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Massive MIMO Transmission for LEO Satellite Communications

Li You, Ke-Xin Li, Jiaheng Wang, Xiqi Gao, Xiang-Gen Xia, Björn Ottersten

arXiv:2002.08148v1cs.ITeess.SP

TL;DR

The paper introduces massive MIMO with full frequency reuse for LEO satellite communications, using statistical channel state information to address practical transmitter-CSI challenges. It develops closed-form transmission designs and space-angle user grouping, achieving asymptotic optimality and data-rate gains while approaching instantaneous-CSI performance.

  • Problem

    Massive MIMO had not been applied to LEO satellite communications, while practical systems face difficulty obtaining instantaneous channel state information at the transmitter.

  • Method

    The paper establishes a massive MIMO channel model, develops closed-form statistical-CSI downlink precoding and uplink reception, and proposes space angle based user grouping with full frequency reuse.

  • Results

    The proposed massive MIMO transmission scheme with full frequency reuse significantly enhances LEO satellite data rates, while statistical-CSI designs achieve similar performance to often-infeasible instantaneous-CSI designs.

  • Takeaways & Limitations

    Massive MIMO with full frequency reuse and statistical-CSI transmission is effective for LEO satellite communications under practical CSI constraints.

Abstract

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Low earth orbit (LEO) satellite communications are expected to be incorporated in future wireless networks, in particular 5G and beyond networks, to provide global wireless access with enhanced data rates. Massive MIMO techniques, though widely used in terrestrial communication systems, have not been applied to LEO satellite communication systems. In this paper, we propose a massive MIMO transmission scheme with full frequency reuse (FFR) for LEO satellite communication systems and exploit statistical channel state information (sCSI) to address the difficulty of obtaining instantaneous CSI (iCSI) at the transmitter. We first establish the massive MIMO channel model for LEO satellite communications and simplify the transmission designs via performing Doppler and delay compensations at user terminals (UTs). Then, we develop the low-complexity sCSI based downlink (DL) precoder and uplink (UL) receiver in closed-form, aiming to maximize the average signal-to-leakage-plus-noise ratio (ASLNR) and the average signal-to-interference-plus-noise ratio (ASINR), respectively. It is shown that the DL ASLNRs and UL ASINRs of all UTs reach their upper bounds under some channel condition. Motivated by this, we propose a space angle based user grouping (SAUG) algorithm to schedule the served UTs into different groups, where each group of UTs use the same time and frequency resource. The proposed algorithm is asymptotically optimal in the sense that the lower and upper bounds of the achievable rate coincide when the number of satellite antennas or UT groups is sufficiently large. Numerical results demonstrate that the proposed massive MIMO transmission scheme with FFR significantly enhances the data rate of LEO satellite communication systems. Notably, the proposed sCSI based precoder and receiver achieve the similar performance with the iCSI based ones that are often infeasible in practice.

I. INTRODUCTION

The paper introduces massive MIMO with FFR for LEO satellite communications, using sCSI to avoid impractical transmitter-side iCSI acquisition. It develops low-complexity transmission and user-grouping strategies whose performance approaches iCSI-based and asymptotically optimal designs.

  • Motivation: FFR increases available bandwidth across neighboring beams but makes inter-beam interference a critical issue requiring transmitter or receiver management.Linear precoding and detection are preferred because of their low complexity and near-optimal performance.
  • Motivation: Accurate transmitter-side iCSI is difficult because satellite-UT propagation delay, mobility, short coherence time, and feedback overhead can make channel information outdated or infeasible.These limitations affect both TDD reciprocity and FDD feedback-based acquisition.
  • Approach: The paper introduces massive MIMO with FFR for LEO satellite systems and focuses on physical-layer transmission design without predefined beamforming.The satellite is equipped with a large number of antennas, and the design uses fully digital implementation.
  • Approach: sCSI-based transmission is used because it varies more slowly than iCSI and can reduce payload computational overhead through less frequent strategy updates.The proposed designs cover downlink precoding, uplink receiving, and user grouping.
  • Results: Closed-form sCSI-based precoders and receivers target ASLNR and ASINR, while SAUG schedules users using channel space-angle information.The sCSI scheme theoretically approaches the iCSI-based one, and SAUG is asymptotically optimal when satellite antennas or UT groups are sufficiently large.
  • Results: The proposed FFR transmission scheme significantly enhances LEO data rates, with sCSI-based precoding and reception achieving performance similar to iCSI-based schemes often infeasible in practice.The achievable-rate lower and upper bounds coincide under the stated large-antenna or large-group conditions.

II. SYSTEM MODEL

The system model considers a LEO satellite with a planar antenna array serving single-antenna UTs. A ray-tracing-based channel represents path gains, Doppler shifts, delays, and array responses, with parameters treated as locally invariant over the interval of interest.

  • A. System Setup: The satellite simultaneously serves multiple single-antenna UTs using a uniform planar array with M = MxMy antennas.Mx and My denote the antenna counts along the x- and y-axes.
  • A. System Setup: The array antennas are separated by one-half wavelength along both axes, and Mx and My are assumed even.The system setup is illustrated in Fig. 1.
  • B. DL Channel Model: The channel between the satellite and each UT is modeled with a ray-tracing-based complex baseband space-domain response.The model represents multiple propagation paths and includes path-dependent channel quantities.
  • B. DL Channel Model: For each propagation path, the model includes complex gain, Doppler shift, propagation delay, and the downlink array-response vector.These quantities characterize the contribution of each path to the channel response.
  • B. DL Channel Model: The physical channel parameters are assumed invariant while relative satellite-UT positions change insignificantly, but they must be updated after large movements.The channel model can apply to different propagation scenarios, with further analysis depending on scenario-specific parameter properties.
  • B. DL Channel Model: Satellite and UT motion contribute to Doppler shifts, while UT-side scattering determines path-dependent Doppler differences and Doppler spread.The satellite-induced Doppler component can be treated as identical across paths of one UT but different across UTs.

2) Delay:

The LEO channel model emphasizes large propagation delays, small delay spreads, and space-angle structure. These properties support a simplified channel representation and asymptotic orthogonality among users as the antenna count grows.

  • Delay: LEO satellite links have much larger propagation delays than terrestrial wireless channels, while their delay spreads can be much smaller.The paper attributes this contrast to the relatively large satellite–UT distance.
  • Angle: Propagation paths associated with one UT can be modeled with identical angles because the satellite altitude is high relative to nearby scatterers.The resulting space-angle parameters characterize propagation in the spatial domain.
  • Angle: As the number of antennas Md tends to infinity, channel direction vectors of different UTs become asymptotically orthogonal.This property follows from the array-response model and underpins spatial separation between users.
  • Channel representation: The channel response is rewritten as a channel gain multiplied by a user-specific channel direction vector, separating gain variation from spatial structure.The representation is introduced to facilitate the later transmission-signal model.

4) Gain:

The paper models LEO channels with line-of-sight and non-line-of-sight components, alongside spatial, temporal, and frequency-domain propagation effects. Doppler and delay compensation at UTs enables OFDM transmission with negligible interference under suitable parameter choices.

  • Gain: LEO satellite systems typically operate under line-of-sight propagation, and the paper considers channels containing both non-shadowed LOS and non-LOS paths.The resulting channel gain is modeled with Rician statistics.
  • Gain: For FDD systems with small carrier-frequency separation, UL and DL physical channel parameters are nearly identical, with fast-fading gains as the major difference.The UL direction vector can be well approximated by the DL direction vector when frequency separation is not significant.
  • Gain: The UL channel direction vectors also exhibit asymptotic orthogonality as the antenna dimensions grow.This parallels the spatial property established for the DL channel.
  • Channel model: The channel and signal models account for LEO propagation properties across space, time, and frequency domains.These models support the demodulated DL and UL transmission representations.
  • Transmission model: After proper UT-side delay and Doppler compensation, selecting suitable OFDM parameters can make intersymbol and intercarrier interference almost negligible.The OFDM symbol and cyclic-prefix lengths are defined from the sampling interval and their respective sample counts.

III. STATISTICAL CSI BASED DL/UL TRANSMISSIONS

The paper replaces impractical instantaneous-CSI-based DL precoding with a closed-form design using slowly varying statistical CSI. The design maximizes average leakage-aware performance while reducing CSI-estimation and implementation overhead.

  • Motivation: Precise instantaneous CSI is generally infeasible at the satellite transmitter, and frequent iCSI-based vector updates are challenging for practical payloads.The proposed designs therefore use slowly varying sCSI.
  • DL precoder: The DL design begins from SLNR maximization, whose conventional precoder requires iCSI for all users.This motivates the average-SLNR formulation based on long-term channel information.
  • DL precoder: The closed-form sCSI-based DL precoder maximizes each user’s average signal-to-leakage-plus-noise ratio.Proposition 1 gives the maximizing precoding vector and its corresponding maximum ASLNR.
  • DL precoder: The proposed DL design requires channel direction vectors and average channel powers rather than full instantaneous channel realizations.This substantially reduces the number of statistical-CSI parameters that must be estimated.
  • Implementation: Because the sCSI-based precoder is independent of subcarriers and OFDM symbols while statistics remain stable, it reduces DL computational overhead.The paper contrasts this property with the iCSI-based approach.

B. UL Receiver

The UL receiver design similarly replaces frequently updated instantaneous-CSI processing with a closed-form statistical-CSI solution. The paper also establishes a statistical-CSI-based DL–UL duality under matched channel-direction and SNR conditions.

  • UL receiver: Instantaneous-CSI-based UL receiving vectors are difficult to compute and update frequently when satellite payload resources are limited.This motivates the average-SINR formulation using statistical CSI.
  • UL receiver: The closed-form sCSI-based UL receiver maximizes each user’s average signal-to-interference-plus-noise ratio.Its corresponding maximum ASINR is given with the receiver solution.
  • UL receiver: The UL receiver uses channel direction vectors and channel-gain statistics, enabling receiver design without instantaneous CSI.The linear receiver recovers each user’s signal from the satellite’s received UL signal.
  • DL–UL duality: When channel statistics are stable, DL and UL SNRs match, and DL and UL direction vectors coincide, the sCSI-based DL and UL vectors are equal after power normalization.The paper presents this as a DL–UL duality that can further reduce transmission complexity.
  • DL–UL duality: Unlike earlier duality results based on perfect iCSI, this DL–UL duality is established using statistical CSI at the satellite.The distinction is stated explicitly in relation to prior work.

D. Upper Bound of ASLNR/ASINR

The proposed sCSI-based precoder and receiver attain their DL ASLNR and UL ASINR upper bounds when simultaneously served UT channel directions are mutually orthogonal. These conditions become asymptotically attainable with many satellite antennas, motivating space-angle-based user grouping.

  • The DL ASLNR and UL ASINR of every served UT can reach their upper bounds when channel direction vectors are mutually orthogonal.Under these conditions, DL channel leakage and UL inter-user interference can be eliminated.
  • The upper-bound conditions can be asymptotically satisfied as the number of satellite antennas M tends to infinity.This supports the potential of massive MIMO for improving satellite communications.
  • The sCSI-based precoder and receiver approach the iCSI-based designs as M tends to infinity, establishing asymptotic optimality.With sufficiently many antennas, the designs also asymptotically approach fixed DFT-based precoders and receivers.
  • Space angle based user grouping: Exhaustive search for the optimal grouping is generally infeasible because satellite systems contain many UTs.SAUG instead uses channel space angles to pursue near-orthogonal channel directions within each group.
  • Space angle based user grouping: SAUG groups UTs by partitioning the x- and y-axis space-angle ranges into equal sectors, scheduling UTs with suitable channel angles together.The procedure creates at most GxGy groups, while UTs in the same group share time-frequency resources.

B. Achievable Rate Performance

This section bounds the achievable ergodic sum rate of the sCSI-based ASLNR precoder combined with SAUG. The lower and upper bounds coincide asymptotically when satellite antennas or scheduled UT groups are sufficiently numerous.

  • The DL achievable ergodic sum rate under linear sCSI-only precoding is upper bounded, with equality under orthogonal channel-direction conditions.The condition concerns UTs sharing the same time-frequency resource blocks.
  • SAUG seeks orthogonal channel directions among UTs sharing resources, while each beamforming vector aligns with its UT’s channel direction.This combines user scheduling with ASLNR-based precoding design.
  • The achievable-rate lower bound asymptotically equals the upper bound as the relevant channel-direction inner products approach zero.The lower bound is expressed using the minimum user SINR within each group.
  • The proposed SAUG and sCSI-based ASLNR precoding are asymptotically optimal when the number of satellite antennas M and/or scheduled UT groups is sufficiently large.This condition coincides with the upper-bound condition from the ASLNR and ASINR analysis.
  • When the orthogonality conditions are not rigorously satisfied, the proposed sCSI-based designs can mitigate inter-user interference and enhance transmission performance.The paper identifies this non-ideal case as usual in practice.

V. SIMULATION RESULTS

Simulations compare sCSI, iCSI, fixed, and interference-free transmission under FFR and FR4 baselines. The proposed sCSI approach closely matches iCSI, approaches interference-free performance with more groups, and substantially outperforms conventional FR4.

  • The proposed sCSI precoder and receiver achieve almost identical performance to iCSI in both UL and DL with significantly lower computational overhead.Using estimated sCSI from averaging 50 samples causes almost negligible sum-rate loss.
  • With FFR, sCSI-based transmission approaches the interference-free performance as the number of scheduled UT groups increases.This behavior demonstrates the proposed approach’s asymptotic optimality.
  • The gap between fixed and sCSI-based precoding and receiving decreases as scheduled groups increase, especially at low SNR.Fixed vectors become near-optimal when interference is not dominant.
  • The proposed sCSI-based design improves sum rate over conventional FR4, while FFR with SAUG provides especially large gains at high SNR and large Rician factors.FR4 schedules one UT per beam on the same time-frequency resource; the proposed design can also improve FR4 when applied there.
  • At 20 dB SNR and κ = 10 dB, the proposed FFR approach with G = 4 achieves about an eight-fold sum-rate gain over conventional FR4.

VI. CONCLUSION

The paper develops massive MIMO transmission for LEO satellite communications using sCSI and FFR, with channel modeling, closed-form transmission designs, and SAUG user grouping. The proposed approach reaches upper bounds under orthogonal channel-direction conditions, is asymptotically optimal, and improves data rates while approaching iCSI-based performance.

  • VI. CONCLUSION: The paper establishes a massive MIMO channel model for LEO satellite communications and simplifies transmission designs through Doppler and delay compensation at UTs.The model accounts for LEO propagation properties before transmission design.
  • VI. CONCLUSION: Closed-form sCSI-based DL precoders and UL receivers maximize ASLNR and ASINR, respectively, while revealing a duality between the two designs.The designs target low-complexity transmission using statistical rather than instantaneous CSI.
  • VI. CONCLUSION: DL ASLNRs and UL ASINRs reach their upper bounds when simultaneously served UTs have orthogonal channel direction vectors.This channel condition motivates the user-grouping strategy.
  • VI. CONCLUSION: The SAUG approach groups UTs according to space angle to support the proposed transmission scheme.The grouping is motivated by the orthogonality condition for channel direction vectors.
  • VI. CONCLUSION: The proposed massive MIMO transmission approach exploiting sCSI is asymptotically optimal.The conclusion reports this result alongside the channel-condition analysis and simulations.
  • VI. CONCLUSION: The proposed massive MIMO transmission scheme with FFR significantly enhances LEO satellite data rates, while sCSI-based processing achieves similar performance to often-infeasible iCSI-based processing.The conclusion also identifies future work on sCSI estimation, multi-antenna or directive UTs, low-PAPR signals, and multiple LEO satellites.

APPENDIX A

Appendix A proves upper-bound achievability for the DL and relates the result to orthogonality among channel direction vectors. It also derives an upper bound for the achievable ergodic rate.

  • APPENDIX A: The appendix focuses on proving the DL case, with the UL proof obtainable similarly.The proof establishes the DL result as representative of the corresponding UL argument.
  • APPENDIX A: The proposed sCSI-based precoder has an upper-bounded ASLNR, and the proof establishes achievability of that bound.The derivation uses the Sherman–Morrison formula and the precoder definition.
  • APPENDIX A: The upper bound is achieved when the relevant channel direction vectors are orthogonal, expressed through zero cross-inner-products.The condition is stated for every distinct pair of simultaneously served UTs.
  • APPENDIX A: The achievable ergodic rate is upper-bounded using nonnegative squared magnitudes and the Cauchy–Schwarz inequality.The appendix then examines the condition required for this rate bound to be tight.
  • APPENDIX A: The rate-bound equality conditions require the corresponding channel-direction relationship stated in the proof.The appendix concludes the achievability argument after imposing these orthogonality conditions.

APPENDIX C

Appendix C develops matrix and eigenvalue bounds used to analyze the proposed transmission scheme and achievable DL rates. The derivation combines quotient, perturbation, and diagonal-dominance arguments.

  • APPENDIX C: The appendix introduces auxiliary variables and matrix representations to analyze ASLNR expressions for a specific UT group.It focuses on the (g,r)th group and temporarily omits the group index.
  • APPENDIX C: UTs in different groups use different time-frequency transmission resources, separating those groups in the rate analysis.This scheduling structure is incorporated into the DL signal and sum-rate derivations.
  • APPENDIX C: The appendix derives inequalities for matrix entries and eigenvalue-related quantities under bounds on off-diagonal terms and group size.The resulting relations are used to control interference-related expressions.
  • APPENDIX C: The analysis uses Gershgorin disc, Wielandt, Weyl, and Rayleigh quotient results to bound eigenvalues and quadratic forms.These inequalities support bounds involving the largest and smallest eigenvalues of the constructed matrix.
  • APPENDIX C: The appendix combines the derived bounds to obtain a lower bound on the DL rate and establishes its limiting behavior.The final steps use the bounds on the relevant auxiliary terms as epsilon approaches zero.
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