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How Rank and Condition Number Affects Beamforming?

 

MIMO Beamforming: Physics to Math

MIMO Beamforming & Channel Analysis for (N X 2)

How spatial separation determines Matrix Rank and Condition Number (assuming number of users are 2)

1. Physical Config

Channel Matrix \(H\) (Derived)

Antenna Array Response in Detail →

Spatial Beam Patterns

Matrix Rank
2

Full Rank

Condition Number
1.0

Excellent

MIMO Insights

The Experiment: Move User 1 and User 2 to the same angle. Watch the Rank drop to 1.

Rank: In a 2-user MIMO system, Rank 2 means we can send two separate data streams. If Rank = 1, the users are "interfering" so much they appear as one.

Condition Number (\(\kappa\)): As users get closer, \(\kappa\) increases.

If \(\kappa > 20\), a "Zero-Forcing" beamformer will accidentally amplify noise, causing a dropped connection even with high signal!

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