# I. Scenario:

1. TX floating in the lossy heterogeneous medium with undetermined positions within a limited region;
2. RX fixed in the air and closed to the boundary of air-lossy medium;
3. Frequency: 500 MHz

# II. The study:

Received signal level was recorded every 30 seconds for a short duration (30 min) and sometimes no signal could be detected for a while. The measurement was repeated several times.

# III. Results:

The received signal varied at each 30-second sampling but overall it could be simplified as a sequence of "square wave with different levels" (the width was around 3 minutes) with a sinusoidal trend.

# Questions:

1. Can I assume 3 minutes to be the coherent time of the channel?
2. Can I assume the no-signal period to be fade duration?
3. How to model the channel when the TX-RX distance was not stable? Can I develop a model for the changes of received signal against time?

An example diagram to explain what I meant(Apparently, it's not the real data but resembles a lot)

• I'm quite confused what you did, and what you are trying to find out. A diagram would help. Then doing something for 30 min every 30 seconds makes no sense at all. – Olin Lathrop Jul 23 '18 at 16:03
• is this a school question? – jsotola Jul 23 '18 at 16:15
• It's from my experiment which is indeed a "school" project to study the transmission in a non-stationary lossy medium. I am trying to explain the phenomenon with theories and would need input from experts. – luw Jul 23 '18 at 16:35
• Every 3 minutes the Tx level changes . If f is constant, perhaps Tx antenna is rotating or moving near trees or perhaps f was changing slightly in your Rx band edge – Tony Stewart Sunnyskyguy EE75 Jul 23 '18 at 17:30
• Tx is immersed inside a mud-like fluid mixed with leaves and small rocks. The mixture fluid keeps moving which I guess causes rotation and displacement of Tx. – luw Jul 23 '18 at 18:45

You're only observing power transmission, not phase - where I come from, we care about that just as much, so coherency would incorporate phase and amplitude of the channel coefficients just as well.

Anyway, if the phase of your channel impulse response doesn't matter to your application, then these measurements are OK.

1. Can I assume 3 minutes to be the coherent time of the channel?

You definitely can't say your coherence time is three minutes.

There's significant jumps that happen between measurement points, for example around 3 minutes, 6 minutes, 9 minutes...

So, we can even say that the coherence time is smaller than 30s, and your measurement isn't fine enough in time domain to even measure that.

The channel is a result of its environment. If there's movement in your medium, and movement in your transmitter, you'll need to measure "often" relative to the amount of time it takes for movement to achieve a displacement in the order of one wavelength. f = 500 MHz = 5 · 10⁸ Hz leads to a wavelength of $\lambda=\frac cf=\frac{3\cdot10^8}{5\cdot 10^8}\,\text m=60 \,\text{cm}$; let's say you'd at least want to look whenever something moves a tenth of that, i.e. 6cm. (realistically, a channel measurement would try to look > 100 times per wavelength of movement, rule of thumb, but 10% does sound like a start)

You don't mention relative movement speeds, but let's roll with 1 m/s. Then, 6cm of movement would take 0.06 s, which is way, way less than the 30s you're measuring, but still larger than the coherence times we observe in microwave indoor communications (e.g. WiFi, but that has significantly smaller wavelengths, too!).

Can I assume the no-signal period to be fade duration?

no, because that could just be a random observation; your observation is too seldom to say whether the channel is "good" in between.

How to model the channel when the TX-RX distance was not stable? Can I develop a model for the changes of received signal against time?

Model path loss as function of time, and model fast movement as Doppler shift if necessary. Use the common methods of describing channels through coherence time, doppler spread, delay spread. Continuously measure channel impulse response rather than just sporadically look at a power transmission coefficient.