Generalized OFDM (GOFDM) for ultra-high-speed serial optical transport networks
View Patent ↗A coded multidimensional modulation system called generalized OFDM (GOFDM) uses orthogonal subcarriers as bases functions, and the signal constellation points of corresponding multidimensional constellation diagram are obtained as N-dimensional Cartesian product of one-dimensional PAM/two-dimensional QAM. In GOFDM, the N-dimensional/2N-dimensional signal constellation point is transmitted over all N subcarriers/2N-subcarriers, which serve as individual bases functions. Even if some of the subcarriers are severely affected by channel distortion, the overall signal constellation point will face only small distortion, when strong channel capacity achieving channel codes are used. In addition, because the channel capacity is a linear function of number of dimensions, the spectral efficiency of optical transmission systems is significantly improved. Finally, since Euclidean distance of multidimensional signal constellation is much larger that that of two-dimensional signal constellations, OSNR sensitivity is dramatically improved.
1. A high speed optical transport network, comprising:
one or more low-density parity-check (LDPC) encoders each receiving a source channel;
an interleaver coupled to the LDPC encoders;
an N-dimensional mapper coupled to the interleaver;
an inverse FFT (IFFT) block coupled to the N-dimensional mapper to generate N-dimensional pulse-amplitude modulation (ND-PAM) signal constellation points' coordinates;
a cyclic extension insertion and parallel to serial (P/S) conversion block coupled to the IFFT block;
means for adding all coordinates, upon multiplication with exp[j2nkt/T], to provide real and imaginary parts of a signal used as in-phase and quadrature signals for Mach-Zehnder modulators (MZMs);
wherein an FFT block provides projections along subcarrier basis functions, and where a kth FFT output represents the projection along a kth coordinate; and
wherein an a posteriori probability (APP) demapper comprises a symbol log-likelihood ratio (LLR) calculator to determine
λ( S i )=log [ P ( S i =S 0 |R i )/ P ( S i ≠S 0 |R i )],
where P(S i |R i ) is determined by Bayes' rule as:
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wherein S i denotes a transmitted signal constellation point, R i denotes a received constellation point, where S 0 denotes a referent constellation point, P(R i |S i ) denotes a conditional probability estimated by collection of histograms, and P(s) denotes a priori probability of symbol S.
2. The network of claim 1 , wherein signal constellation points of an N-dimensional pulse amplitude modulation (ND-PAM) constellation diagram are generated as an N-dimensional Cartesian product of a one-dimensional PAM; and wherein the N-dimensional signal constellation points are transmitted over all N orthogonal subcarriers serving as individual bases functions.
3. The network of claim 1 , wherein signal constellation points are obtained as N-dimensional Cartesian product of a two-dimensional QAM or PSK signal constellations; and wherein the 2N-dimensional signal constellation points are transmitted over all 2N orthogonal subcarriers serving as individual bases functions.
4. The network of claim 3 , comprising digital to analog converters coupled to the cyclic extension insertion and parallel to serial (P/S) conversion block.
5. The network of claim 3 , comprising:
a. digital to analog converters (DACs) coupled to the cyclic extension insertion and parallel to serial (P/S) conversion block; and
b. low pass filters coupled to the DACs, respectively.
6. The network of claim 1 , wherein signal constellation points are obtained maximizing the mutual information of the channel; and wherein the N-dimensional signal constellation points are transmitted over all N orthogonal subcarriers serving as individual bases functions.
7. The network of claim 1 , comprising a receiver to receive ND-PAM signals.
8. The network of claim 1 , comprising a receiver to receive ND-QAM signals.
9. The network of claim 1 , comprising a receiver to receive ND-optimum signal constellation signals.
10. The network of claim 9 , comprising a cyclic extension removal and serial to parallel (S/P) conversion block coupled to the DACs.
11. The network of claim 10 , wherein the FFT block is coupled to the cyclic extension removal and serial to parallel (S/P) conversion block.
12. The network of claim 11 , wherein the APP demapper is coupled to the FFT block.
13. The network of claim 1 , comprising a polarization beam splitter coupled to the receiver for splitting the ND-PAM signals or ND-QAM signals into two orthogonal polarizations that are used as input into two coherent detectors.
14. The network of claim 1 , wherein a coherent detector generates outputs as real and imaginary parts of a complex sequence stream.
15. The network of claim 13 , comprising:
a. digital to analog converters (DACs) coupled to the coherent detectors; and
b. low pass filters coupled to the DACs, respectively.
16. The network of claim 1 , comprising performing an N-dimensional mapper as a look-up table (LUT) with b input bits serving as a memory address that selects the N-coordinates of an ND-PAM signal constellation point.
17. The network of claim 1 , comprising performing an 2N-dimensional mapper as a look-up table (LUT) with b′ input bits serving as a memory address that selects the 2N-coordinates of an ND-QAM signal constellation point.