Omnidirectional Precoding for Massive MIMO With Uniform Rectangular Array-Part II: Numerical Optimization Based Schemes

• Published in: IEEE transactions on signal processing Vol. 67; no. 18; pp. 4772 - 4781
• Main Authors: Su, Dongliang, Jiang, Yi, Wang, Xin, Gao, Xiqi
• Format: Journal Article
• Language: English
• Published: New York IEEE 15.09.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Antenna radiation patterns; Arrays; common signal; Design optimization; Iterative algorithms; Iterative methods; Mathematical analysis; Matrix methods; MIMO communication; Newton method; Newton methods; Newton's method; Omnidirectional precoding; Optimization; Precoding; rank reduction; Signal processing algorithms; uniform rectangular array
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2019.2931208

In Part II of this two-part paper, we develop novel numerical optimization approaches to design omnidirectional precoding schemes for a massive multiple-input multiple-output system equipped with a uniform rectangular array (URA). To this end, we first formulate the omnidirectional precoding design as a semidefinite program (SDP) with rank constraint. An iterative rank-reduction algorithm is then proposed to produce omnidirectional transmission solution with a minimum number of precoding vectors. It is shown that the proposed algorithm can always obtain three precoding vectors (i.e., a rank-3 precoding matrix) to generate a perfectly omnidirectional power radiation pattern for any P × Q URA with min{P, Q} > 2, or yield an omnidirectional transmission solution with (theoretically minimum) two precoding vectors for any P × Q URA with min{P, Q} ≤ 2. In addition, to facilitate analog precoding design, we further impose constant-modulus constraints for every entries of the precoding matrix. Through judicious (re-)formulation, we develop an efficient Newton's method, which can compute four constant-modulus precoding vectors to generate an omnidirectional power radiation pattern for any URA configuration. The numerical results demonstrate the merits of the proposed schemes.