Questions tagged [beamforming]

Forming a beam (directional gain) and, sometimes, shifting the beam direction.

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10
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1answer
151 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,...
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3answers
386 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
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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 ...
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2answers
897 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 --> ...
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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
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1answer
280 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
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1answer
798 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 (...
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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 ...
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2answers
81 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
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1answer
34 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
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2answers
196 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 ...
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0answers
247 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 ...
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3answers
79 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
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1answer
632 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
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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
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1answer
935 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 ...
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1answer
227 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"? ...
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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 ...
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2answers
248 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 ...
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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 ...
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1answer
54 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 ...
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1answer
218 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 ...
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2answers
190 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 ...
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1answer
96 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} / {...
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1answer
177 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 ...
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1answer
184 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 ...
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1answer
827 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 $f_{x_s} = \frac{\sin \theta \cos \phi}{\lambda}$ ...
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1answer
936 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 ?
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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 ...
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0answers
281 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 ...
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0answers
138 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 $c_{M}(\omega)$ ?
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116 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[...
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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 ...
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1answer
313 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 ...
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2answers
450 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....
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2answers
752 views

Beam width of linear array using MVDR beamformer

I did delay and sum beamforming technique and MVDR beamforming technique in MATLAB in ...
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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: <...
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1answer
322 views

What is homogeneous noise field?

What is the formal definition of homogeneous noise field? Is there any example of it? Thanks.
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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:...
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1answer
299 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 ...
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2answers
207 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 ...
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1answer
138 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 $\theta_1,\theta_2,...,\theta_k$?...
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1answer
801 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 ...
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1answer
222 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(...
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2answers
257 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 ...
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1answer
156 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 ...
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1answer
464 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 ...
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0answers
42 views

How to generate a beam pattern from a beamformer on 3D

given a 3D microphone array with $M$ microphones, $d(f,\Theta)\in \mathbb{R}^{f\times M}$ is the steering vector for a given direction $\Theta=(\varphi,\theta)$, inclanation and azimuth respectively. ...
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0answers
15 views

Steering vector for beamforming in 3D

I am trying to implement a steering vector in 3D for beamforming. Let $A\in \mathbb{R}^{M\times 3}$ be a matrix containing the $(x,y,z)$ coordinates for $M$ sensors and the impinging source direction ...
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0answers
9 views

Question on unitary DFT matrix based beamforming

I am trying to experiment with digital beamforming for the first time & found a lot of literature making use of unitary DFT based beamforming but wasnt able to figure why(or how) DFT-based ...