\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={Six Phase Optimal Sequence Design for MIMO Radar},
 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{Six Phase Optimal Sequence Design for MIMO Radar}
\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]{Mr. J.  Pandu}

             \author[2]{Dr.  C.D.Naidu}

             \author[3]{Dr.  N.Balaji}

             \affil[1]{  sreyas Institute of   Engineering and technology}

\renewcommand\Authands{ and }

\date{\small \em Received: 9 December 2016 Accepted: 2 January 2017 Published: 15 January 2017}

\maketitle


\begin{abstract}
        


 Radar   applications desire a set of sequences  with  discretely        peaky    autocorrelation    and    pair_wise    cross  correlation. Invade such sequences is a combinal  problem. If  the autocorrelation and cross correlation are convenient  in the   a  periodic    sense    then  there  are    hardly  any  theoretical  aids   available  thus the problem of  signal design referred  to above  is  a  defying    problem  for  which  many  global  optimization  algorithms  like  ant  colony  optimization  ,artificial  bee  colony  (ABC)  algorithm  and    particle  swarm  optimization  algorithm    were reported in the literature. The paper intent  at  gadget  of  an efficient optimization algorithm is  design to find an optimal  pulse  compression    code  useful  for  radar    applications  .The  proposed        optimization        algorithm            particle    swarm  optimization      algorithm   for   identifying      the   optimal   pulse   compression  codes  and  it  is    a  real-time  signal  processing  solution which identifies  optimal sequences.

\end{abstract}


\keywords{ant colony optimization, artificial bee colony algorithm (ABC), mimo, decentralized radar networks (DRNs, particle swarm optimization (PSO).}

\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& 	 	 		 \par
The above problem solved by the Pulse Compression. Pulse compression shares the inkling of transmitting a long-range pulse with some modulation embedded which spreads the energy over the bandwidth necessary for the required resolution. Pulse compressed Wave forms have larger time bandwidth (BT) product compared to uncompressed pulses whose BT=1.The pulse compression technique in the waveforms is employed either in the Frequency coding or Phase coding. An LFM signal is a waveform of frequency modulated whose carrier frequency varies linearly with time, over a specific period. This is one of the oldest and frequently used waveforms. It finds application in CW and pulsed radars. Since an LFM waveform serves as a constant amplitude waveform, it makes sure that the amplifier works efficiently. Also, this waveform spreads the energy widely in frequency domain.\par
A long pulse is divide in to a number of sub pulses of equal duration and the phase of each sub pulse is modulated with the different phases. This can be merely divided into binary and poly-phaser phase coding. In binary technique, the phase of any sub pulse takes any of the two values, either 1 or -1, in harmony with the sequence. In poly phase coding or Non-Binary coding , the phase of the sub pulse takes any of the M arbitrary values. The poly phase codes are Frank codes,p1 codes,p2 codes , P3 codes and p4 coded waveform are some of the commonly used sequences in Polyphase coding. The range side lobes for polyphase coded waveforms are lower than that of binary-coded waveform of same length, but the Doppler performance gets debilitated. 
\section[{II.}]{II.} 
\section[{Orthogonal Wave forms}]{Orthogonal Wave forms}\par
Orthogonal poly phase code consists of Length of the sequence (N c ),set size of the (L) and Phase of the sequence (M). Signals which probably containing N sub pulses represented by a complex number sequence, the set of the sequence is given by?? ?? (??) = ?? ?? ? ?? (??)\textbf{(1)}\par
Where n=1,2, ?., N c and l=1, 2, ?., L Where Øl (n), (0?Ø l (n)<2?) is the phase of sub pulse n of signal. umber of waveforms are used for radars signal. Several properties of radar waveforms are discussed in \hyperref[b9]{[10]}, \hyperref[b8]{[9]}, \hyperref[b6]{[7]}. An un-modulated or modulated continuous signal is used in continuous wave radar. Such a system can detect targets using Doppler offset, but range measurements become difficult. Since the radar transmits continuous waves, the requirement for secondary antenna for reception arises which is considered as another short coming of such a system. Pulsed radar transmits signals at regular time intervals of time unlike the CW radar. pulsed radars could give range measurements. But the selection of pulse width is a co-operation among the required resolution of the system and the detectable maximum Range. Number of characteristics of the radar system such as the Range resolution, range accuracy, target detection, radar range and Doppler shift. are decided by the radar waveforms. For example, the shorter the pulse width, the more accurate rang resolution the system has. But at the similar instance of time, short pulse will not support a good detection range.? ?? (??)?? ?0, 2?? ?? ?? , 2. 2?? ?? ?? , ? , (?? ?? ? 1). 2?? ?? ?? ? (2) ?? ?? (??) = ?ð??"ð??" 1 , ð??"ð??" 2 , ? , ð??"ð??" ?? ?? ? (3) 
\section[{N}]{N}\par
Year Assume a set a poly phase codes with contains the set as Nc whose set size is L, one can briefly signify the phase values of S with following L× N c phase matrix.(??, ?? ?? , ?? ?? ) = ? ?? 1 (1) ?? 2 (2) ? ?? 1 (?? ?? ) ?? 2 (1) ?? 2 (2) ? ?? 2 (?? ?? ) ? ?? ?? (1) ? ?? ?? (2) ? ? ?? ?? (?? ?? ) ? (4)\par
Here the phase sequence in row (1 ? l ? L) is the sequence of polyphase signal, and complete elements in the matrix can be elected from the set of phases. From the cross correlation and autocorrelation distinguishing of orthogonal polyphase codes, we get.??(?? ?? , ??) = ? ? ? ? ? 1 ?? ?? ? exp ??[?? ?? (??) ? ?? ?? (?? + ??)] = 0 0 < ?? < ?? ?? ?? ?? ?1 ??=1 1 ?? ?? ? exp ??[?? ?? (??) ? ?? ?? (?? + ??)] = 0 ? ?? ?? < ?? < 0 ?? ?? ??=???+1\par
For l=1, 2, ?. L (  {\ref 5})??(?? ?? , ??) ? ? ? ? ? ? 1 ?? ?? ? exp ????? ?? (??) ? ?? ?? (?? + ??)? = 0 0 < ?? < ?? ?? ?? ?? ??? ??=1 1 ?? ?? ? exp ????? ?? (??) ? ?? ?? (?? + ??)? = 0 ? ?? ?? < ?? < 0 ?? ?? ??=???+1\par
or p?q and p, q=1, 2, ? L\par
where and are the aperiodic function of autocorrelation polyphase sequence and the function of cross correlation sequences and .Where k defined as the discrete time index. Therefore, crafting of an orthogonal polyphase code made corresponding to the building of a polyphase matrix in equation 6 with and constraints in equation 5 and equation 6.For the scheme of code sets of orthogonal polyphase used in MIMO radar systems, an the process of optimization is used not only to suppress the auto correlation side lobe peaks and the cross correlation peak but also to suppress the the total autocorrelation sidelobe energy and cross correlation energy in equation 7. Here ? is the weight factor if it is less than one means more weightage is given to auto-correlation and less weightage is given to cross-correlation.?? = ? ? |??(?? ?? , ??)| 2 + ?? ? ? ? ???(?? ?? , ?? ?? , ??)? 2 ?? ?? ?1 ??=?(?? ?? ?1) ?? ??=??+1 ???1 ??=1 ?? ?? ??=1 ?? ??=1 (7) III. 
\section[{Mimo Radar Signal Model}]{Mimo Radar Signal Model}\par
A pure MIMO system is one that operates incoherently where as netted radar (NR) Systems operate Coherently and decentralized radar networks (DRNs) operate incoherently with a two stage processing \hyperref[b11]{[12]}.The basic form of the received signal in a MIMO network is the signal arriving at the k th receiver can be modeled as?? ?? (??) = ? [( ?? ?? =1 ??0 1 ? ?? ,?? (??)?? ?? (?? ? ?? ?? .?? ) + ?? ?? ,?? (?? ? ?? ?? .?? )] + ?? ?? (??) + ?? ?? (??)\textbf{(8)}\par
Where H o/1 is 0 or 1 depending the absence or presence of target respectively; s m is the m th transmitted signal, c m,k is the clutter, z k is the thermal noise, J k is an external disturbance (such as jamming), ? m,k and T m,k are the delays occurring during the path between the m th transmitter and the target/clutter respectively and the k th receiver and ?? ??,?? (?) is a coefficient that accounts for the parameters of the mono/bisatic radar equations, the phase shift ,and the RCS-distribution, specifically .?? ??,?? (??) = ? ?? ?? ?? ? ?? ???? ?? ???? ? 2 ?? (4??) 3 ?? ?? 2 ?? ?? 2 ?????? ???? 2???? ?? .?? ? ?\textbf{(9)}\par
Where G tx and G rx are respectively the gains of the transmitting and receiving antennas, ? is the RCS of the target, P t is the transmitting power, R m and R k are the transmitter-target and target-transmitter distances respectively and R m.k is the distance covered by the signal. \par
The effects of the clutter are not considered, and hence this leads to the following expression for the received signal.\par
The received output may be expressed as the result of the cross correlation of the received signal with the transmitted waveforms as follows. ?? ?,?? = ?? ?? ( ??) ? ?? ? (??) = ??0 1 ? ( ?? ?? =1 ? ?? ,?? (??)?? ?? (?? ? ?? ?? .?? )? ?? ? (??) +[?? ?? (??) + ?? ?? (??)] ? ?? ? (??) = ??0 1 ? ?,?? (??)?? ? (?? ? ?? ?.?? )+??0 1 ? ( ?? ?? =1 ?? ?? ? ?? ,?? (??)?? ?? .?? (?? ? ?? ?? .?? )+[?? ?? (??) + ?? ?? (??)] ? ?? ? (??) = ??0 1 ? ?,?? (??)?? ? (?? ? ?? ?.?? )+??0 1 ? ( ?? ?? =1 ?? ?? ? ?? ,?? (??)?? ?? .? (?? ? ?? ?.?? ) + ?? ?.?? (??)\textbf{(11)}\par
Where R h (t) is the autocorrelation function of sm and R m,h is the cross-correlation function between s m and s h and n h,k is the component of the overall disturbance incoming in the k th receiver after the h th matched filter. Consequently a matrix M x signals from the same area may be written as follows.?? ?? = ? ?? 11 ?? 12 ? ?? 1?? ?? 21 ?? 22 ? ?? 2?? ? ?? ? ?? ??1 ?? ??2 ?? ???? ?\textbf{(12)}\par
Alternatively, this equation may be rearranged into vector X as follows?? = [?? 11 , ? ?? 1?? , ?? 21 , ? ? ?? 2?? , ?? ??1 , ? . ?? 1?? ] ?? (13)\par
Where T is the transpose operator. 
\section[{IV.}]{IV.} 
\section[{Optimization Algorithms for Mimo Radar}]{Optimization Algorithms for Mimo Radar}\par
Many optimization methods have been developed for solving various types of engineering problems.\par
Popular optimization algorithms include particle swarm optimization, neural networks, genetic algorithms, artificial immune systems, and fuzzy optimization. The particle Swarm concept originated as a simulation of simplified social systems. The Particle Swarm Optimization algorithm is basically a populationbased stochastic search algorithm and provides solutions to the complex non-linear optimization problems. PSO has the benefits of being more efficient when compared to most other optimization algorithms.\par
V. 
\section[{SIMULATION RESULTS}]{SIMULATION RESULTS}\par
In this paper Optimization of Orthogonal Polyphase Coded Waveform for MIMO Radar using Particle Swarm Optimization Algorithm is carried out. In the present work, Particle Swarm Optimization Algorithm is to optimize the six phase polyphase coded sequence to achieve good auto correlation properties and crosscorrelation properties. On the basis of projected algorithm the polyphase six phase coded sequences are set with lengths varying from 7 to 128 and number of transmitting ,receiving antennas L=3 and L=4. The auto correlation side lobe peak values obtained for different length of the sequences. the average value of ASPs is 0.0023 it is better than the literature values.  The auto correlation side lobe peak values obtained for different length of the sequences the average value of ASPs is 0.0069 it is better than the literature values.  
\section[{Conclusion}]{Conclusion}\par
Properties of Auto correlation side lobe peaks of Six phase produced order sets with three and four transmitting antennas for Sequence length N= 40 to 128 is obtained and compared with the literature values. From the design result, it conclude that the results obtained have great improvement in ASPs things of all the sequence lengths. In order to carry out the implementation of particle swarm optimization algorithm for the optimization of orthogonal poly phase sequences is developed for MIMO radar.\begin{figure}[htbp]
\noindent\textbf{12}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Fig. 1 :Fig. 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{34}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Fig. 3 :Fig. 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{figure4}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.11184210526315788\textwidth}P{0.3019736842105263\textwidth}P{0.2125\textwidth}P{0.1789473684210526\textwidth}P{0.04473684210526315\textwidth}}
\tabcellsep Si\tabcellsep \multicolumn{2}{l}{x Phase Optimal Sequence Design for MI}\tabcellsep MO Radar\\
\tabcellsep \multicolumn{2}{l}{?? ?? (??) = ??0}\\
??(?? ?? . ??)\tabcellsep \multicolumn{2}{l}{??(?? ?? . ?? ?? . ??)}\\
\tabcellsep \tabcellsep \tabcellsep ?? ??\\
\tabcellsep \tabcellsep \tabcellsep ?? ??\\
?? ??\tabcellsep \tabcellsep \\
F\tabcellsep \multicolumn{2}{l}{??(?? ?? . ??)}\tabcellsep ??(?? ?? . ?? ?? . ??)\end{longtable} \par
  {\small\itshape [Note: 1 ? ( ?? ?? =1 ? ?? ,?? (??)?? ?? (?? ? ?? ?? .?? ) + ?? ?? (??) + ?? ?? (??)]} 
\caption{\label{tab_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.85\textwidth}}
( ) Volume XVII Issue III Version I\\
of Researches in Engineering\\
Global Journal\end{longtable} \par
 
\caption{\label{tab_2}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.07574257425742574\textwidth}P{0.14306930693069309\textwidth}P{0.3141914191419142\textwidth}P{0.316996699669967\textwidth}}
S.No\tabcellsep Length of\tabcellsep Max(ASP)\tabcellsep Max(ASP)\\
\tabcellsep Sequence\tabcellsep Reported\tabcellsep Literature\\
1\tabcellsep 7\tabcellsep 0.0327\tabcellsep 0.079\\
2\tabcellsep 13\tabcellsep 0.0179\tabcellsep 0.0751\\
3\tabcellsep 17\tabcellsep 0.0169\tabcellsep 0.0720\\
4\tabcellsep 21\tabcellsep 0.0126\tabcellsep 0.0731\\
5\tabcellsep 29\tabcellsep 0.0061\tabcellsep 0.0721\\
6\tabcellsep 31\tabcellsep 0.0062\tabcellsep 0.0769\\
7\tabcellsep 37\tabcellsep 0.0041\tabcellsep 0.0777\\
8\tabcellsep 45\tabcellsep 0.0036\tabcellsep 0.0762\\
9\tabcellsep 49\tabcellsep 0.0033\tabcellsep 0.0744\\
10\tabcellsep 53\tabcellsep 0.0026\tabcellsep 0.0731\\
11\tabcellsep 61\tabcellsep 0.0017\tabcellsep 0.0792\\
12\tabcellsep 87\tabcellsep 0.0015\tabcellsep 0.0771\\
13\tabcellsep 95\tabcellsep 0.0017\tabcellsep 0.0762\\
14\tabcellsep 103\tabcellsep 0.0011\tabcellsep 0.0741\\
15\tabcellsep 113\tabcellsep 0.0012\tabcellsep 0.0734\\
16\tabcellsep 117\tabcellsep 0.0011\tabcellsep 0.0733\end{longtable} \par
 
\caption{\label{tab_3}Table 2 :}\end{figure}
 			\footnote{© 2017 Global Journals Inc. (US)} 			\footnote{Year 2017 F © 2017 Global Journals Inc. (US)} 		 		\backmatter  			  				\begin{bibitemlist}{1}
\bibitem[Abramovich and Frazer ()]{b12}\label{b12} 	 		‘Bounds on the Volume and Height Distributions for the MIMO Radar Ambiguity Function’.  		 			Yuri I Abramovich 		,  		 			Gordon J Frazer 		.  	 	 		\textit{IEEE Signal Processing Letters}  		2008. 15 p. .  	 
\bibitem[Singh and Rao (2008)]{b6}\label{b6} 	 		‘Discrete frequency-Coded radar signal design’.  		 			S P Singh 		,  		 			K 		,  		 			Subha Rao 		.  	 	 		\textit{IET Signal Process}  		july. 2008. 3  (1)  p. .  	 
\bibitem[Pandu et al. (2014)]{b9}\label{b9} 	 		‘FPGA based Solution for the Identification of RADAR Pulse Sequences for Defense Applications’.  		 			J Pandu 		,  		 			. N Dr 		,  		 			Dr C D Balaji 		,  		 			Naidu 		.  	 	 		\textit{Global Journal of Researches in Engineering}  		February, 2014. 14  (2)  p. .  	 
\bibitem[Levanon and Mozeson ()]{b3}\label{b3} 	 		 			N Levanon 		,  		 			E Mozeson 		.  		\textit{Radar Signals},  				2004. Wiley.  	 
\bibitem[Chen and Vaidyanathan (2008)]{b13}\label{b13} 	 		‘MIMO Radar Ambiguity Properties and Optimization Using Frequency-Hopping Waveforms’.  		 			Chun-Yang Chen 		,  		 			P P Vaidyanathan 		.  	 	 		\textit{IEEE Transactions on Signal Processing},  				Dec.2008. 56 p. .  	 	 (III Version I) 
\bibitem[Fishler et al. ()]{b1}\label{b1} 	 		‘MIMO radar an idea whose time has come’.  		 			E Fishler 		,  		 			A Haimovich 		,  		 			R Blum 		,  		 			L Cimini 		,  		 			D Chizhik 		,  		 			R Valenzuela 		.  	 	 		\textit{Proc. of the IEEE Int. Conf. on Radar},  				 (of the IEEE Int. Conf. on RadarPhiladelphia)  		2004.  	 
\bibitem[Li and Stoica]{b11}\label{b11} 	 		\textit{MIMO Radar Signal Processing" a johan willey \&sons},  		 			Jain Petre Li 		,  		 			Stoica 		.  		INC. Publication.  	 
\bibitem[Robey et al. ()]{b5}\label{b5} 	 		‘Mimo radar theory and experimental results’.  		 			F C Robey 		,  		 			S Coutts 		,  		 			D Weikle 		,  		 			J C Mcharg 		,  		 			K Cuomo 		.  	 	 		\textit{Proc. of 37th ASILOMAR 2004 Conf. on Signals, Systems and Computers},  				 (of 37th ASILOMAR 2004 Conf. on Signals, Systems and Computers)  		2004. p. .  	 
\bibitem[Fishler et al. ()]{b4}\label{b4} 	 		‘Mimo radar: An idea whose time has come’.  		 			E Fishler 		,  		 			A Haimovich 		,  		 			R Blum 		,  		 			D Chizhik 		,  		 			L Cimini 		,  		 			R Valenzuela 		.  	 	 		\textit{Proc. IEEE Radar Conf},  				 (IEEE Radar Conf)  		2004. p. .  	 
\bibitem[Pandu et al. ()]{b10}\label{b10} 	 		‘Optimal Coded Sequence Design for Radar using Fractional Oppositional Particle Swarm Optimization’.  		 			J Pandu 		,  		 			. N Dr 		,  		 			Dr C D Balaji 		,  		 			Naidu 		.  	 	 		\textit{IEEE International Conference on Recent Advances and Innovations in Engineering (ICRAIE-2014)},  				 (Jaipur ,India)  		May 09-11, 2014.  	 
\bibitem[Deng ()]{b0}\label{b0} 	 		‘Polyphase code design for orthogonal netted radar systems’.  		 			H Deng 		.  	 	 		\textit{IEEE Transactions on Signal Processing}  		2004. 52 p. .  	 
\bibitem[Cook and Bernfeld ()]{b2}\label{b2} 	 		\textit{Radar Signals An Introduction to Theory and Application},  		 			C C Cook 		,  		 			M Bernfeld 		.  		1993. Artech House.  	 
\bibitem[Singh and Rao (2011)]{b7}\label{b7} 	 		‘Sixty-Phase Sequences Design with Good Autocorrelation Properties’.  		 			S P Singh 		,  		 			K 		,  		 			Subha Rao 		.  	 	 		\textit{IETE Journal of research}  		June ,2011. 57  (3)  p. .  	 
\bibitem[Balaji and Subba Rao (2012)]{b8}\label{b8} 	 		‘VLSI -based Real -time Signal Processing Solution Emplyoing Four -Phase Codes for Spread -spectrum Application’.  		 			N Balaji 		,  		 			Kakarla Subba Rao 		.  	 	 		\textit{IETE Journal of Research}  		Jan-Feb.2012. 58  (1)  p. .  	 
\end{bibitemlist}
 			 		 	 
\end{document}
