Transmission demand continues to grow and higher capacity optical communication systems are required to economically meet this ever-increasing need for communication services. This article expands and deepens the study of a novel optical communication system for high-capacity Local Area Networks (LANs), based on twisted optical fibers. The complete statistical behavior of this system is shown, designed for more efficient use of the fiber single-channel capacity by adopting an unconventional

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... ilevel polarization modulation (called "bands of polarization"). Starting from simulative results, a possible reference mathematical model is proposed. Finally, the system performance is analyzed in the presence of shot-noise (coherent detection) or thermal noise (direct detection). freedom provided by the use of the State of Polarization (SOP) of a fully polarized light wave as a "modulation parameter" in a three-dimensional [7] and a four-dimensional Euclidean space [8] . Birefringence causes SOP changes during the propagation of the signal along the optical fiber. Therefore, M-PolSK modulations, despite a better exploitation of the single channel bandwidth [9], require a complex receiver, able to track the birefringence for the correct estimation of the transmitted symbols. In [10] it is shown that by applying a novel M-PolSK modulation in a twisted fiber, it is possible to confine the SOP evolution of the transmitted symbols within specific physical "polarization bands" (on the surface of the Poincaré sphere). In this way, at the receiver end, there is no need to implement a complex mechanism for tracking the birefringence because it is sufficient to identify the band of polarization of the received SOP to estimate the transmitted symbol. This modulation also offers the advantage of a "fluid" constellation of symbols that no longer need to belong to a rigid geometric structure. The advantage of a "fluid" constellation lies in the fact that the decision regions may be associated directly with physical regions. The structure of the constellation is such that the modulator must only change the value of the S 3 component. The drawback is the presence of a limited number of polarization bands (physical tracks), conditioned by the twisting process that is possible to be introduced in the optical fiber. Moreover, the performance of the proposed system is compatible with those systems with a similar number of symbols, but with the advantage of a simpler receiver structure. This paper, starting from the model proposed in [10] , analyzes the statistical properties of this novel multilevel polarization modulation for twisted fibers that can be used in a Local Area Network (LAN) environment. In fact, the proposed system would fit the LAN environment very well, such as the systems mentioned in [11, 12] . In this case, the advantage is not related to the growth of the total throughput, but rather to the complexity reduction of the transmitter and receiver. Moreover, a mathematical model [13] for the evolution of the SOP along the twisted fiber is proposed and compared with the simulative results. Finally, the performance of this system is compared with that of the standard M-PolSK modulations both in the case of coherent detection (shot-noise limited) [7] and direct detection (thermal noise limited) [14] .