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

# Adaptive arrays

Started by ●May 8, 2004

Reply by ●May 8, 20042004-05-08

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

Reply by ●May 9, 20042004-05-09

>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).