Clear definition of Theoretical Probabilty of error for OOK

defination of theoretical

Hi,
While working on the real UWB system, I used both PPM and OOK modulated transmit signals. In either case, the same pulse shape and therefore the same pulse energy is used. For PPM the average energy is taken as Eb and for OOK as Eb/2.

Further, two different receiver positions were chosen for simulation environment. The two positions are separated by 2m.

While analysing the simulated result from either modulation scheme, I require theoretical baseband equations. The simulation of two channels deliver nearly the same performance curve.

The theoretical limit for PPM is taken as Q(sqrt(Eb/N0)) while for OOK as Q(sqrt(0.5*Eb/N0)). Are these equations correct? Secondly, comparing these equations to the simulated result leads to some theoretical violation? (lower bound violation).
I am still ambigous if that can be applied to OOK. Please comment urgently.

I am feeling that the simulations are not wrong but the performance bounds are not set correctly. Can someone clearly state the theoretical equations for the two modulation schemes?

Thanks

definition of theoretically incoherent?

How many sample did you use to obtain the actual results?
Also, its seems funny that the PPM results are ~ 3db off from the theoretical.

R

ook ber

the ~3dB is due to the presence of real hardware components including multipath channel, tx and rx filters, low noise amplifiers and antenna gain patterns etc. so not a pure awgn cjannel and so will always have some implementation loss. (my thought)

theoretical probabilty.com

Hmmmm.....OK...How are you measuring the SNR?

Added after 1 hours 58 minutes:

It's been a few years since I derived these error rates, so I'm a bit rusty.
For On-OFF keying;
1)Amplitude of the pulse =A
2)equal prob of 0 or 1
3)noise spectral density= No/2 = sigma^2
4)ML detection, so a slicer with threshold= A/2
5)q-function = 1/sqrt(2Π)∫exp(-u²/2)du
6)Pr(error)=2*q-funct(sqrt(A²/(4*sigma²))

the average energy per bit (Eb) should be A²/2 so the equation should be

Pr(error)=2*q-funct(sqrt(Eb/No))

error probability ook

Actually, the equation you suggested me, seems to provide logical result for comparison purposes. But it generates another argument. The transmission of PPM using same pulse of amplitude A should also provide error probability equation as Pr=Q(Eb/N0).

Does it mean both PPM and OOK delivers the same equation? Is it so?

Added after 2 minutes:

Secondly, I have computed Eb/N0 from two ways
(1) averaging Power spectral density
(2) averaging time domain received signal over several pulses.
Both methods give nearly the same result.
So pretty sure that it is not the mistake.

Added after 1 hours 7 minutes:

PPM: Q(Eb/N0)
OOK: 2Q(Eb/N0)

What about incoherent PPM and OOK?
I used
incoherent PPM: 2Q(Eb/N0)
incoherent OOK: ?

Added after 8 minutes:

PPM: Q(sqrt(Eb/N0))
OOK: 2Q(sqrt(Eb/N0))

What about incoherent PPM and OOK?
I used
incoherent PPM: 2*Q(sqrt(Eb/N0))
incoherent OOK: 0.5*exp(-0.5*Eb/N0) + 0.5*Q(sqrt(Eb/N0))

Are these correct?

formula bit error ook

Hi,

Sorry but I haven't got to ppm yet, later today(I'm in SE Asia). I think the only difference will be the average bit energy since in ppm a pulse is transmitted whether it's a 0 or a 1.

I'm going to assume a white noise channel, like I did with ook, and perfect synch between tx and rx.

One other thing, why do refer to the calculated BER as a BER bound?

I'm curious, could you show me a simple scematic of you test bed?

R

you easily definitions of theoretical

|TX|->|TxFilter+ |->|RxAntenna+|->|Receiver|
|TxAntenna| |LowNoise Amplifier|
|Channel+ | |RxFilter |
|Noise + Interfernce|

I have the same assumption like you made.
I think lower bound is necessary only to assess the performance of the transmission system.

reclear definition

Hi,

Like I said, I'm a bit rusty at deriving the PR(e). I see a mistake in my first responce for OOK. Looks like the 2 multiplier should be removed. After looking at your test bed it seems like an AWGN estimate should be the lower limit for the BER. That would be the noise measured at the front end of the receiver, dont you think?

R

ook noncoherent

Now I think, you got my idea. The AWGN BER should be the lower limit of the simulated test bed.
I used following equations for different situations:
PPM coherent : Q[sqrt(Eb/N0)]
OOK coherent : Q[sqrt(0.5*Eb/N0)]
PPM non-coherent: 2Q[sqrt(Eb/N0)]
OOK non-coherent: 0.5[exp(-0.5*Eb/N0)+Q(sqrt(Eb/N0)) ]

Re: ook noncoherent

I see all your comments are useful. Can you please explain how to generate the noise variance for OOK for optical communication?
like in RF we can say that Es/N0 = 1/2*sigma^2. so which expression will be useful for optical communication?