No time differencies in modeling phased.Collector

Hi all, I'm trying to model the acquisition of a signal coming from arbitrary direction by a sensor array. I have troubles with time delays at individual sensors. I guess that the system object phased.Collector is the right way to do this.

Example: Assume a plane wave coming from positive x-axes and an array (e.g. ULA) of several sensors located along the x-axes... I have modeled the FreeField propagation from the point in the far field to the origin (where the center of ULA is located). Then, I have used phased.Collector to collect the signal at all the sensors in array. I expected the time as well as amplitude and phase differencies between individual collected signals, however they differ only in amplitudes and phases.

Does anyone have any experiences with this? Should I model it by a FreeField propagation to individual sensors?

Thank you for any advice. A.

Answer 1

[Honglei Chen]

Are you expecting to see 0s in front of certain channels when you talk about time difference? phased.Collector doesn't do that because in real system, signal almost always present. Those 0s only happens when you first start the system so in some sense you can think that phased.Collector models the signal after transient. It is also the model used in most array processing literature I've seen for narrow band signals.

If you really want to see the zeros, you can use a function called delayseq, which also ships with Phased Array System Toolbox. You can try the example below:

    fs = 8e3; t = 0:1/fs:0.005; x = sin(2*pi*100*t).';
    y = delayseq(x,0.001,fs);
    plot(t,x,'r',t,y,'b'); legend('Original','Delayed');

HTH and please let me know if you need further clarifications.

[Adam]

Thank you for your answer, however, I think I meant something different. By the time differences, I mean time of arrivals (TOAs) of a signal (e.g. one plane wave coming from certain direction) to individual sensors in an array - depending on the array geometry and DOA.

I guessed than phased.Collector does this thing, as following: 1) model the signal propagatin by phased.FreeSpace (from far field to the center of the array) 2) collect that signal by an array using phased.Collector -- here it creates N (number of sensors) signals differing in amplitudes and phases, but it seems they are captured at the same time (same TOA) instead of the distances to elements are various

• I solved this for now by modeling phased.FreeSpace propagation to individual sensors separately

I probably do not understand the purpose of phased.Collector. It counts with array properties (geometry), so it could collect the signals accordingly...

[Honglei Chen]

Hi Adam, for a plane wave, the phase difference is the result of time delay, so it does have time delay information in there. Any any moment, all sensors receives the signal, it's the same signal with different delays, which represents itself, for a narrwband signal, as phase shifts. There is certainly nothing wrong if you model the propagation for each element, but all I want to say is that the phased.Collector model could be a more efficient way to do that. If you are interested, you can take a look at the following paper.

http://www.rt.isy.liu.se/~fredrik/spcourse/array.pdf

[Adam]

Hi, thank you for your answers and the paper.

Yes, in case of plane wave it is equivalent to the phase shift. I tried it using kind of impulse signal and it comes at the same time to all elements of the array - no matter from which direction. Finally, I modeled it by an individual FreeSpace propagatin to all the elements separately.

[Jaydeep Roy]

This is from the documentation:

If the Wavefront property value is 'Plane', phased.Collector collects each plane wave signal using the phase approximation of the time delays across collecting elements in the far field.

If the Wavefront property value is 'Unspecified', phased.Collector collects each channel independently.

So, it means that phased.Collector object incorporates delays in the plane wave incident on all array elements.