A fast algorithm to generate the Blocking Matrix for Generalized Sidelobe Canceller (GSC) beamforming is proposed in this paper. The proposed algorithm uses a Simplified Zero Placement Algorithm (SZPA) to directly generate the column vectors of the Blocking Matrix using the polynomial method. The constrained signal incoming angles are converted to spatial frequency and designated as zero locations in the Z domain. Independent vectors that span the whole left null space of the constraint matrix is then built using a simple shift operation. The algorithm also supports the derivative constraints used for robust beamforming. Compared to the conventional methods based on Singular Value Decomposition (SVD), the SZPA algorithm can generate Blocking Matrix more than 9 times faster for scenarios with 15 constraints and will be even more advantageous for more constraints. The Blocking Matrix generated by the SZPA and SVD methods is then implemented in the same GSC architecture for performance evaluation. The numerical simulation confirms that the same overall optimum state performance and learning speed can be achieved. By reducing the calculation time of blocking matrix from 1.541ms of SVD method to 0.168ms, the proposed SZPA algorithm is fast and insensitive to the number of constraints as the required calculation time incremental for each additional constraint with SZPA is only around 1/16 of SVD method. This makes it suitable for scenarios like train to infrastructure communication in High Speed Rail (HSR) where there are multiple constraints and frequent constraints update is required.
This paper presents a new structure and algorithm to improve the tracking speed of a Generalized Sidelobe Canceler (GSC) based adaptive beamformer. Iterative methods like Conjugate Gradient algorithm to calculate the beamformer weight vector eliminates the complexity of Matrix reversing. But the reduced complexity comes with time cost which requires iterations of calculation before converge to the desired direction. To combat the problem, a Simplified Zero Placement algorithm is proposed to set the initial weight vector to make the starting value near the optimum location of weight vector. Numerical simulation and analysis confirms the effectiveness of the proposed solution.
Random Variable (RV) with different Probability Density Function (PDF) and Power Spectral Density (PSD) is a critical component for simulation of different wireless channel fading profile. To get a specific PSD for simulation of different multi-path scenario, the usual method is to pass a white noise through a filter with the required shape. But the filtering process will cause the change of random variable's PDF unless the input noise follows Gaussian Distribution. In this paper, a Particle Swarm Optimization (PSO) based method to generate Non-Gaussian noise by a pre-distortion filter and Inverse Transform Sampling (ITS) that meets both the requirement of PSD and PDF is described. As the solution is based on filtering, after the filter weight is found using PSO, the simulation could be carried out in a real-time manner compared to block-based methods. The numerical simulation confirms that it can generate the required PDF and more than 90% similar to the required PSD.
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