You don't listen to "spectrum". Give up on the spectrum concept! You're listening in the time domain for a specific time-domain waveform.
Yeah it probably takes a while to lock on. At first you don't know when to expect a pulse, so any pulse you receive you guess is the first in the pseudo-random sequence. The you listen for the second pulse in the sequence. Of course you could have received a pulse from another of the 1000 users or one of the 255 other steps in the sequence. But since there's a million pulses a second per channel, even if it takes a few thousand pulses to latch onto the right channel at the right time, that's less than a second to sync up.
And don't misunderstand the channel capacity equation. Capacity is proportional to bandwidth and proportional to the log of (1+S/N). So as BW goes up, C goes up, and as S/N goes up, C also goes up. So if you have 1GHz of BW instead of a more typical 1MHz, you can get away with a much smaller S/N. For larger BW and the same capacity, S/N can be smaller - not a degradation but an improvement!
Actually that is the stndard warning you will see in virtually every annual report from every company traded on every exchange. It is to prevent you from getting sued when your earnings don't meet estimates. Everybody does it!
Forget the USA Today article; the author is clueless. The technology on the other hand sounds very much for real.
The fourier transform and the concept of "spectrum" is so deeply ingrained in so many engineers that they have lost touch with the time domain, essentially the "real world". Many things are a lot simpler in the frequency domain, like AM and FM. But for many probelms the frequency spectrum is the wrong tool. I see so many people who don't understand even simple transistor circuits because they try to think in the frequency domain.
So stop talking about spectrum - it is the wrong tool for understanding this technology. Maybe the power spectral density is useful to figure out if you're polluting radio or TV signals, but that's it.
And don't talk about bit synch either. While that's important in conventional communication systems, it isn't here. With a correlation detector, you just sit waiting around until the output of your correlator jumps up - that's the detection of the pulse - then you read your picosecond stopwatch. No need to expect the signal, just detect it. So simple!
If you're unfamiliar with correlation, and want to hear some math, here goes. The correlation of two functions (say f(t) and g(t)) is the integral S(f(t)*g(t))dt. Essentially multiuply the two signals together and then integrate. For two signals that don't look at all alike, the correlation is small. But when the two signals are very close, the integral is much much larger.
So imagine that you want to detect a pulse with very high resolution. At every instant in time you use a little integrator in some electronics to integrate your incoming signal with the expected signal (whatever shape the pulse has). When there's no pulse, the output of your correlator is very small. When the pulse comes along and lines up with the pulse in your integrator, your correlation gets really big relly fast and then small again as the pulse passes.
Try the math yourself: do the integral S(f(t)*f(t-d))dt where f(t) is the e^-3x pulse and notice that there is a huge peak at d=0.
Since the autocorrelation of that pulse (the pseudo gaussian e^-3x) they are using is very very high, you can detect this pulse with very high precision using correlation techniques. Sub wavelength resolution even.
(For all you communications engineers out there, this is the legendary matched filter technique. Except the typical use of the matched filter samples its output at the middle of the bit interval, when its output is supposed to be biggest(for a one) or smallest (for a zero). Here you do the opposite: when the matched filter output is maximum, that's the middle of the bit!)
So all you need is a correlation detector, a really accurate timer, and a pseudorandom noise generator to whiten up your spectrum and allow multiple channels. And if you do some dsp, your timer allows you to turn reflections off of objects into a pretty good radar image. (Except it's more like typical sonar sounding than typical radar).
If Fullerton's correlator is as good as he says, this stuff is very much for real. Believe it!
Slashdot Mirror
Yeah it probably takes a while to lock on. At first you don't know when to expect a pulse, so any pulse you receive you guess is the first in the pseudo-random sequence. The you listen for the second pulse in the sequence. Of course you could have received a pulse from another of the 1000 users or one of the 255 other steps in the sequence. But since there's a million pulses a second per channel, even if it takes a few thousand pulses to latch onto the right channel at the right time, that's less than a second to sync up.
And don't misunderstand the channel capacity equation. Capacity is proportional to bandwidth and proportional to the log of (1+S/N). So as BW goes up, C goes up, and as S/N goes up, C also goes up. So if you have 1GHz of BW instead of a more typical 1MHz, you can get away with a much smaller S/N. For larger BW and the same capacity, S/N can be smaller - not a degradation but an improvement!
Actually that is the stndard warning you will see in virtually every annual report from every company traded on every exchange. It is to prevent you from getting sued when your earnings don't meet estimates. Everybody does it!
The fourier transform and the concept of "spectrum" is so deeply ingrained in so many engineers that they have lost touch with the time domain, essentially the "real world". Many things are a lot simpler in the frequency domain, like AM and FM. But for many probelms the frequency spectrum is the wrong tool. I see so many people who don't understand even simple transistor circuits because they try to think in the frequency domain.
So stop talking about spectrum - it is the wrong tool for understanding this technology. Maybe the power spectral density is useful to figure out if you're polluting radio or TV signals, but that's it.
And don't talk about bit synch either. While that's important in conventional communication systems, it isn't here. With a correlation detector, you just sit waiting around until the output of your correlator jumps up - that's the detection of the pulse - then you read your picosecond stopwatch. No need to expect the signal, just detect it. So simple!
If you're unfamiliar with correlation, and want to hear some math, here goes. The correlation of two functions (say f(t) and g(t)) is the integral S(f(t)*g(t))dt. Essentially multiuply the two signals together and then integrate. For two signals that don't look at all alike, the correlation is small. But when the two signals are very close, the integral is much much larger.
So imagine that you want to detect a pulse with very high resolution. At every instant in time you use a little integrator in some electronics to integrate your incoming signal with the expected signal (whatever shape the pulse has). When there's no pulse, the output of your correlator is very small. When the pulse comes along and lines up with the pulse in your integrator, your correlation gets really big relly fast and then small again as the pulse passes.
Try the math yourself: do the integral S(f(t)*f(t-d))dt where f(t) is the e^-3x pulse and notice that there is a huge peak at d=0.
Since the autocorrelation of that pulse (the pseudo gaussian e^-3x) they are using is very very high, you can detect this pulse with very high precision using correlation techniques. Sub wavelength resolution even.
(For all you communications engineers out there, this is the legendary matched filter technique. Except the typical use of the matched filter samples its output at the middle of the bit interval, when its output is supposed to be biggest(for a one) or smallest (for a zero). Here you do the opposite: when the matched filter output is maximum, that's the middle of the bit!)
So all you need is a correlation detector, a really accurate timer, and a pseudorandom noise generator to whiten up your spectrum and allow multiple channels. And if you do some dsp, your timer allows you to turn reflections off of objects into a pretty good radar image. (Except it's more like typical sonar sounding than typical radar).
If Fullerton's correlator is as good as he says, this stuff is very much for real. Believe it!