# IR-UWB simulation problem (1 symbol-2 frames)

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#### jodhbirs

##### Newbie level 2 I am generating UWB signal of 2GHz with Matlab sampling frequency(for resolution) of 8GHz.Thus, each UWB pulse has 4 sample values.

Now the number of samples in the received signal are 800.
I do compressed sensing with Phi=randn(400,800)

reconstruct the signal successfully to 800 samples.
Now the question is, the compression in Phi to 400 samples means we are sampling the signal:

1. at 4 GHz (Matlab digital frequency)?
or
2. at 1GHz (signal frequency)?

when I do reduced-rate sampling then do I consider the frequency to be Matlab freq or signal frequency

Moreover, What if both the frequencies are same 2GHz?

#### bulx

##### Full Member level 4 Perhaps you could answer a few questions...

> I am generating UWB signal of 2GHz with Matlab sampling frequency(for >resolution) of 8GHz.Thus, each UWB pulse has 4 sample values.

>Now the number of samples in the received signal are 800.
>I do compressed sensing with Phi=randn(400,800)

So is it correct that you generate samples in matlab as they were coming from a ADC running at 8 GHz, and then choose only some of them for reconstruction?

If so, are these samples randomly chosen? Do you have multiple sets of samples from the same time period?

Also do the chosen samples cover several UWB symbols?

-b

#### jodhbirs

##### Newbie level 2 First of all, thank you very much for your reply. I would highly appreciate if you could help me in understanding it. I am answering your questions is my very basic understanding.

1. Yes, I generate my 800 samples of 1 symbol using 8GHz frequency and I do compressed sensing with those 800 samples. My measurement matrix 'PHI' is randn(400,800) so I think it multiplies each sample value of the signal with a random weight before giving 1 sample of CS in y.
y=PHI*r;

I have a description below for you to better understand how I generate samples.

My pulse frequency is 2GHz,Tp and I use 8GHz of frequency to generate the samples of Gaussian mono cycle pulse.So, let's say

Tp=0.5e-9 or fp=2e9 and Fs=8e9

UWB Gaussian Pulse generation
t=-Tp:1/Fs:Tp ; % time duration of pulse
p=(1-4*pi*(t/Tp).^2).*exp((-2)*pi*(t/Tp).^2); %Gaussian Pulse

Now frame generation,
tf=0:1/Fs:Tf-1/Fs; %Time samples of one frame
s1(1:length(p),1)=p'; % Frame 1

Now 1 symbol has 2 frames. Each consisting frame 400 samples generated using 8GHz frequency.(which I am not able to understand how does it(8GHz) relate to physical world)

2. yes, these samples are chosen randomly. I answered your question partially above. In short, I should say my measurement matrix is Gaussian, which randomly chose the compressed samples.

3. No the whole simulation is only for 1 symbol. However, it can be done for more than 1 symbol.

Actually, I main problem is :

If the pulse frequency is fp=2GHz. But I generate signal using 8Ghz frequency to show the signal look like continuous. However, when I compress the signal from 800 sample(using 8GHz) to 400 samples, so question is AM I sampling the signal at 4GHz(8GHz/2) or Am I sampling the signal at 1GHz(2GHz/2)?

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