Adaptive arrays

Hey,
 I need to design an adaptive array for automatic interference
rejection using the LMS algorithm in MATLAB. There is a target signal
cos(2*pi*f0*t) and three interference signals cos(2*pi*f0*t) coming in
at angles of 45, -30 and -60 degrees. The adaptive array will consist
of eight elements. The input signals are sampled at Ts=2*10^-10 s
where t=0,Ts,2Ts,3Ts,4Ts...f0=3*10^8 Hz,lambda=1 m and distance
between neighboring elements d=lambda/2.
 I know how the LMS algorithm works but i don't know how to
incorporate adaptive arrays with it. After some research I found out
that interference rejection has something to do with radars. If
somewone could provide an example code for designing the adaptive
array it'll be greatly appreciated

John,

Fourier transform works in the space domain exactly as in 
the time domain.
A three-element coordinate vector x is an analog of time and
a wave number k is an analog of circular frequency \omega.
Once you've written a flat-front wave exp(i*omega*t-i*k*x)
and applied FT to it, working with wave numbers is absolutely
similar to working with frequencies.

The spatial sampling interval d is an analog of the temporal sampling
interval ts, and the condition d <= lambda/2 is the spatial sampling
criterion.

Since k is a vector, all the spatial information is contained in
the direction of k, while its magnitude determines the wavelength or,
which is equivalent, the wave frequency, assuming c is a constant.

I would recommend you the Multidimensional Digital Signal
Processing book by Dudgeon and Mersereau, Chpt 6, for a
start reading, athough someone else may have different
preferences. I like it for its clarity in the subject.

Rgds,
Andrew

P.S. The most interesting situation, when c is a function of
lambda is not discussed in this book, unfortunately.

forevermav2001@yahoo.com (John) wrote in message news:<acad27ed.0405071943.2ca5ac30@posting.google.com>...
> Hey,
>  I need to design an adaptive array for automatic interference
> rejection using the LMS algorithm in MATLAB. There is a target signal
> cos(2*pi*f0*t) and three interference signals cos(2*pi*f0*t) coming in
> at angles of 45, -30 and -60 degrees. The adaptive array will consist
> of eight elements. The input signals are sampled at Ts=2*10^-10 s
> where t=0,Ts,2Ts,3Ts,4Ts...f0=3*10^8 Hz,lambda=1 m and distance
> between neighboring elements d=lambda/2.
>  I know how the LMS algorithm works but i don't know how to
> incorporate adaptive arrays with it. After some research I found out
> that interference rejection has something to do with radars. If
> somewone could provide an example code for designing the adaptive
> array it'll be greatly appreciated

>Subject: Adaptive arrays
>From: forevermav2001@yahoo.com  (John)
>Date: 5/7/2004 11:43 PM Eastern Daylight Time
>Message-id: <acad27ed.0405071943.2ca5ac30@posting.google.com>
>
>Hey,
> I need to design an adaptive array for automatic interference
>rejection using the LMS algorithm in MATLAB. There is a target signal
>cos(2*pi*f0*t) and three interference signals cos(2*pi*f0*t) coming in
>at angles of 45, -30 and -60 degrees. The adaptive array will consist
>of eight elements. The input signals are sampled at Ts=2*10^-10 s
>where t=0,Ts,2Ts,3Ts,4Ts...f0=3*10^8 Hz,lambda=1 m and distance
>between neighboring elements d=lambda/2.
> I know how the LMS algorithm works but i don't know how to
>incorporate adaptive arrays with it. After some research I found out
>that interference rejection has something to do with radars. If
>somewone could provide an example code for designing the adaptive
>array it'll be greatly appreciated
>
>
>
I suggest that you look at Chapter 9 of Adaptive Filter Theory by Simon Haykin
(see page 377).