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# microphone array beamforming

## microphone array beamforming

(OP)
Hi
I am working on conventional frequency domain beamforming for linear microphone receive array. I have simulated 32 channels array data with a poin target at 45 deg emiiting 20KHz tonal. I performed beamforming  to make 32 beam time series data.
To calculate array gain (or beamformer gain) I compare the 20 kHz tonal level in individual channel data and in 45degree beam time series data. Problem is that array gain/beamformer gain calculated in this way is approximately 16dB above theoretical array gain (i.e. 10*log10 (32) = 15dB).
Can any one kindly guide me where I am wrong?
Note: I have tried many simulations with different parameters but results were same.

THANKS

### RE: microphone array beamforming

Would this 'discrepancy' be as a result of the difference between voltage (20*log...) versus power (10*log...)?

It's just a guess on my part...

### RE: microphone array beamforming

I think the error might be this.
If you go to 32 elements in any array, you get 10 log 32 gain only if your input power is divided by a 32 factor and the gain is only from the narrowing of the beam width.

If you also power each of the 32 elements of an array with the same power you'd put into one element, then another gain in actual transmitted power of 10 log 32 occurs, hence 20 log 32 is the accurate way to calculate your gain if each of the 32 elements have their own power source.

ON the antenna beam narrowing, the 10 log 32 isn't a definite guarantee, it all depends on the spacing of the elements. If you space them real close to each other vs. further away, you'll get a different gain. But the 10 log 32 is a good assumption for informal discussions.

### RE: microphone array beamforming

(OP)
Thanks for your help Higgler.Actually i am working on the receive microphone array and all 32 channels are half wavelength (corresponding to 20 KHz frequency) apart. Secondly i could not understand input power term since i am only listening not transmitting.
perhaps i could not clearly explain in my first post what i am doing.
First, I simulated signals (20KHz tonal coming from 45deg w.r.t array broadside) receiving on 32 element array with each element 0.0375m (corresponding to 20 KHz frequency) apart.
Second, I performed conventional frequency domain beamforming on the received simulated 32 channel data and made 32 beams covering 0-180 deg.
Third, I calculated array gain(beamformer gain) by dividing the power of 20 Khz tonal in beam(corresponding to 45deg) with power of 20 Khz tonal in single channel and then taking 10*log of result.

Any suggestions will be highly appreciated

### RE: microphone array beamforming

I suggest you post your exact calculation rather than describing it. If you have taken 10*log(P/Pref) then that is almost certainly your error, given that you are talking about tones.

Cheers

Greg Locock

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### RE: microphone array beamforming

(OP)
I took a random simulated channel out of 32 channels (which are in time dmain) and took FFT of this channel. I search a complex number representing 20 KHz and multiply this complex number with its conjugate and i got power Pref (of 20KHz tone).
Then after performing conventional frequency domain beamforming( say by 2D FFT), i got a complex  matrix  with  beam vs Frequency ( 32 rows represent beams from 0 to 180deg and colums represent frequencies ranging from 0 to 30Khz). In this matrix i search a complex number in a column representing 20 KHz frequncy and in a row representing 45deg beam. I multiply this complex number with its conjugate and i got power P (of 20KHz tone in 45 deg beam).
After this i performed the operation as you say 10*log(P/Pref). What can be the error in this approach?

Have a nice day
masudasim

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