PaperlayerView exact revision on arXiv

Source-linked AI summary

Generalized Multicast Multibeam Precoding for Satellite Communications

Vahid Joroughi, Miguel Ángel Vázquez, Ana I. Pérez-Neira

arXiv:1509.01377v1cs.ITmath.IT

TL;DR

Multibeam satellite precoding must address multicast optimization complexity and gateway constraints. The paper proposes a two-stage low-complexity design and reports that MBIM offers larger throughputs than R-ZF across transmit-power values.

  • Problem

    Multibeam multicast precoding must manage computational complexity and gateway constraints, including feeder-link bandwidth that can become unaffordable.

    Source: C. Contributions · p. 4, §VI · p. 17

  • Method

    The paper combines two-stage low-complexity precoding with robust perturbation modeling, per-beam user grouping, and multiple-gateway schemes.

    Source: §VIII · p. 24

  • Results

    Both proposals outperform average MMSE, while MBIM offers larger throughputs than R-ZF across transmit-power values.

    Source: §VII · p. 21

  • Takeaways & Limitations

    The conclusion identifies multiple-gateway schemes as essential tools for increasing throughput in multibeam systems.

    Source: §VIII · p. 24

Abstract

from arXiv · show

This paper deals with the problem of precoding in multibeam satellite systems. In contrast to general multiuser multiple-input-multiple-output (MIMO) cellular schemes, multibeam satellite architectures suffer from different challenges. First, satellite communications standards embed more than one user in each frame in order to increase the channel coding gain. This leads to the different so-called multigroup multicast model, whose optimization requires computationally complex operations. Second, when the data traffic is generated by several Earth stations (gateways), the precoding matrix must be distributively computed and attain additional payload restrictions. Third, since the feedback channel is adverse (large delay and quantization errors), the precoding must be able to deal with such uncertainties. In order to solve the aforementioned problems, we propose a two-stage precoding design in order to both limit the multibeam interference and to enhance the intra-beam minimum user signal power (i.e. the one that dictates the rate allocation per beam). A robust version of the proposed precoder based on a first perturbation model is presented. This mechanism behaves well when the channel state information is corrupted. Furthermore, we propose a per beam user grouping mechanism together with its robust version in order to increase the precoding gain. Finally, a method for dealing with the multiple gateway architecture is presented, which offers high throughputs with a low inter-gateway communication. The conceived designs are evaluated in a close-to-real beam pattern and the latest broadband communication standard for satellite communications.

I. INTRODUCTION · A. Motivation · B. Previous Works

The introduction motivates satellite precoding as a response to interference under full beam-frequency reuse and outlines implementation constraints arising from imperfect channel feedback, gateway distribution, and multicast transmission. It reviews prior precoding approaches addressing these challenges.

A. Motivation

  • Multibeam architectures increase beam gain, spatial multiplexing, and bandwidth reuse, while maintaining low multiuser interference between sufficiently separated beams.These advantages are presented relative to transmission over a single global beam.Source: A. Motivation · p. 2
  • Full frequency reuse is needed to support terabit satellite capacity, making forward-link interference mitigation through precoding or user-terminal detection necessary.The paper identifies larger available user bandwidth as the reason for full reuse.Source: A. Motivation · p. 2
  • Precoding depends on accurate CSI feedback and degrades when CSI is outdated or corrupted, whereas multiuser detection avoids feedback dependence but increases terminal complexity and cost.The authors therefore consider precoding as an interference-relief technique, noting encouraging system-level results [4].Source: A. Motivation · pp. 2–3

B. Previous Works

  • Early satellite precoding designs adapted linear MIMO methods, including zero-forcing and MMSE designs.The cited work also identified implementation challenges for multibeam satellite systems.Source: B. Previous Works · p. 3
  • Low payload complexity shifts most precoding computation to the ground, where transmitting precoded signals through the feeder link creates a large bandwidth requirement.The feeder-link bandwidth requirement is even larger when precoding is deployed at the gateway because feed signals must be precoded and transmitted simultaneously.Source: B. Previous Works · p. 3
  • Multiple gateways can reuse feeder-link spectrum across spatially separated areas, but each gateway accesses only a subset of feeds and prior schemes still reduce overall throughput.A regularized-ZF scheme is described in,, while reduced throughput is also reported for computationally complex on-ground schemes.Source: B. Previous Works · pp. 3–4
  • Each beam serves multiple users with one coded frame, so precoding must account for multiple spatial signatures and rates are dictated by the lowest-SNIR user.This multicast structure is used to increase coding gain.Source: B. Previous Works · p. 4
  • Prior approaches include sequential beamforming, one-shot MMSE precoding with channel averaging,, and designs applicable to a multigroup multicast model.A one-shot scheme must be implemented when a large number of beams over the coverage area is targeted.Source: B. Previous Works · p. 4

C. Contributions

The paper proposes a low-complexity two-stage precoding scheme for multicast multibeam interference, with robust precoding, user grouping, and a multi-gateway design to address channel uncertainty and distributed operation.

C. Contributions

  • A low-complexity two-stage linear precoder, similar to, is proposed to mitigate multibeam interference in multicast transmissions.The design targets the multiuser MIMO scenario.Source: C. Contributions · p. 4
  • The proposed scheme achieves higher spectral efficiency than regularized ZF and average MMSE, while maintaining low computational complexity.The authors prioritize a low-complexity one-shot design over iterative gradient-based schemes,.Source: C. Contributions · p. 4
  • A robust precoding design uses first-order perturbation theory for eigenvectors and eigenvalues to address corrupted gateway CSI while retaining low complexity for many feeds.The authors describe this robust design as novel.Source: C. Contributions · p. 4
  • A user-grouping method selects suitable users per beam with a k-means variation that considers channel magnitudes and phase, and a robust version addresses channel uncertainty.The grouping targets reduced rate when user channel vectors within a beam are not collinear; the method differs from by considering phase effects.Source: C. Contributions · p. 5
  • For multiple gateways, the proposed design reduces CSI-sharing communication and divides precoding-matrix computation among gateways, trading lower achievable rates for a balance of overhead, payload complexity, and throughput.Source: C. Contributions · p. 5

II. PROBLEM FORMULATION · A. Channel Model

The channel model describes a full-frequency-reuse multibeam satellite with an ideal feeder link, N feeds, K beam signals, and Q users served simultaneously per beam. It defines the channel through attenuation, gain/loss, and phase effects, then considers linear precoding to limit multiuser interference.

A. Channel Model

  • An ideal feeder link carries N frequency-multiplexed feed signals that the array-fed reflector routes into K radiated beam signals.The model assumes a multiple-feed-per-beam architecture; the cited alternative single-feed-per-beam case has N = K, while multiple-feed-per-beam has N > K and offers lower scan losses and larger antenna gains.Source: A. Channel Model · pp. 5–6
  • All beams share the frequency band, and each beam simultaneously serves Q users with a codeword intended for all of them.The formulation assumes the same number of users on every beam.Source: A. Channel Model · p. 6
  • The received-signal vector contains one entry per user terminal, with additive noise modeled as zero-mean, unit-variance Gaussian and uncorrelated across users and with the desired signal.The vector and noise dimensions are KQ × 1.Source: A. Channel Model · p. 7
  • The channel matrix F models atmospheric fading and feed radiation, with diagonal A representing user-specific fading and G capturing the remaining gain and loss factors.G is normalized to the receiver-noise term; its factors include user distance, wavelength, bandwidth, receive-antenna gain, noise temperature, and feed-to-user gain.Source: A. Channel Model · p. 7
  • Feed-to-user phase variation can severely affect system performance; the model uses uniform phase variation or, with ultra-stable oscillators, a common uniform phase plus zero-mean Gaussian residual variation.The residual phase term has variance χ.Source: A. Channel Model · p. 7
  • For notation, the model defines H_k as the channel matrix for beam k and h_k,q as the channel vector for user q in that beam.Source: A. Channel Model · p. 8
  • To reduce multiuser interference under full frequency reuse, the system uses linear precoding to form the transmitted-symbol vector.The transmitted symbols are assumed uncorrelated.Source: A. Channel Model · p. 8

B. Precoding Design · III. GENERALIZED MULTICAST MULTIBEAM PRECODING

The paper formulates multicast multibeam precoding as a constrained rate-optimization problem and targets a low-complexity design. Its generalized approach uses two precoding stages to mitigate inter-beam interference and improve the weakest user signal within each beam.

B. Precoding Design

  • The precoding problem is formulated to maximize sum rate subject to satellite power availability and beam precoder constraints.The available power is denoted PT, and wk is the kth column of precoding matrix W.Source: B. Precoding Design · p. 8
  • The design imposes per-feed power limits, assuming available power is shared equally across feed elements.The text notes that beam power sharing is possible,, but its deployment would require costly and complex radio-frequency designs.Source: B. Precoding Design · p. 8
  • The proposed target is a low-computational-complexity precoding scheme that can achieve high throughput in systems with hundreds of beams.The paper identifies computational complexity as essential for multibeam systems, and notes that even convex relaxations of the non-convex problem can be demanding.Source: B. Precoding Design · p. 9

III. GENERALIZED MULTICAST MULTIBEAM PRECODING

  • The generalized design has two aims: minimize inter-beam interference and increase the lowest SINR within each beam.The lowest within-beam SINR determines the weakest user's signal quality.Source: §III · p. 9
  • The first stage, Wa, mitigates inter-beam interference, while the second stage, Wb, optimizes the served users’ intra-frame data rate.For beam k, Wak and wbk denote the precoding components used to optimize that beam's rate.Source: §III · p. 9
  • The parameter α is selected to satisfy the available power constraint, whether per-feed or total.Source: §III · p. 9

A. Inter-beam Interference Mitigation Precoding … B. Intra-beam Precoding

The precoding design first mitigates inter-beam interference, then selects per-beam precoders using each beam’s equivalent channel. The supplied passages describe an MMSE-based MBIM design, a regularized zero-forcing variant, and an average-SNR intra-beam design.

A. Inter-beam Interference Mitigation Precoding — 1) Multibeam Interference Mitigation (MBIM): 

  • The combined channel after applying Wa has blocks HkWaj, exposing each beam’s effective channel and its coupling to other beams.The k-th beam’s effective channel is HkWak; eHkWak represents interference generated to other users.Source: 1) Multibeam Interference Mitigation… · p. 10
  • MBIM designs Wa by minimizing a modified MMSE objective under a total-power constraint, using the solution described with the SVD of eHH.The efficient design is attributed to.Source: 1) Multibeam Interference Mitigation… · p. 10

A. Inter-beam Interference Mitigation Precoding — 2) Regularized Zero-Forcing:

  • The regularized zero-forcing scheme uses the multicast-aware regularization factor and an SVD decomposition with a null space of dimension Q.The null space is spanned by eV(R),0.Source: 2) Regularized Zero-Forcing · p. 11

B. Intra-beam Precoding

  • After Wa, beam k observes equivalent channel Zk = HkWak, which the system designer uses to construct its intra-beam precoder wbk.The q-th user’s equivalent channel in beam k is denoted zkq.Source: B. Intra-beam Precoding · p. 11
  • The intra-beam design maximizes average SNR over the equivalent channel matrix as a suboptimal but efficient approach.Its objective can be rewritten as ∥Zkwbk∥2.Source: B. Intra-beam Precoding · pp. 11–12
  • The optimal wbk is the eigenvector associated with the largest eigenvalue of Zk, requiring only that eigenvector computation.The passage characterizes this design as having low computational complexity.Source: B. Intra-beam Precoding · p. 12

C. Power control · IV. ROBUST MULTICAST MULTIBEAM PRECODING · A. Robust Inter-beam Precoding

The paper scales the computed precoding schemes to meet transmit-power constraints, then extends MBIM to account for imperfect CSI and develops an approximate robust inter-beam design. It notes that choosing perturbation bounds is an empirical challenge and that increasing the uncertainty parameter makes the robust design differ more from the original WMMSE design.

C. Power control

  • The power-control step calculates α after both precoding schemes are computed, to satisfy either maximum per-feed or total-power constraints.The supplied passage does not include the corresponding formulas.Source: C. Power control · p. 12

IV. ROBUST MULTICAST MULTIBEAM PRECODING

  • MBIM is selected for average intra-beam optimization because it is stated to offer larger achievable rates than R-ZF.The comparison is described as something to be shown in the simulation section; no numerical result is supplied here.Source: §IV · p. 12
  • Because receiver-fed CSI is degraded by quantization and transmission delay, the optimization is reformulated to account for possible variations.The perturbation model assumes the transmitter has a degraded version of H, with perturbation matrices subject to constraints.Source: §IV · p. 12
  • Selecting adequate γ bounds for the perturbation matrices requires empirical assessment of error sources and their effects, which is outside this paper’s scope.The paper instead provides a sensitivity analysis in the simulation section.Source: §IV · p. 13

A. Robust Inter-beam Precoding

  • The perturbation matrix affects both eigenvectors and eigenvalues, while robust designs generally consider only eigenvalue effects [28, Chapter 7]; the eigenvector impact cannot be considered negligible.Source: A. Robust Inter-beam Precoding · p. 14
  • As ǫk increases, the resulting robust precoding design becomes more different from the original WMMSE design ak.The passage reports this directional relationship without quantifying the change.Source: A. Robust Inter-beam Precoding · p. 14

B. Robust Intra-beam Precoding … B. Robust k-User Grouping

The section develops robust intra-beam precoding and user grouping to address channel uncertainty and user-channel diversity. It presents approximate robust designs and a random-seed grouping heuristic based on channel-vector proximity.

B. Robust Intra-beam Precoding

  • The robust intra-beam design incorporates channel perturbations into a worst-case optimization under the average-optimization scheme, for which Theorem 2 gives an approximate solution.Source: B. Robust Intra-beam Precoding · pp. 14–15
  • As the perturbation parameter νk increases, the robust solution departs further from the original, while computational complexity remains the same as in the non-robust case.Source: B. Robust Intra-beam Precoding · p. 15

V. USER GROUPING

  • Spatial diversity can make intra-beam precoding unable to deliver intended symbols for orthogonal user channels, motivating simultaneous service of users with collinear channels.Source: §V · p. 15

A. k-User Grouping

  • The k-user grouping heuristic randomly selects a beam user, then forms a group with the Q −1 users closest in Euclidean distance, reducing computational complexity.For small Q, the grouping requires Euclidean-norm comparisons between scheduled users.Source: A. k-User Grouping · p. 16
  • Grouping degrades when channel vectors are corrupted, so the paper proposes a robust grouping method.Source: A. k-User Grouping · p. 16

B. Robust k-User Grouping

  • For uncertain channel vectors, the robust grouping design adds a scalar penalty, and its approximate optimization solutions upper-bound the original worst-case problem.Source: B. Robust k-User Grouping · p. 17
  • When all users have the same uncertainty, the proposed approximate robust grouping solution remains unchanged.Source: B. Robust k-User Grouping · p. 17

VI. MULTIPLE GATEWAY ARCHITECTURE · A. Precoding Scheme

Multiple gateways can reuse feeder-link bandwidth to serve the satellite coverage area, but their distributed precoding and payload constraints require adapting the precoding matrix. The proposed scheme partitions precoding by gateway, with robust designs applicable without additional penalty.

VI. MULTIPLE GATEWAY ARCHITECTURE

  • A 155-feed payload with 500 MHz user-channel bandwidth would require 77.5 GHz of feeder-link bandwidth, an unaffordable requirement even at Q/V band.Source: §VI · p. 17
  • Feeder-link spatial reuse lets multiple gateways simultaneously send data to the coverage area, increasing user bandwidth but requiring reconsideration of precoding.Source: §VI · p. 17
  • Payload receivers route only a limited set of feeds per gateway, so partitioning the overall precoding matrix into gateway submatrices can substantially decrease achievable throughput.The limited feed routing is intended to keep payload complexity low; the passage notes that feeder-link bandwidth supports only a small number of feed signals.Source: §VI · p. 18
  • Because gateways compute their own precoding submatrices and access feedback only for their own feeds, CSI cooperation is needed to mitigate inter-beam interference.Source: §VI · p. 18

A. Precoding Scheme

  • The precoding scheme assumes fixed feed allocation and fixed gateway feed and beam counts; unavailable feed entries are set to zero, producing a block-diagonal precoding matrix.Each gateway serves a subset of beams and users, and the gateways are assumed to have access to overall CSI for the described adaptation of the Section III scheme.Source: A. Precoding Scheme · pp. 18–19
  • Robust designs can be applied to the multiple-gateway precoding scheme without any additional penalty.Source: A. Precoding Scheme · p. 19

B. CSIT Sharing · VII. SIMULATIONS · A. User Grouping

Simulations show higher throughput from MBIM over R-ZF and from user grouping, while the gateway discussion describes ways to limit the overhead of sharing channel information. The simulation setup evaluates precoding under satellite-specific channel and link conditions.

B. CSIT Sharing

  • Gateways need to share channel effects from their assigned feeds to non-intended users over an inter-gateway link to compute the precoding matrix.Source: B. CSIT Sharing · p. 19
  • To reduce communication overhead, gateways can limit sharing to the C closest gateways or compress each transmit-channel submatrix using its dominant eigenvector.Source: B. CSIT Sharing · p. 20
  • More precise channel matrices at each gateway can yield larger throughput.Source: B. CSIT Sharing · p. 20

VII. SIMULATIONS

  • The benchmark evaluates a geostationary-satellite reference scenario with N = K = 245 under full frequency reuse, using 500 channel realizations and a 10-degree phase effect between feeds.Throughput is obtained from user SINR and efficiency (bit/symbol) at a minimum PER of 10−6.Source: §VII · p. 20
  • The simulations also assess imperfect-CSI robustness and multi-gateway cooperation alongside perfect-CSI single-gateway precoding, using 4-coloring as a reference scenario.Source: §VII · p. 21
  • MBIM and R-ZF outperform average MMSE,, with MBIM ahead of R-ZF; conventional 4-coloring has the lowest achievable rate due to bandwidth.Source: §VII · p. 21, Figure 3 · p. 22

A. User Grouping

  • User grouping exploits collinear within-beam channel vectors and increases throughput in all cases, with a larger gain for Q = 3 than Q = 2; its low complexity favors implementation.Source: A. User Grouping · p. 22

B. Robust Design · C. Multiple Gateway Transmission · VIII. CONCLUSIONS

The paper presents a low-complexity two-stage precoder, a robust design for imperfect CSI, and user-grouping and multiple-gateway schemes for multibeam satellite systems. The reported results indicate that the robust design maintains throughput under imperfect CSI, while greater gateway cooperation improves throughput and MSVDGC balances throughput with communication overhead.

B. Robust Design

  • The robust-design simulations use an additive Gaussian perturbation with zero mean and variance 1, set γk to 1, and omit sensitivity analysis due to space limitations.The perturbation values γk are described as the same across submatrices.Source: B. Robust Design · p. 22
  • For Q = 2 and 3, the proposed technique overcomes imperfect transmitter CSI while delivering large throughputs with low precoding complexity.Figure 5 evaluates per-beam average throughput under imperfect CSI without user grouping.Source: B. Robust Design · pp. 22–23, Figure 5 · p. 24

C. Multiple Gateway Transmission

  • The multiple-gateway evaluation spans independent cluster processing, 4- and 7-gateway collaboration, all-gateway collaboration, and a single-gateway scenario.The shared-vector all-gateway method uses the left singular vector associated with the largest singular value of the gateway channel matrix.Source: C. Multiple Gateway Transmission · pp. 23–24
  • MBIR yields larger overall throughput than R-ZF in every evaluated gateway scenario; greater cooperation raises throughput, while MSVDGC trades off throughput and inter-gateway overhead.The evaluated architectures include independent clusters, collaboration with 4 or 7 neighboring gateways, collaboration using a shared singular vector, and single-gateway processing.Source: C. Multiple Gateway Transmission · p. 24, Figure 6 · p. 25

VIII. CONCLUSIONS

  • The proposed low-complexity two-stage precoder first minimizes inter-beam interference and then enhances intra-beam SINR.The paper also presents a robust version based on a first perturbation theory, along with user-grouping and multiple-gateway schemes to increase throughput.Source: §VIII · p. 24
  • In a continental-coverage evaluation, the proposed methods perform better than current approaches while retaining low computational complexity.The conclusion summarizes the evaluated methods as designed for multibeam satellite systems.Source: §VIII · p. 24

APPENDIX A PROOF OF THEOREM 1 · APPENDIX B PROOF OF THEOREM 2

Appendix A derives bounds on the perturbation-dependent objective and uses them to relax its worst-case maximization. Appendix B bounds a second objective to remove its dependence on Δk, using first-order eigenvector perturbation and a lower bound on the perturbed eigenvalues.

APPENDIX A PROOF OF THEOREM 1

  • Because the perturbation matrices are unknown to the transmitter, Appendix A derives upper bounds for both the perturbed eigenvectors and eigenvalues.Source: Appendix A · p. 25
  • Using first-order perturbation analysis, Appendix A derives an eigenvector perturbation expression whose off-diagonal entries depend on eigenvalue differences.Source: Appendix A · p. 26
  • For eigenvector perturbations, Appendix A invokes Weyl’s inequality to support bounding the perturbed eigenvalues.Source: Appendix A · pp. 26–27
  • The resulting bounds on the eigenvalues and eigendecomposition relax the worst-case maximization in (39).Source: Appendix A · p. 27

APPENDIX B PROOF OF THEOREM 2

  • Appendix B bounds its objective function so that it no longer depends on Δk.Source: Appendix B · p. 27
  • Using the first-order perturbation model, Appendix B approximates the eigenvectors of Zk for the perturbed eigendecomposition of HkWak.Source: Appendix B · p. 27
  • Combining an inequality with the preceding appendix’s derivation establishes a lower bound on the eigenvalues of bZk.Source: Appendix B · p. 27
Loading 1509.01377v1…