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Energy Efficient Multi-User MISO Communication using Low Resolution Large Intelligent Surfaces

Chongwen Huang, George C. Alexandropoulos, Alessio Zappone, Merouane Debbah, Chau Yuen

arXiv:1809.05397v1cs.IT

TL;DR

The paper asks whether low-resolution, nearly passive LIS elements can support energy-efficient multi-user MISO communication. It jointly optimizes user transmit powers and LIS phases for EE under the system model, and reports that even 1-bit LIS elements can substantially outperform conventional relay-assisted communication in EE.

  • Problem

    Rising wireless-network energy demands motivate evaluating whether low-resolution LIS hardware can provide energy-efficient multi-user MISO communication.

  • Method

    The paper jointly designs user transmit powers and LIS phase values to maximize EE, using alternating optimization for the discrete LIS design.

  • Results

    Up to 45% higher EE than relay-assisted communication is achieved by the low-resolution LIS cases for P > 15dBm.

  • Takeaways & Limitations

    Even 1-bit phase-resolution LIS elements can increase system EE by more than 40% compared with conventional amplify-and-forward relaying systems.

Abstract

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We consider a multi-user Multiple-Input Single-Output (MISO) communication system comprising of a multi-antenna base station communicating in the downlink simultaneously with multiple single-antenna mobile users. This communication is assumed to be assisted by a Large Intelligent Surface (LIS) that consists of many nearly passive antenna elements, whose parameters can be tuned according to desired objectives. The latest design advances on these surfaces suggest cheap elements effectively acting as low resolution (even $1$-bit resolution) phase shifters, whose joint configuration affects the electromagnetic behavior of the wireless propagation channel. In this paper, we investigate the suitability of LIS for green communications in terms of Energy Efficiency (EE), which is expressed as the number of bits per Joule. In particular, for the considered multi-user MISO system, we design the transmit powers per user and the values for the surface elements that jointly maximize the system's EE performance. Our representative simulation results show that LIS-assisted communication, even with nearly passive $1$-bit resolution antenna elements, provides significant EE gains compared to conventional relay-assisted communication.

I. INTRODUCTION

The paper examines whether low-resolution LIS elements can improve energy efficiency in multi-user MISO networks, motivated by rising wireless-network energy demands. It jointly optimizes user transmit powers and LIS phases, finding substantial EE gains even with 1-bit elements.

  • Motivation: Rising 5G and beyond data-rate demands have heightened concerns about the energy footprint of dense multi-antenna wireless networks.
  • LIS technology: LIS are structures with many small, nearly passive reflecting elements whose parameters can reconfigure wireless propagation.
  • Research gap: Prior theoretical LIS studies predominantly assumed infinite phase resolution, leaving low-resolution element designs less examined.
  • Contribution: The paper jointly designs user transmit powers and LIS phase values to maximize energy efficiency, measured for the LIS-assisted system.
  • System setting: The considered system combines an M-antenna base station, K single-antenna users, and a facade-mounted LIS providing direct and reconfigurable reflected paths.
  • Contribution: The proposed study presents an algorithmic EE-maximization approach for the considered LIS-assisted multi-user MISO system.

A. Signal Model

The signal model describes a base station serving multiple single-antenna users through direct and LIS-reflected channels. Reconfigurable LIS phases, precoded transmit signals, and additive Gaussian noise determine each user's received signal and resulting SINR and sum rate.

  • System model: The system uses an M-antenna base station to simultaneously transmit to K single-antenna users with assistance from N ≥ K nearly passive LIS elements.
  • Channel model: Each user's propagation includes a direct base-station channel and a channel passing through the LIS phase-shifting matrix.
  • Signal model: The transmitted signal contains individually precoded user signals weighted by their transmit powers, while receiver noise is modeled as zero-mean complex AWGN.
  • LIS configuration: The LIS phase matrix is diagonal, with one effective phase-shifting value assigned to each of its N elements.
  • Phase resolution: Finite-resolution LIS elements select phase values from a set containing 2^b options, where b is the phase resolution in bits.
  • Performance measures: The received-signal model yields each user's SINR and the achievable downlink sum rate.

B. Total Power Consumption Model

The power model combines transmit-amplifier power, circuit power, and LIS-element power. LIS consumption scales with the number of elements and their phase resolution, linking hardware configuration directly to total operating power.

  • Link power: The consumed power of user link k includes amplifier-scaled transmit power, circuit power, and LIS power.
  • Circuit components: The amplifier factor is μ = ν^-1, where ν is amplifier efficiency, while Pc represents power dissipated by other transmitter and receiver circuits.
  • Assumptions: The model assumes linear amplifier operation and circuit power independent of communication rate.
  • LIS hardware cost: Measured per-element powers are 15, 45, 60, and 78mW for 3-, 4-, 5-, and 6-bit phase shifting, respectively.
  • Total power: LIS power is PLIS = NPn(b), so total system power includes user transmit terms, K circuit-power terms, and N phase-shifter terms.

III. DESIGN PROBLEM FORMULATION

The design problem maximizes bits-per-Joule EE by jointly selecting user powers and discrete LIS phases under individual QoS constraints. Perfect channel knowledge and ZF precoding are assumed, while the resulting optimization is non-convex and costly to search exhaustively.

  • Optimization objective: The optimization jointly chooses the transmit-power matrix P and LIS phase matrix Φ to maximize EE while satisfying each user's QoS requirement.
  • Precoding: ZF precoding uses the pseudoinverse of the effective channel combining direct and LIS-assisted propagation.
  • Energy efficiency: EE is defined as achievable sum rate divided by total power consumption and is measured in bits per Joule.
  • Constraints: Each LIS phase must belong to a finite set of 2^b discrete values, with Rmin,k specifying user k's QoS constraint.
  • Computational challenge: The non-convex phase optimization has exhaustive-search complexity O(2^bNNKM), which is prohibitive for large surfaces.

IV. TRANSMIT POWER ALLOCATION AND LIS DESIGN

The paper uses alternating optimization to jointly design LIS phase shifts and user transmit powers for energy-efficiency maximization. Each variable block is optimized while the other is fixed, with iterations continuing until convergence or an acceptable solution level.

  • Alternating optimization separates the joint design of the LIS phase-shifting matrix and transmit power allocation matrix.The method first fixes transmit powers to optimize LIS phases, then fixes phases to optimize transmit powers.
  • For fixed transmit powers, the method optimizes the LIS phase-shifting matrix for the EE objective.
  • For fixed LIS phases, the method optimizes user transmit powers for EE performance.
  • The two optimization steps repeat until the objective or solutions reach convergence or an acceptable level.

A. LIS with 1-bit Phase Resolution Elements

For 1-bit LIS elements, phase choices are discrete, making the phase-design problem non-differentiable and non-convex. The approach relaxes these constraints, solves the resulting problem numerically, and discretizes the phases afterward.

  • A. LIS with 1-bit Phase Resolution Elements: 1-bit LIS elements restrict each coefficient to φ_n = {1, −1}, equivalently θ_n = {0, π}.The phase coefficients are represented as φ_n = exp(jθ_n).
  • A. LIS with 1-bit Phase Resolution Elements: The resulting phase-design problem is difficult because its objective is non-differentiable and its discrete phase constraint is non-convex.
  • A. LIS with 1-bit Phase Resolution Elements: The discrete constraint is relaxed to the convex interval 0 ≤ θ_n ≤ 2π, producing a numerically tractable optimization problem.The text identifies interior-point and quasi-Newton methods, including MATLAB’s fmincon, as solution methods.
  • A. LIS with 1-bit Phase Resolution Elements: The relaxed solution is discretized by mapping each phase back to the feasible 1-bit phase set.
  • A. LIS with 1-bit Phase Resolution Elements: For moderately large N, the relaxed-and-discretized phase solution is reported to yield a near-optimal LIS phase-shifting matrix.
  • A. LIS with 1-bit Phase Resolution Elements: With fixed LIS phases, the corresponding optimization becomes the transmit-power subproblem.

2) Optimization with respect to

The fixed-phase transmit-power problem imposes minimum user-power and total-power constraints. Its concavity and convex constraints enable global solution with limited complexity using Dinkelbach’s method.

  • 2) Optimization with respect to: Each user’s transmit power must satisfy p_k ≥ σ^2(2^Rmin,k − 1).
  • 2) Optimization with respect to: For fixed LIS phases, the transmit-power objective is concave in P and the relevant constraints are convex.
  • 2) Optimization with respect to: Dinkelbach’s method globally solves the transmit-power problem with limited complexity.
  • 2) Optimization with respect to: The power-allocation solution is indexed by the i-th iteration of the algorithm.

3) Proposed EE Maximization Algorithm:

Algorithm 2 alternates relaxed LIS phase optimization and transmit-power optimization for 1-bit elements. It iterates until consecutive solutions converge and can terminate when feasibility fails.

  • 3) Proposed EE Maximization Algorithm:: Algorithm 2 summarizes EE maximization for a LIS with 1-bit phase-resolution reflecting elements.
  • 3) Proposed EE Maximization Algorithm:: The algorithm alternates solving the phase problem for fixed powers and the power problem for fixed phases.
  • 3) Proposed EE Maximization Algorithm:: Iterations continue until the squared norm of consecutive solution differences is below a small ε > 0.
  • 3) Proposed EE Maximization Algorithm:: Dinkelbach’s method is used within the alternating procedure to solve the power-allocation subproblem.
  • 3) Proposed EE Maximization Algorithm:: The procedure declares infeasibility when the required feasibility condition is not satisfied.

B. LIS with Finite Phase Resolution Elements

The paper extends the 1-bit LIS phase-optimization approach to any finite phase resolution by relaxing continuous phases and discretizing the resulting solutions.

  • For fixed transmit powers, the phase optimization is relaxed from discrete values to the continuous interval 0 ≤ θ_n ≤ 2π.
  • The relaxed 2-bit solution is discretized by setting θ_n = 0 below π/2 and θ_n = π otherwise.
  • Replacing this discretization step in Algorithm 2 extends the method to 2-bit and, similarly, any finite phase resolution.

V. PERFORMANCE EVALUATION RESULTS

The evaluation examines energy efficiency and achievable sum rate under varying transmit power, LIS size, and phase resolution. Low-resolution LIS configurations can improve EE over relaying, while higher resolution improves sum rate but may require more power.

  • EE increases with BS transmit power before becoming constant, with saturation near 12.5 dBm for 2-bit/infinite resolution and 20 dBm for 1-bit resolution.
  • 1-bit and 2-bit LIS configurations achieve the highest EE, up to 45% above relay-assisted communication for P > 15 dBm.
  • EE rises with the number of LIS elements up to an optimum, then degrades because LIS power consumption increasingly affects EE.
  • Lower phase resolution slows EE degradation as the LIS size increases.
  • Relay-assisted communication achieves up to 20 bps/Hz more sum rate than 1-bit LIS, while the infinite-resolution gap falls below 5 bps/Hz at large SNR.
  • The 2-bit LIS sum rate is close to infinite-resolution performance while requiring much lower power consumption.

VI. CONCLUSION

The paper concludes that low-resolution LIS elements can support energy-efficient multi-user MISO communication through joint transmit-power and phase design. Simulations show substantial EE gains over amplify-and-forward relaying, including with 1-bit elements.

  • The proposed algorithm jointly designs each mobile user's transmit power and the phase values of nearly passive LIS reflecting elements.
  • 1-bit LIS reflecting elements increase system EE by more than 40% compared with conventional amplify-and-forward relaying systems.
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