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摘要: 物聯網是未來賽博使能業務的重要支撐平臺。蜂窩網絡則被認為是廣泛分布在部署區域中的物聯網終端數據接入的主要渠道，尤其在廣域覆蓋方面具有難以替代的價值。在滿足覆蓋要求的條件下，降低蜂窩網絡基站的下行發射功率在綠色通信方面具有重要的研究意義。由此提出了一種基于優化目標平滑近似和均方根傳播策略的梯度下降算法，在滿足物聯網業務覆蓋率的條件下最小化基站的總下行發射功率。首先，使用罰函數方法將復雜約束條件的異構蜂窩網絡優化問題轉化為簡單約束形式的優化問題；其次，將不可導的目標函數通過平滑近似轉化為可導形式，并給出其對天線下傾角和下行功率參數的梯度解析形式；最后，使用均方根傳播梯度下降算法進行轉化后的目標函數優化。仿真實驗結果表明該算法可以在滿足覆蓋率指標的條件下最小化基站的總下行發射功率，與現有元啟發算法和普通梯度下降算法相比，具有良好的收斂速度，并能更好地抑制優化過程中振蕩。Abstract: The Internet of Things (IoT) has become an essential supporting platform for the present and future cyber-enabled services. Cellular networks is considered as the main channel of the data access for IoT terminals distributed in the region of interest, and they have an irreplaceable value, especially in wide-area coverage. Thus, it has a significant application value to reduce the downlink transmit power consumption of base stations under the restrictions of the coverage requirements for the green communication in heterogeneous cellular networks. A gradient descent algorithm was proposed based on smooth approximation and root mean square propagation. The algorithm could minimize the total downlink power consumption of base stations while satisfying the IoT service coverage. First, the penalty function method was used to simplify such an optimization problem with complicated constraints to a new one with simple constraints. Then, the non-derivative objective function was transformed by an approximation method into a derivable form. We also presented the close-form of the gradient of the objective function with respect to both the azimuths of the antennas installed in the base stations and the downlink transmit power levels related to these antennas. Finally, the gradient descent algorithm with root mean square propagation was used to execute the optimization of the newly approximated but smoothed version of the original objective function. Simulation experiments were conducted, and the results show that the proposed algorithm can significantly reduce the total power consumption of the downlink radio frequency transmit under the restrictions of the coverage ratio requirements in the region of interest. Furthermore, not only is the convergence speed of the proposed algorithm very fast, but also the oscillation phenomenon that occurs during the iterative procedure steps of the optimization is greatly suppressed by the proposed algorithm compared with the meta-heuristic algorithms and ordinary gradient descent method.
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Key words:
- internet of things /
- coverage /
- downlink power consumption /
- antenna tilt /
- gradient descent algorithm
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圖 3 覆蓋示意圖。（a）初始狀態（b）第1代（c）第100代（d）第1000代
Figure 3. Illustration of coverage map: (a) initial state (b) the 1th iteration (c) the 100th iteration (d) the 1000th iteration
圖 4 覆蓋率和總下行功率損耗與迭代次數關系圖。（a）梯度下降算法；（b）SGR算法前1000代；（c）SGR算法前10代
Figure 4. Illustration of coverage and power consumption versus iteration: (a) gradient descent algorithm; (b) SGR algorithm with 1000 iterations; (c) SGR algorithm with 10 iterations
表 1 參數設置
Table 1. Parameter settings
Parameter Value Parameter Value Parameter Value ${\rm{Gau}}/{\rm{dBm}}$ ?110 ${\rm{T}}{{\rm{H}}_{{\rm{Cov}}}}$ 0.8 ${l^{{\rm{nat}}}}/{\rm{dB}}$ 20 ${\rm{T}}{{\rm{H}}_{{\rm{RS}}}}/{\rm{dBm}}$ ?92 ${g_{i,j,\hat p}}/{\rm{dB}}$ 10 $\lambda $ 10 ${\rm{T}}{{\rm{H}}_{{\rm{SI}}}}/{\rm{dB}}$ ?3 $c$ 300 $f/{\rm{MHz}}$ 1800 ${\rm{h}}{{\rm{r}}_j}/{\rm{m}}$ 1.5 $\gamma $ 0.9 $\varepsilon $ 10?8 ${G_{{\rm{max}}}}/{\rm{dB}}$ 16.34 ${G_{{\rm{atte}}}}/{\rm{dB}}$ 32 ${A_{{\rm{SL}}}}/{\rm{dB}}$ 32 ${\varphi _{{\rm{3dB}}}}/{(^{\circ} })$ 70 ${\phi _{{\rm{3dB}}}}/{(^{\circ} })$ 9 ${g^{{\rm{term}}}}/{\rm{dB}}$ 2 ${l^{{\rm{shad}}}}/{\rm{dB}}$ 7.25 $\eta $ 0.01 
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