We describe a method to estimate the capacity limit of fiber-optic communication systems (or ?fiber channels?) based on information theory. This paper is divided into two parts. Part 1 reviews fundamental concepts of digital communications and information theory. We treat digitization and modulation followed by information theory for channels both without and with memory. We provide explicit relationships between the commonly used signal-to-noise ratio and the optical signal-to-noise ratio. We further evaluate the performance of modulation constellations such as quadrature-amplitude modulation, combinations of amplitude-shift keying and phase-shift keying, exotic constellations, and concentric rings for an additive white Gaussian noise channel using coherent detection. Part 2 is devoted specifically to the "fiber channel.'' We review the physical phenomena present in transmission over optical fiber networks, including sources of noise, the need for optical filtering in optically-routed networks, and, most critically, the presence of fiber Kerr nonlinearity. We describe various transmission scenarios and impairment mitigation techniques, and define a fiber channel deemed to be the most relevant for communication over optically-routed networks. We proceed to evaluate a capacity limit estimate for this fiber channel using ring constellations. Several scenarios are considered, including uniform and optimized ring constellations, different fiber dispersion maps, and varying transmission distances. We further present evidences that point to the physical origin of the fiber capacity limitations and provide a comparison of recent record experiments with our capacity limit estimation.

Capacity Limits of Optical Fiber Networks

Two 4-bit active phase shifters integrated with all digital control circuitry in 0.13-mum RF CMOS technology are developed for X- and Ku-band (8-18 GHz) and K-band (18-26 GHz) phased arrays, respectively. The active digital phase shifters synthesize the required phase using a phase interpolation process by adding quadrature-phased input signals. The designs are based on a resonance-based quadrature all-pass filter for quadrature signaling with minimum loss and wide operation bandwidth. Both phase shifters can change phases with less than about 2 dB of RMS amplitude imbalance for all phase states through an associated DAC control. For the X- and Ku-band phase shifter, the RMS phase error is less than 10o over the entire 5-18 GHz range. The average insertion loss ranges from to at 5-20 GHz. The input for all 4-bit phase states is typically at -5.4 plusmn1.3 GHz in the X- and Ku-band phase shifter. The K-band phase shifter exhibits 6.5-13 of RMS phase error at 15-26 GHz. The average insertion loss is from 4.6 to at 15-26 GHz. The input of the K-band phase shifter is at 24 GHz. For both phase shifters, the core size excluding all the pads and the output 50 Omega matching circuits, inserted for measurement purpose only, is very small, 0.33times0.43 mm2 . The total current consumption is 5.8 mA in the X- and Ku-band phase shifter and 7.8 mA in the K-band phase shifter, from a 1.5 V supply voltage.

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0.13- $\mu$ m CMOS Phase Shifters for X-, K u -, and K-Band Phased Arrays

A technique for bandwidth enhancement of a given amplifier is presented. Adding several interstage passive matching networks enables the control of transfer function and frequency response behavior. Parasitic capacitances of cascaded gain stages are isolated from each other and absorbed into passive networks. A simplified design procedure, using well-known low-pass filter component values, is introduced. To demonstrate the feasibility of the method, a CMOS transimpedance amplifier (TIA) is implemented in a 0.18-/spl mu/m BiCMOS technology. It achieves 3 dB bandwidth of 9.2 GHz in the presence of a 0.5-pF photodiode capacitance. This corresponds to a bandwidth enhancement ratio of 2.4 over the amplifier without the additional passive networks. The transresistance gain is 54 dB/spl Omega/, while drawing 55 mA from a 2.5-V supply. The input sensitivity of the TIA is -18 dBm for a bit error rate of 10/sup -12/.

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Bandwidth enhancement for transimpedance amplifiers

A fully-integrated, silicon photonic transceiver is demonstrated in a silicon-on-insulator process using photonic microring resonator modulators for low power consumption. The trade-offs between bandwidth and extinction ratio are discussed and motivate the use of transmit pre-emphasis for ring modulators to increase the interconnect data rate. The transmitter and receiver is demonstrated to data rates of 25 Gb/s with a BER of 10 ^-12. The total power consumption of the transceiver is 256 mW and demonstrates a link efficiency of 10.2 pJ/bit excluding laser power. At 25 Gb/s, the driver operates at 7.2 pJ/bit.

A Monolithic 25-Gb/s Transceiver With Photonic Ring Modulators and Ge Detectors in a 130-nm CMOS SOI Process

The transimpedance limit describes the maximum transimpedance that a transimpedance amplifier (TIA) can attain for a given bandwidth and technology. We analyze and compare this limit for a wide variety of TIA topologies thus exposing their relative merits. The topologies considered are the shunt-feedback TIA with single and multistage amplifier, the shunt-feedback TIA with feedback capacitor, the shunt-feedback TIA followed by a post amplifier, the shunt-feedback TIA with a current amplifier, the common-base/gate feedforward TIA, the shunt-feedback TIA with a common-base/gate input stage, and the shunt-feedback TIA with a regulated-cascode input stage. The analysis includes a discussion of the conditions under which the limit is realizable.

Eduard Säckinger

Papers

Broadband Circuits for Optical Fiber Communication: Säckinger/Broadband