RESEARCH ARTICLE New space-time block codes from spectral norm Carlos A. R. Martins 1☯ , Mauro Luiz Brandão Jr. 2☯ , Eduardo Brandani da Silva ID 3☯ * 1 Department of Mathematics, UTFPR, Pato Branco, PR, Brazil, 2 Department of Electrical Engeneering, State University of Maringa ´ , Maringa ´ , PR 87020-900, Brazil, 3 DMA - UEM, Avenida Colombo 5790 - Campus Universita ´ rio, 87020-900-Maringa ´ -PR, Brazil ☯ These authors contributed equally to this work. * ebsilva@uem.br Abstract Current research proposes a natural environment for space-time codes and a new design criterion is obtained for space-time block codes in multi-antenna communication channels. The objective of this criterion is to minimize the pairwise error probability of the maximum likelihood decoder, endowed with the matrix spectral norm. The random matrix theory is used and an approximation function for the probability density function for the largest eigen- value of a Wishart Matrix is obtained. 1 Introduction A consistent theory for communication systems was introduced by Shannon’s [1] classical work, where it was proved that, for any communication channel with capacity C, the data transmission below C may be done efficiently by using an appropriate error-correcting code, or rather, there exists a code such that the error probability may become as small as required. The results of Shannon’s work are valid for channels with only one transmitter antenna and only one receiver antenna, called Single Input and Single Output (SISO) channel. However, during the last decade, we have witnessed a huge demand expansion in telecommunications, and the available technologies will not be sufficient in the future. This is due to the growing need to develop reliable communication systems that allow high rates of data transmission and, consequently, to the study and development of new mathematical methods and structures that provide support for new technologies, mainly wireless communication systems. Wireless transmissions may be impaired by a number of factors, such as great distances, objects between wireless devices, and other wireless networks, which restrict communication speed and reliability. Low capacities and high error rates of fading channels, plus the growing demand for wireless devices, motivated the development of several techniques to overcome these disadvantages. The works of Foschini-Gans [2] and Telatar [3] proved that the multiple- input and multiple-output (MIMO) communication systems attained capacity of data trans- mission greater than SISO systems. These results proved the superiority of MIMO systems and called the attention of researchers, originating several real applications. The foundations of space-time codes were established by Tarokh, Seshadri and Calderbank in [4] and space-time trellis codes (STTC) were introduced. PLOS ONE | https://doi.org/10.1371/journal.pone.0222708 September 26, 2019 1 / 35 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Martins CAR, Brandão ML, Jr., Brandani da Silva E (2019) New space-time block codes from spectral norm. PLoS ONE 14(9): e0222708. https://doi.org/10.1371/journal.pone.0222708 Editor: Muhammad Zubair, Information Technology University, PAKISTAN Received: February 4, 2019 Accepted: September 5, 2019 Published: September 26, 2019 Copyright: © 2019 Martins et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are only within the paper. Funding: The authors received no specific funding for this work. Competing interests: The authors have declared that no competing interests exist.