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Forty years ago this month, nearly 400 seniors at Logan High School were crossing the stage at what was then Logan Memorial Fieldhouse to receive their diplomas. On Friday, June 20, they will gather in Logan to celebrate that day four decades ago.
The countdown has begun for members of the LHS Class of 1974 to contact organizers Barbara Conn Stambaugh, Cheryl Mullins Taylor and Leah Ferguson Luptak about their intentions to participate in the three-day – Friday through Sunday, June 20-22 — weekend celebration.
Luptak is encouraging classmates to contact Stambaugh as soon as possible in order to finalize arrangements.
The schedule is as follows:
— 5:30 p.m. Friday get-together will be held at BJs in Logan.
— 1 p.m. Saturday memorial service will be held in the Little Theater at Logan High School.
— 6:30 p.m. Saturday dinner dance will begin with the class photograph at the Logan Country Club on Route 10 north of Chapmanville.
— Noon Sunday family picnic at the first shelter left of the Y at Chief Logan State Park at Henlawson.
Members of the class are asked to contact Stambaugh at firstname.lastname@example.com or call 304-239-0043. Callers who do not receive an answer are asked to leave a voicemail message. Her mailing address is Box 10, Wilkinson WV 25653.
The fee for all three days is $100 for classmates and $50 for guests.
Payment of $100 includes all events, a t-shirt, photo or video. They are now being accepted.
Graduates are asked to make a note in the memo section of their check or send a separate note detailing what events they plan to attend or if they are interested in purchasing t-shirts, photos or videos.
Those who are unable to attend but wish to purchase a t-shirt, photo or video may do so for $10 each.
Luptak continues to collect contact information at email@example.com.
A closed Facebook page is designated for members of the Class of '74. To be accepted on the page, send a friendship request to Stambaugh or Luptak.
Luptak also issued a reminder that the class is establishing a voluntary gift fund with proceeds from a silent auction being held Saturday. Funds collected will provide a gift to Logan High School from the class.
Those wishing to donate to the fund may do so on a voluntary basis. Contributions will be accepted during the reunion.
June 20 is fast approaching and Stambaugh, Taylor and Luptak urge their classmates to contact them about their plans to participate in the 40-year reunion.


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|MU-WIRELESS - FAQs
This solution covers the most frequently asked questions about Miami's secure wireless network, MU-WIRELESS.
Frequently Asked Questions on MU-WIRELESS Access
Question: What is MU-WIRELESS?
Answer: MU-WIRELESS is the wireless computing network. Students, faculty, and staff may access MU-WIRELESS using a personal computer or laptop with a wireless connection around campus including many outdoor common areas.
Question: Where is it available?
Answer: MU-WIRELESS is available in all buildings on every campus. There are also green spaces (outdoor locations) that have been made available as well. Check out the Maps of Outside Areas (PDF).
Question: Do I need to do anything on my computer before connecting to wireless?
Answer: The operating system or wireless adapter should have the appropriate software integrated for connecting to MU-WIRELESS. If you need drivers, you will need to contact the vendor of your wireless adapter or visit their website to download the driver. The following IT Help solutions provide more information on setting up your computer for wireless services:
Connecting to MU-WIRELESS using 802.1x - Windows 8.x or 7 (Solution ID: 041334709345085)
Connecting to MU-WIRELESS using 802.1x - Mac OS X 10.9.x, 10.8.x, 10.7.x, and 10.6.x (Solution ID: 040811514221348)
Question: My computer found the wireless network; how do I get connected?
Answer: In order to connect, your computer will need to have a wireless adapter installed that is Wi-Fi compatible (802.11b or 802.11b/g). You will have to be in a location that has MU-WIRELESS service. To access MU-WIRELESS, the fully encrypted, preferred network, use the IT Help article for Windows 8.x/7 (Solution ID: 041334709345085), or Mac OS X (Solution ID: 040811514221348)
Question: What type of wireless card will I need to get connected?
Answer: IT Services recommends using a wireless adapter that is capable of connecting to the secure MU-WIRELESS service. It is strongly suggested that you purchase a card that supports Wi-Fi Protected Access (WPA) as MU-WIRELESS uses this technology for encryption. Please note that other wireless cards will have differing levels of success in connecting and staying connected to the wireless network. A wired connection is preferred over a wireless connection. Read more about wireless card recommendations (Solution ID: 040972654065115).
Question: I can't get connected! What do I do?
Answer: Make sure that you are within range. Verify that your wireless networking is working properly, and that the adapters have been installed correctly.
Some laptops feature a switch that enables or disables the wireless adapter. Ensure that this switch is turned on.
Question: I am getting bad connection quality. What can I do?
Answer: Try moving to a different location. Simply turning the computer may also improve your connection quality. You may even want to try disabling your wireless adapter and then re-enabling it again. If the problem persists, or if you notice a dead spot in the wireless network, please contact the Support Desk at (513) 529-7900 or at email@example.com. See the IT Help article Identifying and fixing wireless networking problems (Solution ID: 040972654008653) for more information on troubleshooting wireless problems
Question: Does the wireless network replace the wired network?
Answer: Absolutely not. The wired network is more secure, and reliability is much better because there is always a direct connection. The wired network also offers higher speed. The wireless connection offers you mobility. Wireless connections may encounter interference reaching the Wireless Access Point; the signal goes through walls and furniture, and it has to compete with other wireless clients in your area. For the safest and fastest connection, connect via the wired network any time it is available.
Question: Why am I never able to download at my card's full speed?
Answer: Wireless networking uses a Shared Technology which basically means that, while your card's best speed is what is listed on the box, it is not likely that you will be able to do that with other users sharing service with you. Much like a car has a top-speed that you (hopefully) do not use, driving with others on the road requires that you share responsibility. Interference - like potholes in the road - also prevents you from going as fast as possible. If wireless bandwidth speeds don't meet your needs for a specific download, plug your computer into the wired network. The wired network is much faster!
Question: What services can I access via MU-WIRELESS?
Answer: There are two different levels of wireless service: MU-WIRELESS and MU-GUEST. To read more about the services available through each, read the MU-WIRELESS - Service Levels (Solution ID: 040972654093765) article in IT Help.
Question: Why can't I connect to MU-WIRELESS without configuring my computer?
Answer: MU-WIRELESS uses a more secure, encrypted technology called 802.1x. Since MU-WIRELESS service has specific requirements, it only shows up once a computer is configured properly and is capable of connecting to the service. Once you configure it properly, it will show up in your available networks. Read more information about 802.1x technology.
Question: Will my files and computer be secure on the wireless network?
Answer: No network is truly secure, but IT Services has taken precautions to provide a more secure networking environment for their students, staff and faculty. As more security enhancements are deployed into this service, more functionality will follow. Through MU-WIRELESS, technology is in place (Solution ID: 040972654090630) to encrypt your computer's traffic. You should always be careful when sending private information over the Internet and even more cautious with wireless.
Question: Why would I use VPN when connected to the wireless network?
Answer: The VPN client allows you to connect more securely. Because it is more secure, we allow more services to be used through VPN. For instruction on using VPN, refer to IT Help information about VPN.
Question: Why is there a ban on personal wireless access devices and 2.4 GHz phones?
Answer: These devices are disruptive to the MU-WIRELESS service and can cause problems for other users when used. MU-WIRELESS operates on the 2.4GHz frequency. Note that only devices which operate on the 2.4Ghz spectrum are banned; 900MHz and 5.8GHz phones are still okay to bring on-campus. Personal WAPs are banned due to both the security risk and the interference they pose to MU-WIRELESS.
Related Items:
1873 wireless, connect, wireless FAQ, wireless security, mu wireless security, 802.1x, VPN, 802.11, 802.11b, 802.11g, Wifi, Wi-Fi, muwireless
|Applies To:
|Solution ID: 040972654001873@kpol17
Last Modified Date: 02/04/2015 08:10:14 AM

subset: commoncrawl


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East Buchanan won its district opener over Cristo Rey.
LeBlond and Plattsburg move on to the semifinals in their district.
Lafayette gets a big road win at Platte County, plus Benton overcomes a slow start to beat Maryville
North Andrew, Stanberry win regular season rematches to reach semifinals.
St Joe Christian will meet North Andrew in the District title game
North Andrew remains undefeated; plus St Joe Christian rolls Pattonsburg
St Joe Christian keeps rolling; plus Stanberry overcomes a slow start to stay unbeaten
St. Joe Christian gets a big win; plus Stanberry takes down unbeaten Albany
Albany remains undefeated; plus St. Joe Christian gets a big win against a Kansas opponent.
St. Joe Christian loses a tight one; plus Stanberry stays unbeaten.
Stanberry remains undefeated; plus South Nodaway gets their first win of the season.
St Joe Christian wins their second straight, plus Stanberry rolls South Holt.
Stanberry rolls through Nodaway-Holt; and St Joe Christian notches their first win in Barnard
North Andrew wins its 13th consecutive game dating back to last season.
High school golfers earn trip to state, Class 2 sectional postponed until Tuesday.
Bishop LeBlond, Lathrop, Maysville among the girls teams advancing the second round of district play.
14 wrestlers from northwest Missouri will battle for a state championship on Saturday.
Benton and West Platte get back in the win column Friday night.
LeBlond boys, Cameron girls claim narrow wins while Central drops their sixth straight.
West Platte knocks off Lawson again for the Lawson Invitational Championship; North Andrew girls won the Stanberry Tournament.
Benton picks up first win of the year over Smithville, while Chillicothe holds off LeBlond rally.
Polo was the only lower seed to win in the first round of the Class 1, District 8 tournament Friday.
South Harrison wins a second consecutive Grand River Conference title.
The Warriors are making the transition to 8-man football in 2014.
South Harrison romps Maysville 50-14 to hand Wolverines their first GRC loss.
South Harrison, Polo cruise to victories.
Maysville edged Polo, while South Harrison and Gallatin roll to wins.
South Harrison and Maysville move above .500 with wins Friday.
King City snags first win of the season over Braymer.
South Harrison, Maysville pick up first wins of the season.
Lone Jack escapes King City with 27-20 win.
High School football scores from the GRC for week one.
The Hornets remain undefeated after a big victory over Albany Thursday night.
Polo finishes the season with 6 conference wins.
Warriors lose big, 62-6.
Bulldogs roll Warriors to continue undefeated GRC season.
Princeton gets its first conference win against Albany on Friday.
Maysville stays atop the Grand River Conference standings with Friday's win over Albany.
Albany falls to 1-1 on the season.
Warriors battle their way to a 33-16 triumph.
Maysville gets through Albany, 20-16.
Hamilton dominates Albany, 52-7.
Gallatin beats up on Albany, while Trenton squeaks out a win against Lexington.
Road teams Polo and Albany come away with wins.
The Albany Warriors hope last year's forgettable season will pay off for the present.


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RV Forum logo wear is now available. Click HERE for details.
Best thing I have found for cutting foam is an electric carving knife.
Enough places to look above, so I'll offer one other piece of advice. Go at least 3 inches on the foam, preferably 4. You won't regret it. 2 inches just isn't enough.
I would think that with a very sharp knife you could cut it down to size.
Page created in 0.138 seconds with 21 queries.


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Logan Scott and Brandon Lewis
Hard Friction exclusive model Logan Scott is muscular and lean with handsome dark features. He's immediately on his knees for Brandon sucking down every inch as he moans with pleasure. Brandon is fan of eating ass, Logan's is hairy, muscular and too tempting not to taste. He rims Logan getting his tight wet hole lubed up for a wild ride. Brandon is a masterful top who knows what he's doing. He plows Logan on his back before turning him ***gy style against a chair. In the end Logan takes a seat an strokes himself up into a geyser like explosive load. Cum flies into the air. Then Brandon dumps his juice all over Logan's bristly beard. He's just so beautiful covered in sweat and a spray of white cum.
Website: CLICK HERE
Added: 07 Dec 10
Views: 11569


text:
Cheap TYS to Grand Canyon flights
Popular Flights from Knoxville, Tennessee
Top Knoxville Flights to US Destinations
Top Knoxville International Destinations
Popular Flights from Grand Canyon, Arizona
Top Grand Canyon Flights to US Destinations
Top Grand Canyon International Destinations
TYS to GCN Route Map
Knoxville to Grand Canyon Flights, Stats and Airplanes
Route information for flights from McGhee Tyson to Grand Canyon Natl. Park.
1,570.47 miles
TYS - McGhee Tyson Airlines
Browse the most popular airlines servicing the Knoxville (TYS) airport. Visit their flights pages to learn more about the most popular routes these carriers fly.


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All-American Gospel
By Various
All-American Gospel composed by Various. For Piano/Vocal/Guitar. Creative Concepts Publishing. 136 pages. Creative Concepts #071105. Published by Creative Concepts (HL.315010).
ISBN 1569221081. 9x12 inches.
Features 54 all-time gospel favorites, including: Amazing Grace • Blessed Assurance • Doxology • Go Down, Moses • Good News • In the Garden • Jesus Loves Me • Simple Gifts • Were You There? • and more.


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Help me compare across eras!
View Single Post
Join Date: Jul 2012
Posts: 7,773
Originally Posted by
Sure, I agree with what you're saying completely. You've put a strawman out there for critique, I think it is a valid start for sure.
So, I think the first thing to do would be to look at the results of the model and determine "how close" the results come to what we think is reality. For example, Rod Laver or Ken Rosewall did not come up at all. While we all may disagree on where Laver/Rosewall fall on the Top-10 list... we all can agree that they should at least appear on the list, correct? Even in the Open Era they should appear.
So now we either need to add another variable to the model which would show these results... or modify the existing coefficients (weights) on the current variables to make that happen. The question is... if we add a new variable... what is it? And what coefficient do we apply to that variable... and why?
Laver and old Rosewall (older than Emerson) dominated not only the pro events 1963 to 1967 (they won actually ALL of them) but also the first part of the open era (winning 8 out of the first 10 GS tournaments where they participated). Emerson did nothing then.
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Now Playing
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Movie Reviews
2:21 pm
Tue February 3, 2009
There's no place like home.
By John DeSando, WCBE's "It's Movie Time"
If Edward Gorey's American gothic could be married to Tim Burton's ghoulishness, then what would emerge would be Coraline, a film with the demanding psychology of Neil Gaiman's prose married to the wild imagination of James and the Giant Peach's convoluted film director, Henry Selick.
Yes, 3-D-stop animation Coraline is not for everyone, but aficionados of the eccentric should love the complicated story of a young girl, Coraline Jones (Dakota Fanning) thrust Alice-in-Wonderland style into a parallel universe where the mother ( Teri Hatcher) and father (John Hodgman) she might have thought she wanted are nightmarish knockoffs she needs to run from.
Although the film shows how Coraline, and by extension all children, must have wit and courage to fight the forces of evil, it also emphasizes the need to accept the eccentricities and remoteness of nerdy, bright parents who may have their own demons to fight before the end of the day. The Wizard of Oz in spirit influences this film with the parallel universe motif of characters patterned out of real life and the universal message about the goodness of going home.
This sometimes macabre and challenging animation is mostly not for children and a puzzler for adults who may not want to be challenged at a time when they struggle with financial monsters threatening their real homes.
John DeSando teaches film at Franklin University and co-hosts WCBE 90.5's It's Movie Time and Cinema Classics shows, which can be heard streaming at http://publicbroadcasting.net/wcbe/ppr/index.shtml and on demand anytime at http://www.publicbroadcasting.net/wcbe/arts.artsmain Contact him at email@example.com


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Questions threaten sport institute's legacy
PROVIDENCE, R.I. Created in 1986 to foster goodwill through sportsmanship, Daniel Doyle's Institute for International Sport now stands accused of not playing by the rules.
Rhode Island officials want to know what happened to a $575,000 grant. A major state philanthropist says a signature purported to be his on a 2009 institute document is a forgery. In recent years the institute listed a board of directors that included a man who was already dead and another who says he never served on the board.
The questions threaten to tarnish Doyle's achievements in creating the Institute and its World Scholar-Athlete Games. The games have brought together thousands of young student athletes from around the world and visits by dignitaries including former President Bill Clinton, Archbishop Desmond Tutu and former Secretary of State Colin Powell.
"We had kids from Pakistan, Argentina, Northern Ireland, Africa, all over the world, playing together and talking together," said Scot Enge, a physical education teacher and tennis coach in Overland Park, Kan. Enge is a longtime coach at the World Scholar-Athlete Games. "We need more of these kinds of programs for children. It would just be such a shame if it ends."
Russell Hogg, 84, former president and chief executive of MasterCard International, Inc., said he served on the institute board of directors until 3 1/2 years ago. He recalled being touched by the connections formed by Catholic and Protestant youth from Northern Ireland that participated in programs organized by Doyle.
He said he knew the institute's finances were sometimes shaky.
Doyle "always owed somebody something," but also "always seemed to have money coming from somewhere," Hogg said. "He always said, "Rich people are giving me money.' There were people always funding us from Europe."
Doyle created the Institute in 1986 after approaching state and university leaders with his vision of using youth sports to bridge cultural, geographic and political differences.
Then-Gov. Edward DiPrete signed off the deal after meeting with a university leader and Doyle, whose brother Michael was DiPrete's top aide at the time. DiPrete said Doyle was given $40,000 to get his idea off the ground. Doyle, of West Hartford, Conn., did not respond to attempts to reach him by telephone or email.
"The theory sounded good," DiPrete recalled during a recent interview with The Associated Press. "I looked at it being a `people-to-people' program with international sports being the medium."
The Institute grew quickly, and in 1993 Doyle opened the first World Scholar-Athlete Games, welcoming high-school aged athletes from all 50 states and more than 100 nations.
Unlike other international sporting events where one national team plays another, athletes at the games were placed on teams with participants from other nations. Once a day the student-athletes would break into small groups for discussions on world peace, hunger, cultural understanding or other topics.
Jenny Swank was a standout high school swimmer from Montana when she attended the 2001 games in Rhode Island. She said she still keeps in contact with some of the friends she met during her 10-day trip.


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Narrow your search
If you like GoPro's camera design and just want solid HD video, you might be able to save yourself $100 and get this instead of the $400 Black Edition.
Like the Hero3, the GoPro Hero3+ Black Edition's strongest attributes are its excellent video quality and impressive list of shooting options. If that's what matters most to you, this is the action cam to get.
The GoPro Hero3 Silver and White editions are strong contenders in the sports camera market, but the faster, more powerful Black Edition is head and shoulders the best sports camera on the market today.
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Pricing not available


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This question already has an answer here:
my version of blender is 2.69, Ubunto is 13.10, Processor i7 with Nvidia 640 Graphic card. i was running window,but changed my mind and want to use Lunix, i just installed ubunto first time today morning, and whole day i had been searching net to install blender, i really dont know any thing about lunix , but i did install and followed as bellow found in the forum.
sudo add-apt-repository ppa:irie/blender
sudo apt-get update
sudo apt-get install blender
second command gives some error, as you can see i pasted here, but third one went ok and run well, after getting DONE message, i try to go to Dash Home and run from there, but as soon as i click on blender icon, just dash Home disappears and nothing happens, same as before Please help.
shams@ubuntu:~$ sudo apt-get update
E: Could not get lock /var/lib/apt/lists/lock - open (11: Resource temporarily unavailable)
E: Unable to lock directory /var/lib/apt/lists/
E: Could not get lock /var/lib/dpkg/lock - open (11: Resource temporarily unavailable)
E: Unable to lock the administration directory (/var/lib/dpkg/), is another process using it?
shams@ubuntu:~$ sudo apt-get install blender Reading package lists... Done Building dependency tree
Reading state information...


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Chapel of the Immaculate Conception
Katipunan Avenue, Quezon City, Philippines 1108Map
Ateneo de Manila University campus
+63 2 525 6322
Bright, airy and stripped down to bare essentials, the Chapel of the Immaculate Conception at the Ateneo de Manila University is modern minimalism put to the service of God. As the focus of worship, a solitary cross hovers over the main altar, rotating ingeniously to reveal both the crucified and the resurrected Christ. In an adoration room, worshipers sit on the floor, like Zen monks, while contemplating the divine mysteries. Somehow the clean, simple lines of the minimalist architecture seem particularly apt for a house of God.
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21,000+ 3DMarks on a 9700
Pretty impressive if your into the 3DMark thing.
Now how long will it be before they add this and the other 20,000+ score to the hall of fame and displace some of those Tis.
FSB 9729 MHz
You need to displace THIS ti before talking smack. It may also help for you to be able to recognize a phony score when you see it.
all scores are phony now, no one should be going by it...
Case point: I get about 9600 in 3dmark. A guy I found on the forums got 8600 with an AMD Duron + fsb of 144mhz and a R8500 64ddr. Clearly his system is weaker than mine, yet he only fell a 1000 points behind. This has mostly to do with his FSB, and because he didnt even run half the tests. So I tried running only the tests he run, and behold I gained 200 points myself.
So are there "cheaters" out there, to some extent yes. Is it always intentional, in the case of overclockers no, unless they're knowingly messing with their FSB making their system only stable for a couple minutes so that they can get that 3dmark up just a little higher... LOL :rolleyes:
LOL...ok..how bout dropping your rig to defaults, and Ill displace your score before you can finish typing a reply mr 147 Mhz Bus.
All you got was 12,000 points while jacking your bus that high..be silent please.I got 11,700 on strict defaults.Chances are that a VidCard core OC would put me at your score without even touching my FSB.
And i wasnt talking smack at all, just read at madonion that the record/barrier had been broken, the first at like 20,009 points then the one i posted above that. Thought it was impressive.
As for the phony score comment, im assuming you mean the FSB it noted? It may help you to realize that these kind of reports happen all the time,
Example here: http://www.nvnews.net/vbulletin/show...&threadid=1470
,some people get wrong FSB reports, some get things that say "not run at defaults settings, etc etc"
Doesnt make the score fake.
That would be me.
I will be happy to run at stock speeds, even though that will give you an advantage in raw CPU speed as your proc is a 2000+ and mine is a 1900+. You obviously are going to need some advantage as your card aint one. I will post default score ASAP.
ps: When stating your score you say "11700", when stating mine you understate it by approx. 350 pts. I would love to see you on a good ctf q3 server so that I might show you just how well my ti works for me.
Its obvious you are in denial here. Im sorry you paid the same price for your Ti and still want to believe its the fastest thing since Dale Earnheardt...but sorry...its not...
When UT2k3 is out..Ill meet up with you and show you your Ti cant keep up.
Ill gladly play you in anything more current.
I dont play, or give a rats ass about Q3....and havent for 2+ years now.
lol...wasting new vidcards on Q3...gee even a GF3 gets 200+fps in that weak engine doesnt it? So if you killed me in Q3 thats supposed to be indicative of your cards performance?:p
I guess not since you are unable to recognize the supremacy of this engine at this point in time, there would be no point in trying to explain it to you. :rolleyes:
Why don't we test 3dmark 2k1 at setting you use in games like 16xAF and 4xAA and then lets see how your GF4 performs :D
I can understand why you guys are so sandy: you both are scoring about 3000 points under what you should be. Unquestionably you both own a card that has shown a measure of supremacy over my current one, but you cant make them run for s**t. Put a 9700 in my machine and I score 14000+ guaranteed.
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The Brother of Rabin's Assassin Speaks
+972 Magazine strikes up an unlikely conversation
Ami Kaufman of the mercurial, always incisive +972 magazine posted an article last night about an exchange he had on Facebook with Hagai Amir, the brother of Yigal Amir–who assassinated Israeli Prime Minister Yitzhak Rabin. Hagai Amir recently got out of prison after 16 years for serving as an accomplice to his brother.
It's a very disquieting conversation, but also a sobering look at the political dialogue taking place on the seams in Israel.
Hagai Amir: There is no chance that I will fight for the people who at this moment are torturing my brother.
Ami Kaufman: So let me understand, if any leader – in the present or future – will give away parts of Eretz Israel, you will do nothing because at the moment they are torturing your brother? Meaning, according to this logic, your brother's life is worth more than land?
Hagai Amir: The reason Rabin was eliminated was not because of transferring land but because of the risk to Jewish life as a result of that, there is no Jewish meaning to the Zionist regime which is why it can give this or that land and this will have no Jewish meaning – just as other conquerors did throughout history – as long as this doesn't endanger Jewish lives.
The rest of the thread is worth a read.
Also, for the uninitiated, be sure to check out Liel Leibovitz's fascinating profile of +972 here.
Related: Wake-Up Call
Grim Anniversary
My Facebook Chat with Rabin's killer's accomplice on why 'he was eliminated' [+972]
Click here for access to comments
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DMV to Internet-less New Yorkers: Get in Line
By Jared Chausow
By Katie Toth
By Elizabeth Flock
City Hid Facts From Feds About Rikers
By Albert Samaha
Flood Wall Street Gets Pepper Sprayed and Arrested
By Anna Merlan
By Jon Campbell
Report Sheds Light on Anti-Muslim Bias
By Jon Campbell
Rikers Island Lawsuits Over Diabetic Care
By Albert Samaha
The notebooks taper off in the spring of 1947. Six months later, his subsidy dried up. To this day, the identity of his patron remains a mystery. cummings, who occasionally spoke of Gould in his letters to Ezra Pound, cryptically noted in 1948 that "I've been seeing a lot of Joe G lately & wondered why;parait que his erstwhile refugee-backess decided she'd put her dollars on the foreign poor,pour changer perhaps:or maybe Gould got fresh?"
Joe wandered the streets until 1952, when he was committed to Pilgrim State Hospital. His death and subsequent funeral were memorably reported in the Voice on August 28, 1957.
According to writer Dan Balaban, none of Gould's well-heeled friends attendedno Mitchell, cummings, or William Saroyan. But representatives from NBC, CBS, and the print media mobbed the Frank E. Campbell Funeral Church. The mourners were a cross section of neighborhood characters (Princess Wa-Wachaw, Gould's cousin Lawrence Woodman) and, if you can imagine, the Lions Club of Greater Greenwich Village. The good burghers among the Lions even dreamed up a grandiloquent touch worthy of the deceased. They announced the establishment of a Joseph Ferdinand Gould Scholarship Fund to NYU, with an initial bequest of $100 (no trace of the fund exists today). Why they didn't just spring for a headstone is anyone's guess; today, some 40 years later, the grave at Ferncliff Cemetery in Hartsdale, Westchester County, remains unmarked. His surviving literary corpus provides no epitaph either.
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Improved methods and apparatuses are provided to address a potential "hidden beam problem" in wireless communication systems employing smart antennas. The improved methods and apparatuses utilize complementary beamforming (CBF) techniques, such as, for example, Subspace Complementary Beamforming (SCBF), Complementary Superposition Beamforming (CSBF) and/or Single Beam Complementary Beamforming (SBCBF) techniques.
1. A method, comprising:
determining at least one signal operatively configured for subspace complementary beamforming (SCBF) in a wireless communication system;
generating the at least one signal such that the signal is operatively configured to cause a smart antenna to perform said SCBF and transmit at least one complementary beam; and
determining the at least one signal using a Steering Matrix: A=[a(θ1) a(θ2) . . . a(θk)], wherein a(θk) represents a steering vector of user k;
if W=A*B, where B is a non-singular K-by-K matrix, then using a complementary beamforming matrix of
wherein C0=Nc0 is the level of the main lobe, k0 is the scaling factor and ul is the l-th column vector of U; otherwise using a complementary beamforming matrix of
wherein ū1 is the l-th left singular vector of the matrix
where A*=Ũ{tilde over (Λ)}{tilde over (V)}H is assumed and a scattering channel
H*=Ũ{tilde over (Λ)}{tilde over (V)}H is assumed.
2. A method as recited in
3. A method as recited in
4. A method as recited in
wherein r is rank of Wa.
5. A method, comprising:
determining at least one signal operatively configured for complementary superposition beamforming (CSBF) in a wireless communication system;
generating the at least one signal such that the signal is operatively configured to cause a smart antenna to perform said CSBF and to transmit at least one complementary beam, and
determining the at least one signal using a downlink beamforming matrix: {tilde over (W)}=└w1 . . . wk−1 {tilde over (w)}k wk+1 . . . wk┘, where {tilde over (w)}k=p0wk+Wcp and p is complex conjugate transpose of the l-th row of Wc,
is normalized complex conjugate of the l-th element of wk,
where Wc=√{square root over (c0[uK+1, uK+2, . . . uN])},
C0 is a scalar, K=the number of users, N=the number of antennas and ul is the l-th vector of U.
6. A method as recited in
7. A method as recited in
8. A method as recited in
9. A method as recited in
10. A method as recited in
A=└�(θ1){tilde over (a)}(θ2) . . . �(θK)┘, wherein {tilde over (a)}(θK)=└a(θk−Δθ1)a(θk)a(θk+Δθr)┘.
11. A method as recited in
12. A method as recited in
13. A method as recited in
14. A method as recited in
15. A method as recited in
16. A method, comprising:
determining at least one signal operatively configured for complementary superposition beamforming (CSBF) in a wireless communication system;
generating the at least one signal such that the signal is operatively configured to cause a smart antenna to perform said CSBF and to transmit at least one complementary beam, and
determining the at least one signal using: {tilde over (W)}=[w1 w2 . . . wk Wcp]
p is complex conjugate transpose of the l-th row of Wc,
W c=√{square root over (c 0 [u K+1 , u K+2 , . . . , u N])},
c0 is a scalar, K=the number of users, N=the number of antennas and ul is the l-th column vector of U.
17. A method as recited in
18. A method as recited in
19. A method as recited in
20. A method as recited in
21. A method as recited in
A=└�(θ1)�(θ2) . . . {tilde over (a)}(θK)┘, wherein �(θK)=└a(θk−Δθ1)a(θk)a(θk+Δθr)┘.
22. A method as recited in
23. A method as recited in
24. A method as recited in
25. A method as recited in
26. A method as recited in
27. A method, comprising:
determining at least one signal operatively configured for complementary superposition beamforming (CSBF) in a wireless communication system;
generating the at least one signal such that the signal is operatively configured to cause a smart antenna to perform said CSBF and to transmit at least one complementary beam, and
determining the at least one signal using a downlink beamforming matrix: {tilde over (W)}=└w1 . . . wk−1 {tilde over (w)}k wk+1 . . . wk┘, where {tilde over (w)}k=p0wk+Wcp and p is complex conjugate transpose of the l-th row of Wc,
is normalized complex conjugate of the l-th element of wk,
where Wc=√{square root over (c0[ua,r+1, ua,r+2, . . . , ua,N])},
c0 is a scalar, K=the number of users, N=the number of antennas, r=rank of W and is in the range of K to 2K and ua,l is the l-th left singular vector whose corresponding singular value is zero.
28. A method as recited in
29. A method as recited in
30. A method as recited in
31. A method as recited in
32. A method as recited in
A=└�(θ1)�(θ2) . . . �(θK)┘, wherein {tilde over (a)}(θK)=└a(θk−Δθ1)a(θk)a(θk+Δθr)┘.
33. A method as recited in
34. A method as recited in
35. A method as recited in
36. A method as recited in
37. A method as recited in
38. A method, comprising:
determining at least one signal operatively configured for complementary superposition beamforming (CSBF) in a wireless communication system;
generating the at least one signal such that the signal is operatively configured to cause a smart antenna to perform said CSBF and to transmit at least one complementary beam, and
determining the at least one signal using: {tilde over (W)}=[w1 w2 . . . wk Wcp]
p is complex conjugate transpose of the l-th row of Wc,
W c=√{square root over (c 0 [u a,r+1 , e a,r+2 , . . . , u a,N])},
c0 is a scalar, K=the number of users, N=the number of antennas, r=rank of W and is in the range of K to 2K and ua,l is the l-th left singular vector whose corresponding singular value is zero.
39. A method as recited in
40. A method as recited in
41. A method as recited in
42. A method as recited in
43. A method as recited in
A=└�(θ1)�(θ2) . . . {tilde over (a)}(θK)┘, wherein �(θK)=└a(θk−Δθ1)a(θk)a(θk+Δθr)┘.
44. A method as recited in
45. A method as recited in
46. A method as recited in
47. A method as recited in
48. A method as recited in
This application is a continuation of and claims priority to U.S. patent application Ser. No. 10/700,991 entitled "Complementary Beamforming Methods and Apparatuses" filed Nov. 3, 2003 to Tarokh et al., the disclosure of which is incorporated by reference herein.
U.S. patent application Ser. No. 10/700,991 claims priority from U.S. Provisional Application Ser. No. 60/423,703 filed Nov. 4, 2002, the disclosure of which is incorporated by reference herein.
This invention relates to wireless communications and more particularly to complementary beamforming methods and apparatuses that can be used in wireless data packet communications systems and other like communication systems.
Wireless communication systems continue to change the world that we live in. Wireless telecommunication technology, such as, for example, applied in cellular telephony has created an entirely new mobile communicating society in which people are able to stay in contact regardless of their location, especially in the further case of satellite mobile telephones. Wireless communication systems are also changing the way in which people use their computers and other like devices. Here, for example, wireless local area networks can be configured to allow computer users to become mobile and capable of roaming about coverage area(s) while their computers remain operatively connected to other devices.
In the field of wireless technology there is a continuing desire to increase the effectiveness of the wireless communication system. This desire may lead to lower cost devices, faster communication, increased bandwidth, increases in the size of coverage area(s), etc. One recent improvement to wireless communication systems includes the use of smart antennas. Smart antennas, for example, can be employed in base stations or other like nodes to selectively form directed beams of radiated energy in the direction of another device/node. The smart antennas may also be used to more effectively receive the signals that are transmitted back to it from these and other devices/nodes. These types of smart antenna arrangements within wireless communication systems have proven to be more effective than traditional omni directional antenna arrangements and/or other types of non-smart antenna arrangements in certain environments. U.S. Pat. No. 6,611,231 discloses some exemplary smart antenna systems.
One of the challenges facing wireless communication system designers attempting to use smart antennas is that within an overall supported coverage area there may be multiple devices/nodes supported by a base station and one or more of these devices/nodes may not be able to determine when/if the base station is busy with another device/node due to the selectively reduced coverage area of the transmitted beam(s) from the base station's smart antenna. This type of situation is explained in further examples in the Detailed Description that follows, wherein it is referred to as the "hidden beam problem".
Consequently, there is a need for methods and apparatuses for addressing the hidden beam problem.
In order to reduce the "hidden beam problem" in smart antenna applications, complementary beamforming (CBF) techniques may be employed. In accordance with certain exemplary implementations of the present invention, "Subspace Complementary Beamforming" (SCBF), "Complementary Superposition Beamforming" (CSBF) and single beam CBF techniques are provided.
These exemplary techniques help satisfy needs for improved methods and apparatuses for solving hidden beam problems and/or other like problems that can affect wireless communications.
A more complete understanding of the various methods, apparatuses and systems of the present invention may be had by reference to the following detailed description when taken in conjunction with the accompanying drawings wherein:
This description includes six numbered sections. Section 1 provides an introduction to some exemplary wireless communication systems and the "hidden beam" problem that can significantly reduce the effectiveness of these wireless communication systems. Section 2 describes an exemplary complementary beamforming technique for use with single beam systems. Section 3 describes the hidden beam problem in more detail and introduces further complementary beamforming techniques that may be applied in such wireless communication systems and other like environments. Section 4 introduces a multiple beam uplink and downlink model. Section 5 describes exemplary subspace complementary beamforming techniques that may be applied in wireless communication systems and other like environments having multiple downlink beams to combat hidden beam problems. Section 6 describes some exemplary complementary superposition beamforming techniques that may be applied in such wireless communication systems and other like environments to address the hidden beam problem.
Section 1: Introduction
1.1 Conventional Wireless Communication Systems
One popular form of wireless communication system 100 is an IEEE 802.11 based wireless local area network (WLAN), wherein Sta 1 and Sta 2 are applicably configured computers or other like devices. For example, IEEE 802.11a and IEEE 802.11b are currently popular forms of WLANs. The transmit power levels in such wireless communication systems are typically limited by government regulations. As such, Sta 3 can fall outside of the coverage area of the WLAN.
IEEE 802.11 WLANs are based on a Carrier Sense Multiple Access (CSMA) operation in which a each station transmits only when it determines that no other station is currently transmitting. This tends to avoid collisions that occur when two or more stations transmit at the same time. Collisions usually require that the transmitted packets be retransmitted.
1.2 Smart Antenna Wireless Communication Systems
The smart antenna allows for the (government regulated) limited power of base station 202 to be substantially concentrated in at least one direction or beam. Thus, for example, base station 202 may transmit a beam 203 a to Sta 1, a beam 203 b to Sta 2, and/or a beam 203 c to Sta 3. Even without the additional transmission power, base station 202 has an increased coverage area by focusing the transmit energy to particular direction instead of radiating omni-directionally and is therefore able to service Sta 3. Note that one or more beams 203 a-c may simultaneously be transmitted in certain implementations.
However, if wireless communication system 200 is an IEEE 802.11 based WLAN or some other CSMA or like system, then there is a chance for increased transmission collisions since base station 202 transmits directed beams that may be undetected by one or more of the user stations. Thus, for example, while base station 202 is transmitting downlink beam 203 a to Sta 1, Sta 3 may decide to uplink transmit at the same time since it cannot detect the existing directed beam traffic. This is an example of the hidden beam problem that is addressed herein.
Attention is drawn to
Reference is made to
By way of further example,
With attention directed back to
Section 2: Single Beam Complementary Beamforming (SBCBF)
As described above, increasing the range of 802.11 networks without increased transmit power and using standard clients is possible with smart antennas, such as, for example, directional high-gain antennas. Using directional high gain antennas, it is possible to direct the energy in a given direction and hence increase the range in that direction. However, the media access technique in 802.11 is CSMA which is a listen-before-talk scheme. Forming directional beams has the side effect of hiding the transmitted energy from a large proportion of the clients in the network; i.e., negatively impacting the carrier sense mechanism in the network. An 802.11 user station measures the energy transmitted from access points and other clients. If it cannot detect the presence of other transmissions, it attempts to gain access to the medium. Therefore, when directional antennas are used, many clients detect the medium as idle when in fact it is busy. This hidden beam problem has a severe effect on the performance of the network.
Fortunately, in practice, directional beams are not pencil beams. They generally have a main beam whose width depends on the size of the antenna aperture, and sidelobes which vary in different directions. Nevertheless, these beams tend to have very deep nulls in certain directions. In these directions, the network will suffer from the hidden beam problem the most. Since a given receiver's energy detect threshold is usually lower than it's decoding threshold, it is possible to direct a high power signal towards an intended client and yet ensure a minimum transmit power towards other clients in the network so that the signal may be detected by other clients.
Complementary beamforming, which is introduced in this description, is a novel technique that ensures a minimum transmit power in all directions while preserving the shape of the main beam. The complementary beamforming techniques described in subsequent sections ensure that multiple transmit beams in arbitrary directions are complemented by another beam in all other directions. The complementary beam does not interfere with the intended beams and increases the probability that other users in the network can detect the signal.
In this Section, a complementary beamforming technique is described for use with a single beam communication system. This single beam complementary beamforming (SBCBF) technique is illustrated using an improved base station having a loss-less Butler matrix network as the means of forming the directional beams with phased array antennas. It should be understood, however, that the SBCBF technique can be applied to other types of beamforming networks.
For a single-beam operation, the transmit signal is fed into one of the input ports of the Butler matrix. The result is a directional beam from the antenna in a given direction. For instance, if the transmit signal is fed into input port 0, the beam is directed at boresight. The beam pattern depends on the number of antenna elements and the antenna element spacing.
A graph 500 in
SBCBF reduces the effect of the nulls and increases the sidelobe levels without a severe power penalty to the main beam. SBCBF techniques may be implemented in a variety of ways. In this Seefion, two different exemplary implementations are illustrated, namely a post-combining SBCBF implementation and a pre-combining SBCBF implementation.
An exemplary post-combining SBCBF implementation is depicted in
Mathematically, this may be described as:
To ensure the same output power as with no complimentary beamforming the output voltage on all the ports should be adjusted by a scaling factor:
The power penalty for the main beam will be:
or in dB:
For example, for a 16 element array, if γ=3.5, then the power loss is about 1 dB.
Graph 700 in
2.1 Exemplary Pre-Combining SBCBF Implementation
With an exemplary pre-combining approach, the complementary beam is formed by feeding the transmit signal to the appropriate input port of the Butler matrix and at the same time feeding a fraction (Σ) of the transmit signal to the other input ports.
Mathematically, the signals at the input ports of Butler Matrix due to intended transmission through the ith port may be described as:
In other words, splitter 806 directs the transmitted signal to the appropriate input port xi and an attenuated version of the same signal to the other N−1 input ports of Butler Matrix 250. To ensure the same output power as with no complimentary beamforming the input voltage on all the ports should be adjusted by a scaling factor:
Here, the power penalty for the main beam is:
or in dB:
By way of example, for a 16 element array, if Σ=0.135, the power loss is about 1 dB.
Graph 900 in
Section 3: Complementary Beamforming (CBF)
In this Section, some further exemplary complementary beamforming techniques are described.
As mentioned above, complementary beamforming can substantially reduce or even eliminate the potential for hidden beam problems. One exemplary application of complementary beamforming is in smart antennas enhancements to IEEE 802.11 wireless communication systems that may suffer from the hidden beam problem. Here, for example, some user stations may be nulled out by the beamformer and in a busy period wrongly determine that the channel is idle. This can cause these users to transmit packets in a busy period and cause packet collisions. For the case that the downlink channel is busy, the complementary beamforming (CBF) techniques provided herein are designed to significantly reduce the probability of the aforementioned packet collisions.
In this Section, exemplary CBF techniques are described for both the intended and silent users and prove that, when compared to conventional methods, for a negligible incurred power loss for the intended users, the effects of the hidden beam problem caused by the unintended users in the system can be significantly reduced. Additionally, in this Section, a second application of complementary beamforming to smart antenna enhancement of wireless cellular systems will be discussed. Those skilled in the art will recognize, therefore, that the methods and apparatuses of the present invention are adaptable to other types of wireless communication systems.
3.1 The Hidden Beam Problem
To further illustrate the situation, consider a scenario when a wireless communication system has a base station with m transmit antennas and the base station transmitter simultaneously transmits to k user stations (users). Without loss of generality, it is assumed in this example that k≦m.
A conventional beamformer seeks to increase the power pointed to the k desired users. Consider a scenario where there are m=2 transmit antennas and k=1 intended users. Let the channel matrix to the desired user be given by (α, β). A conventional beamformer then induces weights:
where n1 is the noise.
It can then be observed that the signal to noise power ratio of the desired user improves by a factor of 10 log, (|α|2+∥β∥2) dB.
The above improvement for the above transmission scenario does not come for free, however. Let an unintended user have channel matrix ((−
where n1 is the noise and the unintended user receives no signal.
As such, there is no version of the transmitted signal at this unintended user. This by itself may not seem to pose a serious problem, since after all the transmission was not intended for this user station. But it turns out that this can cause a problem in beamforming enhancements to the IEEE 802.11 WLAN standard based systems. In systems designed based on this standard, all user stations and the base station (e.g., access point) share the same channel for both uplink and downlink transmissions. Each user senses the channel and only transmits packets if it determines that the channel is not busy. In the aforementioned scenario, the unintended user may determine that the channel is idle and transmit uplink packets. These transmissions in turn may cause packet collisions that can reduce the throughput of the system. This then is the hidden beam problem.
3.2 Complementary Beamforming
One important aspect of complementary beamforming is that much less power is needed for an unintended user station to correctly detect a busy period than is required for correct detection of a transmitted packet. This makes it possible to provide improved beamforming schemes that, when compared to conventional beamforming schemes, incur a meager loss to the power pointed to the intended user station(s), while significantly improving the probability of correct detection of busy periods for unintended user stations.
3.3 Exemplary Solution to the Hidden Beam Problem
In wireless communications, it is well understood that detecting channel activity is much simpler than decoding the received word. For example, an error in detection of channel activity may occur when a transmitted codeword is confused with an all zero signal. In contrast, a decoding error may occur when a transmitted signal is confused with other code words.
One may arrive at the above conclusion using tools of information theory. At code rates above the channel capacity, for example, Shannon has proved that the block decoding error probability asymptotically tends to one and that the bit error rate is bounded below by a positive number. However, even at transmission rates above capacity, it is easy to observe that the probability of channel activity detection error asymptotically goes to zero as the block length goes to infinity.
The above is considered in designing the detection criteria for channel activity in IEEE 802.11 WLAN standards. Each device listens to the channel in some time window and compares the energy collected in this window to a threshold called the CCD. Activity is detected only if the collected energy is greater than the CCD value. It has been found that IEEE 802.11 devices generally tend to require much less receive power to correctly determine channel activity than to decode the transmitted signals.
This motivates solutions to the hidden beam problem in that a beam pattern may be constructed which directs most of the transmitted power to the intended recipients while directing a small fraction of the total power to unintended users. With such a beam pattern the unintended users will all sense the transmission to the desired users with high probability and will likely remain silent during a busy downlink period. This in turn reduces the packet collision probability.
To construct such a beam pattern in this Section the following notation is employed:
In most cases, these components are assumed to be Gaussian with σ2 variance per complex dimension. No assumptions are made on the statistics of the matrix A. It will be assumed that ct j, j=1, 2, . . . , k, t=1, 2, . . . , L are elements of a signal constellation with average signal E[c t j].
It is also assumed that the elements of the signal constellation are normalized so that their average power is E[|ct j]2=1. In general Xt=CtB where B is referred to as the beamforming matrix.
The choice of B depends on the beamforming strategy and many approaches for the selection of B are suggested in existing literature. By way of example, assuming that the matrix A is known at the transmitter and the existence of (AHA)−1, for a zero-forcing beamformer
For a maximum SINR beamformer,
Under the above assumptions the total transmit power is easily computed to be 1. Note that a zero-forcing beamformer may not be appropriate in some applications as it may enhance the noise. Thus, a maximum SINR beamformer may be more appropriate in some applications.
For simplicity, however; a technique for the zero-forcing beamformer will be illustrated in this Section. Nonetheless, it is noted that the method presented here generalizes to the maximum SINR case as well. This generalization is described in part.
Here, it is assumed that the spatial signature matrix A is constant during the transmission of a packet and varies from one packet to another.
Thus, for a zero-forcing beamformer, the received signal at the receiver is given by:
and it is observed that each intended user j=1, 2, . . . , k receives a noisy version of its intended signal scaled by a factor Tr((AHA)−1).
If an unintended user has spatial signature B=(b1, b2, . . . , bm)T orthogonal to all the rows of A, then the user receives the signal:
at time t, where ηt is Gaussian noise. This means that such a user does not receive any signal at all. The same is true for maximum SINR beamforming. As mentioned above, such an unintended user can confuse a busy downlink period with a silent period and transmit packets during a busy period. This can cause unwanted collisions and reduce the efficiency of the system.
Whenever a k�m beamforming matrix is fixed during transmission of a packet, then, any unintended user that has spatial signature in the orthogonal complement of the subspace generated by the rows of the beamforming matrix receives no signal at all. This conclusion is also true for the case of maximum SINR beamforming. This motivates the use of different beamforming matrices at different instances of time during the transmission of downlink packets, so that the effects of the hidden beam problem can be reduced.
3.3.1 An Exemplary Proposed Scheme:
It is observed that the subspace WA is a k-dimensional subspace of the complex m-dimensional complex space and has an orthogonal complement WA ⊥ of dimension m−k. Let U0, U1, Um−k−1, form an orthonormal basis for WA ⊥. In other words, U0, U1, . . . , Um−k−1 are mutually orthogonal m-dimensional column vectors of length one in WA ⊥. Clearly, Uj HAi=0 for 0≦j≦m−k−1 and 1≦i≦k.
With this in mind, as part of the scheme the base station transmitter constructs matrices Z1, Z1, . . . , ZL, where L is the length of downlink transmission period, such that these matrices satisfy the following four properties (A-D).
Because p≧1, from the above inequality, for
There are a number of ways to construct matrices of Z1, Z1, . . . , ZL that satisfy Property D approximately or exactly when possible. In one simple approach, let the rows of Z2i-1 be respectively U0⊕i H, U1⊕i H, . . . , Uk−1⊕i H where i⊕j denote (i+j) mod (m−k) for i=1, 2, 3, . . . , [L/2] and let Z2i=−Z2i-1. This gives the matrices Z1, Z1, . . . , ZL whenever L is even. Note that ZL is given by Property C whenever L is odd.
It can be seen that the matrices Z1, Z1, . . . , ZL given by the above construction substantially satisfy the above Properties. Other constructions are also possible.
Once Z1, Z1, . . . , ZL are constructed, at each time t, the transmitter chooses the beamforming matrix:
where ε≧0 is a fixed positive number. The choice of ε governs the trade-off between the power pointed to the intended users and that pointed to unintended users. By increasing the power pointed to intended users, the intended users enjoy better channels, while by pointing more power to unintended users, better channel activity detection during the busy periods can be achieved. This trade-off will be analyzed in the next subsection and criteria for the choice of ε determined.
Note that the same method applies to the case of maximum SINR beamforming. Also, in this exemplary scheme the beamforming matrix varies from one time to another. This causes a small fraction of power to be pointed in every direction of the coverage space such that unintended receivers can determine channel activity periods with higher probabilities.
3.4 Analysis of Complementary Beamforming
We analyze the exemplary complementary beamforming scheme of as proposed above both for the intended and unintended receivers.
3.4.1 The Power Penalty for The Intended Users:
The addition of the term
which is the same as the conventional beamforming. In contrast, in the case of the exemplary complementary beamforming scheme, the matrix equality
and Properties B and D used to compute the average transmitted power
From Property D, we have
One may now prove the following Theorem.
Theorem 1 The intended users in complementary beamforming when compared to the conventional method suffer a loss of at most 10 log, (1|ε|2).
Proof. This follows from the above and from Inequality (6).
3.4.2 Analysis of the Power delivered to Silent Users:
Let B=(b1, b2, . . . , bt)T denote the channel of an arbitrary unintended user. One may then study the power received by this unintended user under complementary beamforming. To this end, it is recognized that the columns of matrix A and the vectors U1, U1, . . . , Um−k span the complex m-dimensional space. Thus,
for some constants e1, e2, . . . , ek and d1, d2, . . . , dm−k. Computing BHB, provides
At time t, the unintended receiver now receives
By replacing for St and B from Equations (7) and (8) and observing that (AHA)−1AHAj=δj, AHUi=0, and ZiAi=0, one arrives at the conclusion that
Next the average expected receive signal power is computed as
However, since Z2i=−Z2l-1 for
Using the above and after manipulation
The sum
One can now proceed to lower bound Pav. To this end, the following theorem can be proven.
Theorem 2. Let λmin(AHA) and λmax(AHA) respectively denote the minimum and maximum eigenvalues of AHA. Then provided that:
complementary beamforming guarantees a fraction
Proof: Let an unintended user with spatial signature given by B=(b1, b2, . . . , bm) be given. Suppose that the Inequality (13) holds. From Equations (8) and (12), it is observed that:
where λmax(G) is the maximum eigenvalue of G
Next, it can be shown that λmax(G)≦0.
which gives:
using Inequality (6). It can be concluded from the above that λmax(G)≦0.
Using Equation (14), this implies that:
Using the Inequality (6), it is determined that
It may not seem natural to the reader that the Condition (13) on ε contains terms of the form λmin(AHA)/λ max(AHA). This condition should not seem surprising, however, since in the case that the ratio λmin(AHA)/λ max(AHA) is small, the matrix AHA is close to being singular. This means that even the intended users, do not receive significant signal powers. Practical beamforming schemes, when scheduling transmission to intended users always assure that the ratio Amin(AHA)/λ max(AHA) is sufficiently large. In fact a ratio
For example, consider the case when there are m=2 and k=1 receive antennas. Assuming that the channel to the intended user is given by A=(α,β)T it is observed that λmin(AHA)/λ max(AHA)=1 and as long as |ε|2≦1, by the above theorem a fraction |ε|2 of the transmitted power is pointed to unintended users at the expense of a loss of at most 10 log10(1+[ε]2) to the intended user. With ε=0.1, a power of 20 dB below transmit power can be guaranteed to any unintended users so that they can detect channel activity, while the power penalty for the intended user is only 0.044 dB.
The beamforming matrices S1, and S2 in this case are given by:
with S2l-1=S, and S2l=S2 for l=1, 2, . . . ,
Considering yet another example, let k=4 and m=16. Then the channel matrix A is a 16�4 matrix. The columns of this matrix are 16-dimensional vectors A1, A2, A3, and A4. Here, two cases may be recognized:
Conventional Beamforming:
In order to do conventional beamforming the beamforming matrix
Complementary Beamforming: In addition to the above computation, one also needs to compute an orthonormal basis of 16 dimensional vectors U0, U1, U2, . . . , U11 for the orthogonal complement of the subspace spanned by the columns of A. This can be done, for example, using the Gram-Schmidt method and requires roughly the same number of operations as the computation of B.
The matrices Z0, Z1, . . . , ZL are constructed as below. When L is odd, let ZL=0. For any L (either even or odd), let Z2i=−Z2i-1 for
One may then periodically define
and let
be the complementary beamforming matrix at time t.
It can be observed from the above that complementary beamforming is approximately twice as much computationally intensive as conventional beamforming in this example.
The above exemplary schemes and others presented herein may be applied to other wireless communication systems. For example, a cellular network application can use this type of beamforming enhancement for TDMA systems. In these systems, beamforming can be used to increase SINR of some intended users, while a small amount of power can be pointed to all other users so that the control information also called USF (uplink state flag) which requires much lower data rates can be transmitted to all the users in the system.
The complementary beamforming technique presented above guarantees that in any flat fading and non-fading environment including even richly scattered environments, the power received by a user under complementary beamforming is at least a fraction of the power received by a user under omni transmission. For this reason the beamforming matrix varies from time to time. For this reason complementary beamforming may not be as easy to implement in analog environments.
Supposing, however, that this requirement is relaxed and to only require that in a non-scatterer free space environment, the power received by a user under complementary beamforming is at least a fraction of the power received by a user under omni-directional transmission. Then there are other ad hoc complementary beamforming solutions using fixed matrices. One such a solution may be to define matrices P0, P1, . . . , Pm−k to be matrices whose rows are respectively U0 H, U1 H, . . . , Um−k H and let the fixed beamforming matrix be given by
Such a solution can be shown using simulations to be a complementary beamforming solution in a non-scattering free space environment. This solution is much more appealing for analog implementation.
Section 4: Multiple Beam Downlink Model
In this Section some exemplary uplink and downlink models are described.
Attention is drawn to
where a(θ) represents a steering vector or spatial signature, d(t)=[d1(t) d2(t) . . . dK(t)]T is a uplink signal vector of K stations and n(t) is a AWGN vector. In the uniform linear array (ULA) 254 with N elements spaced a distance d, the steering vector becomes
where r(t)=[rj(t) r2(t) . . . rK(t)]T, and W=[w1 w2 wK] is the weight matrix.
One can then define steering matrix A=[a(θ1) a(θ2) . . . a(θK)], channel magnitude matrix h=diag(|h1| |h2| . . . |hK|), and channel phase matrix Φ=diag(ejφ
As such, the received downlink vector can be written as:
where H=hAT.
In scattering channel, the received downlink vector can be written as
where channel matrix H is composed of complex numbers.
With perfect knowledge of H, one has several downlink beamforming matrices:
(1) Pseudoinverse: W=H+=H=HH(HHH)−1=A*(ATA*)−1h−1
(2) Matched Filter (MF): W=A*, A*h, A*h−1
(3) Windowed MF: W=diag(b0, b1, . . . , bN−1)A*, where bk is a windowing coefficient.
The following assumptions may be made:
(a) rank(A)=K.
(b) Non-zero channel gain (|hk|≠0). Thus, h is non-singular.
(c) Non-zero windowing coefficient (|bk|0). Thus, rank(diag(b0, b1, . . . , bN−1)A*)=K.
Reference is now made to
Section 5: Subspace Complementary Beamforming (SCBF)
In this Section, "Subspace Complementary Beamforming" (SCBF) is described. Here, by using dummy independent data streams additional energy is radiated in the directions of side lobe so that user stations in the hidden beam can detect the channel activity. As with earlier exemplary schemes, the SCBF technique does not significantly interfere with intended user stations.
The downlink beam pattern of user k is defined as follows:
By assuming each client's data is independent, the total beam pattern of K downlink signals can be written as:
where W=[w1 w2 . . . wK] represents the weight matrix. The total beam will have K main beams. The complementary beam can be generated by either modifying the weight matrix or expanding the weight matrix to larger matrix. In this Section we will take the latter approach. In general designing arbitrary shape of the beam is difficult problem, e.g., as illustrated in
Before describing the exemplary SCBF or SCBF II implementations in greater mathematical detail, reference is first made to
Digital signals x1, . . . , xK are then each provided to a corresponding digital-to-analog converter (DAC) 306. The resulting analog signals x1, . . . , xK are then provided to an RF function 256 and corresponding y1, . . . , yK RF signals are provided to corresponding elements in array antenna 254.
Certain exemplary design approaches include a three step design. First generate omni-directional beam using additional independent data streams. Second, in order to avoid any interference create nulls at intended user's DOAs. Third, control the complementary beam power.
5.1 Generate Omnipattern
The objective is to generate the complementary beam which makes the total beam pattern to be omni-directional. Define the complementary beam pattern zc(θ) as:
where Wc=└w1 c w2 c . . . wL c┘ is a weight matrix for the generation of the complementary beam. The complementary weight matrix Wc should be chosen in the way that the radiated power is constant over entire angles. That is
Note the complementary beam introduces additional interference with the amount of ∥aT(θ)Wc∥2 to the user located at angle θ even with orthogonality between wk and w1 c for any k and l.
Defining {tilde over (W)}=[W Wc], the {tilde over (z)}(θ) can be rewritten as:
where D={tilde over (W)}{tilde over (W)}H=WWH+WcWc
Note for the omni-directional beam pattern the matrix D={tilde over (W)}{tilde over (W)}H should be a diagonal matrix with power constraint Tr{{tilde over (W)}{tilde over (W)}H}=C0. It is of interest whether there exists a complementary weight matrix Wc and if exists whether it is unique. If C0 is greater than a certain threshold which depends on the peak value of the beam, there will be a solution. If there exists a solution, there will be multiple solutions since the constraint (17) considers only the signal power.
Giving a singular value decomposition to W
One needs to find a matrix Wc which makes the matrix D to be a diagonal matrix with Tr{D}=C0. If it is assumed that matrix WcWc
then D becomes
In this particular case, if and only if the matrix ΛΛH+ΛcΛc
where λk=0 is assumed for K<k≦N.
Clearly, c0 should be greater than or equal to max(|λk|2).
The complementary weight matrix Wc is as follows
where Vc
which generates the complementary beam pattern for the omni-directional beam.
5.2 Generate Nulls
To generate nulls at each user's DOA, the following condition should be satisfied
The inner product
Denote S the subspace spanned by vectors a*(θk) and S⊥ the orthogonal complement subspace of S. Now decompose w1 c into two orthogonal components, one lies in S⊥ and the other lies in S⊥ as follows:
where PS and PS
In the scattering channel, the projection matrices are defined by
Clearly, PS
Then, the complementary weight matrix can be obtained by applying the orthogonal projection to (18)
Giving SVD to A*=Ũ{tilde over (Λ)}{tilde over (V)}H (in scattering channel H*=Ū{tilde over (Λ)}{tilde over (V)}H), the complementary weight matrix becomes:
where ũl is the l-th column vector of Ũ.
Certainly, the projection technique can be applied to the downlink beamforming to generate nulls at other user's DOAs.
Theorem 3: rank(Wc)=N−K or N−K−1 and, if the downlink beamforming matrix has a special form W=A*B where B is a non-singular K-by-K matrix, the complementary weight matrix degenerates to Wc=√{square root over (c0)}[uK+1 uK+2 . . . uN] where W=UΛVH is assumed.
Proof: Obviously, the rank of PS
where N is number of columns of A or number of rows of B, since K≧1 the rank of Wc=PS
Define S′ as the subspace spanned by columns of W. Since W=A*B and B is a non-singular matrix, the matrices W and A* are column-equivalent. Hence, the space S and S′ are identical. See, e.g., Dennis B. Ames, Fundamentals of Linear Algebra, International Textbook Company, 1970.
Note the projection matrix PS′ is equal to PS because:
The projection matrices for S′ and S′⊥ are
The complementary weight matrix can be written as:
Since the first K columns of Wc are zero vectors, the complementary weight matrix can degenerate to:
Since the pseudoinverse or MF beamforming matrix satisfy the above condition, the complementary weight matrix can be obtained through SVD to W. On the other hand the windowed MF does not satisfy the above condition and since Wc is an N-by-N matrix, though its rank is N−K at most, one needs to create N independent data streams. However, using SVD to Wc
and the fact that the rank of Wc is N−K if rank(Ac)=N, the complementary weight matrix degenerates to:
Note the column vectors in Wc have different weights. This makes the overall beam pattern to be omni-directional. Since one can scale the complementary beam power level, the overall beam power at the directions of the side lobe cannot be flat. Instead of trying to make the overall beam to be flat, a flat complementary beam is enough. Changing Wc to:
will not generate severe ripple as far as the ripple of W is small because the beam pattern of Wc (19) will have constant level at the hidden beam angles.
5.3 Scale
Since the total beam does not have to be omni-directional for the hidden beam problem, the power level of the complementary beam should be lowered by adjusting k0. For example,
Non-windowed downlink beam: Wc=√{square root over (k0c0)}[uK+1 uK+2 . . . UN]
Windowed downlink beam: Wc=√{square root over (k0c0)}[ū1 ū2 . . . ūN−K].
The side lobe power of the complementary beam is 10 log10 C0+10 log10 k0 where C0=Nc0 is the level of the main lobe.
5.4 Exemplary Subspace Complementary Beamforming II (SCBF II) Technique.
Now assume 2K<N and introduce augmented matrix Wa
In the scattering channel we define the augmented matrix as
The rank r of Wa is in the range of K to 2K. The vectors orthogonal to Wa can generate another complementary beam. Through SVD, one can have SCBF II as follows:
where ua,l is the l-th left singular vector whose corresponding singular value is zero. In the windowed downlink beamforming the rank of Wc is N−2K. This means the number of additional independent data streams required is smaller than that of SCBF and smaller transmitted power is required for the same level of complementary beam. However, because of less degree of freedom for the creation of the complementary beam, more ripple in the complementary beam is observed.
Theorem 4: If the downlink beamforming matrix has a special form W=A*B where B is a non-singular K-by-K matrix, the SCBF II and SCBF yield identical beam patterns.
Proof; The augmented matrix Wa can be written as
Note the rank r of Wa is K. The complementary weight matrix of the SCBF II is given by:
Apparently, Wa c
Remember that the columns of Wc of the SCBF are also orthogonal to columns of W,
It can be observed that the matrices Wa c and Wc have the same column spaces with bases ua,K+1, . . . , ua,N and uK+1, . . . , uN respectively. Hence, the matrices Wa c and Wc are column-equivalent. Thus, there exists a non-singular square matrix Q satisfying following identity
Since ua,k and uk are orthonormal bases, the matrix Q should be unitary.
The beam pattern generated by Wc can be written as:
5.5 Null widening Technique
Until now the ideal DOA estimation has been assumed. In reality, however, since there will likely be a DOA estimation error, this causes a severe SIR penalty. In order to reduce the sensitivity to the DOA estimation error one can generate one or more additional nulls at vicinity of DOA's. This can be obtained by changing the steering matrix A. For example, the steering vector α(θk)may be replaced with:
The new steering matrix for the projection becomes:
The projection using the above steering matrix will generate nulls at not only θk but also θk−Δθl and θk+Δθr. The optimum number and positions of additional nulls will depend on the N, K, DOA estimation error and antenna array structure (i.e. steering vector). The null widening technique creates wider nulls if θk−Δθl and θk+Δθr are chosen properly. Unfortunately, however, one may not be able to generate as many nulls as are needed. If the rank of � is equal to N, the projection matrix becomes PS=I.
Thus, PS
This means that one cannot generate any complementary beam when the rank of � is equal to N. Thus, there is a limitation on the number of additional nulls. The total number of nulls should be less than N. Note that in certain implementations, the null widening technique is applied to the downlink beamforming also to reduce side lobe level or create wider nulls at other intended user's DOAs.
This exemplary null widening technique is useful in non-zero angular and delay spread channels when the downlink beamforming matrix is calculated assuming free space channel. The complementary beam or side lobe of intended user's main beam may cause interference to other intended user's main beam in multipath channels though they have deep nulls. Thus, wider nulls are more desirable in multipath channels in order to reduce the chance of the interference to all intended users. Furthermore, the complementary beam level may be controlled adaptively based on the channel environments.
5.6 Simulations
Here, pseudoinverse downlink beamforming is considered with four active users and N=16 in the ULA 254 with d=λ/2. The channel condition is summarized in Table 1, below. The downlink beam patterns of users are shown in graph 1600 in
As shown in graph 1800 of
Next, consider the Hamming windowed MF beamforming without power control. The beam patterns of each user are shown in graph 2000 of
For the omni-directional radiated power the c0 should be greater than or equal to max(|λk|2). Then, the radiated power has the relation
If C0>z(θ), then the complementary beam's interference to users at θ is C0−z(θ). However, the complementary beam (2204) does not generate any interference to the directions of intended user's DOAs as depicted through the projection shown in graph 2200 of
In graph 2300 of
Graph 2400 in
Section 6: Complementary Superposition Beamforming (CSBF)
In this Section "Complementary Superposition Beamforming" (CSBF) techniques are described. In CSBF the side lobe level of any one of main beams is increased in order for the hidden beam clients not only to detect some power but, in some cases, to decode the data packet as well.
In the subspace complementary beamforming one needs to generate N−K dummy random data streams. The SIR of each dummy data is too low to decode because N independent data streams are transmitted at hidden beam angles. Through the SCBF the hidden beam clients can decide the channel is busy by detecting some energy but cannot decode the data. If the hidden beam clients can decode and extract important information such as CTS and preamble, etc., the hidden beam problem would be more controllable.
6.1 Complementary Superposition Beamforming (CSBF)
Instead of sending additional random data, CSBF increases the side lobe power of one of main beams which has the highest side lobe level so that the hidden beam users are able to not only detect some energy but also decode the data packet. CSBF is created, for example, by modifying one column vector of W as follows:
One decision is how to choose pl. One may start with the K=1 case. The downlink weight matrix can be written as
Then, SCBF provides Wc=√{square root over (c0)}[u2 u3 . . . uN].
The modified weight vector {tilde over (w)}1 becomes:
where p=[p0 p1 . . . pN−1]T. The weight vector {tilde over (w)}1 can be decomposed by two vectors as
If the vector p is chosen as a complex conjugate transpose of l-th row of U, the weight vector can be expressed as
The second vector in (20) has only one non-zero element at l-th antenna. This means the second vector produces omni-directional beam pattern. The beam pattern becomes equation (21) as shown below:
The omnibeam pattern caused by the second vector in (20) increases the side lobe of w1 though there is a ripple because of the cross term in (21). Note when √{square root over (c0)}=λ1 the beam becomes omni-directional. Through the scale one can control the side lobe level. Here, one can expect more ripple in the beam compared to the SCBF method. This larger ripple comes from the less degree of freedom in the CSBF.
This argument can be extended to general cases as follows. First choose the k-th beam which has highest side lobe level. Then, change the k-th weight vector to
where p is complex conjugate transpose of the l-th row of Wc,
With reference to graph 2500 of
Exemplary beam patterns of the windowed MF with the CSBF are depicted in graph 2600 of
Graph 2700 in
Reference is now made to
Digital signals x1, . . . , xK are then each provided to a corresponding digital-to-analog converter (DAC) 306. The resulting analog signals x1, . . . , xK are then provided to an RF function 256 and corresponding y1, . . . , yK RF signals are provided to corresponding elements in array antenna 254.
6.2 Complementary Superposition Beamforming II (CSBF II)
If all user's side lobe levels are low enough, one can set up additional channel to send special data to the hidden beam users. This special channel can carry control data only such as CTS, preamble, etc. From the previous subsection, the following weight matrix is devised:
Graph 2800 in
Graph 2900 in
Graph 3000 in
Reference is now made to
Digital signals x1, . . . , xK are then each provided to a corresponding digital-to-analog converter (DAC) 306. The resulting analog signals x1, . . . , xK are then provided to an RF function 256 and corresponding y1, . . . , yK RF signals are provided to corresponding elements in array antenna 254.
6.3 Performance of CBF
Through the complementary beamforming techniques, put some energy to the hidden beam directions in order for the hidden beam users to detect or decode data. n this subsection the probability that the hidden beam users can detect or decode data is investigated. The hidden beam problem is usually worst when only one beam is transmitted. When K=1, one can use a MF downlink beam. Thus, CSBF yields:
Note when ε=0, W becomes the MF downlink beam and when ε=1, the beam pattern becomes omni-directional. To see how much improvement can be achieved using the complementary beamformings the following parameters are defined:
(i) SNRReq: required SNR for particular data rate
(ii) SNRCCA: SNR for hidden users to decide the channel is busy or decode data packets
(iii) Coverage area for the particular data rate: where SNR≧SNRReq
(iv) Prob(SNR≧SNRCCA): the probability that SNR in the coverage area is equal to or greater than SNRCCA
(v) Δ=SNRReq−SNRCCA.
In graph 3100 of
As shown in similar graph 3200 in
6.4 Extension to Scattering Environment
6.4.1 Non-zero angular spread and zero delay spread
When multipath components are separated in angles but with approximately the same path delay, the spatial signature of the k-th user can be expressed as:
where hk l and θk l represent the fading gain and DOA of the l-th multipath, respectively.
The received uplink and downlink signal can be modified as follows:
respectively, where H=[h1 h2 . . . hK] and the rank of H is assumed K.
The MMSE combining provides optimum uplink combining among the linear combining techniques and the pseudoinverse downlink beamforming yields infinity SIR at intended user's angle.
It is clear that the complementary beamforming techniques can be applied. For the projection, however, one needs to redefine the subspace and consequently the projection matrix also. The subspace S should be the column space of H*. When the downlink beamforming matrix has the special form W=H*B, Theorems 3 and 4 still hold with W=└WH*┘. Using the null generation and the null widening techniques one can create additional nulls at the complementary and downlink beam.
6.4.2 Non-zero angular and delay spread
If multipath arrives at different angles with large delay spread, space-time combining with tapped delay line may be used, for example, as in wideband signal beamformings. See, e.g., Joseph C. Liberti, Jr., and Theodore S. Rappaport, Smart Antennas for Wireless Communications, Prentice Hall, 1999. If the up/downlink signal is an OFDM signal, then the optimum beamforming may, for example, be achieved by space-frequency combining. Since the linear model (22) and (23) hold in the MIMO OFDM signal in frequency domain, one can apply the same rules.
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In Buenos Aires, the tango starts with a gesture that is almost imperceptible to the untrained eye.
At traditional "milongas," as tango social dances are known, men do not approach women and ask them to dance. Rather, the Argentines sit across the room and make eye contact. If the woman does not avert her eyes, the man nods slightly. If the woman nods back, then he approaches her and they move to the floor.
That initial gesture is known as "el arte de cabeceo," or "the art of the nod." This ritual saves the man's dignity from public rejection, and it respects the vulnerability of a woman, as she can easily refuse and not feel obligated to dance with the man.
This is only one ritual among many. Throughout the entire exchange, traditions determine where to place your hands, how many songs you dance together — and strict gender roles are always present. Some dancers claim that the social codes inherent in the tango are necessary because the dance requires strangers to become so intimate with each other.
But there's a new kind of tango taking place. At the gay milonga, known as La Marshall, you'll find several kinds of couples dancing: women with women and a few mixed-gender couples — but mostly men with men. Five o'clock-shadowed cheek to five o'clock-shadowed cheek, they execute their steps with precision and clear intent.
Tango in Buenos Aires is constantly refining and redefining itself. The tango began in the 1800s near the ports on the south side of the city. It evolved from the overlap of slaves brought from Africa, immigrant laborers from Europe, Cuban sailors, and women who arrived or were coerced into working the brothels. During the years the music and dance became less bawdy, as it shifted from whorehouses to high society. Experimental music by masters like Astor Piazzolla, who introduced jazz and classical elements to the tango, opened it up for further experimentation. In the past decade, nuevo tango, in which electronic music is mixed with Belle Epoch classics, has the younger generation in Buenos Aires dancing.
Two of the latest trends, gay and queer tango, are attracting dancers from across the world to Buenos Aires. Many trace gay tango back to one man: Augusto Balinzano, who tours internationally to teach gay tango. When he's in town, he teaches tango at Lugar Gay, a guesthouse exclusively for men in the neighborhood of San Telmo.
A professional tango dancer, he says that gay tango wasn't a deliberate movement; it just happened.
"One night I was dancing with a man," he says. "Then the next time another couple of gay men joined us. And so on. Now we have gay lessons and a gay milonga."
Indicative of major changes in Argentine society, the gay tango is something of a perfect storm that came about from an economic crisis, improved civil rights for homosexuals and a revival in tango's popularity.


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Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/14290
|Bayesian variable selection in parametric and semiparametric high dimensional survival analysis
|Lee, Kyu Ha
Cox model
Gibbs sampler
variable selection
|University of Missouri--Columbia
|In this dissertation, we propose several Bayesian variable selection schemes for Bayesian parametric and semiparametric survival models for right-censored survival data. In the rst chapter we introduce a special shrinkage prior on the coe cients corresponding to the predictor variables. The shrinkage prior is obtained through a scale mixture representation of Normal and Gamma distributions. The likelihood function is constructed based on the Cox proportional hazards model framework, where the cumulative baseline hazard function is modeled a priori by a gamma process. In the second chapter we extend the idea of the shrinkage prior such that it can incorporate the existing grouping structure among the covariates. Our selected priors are similar to the elastic-net, group lasso, and fused lasso penalty. The proposed models are highly useful when we want to take into consideration the grouping structure. In the third chapter we propose a Bayesian variable selection method for high dimensional survival analysis in the context of parametric accelerated failure time (AFT) model. To identify subsets of relevant covariates the regression coe cients are assumed to follow the conditional Laplace distribution as in the rst chapter. We used a data augmentation approach to impute the survival times of censored subjects.
|Other Identifiers:
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Rich Shertenlieb
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Show Your Support For Rich Shertenlieb & Family
Some sad news hit the 98.5 The Sports Hub family on Thursday morning, when Rich Shertenlieb announced his wife, Mary, has been diagnosed with AML – a form of leukemia.


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Spinal Cord Injuries: Beating the Odds
September 11, 2008
Twelve-thousand people in the United States suffer spinal cord injuries every year. Find out how one man is walking after doctors said there was a 99 percent chance he wouldn't.
Topics: Health Medical Pharma, Neurotrauma, Nervous system, Medicine, Kookal Ramunni Krishnan, Kevin Everett, Spinal cord, spinal cord injury, Neurology, Biology, Cord Injuries