\documentclass[11pt,twoside]{article}\makeatletter

\IfFileExists{xcolor.sty}%
  {\RequirePackage{xcolor}}%
  {\RequirePackage{color}}
\usepackage{colortbl}
\usepackage{wrapfig}
\usepackage{ifxetex}
\ifxetex
  \usepackage{fontspec}
  \usepackage{xunicode}
  \catcode`⃥=\active \def⃥{\textbackslash}
  \catcode`❴=\active \def❴{\{}
  \catcode`❵=\active \def❵{\}}
  \def\textJapanese{\fontspec{Noto Sans CJK JP}}
  \def\textChinese{\fontspec{Noto Sans CJK SC}}
  \def\textKorean{\fontspec{Noto Sans CJK KR}}
  \setmonofont{DejaVu Sans Mono}
  
\else
  \IfFileExists{utf8x.def}%
   {\usepackage[utf8x]{inputenc}
      \PrerenderUnicode{–}
    }%
   {\usepackage[utf8]{inputenc}}
  \usepackage[english]{babel}
  \usepackage[T1]{fontenc}
  \usepackage{float}
  \usepackage[]{ucs}
  \uc@dclc{8421}{default}{\textbackslash }
  \uc@dclc{10100}{default}{\{}
  \uc@dclc{10101}{default}{\}}
  \uc@dclc{8491}{default}{\AA{}}
  \uc@dclc{8239}{default}{\,}
  \uc@dclc{20154}{default}{ }
  \uc@dclc{10148}{default}{>}
  \def\textschwa{\rotatebox{-90}{e}}
  \def\textJapanese{}
  \def\textChinese{}
  \IfFileExists{tipa.sty}{\usepackage{tipa}}{}
\fi
\def\exampleFont{\ttfamily\small}
\DeclareTextSymbol{\textpi}{OML}{25}
\usepackage{relsize}
\RequirePackage{array}
\def\@testpach{\@chclass
 \ifnum \@lastchclass=6 \@ne \@chnum \@ne \else
  \ifnum \@lastchclass=7 5 \else
   \ifnum \@lastchclass=8 \tw@ \else
    \ifnum \@lastchclass=9 \thr@@
   \else \z@
   \ifnum \@lastchclass = 10 \else
   \edef\@nextchar{\expandafter\string\@nextchar}%
   \@chnum
   \if \@nextchar c\z@ \else
    \if \@nextchar l\@ne \else
     \if \@nextchar r\tw@ \else
   \z@ \@chclass
   \if\@nextchar |\@ne \else
    \if \@nextchar !6 \else
     \if \@nextchar @7 \else
      \if \@nextchar (8 \else
       \if \@nextchar )9 \else
  10
  \@chnum
  \if \@nextchar m\thr@@\else
   \if \@nextchar p4 \else
    \if \@nextchar b5 \else
   \z@ \@chclass \z@ \@preamerr \z@ \fi \fi \fi \fi
   \fi \fi  \fi  \fi  \fi  \fi  \fi \fi \fi \fi \fi \fi}
\gdef\arraybackslash{\let\\=\@arraycr}
\def\@textsubscript#1{{\m@th\ensuremath{_{\mbox{\fontsize\sf@size\z@#1}}}}}
\def\Panel#1#2#3#4{\multicolumn{#3}{){\columncolor{#2}}#4}{#1}}
\def\abbr{}
\def\corr{}
\def\expan{}
\def\gap{}
\def\orig{}
\def\reg{}
\def\ref{}
\def\sic{}
\def\persName{}\def\name{}
\def\placeName{}
\def\orgName{}
\def\textcal#1{{\fontspec{Lucida Calligraphy}#1}}
\def\textgothic#1{{\fontspec{Lucida Blackletter}#1}}
\def\textlarge#1{{\large #1}}
\def\textoverbar#1{\ensuremath{\overline{#1}}}
\def\textquoted#1{‘#1’}
\def\textsmall#1{{\small #1}}
\def\textsubscript#1{\@textsubscript{\selectfont#1}}
\def\textxi{\ensuremath{\xi}}
\def\titlem{\itshape}
\newenvironment{biblfree}{}{\ifvmode\par\fi }
\newenvironment{bibl}{}{}
\newenvironment{byline}{\vskip6pt\itshape\fontsize{16pt}{18pt}\selectfont}{\par }
\newenvironment{citbibl}{}{\ifvmode\par\fi }
\newenvironment{docAuthor}{\ifvmode\vskip4pt\fontsize{16pt}{18pt}\selectfont\fi\itshape}{\ifvmode\par\fi }
\newenvironment{docDate}{}{\ifvmode\par\fi }
\newenvironment{docImprint}{\vskip 6pt}{\ifvmode\par\fi }
\newenvironment{docTitle}{\vskip6pt\bfseries\fontsize{22pt}{25pt}\selectfont}{\par }
\newenvironment{msHead}{\vskip 6pt}{\par}
\newenvironment{msItem}{\vskip 6pt}{\par}
\newenvironment{rubric}{}{}
\newenvironment{titlePart}{}{\par }

\newcolumntype{L}[1]{){\raggedright\arraybackslash}p{#1}}
\newcolumntype{C}[1]{){\centering\arraybackslash}p{#1}}
\newcolumntype{R}[1]{){\raggedleft\arraybackslash}p{#1}}
\newcolumntype{P}[1]{){\arraybackslash}p{#1}}
\newcolumntype{B}[1]{){\arraybackslash}b{#1}}
\newcolumntype{M}[1]{){\arraybackslash}m{#1}}
\definecolor{label}{gray}{0.75}
\def\unusedattribute#1{\sout{\textcolor{label}{#1}}}
\DeclareRobustCommand*{\xref}{\hyper@normalise\xref@}
\def\xref@#1#2{\hyper@linkurl{#2}{#1}}
\begingroup
\catcode`\_=\active
\gdef_#1{\ensuremath{\sb{\mathrm{#1}}}}
\endgroup
\mathcode`\_=\string"8000
\catcode`\_=12\relax

\usepackage[a4paper,twoside,lmargin=1in,rmargin=1in,tmargin=1in,bmargin=1in,marginparwidth=0.75in]{geometry}
\usepackage{framed}

\definecolor{shadecolor}{gray}{0.95}
\usepackage{longtable}
\usepackage[normalem]{ulem}
\usepackage{fancyvrb}
\usepackage{fancyhdr}
\usepackage{graphicx}
\usepackage{marginnote}

\renewcommand{\@cite}[1]{#1}


\renewcommand*{\marginfont}{\itshape\footnotesize}

\def\Gin@extensions{.pdf,.png,.jpg,.mps,.tif}

  \pagestyle{fancy}

\usepackage[pdftitle={Risk Sensitive Filter for MIMO-OFDM System Channel Estimation using Combined Orthogonal Pilot Approch under Parameter Uncertainty},
 pdfauthor={}]{hyperref}
\hyperbaseurl{}

	 \paperwidth210mm
	 \paperheight297mm
              
\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{3}
\clubpenalty=8000
\emergencystretch 3em
\hbadness=4000
\hyphenpenalty=400
\pretolerance=750
\tolerance=2000
\vbadness=4000
\widowpenalty=10000

\renewcommand\section{\@startsection {section}{1}{\z@}%
     {-1.75ex \@plus -0.5ex \@minus -.2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\Large\bfseries}}
\renewcommand\subsection{\@startsection{subsection}{2}{\z@}%
     {-1.75ex\@plus -0.5ex \@minus- .2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\Large}}
\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}%
     {-1.5ex\@plus -0.35ex \@minus -.2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\large}}
\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}%
     {-1ex \@plus-0.35ex \@minus -0.2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\normalsize}}
\renewcommand\subparagraph{\@startsection{subparagraph}{5}{\parindent}%
     {1.5ex \@plus1ex \@minus .2ex}%
     {-1em}%
     {\reset@font\normalsize\bfseries}}


\def\l@section#1#2{\addpenalty{\@secpenalty} \addvspace{1.0em plus 1pt}
 \@tempdima 1.5em \begingroup
 \parindent \z@ \rightskip \@pnumwidth 
 \parfillskip -\@pnumwidth 
 \bfseries \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}\par
 \endgroup}
\def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
\def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
\def\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
\def\l@subparagraph{\@dottedtocline{5}{10em}{5em}}
\@ifundefined{c@section}{\newcounter{section}}{}
\@ifundefined{c@chapter}{\newcounter{chapter}}{}
\newif\if@mainmatter 
\@mainmattertrue
\def\chaptername{Chapter}
\def\frontmatter{%
  \pagenumbering{roman}
  \def\thechapter{\@roman\c@chapter}
  \def\theHchapter{\roman{chapter}}
  \def\thesection{\@roman\c@section}
  \def\theHsection{\roman{section}}
  \def\@chapapp{}%
}
\def\mainmatter{%
  \cleardoublepage
  \def\thechapter{\@arabic\c@chapter}
  \setcounter{chapter}{0}
  \setcounter{section}{0}
  \pagenumbering{arabic}
  \setcounter{secnumdepth}{6}
  \def\@chapapp{\chaptername}%
  \def\theHchapter{\arabic{chapter}}
  \def\thesection{\@arabic\c@section}
  \def\theHsection{\arabic{section}}
}
\def\backmatter{%
  \cleardoublepage
  \setcounter{chapter}{0}
  \setcounter{section}{0}
  \setcounter{secnumdepth}{2}
  \def\@chapapp{\appendixname}%
  \def\thechapter{\@Alph\c@chapter}
  \def\theHchapter{\Alph{chapter}}
  \appendix
}
\newenvironment{bibitemlist}[1]{%
   \list{\@biblabel{\@arabic\c@enumiv}}%
       {\settowidth\labelwidth{\@biblabel{#1}}%
        \leftmargin\labelwidth
        \advance\leftmargin\labelsep
        \@openbib@code
        \usecounter{enumiv}%
        \let\p@enumiv\@empty
        \renewcommand\theenumiv{\@arabic\c@enumiv}%
	}%
  \sloppy
  \clubpenalty4000
  \@clubpenalty \clubpenalty
  \widowpenalty4000%
  \sfcode`\.\@m}%
  {\def\@noitemerr
    {\@latex@warning{Empty `bibitemlist' environment}}%
    \endlist}

\def\tableofcontents{\section*{\contentsname}\@starttoc{toc}}
\parskip0pt
\parindent1em
\def\Panel#1#2#3#4{\multicolumn{#3}{){\columncolor{#2}}#4}{#1}}
\newenvironment{reflist}{%
  \begin{raggedright}\begin{list}{}
  {%
   \setlength{\topsep}{0pt}%
   \setlength{\rightmargin}{0.25in}%
   \setlength{\itemsep}{0pt}%
   \setlength{\itemindent}{0pt}%
   \setlength{\parskip}{0pt}%
   \setlength{\parsep}{2pt}%
   \def\makelabel##1{\itshape ##1}}%
  }
  {\end{list}\end{raggedright}}
\newenvironment{sansreflist}{%
  \begin{raggedright}\begin{list}{}
  {%
   \setlength{\topsep}{0pt}%
   \setlength{\rightmargin}{0.25in}%
   \setlength{\itemindent}{0pt}%
   \setlength{\parskip}{0pt}%
   \setlength{\itemsep}{0pt}%
   \setlength{\parsep}{2pt}%
   \def\makelabel##1{\upshape ##1}}%
  }
  {\end{list}\end{raggedright}}
\newenvironment{specHead}[2]%
 {\vspace{20pt}\hrule\vspace{10pt}%
  \phantomsection\label{#1}\markright{#2}%

  \pdfbookmark[2]{#2}{#1}%
  \hspace{-0.75in}{\bfseries\fontsize{16pt}{18pt}\selectfont#2}%
  }{}
      \def\TheFullDate{2017-01-15 (revised: 15 January 2017)}
\def\TheID{\makeatother }
\def\TheDate{2017-01-15}
\title{Risk Sensitive Filter for MIMO-OFDM System Channel Estimation using Combined Orthogonal Pilot Approch under Parameter Uncertainty}
\author{}\makeatletter 
\makeatletter
\newcommand*{\cleartoleftpage}{%
  \clearpage
    \if@twoside
    \ifodd\c@page
      \hbox{}\newpage
      \if@twocolumn
        \hbox{}\newpage
      \fi
    \fi
  \fi
}
\makeatother
\makeatletter
\thispagestyle{empty}
\markright{\@title}\markboth{\@title}{\@author}
\renewcommand\small{\@setfontsize\small{9pt}{11pt}\abovedisplayskip 8.5\p@ plus3\p@ minus4\p@
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus2\p@
\belowdisplayshortskip 4\p@ plus2\p@ minus2\p@
\def\@listi{\leftmargin\leftmargini
               \topsep 2\p@ plus1\p@ minus1\p@
               \parsep 2\p@ plus\p@ minus\p@
               \itemsep 1pt}
}
\makeatother
\fvset{frame=single,numberblanklines=false,xleftmargin=5mm,xrightmargin=5mm}
\fancyhf{} 
\setlength{\headheight}{14pt}
\fancyhead[LE]{\bfseries\leftmark} 
\fancyhead[RO]{\bfseries\rightmark} 
\fancyfoot[RO]{}
\fancyfoot[CO]{\thepage}
\fancyfoot[LO]{\TheID}
\fancyfoot[LE]{}
\fancyfoot[CE]{\thepage}
\fancyfoot[RE]{\TheID}
\hypersetup{citebordercolor=0.75 0.75 0.75,linkbordercolor=0.75 0.75 0.75,urlbordercolor=0.75 0.75 0.75,bookmarksnumbered=true}
\fancypagestyle{plain}{\fancyhead{}\renewcommand{\headrulewidth}{0pt}}

\date{}
\usepackage{authblk}

\providecommand{\keywords}[1]
{
\footnotesize
  \textbf{\textit{Index terms---}} #1
}

\usepackage{graphicx,xcolor}
\definecolor{GJBlue}{HTML}{273B81}
\definecolor{GJLightBlue}{HTML}{0A9DD9}
\definecolor{GJMediumGrey}{HTML}{6D6E70}
\definecolor{GJLightGrey}{HTML}{929497} 

\renewenvironment{abstract}{%
   \setlength{\parindent}{0pt}\raggedright
   \textcolor{GJMediumGrey}{\rule{\textwidth}{2pt}}
   \vskip16pt
   \textcolor{GJBlue}{\large\bfseries\abstractname\space}
}{%   
   \vskip8pt
   \textcolor{GJMediumGrey}{\rule{\textwidth}{2pt}}
   \vskip16pt
}

\usepackage[absolute,overlay]{textpos}

\makeatother 
      \usepackage{lineno}
      \linenumbers
      
\begin{document}

             \author[1]{Rajendra Prasad  K}

             \affil[1]{  K L University}

\renewcommand\Authands{ and }

\date{\small \em Received: 13 December 2016 Accepted: 5 January 2017 Published: 15 January 2017}

\maketitle


\begin{abstract}
        


In this paper, risk-sensitive filter (RSF) based channel estimation has been proposed for MIMO-OFDM system. The uniqueness of the risk sensitive filter?s performance in the presence of uncertainty is explored for channel estimation problem. In general, the channel estimation problem is formulated as the estimation of time varying coefficients of FIR filter. Estimation of channel is very critical task to recover the error free signal at the end of the receiver under the unknown statistics of the channel. Several Kalman based algorithms are proposed for channel estimation in MIMO-OFDM system under different channel considerations using traditional pilot based estimation. Auto regressive (AR) model is used to formulate the parameters to be estimated. Unlike to the traditional pilot based approach, in this work combined orthogonal pilot aided (COPA) channel estimation is used to eliminate the same frequency interference created by the OFDM frequency among different transmit-receive antenna pairs. The results proved that proposed estimator is outperforming when compared with Kalman under uncertainty in parameter.

\end{abstract}


\keywords{MIMO-OFDM, channel estimation, combined orthogonal pilots, kalman filter, risk sensitive filter, parameter uncertainty.}

\begin{textblock*}{18cm}(1cm,1cm) % {block width} (coords) 
\textcolor{GJBlue}{\LARGE Global Journals \LaTeX\ JournalKaleidoscope\texttrademark}
\end{textblock*}

\begin{textblock*}{18cm}(1.4cm,1.5cm) % {block width} (coords) 
\textcolor{GJBlue}{\footnotesize \\ Artificial Intelligence formulated this projection for compatibility purposes from the original article published at Global Journals. However, this technology is currently in beta. \emph{Therefore, kindly ignore odd layouts, missed formulae, text, tables, or figures.}}
\end{textblock*}


\let\tabcellsep& 	 	 		 
\section[{I. Introduction}]{I. Introduction}\par
ultiple-Input Multiple-Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) combination will provide high data rates and mitigate the effects of the multipath delay in wireless communication \hyperref[b0]{[1]}. The advantages originate from the multiple spatial channels, which are provided by the multiple antennas together with the scattering environment surrounding the transmitters and the receivers. As the wireless environment is time varying, channel estimation became as essential part of the receiver \hyperref[b1]{[2]}\hyperref[b2]{[3]}\hyperref[b3]{[4]}. The accurate estimation of the channel statistics will provide the better diversity gain and coherence detection and decoding.\par
Pilot aided channel estimation is proved as better approach to estimate the channel with more accuracy \hyperref[b13]{[13,} {\ref 14]}. But it suffers interference created by the OFDM frequency among different transmit-receive antenna pairs. To overcome this Combining the design of the joint orthogonal pilot for the MIMO-OFDM system has proposed in  {\ref [15]} {\ref [16]} {\ref [17]}, which has designed the pilot data format maintaining the orthogonal property between different OFDM subcarriers of different transmitting-receiving antenna pair and same transmitting-receiving antenna pair, at the same time, the pilot symbols are inserted into the data frame at the transmitter according to the polygon form in the change of the OFDM subcarriers in transmitting-receiving antenna pair.\par
Most of the conventional methods work in a symbol-by-symbol scheme using the correlation of the channel only in the frequency domain i.e., the correlation between the sub-channels. More advanced algorithms are based on the Kalman Filter (KF), to also exploit the time-domain correlation \hyperref[b11]{[11,}\hyperref[b12]{12]}. KFs require a linear recursive state-space representation of the channel. However, the exact Clarke model does not admit such a representation. An approximation often used in the literature consists of approaching the fading process as auto-regressive \hyperref[b4]{[5,}\hyperref[b5]{6]}. Hence, a widely used channel approximation is based on a first-order Auto-Regressive model (AR), as recommended \hyperref[b4]{[5]},. The KF appears to be convenient for the very high mobility case, which leads to quasi-optimal channel estimation. In the present study, we consider multi-path channel estimation in multi-carrier systems (i.e., OFDM systems). In this context, we are interested in evaluate the performance of KF and RSF under parameter uncertainty \hyperref[b26]{[26]}\hyperref[b27]{[27]}\hyperref[b28]{[28]} {\ref [29]}. To do this, we use the least-square (LS) estimator at the pilots of current OFDM symbol. This first step explores the frequency-domain correlation of the channel and the knowledge of the delays to convert the primary observation at pilot frequencies. This paper is organized as follows: Section II introduces the MIMO-OFDM system model, In Section III explored the arrangement of pilots in combined orthogonal scheme and its significance in estimation during the same frequency inference, Section IV discussion on time varying channel model and channel model with parameter uncertainty. Section V introduces the KF and RSF channel estimation methodology in parameter uncertainty.  As Figure \hyperref[fig_1]{1} shows, we use N T transmit antennas, N R receive antennas, n OFDM symbols and K subcarriers in a MIMO-OFDM system. The transmitted symbol vector is given as [ ] ( ) [ ] ( ) [ ] 1 , . . . T T N x n k n k x n x k ? ? = ? ? ? , 0 .. 1 n Z k K ? =? ? ,1 2 / 0 , , K 1 1 0, K j mk K CP m n T x n k e m L m el e X KN s ? ? = ? = ? ? ? ? = ? ? ? ?\textbf{(1)}\par
Thus the duration of each OFDM symbol is cp N =K +?? ???? . The overall baseband transmitted signal is[ ] [ ] n n n m x m nN X +? = ?? = ? ?\textbf{(2)}\par
The signal from each receiver is formed by the   
\section[{III. Combined Orthogonal Pilot Scheme}]{III. Combined Orthogonal Pilot Scheme}\par
Use of pilot symbols for channel estimation introduces overhead and it is desirable to keep the number of pilot symbols as minimum as possible. The completely orthogonal pilot data symbol among the different subcarriers position of different transmitting receiving antenna pair  {\ref [15,} {\ref 17]}. And the pilot data symbols are distributed in the entire time-frequency grid of the channel for each transmitting antenna of the OFDM transmitter, the pilot symbols are coded, so that the antenna is unique. The coded pilot symbol was inserted into the OFDM frame, in order to form the  \par
The function ( , ) y t ? in the above equation is just same as Finite Impulse Response (FIR) filter which has time-varying coefficients. In real world scenario there are many factors, as disturbance, affect the medium, which leads to model the system with additive noise and result the system model become (3).i.e.\par
( , ) ( ) ( ) ( )r r r z t h t x v ? ? ? ? = ? + ?\textbf{(6)}\par
To design effective communication, it is necessary to have good knowledge about these coefficients. There are too many parameters to estimate in \hyperref[b4]{(5)}. As observation samples are corrupted with noise, weights of samples will rapidly change from one to others. The weighted taped channel is modeled as Gauss-Markov model. The Gauss-Markov model will be used to fix the correlation between successive values of given taped weight in time.\par
In channel estimation, the state vector is given as[ ] [ ] [ ] 1 h n Ah n u n = ? +\textbf{(7)}\par
where[ ] [ ] [ ] [ ] 0 1 . . 1 n n n h h h n h p ? ? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? ? ? ? ?? is a p p × matrix\par
and [ ] u n is AWGN, with zero mean and variance Q .\par
Standard assumption made that tap weights are joined Gaussian and uncorrelated with each other. Measurement/observation model is written by rearranging (  {\ref 10})[ ] [ ] [ ] [ ] [ ] 1 2 . . . 1 z n x n x n x n x n p ? ? = ? ? ? + ? ? [ ] [ ] h n w n + (8)\par
and it can be expressed as[ ] [ ] [ ] [ ] T z n x n h n w n = +\textbf{(9)}\par
where ??[??] is Gaussian white noise with variance 2 R ? = and ( )\par
x n is known sequence, act as input to the channel. 
\section[{b) Tapped delay line channel Model with uncertainty}]{b) Tapped delay line channel Model with uncertainty}\par
In a circumstance, when there is uncertainty in the channel state vector, (7) may be written as 
\section[{[ ] [ ] [ ]}]{[ ] [ ] [ ]}1 h n Ah n A u n = ? + ? + (10)\par
where A ? is a constant which arises due to channel phase rotation during coding and it is considered as a parameter modeling uncertainty in matrix A . This model is similar to case of random walk process described in \hyperref[b7]{[7]} and in state-space domain the model 
\section[{V. CHANNEL ESTIMATION a) Kalman based channel estimation}]{V. CHANNEL ESTIMATION a) Kalman based channel estimation}\par
The Kalman filter is a mathematical method used to use observed values containing noise and other disturbances and produce values closer to true value and calculate value \hyperref[b21]{[21]}. The basic operation done by the KF is to generate estimates of the true and calculated values, first by predicting a value, then calculating the uncertainty of the above value and finding an weighted average of both the predicted and the measured values \hyperref[b20]{[20]}. Most weight is given to the value with least uncertainty. The result obtained the method gives estimates more closely to true values. It is a recursive predictive filter based on the use of state space techniques and recursive algorithms. It demands the description of the dynamical problem in a statespace form which includes a system model and an observation model which is considered only for linear systems. Kalman filter is a recursive minimum mean square error (MMSE) estimator and it provides optimal estimation solution for linear and unbiased process with additive white noise. There is enough literature on KF, for example \hyperref[b4]{[5,}\hyperref[b21]{21]}.\par
The implementation of KF for channel estimation problem given in above subsection is given in detail as follow steps  {\ref [29]}. Filter initialization1 1 ?h h n n µ ? ? ? ? = ? ? and 1 1 h P n n C ? ? ? ? = ? ?\textbf{(11)}\par
Prior state estimation?1 1 1 h n n Ah n n ? ? ? = ? ? ? ? ? ? ? ?\textbf{(12)}\par
Prior estimate error covariance1 1 1 T P n n AP n n A Q ? ? ? = ? ? ? ? + ? ? ? ? (13) Kalman Filter gain [ ] [ ] [ ] [ ] ( ) 1 1 1 ( T K n P n n V n V n P n n V n R ? = ? ? ? ? ? ? + ? ? ? ?\textbf{(14)}\par
Posterior state estimate[ ] [ ] [ ] ( ) 1 1 ??T h n n h n n K n x n V n h n n ? ? = ? ? ? + ? ? ? ? ? ? ? ? ? ? (15) Posterior estimate error covariance [ ] [ ] (\par
)1 T P n n I K n V n P n n ? ? = ? ? ? ? ? ? ? ?\textbf{(16)}\par
b) Proposed Risk Sensitive Filter approach A RSF which is recursively update a posteriori state and estimate error covariance as given in \hyperref[b23]{[23]} is used here for fading channel estimation. Implementation of fading channel estimation using RSF is follows:\par
For linear system, the posteriori state estimate h ? of h at k th time is obtained by the risk sensitive( ) [ ] 1 0 arg min [exp \{ ( , ) , ?\} ] ?| k m m m m h E l h h l h x n ? ? = ? + ?\textbf{(17)}\par
(Notation T denotes transpose) This is strictly filtering problems. For more details readers can refer \hyperref[b23]{[23]}\hyperref[b24]{[24]}\hyperref[b25]{[25]}\hyperref[b26]{[26]}.\par
As \hyperref[b25]{[25]}, the posteriori state estimation is given as[ ] [ ] [ ] [ ] 1 ?| 1| 1 | T h n n Ah n n P n n V n R ? = ? ? + [ ] [ ] [ ] ( ) | 1 ?1 T x n V n Ah n n ? ? ?\textbf{(20)}\par
Posteriori estimation error covariance is given as [ ] ( )1 1 1 1 [ | ] 1| 1 T P n n A P n n I A Q ? ? ? ? ? ? = ? ? ? ? + ? ? ? ? [ ] [ ] 1 T V n R V n ? +\textbf{(21)}\par
VI. SIMULATION RESULTS \par
The simulation parameters are as follows. The FFT size, N, is 64. The data symbol k X is based on QPSK. The channel n h is the Rayleigh fading channel which has two paths. The space-time coding scheme is Alamouti's STBC with ½ rate and the decoding scheme used is Maximum likelihood (ML) technique with only linear processing. The number of OFDM symbols considered here are 8. The initial values of the for the KF are as follows: 0 h =[0 0]T , 0 P =100 I , 0 S=0 I , 0 q =[0 0]T , and 0 a=1. The comparison factor, MSE, is obtained after 100 independent trials. The linear interpolator is used as we considered slow fading channel. In contrast, the proposed RSF algorithm works well in parameter uncertainty conditions and usual performance and close to KF in absence of parameter uncertainty \hyperref[b22]{[22]}. Although this paper focuses mainly on channel estimation under parameter uncertainty. approach such that  \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_0}?}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Where}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-5.png}
\caption{\label{fig_3},}\end{figure}
      \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.6965703971119134\textwidth}P{0.006137184115523466\textwidth}P{0.003068592057761733\textwidth}P{0.03375451263537906\textwidth}P{0.030685920577617327\textwidth}P{0.003068592057761733\textwidth}P{0.03375451263537906\textwidth}P{0.003068592057761733\textwidth}P{0.039891696750902525\textwidth}}
Year 2017\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
18\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Volume XVII Issue II Version I\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
( ) E\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Global Journal of Computer Science and Technology\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{6}{l}{Here, ?? is a tuning parameter, known as risk}\\
\multicolumn{5}{l}{factor or risk parameter, the function}\tabcellsep l\tabcellsep , ( h h\tabcellsep )\tabcellsep is defined as\\
\multicolumn{6}{l}{1 ?2 l h h , = ( ) ( ) ( ) T h h h h ? ?}\tabcellsep (18)\\
{}[ ] x n =\tabcellsep \{\tabcellsep x\tabcellsep {}[ ] 1 , , ?\tabcellsep \multicolumn{2}{l}{[ ] \} x n}\end{longtable} \par
 
\caption{\label{tab_0}}\end{figure}
 			\footnote{Risk Sensitive Filter for MIMO-OFDM System Channel Estimation using Combined Orthogonal Pilot Approch under Parameter Uncertainty} 			\footnote{© 2017 Global Journals Inc. (US)} 			\footnote{Year 2017 ( )} 			\footnote{© 20 7 Global Journa ls Inc. (US) 1} 		 		\backmatter  			 			 			  				\begin{bibitemlist}{1}
\bibitem[Baddour and Beaulieu ()]{b5}\label{b5} 	 		\textit{},  		 			Kareem E Baddour 		,  		 			Norman C Beaulieu 		.  		2001.  	 
\bibitem[Cai et al. ()]{b17}\label{b17} 	 		\textit{},  		 			Jun Cai 		,  		 			Xuemin Shen 		,  		 			Jon W Mark 		.  		2004.  	 	 (Robust Channel) 
\bibitem[Ahmad et al. ()]{b0}\label{b0} 	 		 			R S Ahmad 		,  		 			Burton R Bahai 		,  		 			Mustafa Saltzberg 		,  		 			Ergen 		.  		\textit{Multicarrier Digital Communications: theory and application of OFDM},  				2004. Springer.  	 	 (Second Edition) 
\bibitem[Autoregressive Model for Fading Channel Simulation IEEE Global Telecommunication Conference]{b6}\label{b6} 	 		‘Autoregressive Model for Fading Channel Simulation’.  	 	 		\textit{IEEE Global Telecommunication Conference},  				2 p. .  	 
\bibitem[Liping ()]{b16}\label{b16} 	 		‘Channel Estimation and Combining Orthogonal Pilot Design in MIMO-OFDM System’.  		 			Wang Liping 		.  	 	 		\textit{Journal of Networks}  		2014. 9.  	 
\bibitem[Song and Lim ()]{b2}\label{b2} 	 		‘Channel Estimation and Signal Detection for MIMO-OFDM with Time Varying Channels’.  		 			Won-Gyu Song 		,  		 			Jong-Tae Lim 		.  	 	 		\textit{IEEE communications letters}  		2006. 10.  	 
\bibitem[Hijazi et al. ()]{b10}\label{b10} 	 		‘Channel Estimation for MIMO-OFDM Systems in Fast Time-Varying Environments’.  		 			Hussein Hijazi 		,  		 			Eric Pierre Simon 		,  		 			Martine Li´enard 		,  		 			Laurent Ros 		.  	 	 		\textit{4th International Symposium on Communications, Control and Signal Processing},  				2010. ISCCSP2010.  	 
\bibitem[Channel estimation for wireless OFDM systems Mehmet Kemal Ozdemir, logus Huseyin arslan ()]{b1}\label{b1} 	 		‘Channel estimation for wireless OFDM systems’.  	 	 		\textit{Mehmet Kemal Ozdemir, logus Huseyin arslan}  		2007. IEEE Communications Surveys \& Tutorials.  	 
\bibitem[Coleri et al. ()]{b13}\label{b13} 	 		‘Channel Estimation Techniques Based on Pilot Arrangement in OFDM Systems’.  		 			Sinem Coleri 		,  		 			Mustafa Ergen 		,  		 			Anuj Puri 		,  		 			Ahmad Bahai 		.  	 	 		\textit{IEEE Trans. on Broadcasting}  		2002. 48.  	 
\bibitem[Communication Systems-An H ? Approach IEEE Trans. on Wireless Communication]{b18}\label{b18} 	 		‘Communication Systems-An H ? Approach’.  	 	 		\textit{IEEE Trans. on Wireless Communication}  		3.  	 
\bibitem[Hye Mi Park and Jae Hong Lee (ed.) ()]{b9}\label{b9} 	 		\textit{Estimation of Time-Variant Channels for OFDM Systems Using Kalman and Wiener Filters, Vehicular Technology Conference},  		Hye Mi Park and Jae Hong Lee (ed.)  		2006.  	 
\bibitem[Biglieri et al. ()]{b3}\label{b3} 	 		‘Fading Channel: Information-Theoretic and Communication Aspect’.  		 			Ezio Biglieri 		,  		 			John Proakis 		,  		 			Shlomo Shamai 		.  	 	 		\textit{IEEE trans. on information theory}  		1998. 44.  	 
\bibitem[Grover Brown et al. ()]{b21}\label{b21} 	 		\textit{Introduction to Random Signal and Applied Kalman Filtering, 3 rd Ed},  		 			Robert Grover Brown 		,  		 			Y C Patrick 		,  		 			Hwang 		.  		1997. John Wily \& Sons.  	 
\bibitem[Omidi et al. ()]{b20}\label{b20} 	 		\textit{Join Data and Kalman Estimation for Rayleigh fading Channel},  		 			M J Omidi 		,  		 			M Pasupathy 		,  		 			P G Gulak 		.  		1999. 1999. p. .  	 	 (Wireless personal communication) 
\bibitem[Dai et al. ()]{b12}\label{b12} 	 		‘Kalman interpolation filter for channel estimation of LTE downlink in high-mobility environments’.  		 			Xuewu Dai 		,  		 			Wuxiong Zhang 		,  		 			Jing Xu 		,  		 			E John 		,  		 			Yang Mitchell 		,  		 			Yang 		.  	 	 		\textit{EURASIP Journal on Wireless Communications and Networking}  		2012.  	 
\bibitem[Alper et al. ()]{b19}\label{b19} 	 		‘on H? equalization of communication channels’.  		 			T Alper 		,  		 			Babak Erdogan 		,  		 			Thomas Hassibi 		,  		 			Kaileth 		.  	 	 		\textit{IEEE transactions on signal Processing}  		2000. 48.  	 
\bibitem[Li ()]{b14}\label{b14} 	 		‘Pilot-Symbol-Aided Channel Estimation for OFDM in Wireless Systems’.  		 			Ye (geoffrey) Li 		.  	 	 		\textit{IEEE transactions on vehicular technology}  		2000. 2012. Gunther Auer. 49.  	 	 (IEEE transactions on communications) 
\bibitem[Ohno et al. ()]{b15}\label{b15} 	 		‘Preamble and pilot symbol design for channel estimation in OFDM systems with null subcarriers’.  		 			Shuichi Ohno 		,  		 			Emmanuel Manasseh 		,  		 			Masayoshi Nakamoto 		.  	 	 		\textit{EURASIP Journal on Wireless Communications and Networking}  		2011.  	 
\bibitem[Banavar and Speyer ()]{b22}\label{b22} 	 		‘Properties of Risk sensitive filters/Estimators’.  		 			R N Banavar 		,  		 			J L Speyer 		.  	 	 		\textit{IEE Proc.-Control Theory Appl}  		1998. 145.  	 
\bibitem[Ford ()]{b28}\label{b28} 	 		\textit{Risk Sensitive Filtering and Parameter Estimation},  		 			Jasan Ford 		.  		 DSTO-TR- 0764.  		1999. Melbourne, Australia.  		 			DSTO Aeronautical and Maritime Research Laboratory 		 	 	 (Technical Report) 
\bibitem[Jayakumar and Banavar ()]{b27}\label{b27} 	 		‘Risk Sensitive Filters for Recursive Estimation of Motion from Images’.  		 			M Jayakumar 		,  		 			R N Banavar 		.  	 	 		\textit{IEEE Trans. of Pattern and Machine Intelligence}  		1998. 20.  	 
\bibitem[Urguner and Gustafsson ()]{b24}\label{b24} 	 		‘Risk sensitive particle filter for mitigating sample impoverishment’.  		 			U Urguner 		,  		 			F Gustafsson 		.  	 	 		\textit{IEEE Transactions on signal processing}  		2008. 56.  	 
\bibitem[Zhang et al. ()]{b26}\label{b26} 	 		‘Risksensitive filtering, prediction and smoothing for discrete-time singular systems’.  		 			H Zhang 		,  		 			L Xie 		,  		 			Y C Soh 		.  	 	 		\textit{Automatica}  		2003. 39.  	 
\bibitem[Prasad et al. ()]{b29}\label{b29} 	 		‘Robust Fading Channel Estimation under Parameter and Process Noise Uncertainty with Risk Sensitive Filter and Its comparison with CRLB’.  		 			K Prasad 		,  		 			M Srinivasan 		,  		 			T Satya 		,  		 			Savithri 		.  	 	 		\textit{WSEAS transactions on communications}  		2014. 13.  	 
\bibitem[Bor-Sen Chen et al. ()]{b11}\label{b11} 	 		‘Robust Fast Time-Varying Multipath Fading Channel Estimation and Equalization for MIMO-OFDM Systems via a Fuzzy Method’.  		 			Chang-Yi Bor-Sen Chen 		,  		 			Wei-Ji Yang 		,  		 			Liao 		.  	 	 		\textit{IEEE Transactions on Vehicular Technology}  		2012. 61.  	 
\bibitem[Wang and Balakrishnan ()]{b25}\label{b25} 	 		‘Robust Steady-State Filtering for Systems With Deterministic and Stochastic Uncertainties’.  		 			Fan Wang 		,  		 			Venkataramanan Balakrishnan 		.  	 	 		\textit{IEEE Trans. On Signal Processing}  		2003. 51.  	 
\bibitem[Boel et al. ()]{b23}\label{b23} 	 		‘Robustness and risk sensitive filtering’.  		 			Rene K Boel 		,  		 			Matthew R James 		,  		 			Ian R Peterson 		.  	 	 		\textit{IEEE Transactions on Automatic Control}  		2002. 47.  	 
\bibitem[Shu et al. ()]{b8}\label{b8} 	 		‘Simplified Random-Walk-Model-Based Kalman Filter for Slow to Moderate Fading Channel Estimation in OFDM Systems’.  		 			Huaqiang Shu 		,  		 			Laurent Ros 		,  		 			Eric Pierre Simon 		.  		 \xref{http://dx.doi.org/10.1007/978-90-481-3662-9}{10.1007/978-90-481-3662-9}.  	 	 		\textit{IEEE transactions on signal processing}  		2014. 62  (15) .  	 
\bibitem[Steven and Key ()]{b4}\label{b4} 	 		 			M Steven 		,  		 			Key 		.  		\textit{Fundamental of Statistical Signal Processing: Estimation Theory},  				 (Prentice Hall, NJ)  		1993. p. .  	 
\bibitem[Jamoos et al. ()]{b7}\label{b7} 	 		‘Two Cross-Coupled ? H Filters for Fading Channel Estimation in OFDM Systems’.  		 			Ali Jamoos 		,  		 			Ahmad Abdo 		,  		 			Hanna Abdel Nour 		,  		 			Eric Grive 		.  	 	 		\textit{Novel Algorithms and Techniques in Telecommunications and Networking},  				 (Netherlands)  		2010. Springer. p. .  	 
\end{bibitemlist}
 			 		 	 
\end{document}
