%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% defmath.tex
% definitions of math macros
%
% author:          K.H. Hofmann
% e-mail:          karlheinrich.hofmann@hs-rm.de
% created:         10.02.1995
% last revision:   30.01.2023, 22.03.2019, 27.01.2019, 09.07.2013, 04.03.2013
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% mathematical symbols and operands
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Laplace Operator horizontal: frequency to time domain
\newcommand{\lphft}{\mbox{$ \ \bullet \hspace{-0.9ex}-\hspace{-01ex}-
                              \hspace{-0.5ex} \circ \ $} }
% Laplace Operator horizontal: time to frequency domain
\newcommand{\lphtf}{\mbox{$ \ \circ \hspace{-0.9ex}-\hspace{-01ex}-
                              \hspace{-0.5ex} \bullet \ $} }
% Laplace Operator vertical: frequency to time domain
\newcommand{\lpvft}{\mbox{$ \renewcommand{\arraystretch}{1}
                            \begin{array}{c}
                            \bullet \\[-1.3ex]
                            \mid    \\[-1.3ex]
                            \circ 
                            \end{array} $} }
% Laplace Operator vertical: time to frequency domain
\newcommand{\lpvtf}{\mbox{$ \renewcommand{\arraystretch}{1}
                            \begin{array}{c}
                            \circ \\[-1.3ex]
                            \mid  \\[-1.3ex]
                            \bullet 
                            \end{array} $} }
% integral: lower limit: - infinity; upper limit: + infinity
\newcommand{\intinf}{\int\limits_{-\infty}^{\infty}}
\newcommand{\devt}{\frac{d}{dt}} 
\newcommand{\devf}{\frac{d}{df}}
\newcommand{\devom}{\frac{d}{d\omega}}
\newcommand{\devpt}{\frac{\partial}{\partial t}} 
\newcommand{\devpf}{\frac{\partial}{\partial f}}
\newcommand{\devpom}{\frac{\partial}{\partial\omega}}
\newcommand{\entsp}{\,\hat{=}\,}
\newcommand{\soll}{\,\stackrel{!}{=}\,}
\newcommand{\lra}{\leftrightarrow} 
\newcommand{\prozent}{\rule[0ex]{0ex}{1ex}^\circ\hspace*{-1mm}/
                      \hspace*{-0.9mm}\rule[-0.5ex]{0ex}{1ex}_\circ }
\newcommand{\promille}{\rule[0ex]{0ex}{1ex}^\circ\hspace*{-1mm}/
                      \hspace*{-0.9mm}\rule[-0.5ex]{0ex}{1ex}_{\circ\circ} }
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% commands with parameters 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% framing of equations 
\newcommand{\mframe}[1]{ \fbox{$\displaystyle #1 $} }
% dx
\newcommand{\md}[1]{\,\mbox{d}#1}
% underline
\newcommand{\unl}[1]{\underline{#1}}
% double underline
\newcommand{\uul}[1]{\underline{\underline{#1}}}
% overline
\newcommand{\ovl}[1]{\overline{#1}}
% norm
\newcommand{\norm}[1]{\parallel #1 \parallel} 
% expectation value
\newcommand{\expec}[1]{E\left\{ #1 \right\}} 
% matrix: 2 rows, 1 column
\newcommand{\matrixze}[2]{\left(\!\begin{array}{c} #1 \\
                                                   #2 
                                \end{array}\!\right)} 
% matrix: 2 rows, 2 columns
\newcommand{\matrixzz}[4]{\left(\!\begin{array}{cc} #1 & #2 \\
                                                    #3 & #4 
                                \end{array}\!\right)} 
% complex variables
\newcommand{\cx}[1]{\underline{#1}}    % complex value, b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% indices , with parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% index _Re
\newcommand{\IRe}[1]{#1_{\mbox{\tiny Re}}}
% Index _Im 
\newcommand{\IIm}[1]{#1_{\mbox{\tiny Im}}}
\newcommand{\omg}[1]{\omega_{#1}}
\newcommand{\jomg}[1]{j\omega_{#1}}
\newcommand{\omgt}[1]{\omega_{#1}t}
\newcommand{\jomgt}[1]{j\omega_{#1} t}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% abbrevations for math mode
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\DM}{\,\mbox{DM}}                   % DM
\newcommand{\GF}{\,\mbox{GF}}                   % GF, Galois Field
\newcommand{\grad}{\mbox{grad}}                 % grad entsp. deg
\newcommand{\ppm}{\,\mbox{ppm}}                 % ppm
\newcommand{\const}{\mbox{const}}               % const
\newcommand{\e}{\mbox{e}}		        % exponential function
\newcommand{\erf}{\mbox{erf}}                   % error function
\newcommand{\erfc}{\mbox{erfc}}                 % complementary erf
\newcommand{\ld}{\mbox{ld}}		        % logarithmus dualis
\newcommand{\mod}{\,\mbox{mod}\,}	        % modulo
\newcommand{\rect}{\mbox{rect}}                 % rectangular function
\newcommand{\sgn}{\mbox{sgn}}                   % signum function
\newcommand{\Si}{\mbox{Si}}                     % Sine function
\newcommand{\si}{\mbox{si}}                     % si function
\newcommand{\sinc}{\mbox{sinc}}                 % sinc function
\newcommand{\tri}{\mbox{tri}}                   % triangle function

\newcommand{\Real}{\mbox{Re}}                   % real part
\newcommand{\Imag}{\mbox{Im}}                   % imaginary part

\newcommand{\baud}{\,\mbox{baud}}               % baud
\newcommand{\bauds}{\,\mbox{baud}}              % baud
\newcommand{\kbauds}{\,\mbox{kbaud}}            % kbaud
\newcommand{\bit}{\,\mbox{bit}}                 % bit
\newcommand{\bps}{\,\mbox{bit/s}}               % bits/s
\newcommand{\kbps}{\,\mbox{kbit/s}}             % kbits/s
\newcommand{\Mbps}{\,\mbox{Mbit/s}}             % Mbits/s
\newcommand{\Mchips}{\,\mbox{Mchip/s}}          % Mchip/s
\newcommand{\bpsy}{\,\mbox{bit/symbol}}         % bits/symbol
\newcommand{\erlkm}{\,\mbox{Erl/km}^2}          % Erlang/km^2
\newcommand{\syps}{\,\mbox{symbols/s}}          % symbols/s
\newcommand{\ksyps}{\,\mbox{ksymbols/s}}        % ksymbols/s
% GSM
\newcommand{\Abis}{\,\mbox{A}_{\mbox{\scriptsize bis}}}  % A_bis (GSM)
\newcommand{\Kc}{\,\mbox{K}_{\mbox{\scriptsize c}}}      % K_c (GSM)
\newcommand{\Ki}{\,\mbox{K}_{\mbox{\scriptsize i}}}      % K_i (GSM)
\newcommand{\Um}{\,\mbox{U}_{\mbox{\scriptsize m}}}      % U_m (GSM)
% DECT
\newcommand{\Ct}{\,\mbox{C}_{\mbox{\scriptsize t}}}  % C_t (DECT)
\newcommand{\Mt}{\,\mbox{M}_{\mbox{\scriptsize t}}}  % M_t (DECT)
\newcommand{\Nt}{\,\mbox{N}_{\mbox{\scriptsize t}}}  % N_t (DECT)
\newcommand{\Pt}{\,\mbox{P}_{\mbox{\scriptsize t}}}  % P_t (DECT)
\newcommand{\Qt}{\,\mbox{Q}_{\mbox{\scriptsize t}}}  % Q_t (DECT)
\newcommand{\RSSImax}{\,\mbox{RSSI}_{\mbox{\scriptsize max}}}  % RSSI_max
\newcommand{\RSSImin}{\,\mbox{RSSI}_{\mbox{\scriptsize min}}}  % RSSI_min
% ISDN
\newcommand{\sz}{\,\mbox{S}_0}                         % S_0 (ISDN)
\newcommand{\stm}{\,\mbox{S}_{2\mbox{\scriptsize M}}}  % S_2M (ISDN)
\newcommand{\ukz}{\,\mbox{U}_{\mbox{\scriptsize k}0}}  % Uk_0 (ISDN)
\newcommand{\upz}{\,\mbox{U}_{\mbox{\scriptsize p}0}}  % Up_0 (ISDN)
\newcommand{\ukt}{\,\mbox{U}_{\mbox{\scriptsize k}2}}  % Uk_2 (ISDN)
\newcommand{\ugt}{\,\mbox{U}_{\mbox{\scriptsize G}2}}  % UG_2 (ISDN)
% UMTS
\newcommand{\BSRx}{\,\mbox{BS}_{\mbox{\scriptsize Rx}}} % BS_Rx
\newcommand{\BSTx}{\,\mbox{BS}_{\mbox{\scriptsize Tx}}} % BS_Tx
\newcommand{\MSRx}{\,\mbox{MS}_{\mbox{\scriptsize Rx}}} % MS_Rx
\newcommand{\MSTx}{\,\mbox{MS}_{\mbox{\scriptsize Tx}}} % MS_Tx
\newcommand{\SIRtarget}{\,\mbox{SIR}_{\mbox{\scriptsize target}}} % SIR_target
%
\newcommand{\om}{\omega}
\newcommand{\Dom}{\Delta\omega}
\newcommand{\dom}{d\omega}
\newcommand{\jom}{j\omega}
\newcommand{\omt}{\omega t}
\newcommand{\jomt}{j\omega t}
%
\newcommand{\omddb}{\omega_{3dB}}
\newcommand{\omk}{\omega_k}
\newcommand{\omkrit}{\omega_{krit}}
%
\newcommand{\omc}{\omega_c} 
\newcommand{\jomc}{j\omega_c} 
\newcommand{\omct}{\omega_c t}
\newcommand{\jomct}{j\omega_c t}
%
\newcommand{\omn}{\omega_0} 
\newcommand{\jomn}{j\omega_0} 
\newcommand{\omnt}{\omega_0t}  
\newcommand{\jomnt}{j\omega_0 t}
%
\newcommand{\omm}{\omega_m}
\newcommand{\jomm}{j\omega_m}
\newcommand{\ommt}{\omega_m t}
\newcommand{\jommt}{j\omega_m t}
%
\newcommand{\ome}{\omega_1}  
\newcommand{\jome}{j\omega_1}  
\newcommand{\omet}{\omega_1 t}
\newcommand{\jomet}{j\omega_1 t}
%
\newcommand{\omz}{\omega_2} 
\newcommand{\jomz}{j\omega_2} 
\newcommand{\omzt}{\omega_2t}
\newcommand{\jomzt}{j\omega_2t}
%
%  
\newcommand{\zp}{2\pi}
\newcommand{\Df}{\Delta f}
\newcommand{\zpf}{2\pi f}
\newcommand{\zpft}{2\pi ft}
\newcommand{\fc}{f_c}
\newcommand{\zpfc}{2\pi f_c}
\newcommand{\zpfct}{2\pi f_ct}
\newcommand{\fn}{f_0}
\newcommand{\zpfn}{2\pi f_0}
\newcommand{\zpfnt}{2\pi f_0t}
\newcommand{\fe}{f_1}
\newcommand{\zpfe}{2\pi f_1}
\newcommand{\zpfet}{2\pi f_1t}
\newcommand{\fz}{f_2}
\newcommand{\zpfz}{2\pi f_2}
\newcommand{\zpfzt}{2\pi f_2t}
%
\newcommand{\jphi}{j\varphi}
\newcommand{\vphit}{\varphi (t)}
\newcommand{\phit}{\phi (t)}
\newcommand{\Dvphi}{\Delta\varphi}
%
\newcommand{\Utt}{\tilde{U}_T}                  % m U_T Temperaturspannung
% dB
\newcommand{\dB}{\,\mbox{dB}}                   % dB
%\newcommand{\dB}{\,\mbox{dBA}}                  % dBA
\newcommand{\dBi}{\,\mbox{dBi}}                 % dBi
\newcommand{\dBm}{\,\mbox{dBm}}                 % dBm
\newcommand{\dBu}{\,\mbox{dBu}}                 % dBu
\newcommand{\dBV}{\,\mbox{dBV}}                 % dBV
\newcommand{\dBmV}{\,\mbox{dBmV}}               % dBmV
\newcommand{\dBuV}{\,\mbox{dB$\mu$V}}           % dBuV
\newcommand{\dBuVm}{\,\mbox{dB$\mu$V$\!$/m}}    % dBuV/m
\newcommand{\dBA}{\,\mbox{dB(A)}}               % dB(A)
\newcommand{\dBFS}{\,\mbox{dBFS}}               % dBFS
% Hertz
\newcommand{\Hz}{\,\mbox{Hz}}                   % Hz
\newcommand{\kHz}{\,\mbox{kHz}}                 % kHz
\newcommand{\MHz}{\,\mbox{MHz}}                 % MHz
\newcommand{\GHz}{\,\mbox{GHz}}                 % GHz
% Volt
\newcommand{\kV}{\,\mbox{kV}}                   % kV
\newcommand{\V}{\,\mbox{V}}                     % V
\newcommand{\mV}{\,\mbox{mV}}                   % mV
\newcommand{\muV}{\,\mu\mbox{V}}                % uV
\newcommand{\nV}{\,\mbox{nV}}                   % nV
\newcommand{\Vm}{\,\mbox{Vm}}                   % Vm
\newcommand{\Vs}{\,\mbox{Vs}}                   % Vs
\newcommand{\Vmus}{\,\mbox{V}\!/\!\mu\mbox{s}}  % V/mus
% Ampere
\newcommand{\A}{\,\mbox{A}}                     % A
\newcommand{\mA}{\,\mbox{mA}}                   % mA
\newcommand{\muA}{\,\mu\mbox{A}}                % uA
\newcommand{\nA}{\,\mbox{nA}}                   % nA
\newcommand{\pA}{\,\mbox{pA}}                   % pA
\newcommand{\As}{\,\mbox{As}}                   % As
% Watt
\newcommand{\kW}{\,\mbox{kW}}                   % kW
\newcommand{\W}{\,\mbox{W}}                     % W
\newcommand{\mW}{\,\mbox{mW}}                   % mW
\newcommand{\muW}{\,\mu\mbox{W}}                % uW
\newcommand{\nW}{\,\mbox{nW}}                   % nW
\newcommand{\pW}{\,\mbox{pW}}                   % pW
\newcommand{\fW}{\,\mbox{f\/W}}                 % fW
% Sekunde
\newcommand{\s}{\,\mbox{s}}                     % s
\newcommand{\ms}{\,\mbox{ms}}                   % ms
\newcommand{\mus}{\,\mu\mbox{s}}                % us
\newcommand{\ns}{\,\mbox{ns}}                   % ns
\newcommand{\ps}{\,\mbox{ps}}                   % ps
% Siemens
\newcommand{\muSie}{\,\mu\mbox{S}}              % uS Siemens
\newcommand{\mSie}{\,\mbox{mS}}                 % mS Siemens
\newcommand{\Sie}{\,\mbox{S}}                   % S Siemens
% Ohm
\newcommand{\mOhm}{\,\mbox{m}\Omega}            % mOhm
\newcommand{\Ohm}{\,\Omega}                     % Ohm
\newcommand{\kOhm}{\,\mbox{k}\Omega}            % kOhm
\newcommand{\MOhm}{\,\mbox{M}\Omega}            % MOhm
\newcommand{\GOhm}{\,\mbox{G}\Omega}            % GOhm
% Farad
\newcommand{\F}{\,\mbox{F}}                     % F
\newcommand{\mF}{\,\mbox{mF}}                   % mF
\newcommand{\muF}{\,\mu\mbox{F}}                % uF
\newcommand{\nF}{\,\mbox{nF}}                   % nF
\newcommand{\pF}{\,\mbox{pF}}                   % pF
% Henry
\newcommand{\He}{\,\mbox{H}}                    % H
\newcommand{\mH}{\,\mbox{mH}}                   % mH
\newcommand{\muH}{\,\mu\mbox{H}}                % uH
\newcommand{\nH}{\,\mbox{nH}}                   % nH
% Temperatur
\newcommand{\Ctemp}{\,\mbox{C}}                 % Celsius
\newcommand{\Ktemp}{\,\mbox{K}}                 % Kelvin
\newcommand{\tempC}{\,\mbox{}^{\circ}\mbox{C}}  % Celsius
\newcommand{\tempK}{\,\mbox{}^{\circ}\mbox{K}}  % Kelvin
% Pascal 
\newcommand{\Pa}{\,\mbox{Pa}}                   % Pascal
\newcommand{\mPa}{\,\mbox{mPa}}                 % m Pascal
\newcommand{\uPa}{\,\mu\mbox{Pa}}               % u Pascal
% Meter
\newcommand{\kmh}{\,\mbox{km/h}}                % km/h
\newcommand{\qm}{\,\mbox{m}^2}                  % m^2
\newcommand{\cbm}{\,\mbox{m}^3}                 % m^3
\newcommand{\km}{\,\mbox{km}}                   % km
\newcommand{\m}{\,\mbox{m}}                     % m
\newcommand{\cm}{\,\mbox{cm}}                   % cm
\newcommand{\qcm}{\,\mbox{cm}^2}                % cm^2
\newcommand{\cbcm}{\,\mbox{cm}^3}               % cm^3
\newcommand{\mm}{\,\mbox{mm}}                   % mm
\newcommand{\qmm}{\,\mbox{mm}^2}                % mm^2
\newcommand{\cbmm}{\,\mbox{mm}^3}               % mm^3
\newcommand{\mum}{\,\mu\mbox{m}}                % um
\newcommand{\nm}{\,\mbox{nm}}                   % nm
% Masse
\newcommand{\mg}{\,\mbox{mg}}                   % mg
\newcommand{\g}{\,\mbox{g}}                     % g
\newcommand{\kg}{\,\mbox{kg}}                   % kg

\newcommand{\Dm}{\Delta m}
\newcommand{\hU}{\hat{U}}                       % amplitude, U
\newcommand{\hu}{\hat{u}}                       % amplitude, u
\newcommand{\DU}{\Delta U}                      % Kleinsignalgr"o"se, U
\newcommand{\hI}{\hat{I}}                       % amplitude, I
\newcommand{\hi}{\hat{i}}                       % amplitude, i
\newcommand{\DI}{\Delta I}                      % Kleinsignalgr"o"se,
\newcommand{\Ds}{\Delta s}                      % Wegdifferenz                              
\newcommand{\DT}{\Delta T}                      % Temperaturdifferenz
\newcommand{\Dt}{\Delta t}                      % Zeitdifferenz
\newcommand{\Dv}{\Delta v}                      % Geschwindigkeitsdifferenz
\newcommand{\Dx}{\Delta x}                      % x fuer Differenzenquotient
\newcommand{\Dy}{\Delta y}                      % y fuer Differenzenquotient
% Lichttechnische Einheiten
\newcommand{\lm}{\,\mbox{lm}}			% Lumen
\newcommand{\lx}{\,\mbox{lx}}			% Lux
\newcommand{\cd}{\,\mbox{cd}}			% Candela
\newcommand{\sr}{\,\mbox{sr}}			% Steradiant
% Komplexe Groessen
\newcommand{\cxb}{\underline{b}}                % complex value, b
\newcommand{\cxc}{\underline{c}}                % complex value, c
\newcommand{\cxe}{\underline{e}}                % complex value, e
\newcommand{\cxg}{\underline{g}}                % complex value, g
\newcommand{\cxI}{\underline{I}}                % complex amplitude, I
\newcommand{\cxi}{\underline{i}\,}              % complex amplitude, i
\newcommand{\cxK}{\underline{K}}                % complex value, K
\newcommand{\cxk}{\underline{k}}                % complex value, k
\newcommand{\cxr}{\underline{r}}                % complex value, r
\newcommand{\cxs}{\underline{s}}                % complex value, s
\newcommand{\cxS}{\underline{S}}                % complex value, S
\newcommand{\cxU}{\underline{U}}                % complex amplitude, U
\newcommand{\cxu}{\underline{u}\,}              % complex amplitude, u
\newcommand{\cxV}{\underline{V}}                % amplification factor V
\newcommand{\cxv}{\underline{v}}                % amplification factor v
\newcommand{\cxw}{\underline{w}}                % complex w
\newcommand{\cxW}{\underline{W}}                % complex W
\newcommand{\cxx}{\underline{x}}                % complex x
\newcommand{\cxX}{\underline{X}}                % complex X

\newcommand{\cxZ}{\underline{Z}\,}              % complex impedance Z
\newcommand{\cxz}{\underline{z}}                % z
\newcommand{\zaa}{\underline{z}_{11}}           % z_11
\newcommand{\zab}{\underline{z}_{12}}           % z_12
\newcommand{\zba}{\underline{z}_{21}}           % z_21
\newcommand{\zbb}{\underline{z}_{22}}           % z_22

\newcommand{\cxY}{\underline{Y}}                % complex admitance Y
\newcommand{\cxy}{\underline{y}}                % y
\newcommand{\yaa}{\underline{y}_{11}}           % y_11
\newcommand{\yab}{\underline{y}_{12}}           % y_12
\newcommand{\yba}{\underline{y}_{21}}           % y_21
\newcommand{\ybb}{\underline{y}_{22}}           % y_22

\newcommand{\cxA}{\underline{A}}                % complex factor A
\newcommand{\cxa}{\underline{a}}                % a
\newcommand{\aaa}{\underline{a}_{11}}           % a_11
\newcommand{\aab}{\underline{a}_{12}}           % a_12
\newcommand{\aba}{\underline{a}_{21}}           % a_21
\newcommand{\abb}{\underline{a}_{22}}           % a_22
\newcommand{\apaa}{\underline{a}'_{11}}         % a'_11
\newcommand{\apab}{\underline{a}'_{12}}         % a'_12
\newcommand{\apba}{\underline{a}'_{21}}         % a'_21
\newcommand{\apbb}{\underline{a}'_{22}}         % a'_22

\newcommand{\cxP}{\underline{P}}                % complex factor P
\newcommand{\cxp}{\underline{p}}                % p
\newcommand{\paa}{\underline{p}_{11}}           % p_11
\newcommand{\pab}{\underline{p}_{12}}           % p_12
\newcommand{\pba}{\underline{p}_{21}}           % p_21
\newcommand{\pbb}{\underline{p}_{22}}           % p_22

\newcommand{\cxH}{\underline{H}}                % complex factor H
\newcommand{\cxh}{\underline{h}}                % h
\newcommand{\haa}{\underline{h}_{11}}           % h_11
\newcommand{\hab}{\underline{h}_{12}}           % h_12
\newcommand{\hba}{\underline{h}_{21}}           % h_21
\newcommand{\hbb}{\underline{h}_{22}}           % h_22
\newcommand{\haae}{\underline{h}_{11e}}         % h_11e
\newcommand{\habe}{\underline{h}_{12e}}         % h_12e
\newcommand{\hbae}{\underline{h}_{21e}}         % h_21e
\newcommand{\hbbe}{\underline{h}_{22e}}         % h_22e
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Indices Text mode tiny
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\idB}[1]{_{{\scriptscriptstyle #1}\mbox{\tiny dB}} }     % x dB

\newcommand{\iAM}{_{\mbox{\tiny AM}}}          % _AM
\newcommand{\iASK}{_{\mbox{\tiny ASK}}}        % _ASK
\newcommand{\ibit}{_{\mbox{\tiny bit}}}        % _bit
\newcommand{\iBP}{_{\mbox{\tiny BP}}}          % _BP
\newcommand{\iBPSK}{_{\mbox{\tiny BPSK}}}      % _BPSK
\newcommand{\iBFSK}{_{\mbox{\tiny BFSK}}}      % _BFSK
\newcommand{\ichip}{_{\mbox{\tiny chip}}}      % _chip
\newcommand{\iCPM}{_{\mbox{\tiny CPM}}}        % _CPM
\newcommand{\iCPFSK}{_{\mbox{\tiny CPFSK}}}    % _CPFSK
% \newcommand{\idB}{_{\mbox{\tiny dB}}}          % _dB
\newcommand{\iDL}{_{\mbox{\tiny DL}}}          % _DL
\newcommand{\iFM}{_{\mbox{\tiny FM}}}          % _FM
\newcommand{\iFSK}{_{\mbox{\tiny FSK}}}        % _FSK
\newcommand{\iGMSK}{_{\mbox{\tiny GMSK}}}      % _GMSK
\newcommand{\iHF}{_{\mbox{\tiny HF}}}          % _HF
\newcommand{\iI}{_{\mbox{\tiny I}}}            % _I
\newcommand{\iIF}{_{\mbox{\tiny IF}}}          % _IF
\newcommand{\iIM}{_{\mbox{\tiny IM}}}          % _IM
\newcommand{\iLF}{_{\mbox{\tiny LF}}}          % _LF
\newcommand{\iLO}{_{\mbox{\tiny LO}}}          % _LO
\newcommand{\iLP}{_{\mbox{\tiny LP}}}          % _LP
\newcommand{\iMPSK}{_{\mbox{\tiny MPSK}}}      % _MPSK
\newcommand{\iMSK}{_{\mbox{\tiny MSK}}}        % _MSK
\newcommand{\iNF}{_{\mbox{\tiny NF}}}          % _NF
\newcommand{\iOQPSK}{_{\mbox{\tiny OQPSK}}}    % _OQPSK
\newcommand{\iPM}{_{\mbox{\tiny PM}}}          % _PM
\newcommand{\iPSK}{_{\mbox{\tiny PSK}}}        % _PSK
\newcommand{\iQ}{_{\mbox{\tiny Q}}}            % _Q
\newcommand{\iQAM}{_{\mbox{\tiny QAM}}}        % _QAM
\newcommand{\iQPSK}{_{\mbox{\tiny QPSK}}}      % _QPSK
\newcommand{\iRC}{_{\mbox{\tiny RC}}}          % _RC
\newcommand{\iRF}{_{\mbox{\tiny RF}}}          % _RF
\newcommand{\iRx}{_{\mbox{\tiny Rx}}}          % _Rx
\newcommand{\iSRRC}{_{\mbox{\tiny SRRC}}}      % _SRRC
\newcommand{\isymbol}{_{\mbox{\tiny symbol}}}  % _symbol
\newcommand{\iTP}{_{\mbox{\tiny TP}}}          % _TP
\newcommand{\iTx}{_{\mbox{\tiny Tx}}}          % _Tx
\newcommand{\iUL}{_{\mbox{\tiny UL}}}          % _UL
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Indices Math mode scriptscriptstyle
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\iA}{\sssty A}
\newcommand{\iR}{\sssty R}
\newcommand{\iS}{\sssty S}
\newcommand{\iU}{\sssty U}
\newcommand{\iV}{\sssty V}
\newcommand{\iW}{\sssty W}
\newcommand{\iX}{\sssty X}
\newcommand{\iY}{\sssty Y}
\newcommand{\iZ}{\sssty Z}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



