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nurul Antenna Theory Regular
Joined: 26 Apr 2011 Posts: 23

Posted: Mon May 02, 2011 12:11 pm Post subject: LMS vs MMSE 


Hello,
A zillion thanks for setting up the antennatheory website. and yep, it serves the purpose of being an alternative selflearning source for 'antennatheory'.
from the antenna array site (weighting method)  there are adaptive (LMS) and MMSE (optimum output) other than dolph and schekulnoff method.
what is the difference between LMS and MMSE?
LMS uses MSE to adaptively place the main lobe at the intended direction, correct? I'm quite confused as it goes the same with MMSE. which brings back what's the difference between LMS and MMSE?
Thanks a lot for the reply. and thanks as well for antenathoery website. 

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Schubert Antenna Wizard
Joined: 08 Apr 2009 Posts: 161

Posted: Mon May 02, 2011 10:58 pm Post subject: 


MMSE is deterministic  that is, it assumes the statistics of the incoming signals and noise are known, and then the optimal weights can be computed.
The LMS algorithm is adaptive  that is, it iterates towards a "MMSE solution". Now, if you are in a static environment, such that the statistics of the noise and incoming signals do not change, then the LMS algorithm will iterate towards the fixed MMSE solution.
The LMS algorithm estimates the noise and signal matrices by sampling the incoming signals over a short amount of time. It uses this information to step towards the solution. In an adaptive or changing environment, the LMS algorithm can be used to iterate the weights towards the optimal weights, as the optimal weights change as a function of the environment.
I hope this clears things up. 

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nurul Antenna Theory Regular
Joined: 26 Apr 2011 Posts: 23

Posted: Tue May 03, 2011 12:46 pm Post subject: 


Thanks Schubert.
Now I see, LMS converge towards 'MMSE' solution while trying to adapt with the environment. Correct?
some books classify antenna beamforming algorithm into power minimization techniques (PSO, GA) and correlation matrix technique (LMS, RLS).
In one of the GA based beamforming article, it says that power minimization technique has an advantage of having a reduced number of hardware (in the receiver) requirements.
How does this differ? as both methods require the info of DoA and current weight (feedback ect..)?
Thanks a lot for the replies. 

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Schubert Antenna Wizard
Joined: 08 Apr 2009 Posts: 161

Posted: Tue May 03, 2011 4:52 pm Post subject: 


Power minimization algorithms do not require estimating a desired signal's direction of arrival. They simply attempt to minimize the received power of the array, while constrianing one of the weights to be equal to 1.
This type of algorithm works in the case of many "jamming" signals, or signals with much stronger power than the received signals. It isn't robust in most environments. 

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