Multiple input, multiple output communications systems

A multiple-input, multiple-output signal transmission system comprising:

• a plurality of signal inputs, each signal input configured to provide an input signal;
• a plurality of multipliers, each multiplier configured to weight a respective input signal with a respective value of a vector (V);
• a plurality of transmit combiners, each transmit combiner configured to combine respective ones of the plurality of weighted input signals;
• a plurality of transmit antennas, each transmit antenna configured to transmit one of the combined weighted input signals;
• a plurality of receive antennas, each receive antenna configured to receive the transmitted signals;
• a plurality of receive vector multipliers, each receive vector multiplier configured to weight a respective received signal from a one of the plurality of receive antennas with a respective value of a vector of the form V−1L−1, wherein L comprises a lower triangular matrix and the inverse of V is designated as V−1;
• a plurality of receive combiners, each receive combiner configured to combine a plurality of the weighted received signals;
• and
• a plurality of signal outputs.

A method of transmitting a signal through a transmission channel comprising:

• calculating a transmission matrix H representing the transmission channel;
• using a first decomposition technique to decompose the transmission matrix H into a product of a lower triangular matrix L and a unitary matrix Q, such that H=LQ;
• orthogonalizing the unitary matrix Q using a second decomposition technique to decompose the unitary matrix Q into a product of:
• a matrix V comprising transmitter weighting coefficients;
• a diagonal matrix Λ comprising at least one eigenvalue;
• and
• an inverse of matrix V represented as V−1, such that Q=V Λ V−1;
• combining the results of the first decomposition and the second decomposition such that the transmission matrix H=L V Λ V−1;
• and
• transmitting the signal through the transmission channel using the transmission matrix H.