[Paper Review] Energy Efficiency Optimization for MIMO Broadcast Channels

Jie Xu, Ling Qiu|arXiv (Cornell University)|Feb 16, 2012

Advanced MIMO Systems Optimization18 references4 citations

TL;DR

This paper proposes a joint transmit covariance optimization and active transmit antenna selection (ATAS) framework to maximize energy efficiency (EE) in MIMO broadcast channels under a practical power model that accounts for circuit and RF chain power. Using a globally optimal iterative water-filling algorithm for EE maximization under fixed antenna sets and low-complexity norm-based or exhaustive ATAS, the method achieves higher EE than conventional sum-rate-optimized schemes, with optimal EE achieved at M=3 or M=4 antennas for K=2 users under realistic power constraints.

ABSTRACT

Characterizing the fundamental energy efficiency (EE) limits of MIMO broadcast channels (BC) is significant for the development of green wireless communications. We address the EE optimization problem for MIMO-BC in this paper and consider a practical power model, i.e., taking into account a transmit independent power which is related to the number of active transmit antennas. Under this setup, we propose a new optimization approach, in which the transmit covariance is optimized under fixed active transmit antenna sets, and then active transmit antenna selection (ATAS) is utilized. During the transmit covariance optimization, we propose a globally optimal energy efficient iterative water-filling scheme through solving a series of concave fractional programs based on the block-coordinate ascent algorithm. After that, ATAS is employed to determine the active transmit antenna set. Since activating more transmit antennas can achieve higher sum-rate but at the cost of larger transmit independent power consumption, there exists a tradeoff between the sum-rate gain and the power consumption. Here ATAS can exploit the best tradeoff and thus further improve the EE. Optimal exhaustive search and low-complexity norm based ATAS schemes are developed. Through simulations, we discuss the effect of different parameters on the EE of the MIMO-BC.

Motivation & Objective

• To address the gap in energy efficiency (EE) optimization for MIMO broadcast channels (BC) under realistic power models that include transmit-independent power from active RF chains.
• To jointly optimize transmit covariance and active transmit antenna set (ATAS) to maximize EE, recognizing the trade-off between sum-rate gain and increased circuit power from more active antennas.
• To develop a globally optimal iterative water-filling algorithm for EE maximization under fixed active antenna sets using block-coordinate ascent.
• To design low-complexity ATAS schemes—exhaustive search and norm-based selection—to further improve EE after covariance optimization.

Proposed method

• Transforms the EE maximization problem under fixed active antenna sets into a concave fractional program using uplink-downlink duality.
• Applies a block-coordinate ascent algorithm to iteratively solve the fractional program, leading to a globally optimal energy-efficient iterative water-filling scheme.
• Derives a closed-form solution for the optimal power allocation per user per stream using the Karush-Kuhn-Tucker (KKT) conditions and the Dinkelbach-type algorithm.
• Introduces two ATAS schemes: exhaustive search for optimal selection and a low-complexity norm-based method using channel vector norms to select the best subset of active antennas.
• Models total power as sum of PA power (proportional to sum transmit power), RF chain power (constant per active antenna), and fixed baseband/cooling power.
• Validates the algorithm via simulations across varying antenna numbers, user counts, and sum-rate constraints, comparing EE and sum-rate performance.

Experimental results

Research questions

• RQ1 What is the optimal transmit covariance for maximizing EE in MIMO-BC under a practical power model with antenna-dependent circuit power?
• RQ2 How does active transmit antenna selection (ATAS) improve EE when the number of active antennas is less than the total number available?
• RQ3 What is the trade-off between sum-rate gain and increased circuit power when activating more transmit antennas in a MIMO-BC?
• RQ4 How do different ATAS schemes (exhaustive vs. norm-based) compare in performance and complexity for EE optimization?
• RQ5 What scaling laws govern multiuser diversity gain in EE for MIMO-BC under the proposed framework?

Key findings

• The optimal EE is achieved at M=3 or M=4 active transmit antennas for K=2 users and N=2 receive antennas, not at the maximum number of antennas, due to the trade-off between sum-rate gain and circuit power.
• When the sum-rate constraint is zero, EE without ATAS degrades significantly for M≥4 due to increasing dynamic power, while EE with ATAS remains optimal at M=3 or M=4.
• For a sum-rate constraint of 35 bps/Hz, EE with norm-based ATAS increases monotonically for M>5, as more antennas provide better channel diversity without violating the rate constraint.
• The norm-based ATAS scheme achieves near-optimal EE performance with significantly lower complexity than exhaustive search, especially in high-user scenarios.
• The multiuser diversity gain scales as M log log(NK) / (M_a P_dyn + P_sta), and for large user numbers, M_a = M (all antennas active) is optimal, unlike in low-user regimes.
• Simulations confirm that the proposed energy-efficient iterative water-filling converges and outperforms conventional sum-rate-optimized schemes in terms of EE, particularly under realistic power models.