Effective Interference and Effective Bandwidth of Multiuser Receivers

In the past decade, much work has been undertaken on the design and analysis of multiuser receivers for direct sequence CDMA systems. However, the network capacity gain that can obtained from these sophisticated receivers is still a subject of intense debate. One impediment to understanding is that the performance measures are often complicated functions of the signature sequences and received powers of the users, and they are difficult to be used for capacity analysis. Moreover, the emphasis is on evaluating worst-case performance given arbitrary received powers from interferers, which gives limited insight to power controlled systems.

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.