Decentralized Beamforming for Weighted Sum Energy Efficiency Maximization in MIMO Systems

Joint Resource Allocation and Transceiver Design for Sum-Rate Maximization under Latency Constraints in Multicell MU-MIMO Systems

“…Centralized and distributed algorithms for sum-power minimization under minimum SINR constrains were also proposed in [19] and [18]. Other works, such as [20], [21], have focused on the sum-energy efficiency maximization problem, that consists in minimizing the energy consumption per transmitted bit. The weighted sum-rate maximization problem with QoS guarantees was considered in [22]- [24].…”

“…Thus, only local CSI is required to be available at the BSs and users. The proposed precoded pilot scheme is required for the update of the receive beamforming matrices from (10) at the user side and transmit beamforming matrices from (20) at the BSs, where both (10) and (20) require some knowledge about interfering CSI.…”

“…where Q 𝑏 𝑢 = 𝑈 𝑖=1 H H 𝑏 𝑢 ,𝑖,𝑛 W 𝑖,𝑛 𝜽 𝑖,𝑛 W H 𝑖,𝑛 H 𝑏 𝑢 ,𝑖,𝑛 and 𝜈 𝑏 𝑢 is the dual variable associated to the power budget constraints of (17). From (20) we can observe that {𝜽 𝑢,𝑛 } ∀(𝑢,𝑛) act as weights of user 𝑢 on sub-channel 𝑛. The value of 𝜈 𝑏 𝑢 ≥ 0 should be chosen to meet the complementary slackness condition of the power budget constraints.…”

“…The value of 𝜈 𝑏 𝑢 ≥ 0 should be chosen to meet the complementary slackness condition of the power budget constraints. Note that if the power constraint is not active when solving (20) for 𝜈 𝑏 𝑢 = 0, then the beamformers are optimal. Otherwise, the optimal value of 𝜈 𝑏 𝑢 can be obtained using one dimensional search techniques (e.g., bisection method) with respect to the power budget constraints [13].…”

“…Otherwise, the optimal value of 𝜈 𝑏 𝑢 can be obtained using one dimensional search techniques (e.g., bisection method) with respect to the power budget constraints [13]. The high complexity due to the matrix inversion in (20) can be reduced by using an eigenvalue decomposition of Q 𝑏 𝑢 + 𝜈 𝑏 𝑢 I, as shown in [13], or by solving the linear system (Q 𝑏 𝑢 + 𝜈 𝑏 𝑢 I)M 𝑢,𝑛 = H H 𝑏 𝑢 ,𝑢,𝑛 W 𝑢,𝑛 𝜽 𝑢,𝑛 , ∀(𝑢 ∈ U 𝑡 , 𝑛). Once the current MSE values, {E 𝑢,𝑛 } ∀(𝑢∈U 𝑡 ,𝑛) are computed, we update the variable r (𝑘+1) 𝑢,𝑠,𝑛 as:…”