The fundamentals of Duobinary

In our current society people are becoming increasingly dependent on the internet which results in a need for larger amounts of data. Moreover, this data needs to be delivered at a higher speeds which puts traditional NRZ signaling under pressure. As a result PAM4 is widely being adopted for achieving higher serial data speeds (56 Gbps and higher). Meanwhile a powerful alternative, Duobinary, is being overlooked by many. This article will give an overview of the fundamentals of Duobinary signaling showing the ease at which Duobinary can be implemented while offering higher performance than PAM4 in most cases.

Figure 1: Eye diagram and power spectral density (PSD) for an NRZ, PAM4 and Duobinary signal.

The goal of most advanced modulation schemes is to limit the needed bandwidth in order to achieve higher serial data rates. In this process SNR is typically traded for needed bandwidth. When using PAM4 this is done by combining two NRZ bits into a single PAM4 symbol resulting in half the required bandwidth. This means that a total of 4 symbols are needed leading to an SNR which is three times smaller compared to NRZ. Duobinary limits the bandwidth in a completely different way.

By adding the previous bit to each current NRZ bit a stream of Duobinary symbols is created (function: 1+z-1). This leads to a three level signal with a symbol rate identical to the original bit rate. However, the bandwidth (shown by means of the power spectral density (PSD) in Fig.1) is compressed due to the adding of bits which makes it impossible to have high speed signals transitions (e.g. a +1 can never go directly to a -1). As the bandwidth is compressed, SNR is traded in by going to three level symbols. Important to note is that in the case of Duobinary less SNR needs to be traded in compared to PAM4.

A Duobinary signal can be created at the transmitter by producing the 1+z-1 function by means of a delay-and-add block as illustrated in Fig.2. However, a more elegant solution consists of sending the NRZ stream through a low pass filter which adds intersymbol interference (ISI) corresponding to 1+z-1. This can be done by using the channel response of the transmission medium together with some equalization at either the transmitter or receiver. In this way part of the channel loss is exploited to create the Duobinary stream from an NRZ signal which means this loss doesn't need to be compensated. Moreover, this allows to have a simple NRZ transmitter providing backwards compatibility to NRZ systems.

Figure 2: Duobinary signal creation by means of delay-and-add block or filtering.

As creating a Duobinary signal is quite straightforward, the question remains how to demodulate the signal. Furthermore, the 1+z-1 function used to create Duobinary from an NRZ stream will result in error propagation: a single wrong interpreted NRZ bit at the receiver affects all following bits. This issue can be resolved by precoding the NRZ stream which not only solves the error propagation, but also allows the Duobinary stream to be demodulated by means of two slicers/comparators followed by a XOR gate as shown in Fig.3.

Figure 3: Implementation of Duobinary precoder and demodulation.

More details about the different trade-offs between NRZ, Duobinary and PAM4 and the possible implementation of Duobinary can be found in the following two papers:

56+ Gb/s Serial Transmission using Duobinary Signaling [paper] [presentation]
T. De Keulenaer, J. De Geest, G. Torfs, J. Bauwelinck, Y. Ban, J. Sinsky and B. Kozicki, DesignCon 2015

100 Gb/s Serial Transmission over copper using Duo-binary Signaling [paper] [presentation]
J. Van Kerrebrouck, T. De Keulenaer, J. De Geest, R. Pierco, et al. DesignCon 2016