Meaning
Linear algebraic transformations rotate vectors in a chosen two-dimensional plane to introduce zeros in specific matrix positions. In wireless transceivers, givens rotations decompose the multi-antenna channel matrix to prepare feedback information for the transmitter. This process compresses the matrix by representing complex coefficients as a sequence of angles.
The algorithm applies these orthogonal transformations until the target matrix is reduced to an upper triangular form.
Angular Compression
Compressing the feedback payload relies on expressing each rotation as a pair of angles representing phase and amplitude. Instead of transmitting full complex numbers, the client station sends these computed angles to the access point. This reduction in data volume improves uplink efficiency during multi-user transmissions.
Hardware Implementation
Coordinate rotation digital computer processors execute these calculations using shift and add operations instead of multipliers. This architecture speeds up the execution of givens rotations in silicon chips. Designers use these hardware blocks to calculate the steering matrices within the tight timing limits of the physical layer.
Precision Limitation
Finite word length in the digital processors introduces rounding errors during each rotation step. As the number of applied givens rotations grows, these errors accumulate and degrade the orthogonality of the resulting matrices. This degradation increases the leakage between spatial streams in multi-user networks.
