Symbol Error Rate as a Function of the Residual ISI Obtained by Blind Adaptive Equalizers for the SIMO and Fractional Gaussian Noise Case

Abstract

A nonzero residual intersymbol interference (ISI) causes the symbol error rate (SER) to increase where the achievable SER may not answer any more on the system's requirements. In the literature, we may find for the single-input-single-output (SISO) case a closed-form approximated expression for the SER that takes into account the achievable performance of the chosen blind adaptive equalizer from the residual ISI point of view and a closed-form approximated expression for the residual ISI valid for the singleinput-multiple-output (SIMO) case. Both expressions were obtained by assuming that the input noise is a white Gaussian process where the Hurst exponent (H) is equal to 0.5. In this paper, we derive a closed-form approximated expression for the residual ISI obtained by blind adaptive equalizers for the SIMO case, valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of 0.5 ≤ < 1. Based on this new expression for the residual ISI, a closed-form approximated expression is obtained for the SER valid for the SIMO and fGn case. In this paper, we show via simulation results that the SER might get improved for increasing values of H.

Golden Ratio Phenomenon of Random Data Obeying von Karman Spectrum

“…From the point of view of our work in data science or big data, this research may not be enough. The future work will investigate possible golden ratio phenomena in other topics of data such as those discussed in [71][72][73][74][75][76][77][78][79][80][81][82], exploring laws associating with the golden ratio in the universe.…”

Symbol Error Rate for Nonblind Adaptive Equalizers Applicable for the SIMO and FGn Case

“…We consider a nonblind deconvolution problem in which we observe the multiple output of a finite impulse-response (FIR) single-input multiple-output (SIMO) channel (unknown channel) from which we want to recover its input using adjustable linear filters (equalizers) and training symbols. In the field of communication, SIMO channels appear either when the signal is oversampled at the receiver or from the use of an array of antennas in the receiver [1][2][3][4][5][6]. It should be pointed out that, for the SIMO case, the same information is transmitted through different subchannels and all received sequences will be distinctly distorted versions of the same message, which accounts for a certain signal diversity [6,7].…”

“…In the field of communication, SIMO channels appear either when the signal is oversampled at the receiver or from the use of an array of antennas in the receiver [1][2][3][4][5][6]. It should be pointed out that, for the SIMO case, the same information is transmitted through different subchannels and all received sequences will be distinctly distorted versions of the same message, which accounts for a certain signal diversity [6,7]. Therefore, it is reasonable to assume that more information about the transmitted signal will be available at the receiver end [6,7].…”

“…It should be pointed out that, for the SIMO case, the same information is transmitted through different subchannels and all received sequences will be distinctly distorted versions of the same message, which accounts for a certain signal diversity [6,7]. Therefore, it is reasonable to assume that more information about the transmitted signal will be available at the receiver end [6,7]. SIMO transmission is widely replacing singleinput single-output (SISO) approach to enhance the performance via diversity combining [6,8].…”

“…Therefore, it is reasonable to assume that more information about the transmitted signal will be available at the receiver end [6,7]. SIMO transmission is widely replacing singleinput single-output (SISO) approach to enhance the performance via diversity combining [6,8]. It is well known that ISI is a limiting factor in many communication environments where it causes an irreducible degradation of the bit error rate (BER) and SER, thus imposing an upper limit on the data symbol rate [1,6].…”