Cross-Entropy Iteration Aided Time-Hopping Pattern Estimation and Multi-hop Coherent Combining Algorithm

MIAO Xiaqing; WU Rui; YUE Pingyue; ZHANG Rui; WANG Shuai; PAN Gaofeng

doi:10.11999/JEIT240677

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MIAO Xiaqing, WU Rui, YUE Pingyue, ZHANG Rui, WANG Shuai, PAN Gaofeng. Cross-Entropy Iteration Aided Time-Hopping Pattern Estimation and Multi-hop Coherent Combining Algorithm[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT240677

Citation:

MIAO Xiaqing, WU Rui, YUE Pingyue, ZHANG Rui, WANG Shuai, PAN Gaofeng. Cross-Entropy Iteration Aided Time-Hopping Pattern Estimation and Multi-hop Coherent Combining Algorithm[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT240677

Citation:

MIAO Xiaqing, WU Rui, YUE Pingyue, ZHANG Rui, WANG Shuai, PAN Gaofeng. Cross-Entropy Iteration Aided Time-Hopping Pattern Estimation and Multi-hop Coherent Combining Algorithm[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT240677

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Cross-Entropy Iteration Aided Time-Hopping Pattern Estimation and Multi-hop Coherent Combining Algorithm

doi: 10.11999/JEIT240677

School of Cyberspace Science and Technology Engineering, Beijing Institute of Technology, Beijing 100081, China

Received Date: 2024-07-31
Rev Recd Date: 2024-12-17

Available Online: 2024-12-20

Abstract

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.
- Time-hopping communication,
- Multidimensional parameter joint estimation,
- Time-Hopping (TH) pattern estimation,
- Cross-Entropy (CE),
- Coherent combination

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References(16)

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