Quantum Limited DPSK Receivers with Optical Mach-Zehnder Interferometer Demodulation

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1 Quantum Limited DPSK Receivers with Otical Mach-Zehnder Interferometer Demodulation Xiuu Zhang, Deartment of Electrical and Comuter Engineering, Concordia University, Montreal, Quebec, CANADA, Guodong Zhang, AT&T, 00 Laurel Avenue, Middletown, NJ 07748, USA Abstract: We resent an analysis of quantum-limited DPSK receivers with otical Mach-Zehnder interferometer (MZI) demodulation. It is shown for the first time that the quantum limits for DPSK/MZI receivers with single-ort and balanced detections exactly differ from 3-dB in receiver sensitivity, obtained by both Poisson and Gaussian noise statistics. The quantum limit for DPSK/MZI receivers with balanced detection is given by BER = ex ( N ) for the first time, instead of BER = ex ( N ) which only alies for DPSK/MZI receivers with single-ort detection, hoton number in bit or 0, i.e. average hoton number. N - the Otical Society of America OCIS codes: ( ) Coherent communications, ( ) Fiber-otics communications, ( ) Fiber-otics links and subsystems References and links. A. Gnauck, Phase-shift keyed transmission, OFC 004, Paer TuF5, 004, and references therein.. A. Gnauck, S. Chandrasekhar, J. Leuthold, and L. Stulz, Demonstration of 4.7-Gb/s DPSK receiver with 45 hotons/bit sensitivity, IEEE Photon. Tech. Lett., vol.5,.99-0, R. Ziemer, and W. Tranter, Princile of communications, 5 th edition, Wiley, 00, T. Okoshi, and K. Kikuchi, Coherent otical fiber communications, Kluwer Academic Pub., 988, G. Agrawal, Fiber-otic communication systems, 3 rd edition, Wiley, 00,.67 and X. Zhang, G. Zhang, C. Xie, and L. Wang, Noise statistics in otically re-amlified DPSK receivers with Mach-Zehnder interferometer demodulation, Otics Letters, Vol.9, , Introduction The differential hase shifted keying (DPSK) modulation has been attracted great attention for its alication for dense wavelength division multilexing (DWDM) transmission since DPSK with otical Mach-Zehnder interferometer (MZI) demodulation and balanced detection rovides several advantages over the conventional intensity modulation/direction detection () []. The quantum limited receiver sensitivity of DPSK receivers, determined by BER = ex ( N ) - the hoton number in bit or 0, i.e. average hoton number (bits and 0 carry the same signal energy in DPSK signal) and BER- bit error ratio, has been widely used for DPSK/MZI receivers with both single-ort and balanced detections [-]. The above quantum limit was obtained for DPSK with electrical demodulation (referred to the conventional DPSK receivers), which consists of an electrical time delay line and a mixer, based on the noise statistics of Rice (bit ) and Rayleigh (bit 0 ) distributions [3-4]. However, the MZI (in DSPK with otical MZI demodulation) converts DPSK otical signal into intensity modulated otical signal before

2 inut to the otical hotodiodes, which is shown in Fig.. Consequently the electrical rocessing of DPSK signal/noise in otical receivers is the same as in receivers, rather than the conventional DPSK receivers. The noise statistic of quantum noise (i.e. shot noise) in DPSK receivers with otical MZI demodulation is not the Rice and Rayleigh robability distributions; instead the Gaussian/Poisson noise distribution should be used as in receivers [5]. Moreover, the DPSK/MZI receivers with balanced detection could be different from DPSK/MZI receivers with single-ort detection in quantum limited receiver sensitivity, because the signal energy used for error detection is different in the two detections. Consequently, it could be exected that the quantum limited BER in DPSK/MZI receivers with single-ort and balanced detections may be different from that of the conventional DPSK receivers. In this aer, we resent a quantum limited analysis for DPSK receiver with otical MZI demodulation and single-ort and balanced detections. Otical DPSK signal MZI electrical rocess Fig. Schematic drawing of a DPSK/MZI receiver. Single-ort detection uses one hotodiode and balanced detection both hotodiodes. MZI is used for conversion from hase modulation to intensity modulation.. Definitions of quantum and quasi-quantum noise When quantum noise is only considered, a small number of hotons and electron-hole airs resent (i.e., the number of hotons and electrons are countable). The noise statistics (only quantum noise is taken into account) for DPSK/MZI receivers should follow the Poisson distribution (a discrete robability distribution) as in receivers [5]. As the number of hotons and electrons becomes large enough, the noise statistics become the Gaussian distribution (a continuous robability distribution). In this aer, quasi-quantum limited (QQL) analysis is referred if the quantum noise is considered to be the Gaussian noise, to distinguish it from the quantum limited (QL) analysis in which the quantum noise is considered to be Poisson noise. For the conventional DPSK receivers, the BER exression of ex ( ) BER = N [3-5] is corresonding to our defined quasi-quantum limited analysis because the continuous Rice and Rayleigh noise statistics are used. 3. Quantum limited analysis We first analyze the quantum limited (Poisson noise statistics) DPSK receivers with otical MZI demodulation. We first consider DPSK/MZI receivers with single-ort detection. m If m > 0 electron-hole airs with the Poisson robability of P( m) = ex m! are generated by hoton number N ( N - the hoton number in bit, and corresonding to the average otical ower of the DPSK signal), no errors from bit occur. Since bit 0 has zero hotons and noise free, bit 0 is not detectable and BER is totally determined by bit similar to receivers [5] (Note m 0 0 the number of electron-hole airs in bit 0 ). Therefore the quantum limited BER is given by setting m = 0 in the above Poisson distribution, i.e. BER ex ( ) 0 S QL = N + ().

3 The receiver sensitivity given by () is 3-dB worse than that in receivers [5] ( BERIM / DD = ex ( N ), the eak ower of bit in is assumed twice the average ower of DPSK signal and thus total signal energy carried by IM and DPSK signals is the same). This can be exlained that only the half signal energy is used for error detection in DPSK/MZI receivers with single-ort detection rather than the full signal energy in receivers. The result indicated by () is already given in [5, Table 0.] for the conventional DPSK receivers. For DPSK/MZI receivers with balanced detection, the bits and 0 contain the same number of hotons. When bit transmitted, no errors occur if m > 0 electron-hole airs m with robability of P( m) = ex m! are generated at the constructive ort. Similarly, no errors occur from bit 0 if m 0 > 0 electron-hole airs with robability of 0 ( ) = m P m0 ex m 0! are created at the destructive ort. Thus, no errors occur if the condition m0 + m > 0 is met by combining the two conditions. For examle, we consider a secial case: m > 0 and m 0 = 0. This case is exactly the same as DPSK/MZI receivers with single-ort detection, in which bit has m > 0 and bit 0 m 0 = 0 and thus no errors occur. In other words, it was shown above that no errors occur if m > 0 and m 0 = 0, and vice versa. Thus, an error shall occur only if m0 + m = 0 with the robability of ( = + ) = ( ) m P m m0 m ex N N m!. Thus, for DPSK/MZI receivers with balanced detection, BER is given by setting m = 0, BERB ex QL= N (). The factor / is due to two bits. By comaring () and (), we can find that the 3-dB quantum limited receiver sensitivity is imroved by DPSKMZI receivers with balanced detection over single-ort detection. On the other hand, the same quantum limit by DPSK/MZI receivers with balanced detection as receivers ( IM / DD = ex ( ) BER N since bit = N in receivers) is obtained. This is because the two receivers use the same signal energy for error detection. The exression () for DPSK/MZI receivers with balanced detection is given for the first time. It is shown that the quantum limits are different for DPSK/MZI receivers with single-ort and balanced detections. Therefore, it is not aroriate to use the exression () for DPSK/MZI receivers with balanced detection [-]. If non-ideal hotodiodes are considered, η N should relace N in () and (), η - the quantum efficiency of the hotodiodes. Furthermore, it is observed that the exression () for DPSK/MZI receivers with single-ort detection is the same as the conventional DPSK receivers. However the BER given by () is obtained based on the discrete Poisson distribution, rather than the continuous Rice and Rayleigh distributions. Particularly, it is worth to emhasize that the quantum-limited BER exression of BER = ex ( η N ), which has been widely used for DPSK receivers [-], only alies for DPSK/MZI receivers with single-ort detection and the conventional DPSK receivers. Additionally, the 3-dB difference of receiver sensitivity by () and () agrees well with the signal constellation which is shown in Fig. []. In Fig. (a), the signal constellations for DPSK/MZI receivers with single-ort detection and 3

4 receivers are given. The distance between bits and 0 in electric field is assumed x for DPSK/MZI receivers with single-ort detection. Thus, the distance becomes x for receivers. Therefore, receivers outerform DPSK/MZI receivers with the single-ort detection by 3 db. Fig. (b) deicts the signal constellations for receivers and DPSK/MZI receivers with balanced detection. It is shown that the distances between bits and 0 are the same for the two receivers. Therefore, receivers have the same quantum limited erformance as DPSK/MZI receivers with balanced detection. Im{E} x Im{E} x Re{E} Re{E} x DPSK/MZI-SD (a) x DPSK/MZI-BD (b) Fig. (a) signal constellation for DPSK/MZI receivers with the single-ort detection (DPSK/MZI-SD) and receivers, (b) signal constellation for DPSK/MZI receivers with the balanced detection (DPSK/MZI-BD) and receivers. 4. Quasi-quantum limited analysis We now start the analysis for the quasi-quantum limited (Gaussian noise statistics) DPSK receivers with otical MZI demodulation. First let s consider the DPSK/MZI receivers with single-ort detection. The decision current I ( t ) for bit is corresonding to the average otical ower rather than the eak ower in receivers. The decision currents for DPSK/MZI receivers with constructive-ort detection are I ( t) = RPs + ns() t for bit and I0 () t = 0 for bit 0, where R is the resonsivity of the hotodiodes, P s denotes the average otical ower, and ns ( t ) is the quantum noise with the variance of σ. The quasi-quantum limited BER for DPSK/MZI receivers with single-ort detection is similar to [5], I η N s BER S QQL = erfc = erfc (3), σ where erfc() is the comlementary error function. In (3) Is = RP s, and σ = eis Be, i.e. the shot noise for bits, e - electron charge, B - the electrical noise bandwidth. For e s = I equal to the half of the bit rate, we obtain ηn, which is used in the last ste of (3). It σ is seen that DPSK/MZI receivers with single ort detection is 3-dB worse than ηn receivers in receiver sensitivity ( BER IM / DD = erfc [5]), again the same conclusion as the quantum-limited analysis. For DPSK/MZI receivers with balanced detection, the decision currents are B e 4

5 I () t = RPs + ns( t ) for bit and 0 ( ) = s + s( ) () I t RP n t for bit 0. The quantum noise ns t of bits and 0 is the same in the variance with σ = eis Be. By combining the two decision conditions as the case of quantum limit, we have the error occurring condition of I t I t < [6]. BER can be obtained by, () () 0 0 ( x I ) ( y+ I ) 0 s s πσ σ πσ σ x I s BERB QQL = Pr ob( I < I ) = ex dx ex dy = = erfc η N (4). In (4) the same conditions as in (3) have been alied in the last ste. By comaring (3) and (4), we have found that BER given by (3) and (4) differs from 3-dB in receiver sensitivity. In other words, the 3-dB receiver sensitivity is imroved by DPSK/MZI receivers with balanced detection over single-ort detection in the quasi-quantum limit. On the other hand, DPSK/MZI receivers with balanced detection has the same quantum limit as receivers, since the total signal energy, used for error detection in DPSK/MZI receivers with balanced detection, is exactly the same as in receivers. The BER exressions of (3) and (4) are different from the exression of BER = ex ( η N ) obtained for the conventional DPSK receivers based on the continuous Rice and Rayleigh distributions. Again the 3-dB receiver sensitivity difference in (3) and (4) can be easily interreted by the signal constellation in Fig.. erfc σ ( ) 5. Conclusion We have resented an analysis of DPSK/MZI receivers with single-ort and balanced detections, considering the quantum noise only. We have found that 3-dB quantum limit is imroved by DPSK/MZI receivers with balanced detection over single-ort detection. This is simly because only the half signal energy is used for error detection in single-ort detection. Moreover, DPSK/MZI receivers with balanced detection has the same quantum limit as receivers rather than 3-dB lower, since the total signal energy for error detection in DPSK/MZI receivers with balanced detection and receivers is the same. The quantum limited BER with BER ex s = ( η N ) for DPSK/MZI receivers with single-ort detection and BER ex ( b = η N ) for balanced detection are given for the first time, based on the Poisson statistic. Acknowledgements: The authors thank Chongjin Xie, Bell Labs. Lucent Technologies, for reading the manuscrit and suggestions. 5