Systems and methods for communication using sparsity based pre-compensation

A system for facilitating pre-compensation of a data signal to be transmitted via communication medium, the system comprising:

• a first processor;
• and
• a first memory in electrical communication with the first processor, the first memory comprising instructions which, when executed by a processing unit comprising at least one of the first processor and a second processor, and in electronic communication with a memory module comprising at least one of the first memory and a second memory, cause the processing unit to:
• receive a data symbol corresponding to a transmission mode of the communication medium, the data symbol being represented at least in part by an original amplitude;
• determine a set of pre-compensated launch amplitudes for the data symbol, the set of pre-compensated launch amplitudes being based on, at least in part, the original amplitude and a nonlinear property of the communication medium, wherein to determine of the set of pre-compensated launch amplitudes, the instructions cause the processing unit to:
• compute using a sparse fast Fourier transform (sFFT) a sparse kernel having a set of values based on the nonlinear property of the communication medium, each value corresponding to a respective unique pair of distance and propagation time values along a selected distance of the communication medium;
• represent propagation of the data symbol through the communication medium over the specified distance as a fixed-point iterative computation based on:
• (i) the sparse kernel, and (ii) a set of amplitudes, each amplitude in the set corresponding to a respective unique pair of distance and propagation time values;
• determine based on the original amplitude an initial value for each amplitude in the set of amplitudes;
• iterate the fix-point iterative computation until an earlier of:
• (i) convergence of the iterative computation, and (ii) performance of a maximum permissible number of iterations, and update in each iteration the values of amplitudes in the set of amplitudes from a previous iteration;
• and
• if the convergence is achieved, designate a subset of the updated amplitude values corresponding to distance value of zero the set of pre-compensated launch amplitudes, and otherwise report pre-compensation failure.