Hi Monika,

you’re right, this is a bit off-topic for this list; however, I kind of

like the fact that there’s much that can be discussed with respect to

actual GNU Radio implementations here, and hence, I find that your

“discussion kickstart” /is/ interesting. I’d therefore like to give you

/one/ short answer, and let you do your decision on your own

That depends on how you define your channel- “wide band wireless

channel” says not very much about its specific properties:

There’s the definition that you consider communication “wide band” when

the channels’ coherence bandwidth, which is typically defined as

$b_c=\frac{2\pi}{d}$, $d$ being the delay spread, is smaller than the

signal bandwidth $b_s$. Now, this would unambigous if not

a) the most interesting case would be when $b_s \approx b_c$ (because

doing $b_c \gg b_s$ is “easy”), and

b) people would completely agree what $d$ is – is it the mean delay

spread (if $h(t)$ is the complex frequency response, $\overline{d}={\int

{h(\tau)\tau d\tau}}\cdot{\left(\int{h(\tau)d\tau} \right)^{-1}}$), or

is it the RMS delay spread ($d_\text{RMS} = \sqrt{\int

{h(\tau){\left(\overline{d} - \tau\right)}^2 d\tau}\cdot{\left(

\int{h(\tau)d\tau} \right)^{-1}}}$), or is it maybe a measure based on

90% of the energy being contained within a time frame?

You might want to think about why you want to consider the delay spread

at all – typically, you care about whether your channel is

inter-symbol-interference free; hence, if whatever measure you use for

the delay spread (most of the time you either use the mean delay spread

or the root mean square delay spread) is smaller than your symbol

duration, you’d call that channel ISI-free, and having ISI otherwise. So

maybe you just want to say “we consider channels for which our

communication suffers ISI”.

Another problem here is: If you model your channel as tapped delay line,

the number of taps alone doesn’t say much about the phase response and

hence, delay over that channel.

If you make some assumptions on the nature / distribution of the

coefficients, then you might come to the conclusion that a channel with

a high delay spread is never flat, and you might then call it wideband

channel (again, you’ll clearly need to define this for yourself). If you

consider your channel to be as general as possible, it might as well

just be an all-pass filter, which means it might have a flat power

profile, but a very high delay spread. This would, for example, be no

problem for e.g. an OFDM system where each subcarrier’s phase is

independent of the others (imagine an OFDM signal with DPSK subcarriers)

– since the amplitude response is flat, you don’t need to equalize the

individual subchannels. However, if your OFDM system was to carry QAM,

then suddenly, you will need to understand the phase effects for every

single subcarrier. That’s when you start adding preambles and pilot

tones all over your OFDM frames.

It’s very much up to you to pick the right channel model. The trick here

is figuring out what existing channel model describes your application

sufficiently well (or can be slightly adapted), and just saying

“adapting the channel model XYZ”, listing the parameters might be much

better than trying to fit your channel model into any specific

terminology - there’s always people who’ll want to understand this for

yourself. If you look at the example above, you might have wondered how

bad the problem of getting that channel state information is –

especially, when not only there’s a change of channel influence over

frequency, but also, if your channel starts exhibiting non-infinite

coherence time (which goes with non-zero Doppler frequency). Like delay

spread, there’s different ways people define the coherence time (Doppler

freq), and different people define the statistic measures based on that

(Doppler spread), and refering to a known and well-tested channel model

makes it harder to argue against the “realism” of your observations.

Now, coming back to GNU Radio (which [I hope] justifies posting this

mail here): You’re doing digital signal processing, so your channels are

digital. The integrals up there break down to finite sums. The fact

alone that your signal, and hence, the operations you apply on it, have

a specific rate and therefore, bandwidth. If you need to oversample your

signal significantly to be able to reconstruct it means that the channel

influence is large compared to your signal’s bandwidth, right? So, if I

was in a situation where I was spontaneously asked whether I had a wide

band channel, and I didn’t prepare for that question, I’d just have a

look at how many samples per symbol I need to reconstruct my signal –

if it’s > 4, I’m pretty surely in wide band channels. As you noticed

from my discussion above, things get a bit subjective when you use words

like “wide”. It’s just often better to give actual relative measurements

than to rely on “squishy” human terms; the interested audience will have

no problem if you tell them that /you /consider the channel to be wide

band, because $b_c$ is only $0.95 b_s$, because that is a valid opinion;

saying “it’s not wide band, because $b_s$ is but $1.05 b_c$” is as much

a valid opinion, if you ask me.

Best regards,

Marcus