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8 votes
Accepted

Intuitive interpretation of Fourier transform in beamforming

The equations relate to how the directivity of a uniformly spaced linear array of sensors works. Let's start with an array: where $\theta$ is our "look" direction (where we want to steer the array), ...
Peter K.'s user avatar
  • 25.8k
7 votes
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Can a narrowband beamformer be used for speech separation

If you are dealing with say 8 kHz for a nominal speech bandwidth of of 4kHz i.e. 0 Hz - 4 kHz, then the speech is essentially a wideband signal. Therefore narrowband beamforming won't work very well. ...
David's user avatar
  • 2,871
7 votes

beam pattern are fourier transform of the beam weight, is it true ? if it's true how?

I'll work out some math that should hopefully capture the gist of the derivation of why the DFT can be used. The magnitude squared of the array factor is the beampattern for an array of isotropically ...
Baddioes's user avatar
  • 1,040
6 votes
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Plotting beam pattern of uniform linear array

You are pretty close, just a few cosmetics will get you there. Your angle resolution isn't quite high enough to hit all the narrow dips in the polar pattern. I increased it to 1000 points. You need ...
Hilmar's user avatar
  • 45.3k
6 votes
Accepted

Is there an intuitive explanation for how adaptive beamformers work?

A basic two-element array suffices to explain the general case. Also, the receiving behaviour is the reciprocal of that of the transmitting. Consider two receivers separated by $d$. A plane harmonic (...
Fat32's user avatar
  • 28.3k
5 votes
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Beamforming using MATLAB

In MATLAB the default direction of orientation of Planar array is y axis, which can be seen as ...
Zeeshan's user avatar
  • 386
5 votes

DSP with 8+ inputs for simple beamforming

8+ high quality inputs for beamfroming and "...beginner friendly..." are competing requirements. There will soon be the audioinjector which attaches on Raspberry Pi and would be a relatively ...
A_A's user avatar
  • 10.7k
5 votes

Can a narrowband beamformer be used for speech separation

The work by Darren Ward, Rod Kennedy, and Bob Williamson investigated how to design filters applied to a delay-and-sum beamformer that allowed broadband signal acquisition. As you can see from their ...
Peter K.'s user avatar
  • 25.8k
5 votes

How to derive the "well-known" solution to Unconstrained Array Gain?

A common way is to make use of the Schwarz inequality. First note that: $$\frac{|w^Hd|^2}{w^HQw} = \frac{|w^HQ^{1/2}Q^{-1/2}d|^2}{w^HQw}$$ Using the Schwarz inequality on the numerator: $$\frac{|w^HQ^{...
Gillespie's user avatar
  • 1,797
4 votes
Accepted

Delay and sum Beamforming

They're essentially the same, with the steering vector typically representing phase shifts (==delays) using complex numbers from the unity circle, and the weight vector often containing real values to ...
Marcus Müller's user avatar
4 votes
Accepted

Beam resolution improvement of linear array using MVDR beamformer

The MVDR beamformer is an adaptive technique - the response is dependent on the the interfering signals i.e. their locations, their SNRs and their correlations. This makes it difficult to say what the ...
David's user avatar
  • 2,871
4 votes

What is the relationship between beamforming and Independent Component Analysis (ICA)?

For question 1, Could they be combined in some way?, a couple of pointers: Blind source separation combining frequency-domain ICA and beamforming, ICASSP 2001 Blind Source Separation Combining ...
Laurent Duval's user avatar
4 votes
Accepted

Why is the null of an adaptive beamformer narrower than antenna beam-width?

Super-resolution techniques such as MUSIC can be used for creating higher resolution nulls (see MUSIC-based steering vector used in adaptive nulling suppression for example), but what I think may be ...
Dan Boschen's user avatar
  • 51.9k
4 votes
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What's the point of differential beamforming?

Introduction To my (rather limited) knowledge, the main advantage that made Differential Microphone Arrays (DMA) popular is their ability to have a frequency invariant beampattern (up to some certain ...
ZaellixA's user avatar
  • 1,314
4 votes

Wideband phase vs time delay beamforming correction

I am studying a 1D beamforming for wide-band signals, so that applying only phase weights to each individual antenna would steer the beam for the central frequency. For other frequencies the steering ...
Marcus Müller's user avatar
4 votes
Accepted

Why is true time delay beamforming more expensive to implement?

Here I am assuming all data is complex baseband (IQ) with digital beamforming. There is an analogous approach for analog beamforming. In phase only beamforming there is a single complex multiply per-...
GrapefruitIsAwesome's user avatar
3 votes

Calculating covariance matrix for MVDR beamforming

MVDR is a narrowband beamformer. For broadband signals it is usually applied for each frequency bin. That means that $\mathbf{R}_{xx}$ is frequency dependent. In other words, for each time you should ...
ThP's user avatar
  • 1,460
3 votes

Intuitive interpretation of Fourier transform in beamforming

If you consider the beam pattern for a linear array - so I'm looking at just the magnitude (or magnitude square) i.e. $|B(\theta)|$. Then the $\sin(\theta)$ is telling you how the response changes to ...
David's user avatar
  • 2,871
3 votes

Implementing MVDR beamformer in the STFT domain

In this context $\Phi_y$ often describes the (estimated) power spectral density matrix of $y(f)$, which is $$\Phi_y(f) = E\{y(f) y^H(f)\} = \begin{bmatrix} y_1 \cdot y_1^*(f),& y_1 \cdot y_2^*(...
Jonas Schwarz's user avatar
3 votes

Beamformer implementation methods

MVDR and LMS beamformers are two different things. The equation you wrote for the MVDR beamformer is the solution to the "Minimum Variance Distortionless Response" (MVDR) criterion (i.e., $...
Gillespie's user avatar
  • 1,797
3 votes

How to derive the "well-known" solution to Unconstrained Array Gain?

You can solve such a problem using the method of Lagrange multipliers. First note that maximizing the expression in your question is equivalent to minimizing the inverse function: $$\min_{\mathbf{w}}\...
Matt L.'s user avatar
  • 90.3k
3 votes

Is there a way to get the "mode" of several recordings? (to remove 1-off noise)

Problem Statement It sounds like you are trying to solve the Cocktail Party Problem, which is to separate different signals (e.g., multiple people speaking simultaneously at a party) that have been ...
Gillespie's user avatar
  • 1,797
2 votes
Accepted

Narrowband DOA Beamforming techniques on Wideband signal

My suspicion is that you can only perform phase shift beamforming techniques on narrowband signals and will not work even if you are looking for a narrowband within a wideband signal. Am I correct? ...
Marcus Müller's user avatar
2 votes
Accepted

Which parameters defines a polar plot?

Some examples would be the null to null bandwidth(s) as well as the sidelobe levels of the first/second sidelobes. Example vector of 5 numbers: [mainlobe gain, first null location, 1st sidelobe gain,...
Robert L.'s user avatar
  • 2,222
2 votes
Accepted

Would a visible light beamforming "telescope" be feasible?

Not in the way you think, no. Digital Beamforming works because the digital receiver is able to sense the phase of the incident radio wave; that phase is retained. Photodiodes don't sense the phase ...
Marcus Müller's user avatar

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