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Recalling the most important win in Bangladesh cricket history
Published at 09:04 pm May 30th, 2020
The win against Pakistan spoke loudly in the cricketing globe about the capacity of this cricket-frenzy nation that helped Bangladesh gain Test status
Exactly 21 years ago on this day, Bangladesh stunned the whole cricketing world with a shocking win against tournament favorite Pakistan in 1999 World Cup. Bangladesh won many matches in the years to follow but that win is still regarded as one of the best due to the strength of the opponents and as it spoke loudly in the cricketing globe about the capacity of this cricket-frenzy nation that helped the country gain Test status.
It was Tigers' first ever World Cup campaign and they finished the tournament with two wins in group stages. The win against Scotland was expected considering the cricketing strength between the two teams back then, but the win against Pakistan created one of the fairy tales in the cricketing folklore.
Dhaka Tribune Sports has decided to recall that sweet memory and picked five points regarding the win.
Expectation was high, Tension mount on and off the field
The whole nation was following Bangladesh in their first ever World Cup campaign as cricket was rising particularly after winning the ICC Trophy in 1997. The expectation was less, perhaps win against Scotland was the only expectation back then. But for the players, playing in a World Cup stage against mighty teams was definitely something special. Bangladesh were facing some off field issues as tension between coach Gordon Greenidge and management was mounting. Before the Pakistan match, Greenidge even left the dressing room as it was learnt that he was sacked. So, literally Bangladesh played without a coach in that game against Pakistan.
Gutsy batting by top order against one of the best bowling attack
Pakistan won the toss and elected to field on a seaming condition at Northampton. With one of the best fast bowling line-ups in the world, comprising Wasim Akram, Waqar Younis, Shoaib Akhter and Azhar Mahmood, Pakistan bowlers were favorite to tame Bangladesh early on a favorable condition. But Bangladesh top order batsmen batted with guts and gave a good start for Tigers. Against the fearsome pace quartet the opening stand between Shahriar Hossain Biddut (39) and Mehrab Hossian Opi (nine) batted for 15.2 overs putting 69 on the board. Number three Akram Khan, who was promoted and was on verge of being dropped from the playing eleven due to a poor World Cup till then, batted with confidence and scored 42, the highest of the match. Pakistani bowlers did not help their cause giving away 40 extras including 28 wides. At one stage Bangladesh were 120 for 2 after 29 overs and were set for a big score but spin wizard Saqlain Mushtaq's 5/35 restricted the total to 223/9.
Brilliant bowling, fielding effort and Khaled Mahmud heroics
After setting a moderate target of 224 in 49 overs, it was Bangladesh bowlers who bowled exceptionally well throughout the innings and created constant pressure in Pakistan batting line-up by checking runs and picking wickets in crucial time. The fielding effort was brilliant as well. Khaled Mahmud Shujon was superb with the ball with his medium pace as the right-hander took three wicket in 10 overs conceding just 31 runs. He also added 27 valuable runs while batting and was later adjudged man of the match. Pakistan were all out for just 161 and when Saqlain was run out as the last wicket, hundreds of fans rushed towards the pitch with joy and ecstacy. Back home, the whole Bangladesh was erupted with joy as it was another historic moment for the fans after winning the 1997 ICC trophy.
Statement to the world and for Test status
Although the win against Pakistan was termed as an upset, but it was a certain message to the cricket World that rookie Bangladesh has entered in the cricketing world and can become a competitive side in coming years. As a consequence Bangladesh got Test status in 2000 and it was believed that Bangladesh's performance in World Cup, particularity their stunning win against Pakistan made a good impact on gaining status in the longest format of the game.
Inspiration for future generation
After winning ICC trophy, such stunning win against Pakistan in 1999 inspired millions of kids and young souls in Bangladesh to take bat and ball in their hands and sow the seed of a dream of becoming cricketers in near future. That changed the sporting landscape of the country and firmly put cricket as the premier game of the nation. Henceforth the meteoric rise of cricket skyrocketed on and off the field here.
Root helps England dominate day two in SL
England cricket fan waits 10 months for Sri Lanka Test - and gets kicked out
Langer goes to bat for under-fire Paine, Smith
WI coach hails Bangladesh as favorites
Saifuddin enjoys competition among fellow pacers
Pakistan cricket team
Bangladesh Cricket Board
Akram Khan
Khaled Mahmud Sujon
1997 ICC Trophy
1999 World Cup Cricket


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Home » Blog » Discover: Butteville, OR
Discover: Butteville, OR
Published by Dawn On April 24, 2020
Along the Banks of the Peaceful Willamette
As long as kids have been kids, any parent driving down I-5 through Oregon has probably heard their young son laugh when they see the exit sign for Butteville. And yet the small town located just off the freeway has a much more romantic history with a dash of European influence, and absolutely no reference to what the boys were thinking.
Pronounced "B-YOOT-vill" some might think it is a form of "Beautiful" which wouldn't be a bad guess, as the area surely is beautiful. The town's name is actually a form of the French word for "hill" which is "butte" as it was settled on the top of a rocky outcrop overlooking the Willamette River. It sits in the center of the beautiful Willamette Valley, with its lush greenery, open agricultural fields, wineries, and gently rolling hills.
Champoeg Heritage Site park by the Willamette River. Photo by Rick Obst
The sleepy little rural town of Butteville, and its neighbor, Champoeg (pronounced "sham-POO-ee") both originated when fur trappers from the Hudson Bay Company based in Vancouver, WA traveled south along the Willamette and set up an outpost in the area. The trappers were French-speaking Canadians and many chose to retire here once their trapping days were over. Most married women from the local Indian tribes and had many children. The area also became known as "French Prairie."
The first Oregon Trail immigrants arriving in 1843 did not find an untamed wilderness – they arrived to find a fairly well established agricultural community and settled local tribes who had lived in the area for thousands of years. The new settlers were no doubt aided by the families that lived there already and helped them flourish in their new homes. It was also in 1843 when an historic meeting and vote took place in Champoeg that began the process of Oregon becoming a state.
Butteville Landing
Friendly Competition
The location of Butteville and neighboring Champoeg along the Willamette River between Portland, Oregon City, and Salem made the area a prime hub of transportation. Goods were primarily transported by the river and soon a competition between the two towns developed. The town of Butteville won out during the great flood of 1861 in which most of the town of Champoeg was washed away, while Butteville, located higher on a hill survived. The success of the town continued until technological advances came into play. The coming of the railroad changed everything. Goods soon were no longer being transported by water, trade declined, and the town slowly settled back into the sleepy little rural town it still remains today. Most of the old commercial buildings have been relocated to a Heritage Site down the road in Champoeg. The competition between Champoeg and Butteville was never truly won. Butteville was the more successful town long ago and has the well-known exit sign off of I-5, but the area is now known as the Champoeg State Heritage Area, an Oregon State Park.
The Newell House Museum
Historic Butteville Store – the longest continually operating business in the state of Oregon. It opened in 1863 and is still going..
The Champoeg History Museum
Champoeg Campground – a lovely, flat, green campground perfect for taking kids to go bike riding or explore the river
The Newell House
Newell House Living History
Pioneer House
Butteville Jail
Champoeg Museum
Heritage Barn on site
The Kitchen Garden. Photo by Rick Obst
Champoeg Heritage Site Walk/Bike Path. Photo by Rick Obst
There is plenty to do to explore the mid-Willamette Valley's history, including The little village of the Aurora Colony National Historic Site, the St. Paul Rodeo, the charming college town of Newberg, ride the ferries at various points across the Willamette River, visit the historic sites in Oregon City including the Oregon City Elevator, or visit Fir Point Farms for some lunch, Tillamook ice cream, climbing goats, and pit full of hazelnuts.
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What Is the Meaning of Sports Fan?
The definition of a sports fan
The different types of sports fans
The benefits of being a sports fan
The downside of being a sports fan
How to become a sports fan
How to become a better sports fan
How to support your team
How to deal with disappointment
How to enjoy sports more
How to find other sports fans
A sports fan is someone who enjoys watching or participating in sports. They are usually loyal to a particular team and follow all the games closely. Some fans even go to great lengths to show their support, such as painting their faces and wearing team jerseys.
When it comes to sports, there are a lot of different ways that people can show their support for their favorite team. Some people go to every game, some people watch every game on television, and some people just follow their team's progress in the standings. But what does it really mean to be a sports fan?
The word "fan" is short for "fanatic," which means someone who is very passionate about something. So a sports fan is someone who is very passionate about sports. But being a fan isn't just about cheering for your team; it's also about knowing a lot about the sport, the teams, and the players.
Sports fans are always looking for ways to show their support for their team. They might wear their team's jersey or hat, or they might decorate their home with team memorabilia. They might even get tattoos of their favorite team's logo. And when their team wins a big game, they feel like they've won too.
Being a sports fan can be a lot of fun, but it can also be frustrating when your team loses. Sports fans often get very emotional about their teams, and they can sometimes take losses personally. But at the end of the day, being a sports fan is all about loving the game and supporting your team through thick and thin.
There are four types of sports fans: the Bandwagoner, the Diehard, the Fringe, and the Complainer.
The Bandwagoner is someone who only likes a team when they are doing well. They will jump on and off of teams frequently, and their loyalty is usually based on how successful a team is at any given moment.
The Diehard is someone who has been a fan of a team through thick and thin. They don't give up on their team no matter how bad they are doing, and they often have a strong emotional attachment to the players and the club.
The Fringe is someone who likes to root for the underdog. They are often drawn to teams that are not traditionally successful, and they take pride in supporting a club that others may not understand.
The Complainer is someone who is never happy with their team no matter how well they are doing. They are always finding fault with the players, the coach, or the front office, and they are quick to jump ship if things start going downhill.
Sports fans are often seen as dedicated, enthusiastic and even obsessed supporters of their team or teams. But what is the real meaning of being a sports fan?
For many people, being a sports fan is about more than just following the scores or cheering on their team – it's a way of life. Being a sports fan can bring people together and create lasting bonds, it can provide an escape from the everyday grind, and it can be a source of great joy and pride.
There are many benefits to being a sports fan, but some of the most common include:
A sense of community: For many fans, being part of a community of like-minded people is one of the best things about being a sports fan. Sharing your passion for your team with other fans can create strong bonds and lasting friendships.
An escape from reality: Sports can be a great way to take your mind off of your everyday problems and relax. Whether you're watching your team play on TV or in person, following their progress can help you forget about your troubles for awhile and just enjoy yourself.
Pride in your team: Seeing your team succeed – whether it's winning a championship or just having a good season – can make you feel proud. Many fans take great pride in their team's accomplishments and feel like they're part of something bigger than themselves.
A source of joy: There's nothing quite like the feeling you get when your team wins a big game or makes an amazing come-from-behind victory. These moments can be some of the most joyful experiences for sports fans.
While being a sports fan has many upsides, there are also some downsides that come along with it. For example, fans can often get too emotionally invested in their team and let their rooting interests cloud their judgment. This can lead to problems such as making bad bets, getting into arguments with other fans, and feeling disappointed or even heartbroken when your team loses.
Another downside of being a sports fan is that it can be costly. If you want to attend games or buy gear for your favorite team, the costs can add up quickly. Additionally, some fans can get so wrapped up in following their team that it starts to consume a significant amount of their time and energy.
A sports fan is a person who supports a particular team or sport. They usually have a strong loyalty to their team and try to follow them as much as possible. For some people, being a sports fan is simply about rooting for their home team. But for others, it can be much more than that. It can be a way of life.
So, how does one become a sports fan? There is no single answer to this question. For some people, it is simply something that they have always been. They grew up watching their parents or older siblings root for certain teams and they just took on that same passion. Others may have become fans later in life, after they developed an interest in a particular sport or team.
Some people become fans because they want to feel like they are part of something larger than themselves. They like the feeling of camaraderie that comes with being part of a group of people who all share the same interest. Others may become fans because they enjoy the sense of competition and the feeling of satisfaction that comes with rooting for a successful team.
Whatever the reason, becoming a sports fan can be a great way to add some excitement and passion to your life. It can give you something to look forward to on days when there is no other news worth paying attention to. And it can provide you with an outlet for all of your pent-up energy and emotion.
die-hard sports fans are a special breed. They live and breathe their team. They know every player on the roster, along with their stats. They can tell you what happened in every game dating back to the team's inception. For them, there is no such thing as too much information when it comes to their team.
Whether you're a casual observer or a hardcore fanatic, if you love sports, you're a sports fan. That said, there are different types of sports fans. Some people only watch their favorite teams, while others follow every game their sport has to offer. Some fans are all about the statistics, while others just want to see good old-fashioned competition. And then there are those who show their support in other ways, like collecting memorabilia or attending live games.
So, what is the meaning of sports fan? A sports fan is someone who enjoys watching or participating in sports. They may follow one or multiple sports, and they may have different reasons for why they enjoy watching. Some fans like the excitement and suspense of not knowing who will win, while others appreciate the physicality and competition of sport. Some follow certain players or teams because they admire their skills or approach to the game, while others just enjoy the camaraderie that comes with being a part of a team's fan base.
Whether you're a fair-weather fan or a diehard supporter, if you love sports, you're sure to find your place among the ranks of other fans.
As a sports fan, you learn to deal with disappointment. Your team may not make the playoffs, or they may suffer a loss in the championship game. But you stick with them through thick and thin, because you know that ultimately, they're still your team.
Sports fandom is more than just cheering for your favorite team; it's about feeling like you're part of something bigger. It's about connecting with other fans and sharing your passion for the game. Whether you're watching from the stands or cheering at home, being a sports fan is all about supporting your team and enjoying the sport.
Whether you are a casual spectator or a hardcore devotee, there are many ways to enjoy sports more. One way is to understand the game better. If you know the rules and objectives, you will be able to follow the action more easily and have a greater appreciation for the skills of the players.
Another way to enjoy sports more is to get closer to the action. If you are able to attend a live event, you will be able to see and hear all the excitement firsthand. You may also get a chance to meet some of the players or other fans.
If you cannot attend a live event, watching on television or listening on the radio can still be enjoyable. You can also follow your favourite team or player online, on social media or through dedicated fan websites.
Whatever your level of interest, there are many ways to enjoy sports more.
Sports fans are passionate about their team and love to show their support. They often feel a strong connection to their team and want to be involved in every aspect of their game. For some, being a sports fan is simply a way to show their loyalty and support. Others take it a step further and live and breathe their team.
There are a few ways to find other sports fans. One is to look for people wearing team jerseys or hats in public. Another is to go to sports bars or restaurants that are known to be frequented by fans of certain teams. You can also attend local games or events related to your favourite team. Finally, you can join online forums or communities dedicated to supporting specific teams.
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There's no need for brides and grooms or their wedding guests to worry about being punctual on the big day anymore. Couples are turning to social media to make it easy for loved ones and guests to be together when the blissful vows are spoken. As many have discovered, it's also an inexpensive way to get married.
Instead of the customary "Something borrowed, something blue" adage, many contemporary brides-to-be are now saying, "Something Facebook, something wireless" before their marriage. The age of the social media wedding is here.
It's not unusual anymore to see a couple and their officiate read from an iPad or navigate to a special app while a close friend records the scene on an iPhone, where it can be streamed live or captured for posterity on YouTube.
Perhaps a family member or colleague is unable to attend the ceremony. That's not a problem. They can still be a witness to the "I do's" via video with Skype.
Have a low budget for things like invitations? Getting around that is simply a matter of sending email invites to the people on your guest list.
Couples are turning to the Internet for all of their wedding needs, including recently married Steve and Caryn Poland, from Buffalo, New York.
The legendary team of Frederick Loewe and Alan Jay Lerner composed the music for the delightfully lighthearted "Get Me to the Church on Time," from the 1956 Broadway smash "My Fair Lady." If the popular song was written today, it would probably sound a lot different than it does now. Think what would have happened if Lerner and Lowe had an iPad.


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Home Games IGN Games PC IGN News IGN Only Very Hard IGN Previews IGN PS4 IGN Xbox One The Witcher 3: Wild Hunt, It's time to ramble on
The Witcher 3: Wild Hunt, It's time to ramble on
N4Gaming February 19, 2015 Games, IGN Games PC, IGN News, IGN Only Very Hard, IGN Previews, IGN PS4, IGN Xbox One,
Despite our best efforts, somewhere along the way we booked a one-way ticket to Rivia and boarded the hype train. It was easy enough to do; after all, everything about CD Projekt RED's perpetually delayed The Witcher 3: Wild Hunt screams 'next-gen starts here'. It is without question the biggest open-world to ever be presented in modern RPG history. It's been awarded so many 'most anticipated' medals that Geralt's armour is beginning to look ostentatious instead of intimidating, and, let's be honest for a second, the raw passion seeping from the pores of CD Projekt RED is electrifying.
But The Witcher 3: Wild Hunt has been kept behind closed doors for so long now we were beginning to wonder whether it was simply a mirage; a hallucination born from the litany of mediocre open-worlds we've trudged through in the last 15 months. That said, we've finally had a chance to get our hands all over Geralt's third and final adventure, and you better believe us when we tell you that something special comes our way, folks.
Unlike The Witcher games of the past, Wild Hunt takes place in an open-world. If we're talking sheer size alone, well, it's pretty bloody impressive. You've no doubt already heard the '20 per cent bigger than Skyrim' statistic thrown around in passing at one time or another, but it turns out that was a gross underestimation. Cobble together just two of The Witcher 3's areas Novigrad and Skellige and you're looking at a playing area of 52 square miles of land to romp around, underwater ecosystems to explore and a metric hell ton of monsters to introduce to your silver blade. To put that in perspective of RPG-to-beat Skyrim, Bethesda's entire map barely covered 16 square miles. It's adorable that a game from 2011 is still considered king of a heavily-populated genre, though we've got a feeling Geralt is just about ready to start an uprising.
"You better believe us when we tell you that something special comes our way, folks"
Then again, a gigantic open world is nothing but a hollow shell without content to populate it. One of the biggest concerns raised following the announcement that The Witcher 3 would be embracing an open-world setting was that players would yearn for a return to the structured, and immensely well-paced, walled garden areas of previous games. We collectively feared CD Projekt RED had bitten off more than it could chew as it attempted its first Xbox One game that the narrative would be lost under our attempt to develop orienteering skills to make it through the dense forests, untamed seas and rolling green hills. Thankfully our chaperoned hands-on session has done an admirable job of relieving us of our fears.
"It has certainly been a big learning experience, that's for sure," confides level designer Miles Tost "Bringing this series into a full open-world setting has always been the ultimate goal, though that's what the studio has always wanted… but previously the team has been hindered by available technology or budget.
"There has been a lot of experimentation to get to the point we're at now with The Witcher 3. Obviously, we didn't just show up on day one of development and nail the entire thing right away. It was a constant process of iteration and trying new things, but I think we've now come to a point where we've achieved a really good balance and we're where we want to be."
Tost doesn't need to tell us about the "constant process of iteration"; it feels like we've been waiting for The Witcher 3 forever. Honestly, there was a time where it felt like it might never come out. But with the renewed 19 May release date in sight, content is locked down and the studio is off hunting bugs. The results are clear; while our playtime was restricted to the prologue area an opening section designed to give new and existing players an opportunity to grasp the core concepts of monster hunting and interrogating the environments for quests and lore it's immensely polished and well considered.
"Wild Hunt takes place in an open-world. If we're talking sheer size alone, well, it's pretty bloody impressive"
"We don't want to build an open-world game, and then withhold that entire open world at the start just because you're a 'beginner', or because past Witcher games haven't been open world," Tost explains. "The open world is really good at serving our goal of teaching players the ways of the game and encouraging them to engage with it. You're very much encouraged from the start to venture away from the obvious routes and see for yourself what is happening away from the main quests."
Admittedly, the early side-quests we encountered outside of our main quest which had us tracking and dispatching an almighty griffin with Geralt's sweet blend of swordplay and magical abilities felt somewhat shallow, we can't deny that it feels great to play. Sure, helping wounded or stranded NPCs, playing pub games and searching for collectibles dotted around the large region aren't the most exciting side-quests in the entire world, but we're just happy to finally play an RPG that places as much emphasis and importance on polish as it does size and scope.
That's the take-away from our first hands-on session with The Witcher 3: it feels like a true next generation experience. It looks stunning, the particle effects and animations in particular make the combat feel slicker and more visceral than we ever anticipated. The freedom to explore and track monsters as you please is liberating. CD Projekt RED has always argued that The Witcher games are about being Geralt; about seeing a world through the eyes of an outcast and getting lost in the danger and excitement of slaying ridiculous monsters. As the studio explores new ways to tell stories, introduces new gameplay mechanics and delivers some of the best graphics we've seen on the Xbox One to date seemingly without sacrificing performance we've got a feeling that The Witcher 3: Wild Hunt might just seta new benchmark for the RPG genre.
Tags # Games # IGN Games PC # IGN News # IGN Only Very Hard # IGN Previews # IGN PS4 # IGN Xbox One
IGN Xbox One
Posted by: N4Gaming at February 19, 2015
Tags: Games, IGN Games PC, IGN News, IGN Only Very Hard, IGN Previews, IGN PS4, IGN Xbox One


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\section{Introduction}

Massive multiuser (MU) multiple-input multiple-output (MIMO) relies on base station~(BS) architectures with hundreds of antenna elements that simultaneously serve  tens of user equipments~(UEs) in the same frequency band.
Massive MU-MIMO promises substantial gains in terms of spectral efficiency, energy efficiency, reliability, and coverage compared to traditional small-scale MU-MIMO systems~\cite{rusek14a, larsson14a} and is hence widely believed to be a core technology in fifth generation (5G) cellular networks~\cite{boccardi14a}.
In order to keep system costs and circuit power consumption within reasonable bounds, massive MU-MIMO has to be realized using low-cost (and, hence, nonideal) hardware components at the BS~\cite{bjornson15a, bjornson15c}.
In this paper, we  analyze an orthogonal frequency-division multiplexing (OFDM)-based massive MU-MIMO uplink system (UEs transmit to the BS) with nonideal hardware components at the BS-side.
Concretely, we analyze the joint distortion introduced  by nonlinear low-noise amplifiers (LNAs), local oscillators (LOs) with phase noise, and oversampling finite-resolution analog-to-digital converters~(ADCs).

\subsection{Previous Work}
The impact of \emph{aggregate} hardware impairments (i.e., from multiple sources of hardware impairments) on small-scale MIMO and massive MU-MIMO systems has been investigated in, e.g.,~\cite{zhang15d, bjornson15c, studer10b}, using a statistical model that treats the distortion caused by nonideal hardware as power-dependent additive white Gaussian noise.
While such simple statistical models have been shown to yield accurate results in some scenarios when characterizing bit error rate (BER) and spectral efficiency~\cite{gustavsson14a, studer10b, bjornson18a}, they do not fully capture the impact of real-world hardware impairments on practical systems~\cite{bjornson18a, larsson18a}.
Indeed, nonideal hardware causes distortion that is, in general, correlated in time, frequency, and across the BS antenna array~\cite{larsson18a, jacobsson17a, blandino17a, moghadam12a}.
It is therefore of practical interest to develop accurate behavioral models of nonideal hardware that capture this inherent correlation.
Behavioral models have been used previously to assess the impact  on the performance of massive MU-MIMO uplink of an isolated hardware impairment, e.g.,  nonlinearity of LNAs~\cite{mollen17b}, phase noise~\cite{wu06a, mehrpouyan12a, pitarokoilis15a, khanzadi15a}, or low-resolution ADCs~\cite{jacobsson17b, mollen16c, zhang12a, li17b}.
A theoretical analysis with an aggregate impairment model that jointly models all these distortions is, however, missing.

\subsection{Contributions}

Starting from  behavioral models of nonideal hardware components, we derive an aggregate statistical hardware-impairment model that can be used in system-level and link-level simulations to accurately analyze the distortion caused by nonlinear LNAs, LOs with phase noise, and oversampling finite-resolution ADCs.
The proposed aggregate hardware-impairment model, which captures the inherent correlation of the induced signal distortion in time, frequency, and over the antenna array, depends only on the second-order statistics of the received signal and on the parameters of the  behavioral hardware models.
We validate the accuracy of the proposed aggregate model by comparing our analytical results with numerical simulations in a massive MU-MIMO-OFDM uplink system.

\begin{figure*}
\centering
\includegraphics[width = .99\textwidth]{system_overview_rf_uplink_fixed.pdf}
\caption{Overview of a massive MU-MIMO-OFDM uplink system with nonideal hardware at the BS-side. Left: $U$ single-antenna UEs with ideal hardware components independently perform  symbol mapping and OFDM modulation.
Right:  The per-antenna received time-domain signal the BS is filtered using a band-pass filter (BPF), amplified using an LNA, mixed with an LO signal,  filtered with a low-pass filter (LPF), and converted into the digital domain by a pair of ADCs. After BS-side OFDM demodulation, the received signals over the $B$ BS antennas are combined using a linear filter (e.g., zero forcing) to detect the transmitted symbols.
}
\label{fig:system}
\end{figure*}

\subsection{Notation}

The $M \times N$ all-zeros matrix and the $M \times M$ identity matrix are denoted by $\veczero_{M \times N}$ and $\matI_M$, respectively.
The real and the imaginary parts of a complex-valued vector $\veca$ are $\Re\{\veca\}$ and $\Im\{\veca\}$, respectively.
We use $\opnorm{\veca}_2$ to denote the $\ell_2$-norm of $\veca$.
The main diagonal of a matrix $\matA$ is $\diag(\matA)$.
The Hadamard product of two equally-sized matrices $\matA$ and $\matB$ is $\matA \circ \matB$.
Furthermore, the elements of the matrix $\abs{\matA}$ are the absolute values of the elements of $\matA$.
The complex-valued circularly symmetric Gaussian distribution with covariance matrix $\matK \in \opC^{M \times M}$ is~$\jpg(\matzero_{M \times 1}, \matK)$.
The expected value of a random vector $\vecx$ is~$\Ex{}{\vecx}$.
Finally, we let $\sinc(x) = \sin(\pi x)/(\pi x)$ for $x\neq0$ and $\sinc(x)=1$ for $x=0$.

\section{System Model} \label{sec:system}

We consider a single-cell massive MU-MIMO-OFDM uplink system as shown in~\fref{fig:system}. Here, $U$ single-antenna UEs use spatial multiplexing to communicate in the same time-frequency resource with a $B$-antenna BS.
Our model considers several nonideal hardware components at the BS, including nonlinear LNAs, phase noise, and oversampling finite-resolution~ADCs.
For simplicity, however, the analog band-pass filter (BPF) and the analog low-pass filter (LPF) at the BS-side shown in \fref{fig:system} as well as all hardware components at the UEs are assumed to be ideal.
Finally, we assume that the sampling rate $F_s$ of the digital-to-analog converters (DACs) at the UE side equals the sampling rate of the ADCs at the~BS side.

\subsection{Transmitted Signals}

We consider the practically relevant scenario in which OFDM is used to simplify equalization when operating over frequency-selective channels.
Without loss of generality, we focus on the transmission of a single OFDM symbol. Let $N$ denote the total number of subcarriers per OFDM symbol, and let $S \le N$ denote the number of occupied subcarriers.
The subcarrier spacing is $F_\text{sub} = F_s/N$.
The oversampling rate (OSR) is defined as~$\textit{OSR} = N/S$. The case $\textit{OSR} = 1$ corresponds to symbol-rate sampling whereas the case $\textit{OSR} > 1$ corresponds to faster-than-Nyquist sampling.
We denote by $\hat{s}_u[k]$ the frequency-domain symbol transmitted from UE  $u = 1, 2, \dots, U$ on  subcarrier $k = 0,1,\dots,N-1$.
Let $\setS$ and $\setG = \{ 0, 1, \dots, N-1\} \setminus \setS$ denote the set of occupied subcarriers and guard subcarriers, respectively.
 We assume that $\hat{s}_{u}[k] = 0$ for $k \in \setG$.
With these definitions, we can write the time-domain sample $n = 0,1\dots,N-1$ of the discrete-time baseband signal transmitted from UE $u$ as follows:
\begin{IEEEeqnarray}{rCl} \label{eq:s_scalar}
s_u[n] = \frac{1}{\sqrt{N}}	\sum_{k \in \setS} \hat{s}_u[k] e^{jk\frac{2\pi}{N}n}. \IEEEeqnarraynumspace
\end{IEEEeqnarray}
To prevent interference between  OFDM symbols, a cyclic prefix of length $L-1$ is prepended to $\big\{s_u[n]\big\}$. Specifically, $s_u[n] = s_u[N+n]$ for $n = -L+1, -L+2, \dots, -1$.

Let $F_c$ denote the carrier frequency. The continuous-time passband signal transmitted from UE $u = 1, 2, \dots, U$ is then
\begin{IEEEeqnarray}{rCl} \label{eq:tx_ct_pb}
\tilde{s}_u(t)
&=& \sqrt{2}\Re\{ s_u(t)e^{j2\pi{F_c}t}\}
\end{IEEEeqnarray}
where we use ideal sinc-based pulse shaping:
\begin{IEEEeqnarray}{rCl} \label{eq:tx_ct_bb}
	s_u(t) &=& \sum_{n=-L+1}^{N-1} s_u[n] \sinc\mathopen{}\left(t/T_s - n\right). \IEEEeqnarraynumspace
\end{IEEEeqnarray}
Here, $T_s = 1/F_s$ is the sampling period of the DACs at the UEs, which equals the sampling period of the ADCs at the BS.

\subsection{Received Signals}

The received signal at each of the $B$ BS antennas is filtered using an analog BPF that, in this work, is assumed to be ideal and matched to the transmit signal.
Specifically, the filtered continuous-time passband signal received at BS antenna $b = 1, 2, \dots, B$ is  contained within the frequency interval $[F_c - F_s/2, F_c + F_s/2]$ and can be written as
\begin{IEEEeqnarray}{rCl} \label{eq:tx_ct_pb}
	\tilde{x}_b(t) &=& \sqrt{2}\Re\mathopen{}\left\{  x_b(t)e^{j2\pi{F_c}t} \right\}
\end{IEEEeqnarray}
where the complex envelope $x_b(t)$ of $\tilde{x}_b(t)$ is given by
\begin{IEEEeqnarray}{rCl} \label{eq:tx_ct_bb}
x_b(t)
&=& \sum_{u=1}^U \int_{-\infty}^\infty h_{b,u}(\tau)s_{u}\mathopen{}\left(t - \tau\right)\fack{\!\tau} + w_b(t). \IEEEeqnarraynumspace
\end{IEEEeqnarray}
Here, $h_{b,u}(\tau)$ is the impulse response of the linear time-invariant channel connecting the $u$th UE to the $b$th BS antenna.
Furthermore, $w_b(t)$ is the filtered continuous-time additive white Gaussian noise (AWGN) with power spectral density (PSD) that is constant  and equal to $N_0$ in the frequency band $[F_c - F_s/2, F_c + F_s/2]$ and zero outside this~interval.

The passband signal $\tilde{x}_b(t)$ is amplified by a nonlinear LNA before being down-converted to baseband.
 The down-conversion step is performed by mixing the LNA output with a carrier signal generated by a LO.
Finally, the baseband signal is converted into the digital domain by a pair of finite resolution ADCs that perform sampling and amplitude quantization.
Each of these operations will introduce hardware impairments to the received signal.
We next discuss  behavioral models for each source of hardware~impairments.

\section{Behavioral Models for Hardware Impairments} \label{sec:behave}

Behavioral models provide a simple   relationship between the input and the output of a device under test, and can be tuned to match empirical measurements.
Their key advantages compared to more sophisticated and accurate physical models are that (i) they use only a small set of parameters and (ii) they do not require deep domain knowledge of the underlying physics governing the functioning of a device~\cite{ghannouchi09a}.
Behavioral models of nonideal hardware are commonly used in the design of impairment-mitigation algorithms, such as digital predistortion and phase-noise tracking.
We next introduce behavioral models for the set of nonideal hardware components considered in this~work.

\subsection{Low-Noise Amplifier: Behavioral Model}
Behavioral models for nonlinear amplifiers rely typically on Volterra series~\cite{benedetto79a} or generalized polynomial models~\cite{morgan06a}, although alternatives exist~\cite{ghannouchi09a, pedro05a, tehrani10a}.
If the bandwidth of the LNAs is large compared to the bandwidth of the received signal,  the impact of the LNA on the complex envelope of the received signal can be accurately modeled as a memoryless nonlinearity that is independent of the carrier frequency~\cite{saleh81a, kaye72a}.
In what follows, we consider a simple memoryless third-order  polynomial model for which  the LNA output at BS antenna $b = 1, 2, \dots, B$ is given by
\begin{IEEEeqnarray}{rCl}
\tilde{y}_b(t) &=& \sqrt{2} \Re\mathopen{}\left\{ y_b(t) e^{j2\pi{F_c}t} \right\}
\end{IEEEeqnarray}
where
\begin{IEEEeqnarray}{rCl}
y_{b}(t)
&=& f_\text{lna}\mathopen{}\left(x_{b}(t)\right) =  \alpha_1 x_{b}(t) + \alpha_2 x_{b}(t) \mathopen{}\left|x_{b}(t)\right|^2. \label{eq:f_lna}
\end{IEEEeqnarray}
Here, the coefficients $\alpha_1 \in \opC$ and $\alpha_2 \in \opC$ are the model parameters, which we assume to be known at the BS. Note that, in~\eqref{eq:f_lna}, we assumed that all LNAs at the BS are~identical.

\subsection{Phase Noise: Behavioral Model}

The output of the LNA is down-converted to baseband by mixing it with a carrier signal generated by a LO.
The down-converted signal is then passed through an analog LPF to eliminate unwanted aliases.
As shown in~\fref{fig:system}, we assume that all BS antennas are connected to a common LO.
The carrier signal generated by the LO typically contains  random phase variations stemming from circuit imperfections and  noise~\cite{razavi96a, lee00a}.
We model the filtered, down-converted signal at BS antenna $b = 1, 2, \dots, B$ as follows:
\begin{IEEEeqnarray}{rCl}
z_b(t)
&=& \text{LPF}\mathopen{}\left\{ \sqrt{2} \, e^{-j2\pi F_c t + j\phi(t)} \tilde{y}_b(t) \right\} \\
&=& \text{LPF}\mathopen{}\left\{ e^{j\phi(t)} y_b(t) + e^{-j4\pi F_c t + j\phi(t)}y_b^*(t)\right\} \IEEEeqnarraynumspace\\
&=& e^{j\phi(t)} y_b(t). \label{eq:f_mixer}
\end{IEEEeqnarray}
Here, $\phi(t)$ is the phase-noise process, and we have assumed that the LPF removes all aliases perfectly.

As we will discuss in~\fref{sec:composite}, we are interested in the realizations of the phase-noise process at the sampling time instances. Let $\phi[n] = \phi(nT_s)$. We model $\{ \phi[n]\}$ as the zero-mean random process defined by
\begin{IEEEeqnarray}{rCl}
\phi[n] &=& \lambda\phi[n-1] + \varphi[n]. \label{eq:phase_noise}
\end{IEEEeqnarray}
Here,  $0 < \lambda \leq 1$ and $\varphi[n] \sim \normal(0, \sigma_\varphi^2)$. The variance of the phase innovation (the phase-noise rate) is $\sigma_\varphi^2 = 2\pi\beta T_s$. We assume that the parameters of the behavioral model, i.e., the constants $\lambda$ and $\beta$, are known to the~BS.

Some comments are in order. By setting $\lambda = 1$ we retrieve the case of a \emph{free-running} LO studied in, e.g.,~\cite{pollet95a, tomba98a, katz04a}.
When $0<\lambda<1$, the process in~\eqref{eq:phase_noise} is stationary and corresponds to  a \emph{partially-coherent} LO. In this case, the process~\eqref{eq:phase_noise} models only residual phase errors after a phase-tracking scheme, e.g., a phase-locked loop (PLL)~\cite{petrovic07a}.
We will focus on this case in the remainder of the paper.

\subsection{Analog-to-Digital Converter: Behavioral Model} \label{sec:adc}

The down-converted signal is further converted into the digital domain---a process that involves discretization in both time and amplitude. The in-phase and quadrature components of the down-converted signal $z_b(t)$ are converted separately using a pair of ADCs with $q$-bit resolution that operate at sampling rate $F_s$.
Let $z_b[n] = z_b(nT_s)$ denote the input to the quantizer in the ADCs of the $b$th BS antenna ($b = 0,1,\dots,B-1$) at time $nT_s$.
Then, the corresponding ADC output can be written as
\begin{IEEEeqnarray}{rCl} \label{eq:f_adc}
	r_b[n] &=& f_\text{adc}(z_b[n]) = \mathcal{Q}\mathopen{}\left(\Re\{z_b[n]\}\right) + j 	\mathcal{Q}\mathopen{}\left(\Im\{z_b[n]\}\right) \IEEEeqnarraynumspace
\end{IEEEeqnarray}
where
\begin{IEEEeqnarray}{rCl} \label{eq:quantizer_uniform}
	Q(z) &=&
	\begin{cases}
		\frac{\Delta}{2}\mathopen{}\left(1-2^q\right)  & \text{if $z < -\frac{\Delta}{2} 2^q$ } \\
		\Delta\mathopen{}\left\lfloor \frac{z}{\Delta} \right\rfloor + \frac{\Delta}{2} & \text{if $\abs{z} < \frac{\Delta}{2} 2^q$} \\
		\frac{\Delta}{2}\mathopen{}\left(2^q-1\right) & \text{if $z > \frac{\Delta}{2} 2^q$}
	\end{cases} \IEEEeqnarraynumspace
\end{IEEEeqnarray}
models a $q$-bit uniform midrise quantizer with step size $\Delta$. We assume that the  parameters of the behavioral model, i.e., the number of bits $q$ and the step size $\Delta$, are known to the~BS.

\subsection{Discrete-Time Channel Input-Output Relation}

Since both the channel input $\{ s_u[n] \}$ and output $\{ r_b[n] \}$ are discrete-time random processes, it is convenient to work with a discrete-time channel input-output relation.
To this end, let $\vecx[n] = [x_1[n], x_2[n], \dots, x_B[n]]^T$ and let $\vecr[n] = [r_1[n], r_2[n], \dots, r_B[n]]^T$. By inserting~\eqref{eq:f_lna} and~\eqref{eq:f_mixer} into \eqref{eq:f_adc} we can write the discrete-time channel input-output relation, including the BS-side nonlinearities, in matrix form as
\begin{IEEEeqnarray}{rCl} \label{eq:inout_vec_discrete}
\vecr[n]  &=& f_\text{adc}\mathopen{}\left(  e^{j\phi[n]} f_\text{lna}\mathopen{}\left( \vecx[n]\right) \right)
\end{IEEEeqnarray}
where the scalar functions $f_\text{adc}(\cdot)$ and $f_\text{lna}(\cdot)$ are applied element-wise to vector inputs.
Now, let $\vecs[n] = [s_1[n], s_2[n], \dots, s_U[n]]^T$
denote the time-domain symbols transmitted from the $U$ UEs at time instant $nT_s$. Then,
\begin{IEEEeqnarray}{rCl} \label{eq:inout_channel_vec_discrete}
	\vecx[n] &=& \sum_{\ell = 0}^{L-1} \matH[\ell]\vecs[n-\ell] + \vecw[n].
\end{IEEEeqnarray}
Here, the entry on the $b$th row and on the $u$th column of $\matH[\ell] \in \opC^{B \times U}$ is $h_{b,u}[\ell]$, where $h_{b,u}[\ell]$ denotes the $\ell$th tap of the discrete-time channel, which corresponds to the $\ell$th sample of the convolution between $h_{b,u}(\tau)$ and $\sinc(\tau/T_s)$. Furthermore, $\vecw[n] = [w_1[n], w_2[n], \dots, w_B[n]]^T \distas \jpg(\matzero_{B \times 1},N_0\matI_B)$ is the discrete-time AWGN with $w_b[n] = w_b(nT_s)$.

\section{Composite Hardware-Impairment Model} \label{sec:composite}

The nonlinearities $f_\text{lna}(\cdot)$ and $f_\text{adc}(\cdot)$ in the behavioral model~\eqref{eq:inout_vec_discrete} renders a theoretical performance analysis challenging.
We now derive an approximate, yet accurate, aggregate statistical model for the distortion caused by the hardware impairments reviewed in~\fref{sec:behave}.
Specifically, our approach consists of the following two steps.
First, by assuming that the input to each nonlinear hardware component is Gaussian and by leveraging Bussgang's theorem~\cite{bussgang52a},  we  write the output of each nonlinear hardware component as a linear function of the input plus an additive distortion term that is uncorrelated with the input.
Second, we combine the individual linearized models to obtain an aggregate linearized model for the joint distortion caused by the nonideal hardware components.

It is worth clarifying at this point that, although the individual linearized models are exact, provided that the input to the corresponding nonlinear hardware component is Gaussian, the resulting aggregated model is only an approximation.
Indeed, although the input to the first nonlinear hardware component can  be assumed Gaussian if the transmitted signal is Gaussian, its output, which becomes the input to the next nonlinear hardware component, is typically not Gaussian.
Nevertheless, as we will demonstrate in~\fref{sec:numerical}, the Bussgang-based aggregate linearized model turns out to be surprisingly accurate.

\subsection{Linearization via Bussgang's Theorem}

We start by formalizing Bussgang's theorem.
Assume that $\{\vecp[n]\}$, where $\vecp[n]\in\opC^B$, is a stationary vector-valued circularly-symmetric Gaussian process and that $\vecq[n] = f(\vecp[n])$ where $f(\cdot)$ is some scalar-valued function that is applied element-wise on a vector.
Let $\matC_\vecp[m] = \Ex{}{\vecp[n]\vecp^H[n-m]}$   and let $\matC_{\vecq\vecp}[m] = \Ex{}{\vecq[n]\vecp^H[n-m]}$  Then, according to Bussgang's theorem~\cite{bussgang52a}, it holds~that
\begin{IEEEeqnarray}{rCl} \label{eq:bussgang}
	\matC_{\vecq\vecp}[m] &=& \matG\matC_{\vecp}[m]
\end{IEEEeqnarray}
where the linear gain $\matG \in \opC^{B \times B}$ is a diagonal matrix with diagonal entries given by
\begin{IEEEeqnarray}{rCl} \label{eq:bussgang_gain}
\mathopen{}\left[\matG\right]_{b,b}
&=& \frac{1}{\Ex{}{|p_b[n]|^2}} \Ex{}{f(p_b[n])p_b^*[n]}.
\end{IEEEeqnarray}
It follows from~\eqref{eq:bussgang}~that
\begin{IEEEeqnarray}{rCl} \label{eq:bussgang_decomp_tot}
	\vecq[n] &=& \matG\vecp[n] + \vece[n]
\end{IEEEeqnarray}
where the distortion $\{\vece[n]\}$, which is not Gaussian distributed in general, is uncorrelated with $\{\vecp[n]\}$.
The autocovariance of the distortion~$\matC_\vece[m] = \Ex{}{\vece[n]\vece^H[n-m]}$ is readily obtained from~\eqref{eq:bussgang_decomp_tot} as follows:
\begin{IEEEeqnarray}{rCl} \label{eq:bussgang_dist}
	\matC_\vece[m] &=& \matC_\vecq[m] - \matG \matC_\vecp[m] \matG^H.
\end{IEEEeqnarray}

In what follows, we  use Bussgang's theorem to linearize the input-output relation of each nonlinear hardware component separately.
We then combine the resulting linearized expressions to obtain a simple, yet accurate, approximation for the ADC output $\vecr[n]$ in~\eqref{eq:inout_vec_discrete} as a function of the LNA input in~\eqref{eq:f_lna}.

Starting from the LNA, if we assume $\vecx[n]$ in~\eqref{eq:inout_channel_vec_discrete} to be circularly symmetric Gaussian distributed, we can write the LNA output $\vecy[n] = [y_1[n], y_2[n], \dots, y_B[n]]^T$ as
\begin{IEEEeqnarray}{rCl}
\vecy[n] &= f_\text{lna}\mathopen{}\left( \vecx[n] \right) &= \matG_\text{lna}\vecx[n] + \vece_\text{lna}[n]. \label{eq:bussgang_decomp_lna}
\end{IEEEeqnarray}
Note that $\vecx[n]$ is Gaussian if we take the input symbols to be Gaussian, i.e., $\vecs[n]\distas\jpg(\veczero_{U \times 1}, \frac{S}{N} \matI_U)$ and the channel $\{\matH[\ell]\}$ to be known at the BS.
We will adopt these two assumptions in the remainder of the paper.

Similarly, if we assume $\{\vecy[n]\}$ to be a circularly-symmetric stationary Gaussian process, we can write the down-converted signal $\vecz[n] = [z_1[n], z_2[n], \dots, z_B[n]]^T$ as
\begin{IEEEeqnarray}{rCl}
\vecz[n] &= e^{j\phi[n]}\vecy[n] &= \matG_\text{osc}\vecy[n] + \vece_\text{osc}[n]. \label{eq:bussgang_decomp_osc}
\end{IEEEeqnarray}
Finally, if we let $\{\vecz[n]\}$ be a circularly-symmetric stationary Gaussian process, we can write the ADC output $\vecr[n]$ as
\begin{IEEEeqnarray}{rCl}
\vecr[n] &= f_\text{adc}\mathopen{}\left( \vecz[n] \right) &= \matG_\text{adc}\vecz[n] + \vece_\text{adc}[n]. \label{eq:bussgang_decomp_adc}
\end{IEEEeqnarray}

Next, we combine~\eqref{eq:bussgang_decomp_lna}, \eqref{eq:bussgang_decomp_osc}, and \eqref{eq:bussgang_decomp_adc}	 to obtain the following approximation for~$\vecr[n]$ in~\eqref{eq:inout_vec_discrete}:
\begin{IEEEeqnarray}{rCl}
\vecr[n]
&\approx& \matG_\text{adc}\matG_\text{osc}\matG_\text{lna}\vecx[n] + \vece_\text{adc}[n]  \nonumber\\
&& +\,  \matG_\text{adc}\vece_\text{osc}[n] + \matG_\text{adc}\matG_\text{osc}\vece_\text{lna}[n] \label{eq:bussgang_approx_1} \\
&=& \matG_\text{tot}\vecx[n] + \vece_\text{tot}[n] \label{eq:bussgang_approx_2}.
\end{IEEEeqnarray}
Here, $\vece_\text{tot}[n] = \vece_\text{adc}[n] + \matG_\text{adc}\vece_\text{osc}[n] + \matG_\text{adc}\matG_\text{osc}\vece_\text{lna}[n]$ and $\matG_\text{tot} = \matG_\text{adc}\matG_\text{osc}\matG_\text{lna}$.
We emphasize that~\eqref{eq:bussgang_approx_1} is an approximation since the output of the first nonlinear hardware component in our chain, i.e., the LNA, is not Gaussian distributed. Nevertheless, as we will demonstrate in~\fref{sec:numerical}, the approximation~\eqref{eq:bussgang_approx_1} turns out to be surprisingly accurate.

The frequency-domain received hardware-impaired vector on the $k$th subcarrier ($k = 0,1,\dots,N-1$) is given by
\begin{IEEEeqnarray}{rCl} \label{eq:rk_vec}
	\hat\vecr[k] &=& \frac{1}{\sqrt{N}} \sum_{n = 0}^{N-1}  \vecr[n]  e^{-jk\frac{2\pi}{N}n}.
\end{IEEEeqnarray}
Let $\hat\vecs[k] = [\hat{s}_1, \hat{s}_2, \dots, \hat{s}_{U}]^T$. Then, by substituting~\eqref{eq:inout_channel_vec_discrete} and~\eqref{eq:bussgang_approx_2} into~\eqref{eq:rk_vec} we obtain the following approximation for $\hat\vecr[k]$:
\begin{IEEEeqnarray}{rCl} \label{eq:bussgang_approx_freq}
\hat\vecr[k]
&\approx& \matG_\text{tot} \mathopen{}\left(\widehat\matH[k]\hat\vecs[k] + \hat\vecw[k]\right) + \hat\vece_\text{tot}[k]. \IEEEeqnarraynumspace
\end{IEEEeqnarray}
Here,~$\widehat\matH[k] = \sum_{\ell = 0}^{L-1}\matH[\ell]e^{-jk\frac{2\pi}{N}\ell}$ is the frequency-domain channel matrix associated with the $k$th subcarrier. Furthermore, $\hat\vece_\text{tot}[k] = \frac{1}{\sqrt{N}} \sum_{n = 0}^{N-1} \vece_\text{tot}[n] e^{-jk\frac{2\pi}{N}n}$ and $\hat\vecw[k] =  \frac{1}{\sqrt{N}}\sum_{n = 0}^{N-1} \vecw[n] e^{-jk\frac{2\pi}{N}n} \distas \jpg(\matzero_{B \times 1}, N_0\matI_B)$ is the frequency-domain distortion and AWGN, respectively.
From~\eqref{eq:bussgang_approx_freq}, we find that the covariance $\matC_{\hat\vecr}[k] = \Ex{}{\hat\vecr[k]\hat\vecr^H[k]}$ of $\hat\vecr[k]$ for $k = 0,1,\dots,N-1$ can be approximated as
\begin{IEEEeqnarray}{rCl} \label{eq:Cr_k}
\matC_{\hat\vecr}[k]
&\approx& \matG_\text{tot} \matC_{\hat\vecx}[k] \matG_\text{tot}^H + \matC_{\hat\vece_\text{tot}}[k] \IEEEeqnarraynumspace
\end{IEEEeqnarray}
where $\matC_{\hat\vecx}[k] = \opE\big[\hat\vecx[k]\hat\vecx^H[k]\big] =\widehat\matH[k]\matC_{\hat\vecs}[k]\widehat\matH^H[k] + N_0\matI_B$.
Here, $\matC_{\hat\vecs}[k] = \opE\big[\hat\vecs[k]\hat\vecs^H[k]\big]$ is the covariance of $\hat\vecs[k]$, which is equal to $\matI_B$ if $k \in \setS$ and to $\matzero_{B \times B}$ if $k \in \setG$. Furthermore,
\begin{IEEEeqnarray}{rCl} \label{eq:Ce_tot_k}
\matC_{\hat\vece_\text{tot}}[k] = \Ex{}{\hat\vece_\text{tot}[k]\hat\vece_\text{tot}^H[k]} = \sum_{m=0}^{N-1} \matC_{\vece_\text{tot}}[m] e^{-jk\frac{2\pi}{N}m} \IEEEeqnarraynumspace
\end{IEEEeqnarray}
where
\begin{IEEEeqnarray}{rCl} \label{eq:Ce_tot_time}
\matC_{\vece_\text{tot}}[m]
&=& \Ex{}{\vece_\text{tot}[n]\vece_\text{tot}^H[n-m]} \\
&=& \matC_{\vece_\text{adc}}[m] + \matG_\text{adc}\matC_{\vece_\text{osc}}[m]\matG_\text{adc}^H \nonumber\\
&&+\, \matG_\text{osc}\matG_\text{adc}\matC_{\vece_\text{osc}}[m]\matG_\text{adc}^H\matG_\text{osc}^H.
\end{IEEEeqnarray}
The covariance matrices~\eqref{eq:Cr_k} and~\eqref{eq:Ce_tot_k} can be used to analyze the PSD of the hardware-impaired signal. Indeed, they describe how the per-subcarrier received signal and the corresponding distortion are correlated in the spatial domain.
They also allow us to separate the contributions due to the intended signal from the one due to  distortion, which is useful in performance analyses, as exemplified in~\fref{sec:ber}.
We now provide closed-form expressions for $\matG_\text{lna}$, $\matG_\text{osc}$, and $\matG_\text{adc}$, as well as for the autocovariance of the three distortion processes $\{\vece_\text{lna}[n]\}$, $\{\vece_\text{osc}[n]\}$, and~$\{\vece_\text{adc}[n]\}$, which are all required for evaluating~\eqref{eq:Cr_k} and~\eqref{eq:Ce_tot_k}.

\subsection{Low-Noise Amplifier: Linearized Model}

By inserting the behavioral model~\eqref{eq:f_lna} into \eqref{eq:bussgang_gain} we find that $\mathopen{}\left[\matG_\text{lna}\right]_{b,b} =  \alpha_1 + 2\alpha_2\Ex{}{|x_b[n]|^2}$ for $b = 1, 2, \dots, B$.
Hence,
\begin{IEEEeqnarray}{rCl} \label{eq:G_lna}
\matG_\text{lna} &=& \alpha_1\matI_B + 2\alpha_2\diag\mathopen{}\left( \matC_\vecx[0]\right).
\end{IEEEeqnarray}
Similarly, we have that
\begin{IEEEeqnarray}{rCl}
	\matC_\vecy[m]
	&=& \Ex{}{\vecy[n]\vecy^H[n-m]} \\
	&=& \Ex{}{f_\text{lna}(\vecx[n])f_\text{lna}(\vecx[n-m])^H} \\
	&=& \abs{\alpha_1}^2\matC_\vecx[m] + 2\abs{\alpha_2}^2 \matC_\vecx[m] \circ \abs{\matC_\vecx[m]}^2 \IEEEeqnarraynumspace\nonumber\\
	&& + 2 \alpha_1^*\alpha_2 \diag\mathopen{}\left( \matC_\vecx[0]\right) \matC_\vecx[m] \nonumber\\
	&& + 2 \alpha_2^*\alpha_1 \matC_\vecx[m] \diag\mathopen{}\left( \matC_\vecx[0]\right) \nonumber\\
	&& + 2\abs{\alpha_2}^2 \diag\mathopen{}\left( \matC_\vecx[0]\right) \matC_\vecx \diag\mathopen{}\left( \matC_\vecx[0]\right). \label{eq:Cy} \IEEEeqnarraynumspace
\end{IEEEeqnarray}
Here,~$\matC_\vecx[m] \!=\! \Ex{}{\vecx[n]\vecx^H[n\!-\!m]} \!= \!\frac{1}{N}\sum_{k=0}^{N-1} \matC_{\hat\vecx}[k]e^{jk\frac{2\pi}{N}m}$.
Let now $\matC_{\vece_\text{lna}}[m] = \Ex{}{\vece_\text{lna}[n]\vece_\text{lna}^H[n-m]}$. By substituting \eqref{eq:G_lna} and \eqref{eq:Cy} into \eqref{eq:bussgang_dist}, we find that
\begin{IEEEeqnarray}{rCl} \label{eq:Ce_lna}
\matC_{\vece_\text{lna}}	[m] &=& 2 \abs{\alpha_2}^2 \matC_\vecx[m] \circ \abs{\matC_\vecx[m]}^2.
\end{IEEEeqnarray}

\subsection{Phase Noise: Linearized Model}

By inserting~\eqref{eq:f_mixer} into \eqref{eq:bussgang_gain} we find that $\mathopen{}\left[ \matG_\text{osc}\right]_{b,b} = \opE\big[e^{j\phi[n]}\big]$ for $b = 1,2,\dots,B$. Since we assumed that $0 < \lambda < 1$, the random process $\{ \phi[n] \}$ in~\eqref{eq:phase_noise} is a stationary Gaussian process with zero mean and~variance $\sigma_\phi^2 = \Ex{}{\phi^2[n]} = \frac{2\pi\beta T_s}{1-\lambda^2}$.
Hence, $\matG_\text{osc}$ in~\eqref{eq:bussgang_decomp_osc} is given by
\begin{IEEEeqnarray}{rCl} \label{eq:G_osc}
	\matG_\text{osc} &=& \opE\big[e^{j\phi[n]}\big]	\matI_B = e^{-\frac{1}{2}\sigma_\phi^2}\matI_B= e^{-\frac{\pi\beta T_s}{1-\lambda^2}}\matI_B.
\end{IEEEeqnarray}
Here, we used that $\opE\big[e^{jv\phi[n]}\big] = e^{-\frac{1}{2}v^2\sigma_\phi^2}$ is the characteristic function of $\phi[n] \distas \normal(0, \sigma_\phi^2)$.
Similarly,
\begin{IEEEeqnarray}{rCl}
\matC_\vecz[m]
&=& \Ex{}{\vecz[n]\vecz^H[n-m]}	\\
&=& \opE\big[e^{j(\phi[n] - \phi[n-m])}\big]\Ex{}{\vecy[n]\vecy^H[n-m]} \\
&=& e^{- \sigma_\phi^2 +  \rho_\phi(m)} \matC_\vecy[m] \label{eq:Cz}
\end{IEEEeqnarray}
where $\rho_\phi(m) = \Ex{}{\phi[n]\phi[n-m]} = \frac{2\pi\beta T_s}{1-\lambda^2}\lambda^{\abs{m}}$.
Let now $\matC_{\vece_\text{osc}}[m] = \Ex{}{\vece_\text{osc}[n]\vece_\text{osc}^H[n-m]}$. By substituting~\eqref{eq:G_osc} and~\eqref{eq:Cz} into~\eqref{eq:bussgang_dist}, we find~that
\begin{IEEEeqnarray}{rCl} \label{eq:Ce_lna}
\matC_{\vece_\text{osc}}[m]
&=& \mathopen{}\left(e^{-\frac{2\pi\beta T_s}{1-\lambda^2}\mathopen{}\left( 1 - \lambda^{\abs{m}} \right)} -  e^{-\frac{2\pi\beta T_s}{1-\lambda^2}} \right)\matC_{\vecy}[m].
\end{IEEEeqnarray}

\subsection{Analog-to-Digital Converter: Linearized Model}

Many recent papers have used Bussgang's theorem to analyze the distortion caused by amplitude quantization (see, e.g.,~\cite{jacobsson17b, mollen16c, zhang12a, li17b, jacobsson17d, jacobsson17e,mezghani12b}).
As pointed out in these contributions (see, e.g.,~\cite[Eq.~(14)]{jacobsson17d}), the matrix  $\matG_\text{adc}$ in~\eqref{eq:bussgang_decomp_adc} is given by
\begin{IEEEeqnarray}{rCl} \label{eq:G_adc}
\matG_\text{adc} &=& \frac{\Delta}{\sqrt{\pi}} \, \diag\mathopen{}\left(\matC_\vecz[0]\right)^{-1/2} \nonumber \\
&&\times\sum_{i=1}^{2^q-1} \exp\mathopen{}\left(-\Delta^2\mathopen{}\left( i - 2^{q-1} \right)^2 \diag\mathopen{}\left(\matC_\vecz[0]\right)^{-1}\right). \IEEEeqnarraynumspace
\end{IEEEeqnarray}
Let now $\matC_{\vece_\text{adc}}[m] = \Ex{}{\vece_\text{adc}[n]\vece_\text{adc}^H[n-m]}$. Unfortunately, no closed-form expression for $\matC_{\vece_\text{adc}}[m]$ is available for $q > 1$. Therefore, in what follows, we  evaluate $\matC_{\vece_\text{adc}}[m]$ using the diagonal approximation put forward in~\cite[Sec.~IV]{jacobsson17e}. Specifically, we approximate $\matC_{\vece_\text{adc}}[m]$ by
\begin{IEEEeqnarray}{rCl} \label{eq:diagonal_approx}
\matC_{\vece_\text{adc}}[0]	&\approx& \frac{\Delta^2}{2}\mathopen{}\left( 2^q - 1 \right)^2\matI_B  -\matG_\text{adc}\diag\mathopen{}\left(\matC_{\vecz}[0]\right)\!\matG_\text{adc}  \nonumber\\
&& -4\Delta^2 \!\sum_{i=1}^{2^q-1} \! \mathopen{}\left(i - 2^{q-1}\right) \nonumber\\
&& \times\mathopen{}\left(1- Q\mathopen{}\left( \sqrt{2}\mathopen{}\left(i - 2^{q-1}\right)\diag\mathopen{}\left(\matC_\vecz[0]\right)^{-1/2} \right)\right) \IEEEeqnarraynumspace
\end{IEEEeqnarray}
for $m=0$ and by $\matC_{\vece_\text{adc}}[m] = \matzero_{B \times B}$ for $m \neq 0$.
Here, $Q(x) = \frac{1}{\sqrt{2\pi}}\int_{x}^\infty e^{-u^2/2} \, \fack{\!u}$.
As shown in \cite[Sec.~V]{jacobsson17e}, this approximation is accurate for ADCs with $q\geq 3$.

\newcommand{0.9}{0.9}
\newcommand{\hspace{1.0cm}}{\hspace{1.0cm}}
\begin{figure*}[!t]
\centering
\subfloat[PSD of $\{\vecr{[n]}\}$ when the only nonideal hardware component at the BS is the LNA; $\alpha_1 = 1.065$ and $\alpha_2 = -0.028$.]{\includegraphics[width=0.9\columnwidth]{psd_amp.pdf}\label{fig:psd_amp}}
\hspace{1.0cm}
\subfloat[PSD of $\{\vecr{[n]}\}$ when the only nonideal hardware component at the BS is the LO; $\lambda = 0.99$ and $\beta = 10^3$.]{\includegraphics[width=0.9\columnwidth]{psd_osc.pdf}\label{fig:psd_osc}}	\\
\subfloat[PSD of $\{\vecr{[n]}\}$ when the only nonideal hardware component at the BS is the ADC; $q = 6$ and $\Delta = 0.086\sqrt{1.172 + N_0}$.]{\includegraphics[width=0.9\columnwidth]{psd_adc.pdf}\label{fig:psd_adc}}
\hspace{1.0cm}
\subfloat[PSD of $\{\vecr{[n]}\}$ when all hardware components, i.e., the LNAs, the LO, and the ADCs, are nonideal; parameters taken from (a), (b), and (c).]{\includegraphics[width=0.9\columnwidth]{psd_all.pdf}\label{fig:psd_all}}
\vspace{0.05cm}
\caption{PSD of $\{\vecr[n]\}$; $B = 32$, $U = 4$, $L=10$, $S = 300$, $N = 1024$, and $N_0 = 0$. The colored markers correspond to numerical simulations; the black lines correspond to analytical results.
Note that the analytical PSDs in \fref{fig:psd_amp} and \fref{fig:psd_osc} are exact for Gaussian inputs.
The analytical PSD in \fref{fig:psd_adc} verifies the accuracy of the approximation~\eqref{eq:diagonal_approx}. The analytical PSD in \fref{fig:psd_all} verifies the accuracy of the composite hardware-impairment model presented in~\fref{sec:composite}.}
\label{fig:psd}
\end{figure*}

\section{Numerical Results} \label{sec:numerical}

We now demonstrate the accuracy of our models and their usefulness in performance analyses.
In what follows, the number of BS antennas is $B = 32$ and the number of UEs is $U=4$. We consider LTE-inspired OFDM parameters. Specifically, the occupied subcarriers are the first $S/2$ to the left and the first $S/2$ to right of the DC subcarrier, i.e., $\setS = \{ 1, 2, \dots, S/2\} \union \{ N-S/2, N-S/2+1, \dots, N-1\}$.
Furthermore, the number of occupied subcarriers is $S = 300$, the total number of subcarriers is $N = 1024$, and the subcarrier spacing is $F_\text{sub} = 15$~kHz. Hence, the sampling rate is $F_s = NF_\text{sub} = 15.36$~MHz and the OSR is $3.41$.
We set the polynomial coefficients of the LNA to $\alpha_1 = 1.065$ and $\alpha_2 = -0.028$. For the phase-noise process, we set $\lambda = 0.99$ and $\beta = 10^3$.
For the ADCs, the number of bits is $q=6$ and the step size is $\Delta = 0.086\sqrt{1.172 + N_0}$.
We draw the elements of $\matH[\ell]$ for $\ell = 0,1,\dots,L-1$ independently from the $\jpg(0, L^{-1})$ distribution.
The number of nonzero channel taps is~$L = 10$.

For the numerical simulations, we draw each transmitted symbol~$\hat\vecs[k]$ for $k \in \setS$ independently from a quadrature phase-shift keying~(QPSK) constellation.
Although our theoretical analysis requires the received time-domain signal to be Gaussian, drawing the input symbols from a QPSK constellation leads to negligible errors.
Indeed, the received time-domain signal is the sum of $US = 1200$ independent and identically distributed random variables, which can be well-approximated by a Gaussian random variable according to the central limit~theorem.

\subsection{Power Spectral Density}

In~\fref{fig:psd}, we plot the PSD of~$\{\vecr[n]\}$.
The average value of the PSD on the $k$th subcarrier, averaged over the $B$ BS antennas, is obtained analytically by computing~$\frac{1}{B}\vecnorm{\diag\mathopen{}\left(\matC_{\hat\vecr}[k]\right)}^2_2$ for $k = 0,1,\dots,N-1$, where $\matC_{\hat\vecr}[k]$ is given in~\eqref{eq:Cr_k}.
The simulated curve is obtained via Monte-Carlo sampling.
We note from \fref{fig:psd_all} that the PSD obtained using the aggregate hardware-impairment model~\eqref{eq:Cr_k} describes accurately the spectral regrowth caused by the nonideal hardware components and agrees perfectly with the numerical simulations, confirming the accuracy of our linearized aggregate model.

\begin{figure}[!t]
\centering
\includegraphics[width=.9\columnwidth]{ber_4x32.pdf}
\caption{Uncoded BER with zero forcing and QPSK; $B = 32$, $U = 4$, $L=10$, $S = 300$, $N = 1024$, $\alpha_1 = 1.065$, $\alpha_2 = -0.028$, $\beta = 10^3$, $\lambda = 0.99$, $q = 6$, and $\Delta = 0.086\sqrt{1.172 + N_0}$. Here, $\textit{SNR} = 1/N_0$. The markers correspond to simulation results and the lines to the analytical approximation proposed in~\eqref{eq:ber}. Clearly, our analysis is extremely accurate.}
\label{fig:ber}
\end{figure}

\subsection{Bit-Error Rate} \label{sec:ber}

A zero-forcing estimate $\hat\vecs_\text{est}[k]$ of the transmitted symbols $\hat\vecs[k]$ is obtained from $\hat\vecr[k]$ for $k = 0,1,\dots,N-1$~as
\begin{IEEEeqnarray}{rCl} \label{eq:forza_zero}
	\hat\vecs_\text{est}[k] &=& \widehat\matA^H[k] \,\hat\vecr[k]
\end{IEEEeqnarray}
where $\widehat\matA[k] = \matG_\text{tot}\widehat\matH[k]\big( \matG_\text{tot}\widehat\matH[k]\widehat\matH^H[k]\matG_\text{tot}^H\big)^{-1}$.
By inserting the approximation~\eqref{eq:bussgang_approx_freq} into \eqref{eq:forza_zero}, we find a linear relationship between $\hat{\vecs}[k]$ and $\hat{\vecs}_\text{est}[k]$, which makes it straightforward to compute the resulting signal-to-interference-noise-and-distortion ratio (SINDR) for the $u$th UE ($u = 1,2,\dots,U$) as follows:
\begin{IEEEeqnarray}{rCl} \label{eq:sindr}
\textit{SINDR}_{u}[k]
&\approx& \frac{\big\lvert\widehat\veca_{u}^H[k] \matG_\text{tot} \hat\vech_{u}[k]\big\rvert^2 }{  I_{u}[k] + N_{u}[k] + D_{u}[k]}.
\end{IEEEeqnarray}
Here, $\hat\veca_u[k] \in \opC^B$ is the $u$th column of $\widehat\matA[k]$, $\hat\vech_u[k] \in \opC^B$ is the $u$th column of $\widehat\matH[k]$, $I_{u}[k] = \sum_{v \neq u}\big\lvert\hat\veca_{u}^H[k]\matG_\text{tot} \hat\vech_{v}[k]\big\rvert^2$, $N_{u}[k] = N_0 \|\hat\veca_{u}^H[k]\matG_\text{tot}\|_2^2$, and $D_{u}[k] = \hat\veca_{u}^H[k]\matC_{\hat\vece_\text{tot}}[k] \,\hat\veca_{u}[k]$.

In~\fref{fig:ber}, we show the uncoded BER with zero forcing and QPSK signaling, which we approximate as
\begin{IEEEeqnarray}{rCl} \label{eq:ber}
\textit{BER} &\approx& \frac{1}{US}\sum_{u=1}^U \sum_{k \in \setS} Q\mathopen{}\left( \sqrt{\textit{SINDR}_u[k]}\right)
\end{IEEEeqnarray}
where $\textit{SINDR}_u[k]$ is given in~\eqref{eq:sindr}.
In~\fref{fig:ber}, we have averaged the BER over $100$ channel realizations. We note that the performance predicted by the composite hardware-impairment model is again in excellent agreement with the numerical results.

\section{Conclusions and Future Work}

In this work, we have presented a linearized aggregate model for BS-side hardware impairments, which is derived from behavioral models of nonideal hardware components via Bussgang's decomposition.
Although the proposed aggregate model is not exact because it relies on the Gaussianity of the input to each nonlinear hardware component (which does, in general, not hold in practice), it turns out to be extremely accurate for many scenarios of interest, such as the massive MU-MIMO-OFDM uplink system considered in~\fref{sec:numerical}.

The analysis presented in this paper can be extended to the case of pilot-based channel estimation and to the MU-MIMO-OFDM downlink.
One limitation of our current framework is that it is confined to memoryless nonlinearities  and does not capture other sources of hardware impairments, such as in-phase/quadrature imbalance and mutual coupling.
An extension of our analysis to incorporate these impairments  is part of ongoing work.

\balance

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


text:
DUI arrests made
By Editor | March 19, 2012 | 0
Posted: Monday, March 19, 2012 4:51 pm
The Messenger, March 19, 2012
Union City police made arrests for driving under the influence in two separate cases over the weekend.
Kelly A. Adam, 31, of 440 Iowa St., Paducah, Ky., was arrested Friday after police received a call of a reckless driver coming from Reelfoot Avenue and turning onto Miles Avenue.
The officer first observed the vehicle in the parking lot at the Woman's Clinic on Bishop Street, but before he could stop and turn around, Ms. Adam allegedly turned east on Bishop Street and then north on Miles Avenue, causing oncoming traffic to have to avoid hitting the vehicle.
Once stopped, the officer noticed Ms. Adam was very nervous. He asked her to step out of the vehicle and to try several field sobriety tests. She tried to perform the tests, but refused a blood test in the emergency room at Baptist Memorial Hospital-Union City. She was charged with DUI second offense and violation of the implied consent law.
Mark Stacey Cobb, 46, of 582 East College St., Jackson, was charged with DUI fifth offense and violation of the implied consent law when he was stopped in the 1500 block of East Reelfoot Avenue after the Union City police received two different complaints of a reckless driver.
The officer reported Cobb appeared unsteady on his feet, admitted to drinking and refused to perform sobriety tests.


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On Sunday 11 February 2018 from 16h30 to 18h00.
On Saturday 3 February 2018 from 09h30 to 18h30.
On Saturday 8 July 2017 from 09h30 to 18h30.
From Friday 9 June 2017 at 09h00 to Saturday 10 June 2017 at 18h00.
On Saturday 2 July 2011 from 18h00 to 23h59.
On Thursday 20 May 2010 from 19h30 to 22h30.


text:
Q: Tracing the "sender hierarchy" in Scala actors I'm maintaining a couple of actor-based Scala applications at the moment, and one question I find myself asking all the time is Who sends that message?
For example, I find the piece of code that prints the scary message I found in the logs:
case ReportFailedUpdates(stuff) =>
  log("The horror! The horror! " + stuff)
  dieHorribly()

and I want to find out what might be the cause.  If I weren't using actors, I could hit Ctrl+Alt+H (at least in Eclipse) and find out who 'called' this 'method' (and who called that, and who called that).  With actors, I find myself searching for ! ReportFailedUpdates( to find which actors send this message, then searching for the senders of the message that actor was reacting to, etc (and usually drawing the result on paper).  This has two disadvantages:

*

*It's slower, since Eclipse is doing a text search over the (potentially many) project(s) and I'm having to note stuff down

*It doesn't necessarily find all occurrences, since maybe this was sent with !?, or maybe someone put two spaces between the ! and the ReportFailedUpdates, or, or, or....

What I'd love is some tooling support that lets me find out where a message could have come from - roughly the equivalent of a call hierarchy for non-actor-based code.
Are there any tools that do it? Is this a feature of the ScalaIDE for Eclipse that I just haven't discovered? If I use IntelliJ will my life be better?
Update
My example may have been misleading.  This isn't just about figuring out what's gone wrong when it all falls over -  I also find myself doing this a lot when I pick up a new system and need to figure out how it works. Seems like there isn't yet a tool to do it. Guess I'll have to have a think myself about how you could start to statically extract (and maybe visualize) the message flow graph...

A: Well, that is quite the hefty desire, and I'd be extremely impressed if someone were to write it, but I haven't seen anything like that as yet.
Tracing it will be very difficult since there's no "stack" to trace.  I'm curious why you don't do this, though:
case ReportFailedUpdates(stuff) =>
    log("The horror! The horror! %s (sent by %s)".format(stuff, sender))
    dieHorribly()

That would at least give you the current link in the chain.
As well - I'm a Vim guy so excuse my ignorance - does your IDE not have a better search mechanism, such as Regexes?

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text:
SYNONYM

#### According to
The Catalogue of Life, 3rd January 2011

#### Published in
Fl. jap. 1:88, t. 43. 1839

#### Original name
null

### Remarks
null

redpajama_set_name: RedPajamaGithub


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James Maybrick had secured his legacy as the most infamous serial killer of all time…his diary would one day shock the world.
Thomas Quinn wants revenge…his actions will give birth to an organisation of unspeakable power.
Together, they unwittingly set in motion a plan that will one day lead to the serial killer, Obadiah Stark.
Stark became The Tally Man.
In Extremis is a novella that picks up immediately after the last murder by Jack The Ripper, the author has another book, Hellbound that people say you should read before this one. I decided to read this first, James Maybrick is The Ripper & in this short novella we get to read his thoughts & state of mind in the immediate aftermath of the killers. Thomas Quinn is one of the Brethren, a group of "individuals" who have an idea of what society should be and see Maybrick as a means to an end. When Maybrick puts them at risk, Quinn and the Brethren set in motion a plan to clean the decks, without exposing the all important Brethren brotherhood.
Ooooh I do love all things Jack The Ripper, he has always been an enigma, so many conspiracy's and theories. I can't believe of the books I have read Maybrick didn't feature or if he did I don't remember him. I now want to go digging and have a read about Maybrick and his diary, In Extremis we get to go behind the scenes and see into the mind of one of the most notorious killers. Excerpts from the journal of James Maybrick which I did struggle with a few of the words with the curved writing however it was very late at night which probably contributed!
Apart from a few big words I needed to look up, the writing flows well, it is well written creating a creepy and eerie atmosphere making the reader pull their blanket just a wee bit closer and listen a bit more keenly to the creaks when late night reading. This was my first dance with this author, it won't be my last, 4/5 for me this time. I would warn, as with all Jack The Ripper themed books, some of the passages are graphic which may upset some of our faint hearted readers, otherwise dive right in.
Oh wow... this could be too creepy for a wimp like me, but you do have me curious. I can deal with some graphic content as long as it doesn't overwhelm.
This sounds good. Jack The Ripper was a such a horrible but fascinating character.
I think that I would want to read the books in order however.


text:
Michael Liam Farnan (born January 29, 1941) is a former politician in Ontario, Canada. He was a New Democratic Party member of the Legislative Assembly of Ontario from 1987 to 1995, and was a cabinet minister in the government of Bob Rae.

Background
Farnan was educated at University College in Dublin, the National University of Dublin, the University of London in England and McGill University in Montreal, Quebec, Canada. He has a Master's degree in Education, and a bachelor's degree of arts. He has worked as a primary and secondary school teacher in London, Montreal, Cambridge, Ontario and Brampton Ontario for twenty-seven years. A devout Roman Catholic working within Ontario's separate school system, he served as provincial director of the Ontario English Catholic Teacher's Association for a time, as well as participating in a variety of community outreach projects in Cambridge. After he retired from teaching in 2002, he studied to become a real estate agent and broker of his own company Mike Farnan Realty in Cambridge. He also served as associate broker for Crown Realty Royal Le Page and for Peak Realty, both located in Cambridge.

Politics
Farnan ran for the federal New Democratic Party in Cambridge during the 1980 federal election. He came second, 3,080 votes behind Progressive Conservative Chris Speyer.  He also served on the Cambridge city council for the period in the 1980s.

Farnan was elected to the Ontario legislature in the 1987 provincial election, defeating Liberal candidate Claudette Millar in the provincial riding of Cambridge (incumbent Progressive Conservative Bill Barlow finished third).  The NDP were the official opposition in this period, and Farnan served as his party's critic for Correctional Services and Tourism and Recreation.

The NDP won a majority government in the 1990 provincial election, and Farnan was re-elected by a landslide in Cambridge. On October 1, 1990, he was appointed as the Rae government's first Solicitor General and Minister of Correctional Services.

As Solicitor-General, Farnan introduced employment equity provisions for Ontario's police force. He also established a "common pause day" which continued the province's previous restrictions on Sunday shopping.  In the spring of 1991, he became involved in a minor controversy concerning two letters which had been sent from his staff to Justices of the Peace in Ontario, one of which requested the review of a case. This was seen by some as inappropriate interference from his office, and while Farnan did not write the letters himself, he was nonetheless dropped from cabinet on July 31, 1991.  In September 1991 he was appointed as Deputy Chairman of the house and he served in that role for the next two years.

On June 17, 1993, Farnan was re-appointed as a Minister without portfolio responsible for Education and Training. In this capacity, he served as an assistant to Minister of Education Dave Cooke.

Farnan returned to a full cabinet position on October 21, 1994, having been appointed Minister of Transportation.

In 1994, Farnan was one of twelve NDP members to vote against Bill 167, a bill extending financial benefits to same-sex partners. Premier Bob Rae allowed a free vote on the bill which allowed members of his party to vote with their conscience.

The NDP were defeated in the 1995 provincial election, and Farnan lost the Cambridge seat to Progressive Conservative Gerry Martiniuk by about 5,500 votes.  He ran a second time for the House of Commons of Canada in the 1997 federal election, but finished third against Liberal Janko Peric.

Cabinet positions

After politics
In the late 1990s, Farnan became a school teacher at St. Thomas Aquinas Secondary School in Brampton, Ontario. He specialized in social science courses (mainly Religion). He retired in December 1996.

In 2021 mike renounced his membership to the NDP and joined the Green Party.
As of December 2021 Mike is currently the campaign manager for Green Party of Ontario candidate Carla Johnson in the riding of Cambridge Ontario.

Electoral record

Provincial

Federal

References

External links

1941 births
Alumni of the University of London
Alumni of University College Dublin
Canadian Roman Catholics
Living people
McGill University alumni
Members of the Executive Council of Ontario
Ontario New Democratic Party MPPs

redpajama_set_name: RedPajamaWikipedia


However, when the PM appears to tell 'porkies' about overseas accounts, it is a different story and it took a week for him to reveal the full facts regarding his £30,000 account. Nice gift too from his mum of £200,000.
We all pay our taxes because we have to and because ultimately that money is used for the essential services that we need. There is no morality when our so called ruling classes are telling us we have to cut, telling us we are all in it together, taking our NHS and everything and right we have away from us, whilst at the same time they 'avoid' paying their tax and playing their part.


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