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Interactive Advanced Beamforming (Spatial multiplexing, Rank, and Condition Number) Simulation


MIMO Beamforming & Matrix Lab

Visualizing Spatial Multiplexing and Channel Orthogonality. (Assuming Antenna Element Spacing is λ/2)

1. System Configuration

Note: If two users are at the same angle, the Rank drops and Condition Number goes to ∞.

Real-Time Wave Propagation

Computed Rank

0

---

Condition Number (\(\kappa\))

1.0

---

Channel Matrix \(H\)

📡 Spatial Multiplexing

The core "magic" of MIMO. It allows us to transmit multiple unique data streams (layers) simultaneously over the same frequency. By using different antennas, we create separate spatial "pipes" for each user.

Read More about Spatial Multiplexing →

📊 Matrix Rank (\(\rho\))

Rank represents the number of independent highways available in the air. If you have 4 antennas and 2 users, you want Rank 2. If users overlap, the Rank drops to 1, meaning you can only send one data stream reliably.

Read More: Array Response (for element spcing, etc.) →

⚖️ Condition Number (\(\kappa\))

This measures how "separable" the users are. A low \(\kappa\) (close to 1) means the channels are perfectly distinct. A high \(\kappa\) (toward \(\infty\)) means the channels are too similar, leading to massive interference and "noise amplification."

Read More: Rank and Condition Number →
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