rzf_precoding_matrix

sionna.phy.mimo.rzf_precoding_matrix(h: torch.Tensor, alpha: float | torch.Tensor = 0.0, precision: Literal['single', 'double'] | None = None) → torch.Tensor

Computes the Regularized Zero-Forcing (RZF) Precoder.

This function computes the RZF precoding matrix for a MIMO link, assuming the following model:

\[\mathbf{y} = \mathbf{H}\mathbf{G}\mathbf{x} + \mathbf{n}\]

where \(\mathbf{y}\in\mathbb{C}^K\) is the received signal vector, \(\mathbf{H}\in\mathbb{C}^{K\times M}\) is the known channel matrix, \(\mathbf{G}\in\mathbb{C}^{M\times K}\) is the precoding matrix, \(\mathbf{x}\in\mathbb{C}^K\) is the symbol vector to be precoded, and \(\mathbf{n}\in\mathbb{C}^K\) is a noise vector.

The precoding matrix \(\mathbf{G}\) is defined as:

\[\mathbf{G} = \mathbf{V}\mathbf{D}\]

where

\[\begin{split}\mathbf{V} &= \mathbf{H}^{\mathsf{H}}\left(\mathbf{H} \mathbf{H}^{\mathsf{H}} + \alpha \mathbf{I} \right)^{-1}\\ \mathbf{D} &= \mathop{\text{diag}}\left( \lVert \mathbf{v}_{k} \rVert_2^{-1}, k=0,\dots,K-1 \right)\end{split}\]

where \(\alpha>0\) is the regularization parameter. The matrix \(\mathbf{D}\) ensures that each stream is precoded with a unit-norm vector, i.e., \(\mathop{\text{tr}}\left(\mathbf{G}\mathbf{G}^{\mathsf{H}}\right)=K\). The function returns the matrix \(\mathbf{G}\).

Parameters:

• h (torch.Tensor) – Channel matrices with shape […, K, M]

• alpha (float | torch.Tensor) – Regularization parameter with shape […] or scalar

• precision (Literal['single', 'double'] | None) – Precision used for internal calculations and outputs. If set to None, precision is used.

Outputs:

g – […, M, K], torch.complex. Precoding matrices.

Examples

h = torch.complex(torch.randn(4, 8), torch.randn(4, 8))
g = rzf_precoding_matrix(h, alpha=0.1)
# g.shape = torch.Size([8, 4])