On behalf of Ihrie O'Brien posted in Divorce on Friday, July 20, 2018.
When most couples get divorced, that's the end of their time together. Yes, they still see each other when they exchange the kids in accordance with the custody plan, but they move on. They get new homes. They date new people. Life moves forward.
What are the 7 steps you need to take after an accident?
On behalf of Ihrie O'Brien posted in Car Accidents on Thursday, July 12, 2018.
Accidents happen so fast that you never have any idea what's coming. One moment you're listening to a podcast and driving calmly through an intersection with a green light. The next minute, you're pulling yourself out of a totaled car on the side of the road.
Will a divorce when your child is in college hurt the child?
On behalf of Ihrie O'Brien on Saturday, July 7, 2018.
It may seem as if there is never a good time for your divorce. For instance, perhaps you were almost ready three years ago, but your mother came down with serious health problems. You had to care for her. Meanwhile, your oldest child started college. Your mother has recovered, but with your child in college, is divorce a good idea? After all, both parents have to cut back on financial expenses.


The Special Race Day at the Mahalaxmi Racecourse in Mumbai on April 14th threw up some wholesome entertainment for enthusiasts. We had picked out two of the Sunday races as part of our last preview article. Here's how our Mahalaxmi Race Course betting top picks for those races fared.
With just five horses on the track, this was certainly not the most crowded affair on Sunday. But it was not short on excitement or surprise (albeit unwanted), with one of our Mahalaxmi Race Course betting picks Princess Annabel being forced to withdraw. That left just four horses in this 1400m race, with Gallantry and Silver Flames as our favourites.
Gallantry was the odds-on favourite for this race and showed exactly why that was the case with a very strong run. Run by jockey Trevor, the young colt cantered home with a time of 1:24:018. With this win, Gallantry has finally returned back to winning ways, proving that the underwhelming performance in early March was just a blip in an otherwise promising career.
Royal Crystal managed to edge out Silver Flames in the final third of the race and came out in second place. Since Gallantry finished at least three lengths ahead of Royal Crystal, the most exciting part of this race was the fight for the second and third places. K Nazil was the jockey who managed to coax this horse into second with a time of 1:24:537.
Silver Flames was our second pick for this race and for much of it, he managed to stay in second. But in the final stretch, he finally ran out of steam a bit and was bested by Royal Crystal. This young horse still has a long way to go, having had only three starts so far. With jockey A Sandesh in the saddle, he ended the race with a time of 1:24:679.
This was always going to be a tough horse race to call, with eleven horses in the running. And the field was also quite strong, with a nice mix of exciting young colts/fillies, and more experienced thoroughbreds all vying for the honours. Since we had to pick three horses for our Mahalaxmi Race Course betting tips, we went with Cormorant and Bakhtawar as our favourites, with Excellent Sorrento as our long-shot choice.
Gentilesse and Notting Hill were the two horses we had chosen to overlook when trying to whittle our top five down to a top three. Trained by Sanjay Kolse, this 5-year-old mare had scored the first win of her career on April 6th. She repeated that feat on Sunday, pipping Excellent Sorrento into second place at the last moment on the final stretch. With jockey Amit in the saddle, Gentilesse finished with a time of 1:22:528.
Excellent Sorrento was outside the leading pack as the horses crossed the 800m mark in this race. While he managed to claw his way back to the top in the final stretch, a late charge by winner Gentilesse put paid to any hopes of adding to his two wins this season. Still, a second place finish in such a closely fought race should only raise the punters' interest in this young colt.
Cormorant was widely considered to be the top runner in this race. And as the horses headed into the final stretch, things seemed to be working with him sitting pretty in first. But that didn't last for long and Cormorant could not complete his hat trick on Sunday. Regardless of that, he did manage to impress with his staying power in the race, ending it in third with a time of 1:22:674.


text:
Home NIGERIA Osun governor swears in new Commissioners, Special Advisers
Osun governor swears in new Commissioners, Special Advisers
Segun Adegoke, Osogbo
Governor of Osun State, Gboyega Oyetola has sworn in a total of 35 new Commissioners and Special Advisers to help him pilot the affairs of the state.
This comes barely a week after he went into a four day Executive Council Retreat with the cabinet members to fashion out strategic plans on how to deliver the Osun Development Agenda.
Oyetola, while inaugurating the team admonished them to stay committed to their brief and shun acts capable of undermining the corporate integrity of the administration and the state.
The Governor said his administration has zero tolerance for corruption and opacity, warning that the government would not hesitate to wield the big stick where necessary on any official found culpable of public misconduct.
"Our Administration is a product of God's Promise, the benevolence of the people and our Mandate. The Almighty God and the people have delivered their own part. The ball is now in our court to deliver on our promise. As heads of Ministries, you are our delivery channel. I charge you to harness the available human and material resources to fulfill our bond to the people.
"This administration has zero tolerance for corruption and opacity. We shall therefore not hesitate to wield the big stick where necessary.
"Ensure that you discharge every duty with utmost probity, accountability and transparency as these are the elements that will deliver stellar service in the face of extant limited resources and earn the trust of the people."
The governor, who called on the newly inaugurated cabinet members to see their appointments as a clarion call to serve the state, also said cabinet members would be assessed from time to time for optimum performance.
Speaking on behalf of the newly-inaugurated cabinet members, Commissioner for Information and Civic Orientation, Mrs. Funke Egbemode, lauded the governor for the confidence reposed in them to serve the state.
She assured the governor and the people of the state of diligent service in their respective ministries.
"We will not disappoint you. We will put in our very best to support the administration and uplift the standard of living of the people of the state.
"We shall take to the lessons garnered at the retreat to effect positive change across sectors" she added.
The newly-inaugurated Deputy Chief of Staff in-charge of General Administration, Barrister Mikhail Adejare Adebisi, also implored all members of the cabinet to see their appointments as a privilege to impact meaningfully on the lives of the people of the state.
The inauguration held at the White House Parking Lot, Bola Ige House, State Secretariat, Osogbo.
Previous articleMinister challenges youths to generate revenue through ICT
Next articleFailed policies caused your problems – US embassy replies Zimbabwe
Aisha John Mark

redpajama_set_name: RedPajamaCommonCrawl


> expect it to work consistently.
> it) but if it is there it should work!
> system (incg) which includes the whole structure.
>>  > by pressing a button really distract from the strength of TeX or LaTex.
>> of texts, not for quick hacks.
>> themselves quite fast that macros are useful.
>> to use a text editor.
>> of them could be processed by TeX.  And indeed, everything was broken.
>> can see what it produces."
>> Actually, he just produced a heap of crap and learned nothing.


Looking for the top Cooking Classes in Stone Mountain GA? You can make a great night out of a cooking class by making it a date – cooking classes are perfect for couples to bond and get to know each other while having fun over a glass of wine. Recreational cooking classes are easy going and are very affordable for the value they create. Classes are being filled up fast, so get signed up now!
If you are looking at cooking classes for professional development, visit our culinary schools section – Cooks normally must possess physical endurance, manual dexterity along with a good sense of taste and scent. They must have the ability to function like a member of the team. Chefs and also head cooks should have the creativity to develop recipes. They have to be strong leaders and have effective communication and time management abilities.


text:
Q: Что делать если удалил папку src с проектом? Я нечаянно удалил src папку в Android Studio. Не могу ее восстановить. В ней лежал весь проект. Что делать?

A: Щелкните правой кнопкой мыши ваш проект в структуре проекта слева. Затем Local History -> Show History.

Вы можете восстановить проект до любой точки.
Для более надежного хранения проектов следует использовать Git.

A: Здравствуйте. Если указанный выше совет не помогает, то можно воспользоваться средствами восстановления данных. Например Recuva Чем меньше аремени прошло с момента удаления, тем больше вероятность успеха, т.к. тем меньшая часть данных будет перезаписана.
Можете посмотреть ответы на вопрос Восстановление удаленных файлов windows.

redpajama_set_name: RedPajamaStackExchange


text:
Jamie Soward believes Damien Cook looks tired and teams are starting to work him out.
Souths 'busted' and rivals have 'worked out' Cook's game
19th Aug 2019 12:50 PM
FORMER Dragons playmaker Jamie Soward has declared that the Rabbitohs' chances of winning the NRL premiership are gone.
After their shock 14-6 loss to the Bulldogs atthe weekend, the Rabbitohs have fallen out of the top four for the first time this season and are now on a three match losing streak.
After their strong start to the season where they only lost one match from ten games, Soward believes the Rabbitohs have struggled to overcome the Origin period.
Live stream the 2019 NRL Telstra Premiership on KAYO SPORTS. Every game of every round live & anytime on your TV or favourite device. Get your 14 day free trial >
"What I would say about the Bunnies is that they've got the rewards from performances earlier in the season, but they haven't been great in and around Origin, and coming after that they just look really tired," Soward said.
The Rabbitohs look to be playing with injuries, with Adam Reynolds and Sam Burgess unfit and star hooker Damien Cook looking tired, according to the former Origin representative.
"Sam Burgess looks busted and Damien Cook looks tired. Cook has played three State of Origin games, he's been the best hooker for the past eighteen months with Cameron Smith, but teams are starting to work him out."
"Teams are starting to push him sideways, which is what the Roosters did last year in that semi-final and it is creating frustration for Cook."
Wayne Bennett's Rabbitohs will take on the Broncos on Friday night.
"They just look tired. The Bunnies are gone.
"They're not going to win this competition. I don't even know if they can make the second week of the finals, because if they come up against Penrith, Cronulla or Newcastle, they'll get rolled."
Wayne Bennett warned his side that their season is on life support after their loss to the Bulldogs.
"I just told them in there it's not terminal but it's getting close," said Bennett when asked what his message to his players was.
"We're not playing our best football and we've played some pretty good football last weekend had some good moments tonight.
"Our execution was poor, we never got a repeat set, we had opportunities to but we couldn't complete a set.
"Those are the type of things that don't allow you to play the football you can play.
"And we're a victim of that right now."
The Rabbitohs face Bennett's former team Brisbane at Suncorp Stadium on Friday in a game they must win to keep their top four hopes alive.
Premium Content Likes, Dislikes: Best team in the NRL
Premium Content Monday Buzz: The dirtiest team in the NRL
Premium Content Crisis point: Another injury blow for Broncos
Premium Content Boyd urged to consider early retirement
damien cook jamie soward nrl rabbitohs rugby league


Stay one step ahead of everyone in this pristine white Eton shirt. While Eton can be worn in casual surroundings their true potential is in formal occasions. Nothing says perfections quite like an Eton, its simple button layout and cotton feel are enough for any style. Adding this to any outfit will create a considerable definition to your desired look.


You can get good decks for cheap. I have an Onkyo that I picked up for $14 at my record store.
I have two boxes of old cassettes from the 80's up to around 96 or so, when i finally bought my first discman. They are just sitting in a closet taking up space but i refuse to throw them away every time my wife ask me to.
Glad to see all you cassette collectors on the loose. Maybe that'll reduce the number of vinyl fans out there so we can have our hobby back!
Now we'll see used cassettes going for $10-$15.
Awesome! How does it sound?
Better than it looks...that tape's PF old and it's been with me since 1986. My initials are on the back and they're sorta faded.
That's a Lie with Russell Simmons and the Owner of a Lonely Heart Yes insert has always been my fave.
Picked up Ten, the Five Against One version of Vs., Vitalogy, and Yield, for less than $20.
Awesome! Gotta let us know how it sounds.
Scored a copy of Live On Two Legs for $2.75.
I have a Neil Young Broken Arrow cassette, $12 ono.


text:
\section{Introduction}

\IEEEPARstart{T}he past few years have witnessed a tremendous increase in the deployment and use    of unmanned aerial vehicles (UAVs) in both commercial and civilian applications, such as for aerial surveillance, traffic control, photography, package delivery, and so on~\cite{zeng2016wireless,van2016lte,seo2018drone,duque2018synthesis}.
Hence, the ground wireless networks are expected to not only serve ground users (GU) but also  provide ubiquitous communication services for the UAVs, i.e., support the communication between the UAVs and their users or controllers~\cite{khosravi2018performance,gapeyenko2018flexible}.
Consequently, ground networks supporting UAV communications have relatively more workload.

Non-orthogonal multiple access (NOMA) and relaying are known as promising techniques enhancing the performance of overloaded networks.
 By applying the successive interference cancellation (SIC) technique, NOMA enables two (or more) users to transmit data packets in a single time-frequency resource block by exploiting differences in channel conditions~\cite{saito2013system}.
Authors in~\cite{ding2016impact} address the impact of user pairing on the NOMA system. In~\cite{ali2016dynamic}, the sum-throughput achieved with NOMA is investigated.
Recently, for a UAV-assisted NOMA network where the UAV serves as  an access-point,     the outage probability of   GUs~\cite{sharma2017uav} and the UAV trajectory designs~\cite{Zhao_2018} are addressed, respectively.
In addition, cooperative relaying has been also shown as an efficient way to improve the system  performance~\cite{zeng2016throughput,johansen2014unmanned} by letting one user (with a better link to the access point) perform as a relay to assist the other weak-link user(s).
For a UAV network,  it has proposed in~\cite{zeng2016throughput} to apply  the UAV as a relay and study the throughput maximization of the system. In addition, experiments on such     UAV-relaying ad hoc networks are     conducted in~\cite{johansen2014unmanned}.
{From a resource allocation perspective, the authors in \cite{tang2018novel}     maximize  the precision of a UAV-aided recommendation system by optimally allocating  the resource  of computing, delay, and traffic resource.
 The allocation of tours of targets to vehicles is investigated in \cite{rathinam2007resource} for a multi-UAV system
  to minimize the sum of the flying distances of UAVs. The     frequency allocation problem is addressed   in~\cite{tang2018ac}    for a UAV-assisted D2D network.}
However, fundamental characterizations and optimal designs for the network of a UAV  in pair with a GU are yet to be identified under both the NOMA and relaying schemes.

Moreover, all the above studies are conducted under the assumption of transmitting arbitrarily reliably at Shannon's capacity. In other words, these results are only accurate for the network with significantly long blocklengths.
Note that both UAV and  GU can be deployed to support latency-critical applications with high reliability requirements,  e.g., remote control.
Due to these critical latency and reliability requirements, data transmissions are realized by codes with short blocklengths, i.e.,  the  networks  operate  in  the  so-called  finite  blocklength (FBL) regime in which the transmissions are no longer arbitrarily reliable~\cite{she2017radio}.
 To tackle this problem,   FBL information theoretic   bounds are developed in \cite{polyanskiy2010channel} for an additive Gaussian noise (AWGN) in a single hop transmission. In addition, the model has been extended to quasi-static fading channels~\cite{Xu_2016,she2017cross},  cooperative relaying networks~\cite{Hu_2016} and NOMA networks~\cite{Hu_2017_PIMRC,NOMA_FBL_2018}.
More recently, a joint blocklength and UAV location optimization is studied in~\cite{Pan_2019} for a FBL network where the UAV is considered as  a flying base-station/relay.
{In addition, the authors in \cite{she2018UAV} consider  a UAV network including   a ground access point (AP) and  UAV-users,  and maximize  the available range of the AP to support FBL  communications for these UAV-users.}
 However,   note that  with  a high probability of having a line-of-sight (LoS) link, a UAV-user generally has   strong channels   from the ground AP and to GUs. On the one hand, significant channel quality difference generally exists between the channels from AP to the UAV-user and     to a GU, which motivates one to apply      NOMA between the two users experiencing the channel difference.
  On the other hand, as the link from the UAV-user to the GU is likely to be strong, this indicates a potential performance improvement (in both IBL and FBL regimes) for the GU when the UAV-user performs as a relay to assist the data transmission to the GU.   Hence, it is essential to study and optimize the performance of such pair of  users.
{To the best of our knowledge, both the IBL and the FBL performances of a UAV-user  paired   with a GU under either the NOMA scheme or the relaying scheme have yet to be     characterized and maximized via optimal resource allocation.}

 In this work, we consider a   ground wireless network supporting UAV transmissions, where a UAV and a GU are served under either the NOMA or relaying scheme.  The throughputs of UAV and GU are characterized in the IBL regime  and the FBL regime, addressing the latency-non-sensitive applications and low-latency high-reliability applications, respectively.
 {Following   these characterizations,   we propose optimal resource allocations to maximize the UAV throughput while guaranteeing the GU's transmission quality.}
The contributions of this paper can be further detailed as follows:
\leftmargini=4mm
\begin{itemize}\itemsep=0.7pt
  \item The throughputs of UAV and GU are characterized in both the IBL and FBL regimes.
  \item  Following   the throughput characterizations,    optimal resource allocation designs are determined  under   the NOMA  and relaying schemes, when the objective is to maximize the UAV throughput while guaranteeing the GU's transmission quality. The designs are addressed  in the IBL regime and the FBL regime, respectively.
  \item We  further address the feasibility of the considered optimization problems.
 {In particular, we prove that the  relaying is able to create a win-win situation, i.e.,   provides transmission service to the UAV while improving the GU's performance.  Moreover, we prove that the relaying scheme potentially offers       a higher throughput to the UAV in the FBL regime than in the IBL regime, as in the FBL regime it likely requires less resources to guarantee the GU's transmission quality and therefore     allocates more resources to   the UAV.}

\end{itemize}

The remainder of the paper is organized as follows:
In Section II, we describe the system model, review the FBL performance metrics and provide the problem statement.
In Section III, throughputs of the considered network are characterized under the  NOMA and relaying schemes, respectively.
Subsequently in Section IV, we  analyze the optimal resource allocation strategies, which maximize the UAV throughput while guaranteeing the GU's transmission quality. The feasibility of the   resource allocation problems are further discussed in Section V.
We provide our simulation results in Section VI
and finally conclude the paper in Section VII.

\section{Preliminaries}

In this section, we first briefly describe the considered scenario of a UAV connected ground wireless network. Subsequently, we introduce the channel model representing the wireless link characteristics. Finally, we review the FBL performance model of a single link transmission in comparison to the IBL performance model.

\subsection{System Description}

We consider a ground wireless network with an AP serving its own GUs. At the same time, a UAV is additionally required to be served beside the GUs. In particular, due to the resource (e.g.,  frequency, power)   limitation in the   network,
the service to the UAV is     provided by using the existing resources
i.e.,  without incurring additional costs in terms of more frequency bands or increased transmit power in the network. To satisfy this condition, one practical approach     is to select a GU and use the frequency   band allocated to this GU to serve both the GU and the UAV jointly, as shown in Fig.\ref{UAVcell}. At the same time, the selected GU's transmission quality (with respect to throughput and reliability) should be guaranteed (in comparison to being solely served) when applying such joint transmission schemes\footnote{{Generally, if we select the GU which has a  poor channel to the AP,     its transmission performance via the AP-GU link (being solely served before paring with the UAV) is   low. Hence a similar transmission performance of this GU is relatively easier to be guaranteed by applying joint transmission schemes to the GU-UAV pair.}}.

\begin{figure}[h]
	\centering
	\includegraphics[width = 0.7\linewidth,trim = 0 10 10 35]{UAVmodelGraph.pdf}
	\caption{An example of the considered network, where the AP-UAV link has the line of sight (LoS), the AP-GU link has no LoS (NLoS), and the UAV-GU link is possible to have the LoS (PLoS).}
	\label{UAVcell}
\end{figure}

We assume that the system operates in a time-slotted fashion where time is divided into frames with a length of $M$ symbols.
The gains of the channels from the AP to the UAV, from the AP to the GU, and from the UAV to the GU are denoted by $G_1$, $G_2$, and $G_3$, respectively.
Then, the   channel gains are modeled by $G_i = z_i 10^{-L_i}$, $i=1,2,3$, where  $L_i$, $i=1,2,3$, represent the path losses (in dB) in   these links.
In addition,  $z_i$, $i=1,2,3$,    denote the gains due to the random channel fading.
In particular, we assume  that channels    experience block-fading, i.e., $z_i$, $i=1,2,3$, are constant within a frame and vary from one frame to the next.

\subsection{IBL Regime vs. FBL Regime}

First of all, it should be pointed out that for a practical communication system, the blocklength is definitely not infinite.
Hence, when we study the performance of such a system in the IBL regime, this only indicates that the impact of the limited length of coding blocks is ignored in the analysis.
In particular, the analysis in the IBL regime follows the assumption which is only true when the blocklength is infinitely long: a packet is
assumed to be decoded with arbitrarily small error probability given that the coding rate is lower than the Shannon capacity.

In an AWGN channel, the Shannon capacity, which quantifies     throughput  in the IBL regime,  is given in bits/symbol~by
\begin{equation}
	C =\log_2(1+\gamma)\, ,
\end{equation}
where $\gamma$ is the signal to     noise ratio (SNR) or signal to interference plus noise ratio (SINR)       at the receiver.

Under the more practical assumption that the coding blocklength is finite, i.e., the system operates in the FBL regime, the decoding error may occur even when   the transmission coding rate is set to be lower than the Shannon capacity.
In  an AWGN channel, the normal approximation of the coding rate $r$ (in bits per channel use) of transmission is derived in~\cite{polyanskiy2010channel}.
 Later on, this approximation is improved to be more tighter in~\cite{Third_Order}, where the third-order term of  the normal approximation is   derived.
 In particular,
with    blocklength $m$, block error probability~$\epsilon$, and SNR (or SINR) $\gamma$, the coding rate $r$ is given by \cite{Third_Order}
\begin{equation} \label{Rfunciton}
\begin{split}
	r &= \mathcal{R}(m, \gamma, \epsilon) \\
	&= \log_2(1+\gamma) - \log_2e\sqrt{\frac{\gamma(\gamma+2)}{(\gamma+1)^2m}}Q^{-1}(\epsilon) + \frac{\log m}{m}  +\frac{o(1)}{l}  \,,
\end{split}
\end{equation}
where $Q^{-1}(x)$ is the inverse $Q$-function and  the $Q$-function is given by $Q(x) = \int_0^{\infty} \frac{1}{\sqrt{2\pi}}e^{-t^2/2}dt$.
On the other hand, when the coding rate is fixed as $r$, the error probability of the transmission is given by
\begin{equation} \label{Rfunciton}
\epsilon = \mathcal{P}(m, \gamma, r)  = Q\left( {\frac{{{{\log }_2}(1 + \gamma ) - r + \frac{{\log m}}{m} -  \frac{o(1)}{l} }}{{{{\log }_2}e\sqrt {\frac{{\gamma (\gamma  + 2)}}{{{{(\gamma  + 1)}^2}m}}} }}} \right).
\end{equation}
According to the characterizations in~\cite{polyanskiy2010channel},  the achievable coding/data rate in the FBL regime increases in the blocklength. In particular, there exists a performance gap between the Shannon capacity and FBL achievable rate.  This performance gap in a single-hop system is numerically shown in Fig.~\ref{Performance-gap}.
{\begin{figure}[!b]
\begin{center}
\includegraphics[width=0.7\linewidth, trim=30 15 30 10]{RegimeGap.pdf}
\end{center}
\caption{Performance gap between the IBL and FBL regimes in a single-hop system with a static channel. The FBL (achievable) rate is calculated according to (2) while  the target error probability is set as $10^{-4}$. }
 \vspace*{-5pt}
\label{Performance-gap}
\end{figure}}
The figure illustrates that the gap is more significant for short blocklengths, and the FBL performance degrades significantly as the blocklength is decreased.

\subsection{Problem Statements}

Our main focus in this work is to investigate the performance of the UAV-connected wireless system. {We propose to apply two transmission schemes and evaluate the throughput to the UAV.} In particular, we address the following fundamental problems: When comparing NOMA and relaying, which one is more preferred under which condition? How to provide an optimal throughput to the UAV (under both the NOMA and relaying schemes) while guaranteeing the GU's transmission quality by applying optimal resource allocation?
What are the performance   differences in the considered network under the IBL and FBL assumptions?  How different the optimal resource allocation solutions are in the FBL regime in comparison to the IBL regime?

\section{Transmission Schemes and Throughput Characterizations}

In this section, we present the NOMA and relaying schemes and characterize the corresponding throughputs in the links    to the UAV and the GU. The characterizations of the two schemes are provided in both the IBL and FBL regimes.

\subsection{IBL Regime}
If the AP serves only its GU and not the UAV,  the   throughput of the GU is given by
\begin{equation}\label{mu_0_IBL}
\mu^{\rm{IBL}}_0 = M \log_2 \left(1+\frac{p_0G_2}{\sigma^2}\right).
\end{equation}

If, on the other hand,  the UAV is served jointly with the GU, the system behavior changes. In the following, we address the throughputs   (including both the UAV and GU) considering the NOMA and relaying schemes, respectively.

\subsubsection{NOMA}
 In the NOMA scheme,   AP transmits two signals $\mathbf{x}_{\text{uav}}$ and $\mathbf{x}_{\text{gu}}$ within the same coding length of $M$ symbols via the same frequency band to the UAV and GU simultaneously.
 Denote by $p_1$ and $p_2$ the per symbol transmit power of the two transmitted signals, i.e., $p_1=\mathbb{E} \{\|\mathbf{x}_{\text{uav}}\|^2\}/M$ and $p_2=\mathbb{E} \{\|\mathbf{x}_{\text{gu}}\|^2\}/M$.
 Note that the AP-UAV link is with high probability to have line of sight (LoS) while the link from the AP to the selected GU (that is paired with the UAV) can experience more severe fading (e.g., due to blockages and multipath fading).
 In other words,  the quality of the AP-UAV link  is higher than that of the AP-GU link, i.e., $G_1>G_2$.  Hence, without loss of generality, in the NOMA process we assume $p_2 > p_1$  and let the UAV apply SIC to cancel the inference of $\mathbf{x}_{\text{gu}}$.

The received signal at the UAV is given by
 \begin{equation}\label{Received_s_uav}
 y_{1} = \sqrt{p_1G_1}\mathbf{x}_{\text{uav}} + \sqrt{p_2G_1}\mathbf{x}_{\text{gu}} + n \, ,
 \end{equation}
 where $n$ denotes the Gaussian noise with power $\sigma^2$.
Note that the interference signal needs to  be successfully cancelled, which requires $\frac{p_2G_1}{p_1G_1+\sigma^2}>\frac{p_2G_2}{p_1G_2+\sigma^2}$.
Moreover, the IBL throughput of the UAV under the NOMA scheme is given by
\begin{equation}\label{muNOMAuavIBL}
\mu^{\rm{IBL}}_{\text{N},1} = M \log_2\left(1+\frac{p_1G_1}{\sigma^2}\right) \, .
\end{equation}

On the other hand, the signal received by the GU is
   \begin{equation}\label{Received_s_ue}
 y_2 = \sqrt{p_1G_2}\mathbf{x}_{\text{uav}}+\sqrt{p_2G_2}\mathbf{x}_{\text{gu}}+n \, .
 \end{equation}
 Decoding the signal $\mathbf{x}_{\text{gu}}$ while treating  $\mathbf{x}_{\text{uav}}$ as   interference, the GU's throughput is given by
 \begin{equation}\label{muNOMAueIBL}
 	\mu^{\rm{IBL}}_{\text{N},2}= M \log_2\left(1+\frac{p_2G_2}{p_1G_2+\sigma^2}\right) \, .
 \end{equation}

\subsubsection{Relaying}
Under the relaying scheme, the UAV becomes both a data receiver and a relay    to forward the GU's data packet.
In this scheme, the total length $M$ of a frame is further divided into two phases with lengths   $m_1$ and $m_2$, satisfying $m_1 +m_2 =M$. In the first phase, the AP transmits a large data packet (containing the messages intended for  both the UAV and GU)  to the UAV.
If the UAV decodes the large data packet correctly and recovers both messages, it forwards the GU's data in the second phase.
Thus, the IBL throughput of  the GU under the relaying scheme is
\begin{equation}\label{RalayIBLue}
 	\mu^{\rm{IBL}}_{\text{R},2}= m_2 \log_2\left(1+\frac{p_2G_3}{\sigma^2}\right) \, .
\end{equation}
Note that the large data transmitted to the UAV includes both the UAV's data and the GU's data.
Hence, under the relaying scheme the throughput via the link to the UAV is given by $m_1 \log_2\left(1+\frac{p_1G_1}{\sigma^2}\right)$, which equals the sum of  the UAV's IBL throughput   $\mu^{\rm{IBL}}_{\text{R},1}$ and the GU's throughput $\mu^{\rm{IBL}}_{\text{R},2}$. Therefore, the IBL throughput of the UAV can be expressed as

\begin{equation}\label{RelayIBLuav}
	\mu^{\rm{IBL}}_{\text{R},1}= m_1 \log_2\left(1+\frac{p_1G_1}{\sigma^2}\right) - \mu^{\rm{IBL}}_{\text{R},2} \, .
\end{equation}

\subsection{FBL Regime}
Note that in the FBL regime, transmissions are not arbitrarily reliable anymore.
We denote by~$\nu_1$ and  $\nu_2$ the reliability requirements of the transmissions to the UAV and the GU, respectively.
When only the GU is served by the BS, the total error probability is exactly the decoding error probability at the GU.
According to~\eqref{Rfunciton}, when the AP only serves the GU, the FBL throughput is given by
\begin{equation}\label{FBL_GU_requirement}
	\mu^{\rm{FBL}}_0 = M\cdot \mathcal {R} \left(M, \frac{p_0G_2}{\sigma^2},
	\nu_2 \right) \cdot (1- \nu_
	) \, ,
\end{equation}

In the following, we discuss the FBL throughput performance of the NOMA and relaying schemes while guaranteeing the GU's reliability requirement.

\subsubsection{NOMA}

In the NOMA scheme, the UE decodes the received signal given in~\eqref{Received_s_ue} by treating $\mathbf{x}_{\text{uav}}$ as   interference.
Hence, the GU's the throughput is given by
\begin{equation}\label{FBLmuUserNOMA}
	\mu^{\rm{FBL}}_{\text{N},2} = M \cdot r_2 \cdot (1-\nu_2) \, ,
\end{equation}
where $r_2=\mathcal{R}\left(M,\frac{p_2G_2}{p_1G_2+\sigma^2},\nu_2\right)$ is the coding rate  of the data to the GU.

On the other hand,
the decoding process at the UAV consists of two steps, i.e.,  UAV first applies SIC and subsequently decodes its own signal. Hence, both the SIC errors and the  decoding errors of the UAV's own signal contribute to the  total error probability.
Denote by $\epsilon_{{\text{SIC}}}$ and $\epsilon_{{\text{N},1}^{\ast}}$
the error probabilities of SIC and decoding the UAV's data packet at the UAV.
Then,     the total error probability of the transmission  to the UAV is given by $1-(1-\epsilon_{{\text{SIC}}})(1-\epsilon_{{\text{N},1}^{\ast}}) $.
Note that the error probability of this SIC process is given by
\begin{equation}
	\epsilon_{\text{SIC}} = \mathcal{P}\left(M,\frac{p_2G_1}{p_1G_1+\sigma^2}, r_2\right) \, .
\end{equation}
Hence, to satisfy the reliability requirement, i.e.,  $1-(1-\epsilon_{{\text{SIC}}})(1-\epsilon_{{\text{N},1}^{\ast}}) = \nu_1$, the target error probability of the UAV's data transmission is required to be set to\footnote{It should be pointed out that the decoding error probability is set as large as possible to ensure the loosest   constraint so that the maximum throughput could be obtained.} $\epsilon_{{\text{N},1}^{\ast}}=1- \frac{1-\nu_1}{1-\epsilon_{\text{SIC}}}$.

After successfully applying the SIC, the UAV subsequently decodes it own data.
The FBL throughput of the UAV in the NOMA scheme is given by
\begin{equation}\label{muNOMAuavFBL}
	\begin{split}
	\mu^{\rm{FBL}}_{\text{N},1}  &= M \cdot  r_1 \cdot (1-\epsilon_{{\text{SIC}}})(1-\epsilon_{{\text{N},1}^{\ast}}) \\
	& = M \cdot  r_1 \cdot (1-\nu_1),
	\end{split}
\end{equation}
where $r_1 = \mathcal{R}(M, \frac{p_1G_1}{\sigma^2}, \epsilon_{{\text{N},1}^{\ast}})$ is the coding rate of the data packet to the UAV.

\subsubsection{Relaying}

Under the relaying scheme, the AP first transmits a large data packet in first phase to the UAV.
The decoding error probability of this transmission is exactly the total error probability of  the UAV's data transmission, i.e., it is required to satisfy the reliability constraint~$\nu_1$.
Hence, the FBL throughput of the transmission to the UAV, including the data for both UAV and GU,  is given by
\begin{equation}
\mu^{\rm{FBL}}_{\text{R},1+2} = m_1 \cdot \mathcal {R}\left(m_1, \frac{p_1G_1}{\sigma^2}, \nu_1\right)\cdot (1-\nu_1)\, .
\end{equation}

As long as the UAV's decoding process is successful, the UAV forwards the GU's data packet in the second phase.
Denote by the $\epsilon_{{\text{R},2}^{\ast}}$ the target decoding error probability at the GU. According to the total reliability constraint of GU $\nu_2$, it holds that $\nu_2=1-(1-\nu_1)(1-\epsilon_{{\text{R},2}^{\ast}})$. Hence, we have $\epsilon_{{\text{R},2}^{\ast}} =1- \frac{1-\nu_2}{1-\nu_1}$.
Then, the GU's FBL throughput is given by
\begin{equation}
\begin{split}
    	\mu^{\rm{FBL}}_{\text{R},2} &= m_2   \mathcal {R}\left(m_2, \frac{P_2G_3}{\sigma^2}, \epsilon_{{\text{R},2}^{\ast}}\right)\cdot(1-\nu_1)(1-\epsilon_{{\text{R},2}^{\ast}})\\
    	&=m_2   \mathcal {R}\left(m_2, \frac{P_2G_3}{\sigma^2}, \epsilon_{{\text{R},2}^{\ast}}\right)\cdot(1-\nu_2) \, .
\end{split}
\end{equation}
Finally, the UAV's throughput can be obtained as
\begin{equation}\label{FBLRelay}
	\mu^{\rm{FBL}}_{\text{R},1}  =  m_1 \cdot \mathcal {R}\left(m_1, \frac{p_1G_1}{\sigma^2}, \nu_1\right)\cdot (1-\nu_1) - \mu^{\rm{FBL}}_{\text{R},2} \, .
\end{equation}

So far, we have characterized the throughput performance of the considered NOMA and relaying schemes in both the IBL and FBL regimes. Following these characterizations, we provide the corresponding optimal resource allocation designs in the next section.

\section{Resource Allocation for Maximal UAV Throughput}

In this section, by applying resource allocation, we investigate the optimal UAV throughput  under both the NOMA and relaying schemes.
{Our objective is to maximize the throughput without using any additional resources (e.g., in terms of transmission blocklength and  transmit power),
while guaranteeing the GU's transmission requirements including throughput and reliability (in the FBL case).} In particular, we seek to guarantee the GU a weighted throughput level of $\beta \mu_0$, where $\mu_0$ is the GU throughput if the UAV is not jointly served, and $\beta >0$ is the minimum rate coefficient, which is a key factor  that indicates the level of service guarantee. For example, $\beta<1$ indicates that
only partial throughput can be provided to the GU in comparison to the   case in which the UAV is not serviced. On the other hand, $\beta>1$ represents the scenario in which GU performance is required to be better than the non-UAV-connected case.

\subsection{UAV Throughput Maximization under the NOMA Scheme }

According to \eqref{muNOMAuavIBL} and \eqref{muNOMAuavFBL},
the UAV throughput in the NOMA scheme can be maximized by choosing an optimal $p_1$.
The general optimization problem of the NOMA scheme (in both the IBL and FBL regimes) is formulated as:
\begin{maxi!}|s|[2]
{p_1}{\mu_{\text{N},1}}
{\label{NOMA_PA_or}}{}
\addConstraint{\mu_{\text{N},2}}{\geq \beta \mu_{0} \label{NOMAg}}
\addConstraint{p_1+p_2} {\leq p_0 },{\quad p_1,p_2 \in R^+ \, . \label{NOMAp}}
\end{maxi!}
We have the following proposition for the above problem
\begin{prop}\label{strict_bound}
	The optimal throughput offered to the UAV is obtained when the inequality constraints in~\eqref{NOMAg} and~\eqref{NOMAp} are satisfied with equality.
\end{prop}
\begin{proof}
 We prove the result by contradiction. Regarding the sum power constraint in \eqref{NOMAp},  we first assume that there exists an optimal solution $(p_1', p_2')$ satisfying the constraints with strict inequality, i.e. $p_0 - p_1'+p_2' = p_n'>0$. Hence the optimal throughput offered to the UAV and the GU are $\mu_{uav}$ and $\mu_{gu}$. On the other hand, we could further allocate the power left to UAV $p_1''$ and GU $p_2''$ in proportion to $p_1'$ and $p_2'$.Thus the data rate to the GU is $c_{gu} = \log_2\left(1+\frac{(p_2'+p_2'')G_2}{(p_1'+p_1''+ p_2'+p_2'')G_2+\sigma^2}\right)$. Since $\frac{(p_2'+p_2'')G_2}{(p_1'+p_1''+ p_2'+p_2'')G_2+\sigma^2} > \frac{p_2'G_2}{(p_1'+p_2')G_2 + \frac{\sigma^2 p_1'}{p_1'+p_1''}}$, the GU could get more throughput. At the same time, the data rate of UAV is $c_{uav} = \log_2\left(1+\frac{(p_1'+p_1'')G1}{\sigma^2}\right)$, and thus the throughput to the UAV is also higher. Therefore, the assumption that $(p_1', p_2')$ is the optimal solution to the problem is violated. i.e., the optimal power allocation satisfies \eqref{NOMAp} with equality.

  Similarly, the strict equality   of~\eqref{NOMAg} and guaranteeing constraint can be proved.
\end{proof}

According to Proposition~\ref{strict_bound}, the original optimization problem for the NOMA scheme is equivalent to
\begin{maxi!}|s|[2]
{p_1}{\mu_{\text{N},1}}
{\label{NOMA_PA}}{}
\addConstraint{\mu_{\text{N},2}}{= \beta \mu_{0}} \label{NOMA_PAb}
\addConstraint{p_1+p_2}{= p_0 },{\quad p_1,p_2 \in R^+}.\label{NOMA_PAc}
\end{maxi!}
We in the following solve the optimization problem given in~\eqref{NOMA_PA}  in the IBL and FBL regimes, respectively.

\subsubsection{UAV Throughput Maximization under the NOMA Scheme in the IBL Regime}
According to~\eqref{muNOMAueIBL}, constraint \eqref{NOMA_PAb} is equivalent to the following equation

\begin{equation}
\label{NOMA_snr_gu}
\gamma^{\rm{IBL}}_{\text{gu}} \triangleq	\frac{p_2G_2}{p_1G_2+\sigma^2} = 2^{\frac{\beta \mu^{\rm{IBL}}_{0}}{M}} + 1,
\end{equation}
where $\gamma^{\rm{IBL}}_{\text{gu}}$ represents the received SINR for the GU   when decoding its own data packet.
Clearly, $\gamma^{\rm{IBL}}_{\text{gu}}$ is a constant for a given $\beta$.

According to \eqref{NOMA_PAc},  $p_2 = p_0 - p_1$ holds. Substituting this into  \eqref{NOMA_snr_gu}, the optimal solution (of the NOMA scheme in the IBL regime) to Problems \eqref{NOMA_PA_or} and \eqref{NOMA_PA} is given by

\begin{equation}\label{SINR_P_2}
	p^{\rm{IBL}}_{{{\rm{N}},1}^*}
	= p_0 - \frac{\gamma^{\rm{IBL}}_{\text{gu}} p_0G_2+\gamma^{\rm{IBL}}_{\text{gu}} \sigma^2}{G_2\left(1+\gamma^{\rm{IBL}}_{\text{gu}}\right)}.
\end{equation}

By inserting $p_1=p^{\rm{IBL}}_{{{\rm{N}},1}^*}$ and $p_2=p_0-p_1$ into \eqref{muNOMAuavIBL},  the optimal throughput of the UAV is obtained.

\subsubsection{UAV Throughput Maximization under the NOMA Scheme in the FBL Regime}
 Similarly, in the FBL regime, to guarantee  constraint   \eqref{NOMA_PAb}, the coding rate of the data packet to the GU should satisfy  $r_2 = \frac{\beta \mu^{\rm{FBL}}_0}{M(1-\nu_2)}$.
  Hence, according to \eqref{FBLmuUserNOMA} the SINR at the GU should satisfy
 \begin{equation}
 	\gamma^{\rm{FBL}}_{\text{gu}} = \mathcal{P}^{-1}(M, \nu_2, r_2).
 \end{equation}
By substituting $p_2 = p_0-p_1$, the optimal power allocation is obtained as
\begin{equation}
    p^{\rm{FBL}}_{{{\rm{N}},1}^*}
	= p_0 - \frac{\mathcal{P}^{-1}(M, \nu_2, r_2) (p_0G_2+ \sigma^2)}{G_2\left(1+\mathcal{P}^{-1}(M, \nu_2, r_2)\right)}.
\end{equation}
Hence, we have $p_2 = p_0 - p^{\rm{FBL}}_{{{\rm{N}},1}^*}$. Then, the   optimal throughput of the UAV and the corresponding throughput of GU in the FBL regime can be immediately  calculated according to \eqref{muNOMAuavFBL} and \eqref{FBLmuUserNOMA}.

\subsection{UAV Throughput Maximization under the Relaying Scheme }
{In the relaying scheme, the total frame length of $M$ symbols is separated into two phases with lengths of $m_1$ and $m_2$.}
Hence, to maximize the throughput of the UAV in  the IBL regime given in~\eqref{RelayIBLuav}  and in the FBL regime given in~\eqref{FBLRelay}, the optimal transmit powers $p_1$ and $p_2$ as well as  the optimal blocklengths $m_1$ and $m_2$ should be determined. The optimization problem in the relaying scheme is formulated as:
\begin{maxi!}|s|[2]
{p_1,m_1}{\mu_{\text{R},1}}
{\label{Relaying_JA}}{}
\addConstraint{\mu_{\text{R},1}}{\geq 0} \label{Relaying_JAb}
\addConstraint{\mu_{\text{R},2}}{\geq \beta \mu_{0}  \label{guaranteeUEJL2}}
\addConstraint{m_1p_1+m_2p_2}{\leq Mp_0},{\quad p_1,p_2 \in R^+}\label{resourceP2}
\addConstraint{m_1+m_2}{\leq M \label{resourceM}},{\quad m_1,m_2 \in R^+},
\end{maxi!}

\vspace{-.3cm}
\noindent where the constraint \eqref{Relaying_JAb} indicates that the   throughput of the first phase  should be higher than the second phase.
Similar to the discussion in Proposition~1, the inequalities in    \eqref{guaranteeUEJL2}, \eqref{resourceP2} and  \eqref{resourceM} should be satisfied with equality
 to maximize ${\mu_{\text{R},1}}$. Hence, the above problem is equivalent to
\begin{maxi!}|s|[2]
{p_1,m_1}{\mu_{\text{R},1}}
{\label{Relaying_JAe}}{}
\addConstraint{\mu_{\text{R},1}}{\geq 0} \label{Relaying_JAbe}
\addConstraint{\mu_{\text{R},2}}{= \beta \mu_{0} \label{guaranteeUEJLe}}
\addConstraint{m_1p_1+m_2p_2} {= Mp_0 ,\label{resourcePe}}{\!\!\! \!\!\! \!\!\! p_1,p_2 \in R^+}
\addConstraint{m_1+m_2}{= M \label{resourceMe}},{\quad m_1,m_2 \in R^+}.
\end{maxi!}
In the following, we solve the problem
in both the IBL and FBL regimes.

\subsubsection{UAV Throughput Maximization   under the Relaying Scheme in the IBL Regime}
We first propose the following key proposition to solve Problem~\eqref{Relaying_JAe} in the IBL regime.
\begin{prop}\label{convexity_prop2}
	Problem~\eqref{Relaying_JAe} is convex in the IBL regime.
\end{prop}
\begin{proof}
Note that  $\mu_{\text{R},2}=\beta \mu^{\rm{IBL}}_0$. Hence, we have $p_2 = \frac{\sigma^2}{G_3} (2^{\frac{ \beta \mu^{\rm{IBL}}_0 }{M-m_1}}-1)$.
To guarantee \eqref{resourcePe} and \eqref{resourceMe}, we should have
\begin{equation}
\label{p_1inproof}
  p_1 = \left(Mp_0-(M-m_1)\left(2^{\frac{ \beta \mu_0}{M-m_1}}-1\right)\sigma^2/G_3\right)/m_1.
\end{equation}

Substituting~\eqref{p_1inproof} into  \eqref{RelayIBLuav}, the   throughput can be expressed as
\begin{equation}\label{objectiveformulate}
\begin{split}
	\mu^{\rm{IBL}}_{\rm{R},1} =  & ~m_1\log_2\!\!\left(\!1\!+\!\frac{\left(Mp_0\!-\!(M\!-\!m_1)\frac{2^{\frac{\beta \mu_0}{M-m_1}}-1}{G_3}\sigma^2\right)G_1}{m_1\sigma^2}\right) \\
	&-\beta \mu_0,
\end{split}
\end{equation}
in terms of the single variable $m_1$.
Hence, the proposition is proved {if $\mu^{\rm{IBL}}_{\rm{R},1}$ in \eqref{objectiveformulate} is   concave in $m_1$}.
We show this concavity as follows.

First, we introduce an auxiliary function $t$ with respect to~$m_1$
\begin{equation}
	t  = \left(Mp_0-(M-m_1)\frac{2^{\frac{\beta \mu_0}{M-m_1}}-1}{G_3}\sigma^2\right)\frac{G_1}{\sigma^2}.
\end{equation}

We further obtain the first and second order derivatives of $t(m_1)$:
\begin{equation}
	\frac{\partial t}{\partial m_1} = \frac{G_1}{G_3}\left(2^{\frac{\beta \mu_0}{M-m_1}}-1-\frac{\beta \mu_0 \log_e(2)}{M-m_1}2^{\frac{\beta \mu_0}{M-m_1}}\right).
\end{equation}
By introducing $g=2^{\frac{\beta \mu_0}{M-m_1}} \ge 0$, we have
\begin{equation}\label{firstpar}
	\frac{\partial t}{\partial m_1} = \frac{G_1}{G_3}\left((1-g\log_e2)2^g-1\right) \le 0.
\end{equation}
In addition, we have
\begin{equation}\label{secpar}
	\frac{\partial^2t}{\partial m_1^2} = - \frac{G_1}{G_3}\frac{\beta^2M^2(\log_e2)^2 2^{\frac{\beta \mu_0}{M-m_1}}}{2(M-m_1)^3} \le 0.
\end{equation}

Then, the objective in (\ref{objectiveformulate}) can be   expressed as
\begin{equation}\label{Obj4Hessian}
	\mu^{\rm{IBL}}_{\rm{R},1}  = m_1\log_2\left(1 + \frac{t }{m_1}\right) - \beta \mu_0.
\end{equation}
We can obtain the   second order derivative of $\mu^{\rm{IBL}}_{\rm{R},1}$
with respect to $m_1$ as
\begin{equation}\label{toproveconcave}
	 \frac{\partial^2 \mu^{\rm{IBL}}_{\rm{R},1} }{{\partial {m_1}^2}}=
	 \frac{m_1^3\frac{\partial^2t}{\partial m_1^2}\!-\!m_1^2 (\frac{\partial t}{\partial m_1})^2\!-\!t ^2\!\!+\!m_1^2t \frac{\partial ^2t}{\partial m_1^2}\!\!+\!2t (\frac{\partial t}{\partial m_1})^2}{\log_e(2)(m_1+t )^2},
\end{equation}
where
$m_1$ is by definition positive.
According to~\eqref{firstpar} and~\eqref{secpar}, $\frac{\partial^2 \mu^{\rm{IBL}}_{\rm{R},1} }{{\partial {m_1}^2}}\le0$ holds.
\end{proof}

According to Proposition~\ref{convexity_prop2}, Problem~\eqref{Relaying_JAe} can be solved efficiently in the IBL regime.

\

\subsubsection{UAV   Throughput Maximization under the Relaying Scheme in  the FBL Regime}
Note that the $\mathcal{R}$ function in \eqref{Rfunciton} is not concave. Hence, the objective function in Problem \eqref{Relaying_JAe} is not concave in the FBL regime, i.e.,  Problem \eqref{Relaying_JAe} is not convex. In the following, we solve the problem in the FBL regime by utilizing the monotonic property.

\begin{prop}\label{Monoton_prop3}
 The objective of Problem \eqref{Relaying_JAe} is a monotonic function with respect to  two variables $p_1$ and $m_1$, if the blocklength and reliability requirements are within a range of practical interest,  i.e., $m\geq 84$ (which is the smallest blocklength in  LTE-A) and $\epsilon<10^{-1}$.
\end{prop}

\begin{proof}
Clearly the proposition holds if it is shown that $r= \mathcal{R}(m_1,\gamma_1,\epsilon_{\text{uav}})$ is monotonically increasing in both $\gamma_1$ and $m_1$.

The first derivatives of $r$ with respect to $\gamma_1$ and $m_1$ are given by
\begin{equation}\label{partialp1}
	\frac{\partial r}{\partial \gamma_1} =  \frac{(\gamma_1+1)\sqrt{\gamma_1^2+2\gamma_1}-Q^{-1}(\epsilon_{\text{uav}})/m_1}{(1+\gamma_1)^2\sqrt{\gamma_1^2+2\gamma_1}} \log_e2 \, ,
\end{equation}
\begin{equation}\label{partialr1}
	\frac{\partial r}{\partial m_1} = \frac{1}{2} Q^{-1}(\epsilon_{\text{uav}})\sqrt{\frac{\gamma_1(\gamma_1+2)}{(\gamma_1+1)^2m_1^3}} \log_e2+\frac{1-\log m_1}{m_1^2} \, .
\end{equation}

We assume that in our scenario the SNR is higher than 0 dB, i.e., $\gamma>1$ and the practical value of $m_1>84$ and $Q^{-1}(\epsilon_{\text{uav}}) \in (2.3263, 5.9978)$.
For \eqref{partialp1},  if $(\gamma_1+1)\sqrt{\gamma_1^2+2\gamma_1}>1$ and $Q^{-1}(\epsilon_{\text{uav}})/m_1<1$ hold, then $\frac{\partial r}{\partial \gamma_1}>0$.
For \eqref{partialr1}, if we denote   $c=\frac{1}{2}\log_e2\cdot Q^{-1}(\epsilon_{\text{uav}})\sqrt{\frac{\gamma_1(\gamma_1+2)}{(\gamma_1+1)^2}}$ for short, the minimum of $\frac{\partial r}{\partial \gamma_1}$ is obtained at $m_1'=(\frac{2}{c})^2$. For $m_1\in (m_1',M]$, \eqref{partialr1} is increasing in $m_1$.
 For $m_1>84$, to guarantee     $\frac{\partial r}{\partial m_1}>0$,
 $c>0.3743$ is required. As for the practical values mentioned above, $\frac{1}{2}\log_e2Q^{-1}(\epsilon_{\text{uav}})\sqrt{\frac{\gamma_1(\gamma_1+2)}{(\gamma_1+1)^2}}\geq 0.4031>0.3743$ holds. We thus have $\frac{\partial r}{\partial m_1}>0$.
\end{proof}

As the objective function is monotonic increasing with respect to both variables $m_1$ and $p_1$, the problem can be solved by applying the framework of monotonic optimization \cite{zhang2013monotonic}, resulting in a global optimum.

\section{Feasibility Analysis on Guaranteeing the Weighted Throughput of the GU}

{So far, we have characterized the IBL and FBL throughputs under both the NOMA and relaying schemes and provided   corresponding optimal resource allocation designs while guaranteeing the weighted throughput of the GU, i.e., guaranteeing $\beta \mu_0$.} In this section, we provide a feasibility discussion on $\beta$ for both     schemes.

We start with the NOMA scheme and introduce the following proposition
\begin{prop}\label{FBLgeqIBLpro_NOMA}
    Under the NOMA scheme, the feasible range of $\beta$ values is $\beta \in [0,1]$ in both the IBL regime and FBL regime.
\end{prop}
\begin{proof}
    Recall  that for both the IBL and FBL regimes, under the NOMA scheme the GU decodes the received signal based on the SINR $\gamma_2 = \frac{p_2G_2}{p_1G_2+\sigma^2}$.

    Under the power constraint $p_0=p_1+p_2$, we have $\max\limits_{p_1} \gamma_2  = \frac{p_0G_2}{\sigma^2}$, which is exactly the SNR of the GU when it is being solely served by the network. In such a   case, $p_1=0$ and $p_2=p_0$, which indicates that allocating zero power to the UAV only guarantees $\beta=1$.
    Hence, the proposition is verified.
\end{proof}

{Proposition~\ref{FBLgeqIBLpro_NOMA} indicates that when additionally serving the UAV (with a positive throughput) under the NOMA scheme, part of the GU's throughput is sacrificed.} On the other hand, the sum throughput of the UAV and the GU is boosted, as the channel from the AP to the UAV is much stronger than the one to the GU.

Next, we discuss the relaying scheme and have the following proposition
\begin{prop}\label{FBLgeqIBLpro_Relay}
    For the relaying scheme, the feasible value of $\beta$ is possible to be higher than~$1$. In such case, a win-win situation is created, i.e., the UAV is additionally served while the GU's performance is improved.
\end{prop}

\begin{proof}
We first show that    $\beta\geq 1$ possibly holds  under the relaying scheme by considering the following example.
We  consider
a relaying scheme

 with $m_1=m_2=M/2$.
Note that the IBL throughput to the UAV is non-negative, i.e., $\frac{M}{2}{\log _2}\left(1 + \frac{{{p_1}{G_1}}}{{{\sigma ^2}}}\right) - \beta M{\log _2}\left(1 + \frac{{{p_0}{G_2}}}{{{\sigma ^2}}}\right) \ge 0$.
Hence, we have
\begin{equation}
 \begin{split}
& \beta  > 1 \\
 \Leftrightarrow~~  &{\log _2}\left(1 + \frac{{{p_1}{G_1}}}{{{\sigma ^2}}}\right) - {\log _2}{\left(1 + \frac{{{p_0}{G_2}}}{{{\sigma ^2}}}\right)^2} > 0 \\
 \Leftrightarrow~~ & \left(1 + \frac{{{p_1}{G_1}}}{{{\sigma ^2}}}\right) > {\left(1 + \frac{{{p_0}{G_2}}}{{{\sigma ^2}}}\right)^2}.
\end{split}
\end{equation}
Note that the channel from the AP to the UAV is generally   LoS and the link from the AP to the selected GU (in pair with the UAV) is generally weak, i.e., it is more likely that  ${G_1} \gg {G_2}$. Hence, there exist  feasible  $p_1$ and $p_0$, which satisfy    $\left (1 + \frac{{{p_1}{G_1}}}{{{\sigma ^2}}}\right) > {\left(1 + \frac{{{p_0}{G_2}}}{{{\sigma ^2}}}\right)^2}$.

The possibility of  $\beta\geq 1$ can be also proved in the IBL regime
based on the following Lemma~\ref{FBLgeqIBLpro_Relay2} which provides that  if $\beta>1$ is   guaranteed in the IBL regime, it also possibly holds in the FBL regime.
\end{proof}

\begin{lem}\label{FBLgeqIBLpro_Relay2}
    In the relaying scheme with   given $\beta$,   $m_1$ and $m_2$, under certain conditions guaranteeing GU's transmission quality in the FBL regime requires less transmit power  $p_2$ to GU  than guaranteeing it in the IBL regime.
\end{lem}

\begin{proof}
We prove Lemma~\ref{FBLgeqIBLpro_Relay2} by discussing the special case in which we have     $\beta = 1$, $m_1=m_2=M/2=m$ and the reliability constraint of UAV is much lower than the GU, i.e., $\nu_1 \ll \nu_2$. In addition, we consider a reliable transmission scenario where the SNRs of all links are higher than 1.

In the IBL regime, according to \eqref{RalayIBLue},  the throughput requirement of the GU is  $\log_2(t_2) = 2\log_2{t_0}$,  where we have defined
 $t_0=1+\frac{p_0G_2}{\sigma^2}$.
Then, the IBL throughput of the UAV is obtained by
\begin{equation}
   	c = \log_2(t_1)-\log_2(t_2) =\log_2\frac{t_1}{t_2},
\end{equation}
 where $t_1=1+\frac{p_1G_1}{\sigma^2}$ and $t_2=1+\frac{p_2G_3}{\sigma^2}$.

In the FBL regime, the GU's throughput requirement is given in \eqref{FBL_GU_requirement}.
Noting that $\nu_1 \ll \nu_2$,  we have $\epsilon_{\rm{R},2}=\nu_2- \nu_1 + \nu_1\epsilon_{\rm{R},2} \approx \nu_2$, i.e.,
$Q^{-1}(\nu_2) \approx Q^{-1}(\epsilon_{\rm{R},2}) $.
We define
$A =  Q^{-1}(\nu_2) \log_2 e \approx Q^{-1}(\epsilon_{\rm{R},2}) \log_2 e$   and $B = \frac{\log_2 m_1}{m_1} = \frac{\log_2 m_2}{m_2}$.
In addition, we denote $t_2'=1+\frac{p_2'G_3}{\sigma^2}$ and $t_1'=1+\frac{p_1'G_1}{\sigma^2}$ where $p_1'$ and $p_2'$ are the power allocation results in the FBL regime. Then, the GU's throughput requirement   given in \eqref{FBL_GU_requirement} can be represented by
\begin{equation}
 	\log_2t_2'-A\sqrt{1-\frac{1}{(t_2')^2}} - B = 2 \left(\log_2t_0-A\sqrt{1-\frac{1}{t_0^2}} - B\right).
\end{equation}
Hence, we have
\begin{equation}
 	\log_2t_2' = 2 \log_2t_0 - A\left(2\sqrt{1-\frac{1}{t_0^2}}-\sqrt{1-\frac{1}{t_2'^2}}\right) - B.
\end{equation}

Noting that SNRs are higher than 1, we have both $t_0>2$ and $t_2'>2$ hold. Therefore $2\sqrt{1-\frac{1}{t_0^2}}-\sqrt{1-\frac{1}{t_2'^2}}\geq 0$ by transforming into $3\geq \frac{4}{t_0^2} - \frac{1}{t_2'^2}$, which is obviously valid. Thus $\log_2t_2' < \log_2t_2$ holds, which is equivalent to $p_2'<p_2$. This indicates that more resources could be allocated for the first hop, i,e, the serving quality of UAV is better than that calculated in the IBL regime.
\end{proof}

\section{Simulation Results and Discussion}

In this section, we provide our simulation results.
We first validate our analytical model and subsequently evaluate the IBL and FBL performances of the considered network. The   simulation results are conducted under the following parameter setups. First, we consider a 3-dimensional topology where the AP is deployed at point $(0,0,20)$, while the UAV and GU positions are set to $(100,0,100)$ and $(700,0,0)$.
In addition, the total transmit power  is   $p_0 = 1 W =30 \rm{dBm}$ while  the noise power

is $\sigma^2 = -80 \rm{dBm}$. Moreover, we set the frame length to $M=400$ symbols. Finally, for the analysis in the FBL regime, the target error probabilities of the transmissions to the UAV and the GU are set to $\nu_1=10^{-4}$ and $\nu_2=10^{-3}$, respectively.
Moreover, noting that the    AP-GU link, the AP-UAV link, and the UAV-GU link have different    probabilities of LoS, in the simulation we consider the following path loss formulations.
We adopt the general path loss model from~\cite{rappaport1996wireless}, which  is given by
\begin{equation}
	L_i = L(d_0) + 10\alpha_i \cdot \log\left(\frac{d_i}{d_0}\right) \, ,
\end{equation}
where $L(d_0)$ is determined by the free space path loss at reference distance $d_0 = 100$m. In addition,  $\{\alpha_i\}$ for $i = 1,2,3$  are the path loss exponents, which are potentially different for the three links with different probabilities of LoS.
In particular, we adopted the setups from~\cite{rappaport1996wireless} and set  $\alpha_1 = 2$ for the AP-UAV link (with LoS) and $\alpha_2=3.5$ for the AP-GU link (without LoS).
Moreover,  following the model in~\cite{azari2018ultra}, we have the following path loss exponent for the UAV-GU link:
	$\alpha_3 = a_1\cdot P(\theta) + b_1$,
where $P(\theta) = \frac{1}{1+a_2e^{-b_2(\theta-a_2)}}$ is the probability of the LoS between UAV and GU, as introduced in \cite{al2014optimal}.
In addition,
we set $a_1 = -1.5$, $a_2 = 2$, $a_2=9.61$, and $b_2=0.16$, according to the rural area setup in~\cite{alzenad20183}.

\subsection{Validations}
In this subsection, we validate our analytical model via simulation and numerical results that depict the instantaneous performances within a single frame.
\begin{figure}[t]
    \centering
    \subfigure[The IBL throughput of UAV  ($\beta=0.5$).]{
    \label{fig:validprop1_beta4}
    \includegraphics[width=0.95\linewidth, trim= 0 0 0 0]{prop_1_3d.pdf}
    }
    \subfigure[Power allocation with different setups of $\beta$]{
    \label{fig:validprop1_betaMul}
    \includegraphics[width=0.95\linewidth, trim= 0 0 0 0]{prop_1_multi.pdf}
    }
    \caption{Validation of optimal method by comparing with exhaustive search.}
    \label{fig:validprop1}
    \vspace{-.3cm}
\end{figure}
\begin{figure}[t]
    \centering
    \includegraphics[width=0.95\linewidth, trim = 0 0 0 0]{prop_2.pdf}
    \caption{Validation of convexity of the relaying scheme in the IBL regime.}
    \label{fig:validprop2}
\end{figure}

We start with Fig.~\ref{fig:validprop1} to show the impact of power allocation on the UAV throughput.
{ The figure has two parts, i.e.,  Fig.~\ref{fig:validprop1_beta4} and Fig.~\ref{fig:validprop1_betaMul}. }
 In particular,  Fig.~\ref{fig:validprop1_beta4} provides the all the feasible values of   IBL throughput of the UAV under the NOMA scheme, i.e.,  the objective in Problem \eqref{NOMA_PA_or},
while satisfying the inequality  constraints \eqref{NOMAg} and  \eqref{NOMAp}.
In addition, the optimal solution to Problem \eqref{NOMA_PA_or} obtained via exhaustive search is also provided in the figure as a red point.
The two cut-surfaces crossing the  optimal solution point  actually represent the equality cases of \eqref{NOMAg} and  \eqref{NOMAp}.
Clearly, Fig.~\ref{fig:validprop1_beta4} shows that under the scenario that $\beta=0.5$, the optimal solution satisfies       \eqref{NOMAg} and  \eqref{NOMAp} with equality. Moreover, a set of corresponding results are provided in Fig.~\ref{fig:validprop1_betaMul}, where different values of $\beta$ are considered. Again, it is observed that the optimal solutions are exactly the crossing points where the  power constraint and the GU's throughput constraint hold with equality, verifying Proposition~1.

Next, we consider the relaying scheme in the IBL regime.
In Fig.~\ref{fig:validprop2}, we show the relationship among the IBL throughput of UAV,  blocklength $m_1$ and transmit power $p_1$,   when $\beta = 1.0$.
Note that only the feasible vaules of the UAV's throughput are visible, i.e. the blocklength and power allocation must satisfy the constraints in \eqref{Relaying_JA}.
Clearly, it is observed that the UAV throughput in the IBL regime is concave in $m_1$ and $P_1$, confirming the characterization in Proposition~\ref{convexity_prop2}.

In addition, in Fig.~\ref{fig:validprop3_BL} we investigate the relationship between the throughput of the UAV with the blocklength $m_1$, while different values of the transmit power $p_1$ are considered.
{ Fig.~\ref{fig:validprop3_BL} shows that the UAV throughput is monotonically increasing in the blocklength of the first hop within the feasible set. Note that the sudden cut after each curve achieving its maximum value is due to the feasibility criterion, i.e.  the  constraint to guarantee GU's performance is violated   if a blocklength longer than that required at the maximum point is allocated.}
In parallel, the impact of transmit power $p_1$ on the throughput of the UAV is given in Fig.~\ref{fig:validprop3_P} for different values of the blocklength $m_1$.
{It is observed that the UAV throughput is monotonically increasing in the transmit power allocated to the first hop within the feasible set.
In other words,
Fig.~\ref{fig:validprop3} confirms    Proposition~\ref{Monoton_prop3} that the UAV throughput under the relaying schemes is a monotonic function with respect to
 $p_1$ and $m_1$ within the corresponding feasible sets.  }

\begin{figure}[t]
    \centering
    \subfigure[Monotonic increasing throughput in blocklength]{
    \label{fig:validprop3_BL}
    \includegraphics[width=0.95\linewidth, trim= 0 0 0 0]{prop_3_bl.pdf}
    }
    \subfigure[Monotonic increasing throughput in power]{
    \label{fig:validprop3_P}
    \includegraphics[width=0.95\linewidth, trim= 0 5 0 -10]{prop_3_p.pdf}
    }
    \caption{Validation of monotonicity of relaying scheme in the FBL regime.}
    \label{fig:validprop3}
      \vspace{-.27cm}
\end{figure}
\begin{figure}[t]
	\centering
	\includegraphics[width = 0.84\linewidth, trim= 10 10 0 -23]{EdgeUser.pdf}
	\caption{Performance comparison between NOMA and Relaying in both IBL and FBL regimes for GU at $700$ m.}
	\label{fig:EdgeUser}
\end{figure}

Moreover, Fig.~\ref{fig:EdgeUser} studies the throughput of the UAV while comparing the NOMA and the relaying schemes in both the IBL and the FBL regimes. In the simulation, we vary the minimum rate coefficient     $\beta$ from 0.5 to 2. The throughput of the UAV under the NOMA scheme is depicted using circle markers, while the performance under the relaying scheme is shown with a plus marker. The solid lines represent the performance in the IBL regime and the dashed line is indicating the performance in the FBL regime.

It is evident in Fig. \ref{fig:EdgeUser} that the feasible ranges of the  minimum rate coefficient  are different in the two schemes.
{In particular, the NOMA curves drop rapidly as $\beta$ gets close to $1$.} This confirms   Proposition~\ref{FBLgeqIBLpro_NOMA} that  the NOMA scheme only serves the UAV with $\beta \in [0,1]$ in both the IBL and FBL regimes.
On the other hand, the relaying scheme could offer more throughput ($\beta > 1$) to the GU and serve the UAV simultaneously, i.e., offer a win-win strategy, which matches our characterization in Proposition~\ref{FBLgeqIBLpro_Relay}.
In addition, we could observe from Fig. \ref{fig:EdgeUser} that under the NOMA scheme, the throughput of the UAV in the FBL regime is smaller than the throughput in the IBL regime.
More interestingly, the FBL throughput under the relaying scheme is higher than the IBL throughput when $\beta$ is higher than 0.6. This   verifies Proposition~\ref{FBLgeqIBLpro_Relay2} that under the relaying scheme,  it is possible that less resource is required in the FBL regime (than in the IBL regime) to guarantee the GU's transmission quality, i.e., more resources could be spent for the UAV.
\begin{figure}[t]
	\centering
	\includegraphics[width = 0.95\linewidth, trim= 5 7 0 21]{UAV_MoreInFBL.pdf}
	\caption{The UAV throughput in the IBL and the FBL regimes. In the figure, we set $\beta=1$.}
	\label{FBLgeqIBL}
\end{figure}

Next, we      show the impact of  $m_1$ on the throughput of the UAV  in Fig.~\ref{FBLgeqIBL} where     results in both the IBL and FBL regimes are provided.
The difference between  Fig.~\ref{FBLgeqIBL}  and Fig.~\ref{fig:validprop3_BL} is that the transmit power $p_1$ in Fig.~\ref{FBLgeqIBL} is optimally chosen.
It is observed that the optimal blocklength of the first hop in the FBL regime   is shorter than the one in the IBL regime, which again confirms Lemma~\ref{FBLgeqIBLpro_Relay2}.
Moreover, this blocklength difference between the two regimes is getting smaller as the total frame length increases.

To discuss the applicability of the model under the proposed schemes, we place another GU at $(400,0,0)$, which is closer to the AP than the setup in Fig.~\ref{fig:EdgeUser}, where the single GU is located at $(700,0,0)$. The throughput results are illustrated in Fig. \ref{MiddleRange}.
\begin{figure}[t]
	\centering
	\includegraphics[width = 0.88\linewidth,trim= 0 15 0 -5]{MiddleUser.pdf}
	\caption{Performance comparison between NOMA and Relaying in both IBL and FBL regime for GU at $400$ m.}
	\label{MiddleRange}
\end{figure}
In contrast to Fig.~\ref{fig:EdgeUser}, the win-win region ($\beta>1$ and UAV throughput is positive) of relaying  is much smaller in Fig.~\ref{MiddleRange}.
On the other hand, for $\beta<0.99$, the NOMA scheme outperforms the relaying scheme in both the IBL and FBL regimes. In other words, when the UAV is paired with the GU which has a good channel link to the AP, the NOMA scheme is generally more preferred in terms of the total throughput.

\subsection{Evaluation}
In this subsection, we evaluate the average system performance over channel fading.
In particular, we have the following setup on the channel fading: (A) for the AP-UAV channel with LoS, we apply Rician fading with non-centrality parameter as $1$;
(B) for the UAV-GU channel, we apply Rician fading with non-centrality parameter as the probability of LoS;
(C) finally we apply Rayleigh fading model for   the AP-GU channel without LoS.

\subsubsection{User Selection}
Fig.~\ref{Distance_evaluation} illustrates the impact of the GU's distance (to the AP) on the UAV throughput performance. Note that the NOMA scheme never works at $\beta>1$. Hence,  we set the  minimum rate coefficient $\beta = 0.95$, and evaluate the performance of the NOMA and relaying schemes    in both the IBL and FBL regimes.
\begin{figure}[t]
	\centering
	\includegraphics[width = 0.95\linewidth,trim= 0 15 0 10]{dist_com.pdf}
	\caption{Performance evaluation in different GU's distance}
	\label{Distance_evaluation}
\end{figure}
The results are consistent with  Fig.~\ref{fig:EdgeUser} and Fig.~\ref{MiddleRange} in that the NOMA scheme is more preferred when the GU is close to the AP.
Moreover, Fig.~\ref{Distance_evaluation} also confirms   the results observed in   Fig.~\ref{fig:EdgeUser} to Fig.~\ref{MiddleRange}    that in the FBL regime relaying provides a relatively higher throughput to UAV than in the IBL regime.

\subsubsection{The Impact of FBL Regime in Resource  Allocation}

In the following, we investigate how the optimization problem in the FBL regime differs from that in the IBL regime, and  what  the performance loss is if  we directly apply the allocation parameters obtained in the IBL regime into practice.
It should be pointed out that the optimal allocation parameter of the NOMA scheme in the IBL regime is not feasible in the FBL regime. It is due to the fact that the power $p_2$ obtained in the IBL regime is not able to  guarantee the GU's reliability and throughput requirement in the FBL regime.
Therefore, we only
  compare the IBL throughput with the FBL throughput under the relaying scheme.
In particular, three types of results are provided: (A) IBL throughput: the optimal throughput of UAV purely according to the design  in the IBL mode; (B) FBL throughput: the optimal throughput of UAV based on the  proposed design in the FBL regime; (C) FBL throughput with IBL blocklength: we obtain the optimal blocklength solution in the   IBL regime (i.e., using the IBL throughput metrics), and calculate the FBL performance based on these blocklength (BL) results (where  the transmit power is reallocated to satisfy the GU's reliability and throughput requirements).

\begin{figure}[b]
	\centering
	\includegraphics[width = 0.95\linewidth,trim= 0 10 0 25]{blocklength_com.pdf}
	\caption{Throughput comparison under the relaying scheme with a varying frame length.}
	\label{BLAnalysis}
\end{figure}
The impact of the frame length $M$ on the optimal throughput of the UAV
is shown in Fig. \ref{BLAnalysis}.
Significant performance difference between the designs in the two regimes are observed clearly from the figure. On the one hand, the FBL throughput of UAV is much higher than the IBL throughput, i.e., the IBL model is inaccurate when the frame length $M$ is relatively short.   On the other hand, directly applying the IBL optimal solution to a system operating with FBL codes also introduces considerable performance loss, i.e., the gap between the FBL throughput and FBL throughput with IBL BL (i.e., using the BL results obtained by considering the IBL throughput characterizations).

Moreover, we study the impact of the GU's reliability requirement on the UAV throughput in Fig.~\ref{ErrAnalysis}.
\begin{figure}[t]
	\centering
	\includegraphics[width = 0.95\linewidth, trim= 0 10 0 10]{Error_com.pdf}
	\caption{Throughput comparison under the relaying scheme,  where we vary the GU's error probability constraint from $10^{-9}$ to $10^{-1}$.}
	\label{ErrAnalysis}
\end{figure}
Again, significant performance gaps are observed between the FBL and IBL regimes, which confirms that it is necessary and essential to   provide the FBL  design (under  relaying scheme)    for a UAV network operating with short blocklengths.
Moreover, this necessity is more obvious when the GU has a stringent reliability constraint, i.e.,  the performance gaps between  the curves are more considerable when the  GU's error probability constraint becomes lower.
\begin{figure}[b]
	\centering
	\includegraphics[width = 0.82\linewidth,trim= -5 10 12 4]{throughput_comp1.pdf}
	\caption{Throughput comparison between the UAV-GU pair and the GU-GU pair.}
	\label{throughput_comp}
\end{figure}
\begin{figure}[b]
	\centering
	\includegraphics[width = 0.90\linewidth, trim= 5 12 0 0]{outage_prob1.pdf}
	\caption{The probability that the first   GU's transmission quality cannot be guaranteed.}
	\label{outage_comp}
\end{figure}

Finally, although the designs (for optimal resource allocations for a UAV-GU pair under relaying and NOMA schemes) in this work are motivated by utilizing the more favorable channel conditions (with a high probability of LoS) in links from/to the UAV and utilizing the channel quality difference  between the AP-UAV and AP-GU links,  it should be pointed out that these designs can be also applied  for the scenario with a pair of   GUs.
In the following, we compare   these two types of user pairs, i.e., UAV-GU and GU-GU, to show how our designs benefit the UAV connected scenario.. We set the locations of the AP and the first (primary) GU to $(0,0,20)$ and $(800,0,0)$, respectively.  In addition, we set the locations of the UAV and the second GU to $(\hat d,0,100)$ and  $(\hat d,0,0)$, i.e.,  letting the UAV and the second GU have the same ground  location/projection,   and vary $\hat d$ from 150 m to 1000 m.   Moreover, we   set the  minimum rate coefficient $\beta = 0.95$.

The throughput results of the comparison are provided in Fig.~\ref{throughput_comp}.
Clearly, owing to the high probability of LoS, the UAV achieves a significantly higher throughput via our designs  than the  second GU. Moreover, relaying has   better performances for both the UAV-GU and GU-GU cases in comparison to NOMA.

The corresponding outage probability results are shown in  Fig.~\ref{outage_comp}, where the outage probability represents the probability that the first (primary) GU's transmission quality cannot be guaranteed, i.e., the probability that   the UAV or the second GU cannot be additionally serviced  by the AP.
 It can be observed that the outage probability of the second GU is significantly higher than that of the UAV. In particular, in order to guarantee the first GU's transmission quality, the GU-GU pair is not able to provide a reliable connection for the second GU when this GU is a relatively far from the AP, e.g., when the distance of the second GU to the AP is longer than 600, the outage probability of the second GU becomes higher than $10^{-1}$. On the other hand, the UAV-GU pair introduces a relatively reliable connection to the UAV. Surprisingly, the NOMA scheme   is more reliable for the UAV connection than relaying, which is totally different from the results in  Fig.~\ref{throughput_comp} with respect to the throughput.  In particular, this performance advantage of NOMA with respect to outage probability is more significant when the UAV is   close  to the AP.

Combining the results in Fig.~\ref{throughput_comp} and Fig.~\ref{outage_comp}, we conclude that {the NOMA scheme has a higher probability to provide a connection to the UAV, while this connection generally results in a lower throughput to the UAV than the relaying scheme.
Hence, the NOMA scheme is more suitable for data traffic with small  data packet sizes and requiring a high probability of connection.}
Moreover,
 a hybrid scheme, which dynamically shifts between NOMA and relaying schemes, is strongly suggested for the considered UAV-connected ground network.
 This hybrid scheme definitely achieves   better throughput and outage probability performances than the pure NOMA and relaying schemes, which is more important for UAVs with low-latency high reliability  applications.

\section{Conclusion}

In this paper, we have studied a ground wireless network supporting UAV transmissions, and considered NOMA and relaying schemes.
The throughputs of UAV and GU are characterized in the IBL regime  and the FBL regime, respectively.
Following the throughput characterizations, {we have provided optimal resource allocation designs for the NOMA and relaying schemes in both the IBL and FBL regimes.
In particular, the objective of the designs is to maximize the UAV throughput while guaranteeing the GU's transmission quality with respect to throughput and reliability.}

Via simulations, we have validated our analytical model and evaluated the system performance. {In particular, the results suggest that the NOMA scheme is more preferred if the GU has a good link to the AP (e.g., GU is  within a short distance to the AP), while the relaying scheme demonstrates its advantage when the GU is relatively far form the AP.}
 Moreover, the relaying scheme is able to create a win-win situation, i.e., improve the performance of the GU while additionally providing a transmission service to the UAV.
 More importantly and surprisingly, we have observed that the relaying scheme offers a higher throughput to the UAV in the FBL regime than in the IBL regime, due to the fact that in the FBL regime less resources are required to guarantee the GU's transmission quality and therefore the extra resources can be allocated to the transmission to the UAV. {However, it is also observed that (in comparsion to relaying)  the NOMA scheme    provides a   higher UAV throughput by slightly sacrificing the GU's performance and is more reliable in  providing a connection to the UAV than relaying with respect to the outage probability.}
 Hence, a hybrid scheme, which dynamically shifts between NOMA and relaying schemes, is strongly advocated to achieve a high throughput while having a lower outage probability.

redpajama_set_name: RedPajamaArXiv


President Barack Obama and Republican nominee Mitt Romney will answer to a pool of about 100 undecided voters in Wednesday's town-hall style presidential debate in Hempstead, N.Y.
The voters were selected by the Gallup Organization, which has been tracking the Obama-Romney matchup on a daily basis throughout the general election.
This is the 20th anniversary of Gallup's partnering with the Commission on Presidential Debates for a town-hall style debate. In 1992, Gallup editor in chief Frank Newport said, no one had any idea what questions would be asked, and moderator Carole Simpson moved through the crowd of voters at random.
"It's a format that works very well, and it's a format that fits with my personal views, because I have a lot of faith in the average citizens of the country," Newport said.
Gallup calls voters and repeats its normal questionnaire. For undecided voters, it probes further and asks if they lean more toward Obama or Romney.
If voters identify as truly undecided, Gallup invites them to participate in the debate.
Newport stressed that the voters have to identify as truly undecided — not even leaners or voters who say their choice could change are considered.
Of the 100, only a select few will be chosen to ask questions by debate moderator Candy Crowley.
Newport said that Gallup has no say in what questions each voter will ask. But he said that the voters will meet with Crowley, who will discuss their questions with them ahead of the debate.
"She will know what the questions are, and she will take that into account when she calls on various people," Newport said.
Wednesday's debate serves as a huge challenge for Obama to reverse a slide from the last presidential debate, when an overwhelming majority of voters and pundits gave a clear victory to Romney. Gallup found that Romney was the biggest debate-winner in history.
In 2008, voters deemed Obama the winner over Republican John McCain in the town hall debate by an overwhelming, 56-23 margin, according to Gallup. The debate produced a big swing in immediate favorability for both candidates.
It's that type of split that could prove crucial for Obama, as he seeks to connect with voters who are on the fence about his re-election.


text:
OpenCon
OpenCon 2018 Highlights
Community Call Guide
Diversity, Equity and Inclusion Report
OpenCon's Revised Code of Conduct: A Detailed Description of Updates
Posted by Nick Shockey 586SC on October 30, 2018
Ahead of OpenCon 2018, we are today releasing an update to the OpenCon Code of Conduct. This update is informed by our experience putting the code to use during and after the 2017 meeting and the lessons learned as a result.
As we described in a blog post earlier this month, healthy communities are only possible when the individuals within them feel safe, and an effective code of conduct is essential to providing a safe and welcoming environment for participants—both in-person and online. We recognize that the work of improving the code of conduct and its implementation is an ongoing process, and the changes that we are releasing today reflect our latest thinking on how to work to create a healthy community, as well as our intention to continue learning and making improvements.
You can read the revised text of OpenCon's code of conduct here and access the previous version here. To help provide clarity, we've cataloged the major changes in the revised code section by section below, in the order they appear in the code. We hope this will help clarify precisely what has changed and also provide insight into the thinking behind the updates. We would also like to note this revision has benefitted from extensive conversations with and feedback from the human resources team at our fiscal sponsor, the New Venture Fund.
As always, we sincerely appreciate your feedback, and avenues for providing feedback are listed at the bottom of this post.
OpenCon Community Values Statement
At the top of the text of the code of conduct, you will now see a link to the OpenCon Community Values Statement. We combined two sections from the previous version of the code—the Diversity Statement and OpenCon Community Values—to create this new document that describes the positive values we want to reflect throughout the OpenCon community.
We separated out these two sections, because we wanted the code of conduct itself to be as clear as possible about the standard of behavior we require of participants in the community and the consequences of behavior that violates these expectations. However, we also wanted to be explicit about the positive values and behaviors we hope community members will exhibit, which are described in the values statement.
Participation Guidelines
We renamed what was referred to as the "Code of Conduct In Brief" at the top of the code to "Participation Guidelines," in order to emphasize that this section provides a summary of behaviors expected of participants in the OpenCon community.
Key changes in this section include updating the title of the second paragraph from "Be careful about the words you use. Is the language that you're using discriminatory?" to "Be considerate in your interactions with others and careful about the words you use. Is the language that you're using discriminatory?" The updated language broadens the point about language to cover interactions generally. This change has been accompanied by guidance on unconscious bias and microaggressions, with a definition of the latter added as a footnote. We also replaced some specific examples of problematic language with more general text describing the types of language that should be avoided.
Anti-Harassment Policy: At Events & Online
The opening of this section was modified from "We value your attendance" to "We value your participation." This change speaks to the range of activities this code of conduct covers—both in-person and online. We felt that "participation" was a better way to describe how individuals engage with the community, since "attendance" fits well with participation in events but is not as accurate for online engagement.
This section was also updated to clarify exactly when the code of conduct applies. The previous language (which appeared in the "Definitions" section) read that "Our Code of Conduct and Anti-Harassment policy extends to all hours and aspects of OpenCon." This was updated to instead read that the code "extend[s] to all aspects of OpenCon where an individual's behavior affects the ability of others to participate." Instead of referencing time (i.e. "all hours"), we felt it was more appropriate to clarify the code covers all areas within the scope of OpenCon—in-person and online—where an individual's behavior can negatively impact the ability of another to participate in the community.
We also adjusted language in this section to ensure that we can fully commit to following through on actions as described. The main change here was to modify the language that said "conference staff will… provide escorts" [to those making reports] to "conference hosts will make efforts to provide escorts." This does not signal a change in our intention to support those making reports as much as we possibly can; however, we believe it better captures the potential complexity involved in providing support mechanisms to reporters and reflects that despite our best efforts, there may be circumstances where we might not be able to provide an escort at all times.
We also removed language in this section reserving the right to remove someone from the conference without a refund. While removal from the conference and community are still potential sanctions, doing so without a refund (if a registration fee is paid, for example) could create unintended legal liability that is best avoided.
While we kept the important clarification that sponsors are subject to the code of conduct in the same way as participants, we removed language that specifically referenced sponsors' use of sexualized imagery or creation of a sexualized environment. We felt the prohibition against these activities was sufficiently captured in the rest of the code of conduct.
The Definitions section contains the most significant updates. The main adjustment was to separate sexual harassment from other types harassment, to define sexual harassment independently, and to provide specific examples of what constitutes sexual harassment. Based on past incidents submitted through the OpenCon code of conduct reporting process, we felt it was crucial to make the prohibition against sexual harassment as visible as possible and to enumerate the behaviors that constitute sexual harassment.
We also updated this section to provide a definition of other types of harassment, as well as additional specific examples of what constitutes other harassment, where the previous version of the code only defined harassment through examples.
Finally, we kept the clarification on the types of complaints we will not act on, but we reformatted them from a list to a paragraph for concision.
We changed the primary suggested route for submitting a report to a Google Form. Our past experience indicates that the structure of a form may help facilitate submitting a report.
We have also kept our previous primary methods of submitting reports—emailing, texting, or calling key organizing staff who are also on the OpenCon Code of Conduct Committee at the contact information provided—as well as a separate Google Form for anonymous reports. Though the anonymous and non-anonymous forms are nearly identical, we felt it was important to maintain a totally separate form for anonymous reports (rather than simply making the reporter name field optional on a single form) to avoid creating unintended pressure on anyone to provide their name.
This section was also updated to clarify how the code of conduct operates in spaces that are organized by the OpenCon team directly (the flagship conference and virtual spaces like community calls) and those that are organized locally (OpenCon satellite events). This revision clarifies that satellite hosts are responsible for implementing the code of conduct at their events, but that individuals who are not satisfied with how reports are handled by satellite hosts can contact the OpenCon Code of Conduct Committee for support. This change is also reflected in the following section, "How We Respond to Reports."
We've identified providing more support to satellite event hosts in areas related to the code of conduct and reviewing the relationship between satellites and the overall OpenCon Code of Conduct Committee as an important area for review as we continue to refine the code of conduct and its guidelines and implementation.
How We Respond to Reports
This section describing how we respond to reports was updated to reflect our use of a Code of Conduct Committee, comprising members of the OpenCon organizing team and representatives from the community.
The updates in this section also clarify that anonymity or wishing not to disclose key details (like the name of the person being reported) may inhibit the ability of the committee to take action as a result of a report.
Throughout this section, we replaced the word "harasser" with "the accused." This change was made to reflect that, if necessary for the safety or well-being of the community or individual participants, some sanctions may be imposed before it is possible for a full investigation to occur.
We also want to ensure that we can confidently follow through on the sanctions listed in the code of conduct. For this reason, we removed a few of the sanctions previously listed, including:
"Requiring that the harasser avoid any interaction with, and physical proximity to, their victim for the remainder of the event." We felt that this would be difficult to guarantee, especially at an in-person event where participants are often all in the same room. If a participant's behavior violated the code of conduct in such a way that they should avoid physical proximity with another participant, we felt removal from the event altogether would be the most appropriate action to take.
"Removing a harasser from membership of relevant organizations." Since we can only control who can participate in the OpenCon community, we can only commit to removing individuals who violate our code of conduct from OpenCon spaces, both in-person and online.
"Requiring that the harasser refund any travel grants and similar they received (this would need to be a condition of the grant at the time of being awarded)." As mentioned in the Anti-Harassment Policy section above, we felt it was best to remove any financial components from potential sanctions to avoid unintended legal liability. Due to the financial precarity many OpenCon participants may face, requiring the refund of travel grants or removal from scholarship-funded accommodations could negatively impact those accused of violating the code of conduct in ways that are not appropriate or that could create an unsafe situation. If removal from the conference hotel where other participants are present is felt to be necessary, we will arrange for alternate accommodations as needed and at the organizer's expense.
"Publishing an account of the harassment and calling for the resignation of the harasser from their responsibilities (usually pursued by people without formal authority: may be called for if the harasser is the event leader, or refuses to stand aside from the conflict of interest, or similar, typically event staff have sufficient governing rights over their space that this isn't as useful)." In certain circumstances, we may disclose that a named individual has been removed from the community; however, we are unlikely, as organizers, to disclose the detailed specifics of a report in order to protect the identity of the person making the report and respect their privacy.
We also added an additional item to the sanctions list: "Being reported to the proper authorities." In circumstances where we believe a participant's behavior has violated the law and that they pose a significant threat to the safety of the community, we reserve the right to contact the proper authorities. While we would never take such action lightly, we feel it is important to be clear that we will contact the proper authorities if we feel it is necessary. As with other sanctions, this decision will be made in consultation with the person submitting the report.
The revised code of conduct we are implementing today reflects the lessons we've learned to date and our best judgment in how to make OpenCon a safe, welcoming environment. We will continue working to strengthen both the code itself and its implementation. We welcome your feedback on this revision and will carefully consider the community's suggestions when making future revisions.
Comments and suggestions on the code of conduct should be sent to joe(at)sparcopen.org or commented on our public Github issue regarding the OpenCon Code of Conduct. As with previous codes, we encourage others to reuse and remix our code of conduct for their purposes if helpful.
The safety of the OpenCon community is always our top priority. If at any time you need to make a report, you can submit one through our reporting form, or if you would prefer to remain anonymous, please use our anonymous form. Alternatively, you can make a report by email to either of the addresses below:
Nick Shockey: nick(at)sparcopen.org
Nicole Allen: nicole(at)sparcopen.org
Host a Satellite Event Get updates Take part in the community
Tweets by @open_con
Except where otherwise noted, content on this site is licensed under Created with NationBuilder..


Navigating the various regulations around "improper" exports is no easy feat in Italy.
Navigating the various regulations around "improper" exports is no easy feat in Italy. The current regulations raise doubts and do not comply with EU laws, as confirmed by a ruling of the European Court of Justice. Even the Italian tax authority has changed its attitude on several points.
These are those goods sent outside the European Economic Community by (or on behalf of) a non-resident, within 90-days of delivery. The transport must be handled by the non-resident transferee, rather than the Italian national supplier/transferor, and a copy of the invoice must be stamped by the Customs Office or Post Office to endorse the export.
It's important to be aware that a tax-exemption only applies if the export is completed within 90 days from the delivery of goods to the non-resident transferee, and the goods should be exported without being processed in the transferee's country.
The delivery time is defined as either the actual time of delivery (when the transferee takes physical possession of the goods) or the time when documentation (required to obtain the goods) is transferred. If the 90-day window is not respected, the goods are no longer exempt from tax and the national transferor must apply VAT to the transaction. If the situation is not rectified, a penalty ranging from 50-100% of the tax applies.
What's important to note is that this penalty is applied against the national supplier/transferor and not the non-resident transferee. For suppliers operating in Italy, the challenge is to know how and when to act, if goods are not exported in time, and how to recognise the transaction in the annual VAT statement.
The following scenario explains what actions must be taken to mitigate the risk of a penalty.
An invoice for "improper" export goods is issued on 1 January 2016 (pursuant to section 8, paragraph b) of the Presidential Decree 633/72).
The goods must be exported by (or on behalf of) the non-resident transferee before 30 March 2016 (within 90 days). Proof of export must be provided back to the national supplier/transferor.
if the invoice has not been regularised and the tax has not been paid a voluntary correction should be filed. After the correction, the transaction is no longer considered non-taxable.
Once a transaction has been regularised, the national seller must enter the transaction as taxable in its annual VAT return.
Current Italian regulations raise some doubts about precisely when the 90-day period begins: from the transfer of ownership or the invoice date. The different provisions in the law suggest that, in the case of movable property (not registered), the 90-day term should be calculated from the date of the invoice (if there is no proof of delivery), while for registered goods, the period should begin from the transfer of ownership of the goods sold.
It's also important to be aware that the 90-day term set forth by Italian law does not comply with EU laws. In December 2013, the European Court of Justice challenged the Italian law on the basis that it denies the benefit of non-taxability even when it may be demonstrated that goods indeed left the customs territory of the EU (but did so after the 90-day period had expired).
goods leave the EU territory after the 90-day term has expired, as long as proof of the export is obtained.
As a result, it is expected that Italian law will be updated to align with EU regulations.
Our experts in Italy remain up-to-date with tax regulations, and can provide you with further information on the implications of these rules. We can also take care of your tax fulfilments in order to help you comply with Italian requirements.
Need more information? Get in touch with our team in Milan.


Let me just start by saying that I read this book in a few hours, which might not sound that impressive but as a notoriously slow reader, it says a lot! White Stag by Kara Barbieri is such a fun, fast-paced read that I couldn't put it down. Sadly, I had to put it down because life often gets in the way of reading, but I was back to it as soon as possible!
Kara Barbieri's book started out on Wattpad and became a sensation. With over a million reads, how could it not get noticed? Her publishers helped her to expand the story and now it has been released as this stunning and thrilling book.
It's a little bit Beauty and the Beast, a little bit A Court of Thorns and Roses and even a little bit The Hunger Games.
Basically you've got Janneke – a human girl who was kidnapped from her home when she was seventeen and enslaved by a cruel goblin called Lydian across the border in a land known as Permafrost. Time is different there and Janneke has been living in this land for over 100 years, all the while retaining her youthfulness.
Although she wouldn't call it luck, Janneke is lucky enough to be passed onto Lydian's nephew Soren for the majority of her time so far in the Permafrost. Our story picks up after these hundred-or-so years have passed and Janneke has formed a routine with Soren. They aren't friends, but they aren't slave and master either.
Janneke is a really strong character, determined not just to live, but to live true to her beliefs, desires and will. She is stubborn, bold and a survivor! Most humans who are taken as slaves in the Permafrost die after a few years… but not Janneke.
Our story revolves around Janneke and Soren's involvement in this ancient hunt. When the Goblin King dies, a hunt begins to find the next king. It's goblin vs goblin, and Soren takes Janneke along. Why? He has his reasons.
I thought I had the end figured out from the get-go but I'm pleased to say that I was wrong! Barbieri did a great job of taking me by surprise with her inventive and emotional ending, I'm very eager to see where this story goes from here!


Home Bible Are the historical statements of the Bible accurate?
Are the historical statements of the Bible accurate?
The Cyrus Cylinder, discovered in 1879, records Cyrus' overthrow of Babylon and his subsequent deliverance of the Jewish captives (Isaiah 45; 2 Chronicles 36; Ezra 1).
The Moabite Stone, discovered in 1868 at Dibon, Jordan, confirmed Moabite attacks on Israel as recorded in (2 Kings 1 and 3).
The Lachish Letters, discovered in 1932-1938, 24 miles north of Beersheba, described the attack of Nebuchadnezzar on Jerusalem in 586 BC (2 kings 25:1).
Skeptics said the Bible record of Moses was not reliable because it mentions writing (Exodus 24:4) and wheeled vehicles (Exodus 14:25), neither of which they said existed at the time. Recent discoveries in the Red sea proved the reliability of the Biblical story of Moses.
The ancient city of Petra (in the heart of Mount Seir) was virtually unknown to archaeologists, with only the Bible to give account of its existence (Ezekiel 35:7). But 200 years ago all of that changed when the Swiss explorer Johann Burckhardt made the legendary discovery.
For years skeptics said the Bible was unreliable because it mentioned the Hittite nation (Deuteronomy 7:1) and cities like Nineveh (Jonah 1:1, 2) and Sodom (Genesis 19:1), which they denied ever existed. But now modern archaeology has confirmed that all three did exist.
Critics also said that Bible-mentioned kings Belshazzar (Daniel 5:1) and Sargon (Isaiah 20:1) never existed. It has now been confirmed they did exist.
At one time the 39 kings of ancient Israel and Judah who reigned during the divided kingdom were authenticated only from the Bible record, so critics charged fabrication. But then archaeologists found cuneiform records that mentioned many of these kings.
A Biblical prophecy accurately foretold the destruction of the ancient city of Tyre (Ezekiel 26:3-5).
Babylon was excavated in 1898. The archaeological findings point to the truth of Scripture's prophecies about that great city (Isaiah 13:19-22).
All this show that Bible historical statements are accurate and true.