Adaptive Beamforming Algorithm Based On Convex Optimization

The array signal processing as an important branch of the signal processing domain is applied for many areas such as radar, sonar, communication and biomedical testing. It can exploit sufficiently the information of the signal by sampling the signal in time-spatial domain to suppress the interference and increase the signal to interference and noise ratio of the system. The adaptive array signal processing can obtain good performance in the ideal cases. But the errors in the system always severely affect the performance of the array signal processing. So many researchers are trying to research robust array signal processing algorithms. This paper introduces several algorithms to improve the robustness, which makes the system more robust for the complicated scenario. The main work in this paper is listed as follows:1. A powerful adaptive beamforming algorithm in the presence of the pointing error is proposed by probabilistic constraints, aiming at the shortcoming of the sensitivity to the pointing error. It is under the assumption that the random steering vector mismatch has Gaussian distribution, we guarantee that the pointing constraint is greater than unit response with some selected probability. Then by convex approximation, the original problem is converted to an iterative second-order cone programming problem, which can be solved efficiently via well-established interior-point method. Furthermore, a mathematical convergence analysis of the iterative solution is also provided. Compared to existing approaches, our proposed method enjoys the advantages of easier implementation and lower computational complexity, and has better performance. So it is more appropriate in practice.2. The most signals in the communication system have the cyclostationary property. Many algorithms based on the cyclostationary of the signal in the array signal processing have been exploited. They can well worked without knowing the steering vector of interested signal, thus they all belong to the blind algorithms. In the presence of cycle frequency error, a mathematical analysis of gradient decent-based algorithm is provided. It points out that due to the effect of the sinc function, the above approach have periodic zeros point as the number of snapshot increasing. Hence, a novel robust cyclostationary beamformer based on conjugate gradient algorithm, which can be used to extract signals with cy-clostationarity in the presence of cycle frequency error, is proposed. Because of its fast convergence, periodic nulls can be circumvented, and the steering vector of interested signal is estimated. Then we use traditional beamformer to avoid the influence of cycle frequency error. Simulations show that our new algorithm performs well under cycle frequency mismatches.3. On the other hand, many researchers are also trying to research the linear receiver based on multiple-input multiple-output system. The key idea of it is similar to adaptive beamforming algorithms. Both of them are trying to extract the information of interested user, while rejecting the interference and noise component. However, the performance of linear receiver highly depends on the channel state information. Hence, based on probability-constrained optimization, a robust linear receiver with worst-case probability guarantee is proposed in this paper. Using the multivariate Chebyshev inequality, the deterministic expressions of the worst-case probabilistic constraints are derived in the presence of statistical property of channel state information. Then an iterative convex programming algorithm is developed to obtain the robust solutions, and the mathematical convergence analysis is also provided. Compared to the existing receivers, our proposed receiver improves the performance by allowing small outage probability and more general uncertainty model, and some significant conclusions are also obtained.