Orthogonal Frequency Division Multiplexing

This work was supported by the National Science Foundation under CAREER Award NCR-9875482.

Orthogonal frequency division multiplexing (OFDM) systems are now widely employed in a number of wireless applications. In the late 1990's, when OFDM was being considered for use, it was dogged with implementation questions, particularly with regards to its high peak-to-average power ratio (PAPR). Thus, we set off to characterize and address this problem. While seeking to address such, we designed a coded modulation scheme that provided an attractive performance versus complexity benefit [Goeckel/Ananthaswamy, ICC 1999, IEEE T-COM 2002] (albeit only small gains in the PAPR); in fact, this was an independent alternate and nearly simultaneous derivation of the "complex field coding" approach widely championed by Giannakis.

Next, we considered how to rigorously characterize the PAPR of an OFDM signal. We observed a number of groups employing a Gaussian approximation for the envelope, but we noted that, even asymptotically in the number of subcarriers, the convergence of the OFDM signal to a Gaussian random process had not been established. We established such a convergence, which in turn motivated us to employ powerful tools from extrema value theory to characterize the envelope of the OFDM signal [Wei/Goeckel/Kelly, ICC 2002, IEEE Info Theory revision submitted].

  • D. L. Goeckel, "Coded Modulation with Non-Standard Signal Sets for Wireless OFDM Systems," (PDF file) Proceedings of the 1999 IEEE International Conference on Communications (ICC), pp. 791-795, May 1999.

  • D. L. Goeckel and G. Ananthaswamy, "On the Design of Multi-Dimensional Signal Sets for OFDM," (PDF file) IEEE Transactions on Communications, Vol. 50: pp. 442-452, March 2002.

  • S. Wei, D. Goeckel, and P. Kelly, "A Modern Extreme Value Theory Approach to Calculating the Distribution of the Peak-to-Average Power Ratio in OFDM Systems," (PDF file) Proceedings of the IEEE International Conference on Communications (ICC), , May 2002.

  • S. Wei, D. L. Goeckel, and P. A. Kelly, "The Complex Envelope of a Bandlimited OFDM Signal Converges Weakly to a Gaussian Random Process," (PDF file) accepted pending revision, revision submitted to the IEEE Transactions on Information Theory, , March 2006.