CN105812111A

CN105812111A - Optimal power distribution method for SM-OFDM system under imperfect channel estimation

Info

Publication number: CN105812111A
Application number: CN201610125837.8A
Authority: CN
Inventors: 喻凤; 雷霞; 蒋兆翔; 和禄; 肖悦
Original assignee: University of Electronic Science and Technology of China
Current assignee: University of Electronic Science and Technology of China
Priority date: 2016-03-03
Filing date: 2016-03-03
Publication date: 2016-07-27

Abstract

The invention belongs to the technical field of communication anti-jamming, and specifically provides an optimal power allocation method of an SM-OFDM system under imperfect channel estimation. The method is mainly for the receiving end to obtain the upper bound of the system BER according to the estimated channel, and then obtain the optimal power distribution plan. The specific method is as follows: according to the estimated channel of the n pilot sub-channels closest to the data sub-channel, the estimated channel of the data sub-carrier is obtained by using the n-order generalized linear interpolation technique, and then the average BER upper bound of the data sub-carrier is calculated and calculated. Finally, the optimal power allocation scheme between pilot symbols and data symbols is obtained by minimizing the upper bound of BER. Under the condition of limited total power, the optimal power allocation scheme of the present invention can significantly improve the BER performance of the SM-OFDM system without increasing the computational complexity; the present invention is applicable to all generalized linear interpolation techniques .

Description

An Optimal Power Allocation Method for SM-OFDM Systems with Imperfect Channel Estimation

技术领域technical field

本发明属于通信抗干扰技术领域，涉及空间调制(Spatial Modulation,SM)技术，正交频分复用技术(Orthogonal Frequency Division Multiplex，OFDM)，信道估计技术，及其相关的SM-OFDM技术，具体为一种不完美信道估计下SM-OFDM系统的最优功率分配方法。The present invention belongs to the technical field of communication anti-jamming, and relates to spatial modulation (Spatial Modulation, SM) technology, orthogonal frequency division multiplexing technology (Orthogonal Frequency Division Multiplex, OFDM), channel estimation technology, and related SM-OFDM technology, specifically It is an optimal power allocation method for SM-OFDM systems under imperfect channel estimation.

背景技术Background technique

多入多出(Multiple Input Multiple Output，MIMO)技术是一种无线环境下的高速传输技术，它在发射端和接收端配置更多的天线单元，并结合先进的空时编码调制方案，通过对空间自由度的充分利用，可以带来额外的分集，复用和波束成型增益。SM技术是一种高效低复杂度的MIMO调制方案，它可以利用传输数据的天线索引来携带额外的信息比特。OFDM技术能充分利用频谱资源，有效对抗多径衰落和大时延扩展引起的符号间干扰。SM-OFDM技术被认为是未来移动通信系统很有可能选用的技术方案之一。Multiple Input Multiple Output (MIMO) technology is a high-speed transmission technology in a wireless environment. It configures more antenna units at the transmitter and receiver, and combines advanced space-time coding and modulation schemes. The full utilization of spatial degrees of freedom can bring additional diversity, multiplexing and beamforming gains. SM technology is a high-efficiency and low-complexity MIMO modulation scheme, which can use the antenna index of the transmitted data to carry additional information bits. OFDM technology can make full use of spectrum resources and effectively combat inter-symbol interference caused by multipath fading and large delay spread. SM-OFDM technology is considered to be one of the most likely technical solutions for future mobile communication systems.

SM-OFDM系统的信道估计误差会影响接收机对信号的检测准确度，使系统性能降低，通常是增加导频数量来提高信道估计的准确性，但其会降低系统传输效率。本发明即是针对这一问题，本发明通过最小化采用最小均方误差(minimum mean square error，MMSE)信道估计法时SM-OFDM系统的误比特率(Bit Error Rate，BER)上界并集界给出采用所有广义线性内插技术时导频符号和数据符号间的最优功率分配方法。The channel estimation error of the SM-OFDM system will affect the receiver's detection accuracy of the signal and reduce the system performance. Usually, the number of pilots is increased to improve the accuracy of channel estimation, but it will reduce the system transmission efficiency. The present invention is aimed at this problem, and the present invention adopts minimum mean square error (minimum mean square error, MMSE) channel estimation method when the present invention adopts minimum mean square error (Bit Error Rate, BER) upper bound union of SM-OFDM system The bounds give the optimal power allocation between pilot symbols and data symbols for all generalized linear interpolation techniques.

发明内容Contents of the invention

本发明的目的在于针对信道估计误差对SM-OFDM系统BER性能影响较大这一缺陷，提供一种适用于所有广义线性内插技术的导频符号和数据符号间的最优功率分配方法。The object of the present invention is to provide a method for optimal power allocation between pilot symbols and data symbols applicable to all generalized linear interpolation techniques for the defect that channel estimation errors have a greater impact on BER performance of SM-OFDM systems.

本发明的技术方案为：一种不完美信道估计下SM-OFDM系统的最优功率分配方法，其特征在于，包括以下步骤：The technical solution of the present invention is: an optimal power allocation method of SM-OFDM system under a kind of imperfect channel estimation, it is characterized in that, comprises the following steps:

步骤A.初始化处理Step A. Initialization Processing

SM-OFDM系统中有N_t根发送天线、N_r根接收天线和N个子载波，相干带宽内有N_c个子载波，其中前N_p个子载波发送导频符号，后N_d个子载波发送数据符号，并且N_p＝N_t；在相干带宽内，发送导频的子载波信道所占比例为在SM-OFDM系统中每个导频符号的功率为E_p,每个数据符号的功率是E_d，因此平均每个符号的功率为：In the SM-OFDM system, there are N _t transmitting antennas, N _r receiving antennas and N subcarriers, and there are N _c subcarriers in the coherent bandwidth, among which the first N _p subcarriers transmit pilot symbols, and the last N _d subcarriers transmit data symbols , and N _p =N _t ; within the coherent bandwidth, the proportion of sub-carrier channels that transmit pilots is In the SM-OFDM system, the power of each pilot symbol is E _p , and the power of each data symbol is E _d , so the average power of each symbol is:

${E E.}_{00} = = \frac{{N N}_{t t} {E E.}_{P P} + + {N N}_{d d} {E E.}_{d d}}{{N N}_{c c}} = = {δE δE}_{P P} + + ((11 - - δ δ)) {E E.}_{d d}$

定义数据符号的总功率与导频符号的总功率的比值为因此：Define the ratio of the total power of data symbols to the total power of pilot symbols as therefore:

${E E.}_{p p} = = \frac{{E E.}_{00}}{δ δ ((11 + + a a))} {E E.}_{d d} = = \frac{{aE aE}_{00}}{((11 - - δ δ)) ((11 + + a a))}$

步骤B.计算数据子载波处的估计信道Step B. Calculate the estimated channel at the data subcarrier

常规内插技术，如：二阶线性内插、高斯内插和基于维纳滤波的内插等，本质上都是通过对导频处信道系数进行加权线性组合得到数据位置处的信道估计，本发明将其统称为广义线性内插技术；Conventional interpolation techniques, such as: second-order linear interpolation, Gaussian interpolation, and interpolation based on Wiener filtering, etc., essentially obtain the channel estimate at the data position by performing a weighted linear combination of the channel coefficients at the pilot. The invention collectively refers to them as generalized linear interpolation techniques;

当采用η阶广义线性插值技术时，接收端根据MMSE估计得到与数据子载波相邻的η处导频子载波的信道估计矩阵且的每个元素都是均值为0、方差为的复高斯随机变量，其中是高斯白噪声的功率；相干带宽内的第k个数据子载波处的估计信道为：When the n-order generalized linear interpolation technique is used, the receiving end obtains the channel estimation matrix of the pilot subcarriers at n adjacent to the data subcarriers according to MMSE estimation and Each element of has a mean of 0 and a variance of The complex Gaussian random variable of , where is the power of Gaussian white noise; the estimated channel at the kth data subcarrier within the coherence bandwidth is:

因此中的每个元素的方差为：therefore The variance of each element in is:

${σ σ}_{\overset{^^}{h h},, k k}^{22} = = \frac{{w w}_{k k} {E E.}_{p p}}{{E E.}_{p p} + + {σ σ}_{z z}^{22}},,$

其中， $w_{k} = Σ_{ϵ = 1}^{_{η}} {(ξ_{ϵ}^{k})}^{2};$ in, $w_{k} = Σ_{ϵ = 1}^{_{η}} {(ξ_{ϵ}^{k})}^{2};$

步骤C.计算等效噪声Step C. Calculate equivalent noise

第k个数据子载波信道的传播模型为The propagation model of the kth data subcarrier channel is

其中，估计误差矩阵中的元素都是均值为0，方差为的复高斯随机变量，白噪声向量Z^k中的元素是均值为0方差为的复高斯随机变量，为第k个数据子载波上的发送符号向量；将Z′_k视为等效的加性高斯白噪声向量，且其中的每个元素都是均值为0，方差为 $σ_{z_{k}^{'}}^{2} = σ_{z}^{2} + E_{d} - \frac{w_{k} E_{d} E_{p}}{E_{p} + σ_{z}^{2}}$ 的复高斯随机变量；Among them, the estimated error matrix The elements in all have a mean of 0 and a variance of A complex Gaussian random variable, the elements in the white noise vector Z ^k have a mean of 0 and a variance of The complex Gaussian random variable of , is the transmitted symbol vector on the kth data subcarrier; Z′ _k is regarded as an equivalent additive white Gaussian noise vector, and each element in it has a mean value of 0 and a variance of $σ_{z_{k}^{'}}^{2} = σ_{z}^{2} + {E.}_{d} - \frac{w_{k} {E.}_{d} {E.}_{p}}{{E.}_{p} + σ_{z}^{2}}$ The complex Gaussian random variable of ;

步骤D.计算相干带宽内数据子载波的平均BER上界并集界Step D. Calculate the average BER upper bound and union bound of the data subcarriers within the coherent bandwidth

采用M阶正交幅度调制时，第k个数据子载波信道的BER上界并集界为When M-order quadrature amplitude modulation is used, the upper bound of the BER union of the kth data subcarrier channel is

${P P}_{b b - - M m A A X x} (({w w}_{k k})) = = \frac{11}{m m 22^{m m}} {Σ Σ}_{i i = = 11}^{22^{m m}} {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{22^{m m}} d d (({x x}_{i i}^{k k},, {x x}_{j j}^{k k})) {Σ Σ}_{n no = = 00}^{{N N}_{r r} - - 11} [\begin{matrix} {N N}_{r r} - - 11 + + n no \\ n no \end{matrix}] {[[11 - - γ γ ((\frac{\frac{{E E.}_{P P} {E E.}_{d d}}{{E E.}_{P P} + + {σ σ}_{z z}^{22}} {w w}_{k k} {λ λ}_{i i j j}^{k k}}{44 {σ σ}_{{z z}_{k k}^{' '}}^{22}}))]]}^{n no} γ γ {((\frac{\frac{{E E.}_{P P} {E E.}_{d d}}{{E E.}_{P P} + + {σ σ}_{z z}^{22}} {w w}_{k k} {λ λ}_{i i j j}^{k k}}{44 {σ σ}_{{z z}_{k k}^{' '}}^{22}}))}^{{N N}_{r r}}$

其中，是向量与间的汉明距离，是归一化后的向量，并且in, is a vector and The Hamming distance between yes the normalized vector, and

${λ λ}_{i i j j}^{k k} = = {(({x x}_{11 i i}^{k k} - - {x x}_{11 j j}^{k k}))}^{H h} (({x x}_{11 i i}^{k k} - - {x x}_{11 j j}^{k k})),,$

$γ γ ((x x)) = = 0.5 0.5 ((11 - - \sqrt{x x / / ((11 + + x x))})),,$

则相干带宽内N_d个传送数据符号的子载波信道的平均BER上界为：Then the upper bound of the average BER of N _d subcarrier channels transmitting data symbols within the coherent bandwidth is:

${\overset{&OverBar; &OverBar;}{P P}}_{b b - - M m A A X x} = = \frac{11}{{N N}_{d d}} {Σ Σ}_{k k = = 11}^{{N N}_{d d}} {P P}_{b b - - M m A A X x} (({w w}_{k k})),,$

因此平均BER满足 Therefore the average BER satisfies

步骤E.基于最小化平均BER上界的最优功率分配Step E. Optimal Power Allocation Based on Minimizing the Upper Bound of Average BER

E1.相干带宽内的第k个数据符号处子载波信道的并集界可简化为如下形式E1. The union boundary of the subcarrier channel at the kth data symbol within the coherent bandwidth can be simplified to the following form

${P P}_{b b - - M m A A X x} (({w w}_{k k})) = = \frac{11}{m m 22^{m m}} {Σ Σ}_{i i = = 11}^{22^{m m}} {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{22^{m m}} d d (({x x}_{i i},, {x x}_{j j})) {Σ Σ}_{n no = = 00}^{{N N}_{r r} - - 11} (\begin{matrix} {N N}_{r r} - - 11 + + n no \\ n no \end{matrix}) {((11 - - {A A}_{k k}))}^{n no} {(({A A}_{k k}))}^{{N N}_{r r}}$

其中，in,

${A A}_{k k} = = γ γ ((\frac{\frac{{E E.}_{P P} {E E.}_{d d}}{{E E.}_{P P} + + {σ σ}_{z z}^{22}} {w w}_{k k} {λ λ}_{i i j j}^{k k}}{44 {σ σ}_{{z z}_{k k}^{' '}}^{22}}));;$

设两个变量，分别为：Let two variables be:

${S S}_{k k} = = \frac{\frac{{E E.}_{P P} {E E.}_{d d}}{{E E.}_{P P} + + {σ σ}_{z z}^{22}} {w w}_{k k} {λ λ}_{i i j j}^{k k}}{44 {σ σ}_{{z z}_{k k}^{' '}}^{22}},,$

${B B}_{k k} = = \sqrt{(({S S}_{k k} / / ((11 + + {S S}_{k k}))))})),,$

显然0＜B_k＜1。将和代入B_k得到：Obviously 0<B _k <1. Will and Substitute into B _k to get:

${B B}_{k k} = = \sqrt{\frac{{aE aE}_{00}^{22} {w w}_{k k} {λ λ}_{i i j j}^{k k}}{44 ((δ δ ((11 - - δ δ)) {((11 + + a a))}^{22} {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + ((11 - - δ δ)) ((11 + + a a)) {E E.}_{00} {σ σ}_{z z}^{22} + + {σ σ}_{z z}^{22} γ γ ((11 + + a a)) {aE aE}_{00} + + {aE aE}_{00}^{22} {w w}_{k k})) + + {aE aE}_{00}^{22} {w w}_{k k} {λ λ}_{i i j j}^{k k}}}$

E2.B_k对功率分配因子a求导数E2.B _k calculates the derivative of the power allocation factor a

$\frac{\partial \partial {B B}_{k k}}{\partial \partial a a} = = 0.5 0.5 * * \frac{44 ((δ δ ((11 - - δ δ)) {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + ((11 - - δ δ)) {E E.}_{00} {σ σ}_{z z}^{22})) - - 44 ((δ δ ((11 - - δ δ)) {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + {σ σ}_{z z}^{22} {δE δE}_{00})) {a a}^{22}}{{((44 ((δ δ ((11 - - δ δ)) {((11 + + a a))}^{22} {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + ((11 - - δ δ)) ((11 + + a a)) {E E.}_{00} {σ σ}_{z z}^{22} + + {σ σ}_{z z}^{22} δ δ ((11 + + a a)) {aE aE}_{00} + + {aE aE}_{00}^{22} - - {aE aE}_{00}^{22} {w w}_{k k})) + + {aE aE}_{00}^{22} {w w}_{k k} {λ λ}_{i i j j}^{k k}))}^{1.5 1.5}} \sqrt{\frac{{E E.}_{00}^{22} {w w}_{k k} {λ λ}_{i i j j}^{k k}}{a a}}$

由于A_k＝0.5(1-B_k)，因此0<A_k＜0.5，并且Since A _k =0.5(1-B _k ), 0<A _k <0.5, and

$\frac{\partial \partial {A A}_{k k}}{\partial \partial a a} = = - - 0.5 0.5 * * \frac{\partial \partial {B B}_{k k}}{\partial \partial a a} = = {F f}_{i i j j}^{k k} G G$

其中，in,

$\begin{matrix} {F f}_{i i j j}^{k k} = = \frac{\sqrt{\frac{{E E.}_{00}^{22} {w w}_{k k} {λ λ}_{i i j j}^{k k}}{a a}}}{{((44 ((δ δ ((11 - - δ δ)) {((11 + + a a))}^{22} {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + ((11 - - δ δ)) ((11 + + a a)) {E E.}_{00} {σ σ}_{z z}^{22} + + {σ σ}_{z z}^{22} δ δ ((11 + + a a)) {aE aE}_{00} + + {aE aE}_{00}^{22} {w w}_{k k})) + + {aE aE}_{00}^{22} {w w}_{k k} {λ λ}_{i i j j}^{k k}))}^{1.5 1.5}} \\ G G = = ((δ δ ((11 - - δ δ)) {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + {σ σ}_{z z}^{22} {δE δE}_{00})) {a a}^{22} - - ((δ δ ((11 - - δ δ)) {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + ((11 - - δ δ)) {E E.}_{00} {σ σ}_{z z}^{22})) \end{matrix}$

E3.第k个数据符号子载波信道的上界对功率分配因子a求导数E3. The upper bound of the kth data symbol subcarrier channel is derived from the power allocation factor a

$\frac{\partial \partial {P P}_{b b - - M m A A X x} (({w w}_{k k}))}{\partial \partial a a} = = \frac{G G}{m m 22^{m m}} {Σ Σ}_{i i = = 11}^{22^{m m}} {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{22^{m m}} d d (({x x}_{i i},, {x x}_{j j})) {Σ Σ}_{n no = = 00}^{{N N}_{r r} - - 11} (\begin{matrix} {N N}_{r r} - - 11 + + n no \\ n no \end{matrix}) {F f}_{i i j j}^{k k} {β β}_{k k}^{n no}$

其中，由于1-A_k＞0.5＞A_k，所以N_r(1-A_k)-nA_k＞0， ${(A_{k})}^{N_{r} - 1} > 0, {(1 - A_{k})}^{n - 1} > 0, &ForAll; n = 0, 1, 2, ... ..., N_{r} - 1,$ 因此又因为w_k＞0，且所以并且当x_i≠x_j时，汉明距离d(x_i,x_j)＞0；因此等价为G＝0；in, Since 1-A _k >0.5>A _k , N _r (1-A _k )-nA _k >0, ${(A_{k})}^{N_{r} - 1} > 0, {(1 - A_{k})}^{no - 1} > 0, &ForAll; no = 0, 1, 2, ... ..., N_{r} - 1,$ therefore And because w _k > 0, and so And when x _i ≠ x _j , the Hamming distance d(x _i , x _j )>0; therefore Equivalent to G=0;

E4.平均BER上界对功率分配比例a求导数E4. Calculate the derivative of the upper bound of the average BER to the power allocation ratio a

$\frac{\partial \partial {\overset{&OverBar; &OverBar;}{P P}}_{b b - - M m A A X x}}{\partial \partial a a} = = \frac{G G}{{N N}_{d d}} {Σ Σ}_{k k = = 11}^{{N N}_{d d}} \frac{11}{m m 22^{m m}} {Σ Σ}_{i i = = 11}^{22^{m m}} {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{22^{m m}} d d (({x x}_{i i},, {x x}_{j j})) {Σ Σ}_{n no = = 00}^{{N N}_{r r} - - 11} (\begin{matrix} {N N}_{r r} - - 11 + + n no \\ n no \end{matrix}) {F f}_{i i j j}^{k k} {β β}_{k k}^{n no}$

显然也等价为G＝0；等式G＝0的解为：obviously It is also equivalent to G=0; the solution of the equation G=0 is:

$a a = = &PlusMinus; &PlusMinus; \sqrt{\frac{((δ δ ((11 - - δ δ)) + + ((11 - - δ δ)) {r r}_{00}))}{((δ δ ((11 - - δ δ)) + + {δr δr}_{00}))}}$

其中是平均符号信噪比，因为功率分配因子a＞0，因此符号条件的解为：in is the average symbol SNR, since the power allocation factor a > 0, the solution to the symbol condition is:

${a a}^{* *} = = \sqrt{\frac{((δ δ ((11 - - δ δ)) + + ((11 - - δ δ)) {r r}_{00}))}{((δ δ ((11 - - δ δ)) + + {δr δr}_{00}))}}$

由于a^*是P_b-MAX(w_k)和的最小值点，因此a^*是最优功率分配方案。Since a ^* is P _b-MAX (w _k ) and The minimum point of , so a ^* is the optimal power allocation scheme.

在广义线性内插技术中，同一频率位置处数据子载波的估计信道的方差系数通常是不相同的，由于最优功率分配因子a^*与w_k(k＝1,2,…N_d)无关，因此可以得出如下结论，SM-OFDM系统无论采用何种线性内插技术，导频与数据符号间的最优功率分配因子都是a^*。In the generalized linear interpolation technique, the variance coefficients of the estimated channel of the data subcarriers at the same frequency position are usually different, because the optimal power allocation factor a ^* has nothing to do with w _k (k=1,2,…N _d ) , so it can be concluded that no matter what kind of linear interpolation technology is used in the SM-OFDM system, the optimal power allocation factor between pilot and data symbols is a ^* .

本发明的有益效果为，本发明提供了一种能改善不完美信道估计下SM-OFDM系统BER性能的导频与数据符号间的最优功率分配方法，该技术首先计算采用MMSE估计法和η阶广义线性内插技术的系统平均BER上界并集界，然后通过最小化BER上界得到适用于任何广义线性内插技术的最优功率分配方法；在总功率有限的条件下，该最优功率分配方法能够显著提高系统的BER性能。The beneficial effects of the present invention are that the present invention provides a method for optimal power allocation between pilot and data symbols that can improve the SM-OFDM system BER performance under imperfect channel estimation. The upper bound of the system average BER of the second-order generalized linear interpolation technology is bounded by the union, and then the optimal power allocation method suitable for any generalized linear interpolation technology is obtained by minimizing the upper bound of the BER; under the condition of limited total power, the optimal The power allocation method can significantly improve the BER performance of the system.

附图说明Description of drawings

图1是SM-OFDM系统框图和信息的传输模型。Fig. 1 is the transmission model of SM-OFDM system block diagram and information.

图2是η阶广义线性内插技术导频和数据符号分布模型。Fig. 2 is the pilot frequency and the data symbol distribution model of n order generalized linear interpolation technology.

具体实施方式detailed description

下面结合实施例和附图对本发明进行进一步详细的描述，以便本领域的技术人员更好地理解本发明。为更好地对本发明进行说明，先介绍本发明技术方案所用到的术语和空间调制系统发射机结构。The present invention will be described in further detail below with reference to the embodiments and accompanying drawings, so that those skilled in the art can better understand the present invention. In order to describe the present invention better, the terms used in the technical solution of the present invention and the transmitter structure of the spatial modulation system are introduced first.

SM-OFDM系统：如图1所示，空间调制前的数据是需要传输的比特数据b，可以被视为一个m×N的矩阵，其中N是OFDM系统中的子载波数，m＝log2(N_t)+log2(M)是一个SM调制符号所携带的比特数量，M是正交幅度调制(Quadrature Amplitude Modulation,QAM)阶数。可以看出，一个SM调制符号所能携带的比特数量由QAM调制阶数和发射天线数量共同决定。SM调制准则是根据SM转化表将b转化成为一个M×N的矩阵X。在X中，一列代表一个子载波上发送的数据，任意一列只有一个非零数据，意味着任意时刻只有一根天线发送数据。如图2所示给了采用广义线性内插技术时导频和数据符号的分布情况。SM-OFDM system: as shown in Figure 1, the data before spatial modulation is the bit data b that needs to be transmitted, which can be regarded as an m×N matrix, where N is the number of subcarriers in the OFDM system, m=log2( N _t )+log2(M) is the number of bits carried by one SM modulation symbol, and M is the quadrature amplitude modulation (Quadrature Amplitude Modulation, QAM) order. It can be seen that the number of bits that can be carried by one SM modulation symbol is jointly determined by the QAM modulation order and the number of transmit antennas. The SM modulation criterion is to convert b into an M×N matrix X according to the SM conversion table. In X, one column represents the data sent on a subcarrier, and any column has only one non-zero data, which means that only one antenna sends data at any time. As shown in Figure 2, the distribution of pilot and data symbols is given when the generalized linear interpolation technique is adopted.

本发明的具体实施例如图1所示的系统模型图，发射机结构大致分为如下几步：The specific embodiment of the present invention is the system model diagram shown in Fig. 1, and the transmitter structure is roughly divided into the following steps:

步骤1：确定要选择的系统的参数，即确定子载波数个数N，相干带宽内的子载波数N_c，平均符号功率E₀，发射天线个数N_t，接收天线个数N_r，调制阶数M；Step 1: Determine the parameters of the system to be selected, that is, determine the number of subcarriers N, the number of subcarriers N _c within the coherent bandwidth, the average symbol power E ₀ , the number of transmitting antennas N _t , the number of receiving antennas N _r , Modulation order M;

步骤2：根据信噪比r₀，计算出最优功率分配因子a^*，然后计算出导频符号的功率E_P和数据符号的功率E_d；Step 2: Calculate the optimal power allocation factor a ^* according to the signal-to-noise ratio r ₀ , and then calculate the power E _P of the pilot symbol and the power E _d of the data symbol;

步骤3：计算出一帧的比特数量，将此帧数据分成两组，一组为天线索引比特，用于选择被激活的发射天线，一组为调制比特，用于进行MQAM调制；再对得到的发送向量进行SM调制；得到调制后的符号向量，导频符号向量乘以数据符号向量乘以 Step 3: Calculate the number of bits in a frame, and divide the frame data into two groups, one group is antenna index bits, which are used to select the activated transmit antenna, and one group is modulation bits, which are used for MQAM modulation; and then get SM modulation is carried out on the transmission vector; the modulated symbol vector is obtained, and the pilot symbol vector is multiplied by data sign vector multiplied by

针对接收机部分，接收机根据信道信息和系统的参数，计算出最优的功率分配方案，在计算导频符号和数据符号的功率因子，具体方法已经在发明内容中给出。For the receiver part, the receiver calculates the optimal power allocation scheme according to the channel information and system parameters, and calculates the power factors of pilot symbols and data symbols. The specific method has been given in the summary of the invention.

以上所述，仅为本发明的具体实施方式，本说明书中所公开的任一特征，除非特别叙述，均可被其他等效或具有类似目的的替代特征加以替换；所公开的所有特征、或所有方法或过程中的步骤，除了互相排斥的特征和/或步骤以外，均可以任何方式组合。The above is only a specific embodiment of the present invention. Any feature disclosed in this specification, unless specifically stated, can be replaced by other equivalent or alternative features with similar purposes; all the disclosed features, or All method or process steps may be combined in any way, except for mutually exclusive features and/or steps.

Claims

1. an optimal power allocation method of SM-OFDM system under a kind of imperfect channel estimation, is characterized in that, comprises the following steps:

Step A. Initialization processing

In the SM-OFDM system, there are N _t transmitting antennas, N _r receiving antennas and N subcarriers; there are N _c subcarriers in the coherent bandwidth, among which the first N _p subcarriers transmit pilot symbols, and the last N _d subcarriers transmit data symbols , and N _p =N _t ; within the coherent bandwidth, the proportion of sub-carrier channels that transmit pilots is In the SM-OFDM system, the power of each pilot symbol is E _p , and the power of each data symbol is E _d , so the average power of each symbol is:

E ₀ =δE _P +(1-δ)E _d ,

Define the ratio of the total power of data symbols to the total power of pilot symbols as but:

{E E.}_{p p} = = \frac{{E E.}_{00}}{δ δ ((11 + + a a))},, {E E.}_{d d} = = \frac{{aE aE}_{00}}{((11 - - δ δ)) ((11 + + a a))},,

Step B. Calculate the estimated channel at the data subcarrier

Using the nth-order generalized linear interpolation technique, the receiving end obtains the channel estimation matrix of the pilot subcarrier at n adjacent to the data subcarrier according to MMSE estimation and Each element of has a mean of 0 and a variance of The complex Gaussian random variable of , where is the power of Gaussian white noise; the estimated channel at the kth data subcarrier within the coherence bandwidth is:

therefore, The variance of each element in is:

{σ σ}_{\overset{^^}{h h},, k k}^{22} = = \frac{{w w}_{k k} {E E.}_{p p}}{{E E.}_{p p} + + {σ σ}_{z z}^{22}},,

in,

Step C. Calculate equivalent noise

The propagation model of the kth data subcarrier channel is:

Among them, the estimated error matrix The elements in have a mean of 0 and a variance of The complex Gaussian random variable of , the elements in the white noise vector Z ^k have a mean of 0 and a variance of The complex Gaussian random variable of , is the transmitted symbol vector on the k-th data subcarrier, and Z′ _k is an equivalent additive white Gaussian noise vector, where the elements have a mean value of 0 and a variance of The complex Gaussian random variable of ;

Step D. Calculate the average BER upper bound and union bound of the data subcarriers within the coherent bandwidth

Using M-order quadrature amplitude modulation, the upper bound of the BER union of the kth data subcarrier channel is

{P P}_{b b - - M m A A X x} (({w w}_{k k})) = = \frac{11}{m m 22^{m m}} {Σ Σ}_{i i = = 11}^{22^{m m}} {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{22^{m m}} d d (({x x}_{i i}^{k k},, {x x}_{j j}^{k k})) {Σ Σ}_{n no = = 00}^{{N N}_{r r} - - 11} (\begin{matrix} {N N}_{r r} - - 11 + + n no \\ n no \end{matrix}) {[[11 - - γ γ ((\frac{\frac{{E E.}_{P P} {E E.}_{d d}}{{E E.}_{P P} + + {σ σ}_{z z}^{22}} {w w}_{k k} {λ λ}_{i i j j}^{k k}}{44 {σ σ}_{{z z}_{k k}^{' '}}^{22}}))]]}^{n no} γ γ {((\frac{\frac{{E E.}_{P P} {E E.}_{d d}}{{E E.}_{P P} + + {σ σ}_{z z}^{22}} {w w}_{k k} {λ λ}_{i i j j}^{k k}}{44 {σ σ}_{{z z}_{k k}^{' '}}^{22}}))}^{{N N}_{r r}}

in, is a vector and The Hamming distance between yes the normalized vector, and

{λ λ}_{i i j j}^{k k} = = {(({x x}_{11 i i}^{k k} - - {x x}_{11 j j}^{k k}))}^{H h} (({x x}_{11 i i}^{k k} - - {x x}_{11 j j}^{k k})),,

γ γ ((x x)) = = 0.5 0.5 ((11 - - \sqrt{x x / / ((11 + + x x))})),,

Then the upper bound of the average BER of N _d subcarrier channels transmitting data symbols within the coherent bandwidth is:

{\overset{&OverBar; &OverBar;}{P P}}_{b b - - M m A A X x} = = \frac{11}{{N N}_{d d}} {Σ Σ}_{k k = = 11}^{{N N}_{d d}} {P P}_{b b - - M m A A X x} (({w w}_{k k}));;

Step E. Optimal Power Allocation Based on Minimizing the Upper Bound of Average BER

E1. The union boundary of the subcarrier channel at the kth data symbol within the coherent bandwidth is simplified as:

{P P}_{b b - - M m A A X x} (({w w}_{k k})) = = \frac{11}{m m 22^{m m}} {Σ Σ}_{i i = = 11}^{22^{m m}} {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{22^{m m}} d d (({x x}_{i i},, {x x}_{j j})) {Σ Σ}_{n no = = 00}^{{N N}_{r r} - - 11} (\begin{matrix} {N N}_{r r} - - 11 + + n no \\ n no \end{matrix}) {((11 - - {A A}_{k k}))}^{n no} {(({A A}_{k k}))}^{{N N}_{r r}}

in,

Let two variables be:

{S S}_{k k} = = \frac{\frac{{E E.}_{P P} {E E.}_{d d}}{{E E.}_{P P} + + {σ σ}_{z z}^{22}} {w w}_{k k} {λ λ}_{i i j j}^{k k}}{44 {σ σ}_{{z z}_{k k}^{' '}}^{22}},, {B B}_{k k} = = \sqrt{\frac{{S S}_{k k}}{{S S}_{k k} + + 11}},,

Will and Substitute into B _k to get:

{B B}_{k k} = = \sqrt{\frac{{aE aE}_{00}^{22} {w w}_{k k} {λ λ}_{i i j j}^{k k}}{44 ((δ δ ((11 - - δ δ)) {((11 + + a a))}^{22} {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + ((11 - - δ δ)) ((11 + + a a)) {E E.}_{00} {σ σ}_{z z}^{22} + + {σ σ}_{z z}^{22} δ δ ((11 + + a a)) {aE aE}_{00} + + {aE aE}_{00}^{22} - - {aE aE}_{00}^{22} {w w}_{k k})) + + {aE aE}_{00}^{22} {w w}_{k k} {λ λ}_{i i j j}^{k k}}}

E2.B _k calculates the derivative of the power allocation factor a

\frac{\partial \partial {B B}_{k k}}{\partial \partial a a} = = 0.5 0.5 * * \frac{44 ((δ δ ((11 - - δ δ)) {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + ((11 - - δ δ)) {E E.}_{00} {σ σ}_{z z}^{22})) - - 44 ((δ δ ((11 - - δ δ)) {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + {σ σ}_{z z}^{22} {δE δE}_{00})) {a a}^{22}}{{((44 ((δ δ ((11 - - δ δ)) {((11 + + a a))}^{22} {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + ((11 - - δ δ)) ((11 + + a a)) {E E.}_{00} {σ σ}_{z z}^{22} + + {σ σ}_{z z}^{22} δ δ ((11 + + a a)) {aE aE}_{00} + + {aE aE}_{00}^{22} - - {aE aE}_{00}^{22} {w w}_{k k})) + + {aE aE}_{00}^{22} {w w}_{k k} {λ λ}_{i i j j}^{k k}))}^{1.5 1.5}} \sqrt{\frac{{E E.}_{00}^{22} {w w}_{k k} {λ λ}_{i i j j}^{k k}}{a a}}

Since A _k =0.5(1-B _k ), 0<A _k <0.5, and

\frac{\partial \partial {A A}_{k k}}{\partial \partial a a} = = - - 0.5 0.5 * * \frac{\partial \partial {B B}_{k k}}{\partial \partial a a} = = {F f}_{i i j j}^{k k} G G

in,

{F f}_{i i j j}^{k k} = = \frac{\sqrt{\frac{{E E.}_{00}^{22} {w w}_{k k} {λ λ}_{i i j j}^{k k}}{a a}}}{{((44 ((δ δ ((11 - - δ δ)) {((11 + + a a))}^{22} {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + ((11 - - δ δ)) ((11 + + a a)) {E E.}_{00} {σ σ}_{z z}^{22} + + {σ σ}_{z z}^{22} δ δ ((11 + + a a)) {aE aE}_{00} + + {aE aE}_{00}^{22} - - {aE aE}_{00}^{22} {w w}_{k k})) + + {aE aE}_{00}^{22} {w w}_{k k} {λ λ}_{i i j j}^{k k}))}^{1.5 1.5}}

G G = = ((δ δ ((11 - - δ δ)) {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + {σ σ}_{z z}^{22} {δE δE}_{00})) {a a}^{22} - - ((δ δ ((11 - - δ δ)) {σ σ}_{z z}^{22} {σ σ}_{z z}^{22} + + ((11 - - δ δ)) {E E.}_{00} {σ σ}_{z z}^{22}))

E3. The upper bound of the kth data symbol subcarrier channel is derived from the power allocation factor a

\frac{\partial \partial {P P}_{b b - - M m A A X x} (({w w}_{k k}))}{\partial \partial a a} = = \frac{G G}{m m 22^{m m}} {Σ Σ}_{i i = = 11}^{22^{m m}} {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{22^{m m}} d d (({x x}_{i i},, {x x}_{j j})) {Σ Σ}_{n no = = 00}^{{N N}_{r r} - - 11} (\begin{matrix} {N N}_{r r} - - 11 + + n no \\ n no \end{matrix}) {F f}_{i i j j}^{k k} {β β}_{k k}^{n no}

in, Derivation can be known That is equivalent to G=0;

E4. Calculate the derivative of the average BER upper bound on the power allocation ratio a

\frac{\partial \partial {\overset{&OverBar; &OverBar;}{P P}}_{b b - - M m A A X x}}{\partial \partial a a} = = \frac{G G}{{N N}_{d d}} {Σ Σ}_{k k = = 11}^{{N N}_{d d}} \frac{11}{m m 22^{m m}} {Σ Σ}_{i i = = 11}^{22^{m m}} {Σ Σ}_{j j = = 11,, j j &NotEqual; &NotEqual; i i}^{22^{m m}} d d (({x x}_{i i},, {x x}_{j j})) {Σ Σ}_{n no = = 00}^{{N N}_{r r} - - 11} (\begin{matrix} {N N}_{r r} - - 11 + + n no \\ n no \end{matrix}) {F f}_{i i j j}^{k k} {β β}_{k k}^{n no}

Depend on That is, it is equivalent to G=0; then the solution is:

a a = = &PlusMinus; &PlusMinus; \sqrt{\frac{((δ δ ((11 - - δ δ)) + + ((11 - - δ δ)) {r r}_{00}))}{((δ δ ((11 - - δ δ)) + + {δr δr}_{00}))}},,

in, is the average symbol SNR, and the power allocation factor a>0, then the optimal power allocation scheme is:

{a a}^{* *} = = \sqrt{\frac{((δ δ ((11 - - δ δ)) + + ((11 - - δ δ)) {r r}_{00}))}{((δ δ ((11 - - δ δ)) + + {δr δr}_{00}))}} . .