获取多维频谱占用状态是实施机会频谱接入的前提，是解决频谱资源紧张，提升频谱利用率的基础。在实际系统中，由于受到硬件处理速度、网络部署代价等限制，获取全面的频谱占用状态十分困难，通过感知仅能获得稀疏的频谱数据样本。然而频谱数据具有时间、频率、空间各个维度上的相关性，频谱预测正是一种利用相关性实现由已知频谱数据样本推演未知频谱数据，由稀疏样本推演完整数据的方法。基于此，本课题以多维频谱占用状态为研究对象，以稀疏样本条件下多维频谱占用状态的获取为基本科学问题，提出多维频谱数据的跨维度相关性建模方法，为后续的联合预测提供模型基础；提出基于小样本学习理论的多维频谱数据滤波方法，降低异常数据引起的负面影响，提高频谱数据的可靠性；提出基于张量完成理论的多维频谱联合预测方法，实现稀疏样本条件下多维频谱联合预测性能的提升。本课题的研究成果将为解决"无线频谱资源紧张"这一重大现实需求提供理论支撑。

To obtain the multi-dimensional spectrum occupancy information is the precondition of successful opportunistic spectrum access and the cornerstone of solving the radio spectrum scarcity problem. In practical systems, due to limited hardware processing speed and high network deployment price, we can only obtain sparse spectrum measurement samples from spectrum sensing and it is difficult to obtain complete spectrum occupancy information. However, it is observed that one spectrum data presents correlations with other spectrum data in dimensions of time, frequency, and space. By exploiting these correlations, spectrum prediction is a promising method to infer unknown spectrum data from known spectrum samples, and infer the complete multi-dimensional spectrum occupancy information from sparse samples. Motivated by the observations above, this program investigates the issue of joint prediction of multi-dimensional spectrum occupancy with sparse samples. Firstly, we propose a cross-dimensional correlation modelling method for multi-dimensional spectrum occupancy, which serves as the base for the following work. Secondly, using small sample learning theory, we develop filtering algorithms of multi-dimensional spectrum data to decrease the negative effect of the abnormal data and improve the reliablity of the spectrum data. Most importantly, based on the recent advances in tensor completion theory, we develop joint prediction algorithms of multi-dimensional spectrum occupancy to improve the prediction precision. The achivements of this program will provide sound theoretical support for the urgent need to seek effective solutions for the radio spectrum scarcity problem.