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

Monika Pinchas

doi:10.1155/2014/606843

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. Recently, a closed-form approximated expression was derived by the same author for the residual ISI obtained by nonblind adaptive equalizers for the single-input single-output (SISO) case. Up to now, there does not exist a closed-form expression for the residual ISI obtained by nonblind adaptive equalizers for the single-input multiple-output (SIMO) case. Furthermore, there does not exist a closed-form expression for the SER valid for the SISO or SIMO case that takes into account the residual ISI obtained by nonblind adaptive equalizers and is valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of0.5≤H<1. In this paper, we derive a closed-form approximated expression for the residual ISI obtained by nonblind adaptive equalizers for the SIMO case (where SISO is a special case of SIMO), valid for fGn input where the Hurst exponent is in the region of0.5≤H<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.

Highlights

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 from which we want to recover its input using adjustable linear filters and training symbols
[19], a closed-form approximated expression was derived for the residual intersymbol interference (ISI) obtained by nonblind adaptive equalizers for the singleinput single-output (SISO) case that depends on the stepsize parameter, equalizer’s tap length, input signal statistics, signal-to-noise ratio (SNR), and channel power and is valid for the fractional Gaussian noise (fGn) case where the Hurst exponent is in the region of 0.5 ≤ H < 1
We propose a closed-form approximated expression for the residual ISI obtained by nonblind adaptive equalizers for the SIMO case

Summary

Introduction

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. [19], a closed-form approximated expression (or an upper limit) was derived for the residual ISI obtained by nonblind adaptive equalizers for the SISO case that depends on the stepsize parameter, equalizer’s tap length, input signal statistics, signal-to-noise ratio (SNR), and channel power and is valid for the fGn case where the Hurst exponent is in the region of 0.5 ≤ H < 1 This expression is not valid for the SIMO case. We propose a closed-form approximated expression for the residual ISI obtained by nonblind adaptive equalizers for the SIMO case (where SISO is a special case of SIMO) This new expression depends on the stepsize parameter, equalizer’s tap length, input signal statistics, SNR, channel power, and the number of receiving antennas and is valid for the fGn case where the Hurst exponent is in the region of 0.5 ≤ H < 1.

System Description

Residual ISI and SER for the SIMO and Fractional Gaussian Noise Case

Simulation

Conclusion