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将VLC信道理想化为线性时不变系统,建立室内VLC系统光源辐射模型如图1所示。
VLC信道的冲激响应
$h(t)$ 表示为:$$h(t;{R_t};{R_r}) = \sum\limits_{K = 0}^\infty {h_E^{(K)}} (t;{R_t};{R_r})$$ (1) 式中:
${R_t}$ 为发射端特征;${R_r}$ 为接收端特征;$K$ 为光传输中的反射次数。对接收端冲激响应,通常将发射端$t = 0$ 时发射的脉冲视为功率1 W的冲激响应[11],可表示为:$$h(t;{R_t};{R_r}) = T(\phi )\frac{{Ar \times \cos (\varphi )}}{{{D^2}}}\delta \left(t - \frac{D}{{c}}\right)$$ (2) 式中:
$T(\phi )$ 为发射端辐射模式,文中采取朗伯辐射模式;$\phi $ 为LED发射角;$Ar$ 为接收器面积;$\varphi $ 为光电探测器(PD)入射角;$c$ 为光速;$D = \left| {\overrightarrow {{R_t}} - \overrightarrow {{R_r}} } \right|$ 为收发端间距离。以用户1为例,位置为(xi,yi,0),方向矢量n1与其入射光线夹角为${\varphi _1}$ ,由图1可具体表示为:$$D = \frac{3}{{\cos \phi }} = \frac{3}{{\cos {\varphi _1}}}$$ (3) 在LED光源的朗伯辐射模式中有:
$$T(\phi ) = \frac{{m + 1}}{{2\pi }}{\cos ^m}(\phi )$$ (4) 式中:
$m$ 为朗伯指数。因此$h(t)$ 可表示为:$${H_E} = \frac{{{P_r}}}{{{P_t}}} = \frac{{(m + 1)Ar \times \cos (\varphi )}}{{2\pi {D^2}}}{\cos ^m}(\phi )$$ (5) ${R_t}$ 与${R_r}$ 之间的直流增益${H_{\rm DC}}$ 表示为:$${H_{{\rm{DC}}}}(0;{R_{t}};{R_r}) = \int_{ - \infty }^\infty {h({t};{R_t};{R_r})} {\rm d}t$$ (6) 结合公式(5)与公式(6),
${H_{\rm DC}}$ 可表示为:$${H_{\rm DC}}(0;{R_{t}};{R_r}) = \frac{{(m + 1)Ar \times \cos (\varphi )}}{{2\pi {D^2}}}{\rm co}{{\rm s}^m}(\phi )$$ (7) 接收器的信号功率为:
$${P_r} = {P_{t}}{H_{{\rm{DC}}}}(0;{R_{t}};{R_r})$$ (8) 式中:
${P_t}$ 为发射端功率;${P_r}$ 为接收端功率。进一步推导得到信道增益为:$${H_E} = \frac{{{P_r}}}{{{P_t}}} = \frac{{(m + 1)Ar \times \cos (\varphi )}}{{2\pi {D^2}}}{\cos ^m}(\phi )$$ (9) 设定
$m = 1$ ,$Ar = 1\;{\rm{ c}}{{\rm{m}}^2}$ ,$\phi = {70^o}$ ;房间大小$4\;{\rm{m}} \times $ $ 4\;{\rm{m}} \times 3\;{\rm{m}}$ ;光源位置为(2,2,3),得到信道增益的仿真图如图2所示,其中,x轴与y轴表示室内的位置,z轴表示信道增益。由图2可知,边缘位置处用户信道增益大,因其信道环境差,故需分配较多功率保证信息传输的正确性。而中心位置处的用户信道增益小,因此可分配较少的功率。根据公式(9)计算出的信道增益进行NOMA用户的功率分配可有效保证多用户系统的公平性。
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根据室内VLC系统的信道特性,假设用户i的位置为(xi,yi,0),光源位置为(2,2,3),根据公式(3)可求得两者之间的距离为:
$$ \begin{split} \\ D = \frac{3}{{\cos \phi }} = \frac{3}{{\cos {\varphi _1}}} {\rm{ = }}\sqrt {{{({x_i} - 2)}^2} + {{({y_i} - 2)}^2} + {{(0 - 3)}^2}} \\ \end{split} $$ (10) 根据用户信道增益进行功率分配,结合公式(9)与公式(10),用户i的信道增益为:
$${H_{i}} = \frac{{(m + 1)Ar \times \cos (\varphi )}}{{2\pi [{{({x_i} - 2)}^2} + {{({y_i} - 2)}^2} + 9]}}{\cos ^m}(\phi )$$ (11) 则第i个用户分配的功率为:
$${P_{i}}{\rm{ = }}{P_t}{\alpha _i}$$ (12) 式中:
${P_{i}}$ 为用户$i$ 的功率;${\alpha _i}$ 表示功率分配因子[12],且$0 \leqslant {\alpha _i} \leqslant 1$ ,其具体值为:$${\alpha _i}{\rm{ = }}\frac{{{H_i}}}{{\displaystyle\sum\limits_{{i = }1}^{i} {{H_i}} }}$$ (13) 假设用户i发射信号为
$X(i){\rm{ = }}{P_t}{{\rm e}^{ - j\varpi t}}$ ,$\varpi $ 为相位,各信号平均功率为1,即$E[{\left| {X(i)} \right|^2}] = 1$ ,经星座映射与叠加编码的调制符号为:$$\mathop {X(i)}\limits^ \wedge = {P_t}{\alpha _i}{{\rm e}^{ - j\varpi t}}$$ (14) -
为将调制后的信号实数化,需要对频域OFDM符号结构进行共轭对称处理[10],同时保证
${X_0} = $ $ {X_{N/2}} = 0$ ,如下:$$\mathop {X{{{(i)}}_{co}}}\limits^ \wedge {\rm{ = }}[0,{X_1}(i), \cdot \cdot \cdot ,{X_{\frac{N}{2} - 1}}(i),0,{X_{\frac{{N}}{2} - 1}}{(i)^*}, \cdot \cdot \cdot ,{X_1}{(i)^*}]$$ (15) 共轭对称后进行IFFT,得到用户i的信号为:
$$\mathop {X{{(i)}_{tr}}}\limits^ \wedge = \frac{1}{{\sqrt N }}\sum\limits_{k = 0}^{N - 1} {\mathop {X{{(i)}_{co}}}\limits^ \wedge \exp (\frac{{j2\pi \varpi n}}{N})} {\rm{ }}$$ (16) 式中:exp()表示指数运算,双极性信号
$\mathop {X(i)}\limits^ \wedge $ 在添加循环前缀并附加直流偏置以保证信号的非负性后,最终形成待传输信号,驱动LED光源进行通信信号传输。 -
发送信号通过室内光信道后被用户给接收,接收信号可表示为:
$${Y} = \sum\limits_{i = 1}^{i} {\sqrt {{p_i}} }{H}_{i} \mathop{X{{(i)}_{tr}}}\limits^ \wedge + n$$ (17) 结合公式(11)可表示为:
$${Y} = \sum\limits_{i = 1}^{i} {\sqrt {{p_i}} } \frac{{(m + 1)Ar \times \cos (\varphi )}}{{2\pi [{{({x_i} - 2)}^2} + {{({y_i} - 2)}^2} + 9]}} \times {\cos ^m}(\phi )\mathop{X{{(i)}_{tr}}}\limits^ \wedge + n$$ (18) 式中:n为噪声;N0为功率谱密度。为提高可靠性,文中在系统中采用SIC减小用户间干扰。相应的多用户信号检测原理如图4所示。图4中,假设p1>p2,先将UE2信号看做噪声,解调出UE1信号,然后从接收信号Y中减去UE1信号,再解调出UE2信号,以此类推,直到解调出用户UEi的信号。
在2用户下,减去用户1信号后,系统存在的干扰仅为高斯白噪声,则用户2最大可达速率为单用户的界限。NOMA用户的速率可用表述为:
$$\left\{ {\begin{array}{*{20}{l}} {{R_1} = {{\log }_2}\left(1 + \dfrac{{{p_1}{{\left| {{H_1}} \right|}^2}}}{{{p_2}{{\left| {{H_2}} \right|}^2} + {N_0}}}\right)} \\ {{R_2} = {{\log }_2}\left(1 + \dfrac{{{p_2}{{\left| {{H_2}} \right|}^2}}}{{{N_0}}}\right)} \end{array}} \right.$$ (19) 对OFDM系统,不同用户占用相互正交频谱,其中β Hz带宽分配给用户1,(1-β) Hz带宽分配给用户2,因此用户间不存在相互干扰,用户速率[11, 13]可表示为:
$$\left\{ {\begin{array}{*{20}{l}} {{R_1} = \beta {{\log }_2}\left(1 + \dfrac{{{p_1}{{\left| {{H_1}} \right|}^2}}}{{\beta {N_0}}}\right)} \\ {{R_2} = \left((1 - \beta ){{\log }_2}(1 + \dfrac{{{p_2}{{\left| {{H_2}} \right|}^2}}}{{(1 - \beta ){N_0}}})\right)} \end{array}} \right.$$ (20) 在可见光通信中,用户i在第m个子信道的信噪比[10]如下式所示:
$${\varGamma _{SINR,{i}}}(m) = \frac{{{\gamma ^2}{\rho ^2}{H_i}{p_i}}}{{{\gamma ^2}{\rho ^2}{H_i}\displaystyle\sum\limits_{i = 1}^i {{p_i}} + {\gamma ^2}{H_i}\sigma _{clip}^2 + 1}}$$ (21) 式中:
$\gamma $ 为光电转换因子,假设$\gamma {\rm{ = }}1A/W$ ;$\rho $ 为限幅尺度衰减因子,${\sigma _{clip}}$ 为限幅噪声的标准差。用户i在第m个子信道的和速率[10]为:$${R_{i}}(m) = \frac{{{W_i}}}{2}{\log _2}[1 + {\varGamma _{SINR,{\rm{i}}}}(m)]$$ (22) 式中:
${W_i}$ 表示用户i的带宽,共轭对称使频带利用率降低一半。可以看出,当总功率为定值时,整个系统的合速率会受功率分配影响,因而系统合速率与用户功率分配有关[14]。 -
在图1的室内环境模型下对系统通信速率与误码率性能进行仿真分析与实验验证。
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仿真设置LED位于屋顶中心处,光电转化因子为1,光电探测器如图1所示分布在房间地面,其他仿真参数如表1所示。
表 1 仿真参数
Table 1. Simulation parameter
Parameter Value LED Optical power/W 1 Modelation bandwidth/Hz 5×107 LED transmitting angle/(°) 75 Subcarrier bandwidth/Hz 1.56×106 FOV at PD/(°) 70 Physical area of PD/cm2 1 NOMA-DCO-OFDM系统用户数为10,采用16QAM调制,64个子信道,IFFT/FFT点数N=128,功率分配采用公式(12)的分配算法。仿真得到的室内VLC系统用户数和通信速率之间的关系曲线如图5所示。
图 5 基于NOMA与基于OFDM的VLC系统通信速率
Figure 5. Comparison of NOMA-based and OFDM-based VLC system communication rate
由图5可知,基于OFDM的VLC系统通信速率不稳定,随用户数量增多,速率呈指数型增大。而基于NOMA的VLC系统通信速率稳定,随用户数量增多,其合速率有所下降,但并不明显。同时,NOMA-DCO-OFDM系统的通信速率明显高于DCO-OFDM系统。
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以2用户系统为例,将用户1设置在室内边缘处,用户2设置在室内中心处,仿真参数与表1一致。在下行系统的并串转换后,首先基于星座图进行可靠性的分析,其次根据误码率曲线进行可靠性定量分析,仿真得到的接收端用户1和用户2星座图如图6所示。
图 6 解调之前用户1和用户2星座图。(a) 用户1; (b) 用户2
Figure 6. User 1 and user 2 constellation before demodulation. (a) User 1;(b) User 2
对星座图采用调制误差率(Modulation Error Rate, MER)分析,其定义如下:
$${\rm{MER = }}10\lg \dfrac{{\displaystyle\sum\limits_{j = 1}^k {({I_j}^2 + {Q_j}^2)} }}{{\displaystyle\sum\limits_{j = 1}^k {(\delta {I_j}^2 + \mu {Q_j}^2)} }}$$ (23) 式中:
${I_j}$ 和${Q_j}$ 为理想星座图中数据点;$\delta {I_j}$ ,$\mu {Q_j}$ 为接收数据点与理想点的差值;k表示星座图点数。对64QAM,MER经验门限值为23.5 dB,调制阶次越低,要求的经验门限值越低。由公式(23)进行MER计算,得到用户1 MER值为25.9 dB,用户2 MER值为26.3 dB,均大于门限值。采用蒙特卡洛方法进行误码率计算,仿真得到的两用户误码率性能曲线如图7所示。
由图7可以看出,误码率为10−4时,对于用户1,NOMA系统相较OFDM系统有5.2 dB左右的性能提升;对于用户2,NOMA系统相较OFDM系统有2.3 dB左右的性能提升。进一步,NOMA系统用户间误码率性能差异明显小于OFDM系统。表明NOMA提高了通信可靠性,并保证了用户公平性。
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为验证文中提出的NOMA-DCO-OFDM系统,进行半实物实验。图8所示为包含发送模块与接收模块。将LED和PD放置在导轨上,传输距离设置为35 cm,LED型号4.8 mm LISUNG,光电探测器型号为LSSAPD9-500,聚光片为凸透镜。
发送端由上位机产生2用户NOMA-DCO-OFDM信号,经任意信号发生器将信号传输给可见光发送模块,激励LED传输信号。接收端,用示波器观察接收信号的波形,与发送端的波形对比验证系统通信的可行性;同时通过数字示波器采集并由分析软件进行解调验证通信性能。图8为信号发生器输入的连续的2用户功率域叠加后的发送波形,在示波器上显示的接收波形,通过对比发收前后波形发现,接收波形和发送波形的频率基本一致,验证了文中所提出的可见光通信系统的合理性。通过把发送端生成的2用户通信数据和接收端接收并解调出的2用户通信数据进行对比分析,验证了文中所提出的可见光通信系统的性能。
Performance optimization method of indoor visible light communication system based on non-orthogonal multiple access
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摘要: 室内可见光通信(Visible Light Communication, VLC)系统常用的非对称限幅光OFDM(Asymmetrically Clipped Optical Orthogonal Frequency Division Multiplexing, ACO-OFDM)与直流偏置光OFDM(DC-biased Optical OFDM, DCO-OFDM)采用加循环前缀、信道均衡和载波复用等方法解决信道干扰及多用户复用问题,但均以牺牲有效性为代价。非正交多址(Non-orthogonal Multiple Access, NOMA)通过功率域复用提高频谱利用率,利用串行干扰消除(Successive Interference Cancelling, SIC)进行多用户信号处理,有效兼顾可靠性与有效性。将NOMA应用于室内可见光系统,建立基于NOMA-DCO-OFDM的可见光信号传输及信道增益模型。通过功率域多用户信道差异计算信道增益,进行功率分配实现功率域复用,提高系统容量和通信速率;利用SIC按功率分配算法对用户逐一解调,减弱信道干扰,提高可靠性。通过理论分析和仿真实验验证表明:该系统的通信速率达到6.8×107 bit·s−1,且合速率受用户数量的影响不显著。2用户下,误码率(Bit Error Rate, BER)为10−4时用户1有5.2 dB左右的性能提升,用户2有2.3 dB左右的性能提升,通信可靠性也明显提高。Abstract: Indoor visible light communication (VLC) systems are usually designed based on asymmetric clipped optical orthogonal frequency division multiplexing (ACO-OFDM) and DC biased optical OFDM (DCO-OFDM). These system models usually use CP, channel equalization and carrier multiplexing to solve the problems of channel interference and multi-user multiplexing. But these are at the expense of effectiveness. Non-orthogonal multiple access (NOMA) improves spectrum utilization by sub-carrier multiplexing in power domain, and uses serial interference cancellation (SIC) for multi-user signal processing. It is an effective method to balance communication reliability and effectivity. An indoor VLC system based on NOMA was proposed, and a VLC signal transmission and channel gain model based on NOMA-DCO-OFDM were established. According to channel gain of multi-user, the power allocation of NOMA was carried out to realize the multiplexing in power domain and improve the capacity of system and the communication rate. SIC was used to demodulate the multi-user signals one by one according to the power allocation algorithm to reduce channel interference and improve the reliability of the system. Theoretical analysis and experimental verification show that the communication rate of the system reaches 6.8×107 bit·s−1, the combined rate is not significantly affected by the number of users, and the communication efficiency is significantly improved. For 2 users, when BER is 10−4, user 1 has about 5.2 dB performance improvement, user 2 has about 2.3 dB performance improvement, the communication reliability is also improved.
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表 1 仿真参数
Table 1. Simulation parameter
Parameter Value LED Optical power/W 1 Modelation bandwidth/Hz 5×107 LED transmitting angle/(°) 75 Subcarrier bandwidth/Hz 1.56×106 FOV at PD/(°) 70 Physical area of PD/cm2 1 -
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