Abstract

Kramers-Kronig (KK) receivers have been shown to be able to cancel the signal-signal beat interference that occurs upon direct-photodetection in optical single-sideband systems, where the transmitted optical field is proportional to the modulation signal (Field-Modulated Direct-Detection systems). They can support complex modulation formats, and being single-sideband, electronic dispersion compensation, without the need for a coherent receiver. All current research has used digital-signal processing (DSP) to implement the KK algorithm. Radio-frequency KK receivers using analog processing were first introduced in the 1960's, and offer an alternative to DSP, particularly in their approximate form. Analog processing is inherently real-time and offers the lowest latency (processing delay). In this paper, we show that with minor changes, analog processing can also be used with signals from a photodetector. We have built an experimental receiver, using standard parts that have functionality that approximates to the desired algorithm. In particular, we show that a differential pair of bipolar transistors can approximate a square-root function, that the Hilbert transform can be approximated by an 8-tap transmission-line delay, and that a commercial analog multiplier chip can be used for a squaring and subtraction function. The system is demonstrated with 16-QAM at 500 Mbit/s with the photocurrent emulated in software and the KK algorithm performed in hardware. Finally, software band-limits the signal, down-converts it to form a constellation, and calculates symbol error rates. We show that the analog KK reduces the symbol error rate by at least a factor of ten, enabling low carrier-to-signal power ratios to be used with standard forward error correction. Much higher data rates could be supported using custom-designed microwave ASICs, which could be incorporated in packaged receivers. This would enable miniaturized receivers using standard DSP to work with dispersion-limited links. Interestingly, half the benefit could be gained by simply re-biasing the differential stage of a standard photoreceiver.

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