Transmit power optimization for multi-user communication

Transmit power optimization under rate constraints reverses the perspective of multi-user capacity, and usually occurs in quality of service (QoS) problems in multi-user communication. This dissertation expands the scope of rate and power control to consider minimization of transmit power. This dissertation introduces a family of water-filling techniques that include power minimizing iterative water-filling and sub-band water-filling.; The research contributions are summarized as follows: First, this dissertation shows that transmit power minimization in the multiple-access channel can be formulated as a convex optimization problem. By the duality between the Gaussian multiple-access and broadcast channels, it is also shown that a transmit power minimization problem in the broadcast channel is easily transformed into an equivalent power minimization problem in the dual multiple-access channel. Second, Lagrangian multipliers are employed to devise an efficient iterative method as a solution to the transmit power optimization problem for multi-user orthogonal frequency division multiplexing (OFDM) systems. Although conventional algorithms for convex programming problems can solve the transmit power minimization numerically, they often require intensive computational complexity and do not give insight on how the power allocation is performed for the multi-user channel. However, the iterative method proposed in this thesis shows how one user's power allocation affects the other users' power allocations to maintain the specific data rates required by the users. The iterative method can be further extended to multi-user multi-input multi-output (MIMO) systems where a non-degraded Gaussian vector channel is assumed. Third, this dissertation proposes a sub-optimal rate and power control for the case of imperfect channel information at the transmitter. When the feedback channel information is inaccurate because of the time-variation of the channel, the rate and power control often employs stochastic optimization that is numerically complex. An efficient rate-and-power control algorithm is proposed with sub-band water-filling. By grouping a few subchannels into a sub-band, sub-band water-filling mitigates the effect of channel fading. It is shown that sub-band water-filling is still applicable to multi-user cases with imperfect channel information.