STRLCPY/wirelesscomm

Minor changes in the problems.
Sundeep Rangan committed 3 years ago

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unit02_propagation/prob/prob_propagation.pdf

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unit02_propagation/prob/prob_propagation.tex

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14	14		\usetikzlibrary{shapes,arrows}
15	15		\usepackage{mdframed}
16	16		\usepackage{mcode}
	17	+	\usepackage{siunitx}
17	18		%\usetikzlibrary{dsp,chains}
18	19
19	20		%\restylefloat{figure}
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46	47		\def\limn{\lim_{n \rightarrow \infty}}
47	48		\def\liminfn{\liminf_{n \rightarrow \infty}}
48	49		\def\limsupn{\limsup_{n \rightarrow \infty}}
49		-	\def\GV{Guo and Verd{\'u}}
50	50		\def\MID{\,\|\,}
51	51		\def\MIDD{\,;\,}
52	52
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163	163
164	164		\def\Rect{\mathop{Rect}}
165	165		\def\sinc{\mathop{sinc}}
	166	+	\def\NF{\mathrm{NF}}
166	167		\def\Real{\mathrm{Re}}
167	168		\def\Imag{\mathrm{Im}}
168	169		\newcommand{\tran}{^{\text{\sf T}}}
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177	178
178	179		\begin{document}
179	180
180		-	\title{Problems: Non-LOS Propagation and Link Budget Analysis\\
	181	+	\title{Problem Solutions: Non-LOS Propagation and Link Budget Analysis\\
181	182		EL-GY 6023. Wireless Communications}
182	183		\author{Prof.\ Sundeep Rangan}
183	184		\date{}
184	185
185	186		\maketitle
186	187
	188	+	In all the problems below, unless specified otherwise, $\phi$ is the
	189	+	azimuth angle and $\theta$ is elevation angle.
	190	+
187	191		\begin{enumerate}
188	192
189	193		\item \emph{Noise:}
190		-	Suppose a receiver consists of an low noise amplifier with a gain of 30 dB
	194	+	Suppose a receiver consists of an low noise amplifier with a gain of 20 dB
191	195		and noise figure of 2 dB, followed by a second stage of amplification of
192		-	another 20 dB with a noise figure of 10 dB.
	196	+	another 15 dB with a noise figure of 10 dB.
193	197		\begin{enumerate}[label=(\alph*)]
194	198		\item What is the total noise figure and gain of the system?
195	199		\item Suppose a 10 dB attenuator is placed at the input of the LNA.
196	200		What is the resulting overall gain and noise figure?
197	201		\item What if the attenuator is placed at the output of the LNA?
198	202		\end{enumerate}
	203	+
199	204
200	205		\item \emph{SINR:}
201	206		Suppose when a transmitter, TX1, sends data to a receiver RX
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205	210		TX2 to RX is 5 dB greater than the path loss from TX1 to RX.
206	211		What is the resulting SINR from TX1 to RX when TX2 is transmitting?
207	212
	213	+	\item \emph{Reflection loss:} Consider a reflection at an
	214	+	interface going from a characteristic impedance $\eta_1$ to $\eta_2$ at
	215	+	an incident angle of $\theta_i = 0$.
	216	+	\begin{enumerate}[label=(\alph*)]
	217	+	\item What is the reflected angle $\theta_r$ and refracted
	218	+	angle $\theta_t$?
	219	+	\item Show that the reflection coefficient $\Gamma$ is
	220	+	identical in the parallel and perpendicular polarizations.
	221	+	Find $\Gamma$ in terms of $\eta_1$ and $\eta_2$.
	222	+	\item Estimate the expected reflected power gain $\|\Gamma\|^2$
	223	+	when a wave in free space strikes dry concrete.
	224	+	Assume concrete has a relative permittivity of $\epsilon_r \approx 4.5$.
	225	+	\end{enumerate}
208	226
209		-	\item \emph{Reflection loss:} Let $\Gamma$ be the reflection coefficient from
210		-	an interface going from a characteristic impedance $\eta_1$ to $\eta_2$ and let
211		-	$\Gamma'$ be the reflection coefficient from
212		-	$\eta_2$ to $\eta_1$. Show that if the angle of incidence is
213		-	zero $\theta_i=0$, $\Gamma = -\Gamma'$.
214	227
215	228
216	229		\item \emph{SNR requirements:}
217		-	A signal is received at power of $P = $-100 dBm and the noise power density
	230	+	A signal is received at power of $P_{rx} = $-100 dBm and the noise power density
218	231		(including the noise figure) is $N_0 = $ -170 dBm/Hz.
219		-	If a transmission of $b=100$ bits requires an $E_b/N_0$
220		-	of 6~dB, what is the time to transmit the packet?
	232	+	If the receiver requires $E_b/N_0=$ \SI{6}{dB},
	233	+	what is the minimum time to transmit $b=1000$ bits?
	234	+
221	235
222	236		\item \emph{Simulating a statistical model:}
223	237		Write short MATLAB code to do the following. You do not need to run the code,
224	238		just write the code.
225	239		\begin{enumerate}[label=(\alph*)]
226		-	\item Drop \mcode{nrx=1000} RX locations randomly in a circle of radius \mcode{radius = 100}m.
227		-	\item Assuming the transmitter is at the origin at a height \mcode{htx=2}m higher
228		-	than the RX, compute the distances \mcode{dist} to the RXs.
	240	+	\item Suppose \mcode{nrx=1000} RX locations are randomly located uniformly
	241	+	in a circle of radius \mcode{rmax = 100}\, \si{m} from the origin.
	242	+	Generate a random vector \mcode{dist2} representing the random distances
	243	+	from the origin of the RX locations.
	244	+	\item Assuming the transmitter is at the origin at a height \mcode{htx=2}\, \si{m} higher than the RX, compute the distances \mcode{dist} to the RXs.
229	245		\item Assuming a path loss model,
230	246		\[
231		-	PL = 32.4 + 14.3\log_{10}(d) + 20\log_{10}(f_c) + \xi,
232		-	\quad \xi \sim \mathcal{N}(0,\sigma^2),
	247	+	PL = 32.4 + 14.3\log_{10}(d \mbox{\, [m]}) + 20\log_{10}(f_c \mbox{\, [GHz]}) + \xi,
	248	+	\quad \xi \sim \mathcal{N}(0,\sigma^2), \mbox{ [dB]}
233	249		\]
234		-	generate random path losses to the RXs. Assume $\sigma = 4$ and
235		-	$f_c = 2.3$ GHz.
236		-	\item Compute the SNR, $E_s/N_0$, to the RX. State all the parameters that you would need.
	250	+	generate random path losses to the RXs. Assume $\sigma = 4$\, \si{dB} and
	251	+	$f_c = 2.3$\, \si{GHz}.
	252	+	\item Finally plot a CDF of $E_s/N_0$ with transmit power, \mcode{Ptx = 15}\,
	253	+	\si{dBm}, bandwidth \mcode{B = } \SI{20}{MHz} and thermal noise \mcode{N0=-170}\, \si{dBm/Hz}.
237	254		\end{enumerate}
	255	+
238	256
239	257
240	258		\item \emph{Simulating a statistical model:}
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254	272		to generate random path loss values as function of a vector of distances.
255	273		State all the other parameters this function needs. You may assume you have
256	274		access to a function \mcode{fspl(lambda,d)} for the free-space path loss.
	275	+	Place comments in your code describing all the input arguments.
257	276
258	277		\item \emph{Outage probability:} Suppose that a link has the following properties:
259	278		\begin{itemize}
260	279		\item TX power, $P_{tx} =$ 20 dBm
261		-	\item Bandwidth, $W =$ 20 MHz
	280	+	\item Bandwidth, $B =$ 20 MHz
262	281		\item Noise power density (including noise figure) $N_0=$ -170 dBm/Hz.
263	282		\end{itemize}
264	283		Answer the following:
265	284		\begin{enumerate}[label=(\alph*)]
266		-	\item What is the maximum path loss, $PL_{max}$, that the link can
	285	+	\item What is the maximum path loss, $PL_{\rm max}$, that the link can
267	286		have to meet an SNR target of 10 dB?
268	287		\item Suppose that the path loss is lognormally distributed with
269	288		\[
270	289		PL = PL_0 + \xi, \quad \xi \sim {\mathcal N}(0,\sigma^2),
271	290		\]
272		-	where $PL_0 = $ 110 dB and $\sigma$ = 8~dB.
273		-	What is the outage probability $P_{out}=\Pr(PL \geq PL_{max})$
	291	+	where $PL_0 =$ \SI{100}{dB} and $\sigma =$ \SI{8}{dB}.
	292	+	What is the outage probability $P_{out}=\Pr(PL \geq PL_{\rm max})$
274	293		using the value $PL_{max}$ from part (a)?
275	294		Your answer should have
276	295		a $Q$-function. You can evaluate it with MATLAB's function \mcode{qfunc}.
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290	309		0 & \mbox{else, }
291	310		\end{cases}
292	311		\]
293		-	and the loss per wall is $D=$ 7~dB.
	312	+	and the loss per wall is $D=$ \SI{7}{dB}.
294	313		What is the outage probability $P_{out}$?
295	314		\end{enumerate}
	315	+
296	316
297	317		\end{enumerate}
298	318
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Minor changes in the problems.