Questions tagged [beamforming]
Forming a beam (directional gain) and, sometimes, shifting the beam direction.
75
questions
10
votes
1answer
169 views
How can one improve the robustness of adaptive beamformers to signal mismatches?
Compared to standard (conventional) beamformers, adaptive beamformers such as minimum variance distortionless response (MVDR) have much better resolution and interference nulling capabilities. Briefly,...
9
votes
3answers
394 views
Practical wideband digital beamforming for large arrays in radar applications
I do understand the mathematics behind digital beamforming but I am not sure how such systems are practically implemented. For example, in a typical wideband FMCW radar operating in S-band, the (...
8
votes
1answer
2k views
Difference between 'conventional' and 'adaptive' beamformers?
This might be a terminology question but I am not sure.
Basically, what is the difference between conventional beamformers, and adaptive beamformers? I thought that all beamformers were inherently ...
7
votes
2answers
915 views
Can a narrowband beamformer be used for speech separation
In my master thesis I am trying to implement a beamformer.
I've already done the delay-sum part 1 year ago. I have been told:
in FIR filtering we can do
FFT --> null the unwanted frequency bin --> ...
4
votes
2answers
2k views
Intuitive interpretation of Fourier transform in beamforming
When applying Fourier transform in time domain the signal will be carried to frequency domain. And when we apply Fourier transform in spatial domain the signal will be carried to directivity domain.
...
4
votes
1answer
288 views
Is it possible to do further beamforming on already beamformed data?
I've a circular array of eight FM antennas. I'm doing digital beamforming to form eight beams with the following beam patterns:
The objective is to reduce my side lobes even further, and to get ...
4
votes
1answer
826 views
Calculating Beam pattern, Directivity of microphone array
As answered in Relationship of Fourier Transform and Spatial Directivity Pattern the relation between directivity pattern and weights is given. But I am bit confused, I have Beamformer weights (...
3
votes
2answers
1k views
Relationship of Fourier Transform and Spatial Directivity Pattern
I am reading over and over the Section 1.2 of most understandable mic array tutorial for me .
A sound wave is dependent on time and space which can be observed in the great link.
But I can't ...
3
votes
2answers
82 views
Proving that a product of matrices invertible
Given $R_x$ a Positive Definite (PD) covariance matrix of size $M\times M$ and $C$ a full rank $M \times N$ matrix, I want to prove that $C^* R_x^{-1} C$ is invertible to derive the Linearly ...
3
votes
1answer
40 views
Beamforming back lobes question
When performing a conventional digital beamforming I see in some textbooks they show beam patterns as
where the arrival angle ranges between -90 to 90 degrees. But then other places show the full ...
3
votes
2answers
205 views
Tetrahedral microphone array beamforming
I have a microphone array of 4 channels taken as channels [6,10,22,26] from Eigenmike spherical microphone array. I wish to do 3D beamforming and create $8\times 4$ beams, 4-elevations with 8 ...
3
votes
0answers
41 views
Beamformer implementation methods
I'm currently reading articles about the different type of beamformers. This spatial filtering is gonna be used for acoustic purposes, to focus the beam on the person we need to hear talking in a ...
3
votes
0answers
250 views
Question on spatial sampling for non-linear and/or non-uniform arrays
I am a little confused as to how to compute the nyquist criterion for a sensor array that is not linear, and/or non-uniform. For the linear, uniformly spaced case, the spatial nyquist is delimited by ...
2
votes
3answers
84 views
Amplify Sound From Known Direction
I have microphone array which records sound. There is one main sound which direction I know and some noises in the background. Now I want to selectively amplify sound from known direction. This looks ...
2
votes
1answer
685 views
DSP with 8+ inputs for simple beamforming
Does anyone know of a DSP that is cheap and has 8+ inputs (8 I2s mics) and that can perform beam forming calculations? I'm super new to circuit design so preferably one thats beginner friendly.
...
2
votes
1answer
1k views
Directivity Pattern of microphone array
Directivity pattern of a microphone array is fourier transfrom of microphone weight values. By modifying the amplitude weights, we can modify the shape of the directivity pattern.
I can really see ...
2
votes
1answer
967 views
Delay and sum Beamforming
What is the difference between the weight vector (w) and the steering vector a(θ)?
I initially assumed they were the same thing, but the literature seems to be to be a bit fuzzy with this (or maybe ...
2
votes
1answer
233 views
Would a visible light beamforming “telescope” be feasible?
If you had a phased array of high speed photodiodes that were spaced sufficiently far apart, would it be possible to apply beamforming theory to create a steerable visible light "telescope"?
...
2
votes
0answers
52 views
Physical Interpretation of $\mathbf A$ beamforming Matrix
The directivity of an array is defined as:
$$ D = \frac{1}{2} \int_{-1}^{1} \lvert B_{u}(u)\rvert^{2} du$$
Where $B_{u}(\cdot) = \mathbf{w}^{H} \mathbf{v}(\cdot) $ is the beampattern of the array in ...
1
vote
2answers
281 views
how to calculate the maximum obtainable directivity for a microphone array?
Introduction
The relationship between the maximum obtainable directivity and aperture of an antenna is described by:
$$ D = \frac{4\pi A_e}{\lambda^2} $$
Where $D$ is the directivity, $A_e$ the ...
1
vote
1answer
1k views
Calculating covariance matrix for MVDR beamforming
I am trying to calculate the covariance matrix that is required for the calculation of an MVDR beamformer. I am getting confused as to how to calculate it. I have an array of 3 microphones each with a ...
1
vote
1answer
75 views
Implementing MVDR beamformer in the STFT domain
I am trying to implement an MVDR beamformer for the first time. I was reading a couple of papers and books with many different notations and I am a bit confused.
In my case, without loss of ...
1
vote
1answer
239 views
Which parameters defines a polar plot?
I need to convert a polar plot into a short array of 3-5 values. This array should describe the polar plot as best as possible.
For example, I know that I can use the beamwidth which is also known as ...
1
vote
2answers
191 views
What does the $n$ do in $1/(j \omega)^n$
I'm currently working through a research paper on beam forming. In this paper a magnitude compensation is introduced to compensate for frequency dependency. Due to other calculations low frequencies ...
1
vote
1answer
97 views
What is the best way to show beamformer enhances signal of interest over interference
I need to study an array's performance in terms of interference.
I have already analyzed the array's white noise gain which is the ratio of output and input SNR of the beamformer i.e. $\rm{SNR_o} / {...
1
vote
1answer
181 views
Relationship between matrix rank and beamforming
I always encounter the term matrix rank in papers related to beamforming. I am only familiar with the basics of beamforming (delay sum beamformer, basic capon). Can someone explain the significance of ...
1
vote
1answer
188 views
Filter signal for beamforming and phase response
I was wondering this for quite some time but couldnt find a satisfied answer. Seems like not a lot worry about phase response in general. But maybe I'm thinking about it in a wrong way...
I want to ...
1
vote
1answer
882 views
Spatial sampling frequency equation
Upon reading this microphone array tutorial, I'm stuck in the following piece:
The spatial sampling frequency along the x-axis is given by
$f_{x_s} = \frac{\sin \theta \cos \phi}{\lambda}$
...
1
vote
1answer
1k views
Difference between Uniform Linear Array (ULA) 3 dB beamwidth and bearing resolution
Is there a difference between linear array 3dB beam width and linear array bearing resolution ?
1
vote
1answer
1k views
Plotting antenna pattern in MATLAB
I have a beamformed output, say
y = weights * signal,
where the signal is gaussian,i.e signal = randn( 1 , 1e5 ).
Now I want ...
1
vote
0answers
36 views
Sign of manifold vectors in monostatic phased-array radar
I am reading some notes where the impulse response of phased-array to is given by;
$$
\beta S(\theta, \phi) \bar{S}^H(\theta, \phi) \cdot \delta(t-\tau)
$$
where
\begin{align}
\bar{S}(\theta, \phi)...
1
vote
0answers
310 views
Time-Delay beamforming delay computation
I'm trying to implement a beamforming algorithm in python and I'm stuck with the time-delay computation for a rectangular array.
I'm using the following equation to compute the delays based on the ...
1
vote
0answers
140 views
Superdirectivity Beamformer for Circular microphone array
The matrix below represents the inverse of correlation matrix assuming diffuse noise field. I am unable to figure out the values of the elements of this matrix.
how to calculate $c_{M}(\omega)$ ?
1
vote
0answers
125 views
Beam pattern for a linear array comprised of rectangular transducers
I am looking for the beam pattern of a linear array with uniform spacing, $d$, between $n$ elements.
I know for an array comprised of circular pistons it can be derived from
$$\frac{1}{n}\frac{\sin[...
1
vote
0answers
72 views
The Rank Of Broadband LCMV Beamformer Constraint Matrix
So I am wondering why I keep seeing that the rank of the LCMV Broadband Constraint Matrix is equal to the number of constraints, when in practice, I find that the rank is only 1. This is precluding me ...
0
votes
1answer
323 views
Beam resolution improvement of linear array using MVDR beamformer
One of the major advantages of using MVDR beam former is to improve bearing resolution as compared to conventional delay & sum beam forming. The bearing resolution is defined by 3 dB beam width of ...
0
votes
2answers
687 views
what is an alpha filter?
Currently, I'm working on adaptive beamforming using LMS approach, so they change the value of the step factor adaptively in which one of the steps is to pass the weight vector through an alpha filter....
0
votes
2answers
794 views
Beam width of linear array using MVDR beamformer
I did delay and sum beamforming technique and MVDR beamforming technique in MATLAB in ...
0
votes
1answer
1k views
Delay-and-sum beamforming: implementing steering in C
I am currently trying to understand how delay-and-sum beamforming works.
I have found this website which explains the process of this technique very well in which the following C code is provided:
<...
0
votes
1answer
348 views
What is homogeneous noise field?
What is the formal definition of homogeneous noise field? Is there any example of it?
Thanks.
0
votes
1answer
2k views
Beamforming using MATLAB
I'm attempting to beamform some data which has signals coming from all directions in a 180 degree range.
I found an example of using the phased array toolbox, in MATLAB, to beamform a signal in https:...
0
votes
1answer
29 views
Is there a term called “Fourier Beamforming”?
I understand delay and sum beamforming, where we want to add the signals obtained from different sensors. But adding different time samples from different element of the array depending on the angle ...
0
votes
1answer
316 views
How to compute beam pattern given a delay-and-sum filter in spectral domain?
Given a two-mic system (the mic spacing $d$ is known), how can I compute the beam pattern (see the Figure below) over frequency and angle $g(f,\theta)$ for a pair of spectral filters ($H_0$ for ...
0
votes
2answers
209 views
MVDR Beamformer, minimize but do not change pattern in main beam
Is there a way to minimize all signals that are not coming from the mainbeam?
I would like to keep the main beam, or at least +-3° around the main peak stable.
When I estimate the covariance from ...
0
votes
1answer
144 views
Beam Former linear array antenna
How can I design a beam former (with weigth vector $w$) that protects a signal coming from an angle of arrival $\theta_0$ and completely suppresses signals coming from $\theta_1,\theta_2,...,\theta_k$?...
0
votes
1answer
867 views
Beamforming techniques - pros and cons
I would like some advice on which beamforming method to use from someone with experience in the field.
I have radar data from the ocean which has been transmitted by an omnidirectional transmitter ...
0
votes
1answer
229 views
Direction of arrival and distance to source
Suppose we have $3$ receivers $a,b,c$ and one wave source which are all located on the same $XY$ plane and we do not know the position of only $c$ on the plane.
Assume a plane wave is transmitted $s(...
0
votes
2answers
261 views
IFFT of Microphone Array Directivity Response
I am implementing a microphone array simulation in my thesis.
My prof and many documents indicates that microphone array behaves like filters in DSP but instead time-frequency domain there exists ...
0
votes
1answer
157 views
Microphone Array null steering unexpected results after IFFT
I am writing an open source microphone array simulation program:SharpEar.
When I give uniform weight to microphone array elements, the result in the angle is a sinc function as expected. There are 41 ...
0
votes
1answer
475 views
use of complex conjugate of weight vectors in beamforming literature
in beamforming literature, people generally quote the following as a starting point:
$y(k) = \sum_{i} w_i^*\cdot x_i(k)$
Here:
i varies from 1 to N where N is the number of sensors
$w_i^*$ is the ...
