Advanced crosstalk reduction in an [formula omitted] two-stage AWG-based switch with odd [formula omitted

Abstract

When multiple signals of the same wavelength cross an arrayed waveguide grating (AWG) at the same time, crosstalk of the same wavelength can severely degrade the quality of the signals. An N×N two-stage AWG-based switch architecture was proposed in an earlier study to tackle the crosstalk problem, where each scheduling decision is represented by a permutation, and a permutation is called k-legal if signals with the same wavelength appear at most k times. The study showed that each permutation can be decomposed into two 4-legal permutations. In addition, for an N×N switch with 4≤N≤12, it showed that each permutation can be decomposed into two 2-legal permutations, π1 and π2, where π1 is chosen from a small set Π1. But no specific method was proposed to show how to generate Π1. In this paper, we further reduce the crosstalk of the 2-stage AWG-based switch for every odd N by lowering the number of signals using the same wavelength in each decomposed permutation. We derive various sufficient conditions for permutations to be decomposed into two permutations, τ1 and τ2, where τ1 is 1-legal and τ2 is 2-legal. In addition, to decompose each permutation into permutations τ1 and τ2, with the proviso that τ1 and τ2 exist, we propose an algorithm to generate a more compact set than Π1, even less than half, to choose τ1.