On the Time-Varying Non-Linearity Effects Over the Spectrum of MIMO-OFDM Wireless Communications Systems

On the Time-Varying Non-Linearity Effects Over the Spectrum of MIMO-OFDM Wireless Communications Systems

Alexander Hilario Tacuri (Universidad Nacional de San Agustín, Arequipa, Perú)
DOI: 10.4018/IJITN.2018040103

Abstract

This article presents analytical expressions that can be used in the evaluation of the effects of a non-linear mobile (multi-path) channel on the spectrum of MIMO-OFDM communications systems, such as 4G systems (LTE, WiMax) and probably the future 5G systems. The channel is modeled by a time-varying Volterra Series and the MIMO-OFDM signal by a complex, proper, wide-sense stationary Gaussian random process with zero mean. The resulting mathematical expressions are applied to a specific situation, allowing a quantitative evaluation of the out-band spectrum regrowth of MIMO-OFDM wireless communications systems produced by the use of non-linear devices in mobile channels.
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2. Characterization Of Mimo-Ofdm Signals

The mathematical model of the -th transmitted MIMO-OFDM signal can be written as

(1) with denoting the frequency of its first sub-carrier and denoting the complex envelope of the -th transmitted MIMO-OFDM signal, given by
(2) where is the complex symbol transmitted in the antenna , subcarrier on the -th time interval, is the number of OFDM sub-carriers, is the length of the OFDM symbol, and are random variables modeling the phase of the oscillator and the error of synchronization respectively, denote the modulation shaping pulse and denote the duration of the cyclic prefix of the OFDM signal. The random variables and are considered statistically independent and uniformly distributed on and respectively.

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