Duobinary modulation for optical systems

By Hari Shankar

Duobinary modulation turns out to be a much better choice in this case; it is more resilient to dispersion and is also reasonably simple to implement. This paper explains the basics of duobinary modulation and presents lab measurements that clearly show the format’s superiority to NRZ modulation for an uncompensated optical fiber channel.

Duobinary modulation is a scheme for transmitting R bits/sec using less than R/2 Hz of bandwidth.1,2 Nyquist’s result tells us that to transmit R bits/sec with no intersymbol interference (ISI), the minimum bandwidth required of the transmitted pulse is R/2 Hz. This result implies that duobinary pulses will have ISI. However, this ISI is introduced in a controlled manner so that it can be subtracted out to recover the original values.

NRZ is one such scheme and requires a bandwidth of R Hz to transmit R bits/sec (this is twice as large as the Nyquist bandwidth of R/2 Hz).

We then see from (0.1) and (0.3) that at the sampling instance kT, the receiver does not recover the data bit dk, but rather dk-1 + dk). However, this scheme allows for pulses with a smaller bandwidth. By allowing some ISI, the transmitted pulse q(t) can be made longer in the time domain, and hence its spectrum becomes narrower in the frequency domain. With a narrower spectrum, there are also fewer distortion effects of the channel. This outcome is one of the reasons why duo­binary modulation is resilient to dispersion.

One way of generating duobinary signals is to digitally filter the data bits with a two-tap finite impulse response (FIR) filter with equal weights and then low-pass filter the resulting signal to obtain the analog waveform with the property in (0.3) (see Figure 1, left). When the input to the FIR filter is binary (let these binary values be -1 and 1), the output can take on one of three values: 0.5*(-1 + -1) = -1; -1 + 1 = 0; or 0.5*(1 + 1) = 1. Therefore, the duobinary signal is a three-level signal.

An important property of the three-value sequence at the output of the FIR filter is that it is a correlated signal; thus, all possible sequences of the three values cannot occur. For example, the output sequence of the FIR filter cannot contain a 1 followed by a -1, or a -1 followed by a 1; a 1 and a -1 will always have a 0 between them. Similarly, the combinations {1 0 1} and {-1 0 -1} also can never occur at the output of the FIR filter; only a {-1 0 1} or a {1 0 -1} can occur. As will be explained later, this sequence is another reason why duobinary modulation is resilient to dispersion.

On a final note, the FIR filter and the low-pass filter can be combined into a single analog filter for ease of implementation (see Figure 1, right). The two-tap FIR filter is, after all, a simple low-pass digital filter. For a 10-Gbit/sec data stream, a good filter that combines the functions of the FIR filter and the analog filter is a 2.8-GHz Bessel filter.

with q(t) satisfying (0.3). Thus, at the sampling instance kT, the receiver samples the value ck⊕ck-1= ck-1 ⊕dk ⊕ck-1= dk.

Another circuit that does not involve delay in the feedback path is a divide-by-2 counter, which has a clock gated with the data. When the data is high, the counter changes state, which is equivalent to adding a 1 modulo 2. When the data is low, the counter state remains the same, which is equivalent to adding a 0 modulo 2.

The combination of the duobinary encoder and the above mapping to electric fields helps further reduce the effects of dispersion in the fiber.5 As the pulses travel down the fiber, they spread out in time owing to dispersion. In an NRZ scheme, a data sequence of {1 0 1} is mapped onto the optical domain as {+E 0 +E}. In the encoded duobinary sequence, a {1 0 1} sequence cannot occur, but a {1 0 -1} does occur, which is mapped to {+E 0 -E} in the optical domain. The effect of dispersion in the two cases is shown in Figure 2, which depicts why the resulting dispersion is less in the case of duobinary modulation.

The same receiver that is used for an NRZ modulation scheme can be used for duobinary modulation. The power detector squares the electric field to detect power; thus, the +E and -E outputs of the fiber get mapped to the same power level and are detected as logical 1s.

The complete duobinary transmitter is shown in Figure 3. An inverter is added at the input to the differential encoder; without it, the data at the receiver is inverted. This inverter can be placed either at the receiver or the transmitter. Since signal paths are usually differential, the inverter is not an additional piece of hardware that is required but instead can be implemented by reversing the differential lines from the data source to the AND gate.

An interesting property of the 27-1 PRBS sequence used (generator polynomial = 1 + x6 + x7) is that following differential encoding, it is the same PRBS sequence shifted by 6 bits. (The property that a differentially encoded PRBS sequence is a delayed version of the original sequence holds true whenever the generator polynomial is of the form 1 + xn + xn+1, n > 0, and the resulting delay between the PRBS sequence and the differentially encoded sequence is (n - 1)). Since the BERT is capable of aligning the transmitted and received data streams, the delay is of no consequence, and the step of differentially encoding the data can be eliminated.

Thanks to Anjali Singh, Joe Lynch, Tom Broekaert, and others at Inphi for the lab measurements.

Hari Shankar is principal engineer at Inphi Corp. (www.inphi-corp.com).

1. A. Linder, “The Duobinary technique for High Speed Data Transmission,” IEEE Trans. Commun. and Electron., Vol. 82, pp. 214-218, 1963.

2. J. Proakis, “Digital Communications.”

3. G. May, A. Solheim, and J. Conradi, “Extended 10 Gb/s Fiber Transmission Distance at 1538 nm Using a Duobinary Receiver,” IEEE Photon. Technol. Lett., Vol. 6, No. 5, August 1997.

5. T. Franck, P.B. Hansen, T.N. Nielsen, and L. Eskildsen, “Duobinary Transmitter with Low Intersymbol Interference,” IEEE Photon. Technol. Lett., Vol. 10, No. 4, April 1998.