Telecommunication Systems

, Volume 70, Issue 2, pp 277–293 | Cite as

BER minimisation via optimal power allocation and eigenbeamforming in MIMO systems

  • Ricardo Tadashi Kobayashi
  • Alex Miyamoto Mussi
  • Taufik AbrãoEmail author


In this contribution, the convex optimisation technique is deployed to optimize the data transmission in MIMO systems operating via eigenbeamforming. Initially, we study three optimal Power Allocation (PA) policies: the first one is used for maximising the total capacity, the equal power allocation and a PA proportional to the channel gains. In the sequence and more importantly, we propose a PA capable of minimising the average Bit Error Rate (BER) with a variable number of transmit antennas. In order to do so, the optimisation problem is first stated in the standard form; then the convexity of the problem will be proven; and finally, the optimisation problem is solved by using the Karush–Kuhn–Tucker conditions. Numerical results corroborate the analytic solution. Moreover, simulation results for both the average BER and sum capacity performance metrics demonstrate the effectiveness of the proposed beamforming MIMO power allocation schemes in terms of system capacity maximisation or alternatively the BER minimisation (reliability).


MIMO systems Convex optimisation Lambert function KKT conditions Water-filling algorithm 



This work was supported in part by the National Council for Scientific and Technological Development (CNPq) of Brazil under Grant 304066/2015-0, Fundação Araucária under Grant 302/2012, and in part by State University of Londrina – Paraná State Government (UEL), and CAPES/DS scholarship.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical Engineering (DEEL)State University of Londrina (UEL)LondrinaBrazil

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