In Orthogonal Frequency Division Multiple Access (OFDMA) systems, all users transmit and receive data at the same time. Each subchannel is allocated to at most one user, although more recent standards have allowed fractional reuse of spectrum at the cell edge. For the downlink direction, i.e. from basestation to mobile user, the mobile user could be allocated subchannels from across the downlink transmission band. In the uplink direction, a mobile user could receive a cluster of adjacent subchannels. A significant research problem has been, and continues to be, the optimal allocation of power and subchannels (and hence rates) to mobile users, which is known as the multiuser resource allocation problem.

Multiuser resource allocation for downlink OFDMA systems remains an import ant research problem. First, a fundamental result in multiuser downlink OFDMA resource allocation was independently discovered by Prof. John Cioffi's group, Prof. Georgios Giannakis' group and Prof. Brian Evans' group. That result is that there exist optimal solutions to the downlink multiuser OFDMA resource allocation problem that have complexity on the order of the number of users times the number of subchannels. That is, heuristics no longer need to be used because the optimal solution is obtained by an algorithm that is faster than published "near-optimal" heuristics.

Here are the references to this fundamental result:

[1] K. Seong, M. Mohseni, and J. Cioffi, "Optimal resource allocation
for OFDMA downlink systems," *Proc. IEEE International Symposium
on Information Theory*, Seattle, WA, July 2006, pp. 1394-1398.

[2] Y. Yu, X. Wang, and G. B. Giannakis, "Channel-Adaptive Optimal
OFDMA Scheduling", *Proc. Conf. on Info. Sciences and Systems*,
March 2007, pp. 536-541.

[3] I. C. Wong and B. L. Evans, "Optimal Downlink OFDMA Resource
Allocation with Linear Complexity to Maximize Ergodic Rates",
*IEEE Transactions on Wireless Communications*,
vol. 7, no. 3, Mar. 2008, pp. 962-971.

The results in [3] were first published in the IEEE International Conference on Acoustics, Speech and Signal Processing in April 2007. The follow-up journal paper to [3] is the following:

[4] I. C. Wong and B. L. Evans, "Optimal Resource Allocation in the OFDMA
Downlink with Imperfect Channel Knowledge", *IEEE Transactions on
Communications*, vol. 57, no. 1, Jan. 2009, pp. 232-241.

In particular, Wong and Evans [3][4] derive a unified algorithmic framework that uses dual optimization techniques and present optimal downlink resource allocation algorithms that

- have complexity on the order of the number of subcarriers times the num ber of users
- are available for allocating continuous or discrete rates to users
- apply to perfect and partial knowledge of the channel
- are amenable to implementation in fixed-point arithmetic and data types

Second, solving the multiuser resource allocation problem is based on a number of assumptions. Here are some typical assumptions:

- Single cell served by one basestation. Interference from neighboring cells is not included or assumed to be lumped into the additive white Gaussian noise term.
- Perfect or partial knowledge of channel state information
- Perfect knowledge or blind estimation of channel state distribution information
- Perfect sample and symbol synchronization
- Sufficient cyclic prefix length
- Fading distribution is stationary
- Fading for each user is independent

[9] K. Gulati, A. Chopra, B. L. Evans, and K. R. Tinsley,
"Statistical Modeling of Co-Channel Interference",
*Proc. IEEE Int. Global Communications Conf.*,
Nov. 30-Dec. 4, 2009, Honolulu, Hawaii, submitted.

It is important not to assume equal power allocation. Under high SNR, there is little benefit in optimal power allocation as equal power allocation is close to optimal. However, by the same logic, optimum subcarrier allocation also loses its importance under high SNR condition. In general, both subcarrier and power allocation need to be performed in an optimal manner for practical systems, in which not all users have high SNR simultaneously.

Third, there have been many attempts to reduce the amount of feedback overhead from the mobile users to the basestation for downlink OFDMA systems for the dual purposes of fairness and downlink throughput. Here are a few papers on reducing feedback:

[5] X. Qin and R. Berry, "Opportunistic splitting algorithms for
wireless networks", *Proc. IEEE INFOCOM*,
vol. 3, pp. 1662-1672, Mar. 2004.

[6] S. Patil and G. de Veciana, "Feedback and opportunistic scheduling
in wireless networks", *IEEE Trans. Wireless Communications*,
vol. 6, no. 12, pp. 4227-4238, Dec. 2007.

[7] T. Tang, R. W. Heath, Jr., S. Cho, and S. Yun, "Opportunistic
Feedback in Clustered OFDM Systems", *Proc. International Symposium
on Wireless Personal Multimedia Communications*,
San Diego, CA, Sep. 2006.

[8] R. Agarwal, V. Majjigi, Z. Han, R. Vannithamby, and J. Cioffi,
"Low Complexity Resource Allocation with Opportunistic Feedback
over Downlink OFDMA Networks", *IEEE JSAC Special Issue on
Limited Feedback*, Vol. 26, No. 8, Oct. 2008, pp. 1462-1472

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