I. Garrett

Theoretical analysis of heterodyne optical receivers for transmission systems using (semiconductor) lasers with nonnegligible linewidth

We present a general theoretical model of receivers for coherent optical communication systems where transmitters and local oscillators having nonzero linewidth are used. Key issues in the model are the concept of single realization measurements of a stochastic intermediate frequency, and development of the probability density function for this stochastic process. Analytical results are derived for heterodyne ASK and dual filter FSK receivers and include the shot-noise limit, the asymptotic error-probability limits in ASK and FSK receivers, the influence of the IF on receiver noise, and the effective local oscillator strength. Detailed numerical results for typical p-i-n-FET wide-band receivers illustrate the influence on receiver sensitivity of IF filter bandwidth and relative threshold setting in ASK systems and of modulation index and IF filter bandwidth in FSK systems. A receiver sensitivity penalty for nonzero linewidth is found to be, for IF linewidths of 0.1 to 0.3 of the bit-rate, 3 to 9 dB in optimum ASK receivers, and 2 to 8 dB in optimum FSK receivers. Thus DFB lasers of linewidth 5 to 20 MHz could be used without external cavities in simple systems with near-ideal performance, which could find application wherever the great multiplexing advantage of coherent systems is a prime advantage. We present some guidelines for system design based on the results of this work.

Impact of phase noise in weakly coherent systems: a new and accurate approach

Coherent optical systems for future broadband local loops may use lasers with significant phase noise, manifest as broad linewidths. This phase noise can be accommodated if the receiver is correctly designed, i.e. if nonsynchronous (envelope or square-law) IF demodulation is used and sufficient IF bandwidth is provided. It is difficult to analyze the performance of a coherent optical receiver when the signals are corrupted by phase noise. The central theoretical problem arising from filtering a signal with phase noise is defined in a particular form which permits the derivation of the forward or Fokker-Planck partial differential equation for probability density of the output voltage of the receiver. The results are used to discuss the IF bandwidth required for optical heterodyne receivers for amplitude-shift-keying (ASK) signals. >

The effect of laser linewidth on coherent optical receivers with nonsynchronous demodulation

Recent theoretical analysis of the effect of using lasers with significant linewidths in coherent optical fiber transmission systems has shown how the design of the optical receiver, particularly the IF stage, affects the sensitivity. This paper reviews this theory for two classes of coherent systems-those making a differential phase measurement, and those not using phase information-where the requirements on laser linewidth are not stringent. We discuss the factors that affect the performance of systems with significant laser phase noise. Wherever possible, we compare the theoretical results with published system experiments. We show that our theory fits the experimental data well and indicates why experimental results have fallen short of the theoretical limits.

Theory for optical heterodyne narrow-deviation FSK receivers with delay demodulation

A theoretical model is presented that includes the effects of laser phase noise, receiver noise, imperfect modulation, IF bandwidth, and postdetection filtering. Detailed numerical results for 140-Mb/s and 400-Mb/s systems are presented, showing excellent agreement with independent published experimental results and strongly supporting the theoretical analysis. It is found that an IF linewidth of less than 0.25% of bit rate is required to avoid degrading the receiver sensitivity by more than 1 dB in a system with a strong local oscillator and modulation index of 0.7. A larger modulation index allows a larger linewidth to be accommodated. If the demodulation is not optimal, a narrower linewidth is necessary. >

Tuned front-end design for heterodyne optical receivers

A theoretical analysis of the noise performance of optical receivers with front-end tuning, suitable for wideband coherent systems, is presented. An algorithm for choosing the values of the tuning components in the front end so as to minimize the thermal noise output power has been developed. This theory is applied to the well-known simple parallel and serial tuning configurations and also to three more advanced designs. It is shown that any tuning is better than none in the wide-bandwidth designs considered and that the more advanced designs yield up to 12-dB reduction in thermal noise power. Two of the designs can be implemented with discrete components and should yield shot-noise-limited detection with 50-100 mu W of local oscillator power in receivers with 5-GHz bandwidth. The practical problem of equalizing the front-end response is considered, and it is shown that good performance can be expected using realizable components. >

A comparison of coherent digital PPM with PCM

Digital pulse position modulation (PPM) is a preferred modulation format for the ideal photon counting channel and optical intersateilite links. Here we examine its potential for the coherent optical fibre communications channel. We present a thorough performance and optimisation analysis. Comparisons, at a wavelength of 1.5 m, are made with shot-noise limited coherent PCM (homodyne and heterodyne ASK, FSK and PSK) over a range of fibre band-widths and varying PPM word size. We conclude that for moderate to high fibre bandwidths homodyne digital PPM should achieve an improvement in sensitivity of typically 5 dB over homo-dyne PSK PCM

Crosstalk and phase-noise effects in multi-channel coherent optical CP-FSK systems with tight IF filtering

Reported is a rigorous bit error rate analysis appropriate to continuous phase frequency shift keying (CP-FSK) coherent optical receivers with delay demodulation and an integrating IF filter with integration time less than or equal to the delay time. For an integration time equal to the delay time the model is extended to two optical channels. An important result of the analysis is that IF filtering for CP-FSK modulation reduces the phase swing due to modulation at the detector and this leads to a degradation in system performance with regard to phase noise, receiver noise, and crosstalk influence. For a modulation index of 0.5, for a single optical channel a minimum 2.4-dB penalty relative to matched filter detection is found. The required channel separation for CP-FSK systems appears to be significantly larger than for differential phase shift keying systems and phase noise enhances this effect. >

The effect of crosstalk and phase noise in multichannel coherent optical ASK systems

The authors extend the analysis of G.J. Foschini et al. (1988) to a two-channel system and to a wider class of IF filters. The authors carry out a comprehensive study of the sensitivity of an optical receiver in a two-channel ASK system, taking into account phase noise and crosstalk, including crosstalk arising from phase noise in the second channel. They compare the results with previous work in the limit of no phase noise and show how the agreement is good. They compute the penalty due to crosstalk for different linewidths and filter shapes. It is shown that the minimum channel spacing is a few bit rates more than the IF filter bandwidth, and is therefore increased significantly by significant phase noise. The detailed IF filter shape appears to have only a weak effect. >

Towards the fundamental limits of optical-fiber communications

We review the theoretical limits which restrict transmission over optical fibers. The fundamental limit on channel capacity is 1 nat/photon with a coherent detection receiver or with a thermal-noise-limited receiver. With an ideal photon-counting receiver, the theoretical capacity is infinite. A practical limit of a few nats per photon for direct detection requires a bandwidth expansion consistent with monomode fibers and fast digital circuits and is 35-40 dB better than current direct detection receivers. This limit may be approached by receiver improvements (10 dB with direct detection, 17 dB with optimum coherent detection), by using digital pulse-position modulation (PPM) (10-13 dB) and by using error-correcting codes where constraints on system complexity allow.

The effect of crosstalk and phase noise in multichannel coherent optical DPSK systems with tight IF filtering

Results for two-channel differential-phase-shift-keying (DPSK) systems using finite integrator and raised cosine response IF filters are presented. The sensitivity of an optical receiver in a two-channel DPSK system is studied. The results are compared with previous work in the limit of no phase noise and it is shown that the agreement is good. The penalty due to crosstalk for different linewidths and filter shapes is computed, and it is shown that the minimum channel spacing is a few bit rates for an ideal integrator IF filter and is larger for an IF filter with a raised cosine impulse response. The penalty is increased somewhat by phase noise. >