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MIMO Underwater Visible Light Communications: Comprehensive Channel Study, Performance Analysis, and Multiple-Symbol Detection

Mohammad Vahid Jamali, Pooya Nabavi, Jawad A. Salehi

arXiv:1704.00909v2cs.ITmath.IT

TL;DR

Underwater visible-light links are affected by turbulence-induced fading and channel impairments that degrade BER. The paper evaluates UVLC links with spatial-diversity configurations and Gauss-Hermite BER calculations; its reported results show diversity gains and improved performance with generalized multiple-symbol detection.

  • Problem

    Underwater turbulence can cause strong fading even at distances of 10–100 m, and diffusive links can have greater attenuation and delay spread than collimated links.

    Source: B. Turbulence Effects of UVLC Channels · p. 3, §VI · p. 10

  • Method

    The study evaluates BER for spatial-diversity configurations and uses Gauss-Hermite quadrature to approximate BER integrals.

    Source: §VI · p. 13

  • Results

    A 3 × 1 MISO transmission provides about 8 dB gain at BER 10^-9 versus SISO, and GMSD improves BER over symbol-by-symbol detection for the considered link conditions.

    Source: §VI · pp. 13–14

  • Takeaways & Limitations

    Spatial diversity mitigates fading impairments, while generalized multiple-symbol detection alleviates ISI and can make reliable communication possible under the considered link conditions.

    Source: §VI · pp. 13–14

Abstract

from arXiv · show

In this paper, we analytically study the bit error rate (BER) performance of underwater visible light communication (UVLC) systems with binary pulse position modulation (BPPM). We simulate the channel fading-free impulse response (FFIR) based on Monte Carlo numerical method to take into account the absorption and scattering effects. Additionally, to characterize turbulence effects, we multiply the aforementioned FFIR by a fading coefficient which for weak oceanic turbulence can be modeled as a lognormal random variable (RV). Moreover, to mitigate turbulence effects, we employ multiple transmitters and/or receivers, i.e., spatial diversity technique over UVLC links. Closed-form expressions for the system BER are provided, when equal gain combiner (EGC) is employed at the receiver side, thanks to Gauss-Hermite quadrature formula and approximation to the sum of lognormal RVs. We further apply saddle-point approximation, an accurate photon-counting-based method, to evaluate the system BER in the presence of shot noise. Both laser-based collimated and light emitting diode (LED)-based diffusive links are investigated. Since multiple-scattering effect of UVLC channels on the propagating photons causes considerable inter-symbol interference (ISI), especially for diffusive channels, we also obtain the optimum multiple-symbol detection (MSD) algorithm to significantly alleviate ISI effects and improve the system performance. Our numerical analysis indicates good matches between the analytical and photon-counting results implying the negligibility of signal-dependent shot noise, and also between analytical results and numerical simulations confirming the accuracy of our derived closed-form expressions for the system BER. Besides, our results show that spatial diversity significantly mitigates fading impairments while MSD considerably alleviates ISI deteriorations.

I. INTRODUCTION

Absorption, scattering, and turbulence degrade underwater visible-light links through loss, inter-symbol interference, and fading, motivating channel-aware transmission and reception methods. The paper studies collimated and diffusive links and uses Monte Carlo photon tracking to model absorption- and scattering-affected channel impulse responses.

I. INTRODUCTION

  • Absorption, scattering, and turbulence cause loss, inter-symbol interference, and fading, limiting typical UVLC communication ranges to less than 100 m.The introduction motivates intelligent system design and efficient transmission and reception to address this range constraint.Source: §I · p. 1
  • Earlier work modeled absorption and scattering, simulated UVLC impulse responses, and evaluated BER without turbulence; this paper broadens the study to turbulence and system configurations.Prior work also modeled MIMO impulse responses and examined UVLC networks and multi-hop systems.Source: §I · p. 1
  • The study investigates collimated laser and diffusive LED links, MIMO mitigation of turbulence-induced fading, and multiple-symbol detection for inter-symbol interference.The proposed detection algorithms, including generalized MSD, assume no channel state information; BPPM is noted as not requiring CSI for detection.Source: §I · p. 2

A. FFIR Simulation Using Monte Carlo Method

  • Absorption and scattering depend on wavelength and water type, and their effects are lowest in the 400–530 nm interval used by UVLC systems.Absorption removes photon energy, while scattering changes photon direction and can contribute to energy loss and ISI.Source: A. FFIR Simulation Using Monte Carlo… · p. 2
  • Monte Carlo photon tracking produces the fading-free impulse response by recording detected-photon weights across propagation-time bins.Photons are tracked until reaching the receiver plane or falling below a weight threshold, then filtered by aperture and field of view.Source: A. FFIR Simulation Using Monte Carlo… · p. 2
  • For laser and LED links, the main difference in the Monte Carlo simulation is the emitted photons’ initial direction.The paper models lasers as narrow Gaussian beams and LEDs as generalized Lambertian sources.Source: A. FFIR Simulation Using Monte Carlo… · pp. 2–3

B. Turbulence Effects of UVLC Channels

The paper models underwater optical turbulence as multiplicative fading of the channel impulse response. Weak oceanic turbulence is represented by a lognormal fading coefficient, while strong turbulence can arise over distances as short as 10 m in the cited results.

B. Turbulence Effects of UVLC Channels

  • Optical turbulence arises from random refractive-index variations and is modeled by multiplying the fading-free impulse response by a positive fading coefficient.The passage attributes underwater refractive-index variations mainly to temperature and salinity fluctuations.Source: B. Turbulence Effects of UVLC Channels · p. 3
  • The channel coherence time is much longer than typical delay spread, supporting a channel model with one fading coefficient multiplying the fading-free impulse response.The cited coherence-time range is 10^-5 to 10^-2 seconds, while typical delay spreads are mainly below tens of nanoseconds.Source: B. Turbulence Effects of UVLC Channels · p. 3
  • Strong underwater turbulence, defined by scintillation index above 1, can occur at distances from 10 m to 100 m, motivating advanced mitigation such as MIMO.The cited strong-turbulence distances differ from atmospheric channels, where they are on the order of kilometers.Source: B. Turbulence Effects of UVLC Channels · p. 3
  • For lognormal fading, the scintillation index is related to log-amplitude variance by σ^2_Iij = exp(4σ^2_Xij) − 1.The log-amplitude mean is normalized so the fading amplitude has mean one.Source: B. Turbulence Effects of UVLC Channels · p. 3

C. System Model

The system model combines BPPM signaling, multiple transmitters and receiver apertures, and equal-gain combining over channels with fading and multipath response. The BER analysis assumes additive Gaussian noise and bit-by-bit detection for the SISO case, which is suboptimal when ISI is present.

C. System Model

  • The modeled UVLC system uses M transmitters, N receiver apertures, equal-gain combining, and intensity modulation with direct detection and BPPM.Each transmitter-to-receiver channel combines a fading coefficient with its fading-free impulse response.Source: C. System Model · p. 3
  • Multiple scattering lets portions of every transmitter’s signal reach each receiver, producing inter-symbol interference in the received signal.The BPPM data stream selects one of two pulse shapes for each bit slot.Source: C. System Model · p. 4

III. ANALYTICAL STUDY OF THE BER

  • The BER analysis treats incoming optical signal as constant conditional on fading and aggregates noise as additive white Gaussian noise with signal-independent variance.This analysis assumes signal-dependent shot noise has negligible effect compared with other noise components.Source: §III · p. 4

A. SISO-UVLC

  • In SISO bit-by-bit detection, the receiver compares integrated current across the first and second halves of each slot, a suboptimal approach in the presence of ISI.The same fading coefficient is assumed for consecutive bits because channel coherence time greatly exceeds bit duration.Source: A. SISO-UVLC · p. 4

P SISO

The SISO BER is averaged over fading and possible data sequences. For weak oceanic turbulence, Gauss-Hermite quadrature provides a way to calculate the fading average under a lognormal model.

P SISO

  • The final SISO BER averages conditional error probability over the fading coefficient and all 2^L possible transmitted data sequences.L denotes channel memory.Source: P SISO · p. 4
  • Under weak oceanic turbulence, the fading average can be calculated using Gauss-Hermite quadrature for a lognormal fading coefficient.The approximation is specified by its order, weights, and Hermite-polynomial zeros.Source: P SISO · pp. 4–5

B. MIMO-UVLC

For the MIMO UVLC receiver with EGC, the bit-by-bit decision uses integrated currents from the two halves of a bit interval. Channel memory and Gaussian integrated noise enter the receiver description.

B. MIMO-UVLC

  • Lij denotes the channel memory between transmitter i and receiver j.Source: B. MIMO-UVLC · p. 5
  • The integrated noise in each half of the bit interval is Gaussian with zero mean and variance σ2.Source: B. MIMO-UVLC · p. 5
  • The receiver compares the integrated currents from the first and second halves of the bit interval to detect each bit.Source: B. MIMO-UVLC · p. 5
  • The conditional error probabilities are calculated separately for transmitted bits 0 and 1.Source: B. MIMO-UVLC · p. 5

P MIMO

The MIMO BER calculation averages over fading coefficients and prior bit sequences, using channel memory to set the sequence length. For lognormal fading, quadrature and a lognormal approximation simplify the averaging.

P MIMO

  • EGC is treated as a practical MIMO UVLC combiner because it provides performance close to the optimal combiner at lower complexity.Source: P MIMO · p. 5
  • The final BER averages over the fading coefficients and all 2^Lmax possible prior data sequences, where Lmax is the maximum channel memory.Source: P MIMO · p. 5
  • For lognormal fading, Gauss-Hermite quadrature evaluates the multidimensional fading average through a finite series.Source: P MIMO · p. 5
  • Approximating the weighted sum of link fading coefficients as an equivalent lognormal random variable reduces the multidimensional integrals to one-dimensional integrals.Source: P MIMO · p. 5

IV. BER EVALUATION USING PHOTON-COUNTING METHOD

The section evaluates BER with a photon-counting receiver and saddle-point approximation in the presence of shot noise. Conditional error probabilities use receiver-output moment-generating functions, then average over fading and prior bits.

IV. BER EVALUATION USING PHOTON-COUNTING METHOD

  • The photon-counting receiver compares photoelectron counts in the two halves of the bit interval, with saddle-point approximation used to evaluate conditional error probability.Source: §IV · p. 6
  • The model treats incoming optical signal and background and dark-current noise as Poisson distributed, and thermal noise as Gaussian.Source: §IV · p. 6
  • Conditional BERs are obtained from receiver-output moment-generating functions, and final BER averages over fading coefficients and prior bit sequences.Source: §IV · p. 6

A. SISO UVLC Link

For the SISO link, photoelectron counts and receiver noise define the integrated outputs used to obtain conditional error probabilities. The section applies saddle-point approximation to evaluate BER.

A. SISO UVLC Link

  • SISO photoelectron counts from the optical signal, dark current, and background light are modeled as Poisson random variables conditioned on the channel fading.Source: A. SISO UVLC Link · p. 6
  • Background-light and dark-current counts have equal mean and variance, with mean count rate integrated over half the bit interval.Source: A. SISO UVLC Link · p. 6
  • The SISO receiver-output moment-generating functions combine the component MGFs for each half of the bit interval.Source: A. SISO UVLC Link · p. 6
  • Saddle-point approximation yields conditional SISO error probability, which is then averaged to evaluate final BER.Source: A. SISO UVLC Link · p. 6

B. MIMO UVLC Link

The MIMO receiver’s integrate-and-dump outputs are described through photoelectron counts and combined thermal noise over each half of the bit interval. The resulting conditional error probability leads to BER evaluation, with an approximation that reduces the lognormal integrals.

B. MIMO UVLC Link

  • The receiver’s integrate-and-dump outputs include photoelectron counts and combined thermal-noise components for the first and second halves of the bit interval.The MIMO receiver’s integrated outputs are used to obtain their moment-generating functions.Source: B. MIMO UVLC Link · pp. 6–7
  • The moment-generating functions of the integrated receiver outputs are used to obtain the conditional probability of error.The passage refers to substitution of expressions (34) and (35) into expressions (24)–(27).Source: B. MIMO UVLC Link · p. 7
  • The conditional MIMO error probability yields the final BER, and approximating the sum of lognormal random variables reduces the multidimensional integrals to one-dimensional counterparts.The BER is evaluated similarly to the earlier expression (18).Source: B. MIMO UVLC Link · p. 7

V. MULTIPLE-SYMBOL DETECTION

Multiple-symbol detection addresses strong ISI in UVLC, especially for diffusive links, by detecting consecutive BPPM bits together. The paper also proposes GMSD to estimate the transmitted sequence and fading coefficient jointly with lower complexity.

V. MULTIPLE-SYMBOL DETECTION

  • Strong ISI from UVLC channel scattering, particularly in diffusive links, motivates detecting a block of consecutive BPPM bits to improve BER.The section derives MSD algorithms for SISO UVLC systems.Source: §V · p. 7
  • The received signal is projected onto orthogonal functions to form observable random variables, and maximum-likelihood symbol estimates maximize their joint likelihood as the number of projections approaches infinity.The detection window contains P transmitted bits; projected noise components are Gaussian with zero mean.Source: §V · p. 7
  • The MSD criterion integrates over the log-amplitude fading factor, whose mean and variance are specified, before simplifying to a transmitted-symbol estimation rule.The fading factor is defined as X = 0.5 ln(h̃).Source: §V · p. 7
  • The proposed GMSD jointly estimates the transmitted sequence and fading coefficient from an observation window of consecutive received symbols.It is presented as a low-complexity alternative because integrating over fading makes the MSD criterion intractable.Source: §V · p. 7
  • GMSD assumes a constant fading coefficient across the consecutive bits in each summation, consistent with the stated slow-fading nature of UVLC channels.The method is stated not to require instantaneous or statistical channel state information and to apply to fading modeled by distributions beyond lognormal.Source: §V · p. 8

VI. NUMERICAL RESULTS AND DISCUSSION

The results show that water turbidity and link diffusivity shape channel loss, temporal spread, and spatial coverage, while spatial diversity and multiple-symbol detection improve performance in the studied conditions. Analytical BER results agree with photon-counting and simulation results, and the reported examples show that detection strategy and link type matter strongly under ISI and alignment constraints.

Evaluation scope

  • The study evaluates laser collimated and LED diffusive links across clear-ocean, coastal, and turbid-harbor waters using Monte Carlo channel simulations and receiver-noise parameters.The results section reports first-five loss coefficients and RMS delay spread for direct and indirect links with a 1 ns bit duration.Source: §VI · pp. 8, 12, Table III · p. 12

Channel conditions and link type

  • Greater water turbidity increases channel delay spread and attenuation; a 10 m laser harbor link has worse channel quality than a 25 m laser coastal link and even a 60 m clear-ocean link.LED transmission increases loss and temporal dispersion in clear ocean, but changes channel quality less in turbid harbor water, where multiple scattering is already substantial.Source: §VI · pp. 9–10

Spatial and temporal channel spread

  • Laser links in clear ocean and coastal water concentrate energy near the beam center, whereas harbor laser and LED links spread illumination more uniformly across a larger receiver-plane area.Diffusive links increase channel loss and delay spread but ease tracking and alignment; the paper suggests lower data rates to reduce loss and ISI and improve coverage uniformity.Source: §VI · pp. 10–11, Figure 3 · p. 11

BER performance

  • For the 10 m laser-based harbor link at 1 Gbps, BER is worse than for a clear-ocean link six times longer, and ISI can prevent power increases from improving performance.Analytical, photon-counting, and simulation results agree well, supporting negligible shot-noise effects and the accuracy of the analytical expressions.Source: §VI · p. 12, Figure 4 · p. 12

Spatial diversity

  • A 3 × 1 MISO link gains about 8 dB over SISO at BER 10^-9 in the 6 m LED-based harbor-water scenario; adding independent branches increases BER-curve slopes.Receiver diversity performs slightly worse than transmit diversity because the total receiving aperture is divided among receivers and each receiver adds thermal noise.Source: §VI · pp. 12–13

BER evaluation and receiver diversity

  • A 60 m laser-based clear-ocean channel has negligible spatial spread, so off-axis SIMO receivers can make performance worse than SISO by splitting aperture area and adding thermal noise.The 30-point Gauss-Hermite quadrature result predicts exact BER accurately, while the approximated one-dimensional integral slightly overestimates BER.Source: §VI · p. 13, Figure 6 · p. 13

Data rate and ISI

  • Increasing data rate significantly worsens BER through ISI, especially in channels with greater delay spread; the 6 m LED harbor link performs well at 100 Mbps but requires excessively large power at 500 Mbps for reliable communication.This motivates using detection algorithms that account for interference among received symbols.Source: §VI · p. 13, Figure 7 · p. 13

Multiple-symbol detection

  • GMSD with a two-bit window improves BER by 7 dB over SBSD at BER 10^-6 for the 10 m laser-based harbor link at 500 Mbps.The reported GMSD windows are P = 2, 4, and 10; the stated improvement makes reliable communication possible with realistic average transmitted power per bit under these link conditions.Source: §VI · p. 14, Figure 8 · p. 14

VII. CONCLUSION

The paper studies UVLC channel characteristics and BER for collimated laser and diffusive LED links, using MIMO to mitigate fading and multiple-symbol detection to alleviate ISI. Its results include improved BER with GMSD and close agreement between analytical results and simulations.

VII. CONCLUSION

  • The study covers channel characteristics and system design for collimated laser and diffusive LED UVLC links, accounting for absorption, scattering, and turbulence-induced fading.It applies MIMO to mitigate fading and multiple-symbol detection to alleviate ISI.Source: §VII · p. 14
  • Analytical BER expressions matched numerical simulations, confirming the reported expressions' accuracy.The conclusion also reports a close match between analytical and photon-counting results.Source: §VII · p. 14
  • GMSD with detection window P = 2 improved BER by 7 dB over symbol-by-symbol detection at BER 10^-6.The conclusion also reports about 8 dB gain for 3 × 1 MISO at BER 10^-9, but the supplied passage does not complete the comparison baseline.Source: §VII · p. 14
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