# A Vision of 6 th Generation of Fixed Networks (F6G): Challenges and Proposed Directions
## 4 Optical Transmission: Key Challenges and Proposed Directions
### Capacity Increase Using More Spectrally Efficient Modulation Formats  
As analyzed above, one option to increase the transportation capacity is to boost the spectral efficiency (SE). SE is a measure of how efficiently the available bandwidth is utilized and equals the data rate divided by the allocated bandwidth. Higher SE, in essence,means that a higher rate of data can be transmitted using the same spectral width. This can be easily understood, for example, if we consider the 100G and 200G cases of Table 4, where the 200G channels double the data rate by simply tuning the modulation format from QPSK to 16 QAM. This increase in the number of \"M\" states in the M-QAM modulation formats is the most common way to increase the SE in modern coherent optical transmission systems. In addition to this method, there are two other techniques that can aid us in exploiting the available channel capacity closer to its theoretical limit, which are Probabilistic Constellation Shaping (PCS) and Geometric Constellation Shaping (GCS) [85, 86]. These methods deviate from uniform square constellations and can provide important gains in terms of the Signal-to-Noise Ratio (SNR). These two methods are pictorially described in Figure 21.  
In GCS, the location of the constellation points in the complex plane mainly focuses on the areas where the amplitude is small and less on the areas where the amplitude is high, optimizing the signal constellation and allowing it to approach the fundamental Shannon limit. Two methods for realizing GCS are (a) multi-ring constellations, which are used to estimate the Shannon limit of the nonlinear optical fiber channel, and (b) iterative polar modulation (IPM), which is used to achieve experimental SE records [86]. However, the use of GCS comes with the cost of greater complexity, as more computationally \"heavy\" DSP modules are required compared with uniform constellations. A second disadvantage of this method is that there are no simple solutions for finding locations of the GCS constellation  
Figure 21: Examples of (a) geometric and (b) probabilistic constellation shaping [86].  
Figure 20: BER performance vs. laser-linewidth when QPSK is employed [84]. CPE: Common phase error, OBE: Orthogonal basis expansion.  
points for arbitrary channel conditions, and third, Gray mapping increases the complexity of demapping symbols to soft-decision bit metrics [86].  
The second shaping method is PCS. This method more frequently exploits the inner constellation points that are less energy/power demanding while the outer points require higher energy and are exploited less frequently. In essence, PCS shapes the probability of occurrence of the constellation points rather than their locations to approximate Gaussian signaling [86]. This method provides significant gains compared with GCS, which are as follows: (a) It is simple to optimize these probabilities through a single parameter, to match any given channel condition, (b) the constellation points are placed on the rectilinear grid of a square QAM template, which facilitates coherent DSP by robust state-of-the-art square-QAM algorithms, and (c) Gray mapping facilitates symbol demapping for subsequent SD FEC. Moreover, PCS shows important advantages compared with uniform M-QAM constellations: (a) There is a much smaller drop in capacity vs. reach relation, allowing for a smoother curve; (b) the impacts of nonlinear effects are reduced, as for the same average power and spectral efficiency, there is a longer Euclidean distance between the constellation points relative to conventional QAM, increasing the overall Optical Signal to Noise Ratio (OSNR); and (c) it allows one to select a baud rate that can guarantee the optimal physical layer performance [87]. It goes with a saying that since PCS is an already commercially deployed technology able to reach 800 Gb/s rates, as shown in Table 4, it will keep advancing in order to become one of the key constellation shaping technologies in F6G long-haul and regional transmission.