Tag Archives: information theory

From Professor Irving Kalet….

This is a post written by Professor Kalet:

Analog Modulation-Back to the Future?

Or was Armstrong’s Frequency Modulation the “Last Word” in Analog Modulation

In recent times there has been a renewed interest in Edwin Armstrong, his work, his career and his life. This “blog” is probably the best evidence of that renewed interest.

A few years ago I also became interested, or rather “re-interested” in Armstrong’s work on frequency modulation (FM).

Many years earlier when I was studying for my doctorate here at Columbia University, I had decided that I was going to discover a better analog modulation than FM. I was going to outdo Armstrong!

Luckily for me, my thesis advisor, the late Professor William R. Bennett, asked me a very simple question, “How do you know that there is a better analog modulation than FM?” And so he sent me back to the drawing board to find the bounds on analog modulation, based on information theory.

This I did, and so did someone else at MIT, named Tom Cruise, yes, Tom Cruise, but not that Tom Cruise!

Both of us came up [1, 2] with basically the same result. Our work was essentially an extension of an earlier paper by Goblick [3]. Our work (also to be found in Van Trees’ book [4]) showed, that at least theoretically there is a possibility of an analog modulation (or at least a transmission technique for analog sources), which may outperform FM. In fact, the actual results predicted by information theory can more or less be achieved by a digital communications scheme, which utilizes a good quantization scheme for the analog source, a good modulation scheme, e.g., QAM for transmitting the bits and a good code like a turbo-code, or an LDPC code, for improving error probability. However, these results are really based on converting the analog information source into bits and then using digital communications to transmit the bits.

What interested me years ago and what has re-kindled my interest now, is the old question as whether some truly analog phase (or frequency) modulation, or combined amplitude-phase analog modulation scheme, can be found which approaches the bounds predicted by information theory.

As far as I can recollect, the only real serious efforts, to find better analog,  (or at least different analog) modulations, since Armstrong’s monumental work in the mid 1930’s, was the work of Boardman and Van Trees, on Optimum Angle Modulation [5], in the late 1960’s, which involved the optimization of linear phase (or frequency) modulation with a bandwidth constraint. There was also some work done on the so-called “single-sideband FM” concept [6], also in the 1960’s. And again, during the 1960’s there was an attempt by Voelcker to look at the modulation process using a unified approach. He called this a “Unified Theory of Modulation” [7,8].   

However, as is well known, since the 1960’s the world has gone digital, even to the point of having only digital television broadcasting in the United States.

The reader might ask the following reasonable question, “Why look at analog modulation again after so many years?”

Well, the simple answer to that question could just be, “Why not?”

The fact that there might be a chance for an improved analog modulation is of itself (in my opinion!) an interesting question for any researcher in communications.

However, there may be other practical reasons as well. As mentioned earlier, it is more than forty years since there has been any serious research into analog modulation. During this period of time, there has been a phenomenal development in the implementation of communication systems. The fields of integrated circuits and circuit miniaturization have allowed the development of digital signal processing beyond belief. There have also been unbelievable advancements in analog processing and circuitry, allowing miniaturization of analog circuits. Furthermore, many of the sources of transmitted information are still analog in nature, e.g., voice and music.

If new analog modulation techniques were to be invented, it may now be possible to cheaply implement these ideas with the new technologies, developed in the past forty years.

Another interesting question might be, “How do we apply new concepts which have arisen in digital communications, such as multi-imput multiple output (MIMO) antenna arrays, to analog communications?”

I guess what I am asking the readers of this blog is whether any of you are still interested in analog modulation, or has analog modulation gone the way of the “horse and buggy”, and the “dial-up” telephone” ?

I would be interested in hearing any comments from anyone out there??

Irving Kalet

References:

  1. T. J. Cruise, Channel capacity for a RMS bandwidth constraint”, MIT, Research Laboratory of Electronics, Quarterly Progress Report, July 1968, pp. 201-205.
  2. I. Kalet, “Bounds on optimum analog modulation over gaussian channel with second-moment bandwidth constraints”, Proceedings IEEE International Conference on Information Theory, Ellenville, N.Y., January 1969.
  3. T. J. Goblick, Jr., “Theoretical limitations on the transmission of data from analog sources”, IEEE Transactions on Information Theory, Vol. 11, No. 4, October 1965, pp. 558-567.
  4. H. L. Van Trees, “Detection, Estimation and Modulation Theory-Nonlinear Modulation Theory, Part II”, J. Wiley and Sons, 1971, Chapter V.
  5. C. J. Boardman and H. L. Van Trees, “Optimum angle modulation”, IEEE Transactions on Comm. Tech., Vol. 13, December 1965, pp. 452-464.
  6. R. E. Kahn and J. B. Thomas, “Bandwidth properties and optimum demodulation of Single-Sideband FM”, IEEE Transactions on Communications Technology, Vol. 14, No.2, April 1966, pp. 113-117.
  7. H. B. Voelcker, “Toward a unified theory of modulation-Parts I and II”, Proceedings of the IEEE, Vol. 54,No. 3, March 1966, pp.340-353, 735-755.

Professor Kalet:

Irving Kalet, Eng.Sc.D., has been teaching and working in the area of digital communications in both Israel and the United States for over 25 years. He lives in Israel, and is currently a consultant both in Israel and at Lucent Technologies (formerly AT&T Bell Laboratories) in the United States. He has worked in the area of mobile wireless communications and digital transmission (HDSL and ADSL) over the twisted-pair cable at Bell Laboratories, and in the area of satellite communications at MIT Lincoln Laboratories. Dr. Kalet has published many papers on digital communications and is the author of the chapter on multitone modulation in the recently published book, Sublet and Wavelet Transforms—Design and Applications (Kluwer Academic Publishers). He is currently working on digital modulation techniques and multiple access techniques for both terrestrial and satellite mobile wireless communications systems. He received his Eng.Sc.D. from Columbia University.