Códigos de bloco espaço-tempo para canais mimo 2 x 2 via álgebras cíclicas de divisão

• Autor(a) principal: Duarte, Julia Danielli
• Data de Publicação: 2021
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/214071
• topic: Codificação; Quaternios; Sistemas MIMO; Telecomunicações

This work aims to present the construction of the Golden code, which is a perfect 2 2 space-time block code (STBC) built from a cyclic division algebra. This code is said to be perfect because it is of full rate and full diversity, has non-zero determinant, which allows a lower bound for the minimum determinant, and has cubic shaping constellation. Furthermore, we will define STBC in general, and show that Alamouti’s code, the precursor to STBCs, can be constructed via a special division cyclic algebra, the algebra of Hamilton’s quaternions. After the constructions, we will present analyses of these codes in wireless communication systems with multiple antennas at the transmitter and receiver (Multiple-Input Multiple-Output - MIMO) 2 1 and 2 2 in the case of Alamouti and 2 2 in the case of the Golden code, considering that the receiver is coherent, that is, has perfect Channel State Infomartion (CSI) and that we are in a quasi-static Rayleigh fading flat frequency channel with AWGN noise. We use modulations of different orders M-QAM (M-ary Quadrature Amplitude Modulation) and a maximum likelihood decoder (Maximum Likelihood - ML) specific to each encoding. The performance analyses of the codes were done through computer simulations, in which the Monte Carlo method was employed. In these simulations, the symbol error rate (SER) curves are evaluated by the signal-to-noise ratio (SNR). With the results obtained, it was possible to show that the Golden code has a superior performance compared to the Alamouti code. For the same modulation order, the Golden code can have twice the spectral efficiency with only 1 4 of the average energy, compared to the Alamouti code. And for the case that both have the same spectral efficiency, the Golden code is also superior, since it requires less energy for transmission.