Cross-Entropy Iteration Aided Time-Hopping Pattern Estimation and Multi-hop Coherent Combining Algorithm
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摘要: 作为全球化通信网络的重要组成部分，卫星通信因其能够实现全球无缝覆盖和构建天地一体化信息网络而备受关注。跳时(TH)作为一种常用的卫星通信方式，具备强大的抗干扰能力、灵活的频谱利用和高安全性。该文提出一种适用于卫星通信的TH图案随机变化系统，以进一步增强数据传输过程的安全性。针对发射功率受限的问题，该文中提出了多跳信号相干合并策略，并进一步在该策略指导下，面对接收信号信噪比(SNR)低的约束，提出了交叉熵(CE)迭代辅助的跳时图案与多跳载波相位联合估计算法，以合并信噪比损失为目标函数，自适应调整待估参数的概率分布，从而快速收敛至最优解附近。仿真实验证明了该算法在迭代收敛速度、参数估计误差以及合并解调误码率等方面的优异性能。与传统算法相比，该文所提算法在保持较低复杂度的同时，误码率(BER)性能接近理论最优，有效提高了卫星TH通信系统在复杂环境下的稳定性和可靠性。Abstract: As an vital component of the global communication network, satellite communication attracts significant attention for its ability to provide seamless global coverage and establish an integrated space-ground information network. Time Hopping (TH), a commonly employed method in satellite communication, is characterized by its robust anti-jamming capability, flexible spectrum utilization and high security. In pursuit of augmenting data transmission security, a system that employs randomly varying TH patterns is devised. To address the issue of limited transmission power, a multi-hop signal coherent combining strategy is proposed. Additionally, under the constraint of low Signal-to-Noise Ratio (SNR) at the receiver, a Cross-Entropy (CE) iteration aided TH patterns and multi-hop carrier phase joint estimation algorithm is presented, which adaptively adjusts the probability distribution of estimated parameters with the SNR loss of the combined signal serving as the objective function, facilitating rapid convergence towards optimal solutions. Simulations demonstrate the superior performance of the proposed algorithm in terms of iterative convergence speed, parameter estimation error, and combined demodulation Bit Error Rate (BER). Compared with the traditional algorithm, the proposed algorithm achieves near-theoretical BER performance with low complexity, significantly improving the stability and reliability of satellite TH communication systems in complex environments.
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1 交叉熵迭代辅助的跳时图案估计与相干合并算法
输入：载波初相和跳时码的量化候选组数$ {N_{\rm c}} $，优选组数$ {N_{\rm e}} $，平滑系数$ \alpha $，最大迭代次数$ {I_{max}} $，$ {N_{\rm f}} $帧数据，载波初相量化比特位数$ {D_1} $，
跳时码量化比特位数$ {D_2} $；初始化：$ {N_{\rm f}} $帧信号的载波初相和跳时码量化比特生成概率$ {\hat {\boldsymbol{p}}^1} = 0.5 \times {1_{1 \times {N_{\rm f}}({D_1} + {D_2})}} $，$ {\hat {\boldsymbol{p}}^i} $元素为0或1的个数$ M = 0 $，迭代次数$ i = 1 $； while $ M \lt {N_{\rm f}}({D_1} + {D_2}) $ && $ 1 \le i \le {I_{max}} $ do (1) 根据概率$ {\hat {\boldsymbol{p}}^i} $生成$ {N_{\rm c}} $组候选组参数向量； (2) 根据每组参数向量对$ {N_{\rm f}} $帧数据分别进行时隙选择与载波初相补偿，并进行多跳信号的相干合并； (3) 对每组参数向量得到的合并信号进行合并信噪比损失估计，将共$ {N_{\rm c}} $组估计结果按照从小到大排序； (4) 取合并信噪比损失最小的前$ {N_{\rm e}} $组作为优选组，计算优选组量化比特为1的概率$ {{\boldsymbol{p}}^{i + 1}} $，更新概率向量$ {\hat {\boldsymbol{p}}^{i + 1}} $； (5) 将合并信噪比损失最小的一组参数向量记为$ {\boldsymbol{q}}_{{\mathrm{tmp}}}^i $，其损失记为$ \gamma _{{\mathrm{tmp}}}^i $； if $ i = = 1 $ then $ {{\boldsymbol{q}}_{{\mathrm{opt}}}} = q_{{\mathrm{tmp}}}^i $; $ {\gamma _{\min }} = \gamma _{{\mathrm{tmp}}}^i $; else if $\gamma _{{\mathrm{loss}}}^i \lt {\gamma _{\min }}$ then $ {{\boldsymbol{q}}_{{\mathrm{opt}}}} = {\boldsymbol{q}}_{{\mathrm{tmp}}}^i $; $ {\gamma _{\min }} = \gamma _{{\mathrm{tmp}}}^i $; end if (6) 更新$ {\hat {\boldsymbol{p}}^{i + 1}} $元素为0或1的个数$ M $，$ i = i + 1 $； end while 输出：$ {N_{\rm f}} $帧载波初相和跳时码的最优组合$ {{\boldsymbol{q}}_{{\mathrm{opt}}}} $ 
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表 2 不同跳时码变化范围的搜索次数
跳时码量化位数 4 5 6 候选组数 600 1200 2100 迭代次数 30 38 51 所提算法搜索次数(相位5 bit量化) 18 000 45 600 107 100 遍历法搜索次数(相位3 bit量化) 256 264 272 遍历法搜索次数(相位4 bit量化) 264 272 280 遍历法搜索次数(相位5 bit量化) 272 280 288
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