Research on Optimal Spectral Efficiency of Orthogonal Frequency Division Multiplexing Visible Light Communication-Radio FrequencyAggregation System Based on Finite Alphabet Inputs
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摘要: 迄今为止，基于有限字母输入的正交频分复用(OFDM)可见光(VLC)和射频(RF)聚合系统的信息理论界仍然是未知的。基于这种情况，该文推导出OFDM VLC-RF聚合系统的无闭式形式的可达速率及其下界闭式表达式，并且研究了满足平均光功率和总电功率约束的基于可达速率及其下界的频谱效率(SE)最大化问题。该文利用互信息与最小均方误差(MMSE)之间的关系对速率偏导数进行了处理，提出双重注水算法解决谱效最大化问题。由于谱效的非闭式形式导致双重注水方案计算复杂度高，该文进一步研究具有闭式形式的谱效最大化问题，并使用内点法解决。仿真结果表明聚合系统相比于单个链路在通信性能上的优越性，以及基于可达速率下界的频谱效率可以作为基于可达速率的频谱效率的一个很好的低复杂度近似。Abstract: So far, the information theory of Orthogonal Frequency Division Multiplexing (OFDM) Visible Light Communication (VLC) and Radio Frequency (RF) aggregation systems based on finite alphabet inputs is still unknown. Based on this situation, the achievable rate of unclosed expression and the lower bound with closed expression of OFDM VLC-RF aggregation system are derived, and the maximization of Spectral Efficiency (SE) based on achievable rate and its lower bound satisfying the constraints of average optical power and total electric power is studied. In this paper, the relationship between mutual information and Minimum Mean Square Error (MMSE) is used to deal with the rate partial derivative, and the double Water-filling algorithm is proposed to solve the maximization problem of spectral efficiency. Because the non-closed form of spectral efficiency leads to high computational complexity of the double Water-filling algorithm, this paper further studies the problem of spectral efficiency maximization with closed form and uses the interior point method to solve it. The simulation results show that the aggregation system has the advantages in communication performance compared with a single link, and the spectral efficiency based on the lower bound of achievable rate can be used as a good low complexity approximation of the spectral efficiency based on achievable rate.
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图 2 谱效
$ {\text{S}}{{\text{E}}_{\text{F}}} $ 和$ {\text{S}}{{\text{E}}_{\text{L}}} $ 随着总电功率约束$ {P_{{\text{total}}}} $ 的变化情况
图 4 谱效
$ {\text{S}}{{\text{E}}_{\text{F}}} $ 和$ {\text{S}}{{\text{E}}_{\text{L}}} $ 随着光功率约束$ {P_o} $ 的变化情况算法1 双重注水算法 输入：给定$ \beta \in \left[ {0,\hat \beta } \right] $，$ {\delta _\beta } $表示终止参数，$ {\delta _\beta } $是控制算法准确性的一个小的正常数。 (1)进入循环； (2) 令$ \beta = \left( {{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}} \right)\left( {{\beta _{\min }} + {\beta _{\max }}} \right) $； (3) 基于式(32)，可以得到$ {p_{{\text{r}},k}} $；
(4) 找出最小$ \alpha $，$ \alpha \ge 0 $使其满足$\displaystyle\sum\nolimits_{i = 1}^{ {N_{\text{v} } }/2} { {p_{ {\text{v} },2i - 1} } } \le {\text{ } }{ { {4P_0^2}/\mathbb{E} }^2}\left\{ {\left| { {X_{ {\text{v} },2i - 1} } } \right|} \right\}$；(5) 基于式(31)，可以得到$ {p_{{\text{v}},2i - 1}} $；
(6) 如果$ \displaystyle\sum\nolimits_{i = 1}^{{N_{\text{v}}}/2} {p_{{\text{v}},2i - 1}^*} + \displaystyle\sum\nolimits_{k = 0}^{{N_{\text{r}}} - 1} {p_{{\text{r}},k}^*} \le {P_{{\text{total}}}} $，令$ {\beta _{\max }} \leftarrow \beta $；否则$ {\beta _{\min }} \leftarrow \beta $；(7)直到满足$ {\beta _{\max }} - {\beta _{\min }} \le {\delta _\beta } $，结束循环。 
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表 1 仿真参数表
VLC链路 RF链路 仿真参数及符号 参数值 仿真参数及符号 参数值 子载波数$ {N_{\text{v}}} $ $ 64 $ 子载波数$ {N_{\text{r}}} $ $ 32 $ 接收器视场角$ \psi $ $ {90^ \circ } $ 断点距离$ {d_{\text{B}}} $ ${\text{10 m}}$ 各子载波的带宽$ {B_{\text{v}}} $ $ 1{\text{ MHz}} $ RF链路距离$ {d_{2,k}} $ ${\text{5 m}}$ 半功率角$ {\theta _{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}} $ ${60^\circ }$ 各子载波的带宽$ {B_{\text{r}}} $ ${\text{1}}{\text{.25 MHz}}$ 房间反射率$ \rho $ $ 0.8 $ 中心载波频率$ {f_{\text{c}}} $ ${\text{2}}{\text{.4 GHz}}$ 噪声功率谱密度$ \sigma _{\text{v}}^2 $ $1 \times {10^{ - 19}}{\text{ }}{{\text{A}}^{\text{2}}}{\text{/Hz}}$ 到达/离开角度$ {\psi _k} $ $ {45^ \circ } $ 调制方式 $ 4{\text{ - QAM}} $ 噪声功率谱密度$ \sigma _{\text{r}}^2 $ $- 57{\text{ } }{ { {\text{dBm} } } \mathord{\left/ {\vphantom { { {\text{dbm} } } { {\text{MHz} } } }} \right. } { {\text{MHz} } } }$
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表 2
$ {\text{S}}{{\text{E}}_{\text{F}}} $ 和$ {\text{S}}{{\text{E}}_{\text{L}}} $ 计算时间的比较(s)$ {\text{S}}{{\text{E}}_{\text{F}}} $ $ {\text{S}}{{\text{E}}_{\text{L}}} $ 计算时间 123.263 44.64
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