# The Three Factors of Superior Spectral Efficiency

June 1, 2022

By Paul Momtahan

Director, Solution Marketing

As discussed in a previous blog, spectral efficiency is determined by three transmission factors: the number of raw bits per symbol, the overhead efficiency, and the amount of spectrum “wasted” due to the required gaps between wavelengths, as shown in Figure 1. In this follow-on blog I will describe these three factors in more detail, highlighting the optical engine and line system features that enable superior spectral efficiency, and wrapping up with a brief explanation of how Shannon’s law is starting to limit improvements in spectral efficiency.

*Figure 1: The three factors that determine spectral efficiency*

### Factor 1: More Raw Bits Per Symbol

The first factor that enables superior spectral efficiency is getting more bits per symbol for a given set of reach conditions. At shorter distances, this comes down to higher-order modulation. Advanced optical engine features that enable more bits per symbol for a given set of reach conditions include long-codeword probabilistic constellation shaping (LC-PCS), Nyquist subcarriers, and a high modem signal-to-noise ratio (SNR). Dynamic bandwidth allocation (DBA) combines LC-PCS and Nyquist subcarriers to enable more bits per symbol on the inner subcarriers, thus increasing the aggregate number of bits per symbol for the wavelength. Efficient forward error correction (FEC) can also increase the number of bits per symbol for a given set of reach conditions, with SD-FEC gain sharing enabling two wavelengths to share FEC gain, thus increasing the number of raw bits per symbol on the second, more challenged wavelength.

*Figure 2: Multiple modes required to optimize for each part of the spectrum in a submarine fiber*

High levels of optical engine programmability in terms of both the baud rate and modulation (bits per symbol) can also enable superior spectral efficiency, especially on submarine fibers where performance in different parts of the spectrum varies with tilt, ripple, dispersion, and nonlinearities, as shown in Figure 2. For example, the ICE6-powered CHM6 transponder for the GX G42 Compact Modular Platform currently supports over 200 combinations of baud rate and modulation bits per symbol. And while in theory PCS alone can provide the required performance granularity, the need to align to useful bandwidth increments (i.e., 50 Gb/s or 100 Gb/s) makes the combination of modulation and baud rate programmability highly beneficial.

Another factor that can maximize spectral efficiency in subsea networks is a super-Gaussian PCS distribution that results in less variation in the power levels of the symbols and therefore lower nonlinear impairments. This makes super-Gaussian ideal for dispersion-uncompensated large-effective-area fibers that typically operate at high power levels. For legacy dispersion-managed subsea cables, specialized 4D and 8D multi-dimensional modulation formats can be key to maximizing spectral efficiency.

In terrestrial networks, the optical line system can also play a role in enabling more bits per symbol for a given set of reach conditions. Low noise, high gain amplification, low filter narrowing, and advanced optical link control that better optimizes wavelength and amplifier power levels can enable more bits per symbol.

### Factor 2: Higher Overhead Efficiency

The second factor that drives superior spectral efficiency is overhead efficiency – that is, for a given number of raw bits per symbol transmitted, how many of those bits are used for the data payload versus the overhead. Efficient FEC with a high net coding gain is one example of a feature required for high overhead efficiency. A second example of how overhead efficiency can be improved is ICE6’s Ethernet framing mode, which reduces the framing overhead for Ethernet client traffic compared to OTN framing modes that can support both Ethernet and OTN type clients. Probabilistic constellation shaping is also a form of overhead, with PCS-64QAM actually transmitting 12 bits per symbol, with the distribution matcher’s bits-to-symbols mapping acting as overhead. One future strategy for overhead optimization is optimally balancing FEC and PCS overhead and gain.

### Factor 3: Minimized Spectral Waste

*Figure 3: Wasted spectrum*

The third factor that drives superior spectral efficiency is how tightly the wavelengths can be packed together, or to put it another way, minimizing the wasted spectrum between wavelengths, as shown in Figure 3. One way to reduce the wasted spectrum is to have a single high-baud-rate wavelength rather than many low-baud-rate wavelengths occupying the same spectrum, which requires an inter-wavelength gap between each wavelength. Another way to reduce waste is to utilize super-channels, packing multiple individual wavelengths together in a single block of spectrum. Another technique is to create wavelengths with a sharper roll-off, or a squarer frequency-domain shape, as shown on the right of Figure 4. A sharper roll-off reduces wasted spectrum by enabling wavelengths to be packed closer together. A final optical engine capability that can contribute to less spectral waste is a shared wavelocker. This enables the lasers of two or more wavelengths to drift, for example due to changes in temperature, in tandem, thus reducing the amount of guardband that would be required to support uncorrelated frequency shifts.

*Figure 4: Tighter roll-off enables closer wavelength packing*

In addition to these optical engine features, minimizing spectral waste also requires flexible-grid ROADMs with the ability to control both the width and center frequency of each channel with high granularity.

### Spectral Efficiency Limitations

A 1948 paper published by Claude Shannon, the mathematician, electrical engineer, and information theorist who then worked at Bell Labs, established what became known as Shannon’s law, otherwise known as the Shannon-Hartley theorem. This law/theorem puts a limit on the amount of information that can be communicated over a channel with a given bandwidth and amount of noise. Today’s state-of-the-art high-performance embedded optical engines, such as Infinera’s ICE6, are typically between 1 and 2 dB from the Shannon limit, meaning that any future spectral efficiency gains are likely to be incremental.

Optical conference proceedings also sometimes include papers referring to the “nonlinear Shannon limit” which provides a lower bound based on nonlinear penalties that is arrived at by simulations. New nonlinear mitigation techniques can beat this lower nonlinear “limit,” but they can never beat the (linear) Shannon limit or the true, currently unknown, upper limit that would be a function of both linear and nonlinear penalties.

So, to summarize, maximizing spectral efficiency requires both optical engine and line system innovations that can optimize the number of bits per symbol, overhead efficiency, and spectral waste. However, with today’s state-of-the art optical engines getting close to the (linear) Shannon limit for spectral efficiency, other methods for increasing capacity such as lighting new spectrum bands on existing fibers and space-division multiplexing (SDM), either with more fibers per subsea cable or with new multi-core or multi-mode fibers in terrestrial networks, are likely to become increasingly important.

For more information on this important topic, download the Infinera white paper, *Maximizing Spectral Efficiency with Optical Engine and Line System Innovations.*