Energy Efficient Multi-User MISO Communication

• Energy efficient multi-user MISO communication is a paradigm that optimizes energy usage by jointly designing transceiver architectures, hybrid precoding, and resource allocation.
• Hybrid analog-digital precoding and robust power modeling techniques, including saturation power principles, yield up to 20–40% energy efficiency gains by balancing computation and RF power.
• Emerging methods such as IRS/RIS integration and online learning algorithms enhance scalability and robustness in multi-cell, interference-limited environments.

Energy efficient multi-user MISO (multiple-input single-output) communication refers to the design and operation of downlink (and, by extension, uplink) systems wherein a multi-antenna transmitter (base station) simultaneously serves multiple single-antenna receivers while maximizing the ratio of delivered bits to consumed Joules. Maximizing energy efficiency (EE) in such systems is a multi-dimensional problem involving transceiver architectures, signal processing, resource allocation under hardware constraints, and—especially in large-scale systems—the detailed modeling of computation, RF, and ancillary power consumption.

1. System Architectures and Power Consumption Modeling

Modern EE analysis in multi-user MISO encompasses the totality of BS power consumption, acknowledging computation, RF front-end, and fixed overheads. For a BS with $N_t$ antennas, $N_{\rm RF}$ RF chains ($N_{\rm RF}\ll N_t$), and $K$ users, hybrid precoding architectures are crucial: analog/RF ($\mathbf{W}_{\rm RF}$) and digital/baseband ($\mathbf{W}_{\rm BB}$) stages operate jointly (Ge et al., 2018). The total BS power model is

$$P_{\rm total} = P_{\rm comm} + P_{\rm comp} + P_{\rm fix},$$

where:

• $P_{\rm comm}$: transmit/PA power (including per-RF-chain consumption);
• $P_{\rm comp}$: computation (BB) power, inclusive of channel estimation, (de)coding, baseband precoding, phase-shifter network, and algorithmic overhead;
• $P_{\rm fix}$: site cooling, losses, etc.

Contemporary studies underscore a reversal of the "massive MIMO law": as $N_{\rm RF}$0 and $N_{\rm RF}$1 grow, $N_{\rm RF}$2 can dominate, causing $N_{\rm RF}$3 (EE) to decrease even as array gain increases—contradicting analyses based on communication power alone (Ge et al., 2018). This effect is critical in mmWave, small-cell, or large-scale deployments.

2. Energy Efficiency Metrics and Optimization Problems

EE is quantified as the achieved sum-rate normalized by total power consumed: $N_{\rm RF}$4 with $N_{\rm RF}$5,

$N_{\rm RF}$6

The canonical joint EE maximization,

$N_{\rm RF}$7

is subject to transmit power, per-antenna/RF-chain, and constant-modulus constraints (for analog phase-shifters).

In the regime of imperfect or limited CSI, robust EE maximization adopts either statistical error models (Gaussian estimation error) leading to QCQPs, or deterministic norm-bounded uncertainty, leading to SDPs with chance-constrained or worst-case SINR constraints (Vaezy et al., 2018).

3. Precoding and Resource Allocation Strategies

Hybrid Analog-Digital Precoding

For large antenna arrays, partially-connected hybrid precoding offers strong EE/cost tradeoffs. Algorithms such as PHONE achieve efficient decomposition of a fully-digital (upper-bound) precoder into hybrid analog/digital stages, using alternating minimization (SDR for digital, phase-matching for analog) (Ge et al., 2018).

Saturation Power Principles

Closed-form "saturation power" characterizes the point beyond which increasing transmit power reduces EE; below this point, EE and spectral efficiency objectives coincide. This fact enables near-optimal, low-complexity policies based on statistical channel knowledge and analytic MRT/ZF rates, eschewing per-fading realization optimizations (Jung et al., 2015).

Multi-Cell, Interference-Limited Systems

In spatially coupled multi-cell MISO, asymptotic random-matrix methods enable deterministic equivalents for SINR/EE, supporting beam and power allocation based solely on channel second-order statistics. These approaches yield beamformers requiring only sporadic updates as large-scale statistics evolve (Lee et al., 2015).

Symbol-Level Precoding (SLP)

SLP exploits symbol and channel knowledge to engineer inter-user interference as constructive, enabling CI-based power minimization. SLP under relaxed detection region constraints delivers transmit-power reductions and up to 20–40% EE gain compared to traditional ZF or MMSE methods (Alodeh et al., 2015Alodeh et al., 2015). Joint SLP and constellation rotation adds further dB-scale EE improvement, especially for spatially correlated channels (Alodeh et al., 2020).

Table: SLP Approaches and EE Impact

Approach	Power Saving vs. ZF/MMSE	EE Gain (%)
Strict-CI SLP (CIPM)	1–2 dB	20–40
Relaxed-CI SLP (CIPMR)	Additional 2 dB	Up to 20 more
SLP + Rotation (SLPRo)	Extra 2–6 dB	Marked improvement

4. Emerging Technologies: IRS/RIS and Intelligent Surfaces

Intelligent Reflecting/Surface (IRS/RIS)–aided multi-user MISO architectures utilize large, nearly passive, programmable scatterers (IRS) to co-shape the propagation environment. Joint optimization of AP beamforming and IRS reflection phases—via alternating convexification and inner approximation—enables reductions of AP transmit power by 5–10 dB and EE improvements by factors of 2–3× compared to AP antenna upgrades (Yu et al., 2020). The overall EE benefits from

• Linearly increasing EE with IRS element count (up to a threshold set by IRS circuit-power);
• High EE even with low-phase-resolution (1–2 bits) IRS elements (Huang et al., 2018);
• Superior performance under blockage or in environments where direct AP–UE links are weak (Yu et al., 2020).

Model-based energy-efficiency analyses include RIS controller overhead and practical discrete phase quantization. Channel estimation and pilot design overheads, as well as spectral efficiency loss due to RIS phase estimation, set practical EE limits (Wei et al., 2020Wei et al., 2020).

5. Robustness and Algorithmic Efficiency

Robust EE algorithms with respect to CSI errors rely on Dinkelbach-type fractional programming (outer loop; update EE parameter) and convex QCQP/SDP inner loops (for statistical and norm-bounded error models, respectively). S-Procedure and Schur complements facilitate the conversion of robust SINR constraints into tractable LMIs (Vaezy et al., 2018). Dinkelbach iterations typically converge super-linearly (≈5–10 outer iterations). In large-scale systems, strategies leveraging random-matrix theory and are parameterized by statistical knowledge reach near-optimal EE at orders-of-magnitude lower complexity than instantaneous CSI-based methods (Jung et al., 2015Lee et al., 2015).

Online learning algorithms guarantee sublinear regret for distributed, dynamic power and covariance adaptation in time-varying interference/CSI environments, providing substantial EE gains (up to 600% vs. uniform allocation) and proven resilience to channel uncertainty (Mertikopoulos et al., 2015).

6. Design Guidelines and Trade-offs

• Algorithmic/Hardware Integration: Joint (not sequential) optimization of digital and analog subsystems is mandatory; decoupled approaches can lose up to 76% EE (Ge et al., 2018).
• Array Size vs. EE: Blindly increasing $N_{\rm RF}$8 or $N_{\rm RF}$9 reduces EE once $N_{\rm RF}\ll N_t$0 dominates.
• RF Chains and Antenna Count: For high BB power regimes (mmWave, small-cell), optimal $N_{\rm RF}\ll N_t$1, $N_{\rm RF}\ll N_t$2 balance array gain and BB power, favoring hybrid and partially-connected architectures.
• Modulation/Precoding Design: SLP with relaxed or rotating detection regions enables practical trade-offs between power and symbol error; system-level EE is maximized by choosing relaxation parameters to balance rate, SER, and power.
• IRS/RIS Sizing: There exists a per-scenario optimal IRS element number $N_{\rm RF}\ll N_t$3 for maximal EE; exceeding this invites diminishing (or even negative) returns due to IRS circuit power (Huang et al., 2018Wei et al., 2020).
• Channel Estimation Overhead: Overhead-aware throughput and EE must capture pilot resource consumption; optimal pilot length balances estimation NMSE, effective data rate, and estimation-related power cost (Wei et al., 2020Wei et al., 2020).
• Implementation Feasibility: Polynomial-time (QCQP/SDP) or asymptotically analytic (RMT-based) algorithms are preferred in large-scale and rapidly-varying environments. Hardware-friendly precoding (constant-envelope, low-res DAC/PSK) can yield large EE improvements with modest SNR penalty (Noll et al., 2017).

7. Outlook and Open Directions

As MISO systems scale and integrate RIS, NOMA, or advanced hybrid architectures, energy efficiency optimization mandates holistic power modeling, robust and scalable algorithmic schemes, and practical attention to channel acquisition and hardware limitations. Further advances depend on:

• Improved low-overhead channel estimation for RIS-aided systems (Wei et al., 2020Wei et al., 2020);
• Integration of non-linear energy-harvesting models in wireless powered communication networks (WPCNs) with multi-user MISO (Shanin et al., 2022);
• Distributed/online, regret-minimizing policies that adapt to interference and hardware variability (Mertikopoulos et al., 2015);
• Modeling and exploitation of computation power trends in AI/ML-augmented physical layers.

The field remains driven by increasingly realistic, system-wide power models and by methodologies that trade analytic tractability for implementable, recyclable, and scalable designs that retain robustness and near-optimality across practical communication regimes.