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If i said that these two beamformings $\mathbf f_a $ and $ \mathbf f_b $ are orthogonal to each other,does it mean $\mathbf f_a \cdot \mathbf f_b \approx 0$ ?

Because i have see two paper about orthogonal beamforming,but they both doesn't mention this relation.i just want to make sure about that

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If you want to use the orthogonal beamforming to cancel the "interference of the other signal",orthogonal beamforming doesn't mean that the each beamformings are orthogonal to each other.

If $B$ transmits $x_b$ ,and $C$ transmits $x_c$ to $A$ at the same time and frequency.and $h_{AB}$ means the channel between $A$ and $B$,$h_{AC}$ means the channel between $A$ and $C$

orthogonal beamforming means that the beamforming of $x_b$ has to be orthogonal to the channel between $A$ and $C$,that is $ f_b \cdot h_{AC} =0$,not $f_b \cdot f_a =0 $

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Orthogonality might be considered in literature as background knowledge. The definition is somehow a converse version. If $\cdot $ denotes an inner product (or a dot or scalar product), and whenever $\mathbf f_a \cdot \mathbf f_b = 0$, then $f_a$ and $f_b$ are said to be orthogonal.

Note that, if $\mathbf f_a$ is zero, it is orthogonal to everything.

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