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Multicast Multigroup Precoding and User Scheduling for Frame-Based Satellite Communications

Dimitrios Christopoulos, Symeon Chatzinotas, Bjorn Ottersten

arXiv:1406.7699v2cs.IT

TL;DR

Increasing frequency reuse entails a reduction in average performance, motivating frame-based precoding and multicast-aware scheduling. The paper proposes constrained precoding designs and scheduling, achieving more than 30% throughput performance gains for 7 users per frame over conventional configurations.

  • Problem

    Increasing frequency reuse entails a reduction in the system's average performance.

  • Method

    The paper proposes frame-based precoding designs with minimum-rate and modulation-constrained throughput formulations, together with multicast-aware user scheduling.

  • Results

    More than 30% throughput performance gains are achieved for 7 users per frame over conventional system configurations.

  • Takeaways & Limitations

    These gains are achieved without loss in the outage performance of the system.

Abstract

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The present work focuses on the forward link of a broadband multibeam satellite system that aggressively reuses the user link frequency resources. Two fundamental practical challenges, namely the need to frame multiple users per transmission and the per-antenna transmit power limitations, are addressed. To this end, the so-called frame-based precoding problem is optimally solved using the principles of physical layer multicasting to multiple co-channel groups under per-antenna constraints. In this context, a novel optimization problem that aims at maximizing the system sum rate under individual power constraints is proposed. Added to that, the formulation is further extended to include availability constraints. As a result, the high gains of the sum rate optimal design are traded off to satisfy the stringent availability requirements of satellite systems. Moreover, the throughput maximization with a granular spectral efficiency versus SINR function, is formulated and solved. Finally, a multicast-aware user scheduling policy, based on the channel state information, is developed. Thus, substantial multiuser diversity gains are gleaned. Numerical results over a realistic simulation environment exhibit as much as 30% gains over conventional systems, even for 7 users per frame, without modifying the framing structure of legacy communication standards.

I. INTRODUCTION & RELATED WORK

The paper addresses frame-based precoding and per-antenna power constraints in aggressively reused multibeam satellite systems. It uses multigroup multicasting to support co-scheduled users while developing throughput-oriented precoding and scheduling methods.

  • Practical constraints: DVB-S2/S2X framing prevents precoding on a user-by-user basis because each frame serves multiple users with different data requirements.FEC coding over the entire frame requires co-scheduled users to decode it before extracting their information.
  • Practical constraints: Unequal payloads across beams further complicate joint processing of simultaneously served streams.The framing structure and differing user counts create a practical need for frame-by-frame precoding.
  • Multigroup multicast formulation: Physical-layer multigroup multicast precoding provides theoretically optimal precoders when independent common-data sets are sent to distinct user groups.The approach matches frame-based transmission because one symbol or frame is addressed to multiple users.
  • Practical constraints: Per-antenna amplifiers impose individual transmit-power limits and prevent power sharing among antennas.More flexible amplifier architectures can support sharing but incur high costs, while distributed antenna systems also lack power sharing.
  • Proposed direction: The work presents a throughput-maximizing precoding matrix together with a low-complexity user-scheduling algorithm for full-frequency-reuse satellite transmission.The design assumes channel state information is available at the transmitter and extends interference mitigation within the DVB-S2X framing structure.

A. Related Work

Prior work established multicast beamforming criteria and scheduling methods, while this paper extends optimization and scheduling to frame-based multigroup multicast satellite systems under practical constraints.

  • Multigroup multicast optimization: Earlier multigroup multicast work emphasized minimum-SINR maximization and fairness, but service levels can also be adjusted toward sum-rate objectives.Sum-rate maximization had been considered under sum-power constraints using heuristic iterative optimization.
  • User scheduling: CSI-based scheduling can exploit multiuser diversity, and the paper derives a low-complexity scheduler that accounts for the multigroup multicast structure.The proposed algorithms use readily available CSI to select users for frame-based transmissions.
  • Multigroup multicast optimization: The paper formulates and solves max-SR multigroup multicast precoding under per-antenna constraints, then extends it with minimum-rate constraints.These contributions address the distinction between individual antenna limits and conventional sum-power constraints.
  • System-driven optimization: A modulation-aware max-SR optimization incorporates a discretized throughput function and is solved heuristically.The formulation targets system throughput under modulation-dependent spectral-efficiency behavior.
  • Evaluation: The developed techniques are evaluated in a multibeam, full-frequency-reuse satellite environment.The paper evaluates the derived algorithms after formulating the system model, optimization problems, and scheduling procedures.

II. SYSTEM MODEL

The system model represents a multibeam satellite downlink with multiple multicast groups, linear precoding, and per-antenna power constraints. Its channel model includes antenna gains, path loss, noise, propagation phases, and a restricted beam subset.

  • System representation: The model considers a broadband multibeam satellite transmitting to multiple single-antenna users grouped into multicast frames.Each user belongs to one group, and users in the same group share a precoding vector and equivalent transmitted symbol.
  • Multibeam channel: The channel matrix models multibeam antenna radiation, path loss, receive gain, noise power, and propagation-induced phase rotations.The model uses antenna-user gains and user-dependent phases, with normalized receiver noise incorporated into channel coefficients.
  • System representation: The received signal follows the linear model y = Hx + n = HWs + n, with one precoding-matrix column and symbol per multicast group.The precoding matrix is square under the assumed equality between transmitting elements and multicast groups.
  • Power constraints: Per-antenna constraints differ from sum-power constraints because each of Nt constraints involves all precoding vectors.The power radiated by each antenna is a linear combination of the precoders.
  • Multibeam channel: The evaluation uses a European 245-beam pattern but considers only a subset of beams under a multiple-gateway assumption.Interference from adjacent clusters is left for future investigation.

B. Average User Throughput

The paper defines average user throughput using a granular spectral-efficiency mapping from user SINR to MODCOD-dependent rates, then develops per-antenna-constrained sum-rate maximization through decoupled beamforming and power loading.

  • Average user throughput is normalized by the number of beams to enable comparison across multibeam systems of different sizes.
  • The DVB-S2X spectral-efficiency function maps each user’s SINR to the corresponding lower threshold and outputs the associated rate in bps/Hz.
  • Throughput-maximizing precoders are designed under per-antenna constraints, extending multigroup multicast precoding to the satellite setting.
  • The beamforming problem is decoupled into normalized beamforming directions and group power allocation, enabling a two-step optimization.
  • The multigroup multicast sum-rate objective is nondifferentiable because each group rate depends on its minimum user SINR, requiring sub-gradient methods.

B. Complexity & Convergence Analysis

The proposed algorithm combines semidefinite-relaxation-based QoS precoding with iterative sub-gradient power control and per-antenna projection, yielding polynomial asymptotic complexity under diminishing step sizes.

  • The QoS minimization subproblem is a semidefinite program with Nt matrix variables of Nt×Nt dimensions and Nu + Nt linear constraints.
  • The QoS problem is solved using semidefinite relaxation and Gaussian randomization, while each randomization solves a linear problem.
  • Increasing the number of Gaussian randomizations improves solution accuracy, producing an ǫ1-optimal solution under the stated procedure.
  • The projection step is a real-valued least-squares problem subject to Nt quadratic inequality per-antenna constraints.
  • The algorithm’s asymptotic complexity is polynomial and dominated by the QoS multigroup multicast problem under per-antenna constraints.
  • Convergence is guaranteed when the sub-gradient search uses the prescribed diminishing step size, including δ(l + 1) = δ(l)/2.

IV. SYSTEM DRIVEN OPTIMIZATION

Aggressive frequency reuse increases throughput potential but reduces the mean and variance of coverage-wide SINR, making service availability a system-level design concern.

  • Full frequency reuse increases interference, which reduces useful received signal power despite the broader user-link bandwidth.
  • The mean and variance of the SINR distribution across the coverage area are generally reduced under full frequency reuse.
  • Lower SINR increases reliance on lower MODCODs and raises the probability of service unavailability.
  • Outages and retransmissions can burden system efficiency, while outage periods may become comparable to satellite propagation delay.
  • The work introduces minimum-rate constraints across the coverage to guarantee a minimum physical-layer service availability level.

A. Sum Rate Maximization under Minimum Rate Constraints

The paper extends per-antenna sum-rate maximization with minimum-rate constraints, trading throughput for guaranteed service availability through a convex availability-constrained projection.

  • The availability formulation targets an engineering compromise between fairness and maximum sum rate.
  • Minimum-rate constraints are incorporated into the per-antenna-constrained sum-rate problem to address stringent satellite availability requirements.
  • The spectral-efficiency model supports quasi-error-free communication below a user SINR of −2.85 dB, corresponding to 0.4348 bps/Hz.
  • The added linear constraint preserves convexity of the projection problem and can therefore be handled within the sub-gradient method.
  • Availability constraints are added through a minimum-SINR projection that remains a convex subset of the initial feasible set.
  • Introducing minimum-rate constraints decreases throughput performance, but the trade-off can support more favorable system conditions.

B. Throughput Maximization via MODCOD Awareness

The paper formulates throughput maximization for practical modulation-constrained systems using a granular spectral-efficiency function, then proposes an iterative heuristic that preserves throughput and availability while redistributing saved power. It also develops a CSI-based multicast-aware scheduling policy to exploit multiuser diversity without requiring resulting SINR knowledge.

  • Throughput maximization via MODCOD awareness: Practical modulation-constrained throughput is modeled with a finite-granularity DVB-S2X spectral-efficiency function rather than a continuously increasing logarithmic rate.The resulting step cost function is analytically difficult and prevents direct use of gradient-based solutions.
  • Throughput maximization via MODCOD awareness: A heuristic iterative algorithm increases groups toward discrete SINR thresholds while checking feasibility under per-antenna power constraints.Groups are ordered by the power required to reach their next threshold, and infeasible increases are rejected.
  • Throughput maximization via MODCOD awareness: The discretized procedure does not decrease system throughput, saves power for redistribution, and guarantees a minimum system availability.It starts from availability-constrained precoders and uses threshold targets based on the worst user in each group.
  • Throughput maximization via MODCOD awareness: Searching all multi-step SINR combinations has complexity that grows exponentially with the number of groups, motivating the restricted heuristic search.The algorithm avoids allowing more than one step increase per group for complexity reasons; convergence is guaranteed over the available groups.
  • User scheduling: Random grouping can impose each group’s link-layer mode through its worst user, causing performance losses; multicast-aware scheduling instead uses vector CSI to select users.The policy allocates semi-orthogonal users to different groups and then selects users most parallel to each group’s first user.

VI. PERFORMANCE EVALUATION & APPLICATIONS

The evaluation uses a realistic full-frequency-reuse multibeam satellite simulation with uniformly distributed users and measures throughput, SINR, rate distributions, and sensitivity to users per frame. It implements a CSI-based multicast-aware scheduling algorithm that first separates semi-orthogonal users across groups and then selects parallel users within groups.

  • Simulation setup: The simulation models a broadband multibeam satellite with full frequency reuse and four-color reuse configurations.Users are distributed across the coverage area, with 100 users per beam used for accurate averaging.
  • Simulation setup: Performance is evaluated through average user throughput, coverage-wide rate and SINR distributions, and sensitivity to the number of users per frame.Average throughput is averaged over all transmissions needed to serve the initial user pool for fair scheduling comparisons.
  • Multicast-aware scheduling: The multicast-aware scheduler allocates semi-orthogonal users to different groups in Step 1.It selects users using orthogonal rejection components relative to previously selected users.
  • Multicast-aware scheduling: In Step 2, the scheduler selects the most parallel users for each group to form multicast groups.The algorithm projects candidate channels onto each group’s first user and chooses the most parallel candidate.
  • Simulation assumptions: The evaluation uses a minimum SINR of -2.85 dB, corresponding to the minimum supported by normal frame operation in recent satcom standards.The reported gains could increase at lower SINR values because relaxing availability constraints allows greater flexibility.

A. Throughput performance

The proposed precoding methods improve throughput over conventional and fair approaches under aggressive frequency reuse, while availability-constrained methods protect users from outage. Modulation-aware sum-rate maximization provides the strongest reported gains and adapts SINR to discrete spectral-efficiency thresholds.

  • Throughput performance: More than 30% gains over max-min fair formulations and as much as 100% gains over conventional systems are reported for 2 users per frame in the high-power region.The strongest performance is attributed to SRM, the modulation-aware max-sum-rate method, which also guarantees service availability.
  • SINR and throughput trade-offs: Aggressive frequency reuse lowers average SINR and increases its variance but enables more efficient resource utilization and higher throughput.Conventional systems obtain higher SINRs through fractional frequency reuse, yet this does not necessarily produce higher system throughput.
  • Availability and MODCOD awareness: SRA guarantees a minimum SINR of -2.85 dB, while SRM shapes the SINR distribution around DVB-S2X thresholds and largely avoids intermediate values.This threshold adaptation explains the increased SRM gains while preserving availability.
  • Availability and MODCOD awareness: SRA and SRM guarantee at least 0.3 Gbps to all users, whereas SR records a 5% outage probability.The availability guarantee represents a throughput trade-off relative to unconstrained sum-rate optimization.
  • Users per frame: More than 30% gains are obtained for 3 users per frame, and positive gains over conventional systems remain for 6 users per frame.Increasing users per frame generally degrades performance because the worst user determines the MODCOD for the group.
  • Scheduling limitations: Random scheduling compromises performance because users with very different SINRs are co-scheduled and constrained by the worst user.An optimal joint scheduling policy is computationally prohibitive at the examined system dimensions, motivating the heuristic alternative.

B. Example

A two-user-per-frame example compares conventional, fair, sum-rate, and modulation-aware optimizations using per-user throughput distributions. The modulation-aware design builds on sum-rate maximization and achieves the highest reported average throughput while improving rates across users.

  • Example: The conventional system achieves an average user throughput of 1.06 Gbps/beam, while the fair optimization reaches 1.26 Gbps/beam.The conventional system shows substantial variance between group rates, whereas the fair optimization balances minimum rates.
  • Example: The sum-rate optimization reduces the rate for beam 5 while increasing rates for the other users, raising system throughput to just over 1.6 Gbps/beam.This illustrates a deliberate redistribution of rates in favor of aggregate throughput.
  • Example: The modulation-aware optimization builds on sum-rate maximization by adapting power allocation to modulation-constrained performance.It allocates each user equal or better rates and achieves Ravg = 1.72 Gbps/beam.

C. User scheduling

The paper develops multicast-aware channel-based user scheduling for frame-based precoding and evaluates its throughput under varying frame sizes, power budgets, and user-pool sizes. Scheduling improves throughput and mitigates degradation as more users share each frame, with gains exceeding 30% for up to 7 users per frame over conventional configurations.

  • Power-budget evaluation: Approximately 25% improvement is obtained as the on-board power budget increases for 2 users per group.The comparison is made against the random scheduling of Sec. VI-A.
  • Frame-size evaluation: Scheduling significantly improves the degradation in system performance as the number of users per group increases.Results compare scheduling with SRM without scheduling at a nominal on-board available power of 50 Watts.
  • Integrated design: The overall design includes sum-rate optimization under per-antenna power constraints, minimum-rate constraints, and modulation-constrained throughput.These extensions address throughput, availability, and practical spectral-efficiency behavior.
  • Performance gains: More than 30% throughput gains are achieved over conventional systems for as many as 7 users per frame.The gains are reported for frame-based precoding combined with multicast-aware scheduling.
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