# Optical Transmitters without Driver Amplifiers--Optimal Operation Conditions
## 4 Influence of DPreD on the Electrical Eye-Opening  
In this section, we describe how the complex frequency response of the link is measured, and we show the influence of DPreD on the RMS amplitude and the bit error ratio (BER) performance as derived from optical measurements. When speaking of DPreD, we correct the transmitter frequency response in the transmitter digital signal processing (DSP) before the digital-to-analog conversion; in the case of DPostD, the finite impulse response (FIR) filter correcting the transmitter frequency response is applied right at the beginning of the receiver DSP. To measure the frequency and phase response of the link, we generated a test signal and measured its frequency and phase response at the receiver. The test signal consisted of a frequency comb with predefined phase relations. The best results were obtained for a frequency comb that was only constructed with spectral coefficients that correspond to prime numbers [56]. If equidistant spacing was taken, mixing products, e.g., due to non-linearities (NL), would have interfered with the desired spectral lines and possibly could have impaired the measurements. The phase relations of the spectral lines were chosen randomly; this reduced the peak-to-average power ratio of the test signal [57]. This signal was generated with the Micram DAC4 and measured in an electrical back-to-back configuration with an oscilloscope. The measured signal was Fourier-transformed and the difference to the transmitted signal was evaluated. The FIR filter impulse response for the DPreD, as well as that for the DPostD, was then determined by the inverse Fourier transform of the relative change in the coefficients. Our experimental evaluations showed that the frequency comb is a good test signal to analyze the operation conditions of the set-up (e.g., for the bias voltage of the Mach-Zehnder modulator), minimizing the mixing products between the lines and maximizing the spectral lines lead to a linear operation point with the smallest non-linear mixing products. Figure 3a shows the amplitude spectrum of a measured frequency comb with 34 spectral lines (chosen as discussed above) for the digitally designed signal in blue and the measured signal in red. The small number of spectral lines was chosen for depictive reasons only. It was previously shown that more spectral lines give an improvement in final signal quality after application of the correction filter. The frequency and phase response, as plotted in Figure 3b, were determined as the difference of the transmitted and received signal for a frequency comb with 331 spectral lines. This measurement shows 3-dB and 6-dB bandwidths of 33 GHz and 44 GHz, respectively. Applying the correction filter to a new iteration of a comb-based frequency response measurement led to a flat response in frequency and phase. Afterward, the correction filter could be updated to slight changes in the experimental set-up or drifts by the impulse response of the least-mean-square equalizer of transmitted data. The update was done by a convolution of both impulse responses. Figure 2: Investigation of clipping on signals with SRRC pulse shape. The simulations were done with two samples per symbol, one million symbols, 30 roll-off factors, and eight clipping values (0, 0.05, 0.10, 0.14, 0.19, 0.24, 0.29, and 0.33). The black crosses indicate examples at ROFs of 0.2 and 0.4, which are discussed in the text in more detail. (**a**) RMS amplitude of clipped and normalized (to maximum) waveforms against roll-off factor. Clipping was done between 0% up to 33%, which corresponds to a saturation of the amplitude at 100% down to 67%. (**b**) Resulting signal-to-noise ratio (SNR) penalty of clipped SRRC waveforms. The SNR was evaluated after matched filtered detection. In the next step, we evaluated the influence of DPreD on the output of our DAC. The measurements were done with an electrical back-to-back set-up, where the RMS amplitude of the DAC output was directly measured with an oscilloscope with 160 GSa/s.