The first time I started thinking about wireless networks was around 1997. It was an emerging hot technology, as it still is. I wanted to see what kinds of problems were involved and what I could say about them.

The excitement of wireless, obviously, is that you can dispense with all these wires. You don’t need them to communicate. If you have a laptop and some kind of wireless modem, you can open up your laptop and spontaneously, at any given time, form a network with maybe 1,000 people on your campus or 100 people in your office building. This is what’s called an ad hoc wireless network. There’s no prior infrastructure. What makes them interesting is that they need to be very adaptive. For instance, in the morning there may only be 50 people in this building; in the afternoon, 100. So the number of nodes may change. The position of the nodes changes. But the network itself has to keep functioning.

“A wireless medium is more like a cocktail party than a telephone call.”

It’s a very volatile situation yet with enormous potential for all kinds of applications. Wouldn’t it be great, for instance, if we could construct a huge wireless network that spans thousands or hundreds of thousands of nodes, if we could surround ourselves with communication and intelligence everywhere? That excited me, and I started wondering whether this is possible. Are there limits? Can the whole world become wireless or are there some fundamental constraints? Just like the laws of thermodynamics which tell you that perpetual motion machines are impossible, are there some fundamental limits to wireless networks, or is it open-ended?

Piyush and I actually showed that there are indeed some fundamental limits. In effect the world cannot become wireless. Basically wireless networks can only provide the equivalent of nearest-neighbor communication, but not long-distance communication unless you’re willing to sacrifice throughput.

When you connect a modem, you are interested in the data rate. Maybe it’s 19.2 kilobits per second or close to one megabit per second. That’s called throughput. It’s the rate at which you can pump data into or out of network—the rate of communication. We showed there are some limits to communication that can be supported by wireless networks.

The first point to understand is that a wireless medium is different from a wired medium. A wireless medium is more like a cocktail party than a telephone call. At a cocktail party, if you’re listening to somebody nearby who is talking to you, then you don’t want somebody else talking in your other ear. You don’t want two people talking in your vicinity. You can’t make out anything. Roughly the same thing happens in the wireless world. It’s a shared medium. When I’m broadcasting a data packet to you, you don’t want somebody else doing another broadcast in your neighborhood.

This sharing problem puts constraints on what wireless networks can do. So that’s how you can think about it. You ask the question, "If I have a cocktail party, with everybody chatting away, what’s the maximum bit of information that can flow across the room?" That’s the kind of question we asked for wireless networks.

Almost 60 years ago Claude Shannon studied the limits to communication of a single link, like a wire. Say one person talking to another over a noisy channel. Shannon studied the issue of how much information could be pumped from one to the other. This led to the field of what is now called information theory. Ever since Shannon’s work, there’s been a lot of interest in trying to generalize information theory from two users to multiple users. What happened is that this theory had more or less been stuck because even some small-scale problems had defied solution for several decades. For example, even fundamental issues related to how much information can be communicated between two nodes when there is a helper relay node are unknown. People worked on it for decades. It’s still a wide-open problem.

Our contribution was to say, let’s not look at small systems with three or four modes, but really huge systems. What can we say about those? Can we say something about scaling behavior? And that’s where we were able to provide answers. A good analogy is in thermodynamics. Instead of trying to study the behavior of just three or four molecules and how they move around, you study the behavior of billions and trillions of molecules. Then you have aggregate variables like temperature and pressure that you can describe. Similarly, we want to see what you can say about wireless networks in the aggregate.

Well, this attracted a lot of attention for several reasons. One is that people in the field of wireless networking were struggling to find a theoretical framework in which to understand wireless networks. Ours apparently provided the kind of theoretical statement about what you could do that these people were looking for. Second, we seemed to ask the right questions; that is, what happens when things get large? And we posed questions that could be answered and were still extremely useful. Third, it was not just something superficial in terms of theoretical techniques, and the theorists liked it because of that.

Fourth, it spoke to the network designers. It said if you want to do back-of-the-envelope calculations about networks, here’s a way to think about it. And, fifth, because it showed that there were limits to growth, it led to a reevaluation of what could be done with wireless networks, particularly for those people dreaming big dreams—at the Department of Defense, for instance. All in all, it satisfied a kind of hunger for a theoretical framework that would answer useful questions.

Actually, when we wrote the paper, we were trying to prove an even deeper statement, and we couldn’t do it. So we were a little bit disappointed that we couldn’t answer these deeper questions. On the other hand, I always felt it was a good solid effort. But, you know, just because a paper is a good solid paper doesn’t mean that it will get attention. What surprised me here was the enormous attention received; the enormous acceptance and influence it’s had. I always felt that it was a good piece of work. I just didn’t know whether that would be recognized.

My students and I have been exploring several dimensions of wireless networks. We have been exploring how to actually design protocols, which are essentially operating procedures for wireless networks. We’ve tried to come out with some new designs with some new ideas. We’ve also done large-scale testing in our office buildings of 20-, 30- and 40-node wireless networks, which at the time might have been some of the larger networks that people were testing.

On the theoretical side, we went even more deeply into Shannon’s information theory and subsequently wrote another paper with another collaborator, Liang-Liang Xie, which I thought was equally fundamental and that has also apparently attracted a lot of attention in the information theory world. The first piece of work with Piyush attracted a lot of attention among practitioners, designers, and also theorists. This second article with Liang-Liang is for aficionados, and it’s very theoretical. The other thing we’re doing is something very exciting: my now ex-students Scott Graham, Girish Balinga, and Kun Huang built a laboratory where we’re not look at just communication but at what we think is the next phase of the information technology revolution.

The idea is this: over the past 20 years there’s been a convergence of communication and computation. Think about it this way: in the old days you used your telephone for communication and your calculator for computation, but you didn’t mix them. Now what’s happened is that your calculator and your telephone have become merged into your networked computer. And, in fact, your computer is probably used more for communication and browsing than for calculation. So the internet has led to this convergence of communication and calculation.

But if that revolution stops right there, it achieves only some passive functionality. In other words, we can read web pages and e-mails but it doesn’t allow us to alter physical reality. It doesn’t change the temperature in a room, the speed of a car. It doesn’t do better air traffic control or building management or run a power grid. It doesn’t change the physical universe. It’s just an information exchange medium.

So the next step is for this internet to start interacting with the physical environment. To automate things like traffic lights, for instance, and building control and so on. When you start interacting, sensing the environment and interacting on it, that’s called control. So I foresee a convergence of control with communication and computation. And that leads to an active information technology revolution. So we’ve built a laboratory, done a lot of software development, where we’re looking at creating a theory for a new third generation of control systems.

What we’d like to create, and it may be feasible, is a fundamental framework for understanding how to build systems that can compute, communicate and control. I will give you one example. A modern automobile contains about 50 microprocessors. It turns out that in the old days, the core competence of automobile companies was the drive train, the transmission, the engine, the tires, etc. Now it’s the I-pod in the car; it’s your trip computer, your anti-lock braking, etc. That’s all information technology. But even with 50 computers in your car, people actually don’t understand how to interconnect them to make them work extremely reliably and efficiently.

This revolution has come on really fast without a matching development of the fundamental theory. And it’s not just about cars. People say that the Boeing 777 is the most computerized plane ever. Xerox has built printers with about 100 microprocessors. It turns out that 98% of all computers are what’s called embedded computers. They’re embedded in the real world, and that percentage is increasing—it’s going from 98 to 99 and so on. And these gadgets are not just passive. At the simplest level the embedded processor in your toaster may control when the toast pops up. What I would like to do is create a framework of design and understanding of such networks, such embedded control systems; something that would allow mass production of control systems, easy design of these networks, and massive proliferation. That’s my current goal.

P.R. Kumar
University of Illinois
Urbana-Champaign, IL, USA