Random Beamforming with Heterogeneous Users and Selective Feedback: Individual Sum Rate and Individual Scaling Laws

TL;DR

This paper analyzes the performance of random beamforming systems with heterogeneous users and selective feedback, deriving closed-form expressions for individual sum rates and examining the effects of feedback schemes on multiuser diversity and rate scaling.

Contribution

It introduces a unified framework for analyzing individual sum rates under various feedback schemes in heterogeneous user scenarios, including closed-form formulas and diversity analysis.

Findings

Closed-form individual sum rate under full feedback

Rate approximation with selective feedback in spatial and spectral dimensions

Selective feedback impacts multiuser diversity and rate scaling

Abstract

This paper investigates three open problems in random beamforming based communication systems: the scheduling policy with heterogeneous users, the closed form sum rate, and the randomness of multiuser diversity with selective feedback. By employing the cumulative distribution function based scheduling policy, we guarantee fairness among users as well as obtain multiuser diversity gain in the heterogeneous scenario. Under this scheduling framework, the individual sum rate, namely the average rate for a given user multiplied by the number of users, is of interest and analyzed under different feedback schemes. Firstly, under the full feedback scheme, we derive the closed form individual sum rate by employing a decomposition of the probability density function of the selected user's signal-to-interference-plus-noise ratio. This technique is employed to further obtain a closed form rate approximation with selective feedback in the spatial dimension. The analysis is also extended to random beamforming in a wideband OFDMA system with additional selective feedback in the spectral dimension wherein only the best beams for the best-L resource blocks are fed back. We utilize extreme value theory to examine the randomness of multiuser diversity incurred by selective feedback. Finally, by leveraging the tail equivalence method, the multiplicative effect of selective feedback and random observations is observed to establish the individual rate scaling.