Systems and methods for lattice reduction

A lattice reduction method for a multiple-input multiple-output communication system, the method comprising:

• providing a channel matrix corresponding to a channel in a multiple-input multiple-output communication system;
• preprocessing the channel matrix to form at least an upper triangular matrix;
• performing a size reduction process on elements of the upper triangular matrix;
• and
• implementing a rapid basis update process on diagonal elements in the upper triangular matrix, comprising
• choosing an efficient Siegel condition factor;
• and
• evaluating whether a first Siegel condition is satisfied between a first pair of adjacent diagonal elements of the upper triangular matrix comprising a first diagonal element and a second diagonal element without using multiplication operations, the first Siegel condition based in part on the efficient Siegel condition factor.

A lattice reduction method for a multiple-input multiple-output communication system, the method comprising:

• providing a channel matrix corresponding to a channel in a multiple-input multiple-output communication system;
• preprocessing the channel matrix to form at least an upper triangular matrix;
• performing a size reduction process on elements of the upper triangular matrix;
• and
• implementing an iterative basis update process on elements in the upper triangular matrix, comprising computing a 2×2 unitary matrix using a number of vectoring iterations,
• wherein the computing the 2×2 unitary matrix is completed in a number of cycles equal to a number of pipeline stages plus the number of vectoring iterations minus one.

A lattice reduction system, comprising:

• a master processor configured to transmit a complex-integer output to a first First-In First-Out (“FIFO”) queue and a 2×2 unitary matrix output to a second FIFO queue;
• a first slave processor in indirect communication with the master processor by way of at least the first FIFO queue and configured to receive the complex-integer output from the first FIFO queue and process a unimodular matrix;
• and
• a second slave processor in indirect communication with the master processor by way of at least the second FIFO queue and configured to receive the 2×2 unitary matrix output from the second FIFO queue and process a second unitary matrix,
• wherein the master processor, the first slave processor, and the second slave processor utilize a single multiplier pipeline structure.