Cross-Entropy Iteration Aided Time-Hopping Pattern Estimation and Multi-hop Coherent Combining Algorithm
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School of Cyberspace Science and Technology Engineering, Beijing Institute of Technology, Beijing 100081, China
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摘要: 作為全球化通信網(wǎng)絡的重要組成部分，衛(wèi)星通信因其能夠實現(xiàn)全球無縫覆蓋和構建天地一體化信息網(wǎng)絡而備受關注。跳時(TH)作為一種常用的衛(wèi)星通信方式，具備強大的抗干擾能力、靈活的頻譜利用和高安全性。該文提出一種適用于衛(wèi)星通信的TH圖案隨機變化系統(tǒng)，以進一步增強數(shù)據(jù)傳輸過程的安全性。針對發(fā)射功率受限的問題，該文提出多跳信號相干合并策略，并進一步在該策略指導下，面對接收信號信噪比(SNR)低的約束，提出了交叉熵(CE)迭代輔助的跳時圖案與多跳載波相位聯(lián)合估計算法，以合并信噪比損失為目標函數(shù)，自適應調整待估參數(shù)的概率分布，從而快速收斂至最優(yōu)解附近。仿真實驗證明了該算法在迭代收斂速度、參數(shù)估計誤差以及合并解調誤碼率等方面的優(yōu)異性能。與傳統(tǒng)算法相比，所提算法在保持較低復雜度的同時，誤碼率(BER)性能接近理論最優(yōu)，有效提高了衛(wèi)星TH通信系統(tǒng)在復雜環(huán)境下的穩(wěn)定性和可靠性。
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關鍵詞:
- 跳時通信 /
- 多維參數(shù)聯(lián)合估計 /
- 跳時圖案估計 /
- 交叉熵 /
- 相干合并
Abstract:Objective: As a vital component of the global communication network, satellite communication attracts significant attention for its capacity to provide seamless global coverage and establish an integrated space-ground information network. Time-Hopping (TH), a widely used technique in satellite communication, is distinguished by its strong anti-jamming capabilities, flexible spectrum utilization, and high security levels. In an effort to enhance data transmission security, a system utilizing randomly varying TH patterns has been developed. To tackle the challenge of limited transmission power, symbols are distributed across different time slots and repeatedly transmitted according to random TH patterns. At the receiver end, a coherent combining strategy is implemented for signals originating from multiple time slots. To minimize Signal-to-Noise Ratio (SNR) loss during this combining process, precise estimation of TH patterns and multi-hop carrier phases is essential. The randomness of the TH patterns and multi-hop carrier phases further complicates parameter estimation by increasing its dimensionality. Additionally, the low transmission power leads to low-SNR conditions for the received signals in each time slot, complicating parameter estimation even more. Traditional exhaustive search methods are hindered by high computational complexity, highlighting the pressing need for low-complexity multidimensional parameter estimation techniques tailored specifically for TH communication systems. Methods: Firstly, a TH communication system featuring randomly varying TH patterns is developed, where the time slot index of the signal in each time frame is determined by the TH code. Both parties involved in the communication agree that this TH code will change randomly within a specified range. Building on this foundation, a mathematical model for estimating TH patterns and multi-hop carrier phases is derived from the perspective of maximum likelihood estimation, framing it as a multidimensional nonlinear optimization problem. Moreover, guided by a coherent combining strategy and constrained by low SNR conditions at the receiver, a Cross-Entropy (CE) iteration aided algorithm is proposed for the joint estimation of TH patterns and multi-hop carrier phases. This algorithm generates multiple sets of TH code and carrier phase estimates randomly based on a predetermined probability distribution. Using the SNR loss of the combined signal as the objective function, the CE method incorporates an adaptive importance sampling strategy to iteratively update the probability distribution of the estimated parameters, facilitating rapid convergence towards optimal solutions. Specifically, in each iteration, samples demonstrating superior performance are selected according to the objective function to calculate the probability distribution for the subsequent iteration, thereby enhancing the likelihood of reaching the optimal solution. Additionally, to account for the randomness inherent in the iterations, a global optimal vector set is established to document the parameter estimates that correspond to the minimum SNR loss throughout the iterative process. Finally, simulation experiments are conducted to assess the performance of the proposed algorithm in terms of iterative convergence speed, parameter estimation error, and the combined demodulation Bit Error Rate (BER). Results and Discussions: The estimation errors for the TH code and carrier phase were simulated to evaluate the parameter estimation performance of the proposed algorithm. With an increase in SNR, the accuracy of TH code estimation approaches unity. When a small phase quantization bit width is applied, the Root Mean Square Error (RMSE) of the carrier phase estimation is primarily constrained by the grid search step size. Conversely, as the phase quantization bit width increases, the RMSE gradually converges to a fixed value. Regarding the influence of phase quantization on combined demodulation, as the phase quantization bit width increases, nearly theoretical BER performance can be achieved. A comparison between the proposed algorithm and the exhaustive search method reveals that the proposed algorithm significantly reduces the number of search trials compared to the grid search method, with minimal loss in BER performance. An increase in the variation range of the TH code necessitates a larger number of candidate groups for the CE method to maintain a low combining SNR loss. However, with a greater TH code variation range, the number of search iterations and its growth rate in the proposed algorithm are significantly lower than those in the exhaustive search method. Regarding transmission power in the designed TH communication method, as the number of hops in the multi-hop combination increases, the required SNR per hop decreases for the same BER performance, indicating that maximum transmission power can be correspondingly reduced. Conclusions: A TH communication system with randomly varying TH patterns tailored for satellite communication applications has been designed. This includes the presentation of a multi-hop signal coherent combining technique. To address the multidimensional parameter estimation challenge associated with TH patterns and multi-hop carrier phases under low SNR conditions, a CE iteration-aided algorithm has been proposed. The effectiveness of this algorithm is validated through simulations, and its performance regarding iterative convergence characteristics, parameter estimation error, and BER performance has been thoroughly analyzed. The results indicate that, in comparison to the conventional grid search method, the proposed algorithm achieves near-theoretical optimal BER performance while maintaining lower complexity. -
1 交叉熵迭代輔助的跳時圖案估計與相干合并算法
輸入：載波初相和跳時碼的量化候選組數(shù)$ {N_{\rm c}} $，優(yōu)選組數(shù)$ {N_{\rm e}} $，平滑系數(shù)$ \alpha $，最大迭代次數(shù)$ {I_{\max}} $，$ {N_{\rm f}} $幀數(shù)據(jù)，載波初相量化比特位數(shù)$ {D_1} $，
跳時碼量化比特位數(shù)$ {D_2} $；初始化：$ {N_{\rm f}} $幀信號的載波初相和跳時碼量化比特生成概率$ {\hat {\boldsymbol{p}}^1} = 0.5 \times {{\bf{1}}_{1 \times {N_{\rm f}}({D_1} + {D_2})}} $，$ {\hat {\boldsymbol{p}}^i} $元素為0或1的個數(shù)$ M = 0 $，迭代次數(shù)$ i = 1 $； while $ M \lt {N_{\rm f}}({D_1} + {D_2}) $ && $ 1 \le i \le {I_{\max}} $ do (1) 根據(jù)概率$ {\hat {\boldsymbol{p}}^i} $生成$ {N_{\rm c}} $組候選組參數(shù)向量； (2) 根據(jù)每組參數(shù)向量對$ {N_{\rm f}} $幀數(shù)據(jù)分別進行時隙選擇與載波初相補償，并進行多跳信號的相干合并； (3) 對每組參數(shù)向量得到的合并信號進行合并信噪比損失估計，將共$ {N_{\rm c}} $組估計結果按照從小到大排序； (4) 取合并信噪比損失最小的前$ {N_{\rm e}} $組作為優(yōu)選組，計算優(yōu)選組量化比特為1的概率$ {{\boldsymbol{p}}^{i + 1}} $，更新概率向量$ {\hat {\boldsymbol{p}}^{i + 1}} $； (5) 將合并信噪比損失最小的一組參數(shù)向量記為$ {\boldsymbol{q}}_{{\mathrm{tmp}}}^i $，其損失記為$ \gamma _{{\mathrm{tmp}}}^i $； if $ i = = 1 $ then $ {{\boldsymbol{q}}_{{\mathrm{opt}}}} = {\boldsymbol{q}}_{{\mathrm{tmp}}}^i $; $ {\gamma _{\min }} = \gamma _{{\mathrm{tmp}}}^i $; else if $\gamma _{{\mathrm{tmp}}}^i \lt {\gamma _{\min }}$ 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}} $元素為0或1的個數(shù)$ M $，$ i = i + 1 $； end while 輸出：$ {N_{\rm f}} $幀載波初相和跳時碼的最優(yōu)組合$ {{\boldsymbol{q}}_{{\mathrm{opt}}}} $ 
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表 1 仿真參數(shù)
參數(shù)名稱 參數(shù)設置 調制方式 BPSK 信道類型 AWGN 跳數(shù) 2, 4, 8 每時幀的時隙數(shù) 4, 16, 32, 64 每跳的符號數(shù) 1 000
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表 2 不同跳時碼變化范圍的搜索次數(shù)
跳時碼量化位數(shù) 4 5 6 候選組數(shù) 600 1200 2100 迭代次數(shù) 30 38 51 所提算法搜索次數(shù)(相位5 bit量化) 18 000 45 600 107 100 遍歷法搜索次數(shù)(相位3 bit量化) 256 264 272 遍歷法搜索次數(shù)(相位4 bit量化) 264 272 280 遍歷法搜索次數(shù)(相位5 bit量化) 272 280 288
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