% HERO STYLE FILE - Modified Mar. 97
%\topmargin -0.3in
\topmargin .5in  % For printing on systems printer
\oddsidemargin 0.1in
\textheight 8.3in
\textwidth 6.5in 
\parskip 0.1in

%

\newcommand{\myepsfig}[4]{%
\begin{figure}[htbp]%
\centering%
\leavevmode%
\epsfxsize=#3%
\epsffile{#1/#2}%
\caption{\it #4}%
\label{#2}%
\end{figure}%
}
% Sample Call: \myepsfig{.}{filename.ps}{4in}{A caption}

% This allows arbitrary scaling of figures
%
\newcommand{\mypsfig}[5]{%
\begin{figure}[htbp]%
\psscalefirst
\centering%
\leavevmode%
\psfig{file=#1/#2,width=#3,height=#4}%
\caption{\it #5}%
\label{#2}%
\end{figure}%
}
% Sample Call: \mypsfig{.}{filename.ps}{4in}{2in}{A caption}

\newcommand{\be}{\begin{eqnarray}} \newcommand{\ee}{\end{eqnarray}}
\newcommand{\ben}{\begin{eqnarray*}} \newcommand{\een}{\end{eqnarray*}}
\newcommand{\bc}{\begin{center}} \newcommand{\ec}{\end{center}}
\newcommand{\bt}{\begin{tabbing}} \newcommand{\et}{\end{tabbing}}
\newcommand{\ul}{\underline} \newcommand{\ol}{\overline}
\newcommand{\qed}{\mbox{} \hfill $\Box$ }
%\newcommand{\Reals}{\mbox{\rm I\kern-.2em R}}  % This is for use with cmr12
\newcommand{\Reals}{\mbox{\rm I\kern-.25em R}}  % This is for use with cmr11
\newcommand{\Integers}{\mbox{\rm Z\kern-.25em Z}}  % This is for use with cmr11
\newcommand{\Complex}{\mbox{$ {C} \!\!\! {l} $} \; }
\newcommand{\0}{\mbox{$O$}}
%
\newcommand{\var}{\mbox{\rm var}}
\newcommand{\cov}{{\mathrm{cov}}}
\newcommand{\sinc}{\mbox{\rm sinc}}
\newcommand{\defined}{\; \mbox{$\stackrel{\mbox{\rm def}}{=}$}\;}
\newcommand{\argmax}{{\mbox{\rm argmax}}}
\newcommand{\argmin}{{\mbox{\rm argmin}}}
\newcommand{\argzero}{{\rm argzero}}
\newcommand{\plusminus}{\stackrel{+}{-}}
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\newcommand{\half}{\mbox{\small $\frac{1}{2}$}}
\newcommand{\halfT}{\mbox{\small $\frac{T}{2}$}}
\newcommand{\Hhalf}{\mbox{\small $\frac{H}{2}$}}
\newcommand{\halfplus}{\mbox{\small $\frac{+}{2}$}}
%
\newtheorem{lemmas}{Lemma}
\newtheorem{propositions}{Proposition}
\newtheorem{theorems}{Theorem}
\newtheorem{corollaries}{Corollary}
\newtheorem{properties}{Property}
\newtheorem{conjectures}{Conjecture}
\newtheorem{definitions}{Definition}

%\def\VVert{\delimiter''026A30C\negthinspace\delimiter''026A30C\negthinspace\delimiter''026A30C}
%\def\mn{\|}
\def\leftmn{\left\vert\!\left\vert\!\left\vert}
\def\rightmn{\right\vert\!\right\vert\!\right\vert}
%\def\mn{\delimiter''026A30C\negthinspace\delimiter''026A30C\negthinspace\delimiter''026A30C}

\def\conv{\star}
\def\MSE{{\mathrm MSE}}
\def\DFT{\mathrm{DFT}}
\def\trace{{\mathrm{tr}}}
\def\SNR{{\mathrm{SNR}}}
\def\erfc{{\mathrm{erfc}}}
\def\card{{\mathrm{card}}}
\def\kron{\bigotimes}
\def\bigtimes{\mbox{ \Large $\times$}}
\def\kronecker{\kron}
\def\diag{{\mathrm{diag}}}
%%%%%\def\span{{\mathrm{span}}}
\def\lspan{{\mathrm{span}}}
\def\ones{\ul{1}}
\def\bfones{{\mathbf{1}}}
\def\ula{\ul{a}}
\def\ulb{\ul{b}}
\def\ulc{\ul{c}}
\def\uld{\ul{d}}
\def\ule{\ul{e}}
\def\ulf{\ul{f}}
\def\ulg{\ul{g}}
\def\ulh{\ul{h}}
\def\uli{\ul{i}}
\def\ulj{\ul{j}}
\def\ulk{\ul{k}}
\def\ull{\ul{l}}
\def\ulm{\ul{m}}
\def\uln{\ul{n}}
\def\ulo{\ul{o}}
\def\ulp{\ul{p}}
\def\ulq{\ul{q}}
\def\ulr{\ul{r}}
\def\uls{\ul{s}}
\def\ult{\ul{t}}
\def\ulu{\ul{u}}
\def\ulv{\ul{v}}
\def\ulw{\ul{w}}
\def\ulx{\ul{x}}
\def\uly{\ul{y}}
\def\ulz{\ul{z}}
\def\ulA{\ul{A}}
\def\ulB{\ul{B}}
\def\ulC{\ul{C}}
\def\ulD{\ul{D}}
\def\ulE{\ul{E}}
\def\ulF{\ul{F}}
\def\ulG{\ul{G}}
\def\ulH{\ul{H}}
\def\ulI{\ul{I}}
\def\ulJ{\ul{J}}
\def\ulK{\ul{K}}
\def\ulL{\ul{L}}
\def\ulM{\ul{M}}
\def\ulN{\ul{N}}
\def\ulO{\ul{O}}
\def\ulP{\ul{P}}
\def\ulQ{\ul{Q}}
\def\ulR{\ul{R}}
\def\ulS{\ul{S}}
\def\ulT{\ul{T}}
\def\ulU{\ul{U}}
\def\ulV{\ul{V}}
\def\ulW{\ul{W}}
\def\ulX{\ul{X}}
\def\ulY{\ul{Y}}
\def\ulZ{\ul{Z}}

\def\ol{\overline}
\def\ola{\ol{a}}
\def\olb{\ol{b}}
\def\olc{\ol{c}}
\def\old{\ol{d}}
\def\ole{\ol{e}}
\def\olf{\ol{f}}
\def\olg{\ol{g}}
\def\olh{\ol{h}}
\def\oli{\ol{i}}
\def\olj{\ol{j}}
\def\olk{\ol{k}}
\def\oll{\ol{l}}
\def\olm{\ol{m}}
\def\oln{\ol{n}}
\def\olo{\ol{o}}
\def\olp{\ol{p}}
\def\olq{\ol{q}}
\def\olr{\ol{r}}
\def\ols{\ol{s}}
\def\olt{\ol{t}}
\def\olu{\ol{u}}
\def\olv{\ol{v}}
\def\olw{\ol{w}}
\def\olx{\ol{x}}
\def\oly{\ol{y}}
\def\olz{\ol{z}}
\def\olA{\ol{A}}
\def\olB{\ol{B}}
\def\olC{\ol{C}}
\def\olD{\ol{D}}
\def\olE{\ol{E}}
\def\olF{\ol{F}}
\def\olG{\ol{G}}
\def\olH{\ol{H}}
\def\olI{\ol{I}}
\def\olJ{\ol{J}}
\def\olK{\ol{K}}
\def\olL{\ol{L}}
\def\olM{\ol{M}}
\def\olN{\ol{N}}
\def\olO{\ol{O}}
\def\olP{\ol{P}}
\def\olQ{\ol{Q}}
\def\olR{\ol{R}}
\def\olS{\ol{S}}
\def\olT{\ol{T}}
\def\olU{\ol{U}}
\def\olV{\ol{V}}
\def\olW{\ol{W}}
\def\olX{\ol{X}}
\def\olY{\ol{Y}}
\def\olZ{\ol{Z}}

\def\ba{{\mathbf{a}}}
\def\bs{{\mathbf{s}}}
\def\Bh{{\mathbf{h}}}
\def\Bf{{\mathbf{f}}}
\def\bg{{\mathbf{g}}}
\def\bU{{\mathbf{U}}}
\def\bu{{\mathbf{u}}}
\def\bS{{\mathbf{S}}}
\def\bV{{\mathbf{V}}}
\def\bv{{\mathbf{v}}}
\def\bP{{\mathbf{P}}}
\def\bA{{\mathbf{A}}}
\def\bB{{\mathbf{B}}}
\def\bC{{\mathbf{C}}}
\def\bD{{\mathbf{D}}}
\def\bE{{\mathbf{E}}}
\def\bF{{\mathbf{F}}}
\def\bG{{\mathbf{G}}}
\def\bH{{\mathbf{H}}}
\def\bI{{\mathbf{I}}}
\def\bJ{{\mathbf{J}}}
\def\bK{{\mathbf{K}}}
\def\bL{{\mathbf{L}}}
\def\bM{{\mathbf{M}}}
\def\bN{{\mathbf{N}}}
\def\bO{{\mathbf{O}}}
\def\bP{{\mathbf{P}}}
\def\bQ{{\mathbf{Q}}}
\def\bR{{\mathbf{R}}}
\def\bS{{\mathbf{S}}}
\def\bT{{\mathbf{T}}}
\def\bU{{\mathbf{U}}}
\def\bV{{\mathbf{V}}}
\def\bW{{\mathbf{W}}}
\def\bx{{\mathbf{x}}}
\def\bX{{\mathbf{X}}}
\def\by{{\mathbf{y}}}
\def\boldr{{\mathbf{r}}}
\def\bY{{\mathbf{Y}}}
\def\bZ{{\mathbf{Z}}}
\def\bz{{\mathbf{z}}}
\def\bw{{\mathbf{w}}}



\def\bfe{{\mathbf{e}}}
\def\bfh{{\mathbf{h}}}
\def\bff{{\mathbf{f}}}
\def\bfg{{\mathbf{g}}}
\def\bfU{{\mathbf{U}}}
\def\bfu{{\mathbf{u}}}
\def\bfS{{\mathbf{S}}}
\def\bfV{{\mathbf{V}}}
\def\bfv{{\mathbf{v}}}
\def\bfP{{\mathbf{P}}}
\def\bfA{{\mathbf{A}}}
\def\bfB{{\mathbf{B}}}
\def\bfC{{\mathbf{C}}}
\def\bfD{{\mathbf{D}}}
\def\bfE{{\mathbf{E}}}
\def\bfF{{\mathbf{F}}}
\def\bfG{{\mathbf{G}}}
\def\bfH{{\mathbf{H}}}
\def\bfI{{\mathbf{I}}}
\def\bfJ{{\mathbf{J}}}
\def\bfK{{\mathbf{K}}}
\def\bfL{{\mathbf{L}}}
\def\bfM{{\mathbf{M}}}
\def\bfN{{\mathbf{N}}}
\def\bfO{{\mathbf{O}}}
\def\bfP{{\mathbf{P}}}
\def\bfQ{{\mathbf{Q}}}
\def\bfR{{\mathbf{R}}}
\def\bfS{{\mathbf{S}}}
\def\bfT{{\mathbf{T}}}
\def\bfU{{\mathbf{U}}}
\def\bfV{{\mathbf{V}}}
\def\bfW{{\mathbf{W}}}
\def\bfx{{\mathbf{x}}}
\def\bfX{{\mathbf{X}}}
\def\bfy{{\mathbf{y}}}
\def\bfr{{\mathbf{r}}}
\def\bfY{{\mathbf{Y}}}
\def\bfZ{{\mathbf{Z}}}


\def\calh{{\mathcal{h}}}
\def\calU{{\mathcal{U}}}
\def\calu{{\mathcal{u}}}
\def\calS{{\mathcal{S}}}
\def\calV{{\mathcal{V}}}
\def\calv{{\mathcal{v}}}
\def\calP{{\mathcal{P}}}
\def\calA{{\mathcal{A}}}
\def\calB{{\mathcal{B}}}
\def\calC{{\mathcal{C}}}
\def\calD{{\mathcal{D}}}
\def\calE{{\mathcal{E}}}
\def\calF{{\mathcal{F}}}
\def\calG{{\mathcal{G}}}
\def\calH{{\mathcal{H}}}
\def\calI{{\mathcal{I}}}
\def\calJ{{\mathcal{J}}}
\def\calK{{\mathcal{K}}}
\def\calL{{\mathcal{L}}}
\def\calM{{\mathcal{M}}}
\def\calN{{\mathcal{N}}}
\def\calO{{\mathcal{O}}}
\def\calP{{\mathcal{P}}}
\def\calQ{{\mathcal{Q}}}
\def\calR{{\mathcal{R}}}
\def\calS{{\mathcal{S}}}
\def\calT{{\mathcal{T}}}
\def\calU{{\mathcal{U}}}
\def\calV{{\mathcal{V}}}
\def\calW{{\mathcal{W}}}
\def\calx{{\mathcal{x}}}
\def\calX{{\mathcal{X}}}
\def\caly{{\mathcal{y}}}
\def\calY{{\mathcal{Y}}}
\def\calZ{{\mathcal{Z}}}


\def\tr{{\mathrm{tr}}}
\def\erf{{\mathrm{erf}}}
\def\erfc{{\mathrm{erfc}}}
\def\thub{\theta}
\def\thetabar{\ol{\theta}}
\def\thetahat{\hat{\theta}}
\def\cA{{\mathcal{A}}}
\def\cP{{\mathcal{P}}}
\def\bR{{\mathbf{R}}}
\def\tauhat{\hat{\tau}}
\def\muhat{\hat{\mu}}
\def\ulX{\ul{X}}
\def\ulx{\ul{x}}
\def\uly{\ul{y}}
\def\ultheta{\ul{\theta}}
\def\ulS{\ul{S}}
\def\uls{\ul{s}}
\def\bighalf{\frac{1}{2}}
\def\ulY{\ul{Y}}
\def\uln{\ul{n}}
\def\ulr{\ul{r}}
\def\ut{\ul{\theta}}
\def\uth{\ul{\theta}}
\def\infinity{\infty}

\def\comp{\; \;\;  
{ { {H_{1}} \atop {>} }  
\atop  
{ {<} \atop {H_0} } }  
\;\;\;}


\def\compo{\; \;\;  
{ { {H_{0}} \atop {>} }  
\atop  
{ {<} \atop {H_1} } }  
\;\;\;}





\def\bigspace{\vspace{.05in}}
\def\smallspace{\vspace{.025in}}