We presented a new approach is taken to study the
performance of linear multiuser receivers in power-controlled
networks. Based on a synchronous model with random signature
sequences, we showed that in a large system, the performance of
several important linear receivers does not depend on the specific
realization of the sequences, and moreover can be simply characterized
via two key notions: ** effective interference **:
a decomposition of the aggregate
interference at the output of the multiuser receiver into a sum of the
effects of individual interferers; ** effective bandwidth**:
a measure of the number of degrees of
freedom occupied by a user in a power-controlled cell, as a simple function
of the user's target signal-to-interference ratio requirement.
The effective bandwidth of a user depends on the specific multiuser
receiver used, and thus provides a simple basis for performance
comparison among different receivers. Moreover, it can be viewed as an
abstraction of the amount of resources consumed by a user and serves
as a bridge between the physical and networking layers.

D. Tse and S. Hanly, "Linear Multiuser Receivers: Effective Interference, Effective Bandwidth and User Capacity", IEEE Transactions on Information Theory, v.45, No. 2, Mar. 1999, pp. 641-657.

In subsequent
work, these notions are extended to more complex channel models with
user asynchronism, multipath fading with imperfect channel
measurements, and multi-antenna diversity. In
the latter case, a curious phenomenon of ``resource pooling'' of all
the antennas is observed. The theory is based on a set of random
matrix results proved using ** free probability ** theory.

Kiran and D. Tse, ``Effective Bandwidths and Effective Interference for Linear Multiuser Receivers in Asynchronous Systems'', IEEE Transactions on Information Theory, vol 46(4), July 2000, pp. 1426-1447.

J.S. Evans and D. Tse, "Large System Performance of Linear Multiuser Receivers in Multipath Fading Channels", IEEE Transactions on Information Theory, vol. 46(6), Sept 2000, pp. 2059-2078.

S. Hanly and D. Tse, "Resource Pooling and Effective Bandwidths in CDMA Systems with Multiuser Receivers and Spatial Diversity", IEEE Transactions on Information Theory, vol. 47(4), May 2001, pp. 1328-1351.

The curious connection between multiuser detection and free probability is explored in the short paper:

D. Tse, ``Multiuser Receivers, Random Matrices and Free Probability'' , Proc. of Allerton Conference, Monticello, IL, Sept 1999.

A parallel set of results for ** optimal ** sequences for multiuser
receivers are obtained. These results reveal
interesting deterministic **conservation laws** governing the
performance tradeoffs among different users when multiuser dtection is
used. These conservation laws provide
insights to explain the existence of effective bandwidths for
multiuser receivers.

P. Viswanath, V. Anantharam and D. Tse, "Optimal Sequences, Power Control and Capacity of Synchronous CDMA Systems with Linear MMSE Multiuser Receivers", IEEE Transactions on Information Theory, vol. 45(6), Sept., 1999, pp. 1968-1983.

This work is supported by the National Science Foundation under grant #NCR-9734090.