TY - GEN

T1 - On the fairest corner point of the MIMO-BC capacity region

AU - Maddah-Ali, Mohammad A.

AU - Mobasher, Amin

AU - Khandani, Amir K.

PY - 2005

Y1 - 2005

N2 - A number of recent works have addressed the problem of characterizing the sum-capacity of the multiple-input multiple-output broadcast channels (MIMOBC). However, the issue of the fairness remains an open problem. This article aims at finding a point on the sum-capacity hyperplane which satisfies a notion of fairness among active users. To facilitate the derivation of the results, we focus on a subset of capacity region which includes the corner points and their convex hull. It is shown that this region is a Polymatroid. The properties of polymatroids are exploited to locate a rate-vector on the sum-capacity hyperplane which is optimally fair. This means the minimum rate among all users is maximized (max-min rate). In the case that more than one user attain the max-min value, the algorithm recursively maximizes the minimum rate among the rest of the users. It is shown that the problem of deriving the time-sharing coefficients to attain this point can be decomposed to some lower-dimensional problems. In some cases, the complexity of computing and implementing an appropriate time-sharing strategy is not feasible. This motivates us to compute the corner point for which the minimum rate of the active users is maximized (max-min corner point). A simple greedy algorithm is introduced to find the max-min corner point.

AB - A number of recent works have addressed the problem of characterizing the sum-capacity of the multiple-input multiple-output broadcast channels (MIMOBC). However, the issue of the fairness remains an open problem. This article aims at finding a point on the sum-capacity hyperplane which satisfies a notion of fairness among active users. To facilitate the derivation of the results, we focus on a subset of capacity region which includes the corner points and their convex hull. It is shown that this region is a Polymatroid. The properties of polymatroids are exploited to locate a rate-vector on the sum-capacity hyperplane which is optimally fair. This means the minimum rate among all users is maximized (max-min rate). In the case that more than one user attain the max-min value, the algorithm recursively maximizes the minimum rate among the rest of the users. It is shown that the problem of deriving the time-sharing coefficients to attain this point can be decomposed to some lower-dimensional problems. In some cases, the complexity of computing and implementing an appropriate time-sharing strategy is not feasible. This motivates us to compute the corner point for which the minimum rate of the active users is maximized (max-min corner point). A simple greedy algorithm is introduced to find the max-min corner point.

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M3 - Conference contribution

AN - SCOPUS:84961933312

T3 - 43rd Annual Allerton Conference on Communication, Control and Computing 2005

SP - 327

EP - 336

BT - 43rd Annual Allerton Conference on Communication, Control and Computing 2005

PB - University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering

T2 - 43rd Annual Allerton Conference on Communication, Control and Computing 2005

Y2 - 28 September 2005 through 30 September 2005

ER -