As mentioned earlier, one of the main reasons OFDM has been promoted for high data rate communication systems is that it has the ability to work in highly dispersive channels. The time dispersion will cause the channel to be frequency selective. However, by splitting the total transmission bandwidth to narrower channels, it is ensured that within each subchannel the channel frequency response is flat. Therefore, if the receiver is able to estimate the channel response over each carrier, the effect of channel dispersion (frequency selectivity) can be removed easily.

If the channel is assumed to be varying slowly in time (which is a valid assumption for low mobility and fixed wireless applications), the received signal at each carrier can be represented as:

where:

H(k) = the complex channel frequency response (which is assumed to be constant within a subframe).

Note that the response is carrier dependent. However, the variation across the carriers is smooth (i.e., the channel responses in closely spaced carriers are not independent). The memory across the carriers can be used to develop improved channel-estimation algorithms.

In this study, all the interference sources (including co-channel, adjacent channel, inter-carrier interferences, etc.) are folded into the additive white Gaussian noise (AWGN) term to simplify receiver design and analysis. In future studies, the authors intend to treat these interference sources differently so that we can exploit the color and structure of the interferer to design better transceiver algorithms. When all the additive interfering sources are folded into AWGN term, the received signal can be represented as:

where:

Z_m(k) = the AWGN term.

The transmitted signal, that goes through the I/Q vector modulator, experiences several levels of signal distortion due to imperfection in the modulator. These distortions can greatly affect the performance of the received signal and the overall system performance. The major I/Q impairments can be classified as I/Q offset, I/Q gain imbalance, and I/Q quadrature-error. Note that the I/Q impairments in the received signal will have quite different impact on OFDM based systems compared to the conventional single-carrier systems.

I/Q offset, also called I/Q origin offset-or carrier leakage, indicates the magnitude of the carrier feedthrough. I/Q Offset can be observed as an offset in the constellation. Gain mismatch or gain imbalance will result in the amplitude of one channel being smaller that the other. By comparing the gain of the I signal with the gain of the Q signal, 20log(I_scale/Q_scale), the I/Q gain imbalance can be obtained.

Next month, this discussion on developing a receiver for testing WiMAX will continue with an approach for modeling baseband I/Q origin offset (Fig. 7) and I/Q gain imbalance (Fig. 8) as part of a time-domain signal.

Editor's Note: This is the first installment in a three-part article. Next month, the authors will examine the structure of a proposed receiver for testing WiMAX products, along with algorithms necessary for performing packet detection and symbol estimation.

ACKNOWLEDGMENT

The authors would like to thank Dr. Larry Dunleavy for his comments and for the review of this article prior to publication.

REFERENCES

1. A.R.S. Bahai, B.R. Saltzberg, and M. Ergen, Multi-Carrier Digital Communication: Theory and Applications of OFDM, Kluwer Academic/Plenum Publishers, New York, 1999.
2. R. Prasad and R.V. Nee, OFDM for Wireless Multimedia Communications, Artech House, Norwood, MA, 2000.
3. M. Engels, Wireless OFDM Systems: How to Make Them Work, Kluwer Academic Publishers, New York, 2002.
4. J. Heiskala and J. Terry, OFDM Wireless LANs: A Theoretical and Practical Guide, Sams Publishing, Indianapolis, 2002.
5. H. Beigi, S. Maes, and J. Sorenson, "The cyclic prefix of OFDM/DMT—An Analysis," in International Zurich Seminar on Broadband Communications Access, Transmission, Networking, Zurich, Switzerland, 2002, pp. 1-3.
6. IEEE Standard for Local and Metropolitan Area Networks, Part 16: Air Interface for Fixed Broadband Wireless Access Systems, Standard IEEE 802.16-2004, The Institute of Electrical and Electronics Engineers, New York, 2004.
7. IEEE 802.16e, "Mobile WirelessMAN," http://www.eee802.org/16/tge/index.html.
8. F. Tufvesson, "Design of wireless communications systems—issues on synchronization, channel estimation, and multicarrier systems," Ph.D. dissertation, Lund University, Lund, Sweden, 2000.
9. A.G. Armada, "Understanding the effects of phase noise in orthogonal frequency division multiplexing (OFDM)," IEEE Transactions on Broadcasting, Vol. 47, No. 2, June 2002, pp. 153-159.
10. K. Sathananthan and C. Tellambura, "Performance analysis of an OFDM system with carrier frequency offset and phase noise," in Proceedings of the IEEE Vehicular Technology Conference, Vol. 4, Atlantic City, NJ, October 2001, pp. 2329-2332.
11. S. Muller and J. Huber, "A comparison of peak power reduction schemes for OFDM," in Proceedings of IEEE Globecom Conference, Vol. 1, Phoenix, AZ, 1997, pp. 1-5.
12. H. Ochiai and H Imai, "On the distribution of the peak-toaverage power ratio in OFDM signals," IEEE Transactions on Communications, Vol. 49, No. 2, February 2001.
13. P.H. Moose, "A technique for orthogonal frequency division multiplexing frequency offset correction," IEEE Transactions on Communications, Vol. 42, No. 10, October 1994, pp. 2908-2914.
14. P. Panagiotou, A. Anastasopoulos, and A. Polydoros, "Likelihood ratio tests for modulation classification," in Proceedings of IEEE Military Communications (MILCOM) Conference, Vol. 2, Los Angeles, CA, 2000, pp. 670-674.
15. B.G. Mobasseri, "Constellation shape as a robust signature for digital modulation recognition," in Proceedings of IEEE Military Communications (MILCOM) Conference, Vol. 1, Atlantic City, NJ, 1999, pp. 442-446.
16. T. Keller and L. Hanzo, "Blind detection assisted sub-band adaptive "Turbo-coded OFDM schemes," in Proceedings of IEEE Vehicular Technology Conference (VTC), Vol. 1, Houston, TX, 1999, pp. 489-493.