Continuous-time Adaptive Equalizers with Power Spectrum Estimation

Transcription

1 Continuous-time Adaptive Equalizers with Power Spectrum Estimation C. Gimeno, B. Calvo, S. Celma and C. Aldea Group of Electronic Design. Aragon Institute of Engineering Research (I3A). University of Zaragoza, María de Luna 3, 50015, Zaragoza, Spain. Tel , Fax , s: {cegimeno, becalvo, scelma, Abstract This paper describes and compares the different approaches most commonly used for power spectrum estimation in continuous-time linear adaptive equalizers based on the conventional feedback scheme for Gbps digital communications. In addition, a new equalization approach based on the feedforward topology is proposed. As an example, simulation results demonstrate some advantage of feedforward against to the feedback scheme in serial communications on polymer optical fiber (POF). Keywords: Adaptive Equalizer, Feedforward and Feedback Control, Polymer Optical Fiber, Serial Communication. 1 Introduction Digital data have a broad spectrum, and unfortunately a practical baseband communication channel does not behave like an all-pass filter, i.e., adding only a constant delay; it usually behaves like a low-pass filter (Ziemann et al., 2008). As a consequence, different frequency components will lose different amount of power (frequency-dependent loss) and experience different amount of phase distortion (frequency-dependent dispersion) when propagating through the channel. This bandwidth limitation causes inter-symbol interference (ISI) and consequently increases de bit error ratio (BER). The bandwidth of most of the electrical communication channels are below GHz. Thus, to maintain a reliable data communication running at several Gbps or even higher, equalization is needed to reduce ISI. An equalizer provides the inverse frequency response of the channel such that the frequency response of the combination of channel and equalizer is flat over the bandwidth of interest. Equalization has been widely used to compensate the attenuation of many different electrical communication channels (twisted pairs, coaxial cables, printed circuit board traces, etc.), as well as in fiber-optic long-distance communications in order to correct the dispersion, both modal and chromatic, produced in multimode fibers (Ziemann et al., 2008; Liu et al., 2004). In medium-speed applications with silica fiber, equalization is usually not required because the bandwidth of the channel is several times higher than the frequency of transmission.

2 Nevertheless, it is essential in short-distance communications using the low-cost polymer optical fiber (POF) to achieve high bandwidth at competitive prices compared to transmission with copper wire (Bandyopadhyay et al., 2008): in this type of fiber, a short pulse of light is slightly widened as it travels through the length of the fiber due to the different types of dispersion, which considerably reduces the transmission bandwidth. In a practical POF transmission system, the exact frequency response of the channel is not known a priori. Furthermore, the characteristics of a communication channel can vary significantly. Temperature, material properties and the length of the channel are all variable; this produces that the dispersion and the attenuation of the fiber change substantially, modifying the bandwidth of the fiber. Therefore, a fixed equalization would result in overcompensation or subcompensation, and, consequently, the bit error rate will rise (Hermans et al., 2006; Sun, 2005). It is thus desirable to design an adaptive equalizer. This means that the frequency response of the equalizer must be accurately adapted depending on the frequency response of the channel. In short, an adaptive solution is faster, easier and cheaper to implement, and to maintain. The equalizer can be implemented either in the transmitter or in the receiver. The implementation of a fixed equalizer in the transmitter is relatively easier, since it can be implemented in the digital domain (Hong et al., 2007). However, it is rather difficult to apply the adaptive technique at the transmitter and the adaptability is very low (Sun, 2005). Thus, an adaptive equalization at the receiver is preferable to adapt the channel length, temperature or other process variations. The equalization at the receiver can be carried out in the digital or analogue domain. As the data rate increases, the required speed and power consumption of the analog-digital converters increase dramatically. Discrete-time equalizers require high frequency clock and high bandwidth sample-and-holds. To avoid using high-speed converters and/or high-frequency clocks, continuous-time equalizers can be used: continuous-time equalizers exhibit a good performance for low-power high-speed applications (Gimeno, 2009). This paper describes and compares different configurations of continuous-time adaptive equalizers reported in the literature. In section II, conventional feedback structures are explained and their simulation results are shown. Section III presents two new feedforward architectures of adaptive equalization, along with the obtained simulation results. Finally, in section IV the main conclusions are drawn. 2 Feedback Architectures One of the most widely used continuous-time adaptive equalization techniques is shown in Fig. 1 (Fayed et al., 2008; Babanezhad, 1998; Baker, 1996). After a first-order high-pass equalization, the input signal is applied to a slicing comparator. In order to place the zero of the equalizer effectively, a servo loop compares the slope of the slicer input signal against that of its output. 2

3 Figure 1: Block diagram of a conventional continuous-time adaptive equalizer based on the time domain comparison. The main drawback of this architecture is that the feedback output is only determined by the slope of the data response which is essentially the high-frequency information of the signal. Therefore, if the signal amplitude at the input of the slicer is not equal to the signal amplitude at the output, although the ISI is removed at the output of the equalization filter, the adaptive control loop may still output an error signal which will change the filter response. More importantly, the use of the slicer would limit the maximum speed, since the purpose of the slicer is to generate a clean waveform and to realize such a slicer becomes extremely difficult as the data rate increase. Another approach to generate the error signal is to use the power spectrum of the data stream. The key idea is that if the data has been scrambled, i.e, the bit sequence is random and length enough, then its spectrum is mathematically predictable. Consider an ideal random binary data. The normalized spectrum can be expressed as (Lee, 2006): 2 sin( f Tb ) S ( f ) Tb (1) f T b where 0 1 S ( f ) df (2) 2 and T b denotes the bit period of the data stream. To properly restore the signal, an equalizer must present an output spectrum very close to an ideal one. In other words, we can examine the power spectrum at the equalizer output, determining whether the high-frequency part is under or over compensated and accordingly adjust the boost. This is possible because the ratio of the signal power within two different 3

4 frequency ranges is constant, as we can see in Fig.2. Thus, we are able to obtain an error signal to control the equalizer, as shown in Fig.3. Figure 2: Spectrum of an ideal random sequence (left) and the effect of different compensations (right). Figure 3: Block diagram of a power spectrum based adaptive equalizer. Note that the slicer is no longer needed into the feedback loop and issues such as imbalanced swings are fully eliminated. We will thus focus on this second approach. Fig.4 illustrates four different power spectrum estimator methods. Two band-pass filters are used in (Maxim, 2003) to compare the power at two specific frequencies, see Fig.4 (a). In (Lee, 2006), one low-pass filter and one high-pass filter are used to compare the power between the low-frequency and high-frequency portions of the signal, see Fig.4 (b). In (Sun, 2005), only one low-pass filter is used and the entire signal power is compared to the power of the lowfrequency portion of the signal, see Fig.4 (c). Moreover, we can use two low-pass filters to compare the power in other two different ranges, as show in Fig.4 (d). 4

5 Normalized Transmission (db) Figure 4: Four different arrangements for power spectrum estimation. (a) Two band-pass filters, (b) a low-pass filter and a high-pass filter, (c) only a low-pass filter and the entire signal, and (d) two different low-pass filters. 2.1 Feedback Architectures Comparation In order to analyze the response for the different possibilities of power spectrum based adaptive equalizers, behavioural simulations were carried out in Matlab using Simulink, a tool for modelling, simulating and analyzing multi-domain dynamic systems (Matlab, undated). Thus, Simulink models for the power spectrum comparator (for the four configurations in Fig.4), the rectifier, the adder and the integrator were implemented, while a second order high-pass filter with a tunable zero is used like the equalizer block. All the cases will undergo the same test conditions so that a direct comparison can be made. We use a 1 Gbps, non return to zero (NRZ), pseudo random bit sequence (PRBS) with a length. This sequence passes through a block that reproduces the behavior of a commercial Mitsubishi GH POF. Its frequency response for several fiber lengths (L) from 10 to 45 m, shown in Fig. 5, makes patent the need of an adaptive equalizer because the bandwidth of the fiber changes significantly with its length. Fig. 6 shows the signal at the input of the equalizer. Note that the ISI, which can be clearly observed, is more severe after the length change at 0.1 µs dB m 12.5 m 15 m 17.5 m 20 m 25 m 30 m 35 m 40 m 45 m Frequency(Hz) Figure 5: Normalized frequency response for different lengths of Mitsubishi GH polymer optical fiber. 5

6 Amplitude (V) L Time (s) x 10-7 Figure 6: Equalizer input signal for two different lengths: L=10 m left data strean and L=40 m right data stream. To verity the proper operation of the adaptive loop, we change the length (L) of the fiber in 30 m at a certain time and observe wether the output of the equalizer and the error signal change accordingly. For example, Fig. 7 shows the output of the equalizer and how it responds when the fiber length increases or decreases 30 m in the case of using a low pass filter and comparing its output with the total signal (LPF-APF). Fig. 8 shows the control signal that is carried to the equalizer to change its response. Figure 7: Adaptive equalizer output for length changes: L = +30 m and L = -30 m. 6

7 Figure 8: Example of a control signal for length changes: L = +30 m and L = -30 m. To compare the convergence speed of different power spectrum estimators we measured the rise time (T R ) and the fall time (T F ) of the error signal, defined as the time required for the control signal to change from 10% to 90% of its total step, as we can see in Fig. 8. Table I summarizes the obtained rise and fall time of the error signal for each of the four studied feedback configurations, along with the constant time of the integrator T INT because this is a critical parameter in the implementation of the loop. Filter Tr(µs) TF(µs) τint (µs) LPF-APF 2,43 3, LPF-HPF BPF-BPF 6,70 6, LPF-LPF 3,06 5, Table 1: Comparison of Feedback Configurations We can see that the worst configuration is the two band-pass filter configuration, because it has the largest rise and fall times. The LPF-APF and LPF-HPF are two good choice because they have similar settling times. The best configuration is using a low-pass filter and comparing its output with the output of a high-pass filter. This configuration has lower rise and fall times. However, it is important to note that the structure that uses only a low-pass filter (LPF-APF) is likely to have lower power consumption because it uses a block less. 3 Feedforward Architectures Feedback architectures have the advantage that the control signal is derived from the output of the equalizer avoiding an overcompensation or subcompensation. However, the feedback configuration can suffer severe instabilities if the constant time is not larger enough (THAT, undated). 7

8 Alternatively, a feedforward architecture, which is shown in Fig. 9, can be used. It employs the signal at the input of the equalizer to generate the control signal (Israelsohn, 2002). This configuration reduces the required time constant without instability problems. Figure 9: Feedforward architecture We can use the same topology as in the feedback configuration, as shown in Fig. 10. In this case we have used only the two filter architectures that gave us better results in the case of the feedback topology: LPF-APF and LPF-HPF. The same simulation conditions have been employed as in the previous case. Results for the rise time, fall time and the constant time of the integrator are expressed in Table 2. Figure 10: Block diadram of a spectrum based adaptive feedforward equalizer. Filter TR(µs) TF(µs) τint (µs) LPF-APF LPF-HPF Table 2: Comparison of Feedforward Configurations 8

9 From the results obtained with the different feedback and feedforward configurations, it can be seen that the feedforward configuration improve the rise and fall time, as expected. It also requires the use of capacitors in the integrator approximately 500 times smaller than with a feedback architecture, allowing to improve the specifications of area in a fully integrated equalizer. 4 Conclusions In this paper the most commonly used analogue continuous-time linear equalization techniques based on the power spectrum estimation criteria have been reviewed. Matlab-Simulink simulation shows that the feedback topology based on LPF-APF, where the entire signal power is compared to the power of the low frequency portion of the signal, as power error estimator is the best option. On the other hand, a feedforward-based topology can achieve the same BER as the feedback counterpart, but with lower settling time (at least 30% lower) and time constant at least 500 times lower. At the moment of writing this paper we are designing the basic building blocks with a standard 0.18 µm CMOS process for 1 Gbps feedforward equalizer on SI-POF. 5 Acknowledgments This work has been partially supported by I3A Fellowship Program, MICINN (TEC /TEC, PET ) and DGA (PI127/08). References Babanezhad, J.N. (1998). A 3.3 V Analog Adaptive Line-Equalizer for Fast Ethernet Data Communication.In: Proc. IEEE Custom Integrated Circuits Conf., pp Baker, A.J. (1996). An Adaptive Cable Equalizer for Serial Digital Video Rates to 400Mb/s. In: ISSCC., pp Bandyopadhyay, S. et al. (2008). Integrated TIA-Equalizer for High Speed Optical Link. In: 21st International Conference on VLSI Design, VLSID, Fayed, A.A. and Ismail, M. (2008). A Low-Voltage Low-Power CMOS Analog Adaptive Equalizer for UTP-5 Cables. IEEE Transactions on Circuits and Systems-I: Regular Papers, 55(2), Gimeno, C. (2009). Diseño de Ecualizadores para Comunicaciones Ópticas de Banda Ancha en Tecnologías CMOS Nanométricas. Memoria del Postgrado de Iniciación a la Investigación en Áreas Científicas, Universidad de Zaragoza. 9

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