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 IJITN.2018040103.m01-th transmitted MIMO-OFDM signal IJITN.2018040103.m02 can be written as

IJITN.2018040103.m03
(1) with IJITN.2018040103.m04 denoting the frequency of its first sub-carrier and IJITN.2018040103.m05denoting the complex envelope of the IJITN.2018040103.m06-th transmitted MIMO-OFDM signal, given by
IJITN.2018040103.m07
(2) where IJITN.2018040103.m08 is the complex symbol transmitted in the antenna IJITN.2018040103.m09, subcarrier IJITN.2018040103.m10 on the IJITN.2018040103.m11-th time interval, IJITN.2018040103.m12 is the number of OFDM sub-carriers,IJITN.2018040103.m13 is the length of the OFDM symbol, IJITN.2018040103.m14 and IJITN.2018040103.m15 are random variables modeling the phase of the oscillator and the error of synchronization respectively, IJITN.2018040103.m16 denote the modulation shaping pulse and IJITN.2018040103.m17 denote the duration of the cyclic prefix of the OFDM signal. The random variables IJITN.2018040103.m18 and IJITN.2018040103.m19 are considered statistically independent and uniformly distributed on IJITN.2018040103.m20 and IJITN.2018040103.m21 respectively.

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