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Spectral Efficiency Limits and Modulation/Detection Techniques for DWDM Systems Joseph M IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 10, NO. 2, MARCH/APRIL 2004 259 Spectral Efficiency Limits and Modulation/Detection Techniques for DWDM Systems Joseph M. Kahn, Fellow, IEEE, and Keang-Po Ho, Senior Member, IEEE Invited Paper Abstract—Information-theoretic limits to spectral efficiency the more economical alternative. Ultimate limits to spectral in dense wavelength-division-multiplexed (DWDM) transmission efficiency are determined by the information-theoretic capacity systems are reviewed, considering various modulation techniques (unconstrained, constant-intensity, binary), detection techniques per unit bandwidth [1], [2]. While closely approaching these (coherent, direct), and propagation regimes (linear, nonlinear). limits may require high complexity and delay [3], [4], estab- Spontaneous emission from inline optical amplifiers is assumed lishing accurate estimates of the limits can yield insights useful to be the dominant noise source in all cases. Coherent detection in practical system design. In this paper, we review spectral allows use of two degrees of freedom per polarization, and its spectral efficiency limits are several b/s/Hz in typical terrestrial efficiency limits, considering various modulation techniques systems, even considering nonlinear effects. Using either con- (unconstrained, constant-intensity [5]–[7] or binary), various stant-intensity modulation or direct detection, only one degree detection techniques (coherent or direct [8]), and various of freedom per polarization can be used, significantly reducing propagation regimes (linear or nonlinear [9], [10]). In all cases, spectral efficiency. Using binary modulation, regardless of de- tection technique, spectral efficiency cannot exceed 1 b/s/Hz per amplified spontaneous emission (ASE) from inline optical polarization. When the number of signal and/or noise photons amplifiers is assumed to be the dominant noise source. We show is small, the particle nature of photons must be considered. The that coherent detection allows information to be encoded in two quantum-limited spectral efficiency for coherent detection is degrees of freedom per polarization, and its spectral efficiency slightly smaller than the classical capacity, but that for direct detection is 0.3 b/s/Hz higher than its classical counterpart. Var- limits are several b/s/Hz in typical terrestrial systems, even ious binary and nonbinary modulation techniques, in conjunction considering nonlinear effects. Using either constant-intensity with appropriate detection techniques, are compared in terms of modulation or direct detection, only one degree of freedom their spectral efficiencies and signal-to-noise ratio requirements, assuming amplified spontaneous emission is the dominant noise per polarization can be exploited, reducing spectral efficiency. source. These include a) pulse-amplitude modulation with direct Using binary modulation, regardless of detection technique, detection, b) differential phase-shift keying with interferometric spectral efficiency cannot exceed 1 b/s/Hz per polarization. detection, c) phase-shift keying with coherent detection, and When the number of signal and/or noise photons is small, the d) quadrature-amplitude modulation with coherent detection. information-theoretic capacity of optical communication sys- Index Terms—Differential phase-shift keying, heterodyning, tems is also limited by the particle nature of photons. Coherent homodyne detection, information rates, optical fiber communi- cation, optical modulation, optical signal detection, phase-shift communication is equivalent to detecting the real and imagi- keying, pulse-amplitude modulation. nary parts of the coherent states [11], [12]. Direct detection is equivalent to counting the number of photons in the number states [11], [12]. In the coherent states, quantum effects add I. INTRODUCTION one photon to the noise variance [12] (if both signal and noise HE throughput of a dense wavelength-division-multi- are expressed in terms of photon number), yielding a channel T plexed (DWDM) transmission system can be increased capacity slightly smaller than the classical limit of [1] and [2]. by using a wider optical bandwidth, by increasing spectral The quantum limit of direct detection is determined by photon efficiency, or by some combination of the two. Utilizing a statistics and yields a slightly higher channel capacity than the wider bandwidth typically requires additional amplifiers and classical limit of [8]. other optical components, so raising spectral efficiency is often While currently deployed DWDM systems use binary on–off keying (OOK) with direct detection, in an effort to improve Manuscript received November 3, 2003; revised December 17, 2003. This spectral efficiency and robustness against transmission impair- work was supported in part by the National Science Foundation under Grant ments, researchers have investigated a variety of binary and ECS-0335013 and in part by the National Science Council of R.O.C. under nonbinary modulation techniques, in conjunction with various Grant NSC-92-2218-E-002-034. J. M. Kahn is with the Department of Electrical Engineering, Stanford Uni- detection techniques. In this paper, we compare the spectral effi- versity, Stanford, CA 94305 USA (e-mail: [email protected]). ciencies and power efficiencies of several techniques, assuming K.-P. Ho is with the Institute of Communication Engineering and Depart- in all cases that ASE is the dominant noise source. Techniques ment of Electrical Engineering, National Taiwan University, 106 Taipei, Taiwan, R.O.C. (e-mail: [email protected]). considered include pulse-amplitude modulation (PAM) with di- Digital Object Identifier 10.1109/JSTQE.2004.826575 rect detection [13], [14], differential phase-shift keying (DPSK) 1077-260X/04$20.00 © 2004 IEEE 260 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 10, NO. 2, MARCH/APRIL 2004 Fig. 1. Equivalent block diagram of multispan system. After each of the x fiber spans, an amplifier of gain q exactly compensates the span loss. The average power level per channel at key locations is indicated. At the output of the final amplifier, the total amplified spontaneous emission has a power spectral density per polarization given by . with interferometric detection1 [15]–[17], phase-shift keying indicates that we must use strong error-correcting codes [3], (PSK) with coherent detection [18], [19], and (d) quadrature- [4], and that the decoding complexity and delay must increase amplitude modulation (QAM) with coherent detection [20]. We exponentially as we approach the capacity. argue that at spectral efficiencies below 1 b/s/Hz per polariza- In a DWDM system, the spectral efficiency limit is simply tion, binary PAM (OOK) and binary DPSK are attractive op- the capacity per channel divided by the channel spacing. In tions. At spectral efficiencies between 1 and 2 b/s/Hz, quater- the linear regime, the spectral efficiency limit is independent nary DPSK and PSK are perhaps the most attractive techniques. of chromatic dispersion, because it is possible, in principle, to Techniques such as 8-PSK or 8- and 16-QAM are necessary fully compensate dispersion at the receiver. Alternatively, dis- to achieve spectral efficiencies above 2 b/s/Hz per polarization. persion effects may be avoided by using narrow-band chan- Historically, the main advantages of coherent optical detection nels with small channel spacing. Initially, we consider propaga- were considered to be high receiver sensitivity and the ability to tion in a single polarization, neglecting the impact of polariza- perform channel demultiplexing and chromatic dispersion com- tion-mode dispersion. Polarization effects are addressed briefly pensation in the electrical domain [21]. In this paper, we argue in Section II-B4. that from a more modern perspective, the principal advantage of Throughout Section II, denotes the occupied bandwidth coherent detection is superior spectral efficiency. We remind the per channel, denotes the channel spacing, denotes the reader that in ASE-limited coherent systems, there is no funda- capacity per channel, and denotes the spectral mental sensitivity difference between 2- and 4-PSK, nor is there efficiency limit. Note that and have units of bits per second one between synchronous homodyne and heterodyne detection. (b/s) and b/s/Hz, respectively. For concreteness, we consider The remainder of this paper is organized as follows. In a multispan system as shown in Fig. 1. The system comprises Section II, we review information-theoretic spectral efficiency fiber spans, each with gain 1 . After each span, an limits for various modulation and detection techniques, in amplifier of gain compensates the span loss. The average linear and nonlinear propagation regimes. We also calculate the transmitted power per channel is , while the average power quantum-limited capacity due to the particle nature of photons. at the input of each amplifier is . We assume that In Section III, we compare the power efficiencies and spectral for all detection schemes, ASE noise dominates over other efficiencies of various uncoded modulation and detection noise sources, including local-oscillator shot noise or receiver thermal noise, thereby maximizing the receiver signal-to-noise techniques, and comment on nonlinear phase noise and on ratio (SNR) [22]. At the output of the final amplifier, the ASE coding techniques for nonbinary modulation. Conclusions and in one polarization has a power spectral density
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