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Performance Characterization of Relay-Assisted Wireless Optical CDMA Networks in Turbulent Underwater Channel

Mohammad Vahid Jamali, Farhad Akhoundi, Jawad A. Salehi

arXiv:1508.04030v3cs.ITmath.IT

TL;DR

UWOC links are typically limited to ranges below 100 m by absorption, scattering, and turbulence. The paper models relay-assisted OCDMA over turbulent underwater channels and evaluates multi-hop transmission. In a 90 m clear-ocean point-to-point link, dual-hop transmission improves BER by 32 dB at 10^-6.

  • Problem

    UWOC is typically suitable only for ranges below 100 m, with absorption, scattering, and turbulence impairing received signals.

    Source: §I · p. 1

  • Method

    The paper models relay-assisted OCDMA networks over underwater channels and uses chip detect-and-forward relays with Gaussian approximation based on photon-counting to evaluate end-to-end BER.

    Source: §V · p. 12

  • Results

    32 dB improvement in the BER of 10^-6 is achieved using dual-hop transmission in a 90 m clear-ocean point-to-point link.

    Source: §IV · p. 11

  • Takeaways & Limitations

    Dividing a long communication distance into shorter hops yields reduced absorption, scattering, and fading effects on each hop.

    Source: §V · p. 12

    The simple receiver decision rule provides an upper bound on BER; an optimum threshold based on interfering users and channel conditions would yield lower BER.

    Source: §IV · p. 10

Abstract

from arXiv · show

In this paper, we characterize the performance of relay-assisted underwater wireless optical code division multiple access (OCDMA) networks over turbulent channels. In addition to scattering and absorption effects of underwater channels, we also consider optical turbulence as a log-normal fading coefficient in our analysis. To simultaneously and asynchronously share medium among many users, we assign a unique optical orthogonal code (OOC) to each user in order to actualize OCDMA-based underwater network. The most significant challenge in underwater optical communication is in the ability to extend the short range of its coverage. In order to expand the viable communication range, we consider multi-hop transmission to the destination. Moreover, we evaluate the performance of a relay-assisted point-to-point UWOC system as a special case of the proposed relay-assisted OCDMA network. Our numerical results indicate significant performance improvement by employing intermediate relays, e.g., one can achieve $32$ {dB} improvement in the bit error rate (BER) of $10^{-6}$ using only a dual-hop transmission in a $90$ {m} point-to-point clear ocean link.

I. INTRODUCTION

UWOC links are typically shorter than 100 m because absorption, scattering, and turbulence impair signals, and the paper proposes relay-assisted multi-hop transmission to extend viable range. It models underwater optical turbulence as log-normal fading alongside absorption and scattering.

I. INTRODUCTION

  • UWOC is typically suitable only for ranges below 100 m, with absorption, scattering, and turbulence causing loss, inter-symbol interference, and fading, respectively.The paper notes that these impairments hinder wider use of UWOC.Source: §I · p. 1
  • Prior work on underwater fading had received relatively less attention than free-space optical turbulence, while earlier OCDMA-based UWOC work considered user-specific OOCs.The paper studies relay-assisted OCDMA over turbulent underwater channels.Source: §I · p. 1
  • Dividing long links into shorter relay hops is proposed to reduce the absorption, scattering, and fading effects that increase with distance.The introduction presents an underwater optical sensor network as an example topology.Source: §I · p. 1

A. Channel Model

  • The channel model combines a Monte Carlo absorption-and-scattering impulse response with a positive multiplicative fading coefficient modeled as log-normal under weak oceanic turbulence.The fading coefficient represents optical turbulence effects on the fading-free impulse response.Source: A. Channel Model · p. 2
  • Turbulence severity depends on oceanic parameters, and strong turbulence can occur over ranges as short as 10 m or as long as 100 m.The authors state that alleviating such strong turbulence requires further study.Source: A. Channel Model · p. 3

B. System Model

The system assigns optical orthogonal codes to users and places serial relays between users and the destination. Relays use chip detect-and-forward, while the model also specifies signal timing, noise, and link-design considerations.

B. System Model

  • Each user receives a specific OOC for simultaneous, asynchronous access, with code weight W and length F = Tb/Tc, and the allowable user count is bounded by code-correlation constraints.The codes have autocorrelation and cross-correlation constraints λa and λc equal to unity.Source: B. System Model · p. 3
  • Serial relays use chip detect-and-forward, detecting received chips with a threshold and forwarding them to the next node; multiple-access interference affects only the first relay's chip detection.The topology can also accommodate cases without line of sight to the destination.Source: B. System Model · p. 3
  • Users' received contributions are aggregated at the first relay, with each user's delay measured relative to its receiver clock and assumed chip-synchronous at an integer multiple of Tc.The model includes OOK modulation for transmitted bits.Source: B. System Model · pp. 3–4
  • The model adopts Poisson-distributed background light and dark current, and Gaussian-distributed thermal noise.Source: B. System Model · p. 4
  • The analysis supports collimated lasers or diffusive LEDs, while the authors favor wider divergence and larger-FOV first-hop links for mobile users to ease pointing and tracking.For fixed intermediate relays, narrower collimated links are described as more suitable for energy savings and reduced channel temporal spreading.Source: B. System Model · p. 4

III. BER PERFORMANCE ANALYSIS

The BER analysis averages conditional bit-error probabilities for a desired user under equal bit probabilities. It introduces simplifying assumptions, including confinement of the received signal's main energy to one chip interval.

III. BER PERFORMANCE ANALYSIS

  • The desired user's average BER is evaluated assuming transmitted bits 0 and 1 are equally probable.The average combines the conditional errors Pbe(1|0) and Pbe(0|1).Source: §III · p. 4
  • The analysis obtains Pbe(1|0) and Pbe(0|1) after introducing two simplifying assumptions.Source: §III · p. 4
  • One stated assumption confines the main portion of received optical-signal energy to the interval (0, Tc).Source: 1) No Inter-Symbol Interference (ISI) · p. 4

1) No Inter-Symbol Interference (ISI):

The analysis treats ISI as negligible under its stated assumptions and constrains the chip period according to channel delay spread. Greater range, turbidity, beam divergence, or receiver FOV can require a larger chip period and limit data rate.

1) No Inter-Symbol Interference (ISI):

  • Under the stated assumption, ISI has a negligible effect, and the data rate is kept within the bound specified by (11).The channel delay spread is assumed much smaller than Tc.Source: 1) No Inter-Symbol Interference (ISI) · p. 4
  • Longer range, greater turbidity, or wider transmitter beam divergence increase attenuation and time spreading; a larger Tc then limits transmission data rate.A larger receiver FOV also increases channel spreading time.Source: 1) No Inter-Symbol Interference (ISI) · p. 4
  • All users transmit with power Pc, and each relay forwards detected ON chips with power Pc.Source: 2) Identical Chip Power · p. 4

2) Identical Chip Power:

The analysis carries the preceding assumptions into its BER treatment of both transmission directions.

2) Identical Chip Power:

A. Uplink BER Analysis

The uplink analysis models asynchronous users as multiple-access interference on the desired user's signal and averages error rates over interference patterns and fading. It uses a conservative chip-error approximation across relay hops and calculates each hop's errors using a Gaussian approximation.

A. Uplink BER Analysis

  • The uplink received signal at R1 is analyzed for the desired user's transmitted bit while asynchronous transmissions from other users create MAI.Source: A. Uplink BER Analysis · p. 4
  • The interference pattern α records interferers on each pulsed mark chip, while l counts total interferers and follows a binomial distribution.The joint distribution of interference patterns is represented using,.Source: A. Uplink BER Analysis · pp. 4–5
  • The BER is evaluated conditional on the number and pattern of interferers, then averaged over those conditions and the fading-coefficient vector.The fading vector may differ between uplink and downlink configurations.Source: A. Uplink BER Analysis · p. 5
  • The receiver decides bit 1 only when all detected chips are ON, imposing stricter detection on bit 1 to address MAI's greater risk to OFF chips.The decision rule follows the methodology in and.Source: A. Uplink BER Analysis · p. 5
  • End-to-end chip errors are approximated as correct only when no error occurs on any intermediate hop, neglecting cases where later detection could correct an earlier error.Each intermediate hop's conditional chip-error rate is calculated, using a Gaussian approximation for the first hop that is described as acceptable especially below error probability 0.1.Source: A. Uplink BER Analysis · p. 5, 1) Conditional CER Analysis for the… · p. 5

1) Conditional CER Analysis for the First Hop:

The first-hop conditional chip-error analysis models desired and interfering received counts, approximates the interference fading contribution as log-normal, and uses a Gaussian receiver model to set the detection threshold.

1) Conditional CER Analysis for the First Hop:

  • The first-hop received-count model includes desired and interfering-user contributions, with dark-current and background-light counts included in the received counts.Source: 1) Conditional CER Analysis for the… · pp. 5–6
  • The interference contribution on a pulsed chip is a weighted sum of αq independent log-normal fading variables, approximated by a single log-normal random variable.The weights include aggregated first-hop channel loss for the interfering users.Source: 1) Conditional CER Analysis for the… · p. 6
  • The first-hop receiver uses a Gaussian approximation for conditional chip errors and sets its threshold from the OFF and ON decision-variable means and standard deviations.The approximation replaces Poisson random variables with Gaussian variables of equal mean and variance.Source: 1) Conditional CER Analysis for the… · p. 6
  • The first-hop receiver is synchronized to the desired user and is assumed to know its fading coefficient perfectly.Source: 1) Conditional CER Analysis for the… · p. 6

2) Conditional CER Analysis for the i-th Hop (i=2,...,N+1):

For hops i=2,...,N+1, turbulence and noise affect chip detection, while MAI does not. Conditional chip error probabilities are used to obtain end-to-end CER and BER under fading.

2) Conditional CER Analysis for the i-th Hop (i=2,...,N+1):

B. Downlink BER Analysis

The downlink analysis uses OOC code orthogonality to eliminate MAI under a stated user-count condition, then combines hop-level errors to evaluate end-to-end CER and BER.

B. Downlink BER Analysis

  • Synchronous downlink MAI can be eliminated when the number of concurrent users satisfies the stated condition.Source: B. Downlink BER Analysis · p. 7
  • With nonoverlapping OOC codes, the inner product between distinct users' codes is zero, allowing first-hop chip error probabilities to be derived like those for intermediate hops.Source: B. Downlink BER Analysis · p. 7
  • First-hop conditional chip errors use average received counts for transmitting OFF and ON chips; other hops use the uplink conditional CER formulation.Source: B. Downlink BER Analysis · p. 7
  • Combining hop conditional CERs yields end-to-end CER and BER, with BER averaged over an (N+1)-dimensional vector of independent fading coefficients.Source: B. Downlink BER Analysis · p. 7

C. Single-User Multi-Hop Point-to-Point UWOC Link

The single-user point-to-point link is treated as a special case of the relay-assisted analysis. Its end-to-end BER is assembled from hop-level errors and averaged over fading.

C. Single-User Multi-Hop Point-to-Point UWOC Link

  • Setting M=1, F=W=1, and Tc=Tb specializes the relay-assisted OCDMA analysis to a single-user point-to-point link with bit-detect-and-forward relaying.Source: C. Single-User Multi-Hop… · p. 7
  • The end-to-end BER combines conditional per-hop bit errors and averages them over independent fading coefficients.Source: C. Single-User Multi-Hop… · p. 7
  • Averaging the single-user BER reduces the calculation to one-dimensional integrals, unlike the J-dimensional uplink or (N+1)-dimensional downlink integrals.Source: C. Single-User Multi-Hop… · p. 7
  • The paper uses Gaussian approximation as a relatively accurate, faster photon-counting method, and Gauss-Hermite quadrature approximates multidimensional integrals with finite series.Source: C. Single-User Multi-Hop… · pp. 7–8

IV. NUMERICAL RESULTS

Multi-hop relay assistance improves BER and extends viable communication range in clear-ocean UWOC links, including point-to-point and OCDMA networks. The results also show that user interference, turbulence, beam divergence, and relay placement affect performance.

Channel and turbulence characterization

  • Increasing χT and w strengthens fading, while smaller ε is associated with a smaller scintillation index; at 90 m, the clear-ocean impulse response is approximately an ideal delta function.The impulse-response result supports the paper's use of Tc = 10 ns and a 2 Mbps user data rate.Source: §IV · pp. 8–9, Figure 4 · p. 9, Figure 3 · p. 9

User interference and thermal noise

  • For M ≤ W, MAI does not affect uplink performance; when M exceeds W, BER saturates, with higher saturation as user count rises and larger BER at higher thermal noise variance.The reported M = 4 interference pattern (1, 1, 1) contributes 8.1 × 10^-5 to BER.Source: Figure 5 · p. 9, §IV · p. 9

Direct-link performance and approximation

  • Increasing the direct-link range severely degrades uplink BER, while analytical and numerical results match well, supporting the derived expressions and log-normal-sum approximation.The approximation is more beneficial when M ≥ W + 1, reducing integral dimension from M + N to W + 1 + N.Source: Figure 6 · p. 10, §IV · p. 10

Relay-assisted OCDMA uplink

  • 30 dB improvement in BER at 10^-3 is reported for dual-hop uplink OCDMA transmission over a 90 m link with five users.Multi-hop performance is approximately that of a single-hop link spanning d0/(N + 1) with about 10 log10(N + 1) dB greater average transmitted power per bit.Source: Figure 7 · p. 10, §IV · p. 10

Relay-assisted OCDMA downlink

  • 32.5 dB improvement in BER at 10^-6 is reported for downlink transmission with one intermediate relay.The synchronous downlink scenario satisfies the stated inequality and does not suffer from MAI; the paper reports it can outperform uplink when M ≥ W + 1.Source: Figure 8 · p. 10, §IV · pp. 10–11

Point-to-point relay-assisted UWOC

  • 32 dB improvement in BER at 10^-6 is achieved with dual-hop transmission on a 90 m clear-ocean, single-user point-to-point link.The result is reported for a 100 Mbps link; Fig. 9 presents BER performance for N = 0, 1, 2, 3, and 4 relays.Source: Figure 9 · p. 11, §IV · p. 11

Communication range

  • A three-relay point-to-point system is reported to support a 280 m clear-ocean link with realistic average transmitted power per bit and acceptable BER.The reported achievable distances extend beyond the paper's stated typical UWOC range of less than 100 m.Source: Figure 10 · p. 11, §IV · p. 11

Diffusive links and relay placement

  • About 7.5 dB better performance at BER 10^-6 is reported for relay-placement Mode IV than Mode VI with diffusive first and last hops.Increasing the divergence angle of those hops degrades performance, while the reported placement differences grow with total range and divergence angle; 90 m channel spreading remains negligible relative to chip duration in the diffusive-link analysis.Source: §IV · pp. 11–12, Figure 12 · p. 12

V. CONCLUSIONS

The paper evaluates relay-assisted OCDMA underwater networks for uplink and downlink, including a point-to-point system as a special case. Its numerical results show that relays improve BER, particularly over longer links, and that relay placement can affect performance.

V. CONCLUSIONS

  • 32.5 dB performance enhancement was obtained with one intermediate relay for downlink transmission over a 90 m clear ocean link at BER 10^-6.The paper also reports that relay placement can have an optimal point from the BER perspective.Source: §V · p. 12
  • When simultaneous users exceed the code weight, uplink BER saturates while downlink BER remains unchanged because synchronous downlink transmission removes MAI.Source: §V · p. 12
  • The analysis uses chip detect-and-forward relays and Gaussian approximation based on photon-counting methods to estimate hop chip-error probabilities and end-to-end BER.Source: §V · p. 12
  • For user counts at or below the code weight, MAI does not affect performance and uplink and downlink have the same end-to-end BER.Source: §V · p. 12
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