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Protocols for Relay-Assisted Free-Space Optical Systems

Nestor D. Chatzidiamantis, Diomidis S. Michalopoulos, Emmanouil E. Kriezis, George K. Karagiannidis, Robert Schober

arXiv:1105.3835v1cs.ITmath.IT

TL;DR

FSO performance is affected by atmospheric effects, and all-active relaying requires synchronized relay transmissions. The paper evaluates relay protocols and power allocation, reporting select-max gains over all-active relaying in the examined cases.

  • Problem

    Atmospheric effects degrade FSO performance, while all-active relaying requires relay transmissions to arrive simultaneously.

    Source: §I · pp. 2–3

  • Method

    The numerical analysis compares relaying protocols and power-allocation schemes, with DSSC using CSI from the previous transmission slot and the two paths of minimum end-to-end distance.

    Source: §V · pp. 17–18, §VI · p. 19

  • Results

    Select-max outperforms all-active relaying in every examined case, with gains of 2, 4, and 5 dB for N = 2, 3, and 4, respectively.

    Source: §V · p. 17

  • Takeaways & Limitations

    Suboptimum power allocation is presented as a less complex alternative to optimum power allocation.

    Source: §V · p. 18

    The numerical evaluation assumes clear weather and ρ_SR_i = ρ_R_iD = 1.

    Source: §V · p. 17

Abstract

from arXiv · show

We investigate transmission protocols for relay-assisted free-space optical (FSO) systems, when multiple parallel relays are employed and there is no direct link between the source and the destination. As alternatives to all-active FSO relaying, where all the available relays transmit concurrently, we propose schemes that select only a single relay to participate in the communication between the source and the destination in each transmission slot. This selection is based on the channel state information (CSI) obtained either from all or from some of the FSO links. Thus, the need for synchronizing the relays' transmissions is avoided and the slowly varying nature of the atmospheric channel is exploited. For both relay selection and all-active relaying, novel closed-form expressions for their outage performance are derived, assuming the versatile Gamma-Gamma channel model. Furthermore, based on the derived analytical results, the problem of allocating the optical power resources to the FSO links is addressed, and optimum and suboptimum solutions are proposed. Numerical results are provided for equal and non-equal length FSO links, which illustrate the outage behavior of the considered relaying protocols and demonstrate the significant performance gains offered by the proposed power allocation schemes.

I. INTRODUCTION

Atmospheric effects degrade FSO links, while practical MIMO systems can require many apertures over long distances and become complex. The paper proposes single-relay protocols that avoid relay synchronization, derives outage expressions, and optimizes optical power allocation.

I. INTRODUCTION

  • Atmospheric phenomena such as rain, fog, and turbulence attenuate FSO signals and fluctuate received optical power, degrading performance.The introduction also notes practical MIMO limitations: independent fading may not hold, and long-range links can require many apertures, increasing system complexity.Source: §I · p. 2
  • Relay-assisted communication uses multiple relays with line-of-sight to the source and destination to create a virtual multiple-aperture system without a direct source-destination link.This is presented as an alternative way to achieve spatial diversity.Source: §I · p. 2
  • Single-relay selection avoids synchronizing relay transmissions while using CSI from all links or only selected links.The select-max protocol uses CSI from all available FSO links; DSSC uses CSI from the links used in the previous slot.Source: §I · p. 3
  • The paper derives closed-form outage expressions for relay-selection and all-active protocols under the Gamma-Gamma channel model.The analysis assumes decode-and-forward relays.Source: §I · p. 3
  • The paper uses the derived outage results to optimize optical power allocation across FSO links to minimize outage probability.It proposes optimum and suboptimum allocation solutions.Source: §I · p. 3

II. SYSTEM MODEL

The system uses multiple relays to connect source and destination without a direct line-of-sight link. Its channel model accounts for atmospheric turbulence and treats channel gain as constant within a transmission slot.

II. SYSTEM MODEL

  • The model considers an intensity-modulation/direct-detection FSO system in which multiple relays connect source and destination without a direct line-of-sight link.The source has multiple transmitter apertures aimed at the corresponding relays, with an optical switch for selecting or simultaneously enabling transmission.Source: §II · pp. 3–4
  • Relays use threshold-based decode-and-forward: they decode a received signal and retransmit it only when the incoming-link SNR exceeds a decoding threshold.The model assumes binary pulse position modulation and a large field-of-view detector at the destination.Source: §II · p. 4

A. Signal and Channel Model

  • The signal model assumes background-noise-limited receivers, with additive white Gaussian noise in the signal and non-signal slots.The channel model distinguishes path loss and geometric spread from turbulence-induced irradiance fluctuations.Source: A. Signal and Channel Model · p. 4
  • The channel gain is treated as constant within a transmission slot because atmospheric channel variation is slow relative to the signaling interval.The model represents channel gain with path loss and turbulence-induced irradiance fluctuations, and characterizes turbulence with the Gamma-Gamma distribution.Source: A. Signal and Channel Model · pp. 4–5

B. Mode of Operation

The paper compares all-active relaying with select-max and DSSC, which each activate one relay per transmission slot. All-active relaying requires synchronization, whereas single-relay operation avoids it.

1) All-active:

  • All-active relaying activates all available relays and divides total optical power among the FSO links, but requires accurate timing synchronization for simultaneous signal arrival.Only relays that decode successfully forward the signal; the destination combines their received signals.Source: 1) All-active · pp. 5–6

2) Select-Max:

  • Select-max activates the relay with the strongest end-to-end metric, using CSI from all source-relay and relay-destination links.Its min-equivalent-SNR metric is the minimum of the two intermediate-link SNRs; activating one path removes the need for relay synchronization.Source: 2) Select-Max · p. 6

3) DSSC:

  • The same total optical-power allocation rule applies to select-max and DSSC because each protocol activates only one relay.DSSC’s reduced CSI requirement comes with its use of only the two selected paths.Source: 2) Select-Max · p. 6, 3) DSSC · p. 7
  • DSSC switches between two relays when the active path’s min-equivalent SNR falls below a switching threshold, and requires CSI only for the active path.For more than two relays, it uses the two paths with the minimum end-to-end distance; the method reduces implementation complexity and needs no relay synchronization.Source: 3) DSSC · p. 7

III. OUTAGE ANALYSIS

Outage is tied to whether received SNR falls below a threshold set by the transmission rate. The analysis builds relaying outage probabilities from intermediate-link outage probabilities under the Gamma-Gamma model.

III. OUTAGE ANALYSIS

  • At a given transmission rate, outage occurs when instantaneous SNR falls below the corresponding threshold SNR.The threshold is assumed identical across all links in the relaying system.Source: §III · p. 8

A. Outage Probability of the Intermediate Links

  • Intermediate-link outage probability is a building block for calculating the overall outage probability of decode-and-forward relaying schemes.The link outage expression is obtained by combining the channel model with the SNR-threshold condition and is expressed for the Gamma-Gamma model.Source: A. Outage Probability of the… · p. 8
  • The high-power outage analysis assumes that (α_AB − β_AB) /∈ Z for every possible FSO link.The text says this condition can be relaxed in practice by adding an arbitrarily small perturbation when the difference is an integer.Source: A. Outage Probability of the… · pp. 8–9

B. Outage Probability of All-Active Relaying

The section derives exact and high-power-margin outage analyses for all-active relaying under Gamma-Gamma fading. Its asymptotic analysis also establishes diversity-gain results for the protocol.

1) Exact Analysis:

  • Because no closed-form exact distribution is available for sums of non-identical Gamma-Gamma variates, the analysis evaluates their cdf numerically through an MGF-based method.Source: 1) Exact Analysis · p. 9
  • Theorem 2 gives an outage-probability expression for all-active relaying in Gamma-Gamma fading.Source: 1) Exact Analysis · p. 10

2) Asymptotic Analysis:

  • At high power margin, the section derives an asymptotic outage expression and a corresponding diversity-gain result for all-active relaying.Source: 2) Asymptotic Analysis · pp. 10–12

C. Outage Probability of Select-Max Relaying

Select-max relaying chooses one relay according to its selection rule, and the section analyzes its outage probability under Gamma-Gamma fading. It also derives high-power-margin outage and diversity-gain results.

C. Outage Probability of Select-Max Relaying

1) Exact Analysis:

  • Theorem 5 provides an outage-probability expression for select-max relaying under Gamma-Gamma turbulence-induced fading.Source: 1) Exact Analysis · pp. 11, 13

2) Asymptotic Analysis:

  • The high-power-margin analysis derives an asymptotic outage expression and a diversity-gain result for select-max relaying.Source: 2) Asymptotic Analysis · p. 12

D. Outage Probability of DSSC Relaying

The section analyzes DSSC outage performance and its high-power behavior, then turns to optical-power allocation under a total-power constraint. It describes an all-active allocation approach that uses an asymptotic outage expression when the exact optimization is difficult.

1) Exact Analysis:

  • Theorem 7 gives an outage-probability expression for DSSC relaying, and the minimum outage occurs at T̄ = P_M, where DSSC matches select-max relaying with two relays.Source: 1) Exact Analysis · p. 13

2) Asymptotic Analysis:

  • At high power margin, minimum DSSC outage is approximated by the select-max expression for N = 2, with a corresponding maximum diversity-gain result.Source: 2) Asymptotic Analysis · p. 14

IV. OPTIMAL POWER ALLOCATION

  • The power-allocation objective is to minimize system outage across source–relay and relay–destination links for a given total optical power.Source: §IV · p. 14

A. Power Allocation in All-Active Protocol

B. Power Allocation in Select-Max Protocol

For select-max relaying, the section formulates optical-power allocation across the active relay’s two links and presents optimum and suboptimal schemes. The exact outage expression is difficult to optimize, so the asymptotic expression is used for the optimization formulation.

B. Power Allocation in Select-Max Protocol

C. Power Allocation in DSSC Protocol

Select-max outperforms all-active relaying in the reported equal- and unequal-distance configurations, while optimized power allocation improves outage performance over equal allocation. DSSC can reuse select-max power-allocation schemes, but its performance does not improve when longer paths are added.

C. Power Allocation in DSSC Protocol

  • DSSC power allocation minimizes outage on the active end-to-end path, so the select-max optimum and suboptimum allocation schemes also apply.The optimization problem is stated to be equivalent to the select-max problem.Source: C. Power Allocation in DSSC Protocol · p. 17

V. NUMERICAL RESULTS AND DISCUSSION

  • Analytical and Monte Carlo simulation results agree excellently for the considered relay counts and configurations.The reported agreement verifies the theoretical analysis and is observed again for unequal link distances.Source: §V · pp. 17–18
  • Select-max relaying outperforms all-active relaying, with observed performance gains of 2, 4, and 5 dB for N = 2, 3, and 4, respectively.Source: §V · p. 17
  • For non-equal link distances, the first and second configurations provide gains of 2.5 dB and 3 dB, respectively, compared with the all-active scheme.Source: §V · p. 18
  • DSSC's optimized-threshold performance remains unchanged as relays are added because it uses only the two paths with minimum end-to-end distance.Adding paths with larger end-to-end distances does not improve this protocol's performance.Source: §V · p. 18
  • Optimized power allocation significantly outperforms equal allocation across the considered relaying protocols, and even the suboptimal schemes improve performance.The authors attribute the gains to accounting for distance-dependent path loss and turbulence strength; the suboptimal schemes use parameters based on link distances.Source: §V · p. 18

VI. CONCLUSIONS

For relay-assisted FSO systems without a direct source-destination link, the paper analyzes all-active and single-relay selection protocols under the Gamma-Gamma channel model. Select-max offers performance gains over all-active relaying at the cost of CSI from all links, while DSSC uses less CSI but only two minimum-distance paths.

VI. CONCLUSIONS

  • The study considers relay-assisted FSO systems without a direct link and derives closed-form outage expressions for the considered protocols under the Gamma-Gamma model.The protocols include all-active relaying and alternatives that activate one relay per transmission slot.Source: §VI · p. 19
  • Single-relay selection avoids synchronizing relay transmissions, reducing implementation complexity relative to concurrent all-active transmission.The avoided synchronization is the timing needed for FSO signals to arrive simultaneously at the destination.Source: §VI · p. 19
  • Select-max gains performance over all-active relaying but requires CSI from all available links; DSSC needs less CSI but exploits only the two shortest end-to-end paths.DSSC uses CSI only from links involved in the previous transmission slot.Source: §VI · p. 19
  • Optimum and suboptimum power-allocation solutions are derived for each considered protocol, and numerical results show improved power efficiency.The allocations are based on the derived outage-probability expressions.Source: §VI · p. 19

APPENDIX I

The appendices derive outage and asymptotic expressions from Gamma-Gamma channel distributions. They use series representations and Laplace transforms to obtain the relevant density and distribution expressions.

APPENDIX I

  • The Appendix I outage probability for an FSO link is obtained by integrating the Gamma-Gamma density series over the outage range.The passage identifies the outage probability as the integral from zero to the normalized outage threshold.Source: Appendix I · p. 19
  • At high power margin, the l = 0 term dominates the outage series, yielding the stated asymptotic expression after algebraic reduction.The derivation then uses Euler's reflection formula and introduces pAB and qAB.Source: Appendix I · p. 19

APPENDIX II

  • Appendix II obtains the density and CDF expressions by transforming a Gamma-Gamma series representation through Laplace and inverse Laplace transforms.Keeping only the dominant term yields the asymptotic CDF expression.Source: APPENDIX II · p. 20
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