# Uniformaly spaced linear array problem

Discussion in 'Wireless & RF Design' started by cigarsnob, May 25, 2011.

1. ### cigarsnob Thread Starter New Member

Feb 23, 2010
7
1
Hi,

I'm working on a school simulation project and I'm stuck and would appreciate some help/hint/advice. I'm not a communications student and this is my first class in this area, I'm more of an analog guy...Anyway, the problem is:

A one dimensional linear array of 10 (M=10) sensors spaced d = lambda/2 (lambda = wavelength) apart from each other. Desired signal and interference are pure sinusoidal with the same frequency. Desired signal coming from the boresight and interference coming from an angle phi = 50 degrees. The signal to interference ratio is - 30dB and the signal to noise ratio is -10dB.

a) compute the optimal weight of the array using Minimum Variance Distortionless Response.

b) Compute and plot the antenna pattern in dB

What I have right now is R_s = 10x10 matrix of all 1s (given by professor), R, the correlation matrix = R_s + R_I + I_w. I'm working on R_I and need to find out what I_w is. I also have s(theta), I think, please see below for eqn used.

Also the equation I'm using for part a is, with electrical angle = theta:
w_optimal = (inv(R)*s(theta))/(hermitan of s(theta)*inv(R)*s(theta))

where theta = 2pi*d/lambda*cos(phi)
and s(theta) = transpose([1, exp(-j*theta,...,exp(-j*(M-1)*theta])

I'm sure this is a little difficult to read the equations typed out so my apologies.

One particular question I have though is how do I find d or do I need to even have a numerical value for d?

I'm using MATLAB for all the calculations and what not.

Thank you and I hope to hear back from you guys. I'm not asking for the complete solution here by the way, just something to get my back on track as I am currently at a wall.

Thanks again

2. ### KL7AJ AAC Fanatic!

Nov 4, 2008
2,043
292
Your best source of information will be in Antennas, by Jasek and Kraus, in the phased array radar chapter. (Alas, I've loaned out my copy so can't point to the exact place).

If the array is uniform and the currents in each element are the same, the pattern is very straightforward, you can derive this from a simple antenna modeling program like MININEC. If the array is tapered (shaded), it's a little more involved.

Are you trying to create a specific pattern by current adjustments, or are you trying to figure out the pattern from a known array? The former is much more difficult!

Eric

Nov 4, 2008
2,043
292