Design of downlink beamformer for real-time and non-real-time services

We study the downlink beamformer design problem considering different real-time requirements of users. The problem is formulated mathematically as a non-convex optimization problem. The objective is to maximize the minimum signal to interference plus noise ratio (SINR) of the non-real-time service users, considering the SINR constraints of the real-time users and the total transmission power constraint. We carefully study the feasibility conditions for the original non-convex optimization problem. The results provide both theoretical and physical insights into the beamformer design problem. After a series of equivalence and relaxation of the original problem, the solution can be found via bisection feasibility checking and solving a set of geometric programming (GP) problems obtained from randomization. Combining the feasibility checking algorithm and the randomization procedure, we have our algorithm for computing the beamforming vector. Numerical results are provided for illustration.

[1]  Roy D. Yates,et al.  A Framework for Uplink Power Control in Cellular Radio Systems , 1995, IEEE J. Sel. Areas Commun..

[2]  Daniel Pérez Palomar,et al.  A Dual Perspective on Separable Semidefinite Programming With Applications to Optimal Downlink Beamforming , 2010, IEEE Transactions on Signal Processing.

[3]  Holger Boche,et al.  Optimal Multi-User Interference Balancing Using Transmit Beamforming , 2003, Wirel. Pers. Commun..

[4]  Holger Boche,et al.  Accepted for Publication in Ieee Transactions on Signal Processing 1 Robust Qos-constrained Optimization of Downlink Multiuser Miso Systems , 2022 .

[5]  Zhi-Quan Luo,et al.  SDP relaxation of homogeneous quadratic optimization: Approximation bounds and applications , 2009 .

[6]  Holger Boche,et al.  Solution of the multiuser downlink beamforming problem with individual SINR constraints , 2004, IEEE Transactions on Vehicular Technology.

[7]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[8]  Zhi-Quan Luo,et al.  Semidefinite Relaxation of Quadratic Optimization Problems , 2010, IEEE Signal Processing Magazine.

[9]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[10]  Daniel Pérez Palomar,et al.  Rank-Constrained Separable Semidefinite Programming With Applications to Optimal Beamforming , 2010, IEEE Transactions on Signal Processing.

[11]  Nikos D. Sidiropoulos,et al.  Convex Optimization-Based Beamforming , 2010, IEEE Signal Processing Magazine.

[12]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[13]  Leandros Tassiulas,et al.  Transmit beamforming and power control for cellular wireless systems , 1998, IEEE J. Sel. Areas Commun..

[14]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

[15]  Bjorn Ottersten,et al.  Optimal Downlink Beamforming Using Semidefinite Optimization , 2014 .

[16]  E. Visotsky,et al.  Optimum beamforming using transmit antenna arrays , 1999, 1999 IEEE 49th Vehicular Technology Conference (Cat. No.99CH36363).