Intersymbol interference in DQPSK fibre-optic systems Downloaded from: https://research.chalmers.se, 2020-07-11 08:11 UTC Citation for the original published paper (version of record): Zhao, H., Agrell, E., Karlsson, M. (2009) Intersymbol interference in DQPSK fibre-optic systems European Transactions on Telecommunications, 20(8): 758-769 http://dx.doi.org/10.1002/ett.1354 N.B. When citing this work, cite the original published paper. research.chalmers.se offers the possibility of retrieving research publications produced at Chalmers University of Technology. It covers all kind of research output: articles, dissertations, conference papers, reports etc. since 2004. research.chalmers.se is administrated and maintained by Chalmers Library (article starts on next page) Intersymbol Interference in DQPSK Fiber-Optic Systems Hongxia Zhao†, Erik Agrell†, Magnus Karlsson‡ †Department of Signals and Systems, Chalmers University of Technology, SE-412 96 G¨oteborg, Sweden. E-mail: hz,[email protected] ‡Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-412 96 G¨oteborg, Sweden. Abstract— The limited bandwidth of high-speed transmitter result of having been in the research focus for the last 6–8 and receiver hardware gives rise to intersymbol interference years. Indeed, the current transmission record over a single (ISI) in digital communication systems. The influence of such fiber (25 Tb/s) was enabled by DQPSK modulation [2]. It ISI is investigated in a low-complexity fiber-optical setting, using differential quaternary phase shift keying (DQPSK) modulation. is of crucial importance for system designers, as well as The ISI is approximated by a memoryless, stochastic model, telecom operators, to fully understand the cost/complexity for use in applications where neither equalization nor sequence vs. performance trade-offs of DQPSK and QPSK systems. detection can be afforded. The channel capacity of this model We will return to this trade-off discussion when discussing is calculated and shown to depend strongly on the transmitter the optical transmitters in Section II-A. calibration. More than 3 dB is gained, at a target bit error rate of 10−6, by allowing the transmitted phase levels to deviate from DQPSK modulation is well understood theoretically for their nominal multiples of π/2 by up to 7 %. additive Gaussian noise and ideal transmitters and receivers [3, Sec. 5.2.8]. It is used in numerous wireless standards (such as the IEEE 802.11 standards for wireless LAN) and there is I. INTRODUCTION now a rapidly growing interest in using DQPSK modulation In high-speed fiber-optical communication systems, the also in fiber-optical communications. The performance of nonzero rise time of electrooptical modulators deteriorates the such systems was theoretically analyzed in, e.g., [4], [5] system performance. In combination with the receiver low- and references therein. Experimental realizations of DQPSK pass filters, which are also nonideal, the nonideal transmitters systems were discussed in [6]–[9], and more recently in WDM introduce intersymbol interference (ISI) to the demodulated configurations [2], [10], [11]. Effects of the optical transmitter signal, even at short ranges where the fiber dispersion is and receiver on system performance and channel capacity have insignificant. In a previous paper [1], we analyzed the in- however never been studied theoretically. fluence of nonideal hardware on coherent quaternary phase- The standard method to combat ISI is by equalization shift keying (QPSK) transmission in a fiber-optical system. We or sequence estimation [3, Ch. 10–11]. In a fiber-optical showed that the ISI, if not compensated for, causes unequal differential PSK setting, ISI has been discussed and mitigated, bit error rates (BER) between the two QPSK bit streams and e.g., by skewed precoding [12], convolutional error-correction an overall performance degradation. codes [13], symmetric DPSK [14], electronic processing [15], The work in [1] is here extended to differential QPSK [16], and maximum liklihood sequence estimation [17]. In (DQPSK) systems. The ISI that is visible in PSK constellations those papers, the main ISI source is fiber dispersion and and found to influence the two bits in the QPSK symbol receiver filtering, while ISI from transmitter imperfections was differently is averaged over all transmitted phases for DQPSK, studied to a less extent. and is thus not visible as a BER difference between the two In this work, we consider a scenario where equalization or DQPSK bits. However, the effect is still present as a limitation sequence estimation is too complex. The question is, can this in DQPSK systems. As will be shown, it causes unequal type of ISI be mitigated to some degree, without adding any symbol error rates (SER), conditioned on the transmitted additional hardware or processing resources? The answer is symbol, and it increases the average BER. We also discuss yes, by up to 3 dB. We show this by developing a stochastic and quantify how simple modifications to the transmitter can model for the ISI, calculating the theoretical channel capacity improve the system performance. of the model, finding transmitter parameters that maximize From a communication-theoretical perspective, the differ- the capacity, and simulating the BER using this modified ences between QPSK and DQPSK are significantly altered transmitter. noise statistics and the requirement for differential precoding. From a more practical fiber communication perspective, the II. SYSTEM MODEL DQPSK receiver is significantly easier and less complex to realize than the coherent receiver required for QPSK, although The dominating impairment in the studied communication it comes at the expense of an SNR penalty. In fact, optical system is, apart from the nonideal hardware, the amplified DQPSK systems are significantly more mature and closer to spontaneous emission noise of the erbium-doped fiber ampli- commercialization than coherent QPSK systems, which is a fier (EDFA). Other mitigations like thermal noise, shot noise, and all kinds of dispersion and nonlinear effects are ignored. LP Received Sampling EDFA BP + π The data rate is 20 Gbit/s (10 Gsymbol/s). signal T 4 & Decision LP T − π A. Transmitter 4 At bit rates of 10 Gb/s or higher, the commonly used Differentialdetector transmitter is based on an ideal continuous wave (CW) laser Fig. 1. Structure of the system receiver. and an external modulator [18, p. 122]. In short, the transmitter converts the CW light radiated from the laser into a data- y (t) I YI DDI HL(f) coded pulse train with the proper modulation format. To f(t) r(t) Ho(f) transmit a DQPSK signal, different transmitters with varying y (t) Q YQ DDQ HL(f) complexities have been investigated [19]–[21]. In [19], three n(t) DQPSK transmitters are compared. The two simplest transmit- ters in [19] are used in this paper and are denoted as TX-A and Fig. 2. Equivalent system baseband model. TX-B. TX-A uses two modulators, one amplitude modulator and one phase modulator, which are connected serially, while TX-B uses a single phase modulator [1]. These transmitter Since the transmitted bits modulated by the phase modulator configurations are the simplest from a cost/complexity per- based transmitter are naturally mapped, a DQPSK precoder is spective. It is well known that e.g. the parallel Mach-Zehnder needed, not only to realize the differential encoding but also modulator (MZM) may give better performance, partly from the Gray mapping of the information bits. This precoder is thus the forgiving electrical-to-optical transfer characteristics that more complex compared to what is used in digital wireless reduce the influence of noise from the electric driving sig- communications. The logic operations of the precoder used in nals. From a system vendor perspective, these modulators this paper are [24] have significant drawbacks such as requiring active biasing c1,n = (((d1,n d2,n) c2,n 1) d1,n) c1,n 1 and temperature stabilization, besides being intrinsically more ⊕ ∧ − ⊕ ⊕ − costly and less mature especially at high bandwidths (> 40 c2,n = (d1,n d2,n) c2,n 1 GHz) [22]. Therefore the parallel MZM, being common in ⊕ ⊕ − research, is by no means a commodity in system development. where n stands for the index of the binary streams, di,n and Alternatively, a pulsed DQPSK (often denoted (RZ- ci,n for i 1, 2 denote the information bits and the coded ∈ { } DQPSK) transmitter could be used, requiring the use of an bits, and are exclusive or (XOR) and the AND operation, ⊕ ∧ additional modulator for pulse carving or a mode-locked laser respectively. The precoder outputs, the coded bits c1,n and source. While this solution has less transmitter ISI, it is also c2,n, then pass through a mapping unit and map to an and bn, more com plex and costly, and requires more bandwidth resp., as an 1, 1 and bn 0, 1 . ∈ {− } ∈{ } which is a drawback in wavelength division demultiplexing systems. We therefore believe that there is a strong interest, not B. Receiver least from optical system designers, to evaluate the ultimate In the system receiver (see Fig. 1), the received signal performance of these simpler, low-cost transmitter structures. is first amplified by an EDFA before passing through an The normalized baseband transmitted signals of TX-A and optical bandpass (BP) filter. The output of the BP filter is TX-B, denoted as fA(t) and fB(t), respectively, are split into two branches, subsequently referred to as the inphase π (I) and quadrature (Q) branch. In each branch, the signal is π j bnp(t nT ) fA(t)= η sin (anp(t nT )) e 2 n − , first differentially detected, then filtered by an electrical low- · 2 − " n # P pass (LP) filter. Finally, a sampling and decision unit makes X (1) a decision based on the outputs of the two branches. Note and π j (an+bn)p(t nT ) that there is no equalizer in this system.