Preamplified Pulse Position Modulation Research Articles

Error rates of optically pre-amplified PPM wireless systems with coding and arbitrary optical filter response

We present novel results for the uncoded and coded bit-error probability (BEP) of optically pre-amplified pulse-position modulation (PPM) wireless systems. For uncoded systems, a novel analytic method for the evaluation of the BEP is derived. The method takes into account the non-ideal optical filter response and utilizes a finite Karhunen-Loève series expansion to calculate the BEP. Using the proposed approach, it is possible to accurately evaluate the PPM BEP for arbitrarily shaped filters where the well-established χ2 method only provides approximate results. Considering a Lorentzian filter response, the discrepancy between the two methods amounts to 0.5 dB in a variety of filter bandwidths and PPM modulation orders. The Lorentzian filter response was chosen as an illustrative practical example whose series can be calculated analytically. The proposed method is also valid for any type of optical filter for which the Karhunen-Loève series expansion can be calculated analytically or numerically. Due to the finite number of terms that are required irrespective of the signal energy level, the proposed method can also be applied without loss of accuracy to assess the system performance under the effects of turbulence and adverse weather conditions. For coded systems with Lorentzian filters, Monte-Carlo simulations are utilized to evaluate the BEP performance of the 5G LDPC codes, and it is demonstrated that they impart an energy gain up to 3.3 dB for 4–PPM and 2.3 dB for 16–PPM at a target BEP of 10−5. The optimal code rates are also discussed for several combinations of the optical filter bandwidth and PPM modulation order and it is shown that in almost all of the cases the optimal code rate is 11/13. Moreover, the sum-product and min-sum decoders perform within 0.1 dB from each other for the best code rates, which points towards the utilization of the min-sum decoder in all settings, since its operation does not require knowledge of the filter parameters. Finally, the comparison between the coded systems with Lorentzian and ideal passband filters exhibits the same 0.5 dB discrepancy that was observed for uncoded systems.

Reed Solomon error correction in pre-amplified pulse position modulation receivers

We present results on the bit error probability (BEP) of Reed Solomon (RS) codes for an optically pre-amplified pulse position modulation receiver. We first derive analytical relations for the BEP calculation of the RS coded system and validate their accuracy via Monte Carlo simulations. The analytical relations are then utilized to assess the BEP performance of the system in the presence of weak and strong fading. The performance of diversity techniques is also examined. The simulation results show that coding alone does not improve the performance of the system in a significant manner and the combined use of coding and multiple receivers/transmitters is required.

Average Error Probability of an Optically Pre-Amplified Pulse-Position Modulation Multichannel Receiver under Malaga-ℳ Fading

We present analytical results on the average probability of error (PER) performance of an optically pre-amplified pulse-position modulation (PPM) receiver under Malaga- M fading. The results are in the form of a finite sum whose number of terms depends on the PPM modulation order and the noise modes of the amplifier, enabling the efficient calculation of the average PER. In addition, we utilized the presented analysis to evaluate the performance of a equal-gain-combining (EGC) diversity receiver that operates in conjunction with optical amplification and PPM. The results show that the utilization of diverse and relatively low PPM orders achieves a drastic reduction in the average PER.

Performance evaluation of optically preamplified dicode pulse position modulation receivers

AbstractAn analysis for optically preamplified dicode pulse position modulation (DiPPM) receivers is presented for the first time. The performance at two different bit rates (622 Mbit/s and 2.5 Gbit/s) is analysed and compared with equivalent optically preamplified pulse position modulation (PPM) and on‐off keyed non‐return‐to‐zero (OOK NRZ) systems. Additionally a new derivation for the average power of the DiPPM pulse stream is provided and the sensitivity performance is compared with that obtainable from a previous formula, with results that are somewhat more conservative. For optically preamplified systems it is shown that PPM significantly outperforms DiPPM and OOK NRZ, when using the DiPPM average power formula derived here, but DiPPM could still show a sensitivity benefit over OOK NRZ of 4.2 dB. Copyright © 2007 John Wiley & Sons, Ltd.

A Moment Generating Function Formulation for an Optically Preamplified PPM Intersatellite System

A scheme for the utilisation of optically preamplified pulse position modulation (PPM) receivers in intersatellite laser communications is presented. To facilitate higher bit-rate operation an analysis is presented for a PPM system employing a receiver which integrates over a time slot and compares the result with a fixed threshold. When operating at the SITM-1 bit-rate of 155 Mbit/s and using conservative parameters our model demonstrates a possible receiver sensitivity of 50.7 photons/bit (at a BER of 10 -6 ) in the presence of background noise, indicating the potential of this receiver configuration for use in satellite communications. The analysis is facilitated by the use of a moment generating function approach which enables the use of tight upper bounds on the bit error probability to be derived using Chernoff bound (CB) techniques. We compare results obtained from this technique with those obtained by applying a Gaussian approximation (GA) and find that the GA is consistently less conservative for the cases considered (by 0.5 dB) at a BER of 10 -6 . This nevertheless suggests a reasonable level of accuracy and such a GA could be a useful tool for obtaining a first order approximation.

Optically preamplified pulse-position modulation for fibre-optic communication systems

A Chernoff bound is applied, by means of a recently developed moment-generating function (MGF), to the error probability of an optically preamplified pulse-position-modulation (PPM) receiver assuming Gaussian received pulse shapes. Sensitivity results are presented for various length PPM words and also bit-error-rate curves. The results are compared with those obtainable from an equivalent on–off keyed nonreturn-to-zero (OOK NRZ) system and show a possible benefit of 7.1 dB. The work demonstrates the potential of such an optically preamplified PPM receiver by giving results which surpass the fundamental sensitivity limit of an optically preamplified OOK NRZ receiver and approach the sensitivity of coherent detection systems. In particular, the analysis suggests that, at the STM-4 bit rate of 622 Mbit/s, a sensitivity of 25.27 photon/bit is attainable. In addition, a Gaussian approximation is developed from the variance obtainable from the MGF and the results obtained from the Chernoff bound are compared with those obtainable from the approximation.

An improved analysis for optically preamplified pulse‐position modulation receivers in optical‐fiber systems

AbstractUsing a recently developed moment‐generating function (MGF) we apply a Chernoff bound to the bit‐error probability of an optically preamplified pulse‐position modulation (PPM) receiver. Sensitivity results for PPM coding levels are presented for operation at the STM‐4 bit rate. It is shown that this receiver configuration can outperform an equivalent on‐off‐keyed nonreturn‐to‐zero (OOK NRZ) system by 7.1 dB. We further demonstrate the impressive potential of such an optically preamplified PPM receiver by giving results that improve on the fundamental sensitivity limit of an optically preamplified OOK NRZ receiver and approach the sensitivity of coherent detection. A Gaussian approximation is also developed and we compare it with results obtained from the Chernoff bound. © 1995 John Wiley & Sons, Inc.