receiving end signal, described receiving terminal noise variance.

2. the SINR method of estimation of the generalized multi-carrier transmission system of DFT spread spectrum as claimed in claim 1 is characterized in that: described mathematical relationship is:

\hat{D} = F_{K}^{H} T_{M, K}^{T} F_{M} Γ_{L, M}^{T} γ_{L}^{H} Ω_{N, L}^{H} F_{N}^{H} H^{H} WR

= F_{K}^{H} T_{M, K}^{T} F_{M} Γ_{L, M}^{T} γ_{L}^{H} Ω_{N, L}^{H} F_{N}^{H} H^{H} WH F_{N} Ω_{N, L} γ_{L} Γ_{L, M} F_{M}^{H} T_{M, K} F_{K} D_{K}

+ F_{K}^{H} T_{M, K}^{T} F_{M} Γ_{L, M}^{T} γ_{L}^{H} Ω_{N, L}^{H} F_{N}^{H} H^{H} WZ

Wherein, subscript " T " expression transposition, subscript " H " expression conjugate transpose;

R is the frequency domain representation of received signal, and

R = {HF}_{N} Ω_{N, L} γ_{L} Γ_{L, M} F_{M}^{H} T_{M, K} F_{K} D_{K} + Z;

Z is that variance is σ²The N point DFT conversion output vector of time domain additive white Gaussian noise vector, N is counting of receiving terminal frequency domain equalization;

D_KFor the length of the generalized multi-carrier transmission system transmitting terminal of described DFT spread spectrum transmission is the modulation symbol vector of K, the number of sub-bands that K also takies for transmitting terminal;

F_KFor K point DFT transformation matrix, be used to realize the DFT spread spectrum, and

F_{K} F_{K}^{H} = I_{K},

I_KBe K * K unit matrix;

T_{M, K}Be M * K subband mapping matrix, have only K element in its M * K element for " 1 ", all the other be " 0 ", when hope will upload to m subband through k the element map that K point FFT conversion is exported defeated, then with T_{M, K}The element of the capable k of m row be changed to " 1 ";

Υ_LΓ_{L, M}F_M^HBe M point inverse filterbank conversion (IFBT) matrix, wherein, F_MBe M point FFT conversion unitary matrice, and

F_{M} F_{M}^{H} = I_{M},

Γ_{L, M}Be the cascade extended matrix of L * M, and Γ_{L, M}=[I_M, I_M..., I_M]^T, I_MBe the unit matrix of M * M, L is the integral multiple of M, Υ_LFor L * L is a diagonal matrix, its diagonal element is many Methods of Subband Filter Banks prototype filter L dot factor f_p(t), t=0,1 ..., L-1;

Ω_{N, L} = [\begin{matrix} I_{L} \\ 0_{(N - L) \times L} \end{matrix}],

I_LBe the unit matrix of L * L, 0_{(N-L) * L}Be (N-L) * L null matrix; H is N * N diagonal matrix, its diagonal element vector [H₀H₁H_N-1]^TChannel frequency response for the frequency domain equalization subcarrier;

W is N * N diagonal matrix, its diagonal element vector [ω₀ω₁ω_mω_N-1]^TBe the frequency domain equalization coefficient; F_MΓ_{L, M}^TΥ_L^HBe M point bank of filters conversion (FBT) matrix;

F_MBe M point DFT transformation matrix, and

F_{M} F_{M}^{H} = I_{M};

T_{M, K}^TBe K * M subband solutions mapping matrix, finish transmitting terminal subband solutions mapping matrix T_{M, K}The operation of contrary;

F_K^HBe K * K IDFT despreading matrix.

3. the SINR method of estimation of the generalized multi-carrier transmission system of DFT spread spectrum as claimed in claim 2 is characterized in that: the generalized multi-carrier transmission system of described DFT spread spectrum is the generalized multi-carrier transmission system that comprises the DFT spread spectrum of 1 transmitting antenna and 1 reception antenna.

4. the SINR method of estimation of the generalized multi-carrier transmission system of DFT spread spectrum as claimed in claim 3, it is characterized in that: the generalized multi-carrier transmission system of described DFT spread spectrum adopts zero forcing equalization, described step 2) the middle equalizing coefficient ω that sets m frequency domain equalization subcarrier correspondence_mFor

ω_{m} = \frac{1}{{| H_{m} |}^{2}},

Wherein, H_mIt is the channel frequency response of m frequency domain equalization subcarrier.

5. the SINR method of estimation of the generalized multi-carrier transmission system of DFT spread spectrum as claimed in claim 3, it is characterized in that: the generalized multi-carrier transmission system of described DFT spread spectrum adopts least mean-square error equilibrium, then described step 2) the middle equalizing coefficient ω that sets m frequency domain equalization subcarrier correspondence_mFor

ω_{m} = \frac{1}{{| H_{m} |}^{2} + σ^{2}},

Wherein, H_mBe the channel frequency response of m frequency domain equalization subcarrier, σ²Noise variance for the frequency domain equalization subcarrier.

6. the SINR method of estimation of the generalized multi-carrier transmission system of DFT spread spectrum as claimed in claim 2 is characterized in that: the generalized multi-carrier transmission system of described DFT spread spectrum is the generalized multi-carrier transmission system that comprises the DFT spread spectrum of 1 transmitting antenna and a plurality of reception antennas.

7. the SINR method of estimation of the generalized multi-carrier transmission system of DFT spread spectrum as claimed in claim 6, it is characterized in that: the generalized multi-carrier transmission system of described DFT spread spectrum adopts zero forcing equalization, then described step 2) the middle equalizing coefficient ω that sets m frequency domain equalization subcarrier correspondence_mFor

ω_{m} = \frac{1}{Σ_{n = 1}^{Nr} {| H_{m}^{n} |}^{2}},

Wherein, H_mⁿChannel frequency response for transmitting antenna m frequency domain equalization subcarrier in the multipath channel between n the reception antenna.

8. the SINR method of estimation of the generalized multi-carrier transmission system of DFT spread spectrum as claimed in claim 6, it is characterized in that: the generalized multi-carrier transmission system of described DFT spread spectrum adopts least mean-square error equilibrium, then described step 2) the middle equalizing coefficient ω that sets m frequency domain equalization subcarrier correspondence_mFor

ω_{m} = \frac{1}{Σ_{n = 1}^{Nr} {| H_{m}^{n} |}^{2} + σ^{2}},

Wherein, H_mⁿBe the channel frequency response of transmitting antenna m frequency domain equalization subcarrier in the multipath channel between n the reception antenna, σ²Noise variance for the frequency domain equalization subcarrier.

9. as the SINR method of estimation of the generalized multi-carrier transmission system of the arbitrary described DFT spread spectrum of claim 3 to 6, it is characterized in that: the average power calculating formula of the receiving terminal useful signal in the described step 3) is:

E_{s}^{'} = {| \frac{1}{K} Σ_{k = 0}^{K - 1} {\tilde{H}}_{k} |}^{2}

E_s' be the average power of useful signal,

Be vector T_{M, K}^HK the element of B, promptly

{[\begin{matrix} {\tilde{H}}_{0} & {\tilde{H}}_{1} & . . . & {\tilde{H}}_{k} & . . . & {\tilde{H}}_{K - 1} \end{matrix}]}^{T} = T_{M, K}^{T} B

Wherein,

T_{M, K}^TBe K * M subband solutions mapping matrix,

B = \sqrt{M} F_{M} {Σ_{i, j = 0}^{L / M - 1} b_{i, j}},

And

b_{i, j} = P_{i} h_{i, j} P_{j} [\begin{matrix} 1 \\ 0_{(M - 1) \times 1} \end{matrix}],

P_iBe M * M diagonal matrix, its diagonal element is { f_p(i * M), f_p(i * M+1) ..., f_p(i * M+M-1) },

f_p(t), t=0,1 ..., L-1 is many Methods of Subband Filter Banks prototype filter coefficient,

0_{(M-1) * 1}Be (M-1) * 1 zero column vector,

h_{I, j}Be by with matrixAverage mark is slit into the block matrix of (L/M) * (L/M) and makes the size of each block matrix is that M * M is resultant, wherein h_{I, j}For

The matrix-block of the capable and preceding j row of the i of the block matrix of gained after cutting apart is expressed as:

i，j＝0，1，…L/M-1

h_{I, j}In elementBe matrix

The capable jM column element of iM,

And

\tilde{h} = Ω_{N, L}^{H} h Ω_{N, L}

Be the L * L matrix that constitutes by the capable and preceding L row of the preceding L in the h upper left corner, wherein,

h = F_{N}^{H} Λ_{N} F_{N},

A_N＝H^HWH＝diag{|H₀|²ω₀，|H₁|²ω₁，...，|H_N-1|²ω_N-1}，

[H₀H₁H_N-1]^TBe the channel frequency response of frequency domain equalization subcarrier,

[ω₀ω₁ω_mω_N-1]^TEqualizing coefficient for frequency domain equalization subcarrier correspondence.

10. the SINR method of estimation of the generalized multi-carrier transmission system of DFT spread spectrum as claimed in claim 9 is characterized in that: the average power calculating formula of disturbing between receiving end signal in the described step 4) is:

σ_{ISI}^{2} = \frac{1}{K} Σ_{k = 0}^{K - 1} {| {\tilde{H}}_{k} |}^{2} - {| \frac{1}{K} Σ_{k = 0}^{K - 1} {\tilde{H}}_{k} |}^{2}

Wherein, σ_ISI²Average power for inter-signal interference.

11. as the SINR method of estimation of the generalized multi-carrier transmission system of the arbitrary described DFT spread spectrum of claim 3 to 6, it is characterized in that: receiving terminal noise variance calculating formula is in the described step 5):

σ_{n}^{2} = \frac{σ^{2}}{K} Σ_{k = 0}^{K - 1} {\tilde{H}}_{k}^{'}

Wherein, σ_n²Be the receiving terminal noise variance.

Be vector T_{M, K}^HK the element of B ', promptly

{[\begin{matrix} {\tilde{H}}_{0}^{'} & {\tilde{H}}_{1}^{'} & . . . & {\tilde{H}}_{K - 1}^{'} \end{matrix}]}^{T} = T_{M, K}^{T} B^{'}

Wherein,

B^{'} = \sqrt{M} F_{M} {Σ_{i, j = 0}^{L / M - 1} b_{i, j}^{'}},

And

b_{i, j}^{'} = P_{i} h_{i, j}^{'} P_{j} [\begin{matrix} 1 \\ 0_{(M - 1) \times 1} \end{matrix}],

h_{I, j}' be by with matrix

Average mark is slit into the block matrix of (L/M) * (L/M) and makes the size of each block matrix is that M * M is resultant, wherein h_{I, j}' be

i，j＝0，1，…L/M-1

h_{I, j}In element

Be matrix

The capable jM element of iM,

And

{\tilde{h}}^{'} = Ω_{N, L}^{H} h^{'} Ω_{N, L}

Be the L * L matrix that constitutes by the capable and preceding L row of the preceding L in h ' upper left corner, wherein,

h^{'} = F_{N}^{H} Λ_{N}^{'} F_{N},

Λ_{N}^{'} = H^{H} W^{2} H = diag {{| H_{0} |}^{2} ω_{0}^{2}, {| H_{1} |}^{2} ω_{1}^{2}, . . ., {| H_{N - 1} |}^{2} ω_{N - 1}^{2}},

12. the SINR method of estimation of the generalized multi-carrier transmission system of DFT spread spectrum as claimed in claim 1 is characterized in that: the SINR calculating formula is in the described step 6):