Abstract
The performance of various nonlinear frequency division multiplexed (NFDM) fiber-optic transmission systems has been observed to decrease with increasing signal duration. For a class of NFDM systems known as b-modulators, we show that the nonlinear bandwidth, signal duration, and power are coupled when singularities in the nonlinear spectrum are avoided. When the nonlinear bandwidth is fixed, the coupling results in an upper bound on the transmit power that decreases with increasing signal duration. Signal-to-noise ratios are consequently expected to decrease, which can help explain drops in performance observed in practice. Furthermore, we show that there is often a finite bound on the transmit power of b-modulators even if spectral singularities are allowed.
Highlights
The nonlinear Fourier transform (NFT) [1] is a mathematical tool to solve the normalized nonlinearSchrödinger equation (NSE) i ∂q 1 ∂2 q + + κ |q|2 q = 0,∂z 2 ∂t2 q = q(z, t), (1)which is a model for an ideal lossless single-mode fiber obtained after suitable normalization and path averaging [2]. (The path average can be avoided by using tapered fibers [3].) Here, q(z, t) is the slowly varying pulse envelope, z is the location, and t is retarded time, all in normalized units
A common problem with many nonlinear frequency division multiplexing (NFDM) designs is that the optimum transmit power decreases with signal duration, making it difficult to utilize signals significantly longer than the channel memory [10,11,18,19,20]
In [19], we discovered a new factor contributing to this phenomenon when we derived an upper bound on the transmit power of one specific NFDM system proposed in [21]
Summary
The nonlinear Fourier transform (NFT) [1] is a mathematical tool to solve the normalized nonlinear. It was suggested to embed data in the NFD at the transmitter and use the NFT to recover the data at the receiver [4,5] This idea is known as nonlinear frequency division multiplexing (NFDM). In [19], we discovered a new factor contributing to this phenomenon when we derived an upper bound on the transmit power of one specific NFDM system proposed in [21].
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