Abstract: The implications of increasing the symbol rate for a given digital-to-analog converter (DAC) sampling rate are investigated by considering the generation of 112 Gbit/s PM 16-QAM signals (14 Gsym/s) using a 21 GSa/s DAC with 6-bit resolution.
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#155773 - $15.00 USD Received 30 Sep 2011; accepted 12 Nov 2011; published 1 Dec 2011(C) 2011 OSA 12 December 2011 / Vol. 19, No. 26 / OPTICS EXPRESS B628
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1. Introduction
In coherent optical transmission systems, 28 Gsym/s polarization multiplexed, quadrature phase shift keying (PM QPSK) [1] and 14 Gsym/s polarization multiplexed, 16-ary quadrature amplitude modulation (PM 16-QAM) [2] can be used to achieve a bit rate of 112 Gbit/s. For PM QPSK, two-level drive signals are required for the IQ optical modulator, while for PM 16-QAM, four-level drive signals are required. The four-level drive signals can be generated using either the RF combining of two two-level signals [2] or a high-speed digital signal processor and digital-to-analog converters (DACs) [3–15]. The latter approach has the advantage of being able to generate modulated optical signals with more precise control of the amplitude and phase. Indeed, the flexibility to control the pulse shape is particularly important for spectrally efficient modulation formats [4–7]. This flexibility is achieved by satisfying the sampling theorem which requires the sampling rate to be at least twice the signal bandwidth. For a fixed DAC sampling rate, the achievable symbol rate can be increased by choosing a pulse shape that reduces the modulated signal bandwidth. This is exemplified by a pulse with a raised-cosine spectrum for which the maximum symbol rate for a bandwidth B is given by
2
1max
BSR
r=
+ (1)
where r is the roll-off factor (0 ≤ r ≤ 1). As the symbol rate increases from B to 2B (r decreases from 1 to 0), the number of samples per symbol decreases from 2 to 1. While it is of interest to increase the symbol rate for a given sampling rate, the corresponding decrease in the size of the eye opening must be considered.
In this paper we investigate the use of a raised-cosine pulse (r = 0.5) and a rectangular pulse filtered by a Gaussian response for the generation of 112 Gbit/s PM 16-QAM using a 6-bit 21 GSa/s DAC. For a symbol rate of 14 Gsym/s (1.5 samples per symbol), the modulated signal bandwidth is 10.5 GHz.
2. Pulse shaping
For a fixed DAC sampling rate, pulses with a raised-cosine spectrum provide a straightforward approach for increasing the symbol rate by reducing the modulated signal bandwidth and hence the number of samples per symbol. In the time domain, the pulse shape is given by
#155773 - $15.00 USD Received 30 Sep 2011; accepted 12 Nov 2011; published 1 Dec 2011(C) 2011 OSA 12 December 2011 / Vol. 19, No. 26 / OPTICS EXPRESS B629
0 0
0 2
0 0
sin(2 ) cos(2 )( ) 2
2 1 (4 )
f t rf td t f
f t rf t
π ππ
= −
(2)
where f0 is the 6-dB bandwidth. The spectrum of d(t) is bandlimited to B = (1 + r)f0. For a sampling rate of 21 GSa/s and a symbol rate of 14 GSym/s, r = 0.5. In this case f0 = 7 GHz and B = 10.5 GHz.
For an ideal 6-bit 28 GSa/s DAC, Fig. 1 illustrates the simulated eye diagram obtained for the in-phase component of a 14 GSym/s 16-QAM signal with r = 0.5 and 2 samples per symbol (over-sampling since the signal is bandlimited to 10.5 GHz). The sample values for the modulator drive signals are obtained from the specified optical field (raised-cosine pulse with r = 0.5), back-calculation using a mathematical model for the IQ modulator [16], sampling and quantization. The quantized sample values are at t = nTs/2, n = 0, ±1, ±2, … where Ts is the symbol period. The quantized sample values are then used in a forward-calculation to determine the modulated optical signal. The digital-to-analog conversion is implemented using the interpft function in Matlab. There is no intersymbol interference (ISI) and the relatively small eye opening is due to the value r = 0.5.
0 0.2 0.4 0.6 0.8 1 1.2 1.4
x 10-10
-1
-0.5
0
0.5
1
Time (s)
Am
plit
ude
(A
U)
Fig. 1. In-phase eye diagram for a raised-cosine pulse (r = 0.5) using 2 samples per symbol with quantization.
The eye diagram for the in-phase component of the 16-QAM signal is shown in Fig. 2 when the sampling rate is reduced to 21 GSa/s (1.5 samples per symbol). The sample values are at t = 2nTs/3, n = 0, ±1, ±2, … . For this case, every other pulse has a sample at the symbol center. The eye diagram obtained with commscope.eyediagram in Matlab shows the difference in the signal for alternating symbols when 2 symbol periods are displayed. For the symbols with a sample at the symbol center, the ISI is very small, while for the symbols without a sample at the symbol center, the ISI is increased. This is caused by quantization and the nonlinear response of the IQ modulator which is used to obtain the modulator drive signals by the back-calculation. For a fictitious modulator with a linear response and without quantization, the ISI is zero as expected since the sampling theorem is satisfied (signal bandwidth of 10.5 GHz for r = 0.5 and a sampling rate of 21 GSa/s).
0 0.2 0.4 0.6 0.8 1 1.2 1.4
x 10-10
-1
-0.5
0
0.5
1
Time (s)
Am
plit
ud
e (
AU
)
Fig. 2. In-phase eye diagram for a raised-cosine pulse (r = 0.5) using 1.5 samples per symbol with quantization.
#155773 - $15.00 USD Received 30 Sep 2011; accepted 12 Nov 2011; published 1 Dec 2011(C) 2011 OSA 12 December 2011 / Vol. 19, No. 26 / OPTICS EXPRESS B630
The asymmetry in the signal in Fig. 2 can be reduced by using offset sampling times t = Ts/6 + 2nTs/3, n = 0, ±1, ±2, … so that there is a sample value either Ts/6 or - Ts/6 away from the center of each symbol period. The effect of this offset sampling is illustrated in Fig. 3.
The raised-cosine pulse with r = 0.5 exhibits a relatively small eye opening and thus is sensitive to noise and timing jitter in the receiver. While the symbol rate can be increased further by reducing r (for a fixed sampling rate), this yields a yet smaller eye opening. As an alternative to the raised-cosine pulse, we consider a pulse obtained by filtering an ideal square pulse with a Gaussian response. The filtered pulse is then bandlimited to 10.5 GHz using a rectangular response. For a 3-dB Gaussian filter bandwidth of 9 GHz, Fig. 4 shows the in-phase eye diagram for the case of 28 GSa/s (2 samples per symbol) with quantization of the sample values. In comparison to Fig. 2, the eye opening is larger at the expense of a small increase in the ISI. Figure 5 illustrates the eye diagram for 21 GSa/s (1.5 samples per symbol) with quantization and offset sampling. The eye opening is appreciably larger than the corresponding result in Fig. 3 for the raised-cosine pulse (r = 0.5).
0 0.2 0.4 0.6 0.8 1 1.2 1.4
x 10-10
-1
-0.5
0
0.5
1
Time (s)
Am
plit
ude
(A
U)
Fig. 3. In-phase eye diagram for a raised-cosine pulse (r = 0.5) using 1.5 samples per symbol with quantization and offset sampling.
0 0.2 0.4 0.6 0.8 1 1.2 1.4
x 10-10
-1
-0.5
0
0.5
1
Time (s)
Am
plit
ude (
AU
)
Fig. 4. In-phase eye diagram for a Gaussian filtered rectangular pulse using 2 samples per symbol with quantization.
0 0.2 0.4 0.6 0.8 1 1.2 1.4
x 10-10
-1
-0.5
0
0.5
1
Time (s)
Am
plit
ude (
AU
)
Fig. 5. In-phase eye diagram for a Gaussian filtered rectangular pulse using 1.5 samples per symbol with quantization and offset sampling.
#155773 - $15.00 USD Received 30 Sep 2011; accepted 12 Nov 2011; published 1 Dec 2011(C) 2011 OSA 12 December 2011 / Vol. 19, No. 26 / OPTICS EXPRESS B631
3. Experimental setup
A simplified illustration of the experimental setup for back-to-back measurements of the transmitter performance is shown in Fig. 6. Measured results were obtained for an angle differential encoded 112 Gbit/s PM 16-QAM signal [17,18] generated with a DAC sampling rate of 21 GSa/s (1.5 samples per symbol). For comparison, results were also obtained for an angle differential encoded 85.672 Gbit/s PM 16-QAM signal generated with a DAC sampling rate of 21.418 GSa/s (2 samples per symbol). A 2
16 de Bruijn bit sequence was used for bit to
symbol mapping and the generation of the in-phase and quadrature signals. The output from the IQ modulator was split and then recombined in orthogonal polarizations after delaying one of the signals to decorrelate it from the other signal. The received signal was amplified and filtered (1.3 nm bandwidth) before detection by a polarization- and phase-diverse coherent receiver. The transmitter and local oscillator lasers had nominal linewidths of 100 KHz. The four signals from the balanced photodetectors were digitized by 40 GSa/s analog-to-digital converters using a real-time oscilloscope with a 16 GHz electrical bandwidth. The off-line signal processing included (i) quadrature imbalance compensation [19], (ii) down-sampling to 28 or 21.418 GSa/s (corresponding to the bit rates of 112 and 85.672 Gbit/s, respectively), (iii) digital square and filter clock recovery [20], (iv) polarization recovery and residual distortion compensation using 11-tap adaptive equalizers in a butterfly configuration, (v) carrier frequency recovery using a spectral domain algorithm [21], (vi) phase recovery using a blind phase search algorithm [22], (vii) symbol decisions and (viii) angle differential decoding. The adaptive equalizer used a constant modulus algorithm for pre-convergence followed by a radius directed algorithm [23]. Variable amounts of amplified spontaneous emission (ASE) noise from a broadband source were added in order to measure the dependence of the bit error ratio (BER) on the optical signal-to-noise ratio (OSNR). The OSNR was obtained using the measurement function of an optical spectrum analyzer. The BER was obtained by direct bit error counting using rectilinear decision boundaries.
Figures 7 and 8 show constellation diagrams for the X polarization signals for 85.672 and 112 Gbit/s PM 16-QAM signals without added ASE noise. These results are for data sets comprised of 54,256 and 69,850 symbols, respectively.
The dependence of the BER on the OSNR is shown in Fig. 9 for the 85.672 Gbit/s PM 16-QAM signal. In this case, a raised-cosine pulse shape with r = 1 was used. Theoretical results are also shown without and with differential encoding [17,22]. The convergence parameter for
the adaptive equalizer was 64 10µ −= × . The implementation penalty for 310BER−= is 3 dB,
in part due to the combined bandwidth limitation of the DACs and drive amplifiers. Each value of the BER is based on 271,820 symbols.
#155773 - $15.00 USD Received 30 Sep 2011; accepted 12 Nov 2011; published 1 Dec 2011(C) 2011 OSA 12 December 2011 / Vol. 19, No. 26 / OPTICS EXPRESS B632
Fig. 7. Constellation diagram for the X-polarization of the 85.672 Gbit/s PM 16-QAM signal.
Fig. 8. Constellation diagram for the X-polarization of the 112 Gbit/s PM 16-QAM signal.
14 16 18 20 22 24 26 2810
-6
10-5
10-4
10-3
10-2
Theory
Bit E
rro
r R
atio
Optical Signal-to-Noise Ratio (dB)
Theory with
differential
coding
85.672 Gb/s
Fig. 9. Dependence of the bit error ratio on the optical signal-to-noise ratio (noise bandwidth of 0.1 nm) for 85.672 Gbit/s PM 16-QAM (raised-cosine pulse with r = 1).
#155773 - $15.00 USD Received 30 Sep 2011; accepted 12 Nov 2011; published 1 Dec 2011(C) 2011 OSA 12 December 2011 / Vol. 19, No. 26 / OPTICS EXPRESS B633
Figure 10 illustrates optical spectra for the 112 Gbit/s PM 16-QAM signal using the raised-cosine pulse (r = 0.5) and Gaussian filtered rectangular pulse. The resolution bandwidth of the optical spectrum analyzer was set to 0.01 nm. The 3 and 20 dB bandwidths are very similar for the two pulse shapes.
1549.9 1550.0 1550.1 1550.2 1550.3-30
-20
-10
0
10 Gaussian Filter
Raised-Cosine (r = 0.5)
No
rma
lize
d M
ag
nitu
de
(d
B)
Wavelength (nm)
112 Gb/s
RBW = 0.01 nm
Fig. 10. Optical spectra for 112 Gbit/s PM 16-QAM (Gaussian filtered rectangular pulse and raised-cosine pulse with r = 0.5). The resolution bandwidth is 0.01 nm.
The dependence of the BER on the OSNR is shown in Fig. 11 for the 112 Gbit/s PM 16-QAM signal. Theoretical results are also shown without and with differential encoding [16,
21]. The convergence parameter for the adaptive equalizer was 62 10µ −= × . The
implementation penalty for 310BER−= is 4.8 dB for the Gaussian filtered rectangular pulse
and 5.8 dB for the raised-cosine pulse (r = 0.5). Each value of the BER is based on 349,250 symbols.
16 18 20 22 24 26 28 3010
-5
10-4
10-3
10-2
Theory with
differential
coding
Gaussian filtered
Raised cosine
Bit E
rror
Ratio
Optical Signal-to-Noise Ratio (dB)
Theory
112 Gb/s
Fig. 11. Dependence of the bit error ratio on the optical signal-to-noise ratio (noise bandwidth of 0.1 nm) for 112 Gbit/s PM 16-QAM (Gaussian filtered rectangular pulse and raised-cosine pulse with r = 0.5).
Finally, Fig. 12 illustrates the constellation diagram for the X-polarization signal for the 112 Gbit/s PM 16-QAM signal with an OSNR of 23 dB. The red constellation points indicate the symbol errors, the distribution of which indicates a properly biased IQ modulator.
#155773 - $15.00 USD Received 30 Sep 2011; accepted 12 Nov 2011; published 1 Dec 2011(C) 2011 OSA 12 December 2011 / Vol. 19, No. 26 / OPTICS EXPRESS B634
Fig. 12. Constellation diagram for the X-polarization of the 112 Gbit/s PM 16-QAM signal. The red open constellation points indicate the symbol errors.
5. Conclusion
The required sampling rate for the generation of 112 Gbit/s PM 16-QAM signals can be reduced by decreasing the modulated signal bandwidth. For a sampling rate of 21 GSa/s (1.5 samples per symbol), a Gaussian filtered rectangular pulse provides a significantly larger eye
opening compared to a raised-cosine pulse with a roll-off factor of 0.5. For 310BER−= in a
back-to-back system configuration, the Gaussian filtered rectangular pulse exhibits a 1 dB advantage in terms of the required OSNR.
#155773 - $15.00 USD Received 30 Sep 2011; accepted 12 Nov 2011; published 1 Dec 2011(C) 2011 OSA 12 December 2011 / Vol. 19, No. 26 / OPTICS EXPRESS B635
