Adaptive Subcarrier PSK Intensity Modulation in Free Space Optical Systems

I. INTRODUCTION

• Turbulence-induced fading arises from stochastic atmospheric refractive-index variation and can severely affect FSO-link reliability and communication rate.The introduction notes that vulnerability to adverse atmospheric conditions limits widespread FSO deployment.Source: §I · p. 2
• Spatial diversity can improve FSO performance, but adding apertures increases system cost and physical size..Source: §I · p. 2
• Adaptive transmission varies basic transmission parameters with fading intensity, allowing higher data rates under favorable conditions without additional optical power or sacrificing performance requirements.Prior FSO approaches include adaptive pulse-position modulation, coding with on-off keying, adaptive power, and joint power and PAM-order adaptation.Source: §I · pp. 2–3
• S-PSK transmits properly biased PSK-modulated RF signals through IM/DD optical systems; its constant envelope keeps average and peak optical power constant per symbol.The introduction also states that S-PSK offers increased demodulation performance compared with PAM under turbulence.Source: §I · p. 3
• The proposed S-PSK strategy adapts modulation order to instantaneous turbulence-induced fading and a predefined BER while requiring a modulation-order-independent DC bias.The paper evaluates spectral efficiency and BER across turbulence strengths and target BERs, and applies the policy to MIMO FSO with equal-gain combining.Source: §I · p. 3

II. NON-ADAPTIVE SUBCARRIER PSK INTENSITY MODULATION

• The system uses a subcarrier signal to modulate optical-carrier intensity and transmits it through an atmospheric-turbulence fading channel.A DC bias ensures the transmitted waveform satisfies the non-negativity constraint; average optical power P and modulation index μ set the transmitted power.Source: §II · p. 4, A. System and Channel Model · p. 4

A. System and Channel Model

• The RF PSK signal is shaped by pulse g(t), with carrier frequency fc, symbol period T, phase φk, and modulation order M.The optical signal is detected directly, the DC bias is removed, and a standard RF PSK demodulator processes the received signal.Source: A. System and Channel Model · p. 4
• At high SNR, ambient-light shot noise is approximated as Gaussian, and the received electrical signal is formed after direct detection and bias removal.The model identifies optical-to-electrical efficiency, shaping-pulse energy, turbulence fading, and complex Gaussian noise in the receiver signal.Source: A. System and Channel Model · pp. 4–5
• Turbulence fading is modeled as constant over a block of K symbols, and the analysis assumes a sufficiently long message to reveal long-term ergodic properties.The fading is normalized to avoid changing average power, and Io is set to 1 without loss of generality.Source: A. System and Channel Model · p. 5

B. BER Performance

• Conditional BER depends on turbulence statistics and modulation order, with a BPSK expression for M = 2 and an approximation for M > 2.The BPSK expression is conditioned on fading coefficient I; the higher-order expression is approximate.Source: B. BER Performance · pp. 5–6
• The conditional error expressions use the Gaussian Q-function, introduced as the Q-function in the BER derivation.Source: B. BER Performance · p. 6
• Average BER is obtained by integrating the conditional BER over the turbulence fading probability density function.The section states that the integral can be efficiently evaluated using Gauss-Hermite quadrature.Source: B. BER Performance · p. 6

C. Capacity Upper Bound

• An upper bound for optical-intensity-channel capacity with multiple subcarrier modulation is applied to the one-subcarrier FSO system.The conditioned bound depends on fading coefficient I.Source: C. Capacity Upper Bound · p. 6
• At high electrical SNR, the conditioned capacity bound is approximated using bandwidth W and a residue that vanishes exponentially as noise standard deviation approaches zero.Source: C. Capacity Upper Bound · p. 6
• The unconditional approximative capacity upper bound is obtained by averaging over the fading distribution and is used as a benchmark in subsequent analysis.The paper states that this averaged expression has a closed form in the Appendix.Source: C. Capacity Upper Bound · p. 6

• The adaptive transmission strategy is designed to improve the spectral efficiency of S-PSK FSO systems.Source: §III · p. 6
• It aims to do so without increasing transmitted average optical power.Source: §III · p. 6
• It also aims to preserve the system’s performance requirements.Source: §III · p. 6

A. Mode of Operation

• Pilots let the receiver estimate the block’s fading state and select a modulation order for the remaining symbols, informing the transmitter over a reliable RF feedback path.Source: A. Mode of Operation · p. 7
• The selection objective is to maximize bits per symbol interval using the largest modulation order that meets the target BER.Source: A. Mode of Operation · p. 7
• The fading range is partitioned into regions associated with available modulation orders, with boundaries set to meet the target BER.Source: A. Mode of Operation · p. 7
• Transmission stops when fading is below the first region boundary.Source: A. Mode of Operation · p. 7

1) Achievable Spectral Efficiency:

• Achievable spectral efficiency is based on the average transmitted bits and the information rate over the system bandwidth; pilot overhead is described as insignificant for the block lengths considered.Source: A. Mode of Operation · p. 7, 1) Achievable Spectral Efficiency · p. 8

• Average BER is calculated as the average number of bits in error divided by the total number of transmitted bits.Source: 2) Average Bit Error Rate · p. 8
• Because subcarrier PSK requires twice the bandwidth of PAM, the average bits transmitted in a symbol interval are divided by two.Source: 2) Average Bit Error Rate · p. 8
• The section then gives an expression for the average BER based on the preceding error calculation.Source: 2) Average Bit Error Rate · pp. 8–9

• The MIMO setup uses S-PSK with repetition coding across transmit apertures, and equal-gain combining across receive apertures.Source: C. Application to MIMO FSO systems · p. 9
• Fading coefficients model the links between transmit and receive apertures, with additive white Gaussian noise at reception.Source: C. Application to MIMO FSO systems · p. 9
• The transmit factor preserves total power, while the receive factor keeps combined aperture area equal to the no-diversity system; underlying link fading is assumed statistically independent.Source: C. Application to MIMO FSO systems · p. 9
• The adaptive modulation order is selected according to the MIMO fading state and target BER using region boundaries.Source: C. Application to MIMO FSO systems · p. 9
• The fading probability density is approximated by a lognormal distribution when obtaining average BER.Source: C. Application to MIMO FSO systems · p. 10

IV. RESULTS & DISCUSSION

• 14 dB spectral-efficiency gain over non-adaptive BPSK at σx = 0.5 and Po = 10−3; gains decrease as turbulence weakens.At σx = 0.1, non-adaptive BPSK reaches S = 0.5 at lower SNR, so instantaneous-fading adaptation is particularly effective in moderate-to-strong turbulence.Source: §IV · p. 11
• The adaptive system’s average BER stays below the target Po in every examined turbulence and target-BER case.At high average SNR, its performance approaches that of the non-adaptive system using the largest modulation order, which the adaptive scheme selects in this regime.Source: §IV · p. 11
• With moderate turbulence, Po = 10−3, and N = 3 modulation orders, adding transmit and/or receive apertures increases spectral efficiency except below 8 dB average SNR.Below 8 dB, increasing apertures decreases ξ, raises {yj}, and reduces spectral efficiency; as SNR rises, the aperture increase lowers {yj} and raises spectral efficiency.Source: §IV · p. 11

V. CONCLUSIONS

• Adaptive S-PSK yields a 14 dB spectral-efficiency gain at S = 0.5, Po = 10−3, and σx = 0.5, while low turbulence favors adaptation based on average electrical SNR.In MIMO FSO, spectral efficiency also improves at high SNR as transmit and/or receive apertures increase.Source: §V · p. 12

APPENDIX

• The appendix starts from the turbulence-fading probability density function to derive a closed-form expression for (14).It substitutes y = ln I, applies cited integral identities to reduce intermediate expressions, and obtains (15).Source: APPENDIX · p. 12