Elliptical cell based beamforming design with an improved β-fairness power allocation for HSR communication systems

In this paper, a beamforming scheme to improve the coverage in high-speed railway communication systems is investigated. A dedicated coverage model, where the coverage cell is an ellipse rather than the traditional circular or linear, is considered. Based on the elliptical coverage cell, an optimization problem for the beamforming design is formulated to maximize the percentage of railway coverage, subject to the constraints on equal expected designed propagation gain (the gain obtained by a combination of designed beam and propagation channel) on the elliptical curve, i.e., the expectation of designed propagation gain on the elliptical curve are all equal. Considering that the coverage can be improved by increasing the minimum designed propagation gain on the railway, the problem can be recast to maximizing the equal expected designed propagation gain on the elliptical curve. Subsequently, a beamforming design with an improved β-fairness power allocation, where the optimization problem is formulated to maximize the minimum expected received power over time with the constraints on elliptical cell based beamforming and mobile service amount, is proposed to further improve the coverage. An alternating iteration algorithm is developed to find the optimal beamforming vector and the instantaneous transmit power. Through numerical results, it is found that the beamforming designed on the elliptical curve covers longer railway than beamforming designed on the railway directly, and the coverage of elliptical cell based beamforming can be increased with the eccentricity. In addition, beamforming with the improved β-fairness power allocation can further improve the railway coverage and mobile service amount simultaneously. Moreover, it is shown that the larger eccentricity of the ellipse with appropriately chosen BS location, the larger coverage distance.