 Welcome to the celebrating faculty careers this event here today. The celebration of faculty careers event started in 2013. It was an outcome of multiple actions that were happening at the college level. There was a strategic plan, there was a faculty of 2020, with its own focus on intentional professional development of faculty through all stages in their careers. And so this program started in 2013 and through this program faculty members who are full professors and have been in rank seven years or more have a chance to present in front of colleagues and students and staff both in part a reflective look back upon the career and also looking forward and really the idea is to provide a venue for all of us to celebrate success and to find new venues for collaboration and moving ahead. Today it is my distinct honor of course to introduce Dr. James Leonard. Jim got his PhD in 1985 from the University of Illinois and he joined Purdue and is currently a full professor in electrical computer engineering. He is a widely cited researcher in this area, has won many awards ranging from Purdue's own university faculty scholar to awards through the IEEE and at IEEE he is not only a fellow but has contributed in many times in the capacity of an editor as well. His research area is broadly speaking, I don't understand all of it but broadly speaking the area of spectrum management, CDMA related wireless technologies and many other related things and really without further ado I really want to give Jim a warm welcome and that's a good welcome. Thank you very much. I wanted to thank all my colleagues for being here all of you who are taking your extremely valuable time in my view. I very much appreciate it. Before I get started I want you to glance over at my demos. I can fire up at the end of this talk during the reception but focus in particular on that little generator to the left. It's called a Gen E motor. It was built prior to World War II. It powered amateur radios out during World War II on the battlefield. One day my parents had people over for dinner and I was in the basement. I found that thing. I hooked up my dad's precious voltometer that he really valued because they were pretty pricey in those days. I found a generator, I fired it up. Unfortunately my left finger and my right finger got across 300 volts and I'll never forget the feeling as I lurched back, not only that feeling but when I walked up the stairs I looked at my dad with a company there and I said, Dad, I broke the glass on your meter. But he was one great dad. He didn't blink an eye. I knew he was sad about losing that voltometer. But after the talk there'll be some shocking demos. Okay, so I've been chartered to talk to you about scholarship, research and engagement and not be technical. But to me all those things are technical. I'll see what we can do here. But what I really want you to do is get a feeling for people, the people that have come through Purdue before, the people who are coming out of Purdue and active now that I've had the great privilege to work with. And then I want you to see some huge technological seismic shifts in the world as we move from those vacuum tubes over there to cell phones. Simply amazing. In those very same people that were responsible for those shifts many of them originated in studies at Purdue and many of them come back and continue to visit us. It's really been a wonderful thing. In the 60s when I began you could see electronics, those vacuum tubes glowed, the one tube glowed purple, the other filaments glowed. You imagine the electrons boiling off the filaments. You could tell since electrons were either attracted or repelled depending on the voltage on the grid to see what was going on in that tube and you had an extreme clear view of how things worked. Unfortunately today what we have is a piece of plastic and inside that piece of plastic there's this complicated program running. But nevertheless if you look at the science it's still fascinating and it has been truly fascinating to work in CDMA through these years. We began, many of us began as amateur radio operators and in particular I can still remember the day in the 60s when my dad having survived World War II invited my brother and I down to Chicago Dearborn Avenue to go to the federal building and we took our amateur radio licensing test. My dad watched there to see how many we got wrong. He was pleased with us at the end. We both passed. And that started off a career in electronics for me. In my dad's case he had a newspaper route prior to the start of the war and you could deliver papers for long enough to afford a helicopter Model S20R which is shown on that card over there. And I used to use that radio. I thought it was getting a little old when I worked on it in the 60s. My brother attached the S meter to the back of it just to give you a sense of the physicality of the electronic world in that era. I thought I'd show you some of these crystals. In fact let me read something from this little parched note that came from one of the crystal boxes to give you a flavor. 40 meter crystals require a holder having one full-size electrode and a button electrode consisting of a disc, approximately one half inch in diameter. Place the crystal in the holder with a button at its geometrical center and under a light spring pressure with the crystal oscillating vary the button position and its pressure until maximum output is obtained. How can you get more physical than that? Okay, so academically as we transition into this new world of wireless how did it all begin? Luann personally took this picture in 1973. Do you recognize any of the people? There's Shannon there, the founder of Information Theory. And to the left there's Tom Kovar, Tom Kylath and you can read the other in my advisor to the right, Mike Persley. For some of you in coding the guy there in the middle is Fred Jelenik from the BCJR algorithm that you guys just studied a couple of weeks ago. Well these were fascinating people. If you get on the web and start reading about Shannon you'll find out that around the time my dad was working on that television set publishing a mathematical theory of communications. John Lindenlob here at Purdue gave me that book from Shannon when he moved from working in communications over towards computers. You ought to take a look at this. It's a really clean, elegant Information Theory book. While Shannon was known to have lots of rumors he made all kinds of games. He wrote unicycles. He juggled down the halls of Bell Labs hence the spirit of the thing. I brought in a unicycle and some juggling. We have a Purdue juggling club. The rumor was that he was worried once that his talk was going to get too boring. So he brought his juggling clubs. If it got too boring he'd just do some juggling. There are several people we'll run across. Another one is Galois that did some fascinating things. We can't let Shannon down so to carry on the tradition when I was at the Coordinated Science Lab we all learned to juggle. Bob McLeese would go into the Coordinated Science Lab lecture room. He'd pull out his juggling equipment and he'd toss clubs with the graduate students. Those were great days. They'd even invite us to go running through the cord fields at Illinois with them. They'd run marathons in 6.2 kilometer races. They'd invite the grad students to go running with them. I made a deal with my students. I said, hey, if you'll go running with me I'll buy you a pair of running shoes. I had no takers. They already had running shoes. Okay, here's an interesting fact, I think, to know about Purdue's influence. When I was at Illinois my undergraduate advisor was now ECE Purdue alumnus, Tim Trick. He ran Coordinated Science Lab for a while. And lo and behold, my undergraduate advisor was an OECE Purdue alumnus, Mike Persley, the guy that was talking with Shannon there in 1973 before the first Shannon lecture. What's a joy is thinking, hey, I wrote this master's thesis. I wonder what will ever become of it. I'm going to show you where that ended up in the IS-95 interim standard for CDMA communications at some point in the talk. How did I get to Purdue? Look at this guy on the left. George Cooper. Look at the guy in the front on the far right. That's Claire McGillum. George and Lisa Cooper invited me out for dinner and they said, hey, how would you like to come work at Purdue? I'd very much like to come work at Purdue, George. Thank you for asking. And here I am. Do you see Dave Landry, by the way? Do you see John Lindenlaub? Do I need to point them out? Study that picture. There's Bill Haight in the middle. Here was one that really made an impact for me. I came to Purdue. It was time to start a digital communications course. George and Claire had a new book and they said, teach the course, please. Here's how we began with this book. But you know what? During that time it was more than that. I had already heard of George and Claire. I'd heard of George in working with Nettleton. And they were arguing back and forth about AT&T Bell Labs, where CDMA spread spectrum might be the way cell phones should go in the future. And since I worked in CDMA at Illinois, I really got some attention from them that way. Let me tell you a little bit about how cellular began. Going back here to this book, which will be the future, let's start at where it began. What was happening early on in the early 80s is people said, okay, the more frequency we give people, the better the fidelity of their call. So let's do frequency modulation. And they decided to go with 30 kilohertz. The problem was that if you use 30 kilohertz at the center of a cell and you used FDMA, here we are at the center, you couldn't reuse those frequencies in any of the adjacent cells. So you used up 210 kilohertz. How many calls did you get then in about 1.26 megahertz? You got six calls from FM. Pretty soon we're going to show that CDMA with George and Claire and all the guys ended up getting perhaps 20 times that number of calls in the same area using this new technology. Purdue was always ahead of the game. Everybody knows G-H-G. G-H-G is George Global, of course. And so George let me his phone over here. I got to hold this up. This was the first cell phone that was used in the Lafayette area. His friends called his suitcase the football. I think they were thinking about the president's nuclear codes. But they called it the football. George would go down to Fort Lauderdale Beach. He had to be connected to ECN at any moment. So he'd use the analog phone system with the telebet trail baser modem, a computer that didn't even have a hard disk, only a floppy, and he was online any time. You can't pull a fast one on George Global very well. By the way, ask him someday how he likes charcoal grills. Notice on the web that he's a winner of the Nobel Prize, the Ig Nobel Prize. In fact, some of those winners are also winners of the actual Nobel Prize. That's our George, who I had the pleasure to work with through the years. I want to put one idea in your mind, technically, so we can get started. I'm going to tell you about Hadamard matrices. Consider this giant matrix there, and I want you to run a test in your mind. Take any of the two rows, the blue one and the red one. Multiply them together at add. What do you get, zero? Those rows are orthogonal. You know what, though? If they're adjusted if one slides to the left a little bit and slides to the other direction a little bit, they're no longer orthogonal. In the real world, signals have delays. We can't maintain that perfect orthogonality. We have a problem, but we can solve it. Here's a basic structure of how we convey information. We have one computer, and that computer has to get a file to another computer. And so what we'll do then is track that from this to this. We go through an encoder that increases the rate of our data symbols, a sub k. We modulate onto a carrier to send through the radio frequency channel. After filtering and amplifying, we get corrupted by thermal noise in the front end of our receiver. We filter to get the best possible performance, run a synchronization, estimate the encoded data, estimate the real data, and hope we don't have errors. I like to think about communication in its basics this way. I think about that wild changing noise waveform as a random process. So this thing here is a random process. And then I think to myself, how am I going to get a signal through? Well, I'll get a signal through by correlating. So think of that little time there. You see little t is the present time. And let's go back in history by capital T seconds and let's integrate everything that comes in. The noise is getting integrated out. Half the time it's above the line, half the time it's below the line. But you know what those rectangular pulses do? They produce triangular pulses from rectangular pulses. Then we sample at the peaks in the triangle and we get our data out. This is an important idea to think about because we're going to replace those rectangular pulses soon with a CDMA coded pulse that is multiplied by a quickly changing code waveform, and that's going to give us a new capability. Okay, if I were Mike Persley, and I remember how he used to introduce spread spectrum, it was a lot like this. The concept was to take one of those rectangular pulses and multiply by a spreading waveform. I can show you that right here. See this spreading waveform? We're going to multiply by it. Now an unwanted signal may come in. Maybe it's a jammer. Maybe it's another interferer. Maybe it's another user. But we're going to pass this secret waveform, this randomized waveform to the receiver. Nobody else knows it. But at the receiver we'll multiply by a copy and then we'll integrate. There are indeed some interesting properties. The interesting properties are that our signal contribution doesn't change since we multiplied by the square of the spreading waveform. It's like multiplying by one squared or minus one squared. We get the exact same signal back. And so our strategy then is to get a finite power waveform. But look at this. Let's think about an ergodic random process which is the same as the ensemble average. Then in this correlation process we get the variance here. We can set that to be one and presto. We get the same signal back. We didn't pay a penalty from spreading. But what have we gained? The way to understand what we've gained is by thinking about the power spectrum of that spreading waveform, V of t. Simply we could just say, hey, let's pretend it's thermal noise or something like that. We'll spread the power equally between B and B. And let B be very large. We take the inverse Fourier transform. We get the impulse function. We tell our students, students, let's learn to think in the time domain and the frequency domain and flip back and forth at will. Let's learn to do everything we can do with a deterministic signal. Let's learn to do that with a random signal. And if we can develop those skills in addition to thinking mathematically and graphically, we're on our way. Take the energy of that interfering signal, the norm squared, and that divide by the bandwidth and that ends up being the variance. We've driven that interference to zero. What about a low probability of intercept capability? If we had built V of t by a plus minus one sequence that kept flipping, this would have been the power spectral density before spreading, after spreading it would have looked like this. If we have a lot of chips per bit, a chip duration t sub c shown in this picture is much smaller than the symbol duration and we will spread by that fraction and pretty soon our signal power spectral density will be so small that we can hide it. In addition, we get what's called a multi-path rejection capability. Multi-path is key for fading. I'm about to tell you that in the cellular standard that's what caused the systems not to work. We'd be sending those signals that were producing the triangles, but as soon as we received one of the triangles we were going to sample at its peak to figure out the signal, another multi-path would come in just a very small amount of time later reflected off a metal surface. If we reflect off a metal surface, the polarity flips. That second arrival had the exact magnitude of the first arrival with the opposite polarity. What happens when they add? We get nothing. Our signal fades to zero. The direction of the CDMA is going to be what is key to make it work ultimately in the cellular telephone system. Remember how I said we could reject an unwanted signal? Let the unwanted signal be another user. Imagine the cell phone system that's going to come along. The unwanted signals will be the users that aren't you. You want to talk and they're bothering you. But nevertheless, we can drive their bandwidth to infinity and the variance of their signal goes to zero and the expected value is already zero. We've wiped out the interference from another user someday in a cell phone system. Okay, I have to tell you a little more detail about the construction of these signals now. Take a B of T waveform. That's our data waveform with pulses. Positive, negative, negative, positive, negative, positive, positive, negative. We sense some bits. Now take eight chips. Make it periodic. Select them on a computer randomly and get a C of T times B of T to get C of T. That's how we generate a CDMA signal. Okay, I did that on the computer but I used 31 coin tosses on the computer. If I use 31 coin tosses on the computer, I get the spread spectrum waveform. But you know what? Now I'm going to do the same thing that I used to do. I'm going to do the same thing that I used to do with the rectangular pulses. I'm going to integrate from the present time back in history by capital T seconds. And as a function of time, this blue production will occur, the multiplication of the blue with the black. I get almost nothing until I'm perfectly lined up. Then I get a very large spike. The strategy is to figure out the timing to detect my signal so the key matches up. Now I will produce a spike. At all other times when I don't want to have multi-path bothering me, I won't have that spike. I decided to put the graph from the computer of how that spike looked. It's two chips wide. We used to have a triangular response. Do you remember how the triangular response would look? It would go from this point to this peak, down to this point. Now instead of being two capital T wide, it's two chips wide. That is really going to help us with multi-path. I decided to reduce the size so I can show you more ideas. That's all we did here. Now let's think about taxi cabs, drawn with the true skill of an artist. We have this taxi cab sending a direct pass signal to another taxi cab. We have a bounce off the ground. We have perhaps another bounce off a mountain. We have three arrivals. In the old days, these three arrivals would give us fading, but not if we code them with CDMA. So what I decided to do when I was working on this, this falls in a very early era prior to the implementation of the standard. I wrote a paper called Multi-Path Combining with Diversity for Spread Spectrum. Those were the essence of the paper. It was produced after my advisor did a great thing for me. He invited me to a number of DARPA meetings. He said, Jim, why don't you take my place? So I went out and I met guys like George Turin headed Berkeley who was working in a similar area. He invited me into his office. He said, hey, just sit here for a couple of hours and read all my works and magazines if you like. You can get some research done that way. I always remember George Turin for that. Then I went to the DARPA meetings with Barry Liner, Leonard Kleinrock, George Turin, Vaud Tabaji, a lot of these guys. The days when they were developing DARPANet, they wanted to do packet radio. It was a great time and exciting time of technology and great people. So I wanted you to see the idea I had. Black, red, purple, green, blue. Let's cycle the sequences. We never get the spike unless the black is aligned with the black. If you have the wrong color sequence, we don't get a spike and you have to be aligned. So let's put those spikes into a tap delay line. Three arrivals, we have three chances to receive the signal. We'll use the information inherent in each of the three arriving spikes. And Presto will do really well. We had to make a structure that was matched to black, red, purple, green, blue. Here would be the matched filter. So instead of a single filter, we'd have a bank of filters. The first bank came bit B-0, then B-1, then B-2, then B-3, then B-4, B-5, B-6. We cycled down the row, come back up, cycled down the row again. And we had both the in-phase and quadrature section for those of you who are tuned into communication receivers. Here was the performance. As the number of users went up, of course the performance got worse, but we could drive the performance down by doing better, by doing more spreading. Okay, to talk about engagement, to give you a sense of how exciting those days were, here's a picture where we were doing entrepreneurial activities. I was asked to write the telecommunications article for Encyclopedia Britannica, and if I wrote it, I'd get a whole set. You know, in my memory at the time, my older brother had been in a motorcycle accident in high school. He was going to be an electrical engineer, and he was in a wheelchair all summer. So what did he do? He read Encyclopedias. So hey, a chance to get Encyclopedias. And you know what, it took him away from engineering. He saw the docs doing surgery, so he went into the Bendicle program. You could also go out and make some money if you were on a tight budget, and with kids coming along, we were a little bit on a tight budget. So we gave short courses, and people would actually come. We'd find a hotel. I had another colleague I'd gone to school with, and we'd rent a hotel room. We'd get courses on this new technology. People were interested in it and make some money also. So now let's go to CDMA. Can we turn the analog mobile phone system into a system with more capacity? I want you to think about the same picture again, but now I want you to think about having three sectors that are color-coded, red, blue, and green, and they're going to be color-coded using directional antennas. It turns out that we're going to use CDMA technology now instead of FM, and I want you to think about the environment I was in during that era. One example, I went to the Chicago area. There was a great big hotel room. Inside that hotel room were hundreds of engineers. And what were they doing? They were arguing about what the next cellular standard should be. They said, maybe we should do TDMA. I'm for IS-54. Or, no, IS-136. No, no, CDMA, IS-95. Arguing back and forth about what standard would make sense. People would criticize Qualcomm at that time saying, oh no, they bet the farm on CDMA. If they don't succeed with CDMA, they're going to go bankrupt. But that was the exciting environment during that era. You can see the essence of the argument by writing a simple slide on the back of an envelope. Wayne Stark and I discussed this one day. Take Mike Persley's result for CDMA with multi-axis interference. Write a signal-to-noise ratio expression. And then start modifying it according to the new system. Think about this. If I am talking to you, once in a while I pause in my voice. Do you know that when you're encoding in a vocoder at a very fast rate, if you're pausing you can just gate off the transmitter power. What does that do? It doesn't produce any extra multiple-axis interference. So capitalizing on that, we could have half the variance from D, the voice activity factor. Remember that hexagonal cell pattern? It used to be that we used up to 10 megahertz by using 30 because we couldn't reuse the frequencies in neighboring cells. But didn't I just tell you that CDMA had a multi-axis capability? It does. So now how do we think? We turn on all these radios in a cell. We get interference from within the cell. And sure, interference comes pouring in from outside the cell. About 66% as much interference as we get from within our own cell. So we'll define a frequency reuse factor F. In our frequency reuse factor F, 1 over F will be that 1.66 that I talked about. But that sure is better than 1 over 7. What else happened to us? Well, we continued running this and we figured, oh, we'll use that formula courtesy of Mike Persley in random sequences to get the number of calls per sector. And then because we have three sectors we'll multiply by three. We'll figure out how much signal-to-noise ratio we need to get our code to work. And you know, when CDMA has that anti-multipath capability, all we need is SNR squared to be about 6 dB and we're home-free. We run the calculation. We get 117 users per 1.25 megahertz. We had 6 before. So Qualcomm would push and push and push about this maximum capacity increase. We can also thank Klein-Gilhausen for that, who worked with Alan Salmazzi. Okay, here's a picture of our Purdue grad. Alan Salmazzi, would you please look at the quote? What does he say? Once I took courses with Professors George Cooper and Claire McGillum, my fascination extended to satellite and mobile communications. Eventually my interest in those areas of engineering converged to define my professional career path. Do you realize the importance of Qualcomm to the country for security and nationally today? How was Qualcomm founded? Salmazzi a Purdue grad sitting in these Purdue courses was one of the people who started it with Viterbi and Jacobs. Klein-Gilhausen was involved. It was really a great success. And what made it a success? The application of this exciting CDMA technology. By the way, take a look if you ever have time at a vehicular technology conference paper from 1991 by Salmazzi and Gilhausen. It's a fascinating description of a system. You know, Andy Viterbi many people know also was involved in starting Qualcomm and he came to meet me and our research group at one point and he taught the forward-backward algorithm in the advanced digital communications class. He also chatted with Bob Moro. I'm going to make the case later that Bob Moro, one of my own, actually my first successful graduate student he actually laid the groundwork at sending the data over the cellular system. He figured out not just a signal-to-noise ratio not just an air probability which I had done in some Purdue work but he figured out how to code with air control coding and packets which was ultimately accomplished when data was sent over IS-95. Okay, this is a very, very dense slide. A friend of mine sent it to me as soon as it came over the standards committee. Isn't it great to sit in class and have friends? They go out and become chief technology officers. They get all the material. If it's uncopy-rided, they share it with you. They come back and they visit you. They tell you what the real problems are. Students take advantage of your classmates when you're taking classes here. They grow up to be superstars. One of my classmates I sat next to him discussing our exam. A few years later he sold his company for about $450 million. He invented the digital subscriber link. Another one was CTO at one of the big communication companies. He said, hey Jim, have you ever used Major Theory? How have you used it recently? Because that was a course I took with him. Anyway, let's talk about how this system works. I want you to think about this a minute. We're going to have a system here. I'm going to point at various things. I want you to focus first of all on this long code generator. There's also a short code generator. I want you to think this way. There's going to be a time reference. In that time reference everybody on all phones and all base stations are going to know it. And then in every single phone there's going to be two shift registers, one producing a short code of length 32,768 chips, and another one with a shift register with 42 bits to make a sequence that's of length 2 to 42 minus 1. And here's what's going to happen. Remember that CD-May picture that I showed you with that sequence? Now our sequence is in 31 chips. It's 32,768 chips. And then on that phone, the 3G phone that you're using, what happens? At a 1.2288 megahertz chip rate you search out all possible shifts. If there are three base stations nearby you get a spike. You get a spike from each of the base stations. Pick the base station with the largest spike. That's your base station. The base station then talks back to you and it wants to make your call secure. What does it do? It gives you a particular shift of length 2 to 42 minus 1 to code your call to keep it separate from other calls. And so those two shift registers don't end up in the same state again once they start going for 37 centuries. That's the basic dynamic of the system. But along the way, what do you do in this picture? You take 172 bits off your vocoder. You add a cyclic redundancy check. We're going to talk about a Guy Galois in a minute that made that possible. And then you add an 8-bit encoder tail to clear out your convolutional code to get 192 bits. Then you take your bits from that packet put it through a rate one-third convolutional code. Now your data stream has three times the rate. You go into a block interleaver. You put the bits into a column of a matrix into the columns of a matrix and you transmit the rows of a matrix. Then you go to that 64-area orthogonal modulator that I showed you that picture of earlier. But now the rows are 64 of them. And then you code with CDMA and off you go. Where is my master's thesis used? It's used right here in these baseband filters. How did that work? My master's thesis said, look, to get the best performance in choosing a chip if your frequency limited, the sync pulse is the optimal pulse. How do you get a sync pulse when you have a rectangular pulse? You just heavily filter it. It starts to look like a sync pulse. That's exactly what happens in the standard. Okay, so here's another quick look at the standard. Two data bits become six code word symbols, become one of 64 Walsh functions. Those are orthogonal functions. You think I'm not serious about that? Look at the standard. That's half of the picture of what happens on one page. There's half of the other picture. There are Walsh Hadamard matrices. They show every single entry. Here is the long code generator. This is something that Galois showed us how to do. I'm going to talk about him briefly, but what did he say? He said, okay, you're going to send bits which come from the field GF2. You can send equivalence class at zero as in or equivalence class at one as in. That gives you a Galois field with two elements. I want you to think not of the integer's mod of prime, but of polynomial's mod and irreducible polynomial. Then we can build Galois fields with two to the 42 elements in it to model the state of this shift register. Then we'll use the trace function on that element, and by using the trace function, we'll derive that this shift register has the properties of a random sequence. It can all be done mathematically from this guy's brilliance. I need to talk about him. In addition, IS-95 handles power control. This is the picture out of Salmazian Gilhausen's paper from VTC 1991 May. It shows that as a mobile drives away, you go in and out of fades in that you gradually lose signal strength. What do they propose? Ah, power control! An 800 hertz closed loop feedback power control system in another faster system to just simply increase the power if you go into a deep fade. So we have an issue now. We have to talk about coding. This was a fun part of my life here at Purdue. The woman in the back row of my talk, Heidi, taught this very same code to graduate students when she was three years old on television. And the guy just to the left of her also taught this to the graduate students on television about how coding works. That's how they did it. Let me adjust this just a minute. Okay, they said, okay, blue is for zero, red is for one. Think about red is stop! And think about blue as everything's okay. Zero or one. Is there an alarm or not? Okay, so let's fill up four information bits. We've filled up the four information bits. But let's have a rule. Each circle has to have an even number of blue dots. Circle one, two, and three. There's a code word generated. That's our encoding rule. What would happen if an error occurred? Ah, an error in bit one. How do I know that's where the error occurred? Look at circle one and look at circle three. There's something wrong in both circles. I can't change this middle dot or it would ruin circle two. The only dot I can change is the right dot. I've done my decoding. What if the middle dot was an error? There's not an even number of blue dots in circle one, two, or three. Something's wrong. I can only change one dot. I better change the middle dot. If I only change one, that's the only change that will correct three circles. Okay, what happens if I have two question marks? I'm just not sure about those. What happens then? Well, I can fill in two question marks. Look at circle one. There has to be an even number of blue dots. That must be red. Look at circle two. There must be an even number of blue dots. That must be blue. Done. Okay, so we can take that statement of the even number of blue dots, write three equations in a Galois field with two elements, do mod two arithmetic. We can write it as a matrix equation and define our code as CH transpose equals zero. I first learned of this when Bob McLeese said that he had his daughter teach coding this way. He showed us this one day in a lecture hall after he showed us how to juggle. He also wrote a book for us, finite fields. He even mentions us in the preface saying we were twisting his arm to write the book. And you know one of the greatest things he did? He was Professor Mark Bell's advisor. What a great guy. Came out of Caltech. I had the privilege of knowing him when I was at Illinois. A very clever guy. You know what? Galois is also very clever. You know what he did? He turned the codes into cyclic codes. He said, no, think about them in a bigger field. GF eight. And turned those three equations into one equation in GF eight. Then we can say a code word is a code word if and only if a polynomial has a element from GF eight as a zero. C of alpha has to be zero. That led to the cyclic redundancy check that I showed in the IS-95 standard. That led to the understanding of M sequences through using the trace of the state of that shift register, working in a big field. Galois was truly a great guy. I got to tell you something about him by reading a biography given to me by one of the students when coding theory seemed hard. This is by Carl B. Boyer, a history of mathematics second edition. Young geniuses whose lives were cut short by death from dueling or consumption are part of the real and fictional literary tradition of the Romantic Age. Someone wishing to present a mathematical character no better than to create the characters of Abel and Galois. Galois was born just outside Paris in the village of Borla Rain, where his father served as mayor. His well-educated parents had not shown any particular aptitude for mathematics, but the young Galois did acquire from them an implacable hatred of tyranny. When he first entered school at the age of 12, he showed little interest in Latin Greek or algebra, but he was fascinated by Legendre's geometry. Later he read with understanding the algebra and analysis in the works of masters Grange and Abel, but his routine classwork in mathematics remained mediocre, and his teachers regarded him as eccentric. By the age of 16, Galois knew what his teachers had failed to recognize that he was a mathematical genius. He hoped therefore to enter the school that had nurtured so many celebrated mathematicians. The acopoly technique, but his lack of systematic preparation resulted in his rejection. This disappointment was followed by others. A paper Galois wrote and presented to the Academy when he was 17 was apparently lost by Koshy. He failed in a second attempt to enter the acole polytechnique. Worst of all, his father feeling persecuted because of clerical intrigues committed suicide. Galois entered the acole normale to prepare for teaching. He also continued his research. In 1830 he submitted another paper to the Academy in a prize competition. Fourier, as secretary of the Academy, received the paper but died shortly thereafter, and this memoir too was lost. Faced on all sides by tyranny and frustration, Galois made the case of the 1830 Revolution his own, a blistering letter criticizing the indecision of the director of the acole normale resulted in Galois' expulsion. A third effort to present a paper to the Academy resulted in it being returned by Poisson with a request for proofs. Thoroughly disillusioned Galois joined the National Guard. In 1831 he was twice arrested. He had proposed a toast in a gathering of Republicans that was interpreted as a threat on the life of King Louis Philippe. Shortly afterward he became involved with a coquette and was challenged to a duel. The night before the duel with forebodings of death, Galois spent the hours jotting down in a letter to his friend named Chevalier, notes for posterity concerning his discoveries. He asked that the letter be published as it was within the year in the review encyclopedic and expressed the hope that Jacobian Gauss might publicly give their opinion as to the importance of the theorems. On the morning of May 30th, 1832, Galois met his adversarian duel with pistols, which resulted in his death the following day. He was 20 years old. Okay, so fascinating people is the story. Bob McLeese taking a giant book by Lidl and Niederreiter that is this thick at the request of students reducing it into this thin book, finite fields from computer scientists and engineers. Engineers across the country gaining understanding and that's the way the technology has progressed in a very exciting era. Okay, I have to talk about some of our own work. So CDMA is used for both military and commercial communications. Certainly you know about Link 16 used since the 70s for Air Force planes. There's a CDMA aspect to that. And there's some follow-ons. We had a lot of DARPA research at Purdue. We had experimental work, theoretical work. And we had a lot of fun interactions with data that was real, matching up our theory with it. The people graduated out of the group. Here's one example. He is Tatlock with his own students at Chinese University of Hong Kong. I see Mai in the background from CUHK and I know he brings his unicycle in and I'm encouraged by his continuing the tradition. We have a few completed research programs. We had always thought it was really positive for Purdue to maintain connections with other universities, particularly when you come from a great place like Illinois. So we sent in a focus research initiative worked with Bruce Hayek, Yupman-Yumarov, who was in Dilip Tsawati, also Wayne Stark of Michigan. And then later on we did another group program with some of my former students with Tan Wang at Florida, Neshroff who's now at Ohio State and John Shea also at Florida. The idea of our research was rooted in the same idea, drive the interference out because the sequence doesn't match. Have your desired signal produce a spike. And so we could work on processing a signal. Think about us doing a fixed correlation between time zero and T and the signal coming in with a differing delay. Clearly you see when the blue signal you're listening to is lined up correctly we get a large spike. The wrong signal does not give us such a spike. We decided to exploit something called cyclostationary characteristics. After the system was already implemented we thought what else can we do? Think about it, the chip changes at periodical intervals of a chip duration. That gives a cyclostationary structure. If we can exploit that structure there might be something to have for it. So we decided to look at our filter, take the output and put it through a tap delay line and then we would run a linear MMSC on the calculation of the weights. We would form a correlation matrix. We would look at the signal when the spike was coming in and we'd look when the signal wasn't coming in. When it wasn't coming in we could deduce the characteristics of the multiple axis interference and jamming noise. And then we would project in the direction of the signal plus noise and project onto the space orthogonal to the noise in presto. We would get a picture that would look like this. We would have tap weights on that tap lane adjusting and we could plot the improvement in the signal to noise ratio as a function of time as our tap weights adjusted. This was a typical type of response. So by using a tap delay line and getting just the right taps this is a performance we'd get. We could get a 7 dB gain over what was being performed earlier. We could also, as a byproduct, we could direct our signal if we had multiple antennas towards the desired user and away from an interferer. That was also very useful. And sure enough, from the master thesis days I had to compare the different ship waveforms. And lo and behold, what did I find? For a half sign pulse, for example, the best you could ever do in this situation, 16.24, we would reach it with our system. We'd get 16.21 by sampling every T sub C over 4, four times per chip over this particular range of the spike. What was really fun is working with the Space and Naval Warfare Center on one of these DARPA programs. See that pile of CDs over there on that cart? They would send signals across the San Diego Bay into the jungle. The jungle was the San Diego Zoo. They would collect them at three antennas and send us the samples and say, what can you do for us? Look how much better when we process with our algorithms we got when we combine the data together. Here's antenna one alone, antenna two alone, antenna three alone there, and that picture then combined. Here's the second 300 points. Notice how that constellation is rotating. The third 300 points. The fourth 300 points. Rotating and phase, but we're getting order out of chaos by separating the clouds. If we separate the clouds, we've been able to deduce the bits. Here's how our algorithm would work if we adjusted our taps. Here is the performance of our bit error rate much better than before. SNR much better than before. And here's what we showed our sponsor. The green lines are the short range data. The red lines are the long range data. This is the performance that was obtained before we became involved. After we became involved, the best we can expect is this blue line. We were at these points with these algorithms operating. Our point was, look, algorithms can really help solve the problem of fading. You can mitigate interferes and jammers. You can use diversity and time frequency in space to greatly improve performance. And you know what? It is fun to cooperate with industry, with government, other universities in addition, and do technology transfer. So I started a company. We just celebrated its 17th birthday in my older brother. You know what it's like being a younger brother, he sent me a card for my birthdays of my company. And here's the card he sent. You can deduce what you will. We built a test bed through the years. We really liked equipment. We did it jointly with Michigan using a satellite that we put up. We had worked with Jack Shaw, CEO of Hughes Network Systems, who helped us understand satellites. We got some donated time from Amaco on the satellite. We got the thing licensed in the test bed for a number of years. Here is our vector signal analyzer. Before we operated our algorithm, this was just dots spread across the screen. But then we, on that left, but then we got order out of that chaos. So we invited Bob Lucky to come and give a talk. We wired this thing up. So when he gave his talk, he said, Bob, show us how you built the, invented the adaptive equalizer. Tell us about that. He hit the button. And presto, that adaptive equalizer made this order out of chaos. He told us how he invented this stop to traffic light on his way into Bell Labs. Remember Shannon going up and down juggling and riding unicycles at Bell Labs? Well, we have another one. A Purdue grad, Bob Lucky. We have new people going forward. Here's Brandon Holmes when he was a student. He published a paper on the information theory transactions about how to disperse signals in space optimally, and he even made a picture of it, almost like magnets repelling each other. And he also started using various codes and systems. And so, he went to do a turbo code. He learned about that, where the performance is greatly improved. Here is the plot of the performance which you want. And here is a picture of decoding an image that he had. The more iterations, the clearer the picture gets through iterative decoding of turbo codes, which is currently being studied in our air control class. I was minding my own business one day fixing the plumbing in my house when Janice said, hey, we gotta go. I said, what do you mean? I'm fixing the plumbing in the bathroom. How can I go anywhere? He said, just trust me. I went to a restaurant, and there all my graduate students were for a 50th birthday party. Here is one of the last big programs that we were working on enjoying a former student on the program. Oh, and I gotta tell you this. Two of the students from our research group participated in the spectrum challenge. And they each got these big checks, even though they were competing against each other. Brandon over there, I think he's in the top two. He may win the whole thing, but we'll see how that goes. But they competed, but they're still friendly. Look at him. And then the nice thing has been another student has come back for a sabbatical. I work with Professor Junho Cho from Post-Ex South Korea. He decided to come back and work with us some more. I liked it. Anyway, here's his group in South Korea. He just gave me a call the other day, and we want to work jointly on some 5G that is pretty interesting. And we had published a paper in the information theory transactions about how to grab any wasted capacity that's there when there's a system already operating in a certain frequency band. What can you do? There's information theory capacity there. Let's design a signal so the person using that band doesn't even know you're there. And the capacity of our signal will get anything that's left. There's nothing left to be had. We're studying cyclistationary random processes and certain properties of correlation in the frequency domain. We tried to get a patent on one particular idea of Doppler shifting and it was granted to Purdue University some time back. And then finally we had a big batch of students graduate not all that long ago. One of the fellows here is now a professor himself in Vietnam. Phuong in Vietnam. And guess who this is here on the right? Hung Yee Lo who is here in the room writing papers one after another right now with all his new creative ideas. It's been a great time working with the students through the year. One of the most positive aspects of being a faculty member it's just been great. It's nice to hear about their lives the 5 or 10, 15 years after they leave it's fun to see their successes and I assure you good people coming out of Purdue today as much as there were great people before I ever got here. The demos I'm going to do are in memory of two of my colleagues. 2016 I guess I'll call it early summer was a very difficult time for me and for our department generally. We lost Hanna's Thompson we lost these two great colleagues they did such wonderful demos we lost Ann we lost so many and in fact we lost Klein Gilhausen who started Qualcomm that very same era he passed away so it really sobered me a little bit but I want to appreciate these people they're very very great people and the demos are dedicated to them we're not going to give up in our research we think there might be something out there yet to be had so we keep thinking and thinking and thinking and so far we haven't gone the other way in our work I'd like to thank you all for coming I very much appreciate your valuable time I hope I didn't waste yours too badly today thank you